TSTP Solution File: SWW385+1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW385+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 : n026.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 18:09:01 EDT 2024
% Result : Theorem 81.03s 80.89s
% Output : CNFRefutation 81.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW385+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jun 19 07:15:24 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.51/0.60 start to proof:theBenchmark
% 80.71/80.72 %-------------------------------------------
% 80.71/80.72 % File :CSE---1.7
% 80.71/80.72 % Problem :theBenchmark
% 80.71/80.72 % Transform :cnf
% 80.71/80.72 % Format :tptp:raw
% 80.71/80.72 % Command :java -jar mcs_scs.jar %d %s
% 80.71/80.72
% 80.71/80.72 % Result :Theorem 66.990000s
% 80.71/80.72 % Output :CNFRefutation 66.990000s
% 80.71/80.72 %-------------------------------------------
% 80.71/80.73 %------------------------------------------------------------------------------
% 80.71/80.73 % File : SWW385+1 : TPTP v8.2.0. Released v5.2.0.
% 80.71/80.73 % Domain : Software Verification
% 80.71/80.73 % Problem : Hoare's Logic with Procedures 435658, 5000 axioms selected
% 80.71/80.73 % Version : Especial.
% 80.71/80.73 % English :
% 80.71/80.73
% 80.71/80.73 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 80.71/80.73 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 80.71/80.73 % Source : [Bla11]
% 80.71/80.73 % Names : hoare_435658.5000.p [Bla11]
% 80.71/80.73
% 80.71/80.73 % Status : Theorem
% 80.71/80.73 % Rating : 0.64 v7.5.0, 0.62 v7.4.0, 0.70 v7.3.0, 0.76 v7.1.0, 0.74 v7.0.0, 0.77 v6.3.0, 0.71 v6.2.0, 0.84 v6.1.0, 0.87 v6.0.0, 0.78 v5.5.0, 0.85 v5.4.0, 0.86 v5.3.0, 0.89 v5.2.0
% 80.71/80.73 % Syntax : Number of formulae : 5243 (1734 unt; 0 def)
% 80.71/80.73 % Number of atoms : 12609 (4515 equ)
% 80.71/80.73 % Maximal formula atoms : 13 ( 2 avg)
% 80.71/80.73 % Number of connectives : 8382 (1016 ~; 155 |; 716 &)
% 80.71/80.73 % ( 893 <=>;5602 =>; 0 <=; 0 <~>)
% 80.71/80.73 % Maximal formula depth : 22 ( 6 avg)
% 80.71/80.73 % Maximal term depth : 19 ( 2 avg)
% 80.71/80.73 % Number of predicates : 146 ( 145 usr; 2 prp; 0-7 aty)
% 80.71/80.73 % Number of functors : 382 ( 382 usr; 55 con; 0-7 aty)
% 80.71/80.73 % Number of variables : 16646 (16500 !; 146 ?)
% 80.71/80.73 % SPC : FOF_THM_RFO_SEQ
% 80.71/80.73
% 80.71/80.73 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 80.71/80.73 % 2011-03-01 13:01:08
% 80.71/80.73 %------------------------------------------------------------------------------
% 80.71/80.73 %----Relevant facts (4986)
% 80.71/80.73 fof(fact_ext,axiom,
% 80.71/80.73 ! [V_g_2,V_f_2] :
% 80.71/80.73 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 80.71/80.73 => V_f_2 = V_g_2 ) ).
% 80.71/80.73
% 80.71/80.73 fof(fact_empty,axiom,
% 80.71/80.73 ! [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))) ).
% 80.71/80.73
% 80.71/80.73 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 80.71/80.73 ! [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))) ).
% 80.71/80.73
% 80.71/80.73 fof(fact_MGF,axiom,
% 80.71/80.73 ! [V_ca_2] :
% 80.71/80.73 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 80.71/80.73 => ( c_Com_OWT__bodies
% 80.71/80.73 => ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
% 80.71/80.73 => 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)))) ) ) ) ).
% 80.71/80.73
% 80.71/80.73 fof(fact_cut,axiom,
% 80.71/80.73 ! [V_G_2,V_ts_2,V_G_H_2,T_a] :
% 80.71/80.73 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2)
% 80.71/80.73 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_G_H_2)
% 80.71/80.73 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ).
% 80.71/80.73
% 80.71/80.73 fof(fact_hoare__derivs_Oinsert,axiom,
% 80.71/80.73 ! [V_ts_2,V_t_2,V_G_2,T_a] :
% 80.71/80.73 ( 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))))
% 80.71/80.73 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2)
% 80.71/80.73 => 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)) ) ) ).
% 80.71/80.73
% 80.71/80.73 fof(fact_derivs__insertD,axiom,
% 80.71/80.73 ! [V_ts_2,V_t_2,V_G_2,T_a] :
% 80.71/80.73 ( 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))
% 80.71/80.73 => ( 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))))
% 80.71/80.73 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ).
% 80.71/80.73
% 80.71/80.73 fof(fact_MGF__lemma1,axiom,
% 80.71/80.73 ! [V_ca_2,V_G_2] :
% 80.71/80.73 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 80.71/80.73 => ( ! [B_x] :
% 80.71/80.73 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))
% 80.71/80.73 => 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)))) )
% 80.71/80.73 => ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
% 80.71/80.73 => 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)))) ) ) ) ).
% 80.71/80.73
% 80.71/80.73 fof(fact_MGT__BodyN,axiom,
% 80.71/80.73 ! [V_G_2,V_pn_2] :
% 80.71/80.73 ( 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))))
% 80.71/80.73 => 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)))) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_empty__not__insert,axiom,
% 80.71/80.74 ! [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) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_insert__not__empty,axiom,
% 80.71/80.74 ! [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)) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_doubleton__eq__iff,axiom,
% 80.71/80.74 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 80.71/80.74 ( 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))))
% 80.71/80.74 <=> ( ( V_a_2 = V_ca_2
% 80.71/80.74 & V_b_2 = V_d_2 )
% 80.71/80.74 | ( V_a_2 = V_d_2
% 80.71/80.74 & V_b_2 = V_ca_2 ) ) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_singleton__inject,axiom,
% 80.71/80.74 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.74 ( 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)))
% 80.71/80.74 => V_a_2 = V_b_2 ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_bot__apply,axiom,
% 80.71/80.74 ! [V_x_2,T_b,T_a] :
% 80.71/80.74 ( class_Orderings_Obot(T_a)
% 80.71/80.74 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_com_Osimps_I6_J,axiom,
% 80.71/80.74 ! [V_pname_H_2,V_pname_2] :
% 80.71/80.74 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2)
% 80.71/80.74 <=> V_pname_2 = V_pname_H_2 ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_the__elem__eq,axiom,
% 80.71/80.74 ! [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 ).
% 80.71/80.74
% 80.71/80.74 fof(fact_MGF__complete,axiom,
% 80.71/80.74 ! [V_Q_2,V_P_2,V_ca_2] :
% 80.71/80.74 ( 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))))
% 80.71/80.74 => ( 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))))
% 80.71/80.74 => 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)))) ) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_insert__absorb2,axiom,
% 80.71/80.74 ! [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) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_insert__commute,axiom,
% 80.71/80.74 ! [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)) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_triple_Oinject,axiom,
% 80.71/80.74 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] :
% 80.71/80.74 ( 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)
% 80.71/80.74 <=> ( V_fun1_2 = V_fun1_H_2
% 80.71/80.74 & V_com_2 = V_com_H_2
% 80.71/80.74 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_hoare__sound,axiom,
% 80.71/80.74 ! [V_ts_2,V_G_2,T_a] :
% 80.71/80.74 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2)
% 80.71/80.74 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_BodyN,axiom,
% 80.71/80.74 ! [V_G_2,V_Q_2,V_pn_2,V_P_2,T_a] :
% 80.71/80.74 ( 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))))
% 80.71/80.74 => 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)))) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_weak__Body,axiom,
% 80.71/80.74 ! [V_Q_2,V_pn_2,V_P_2,V_G_2,T_a] :
% 80.71/80.74 ( 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))))
% 80.71/80.74 => 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)))) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_insert__code,axiom,
% 80.71/80.74 ! [V_x_2,V_A_2,V_y_2,T_a] :
% 80.71/80.74 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2))
% 80.71/80.74 <=> ( V_y_2 = V_x_2
% 80.71/80.74 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_triple_Orecs,axiom,
% 80.71/80.74 ! [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) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_triple_Osimps_I2_J,axiom,
% 80.71/80.74 ! [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) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 80.71/80.74 ! [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)))) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_hoare__derivs_OSkip,axiom,
% 80.71/80.74 ! [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)))) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_conseq1,axiom,
% 80.71/80.74 ! [V_P_2,V_Q_2,V_ca_2,V_P_H_2,V_G_2,T_a] :
% 80.71/80.74 ( 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))))
% 80.71/80.74 => ( ! [B_Z,B_s] :
% 80.71/80.74 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 80.71/80.74 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 80.71/80.74 => 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)))) ) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_conseq2,axiom,
% 80.71/80.74 ! [V_Q_2,V_Q_H_2,V_ca_2,V_P_2,V_G_2,T_a] :
% 80.71/80.74 ( 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))))
% 80.71/80.74 => ( ! [B_Z,B_s] :
% 80.71/80.74 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
% 80.71/80.74 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) )
% 80.71/80.74 => 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)))) ) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_Comp,axiom,
% 80.71/80.74 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_P_2,V_G_2,T_a] :
% 80.71/80.74 ( 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))))
% 80.71/80.74 => ( 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))))
% 80.71/80.74 => 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)))) ) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_WT__bodiesD,axiom,
% 80.71/80.74 ! [V_b,V_pn] :
% 80.71/80.74 ( c_Com_OWT__bodies
% 80.71/80.74 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
% 80.71/80.74 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_WTs__elim__cases_I8_J,axiom,
% 80.71/80.74 ! [V_a_2,V_P_2,V_X_2] :
% 80.71/80.74 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2)))
% 80.71/80.74 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P_2))) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_WT_OBody,axiom,
% 80.71/80.74 ! [V_pn] :
% 80.71/80.74 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom)
% 80.71/80.74 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_WT_Oequations_I7_J,axiom,
% 80.71/80.74 ! [V_a_2] :
% 80.71/80.74 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2)))
% 80.71/80.74 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_finite__dom__body,axiom,
% 80.71/80.74 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_WTs__elim__cases_I4_J,axiom,
% 80.71/80.74 ! [V_c2,V_c1] :
% 80.71/80.74 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2)))
% 80.71/80.74 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 80.71/80.74 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_com_Osimps_I12_J,axiom,
% 80.71/80.74 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_com_Osimps_I20_J,axiom,
% 80.71/80.74 ! [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) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_com_Osimps_I13_J,axiom,
% 80.71/80.74 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 80.71/80.74
% 80.71/80.74 fof(fact_com_Osimps_I50_J,axiom,
% 80.71/80.74 ! [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) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_com_Osimps_I21_J,axiom,
% 80.71/80.74 ! [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 ).
% 80.71/80.74
% 80.71/80.74 fof(fact_com_Osimps_I51_J,axiom,
% 80.71/80.74 ! [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) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_com_Osimps_I3_J,axiom,
% 80.71/80.74 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 80.71/80.74 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 80.71/80.74 <=> ( V_com1_2 = V_com1_H_2
% 80.71/80.74 & V_com2_2 = V_com2_H_2 ) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_com_Osimps_I7_J,axiom,
% 80.71/80.74 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] :
% 80.71/80.74 ( 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)
% 80.71/80.74 <=> ( V_vname_2 = V_vname_H_2
% 80.71/80.74 & V_pname_2 = V_pname_H_2
% 80.71/80.74 & V_fun_2 = V_fun_H_2 ) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_com_Osimps_I62_J,axiom,
% 80.71/80.74 ! [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) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_com_Osimps_I63_J,axiom,
% 80.71/80.74 ! [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) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_com_Osimps_I49_J,axiom,
% 80.71/80.74 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_com_Osimps_I48_J,axiom,
% 80.71/80.74 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_WT_Oequations_I4_J,axiom,
% 80.71/80.74 ! [V_a2_2,V_a1_2] :
% 80.71/80.74 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2)))
% 80.71/80.74 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 80.71/80.74 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_WT_OSemi,axiom,
% 80.71/80.74 ! [V_c1,V_c0] :
% 80.71/80.74 ( hBOOL(hAPP(c_Com_OWT,V_c0))
% 80.71/80.74 => ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 80.71/80.74 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_com_Osimps_I18_J,axiom,
% 80.71/80.74 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_com_Osimps_I19_J,axiom,
% 80.71/80.74 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ).
% 80.71/80.74
% 80.71/80.74 fof(fact_WT_OSkip,axiom,
% 80.71/80.74 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_WT_Oequations_I1_J,axiom,
% 80.71/80.74 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_WT_Oequations_I8_J,axiom,
% 80.71/80.74 ! [V_a3_2,V_a1_2,V_a2_2] :
% 80.71/80.74 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2)))
% 80.71/80.74 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_WT_OCall,axiom,
% 80.71/80.74 ! [V_a_2,V_X_2,V_pn_2] :
% 80.71/80.74 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2)))
% 80.71/80.74 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_finite_OinsertI,axiom,
% 80.71/80.74 ! [V_a_2,V_A_2,T_a] :
% 80.71/80.74 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.74 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_finite_OemptyI,axiom,
% 80.71/80.74 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_insert__dom,axiom,
% 80.71/80.74 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] :
% 80.71/80.74 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
% 80.71/80.74 => 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) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_WTs__elim__cases_I7_J,axiom,
% 80.71/80.74 ! [V_P] :
% 80.71/80.74 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P)))
% 80.71/80.74 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_the_Osimps,axiom,
% 80.71/80.74 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ).
% 80.71/80.74
% 80.71/80.74 fof(fact_not__None__eq,axiom,
% 80.71/80.74 ! [T_a,V_x_2] :
% 80.71/80.74 ( V_x_2 != c_Option_Ooption_ONone(T_a)
% 80.71/80.74 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_not__Some__eq,axiom,
% 80.71/80.74 ! [T_a,V_x_2] :
% 80.71/80.74 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y)
% 80.71/80.74 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_option_Osimps_I3_J,axiom,
% 80.71/80.74 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_option_Osimps_I2_J,axiom,
% 80.71/80.74 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_finite__insert,axiom,
% 80.71/80.74 ! [V_A_2,V_a_2,T_a] :
% 80.71/80.74 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)))
% 80.71/80.74 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_finite_Oequations_I1_J,axiom,
% 80.71/80.74 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_Option_Oset_Osimps_I2_J,axiom,
% 80.71/80.74 ! [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))) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_Option_Oset_Osimps_I1_J,axiom,
% 80.71/80.74 ! [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)) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_set__empty__eq,axiom,
% 80.71/80.74 ! [V_xo_2,T_a] :
% 80.71/80.74 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.74 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_finite,axiom,
% 80.71/80.74 ! [V_A_2,T_a] :
% 80.71/80.74 ( class_Finite__Set_Ofinite(T_a)
% 80.71/80.74 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 80.71/80.74
% 80.71/80.74 fof(fact_finite__code,axiom,
% 80.71/80.74 ! [V_A_2,T_a] :
% 80.71/80.74 ( class_Finite__Set_Ofinite(T_a)
% 80.71/80.75 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_option_Oinject,axiom,
% 80.71/80.75 ! [V_a_H_2,V_a_2,T_a] :
% 80.71/80.75 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2)
% 80.71/80.75 <=> V_a_2 = V_a_H_2 ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 80.71/80.75 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 80.71/80.75 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 80.71/80.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.75 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.75 => 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)) ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_option_Orecs_I2_J,axiom,
% 80.71/80.75 ! [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) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_option_Osimps_I5_J,axiom,
% 80.71/80.75 ! [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) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_option_Orecs_I1_J,axiom,
% 80.71/80.75 ! [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 ).
% 80.71/80.75
% 80.71/80.75 fof(fact_option_Osimps_I4_J,axiom,
% 80.71/80.75 ! [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 ).
% 80.71/80.75
% 80.71/80.75 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 80.71/80.75 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.75 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 80.71/80.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 80.71/80.75 => 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)) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_map__comp__None__iff,axiom,
% 80.71/80.75 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
% 80.71/80.75 ( 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)
% 80.71/80.75 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 80.71/80.75 | ? [B_k_H] :
% 80.71/80.75 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H)
% 80.71/80.75 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_is__none__code_I2_J,axiom,
% 80.71/80.75 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_is__none__code_I1_J,axiom,
% 80.71/80.75 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_is__none__def,axiom,
% 80.71/80.75 ! [V_x_2,T_a] :
% 80.71/80.75 ( c_Option_Ois__none(T_a,V_x_2)
% 80.71/80.75 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_folding__one_Osingleton,axiom,
% 80.71/80.75 ! [V_x_2,V_F_2,V_f_2,T_a] :
% 80.71/80.75 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 80.71/80.75 => 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 ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_fold1Set__sing,axiom,
% 80.71/80.75 ! [V_b_2,V_a_2,V_f_2,T_a] :
% 80.71/80.75 ( 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))
% 80.71/80.75 <=> V_a_2 = V_b_2 ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_folding__one__idem_Oidem,axiom,
% 80.71/80.75 ! [V_x_2,V_F_2,V_f_2,T_a] :
% 80.71/80.75 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 80.71/80.75 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 80.71/80.75 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.75 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 80.71/80.75 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_empty__fold1SetE,axiom,
% 80.71/80.75 ! [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)) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_fold1Set__nonempty,axiom,
% 80.71/80.75 ! [V_x_2,V_A_2,V_f_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2))
% 80.71/80.75 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_map__comp__simps_I1_J,axiom,
% 80.71/80.75 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] :
% 80.71/80.75 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 80.71/80.75 => 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) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_map__comp__simps_I2_J,axiom,
% 80.71/80.75 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] :
% 80.71/80.75 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2)
% 80.71/80.75 => 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) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_map__comp__Some__iff,axiom,
% 80.71/80.75 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
% 80.71/80.75 ( 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)
% 80.71/80.75 <=> ? [B_k_H] :
% 80.71/80.75 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H)
% 80.71/80.75 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_folding__one_Oinsert,axiom,
% 80.71/80.75 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 80.71/80.75 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 80.71/80.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.75 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.75 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.75 => 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)) ) ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_folding__one_Oinsert__remove,axiom,
% 80.71/80.75 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 80.71/80.75 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 80.71/80.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.75 => ( ( hAPP(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))
% 80.71/80.75 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 80.71/80.75 & ( hAPP(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))
% 80.71/80.75 => 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)))))) ) ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_finite__nonempty__imp__fold1Set,axiom,
% 80.71/80.75 ! [V_f_2,V_A_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.75 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.75 => ? [B_x1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),B_x1)) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_finite_Osimps,axiom,
% 80.71/80.75 ! [V_a_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a_2))
% 80.71/80.75 <=> ( V_a_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.75 | ? [B_A] :
% 80.71/80.75 ( ? [B_a] : V_a_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A)
% 80.71/80.75 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 80.71/80.75 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 80.71/80.75 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 80.71/80.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.75 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 80.71/80.75 => 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) ) ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 80.71/80.75 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 80.71/80.75 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 80.71/80.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.75 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.75 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.75 => 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)) ) ) ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_ospec,axiom,
% 80.71/80.75 ! [V_x_2,V_P_2,V_A_2,T_a] :
% 80.71/80.75 ( ! [B_x] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Option_Oset(T_a,V_A_2)))
% 80.71/80.75 => hBOOL(hAPP(V_P_2,B_x)) )
% 80.71/80.75 => ( V_A_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 80.71/80.75 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 80.71/80.75 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] :
% 80.71/80.75 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 80.71/80.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.75 => 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) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_dom__minus,axiom,
% 80.71/80.75 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] :
% 80.71/80.75 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a)
% 80.71/80.75 => 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) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_evalc__elim__cases_I6_J,axiom,
% 80.71/80.75 ! [V_s1,V_s,V_P] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_evalc_OBody,axiom,
% 80.71/80.75 ! [V_s1,V_s0,V_pn] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_Body__triple__valid__Suc,axiom,
% 80.71/80.75 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] :
% 80.71/80.75 ( 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))
% 80.71/80.75 <=> 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)) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_order__refl,axiom,
% 80.71/80.75 ! [V_x,T_a] :
% 80.71/80.75 ( class_Orderings_Opreorder(T_a)
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_equalityCE,axiom,
% 80.71/80.75 ! [V_ca_2,T_a,V_B_2,V_A_2] :
% 80.71/80.75 ( V_A_2 = V_B_2
% 80.71/80.75 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 80.71/80.75 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) )
% 80.71/80.75 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_equalityI,axiom,
% 80.71/80.75 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 80.71/80.75 => V_A_2 = V_B_2 ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_emptyE,axiom,
% 80.71/80.75 ! [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)))) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_insertCI,axiom,
% 80.71/80.75 ! [V_b_2,V_B_2,V_a_2,T_a] :
% 80.71/80.75 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 80.71/80.75 => V_a_2 = V_b_2 )
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_insertE,axiom,
% 80.71/80.75 ! [V_A_2,V_b_2,V_a_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)))
% 80.71/80.75 => ( V_a_2 != V_b_2
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_subsetD,axiom,
% 80.71/80.75 ! [V_ca_2,V_B_2,V_A_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_UnCI,axiom,
% 80.71/80.75 ! [V_A_2,V_B_2,V_ca_2,T_a] :
% 80.71/80.75 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) )
% 80.71/80.75 => 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))) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_UnE,axiom,
% 80.71/80.75 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 80.71/80.75 ( 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)))
% 80.71/80.75 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_empty__subsetI,axiom,
% 80.71/80.75 ! [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)) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_DiffE,axiom,
% 80.71/80.75 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 80.71/80.75 ( 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)))
% 80.71/80.75 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_DiffI,axiom,
% 80.71/80.75 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 80.71/80.75 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 80.71/80.75 => 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))) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_finite__Diff,axiom,
% 80.71/80.75 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.75 => 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))) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_evalc_OSemi,axiom,
% 80.71/80.75 ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_evalc_OSkip,axiom,
% 80.71/80.75 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_evalc__elim__cases_I1_J,axiom,
% 80.71/80.75 ! [V_t,V_s] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t))
% 80.71/80.75 => V_t = V_s ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_triple__valid__Suc,axiom,
% 80.71/80.75 ! [V_t,V_n,T_a] :
% 80.71/80.75 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
% 80.71/80.75 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_com__det,axiom,
% 80.71/80.75 ! [V_u,V_t,V_s,V_c] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
% 80.71/80.75 => V_u = V_t ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_linorder__le__cases,axiom,
% 80.71/80.75 ! [V_y,V_x,T_a] :
% 80.71/80.75 ( class_Orderings_Olinorder(T_a)
% 80.71/80.75 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_DiffD2,axiom,
% 80.71/80.75 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 80.71/80.75 ( 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)))
% 80.71/80.75 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_DiffD1,axiom,
% 80.71/80.75 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 80.71/80.75 ( 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)))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_le__funE,axiom,
% 80.71/80.75 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 80.71/80.75 ( class_Orderings_Oord(T_b)
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 80.71/80.75 => 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))) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_equalityE,axiom,
% 80.71/80.75 ! [T_a,V_B_2,V_A_2] :
% 80.71/80.75 ( V_A_2 = V_B_2
% 80.71/80.75 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.75 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_double__diff,axiom,
% 80.71/80.75 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 80.71/80.75 => 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 ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_Diff__mono,axiom,
% 80.71/80.75 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2))
% 80.71/80.75 => 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))) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_Un__mono,axiom,
% 80.71/80.75 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
% 80.71/80.75 => 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))) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_Un__least,axiom,
% 80.71/80.75 ! [V_B_2,V_C_2,V_A_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 80.71/80.75 => 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)) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_xt1_I6_J,axiom,
% 80.71/80.75 ! [V_z,V_x,V_y,T_a] :
% 80.71/80.75 ( class_Orderings_Oorder(T_a)
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_xt1_I5_J,axiom,
% 80.71/80.75 ! [V_x,V_y,T_a] :
% 80.71/80.75 ( class_Orderings_Oorder(T_a)
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 80.71/80.75 => V_x = V_y ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_order__trans,axiom,
% 80.71/80.75 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.75 ( class_Orderings_Opreorder(T_a)
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_order__antisym,axiom,
% 80.71/80.75 ! [V_y,V_x,T_a] :
% 80.71/80.75 ( class_Orderings_Oorder(T_a)
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 80.71/80.75 => V_x = V_y ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_xt1_I4_J,axiom,
% 80.71/80.75 ! [V_c,V_a,V_b,T_a] :
% 80.71/80.75 ( class_Orderings_Oorder(T_a)
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 80.71/80.75 => ( V_b = V_c
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_ord__le__eq__trans,axiom,
% 80.71/80.75 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.75 ( class_Orderings_Oord(T_a)
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.75 => ( V_b = V_c
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_subset__trans,axiom,
% 80.71/80.75 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_set__mp,axiom,
% 80.71/80.75 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_set__rev__mp,axiom,
% 80.71/80.75 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_xt1_I3_J,axiom,
% 80.71/80.75 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.75 ( class_Orderings_Oorder(T_a)
% 80.71/80.75 => ( V_a = V_b
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_ord__eq__le__trans,axiom,
% 80.71/80.75 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.75 ( class_Orderings_Oord(T_a)
% 80.71/80.75 => ( V_a = V_b
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_eq__mem__trans,axiom,
% 80.71/80.75 ! [V_A_2,T_a,V_b_2,V_a_2] :
% 80.71/80.75 ( V_a_2 = V_b_2
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 80.71/80.75 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_Diff__partition,axiom,
% 80.71/80.75 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.75 => 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 ) ).
% 80.71/80.75
% 80.71/80.75 fof(fact_order__antisym__conv,axiom,
% 80.71/80.75 ! [V_x_2,V_y_2,T_a] :
% 80.71/80.75 ( class_Orderings_Oorder(T_a)
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
% 80.71/80.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 80.71/80.75 <=> V_x_2 = V_y_2 ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_in__mono,axiom,
% 80.71/80.76 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_eqelem__imp__iff,axiom,
% 80.71/80.76 ! [V_A_2,T_a,V_y_2,V_x_2] :
% 80.71/80.76 ( V_x_2 = V_y_2
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_eqset__imp__iff,axiom,
% 80.71/80.76 ! [V_x_2,T_a,V_B_2,V_A_2] :
% 80.71/80.76 ( V_A_2 = V_B_2
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__absorb2,axiom,
% 80.71/80.76 ! [V_A_2,V_B_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 80.71/80.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__absorb1,axiom,
% 80.71/80.76 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_le__funD,axiom,
% 80.71/80.76 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 80.71/80.76 ( class_Orderings_Oord(T_b)
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 80.71/80.76 => 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))) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_UnI2,axiom,
% 80.71/80.76 ! [V_A_2,V_B_2,V_ca_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 80.71/80.76 => 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))) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_UnI1,axiom,
% 80.71/80.76 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 80.71/80.76 => 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))) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_order__eq__refl,axiom,
% 80.71/80.76 ! [V_y,V_x,T_a] :
% 80.71/80.76 ( class_Orderings_Opreorder(T_a)
% 80.71/80.76 => ( V_x = V_y
% 80.71/80.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_equalityD2,axiom,
% 80.71/80.76 ! [T_a,V_B_2,V_A_2] :
% 80.71/80.76 ( V_A_2 = V_B_2
% 80.71/80.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_equalityD1,axiom,
% 80.71/80.76 ! [T_a,V_B_2,V_A_2] :
% 80.71/80.76 ( V_A_2 = V_B_2
% 80.71/80.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_ball__Un,axiom,
% 80.71/80.76 ! [V_P_2,V_B_2,V_A_2,T_a] :
% 80.71/80.76 ( ! [B_x] :
% 80.71/80.76 ( 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)))
% 80.71/80.76 => hBOOL(hAPP(V_P_2,B_x)) )
% 80.71/80.76 <=> ( ! [B_x] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.76 => hBOOL(hAPP(V_P_2,B_x)) )
% 80.71/80.76 & ! [B_x] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 80.71/80.76 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_bex__Un,axiom,
% 80.71/80.76 ! [V_P_2,V_B_2,V_A_2,T_a] :
% 80.71/80.76 ( ? [B_x] :
% 80.71/80.76 ( 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)))
% 80.71/80.76 & hBOOL(hAPP(V_P_2,B_x)) )
% 80.71/80.76 <=> ( ? [B_x] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.76 & hBOOL(hAPP(V_P_2,B_x)) )
% 80.71/80.76 | ? [B_x] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 80.71/80.76 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__Diff,axiom,
% 80.71/80.76 ! [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)) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__assoc,axiom,
% 80.71/80.76 ! [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)) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Diff__subset__conv,axiom,
% 80.71/80.76 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 80.71/80.76 ( 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))
% 80.71/80.76 <=> 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))) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__Diff__cancel2,axiom,
% 80.71/80.76 ! [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) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Diff__idemp,axiom,
% 80.71/80.76 ! [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) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__iff,axiom,
% 80.71/80.76 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 80.71/80.76 ( 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)))
% 80.71/80.76 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 80.71/80.76 | hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Diff__iff,axiom,
% 80.71/80.76 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 80.71/80.76 ( 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)))
% 80.71/80.76 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 80.71/80.76 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__left__commute,axiom,
% 80.71/80.76 ! [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)) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__left__absorb,axiom,
% 80.71/80.76 ! [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) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__Diff__cancel,axiom,
% 80.71/80.76 ! [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) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_order__eq__iff,axiom,
% 80.71/80.76 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.76 ( class_Orderings_Oorder(T_a)
% 80.71/80.76 => ( V_x_2 = V_y_2
% 80.71/80.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 80.71/80.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_set__eq__subset,axiom,
% 80.71/80.76 ! [T_a,V_B_2,V_A_2] :
% 80.71/80.76 ( V_A_2 = V_B_2
% 80.71/80.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_subset__Un__eq,axiom,
% 80.71/80.76 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.76 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_linorder__linear,axiom,
% 80.71/80.76 ! [V_y,V_x,T_a] :
% 80.71/80.76 ( class_Orderings_Olinorder(T_a)
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 80.71/80.76 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__commute,axiom,
% 80.71/80.76 ! [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) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_mem__def,axiom,
% 80.71/80.76 ! [V_A_2,V_x_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_le__fun__def,axiom,
% 80.71/80.76 ! [V_g_2,V_f_2,T_a,T_b] :
% 80.71/80.76 ( class_Orderings_Oord(T_b)
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 80.71/80.76 <=> ! [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))) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Diff__subset,axiom,
% 80.71/80.76 ! [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)) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__absorb,axiom,
% 80.71/80.76 ! [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 ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__upper2,axiom,
% 80.71/80.76 ! [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))) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__upper1,axiom,
% 80.71/80.76 ! [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))) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_subset__refl,axiom,
% 80.71/80.76 ! [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)) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_insert__Diff__if,axiom,
% 80.71/80.76 ! [V_A_2,V_B_2,V_x_2,T_a] :
% 80.71/80.76 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 80.71/80.76 => 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) )
% 80.71/80.76 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 80.71/80.76 => 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)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_insert__Diff1,axiom,
% 80.71/80.76 ! [V_A_2,V_B_2,V_x_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 80.71/80.76 => 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) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_insert__subset,axiom,
% 80.71/80.76 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 80.71/80.76 ( 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))
% 80.71/80.76 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 80.71/80.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_subset__insert,axiom,
% 80.71/80.76 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 80.71/80.76 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 => ( 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)))
% 80.71/80.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_diff__single__insert,axiom,
% 80.71/80.76 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 80.71/80.76 ( 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))
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 => 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))) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_subset__insert__iff,axiom,
% 80.71/80.76 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 80.71/80.76 ( 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)))
% 80.71/80.76 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 => 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)) )
% 80.71/80.76 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_evalc_Oequations_I4_J,axiom,
% 80.71/80.76 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2))
% 80.71/80.76 <=> ? [B_s1] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1))
% 80.71/80.76 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_evalc_Oequations_I1_J,axiom,
% 80.71/80.76 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_union__fold__insert,axiom,
% 80.71/80.76 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.76 => 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) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_insert__Diff,axiom,
% 80.71/80.76 ! [V_A_2,V_a_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.76 => 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 ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Diff__insert__absorb,axiom,
% 80.71/80.76 ! [V_A_2,V_x_2,T_a] :
% 80.71/80.76 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 => 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 ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_fold__empty,axiom,
% 80.71/80.76 ! [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 ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Diff__cancel,axiom,
% 80.71/80.76 ! [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)) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Diff__empty,axiom,
% 80.71/80.76 ! [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 ).
% 80.71/80.76
% 80.71/80.76 fof(fact_empty__Diff,axiom,
% 80.71/80.76 ! [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)) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_finite__Diff2,axiom,
% 80.71/80.76 ! [V_A_2,V_B_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.76 => ( 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)))
% 80.71/80.76 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__empty,axiom,
% 80.71/80.76 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.76 ( 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))
% 80.71/80.76 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.76 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__empty__right,axiom,
% 80.71/80.76 ! [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 ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__empty__left,axiom,
% 80.71/80.76 ! [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 ).
% 80.71/80.76
% 80.71/80.76 fof(fact_finite__Un,axiom,
% 80.71/80.76 ! [V_G_2,V_F_2,T_a] :
% 80.71/80.76 ( 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)))
% 80.71/80.76 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 80.71/80.76 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_finite__UnI,axiom,
% 80.71/80.76 ! [V_G_2,V_F_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2))
% 80.71/80.76 => 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))) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__insert__left,axiom,
% 80.71/80.76 ! [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)) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Un__insert__right,axiom,
% 80.71/80.76 ! [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)) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_bot__least,axiom,
% 80.71/80.76 ! [V_x,T_a] :
% 80.71/80.76 ( class_Orderings_Obot(T_a)
% 80.71/80.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_equals0D,axiom,
% 80.71/80.76 ! [V_a_2,T_a,V_A_2] :
% 80.71/80.76 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.76 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_empty__iff,axiom,
% 80.71/80.76 ! [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)))) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_ex__in__conv,axiom,
% 80.71/80.76 ! [V_A_2,T_a] :
% 80.71/80.76 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.76 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_all__not__in__conv,axiom,
% 80.71/80.76 ! [V_A_2,T_a] :
% 80.71/80.76 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.76 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_subset__empty,axiom,
% 80.71/80.76 ! [V_A_2,T_a] :
% 80.71/80.76 ( 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))))
% 80.71/80.76 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_rev__finite__subset,axiom,
% 80.71/80.76 ! [V_A_2,V_B_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_finite__subset,axiom,
% 80.71/80.76 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_insert__absorb,axiom,
% 80.71/80.76 ! [V_A_2,V_a_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.76 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_insertI2,axiom,
% 80.71/80.76 ! [V_b_2,V_B_2,V_a_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 80.71/80.76 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_insert__ident,axiom,
% 80.71/80.76 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 80.71/80.76 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 80.71/80.76 => ( 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)
% 80.71/80.76 <=> V_A_2 = V_B_2 ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_insert__iff,axiom,
% 80.71/80.76 ! [V_A_2,V_b_2,V_a_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)))
% 80.71/80.76 <=> ( V_a_2 = V_b_2
% 80.71/80.76 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_insertI1,axiom,
% 80.71/80.76 ! [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))) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_insert__mono,axiom,
% 80.71/80.76 ! [V_a_2,V_D_2,V_C_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))
% 80.71/80.76 => 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))) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_subset__insertI2,axiom,
% 80.71/80.76 ! [V_b_2,V_B_2,V_A_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.76 => 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))) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_subset__insertI,axiom,
% 80.71/80.76 ! [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))) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_thin,axiom,
% 80.71/80.76 ! [V_G_2,V_ts_2,V_G_H_2,T_a] :
% 80.71/80.76 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2)
% 80.71/80.76 => ( 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))
% 80.71/80.76 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_weaken,axiom,
% 80.71/80.76 ! [V_ts_2,V_ts_H_2,V_G_2,T_a] :
% 80.71/80.76 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_H_2)
% 80.71/80.76 => ( 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))
% 80.71/80.76 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_asm,axiom,
% 80.71/80.76 ! [V_G_2,V_ts_2,T_a] :
% 80.71/80.76 ( 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))
% 80.71/80.76 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_folding__one_Oeq__fold_H,axiom,
% 80.71/80.76 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 => 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) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_insert__Diff__single,axiom,
% 80.71/80.76 ! [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) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Diff__insert2,axiom,
% 80.71/80.76 ! [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) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Diff__insert,axiom,
% 80.71/80.76 ! [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)))) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_finite__Diff__insert,axiom,
% 80.71/80.76 ! [V_B_2,V_a_2,V_A_2,T_a] :
% 80.71/80.76 ( 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))))
% 80.71/80.76 <=> 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))) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_insert__is__Un,axiom,
% 80.71/80.76 ! [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) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_folding__one_Oremove,axiom,
% 80.71/80.76 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 => ( ( hAPP(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))
% 80.71/80.76 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 80.71/80.76 & ( hAPP(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))
% 80.71/80.76 => 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)))))) ) ) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_singletonE,axiom,
% 80.71/80.76 ! [V_a_2,V_b_2,T_a] :
% 80.71/80.76 ( 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)))))
% 80.71/80.76 => V_b_2 = V_a_2 ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_singleton__iff,axiom,
% 80.71/80.76 ! [V_a_2,V_b_2,T_a] :
% 80.71/80.76 ( 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)))))
% 80.71/80.76 <=> V_b_2 = V_a_2 ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_subset__singletonD,axiom,
% 80.71/80.76 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.76 ( 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)))))
% 80.71/80.76 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.76 | 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))) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_domIff,axiom,
% 80.71/80.76 ! [V_m_2,T_b,V_a_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2)))
% 80.71/80.76 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_domI,axiom,
% 80.71/80.76 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
% 80.71/80.76 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2)
% 80.71/80.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_evalc_Oequations_I9_J,axiom,
% 80.71/80.76 ! [V_a3_2,V_a2_2,V_a1_2] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
% 80.71/80.76 <=> 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)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_folding__one__idem_Oin__idem,axiom,
% 80.71/80.76 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 80.71/80.76 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 80.71/80.76 => 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)) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 80.71/80.76 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 80.71/80.76 => 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) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 80.71/80.76 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 80.71/80.76 => 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) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_elem__set,axiom,
% 80.71/80.76 ! [V_xo_2,V_x_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2)))
% 80.71/80.76 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__le__fold__sup,axiom,
% 80.71/80.76 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.76 => 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))) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_fold__sup__insert,axiom,
% 80.71/80.76 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.76 => 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)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 80.71/80.76 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 => 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)))))) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup1E,axiom,
% 80.71/80.76 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 80.71/80.76 ( 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))
% 80.71/80.76 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 80.71/80.76 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup1CI,axiom,
% 80.71/80.76 ! [T_a,V_A_2,V_x_2,V_B_2] :
% 80.71/80.76 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 80.71/80.76 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 80.71/80.76 => 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)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_folding__image__simple_Oremove,axiom,
% 80.71/80.76 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 80.71/80.76 => 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)))))) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 80.71/80.76 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.76 => 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)))))) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 80.71/80.76 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 80.71/80.76 => 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)))))) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_minus__apply,axiom,
% 80.71/80.76 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 80.71/80.76 ( class_Groups_Ominus(T_a)
% 80.71/80.76 => 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)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__apply,axiom,
% 80.71/80.76 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 80.71/80.76 ( class_Lattices_Olattice(T_a)
% 80.71/80.76 => 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)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 80.71/80.76 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 80.71/80.76 => 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)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_folding__image__simple_Oempty,axiom,
% 80.71/80.76 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 80.71/80.76 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_eq__mem,axiom,
% 80.71/80.76 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2)))
% 80.71/80.76 <=> V_x_2 = V_y_2 ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__assoc,axiom,
% 80.71/80.76 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => 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)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_inf__sup__aci_I6_J,axiom,
% 80.71/80.76 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Olattice(T_a)
% 80.71/80.76 => 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)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup_Oassoc,axiom,
% 80.71/80.76 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => 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)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__left__commute,axiom,
% 80.71/80.76 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => 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)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_inf__sup__aci_I7_J,axiom,
% 80.71/80.76 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Olattice(T_a)
% 80.71/80.76 => 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)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup_Oleft__commute,axiom,
% 80.71/80.76 ! [V_c,V_a,V_b,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => 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)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__left__idem,axiom,
% 80.71/80.76 ! [V_y,V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => 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) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_inf__sup__aci_I8_J,axiom,
% 80.71/80.76 ! [V_y,V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Olattice(T_a)
% 80.71/80.76 => 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) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup_Oleft__idem,axiom,
% 80.71/80.76 ! [V_b,V_a,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => 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) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__commute,axiom,
% 80.71/80.76 ! [V_y,V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => 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) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_inf__sup__aci_I5_J,axiom,
% 80.71/80.76 ! [V_y,V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Olattice(T_a)
% 80.71/80.76 => 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) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup_Ocommute,axiom,
% 80.71/80.76 ! [V_b,V_a,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => 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) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__idem,axiom,
% 80.71/80.76 ! [V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Sup__fin_Oidem,axiom,
% 80.71/80.76 ! [V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Olattice(T_a)
% 80.71/80.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup_Oidem,axiom,
% 80.71/80.76 ! [V_a,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_predicate1D,axiom,
% 80.71/80.76 ! [V_x_2,V_Q_2,V_P_2,T_a] :
% 80.71/80.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2))
% 80.71/80.76 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 80.71/80.76 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_rev__predicate1D,axiom,
% 80.71/80.76 ! [V_Q_2,T_a,V_x_2,V_P_2] :
% 80.71/80.76 ( hBOOL(hAPP(V_P_2,V_x_2))
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2))
% 80.71/80.76 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 80.71/80.76 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.76 => 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) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup1I2,axiom,
% 80.71/80.76 ! [V_A_2,T_a,V_x_2,V_B_2] :
% 80.71/80.76 ( hBOOL(hAPP(V_B_2,V_x_2))
% 80.71/80.76 => 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)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup1I1,axiom,
% 80.71/80.76 ! [V_B_2,T_a,V_x_2,V_A_2] :
% 80.71/80.76 ( hBOOL(hAPP(V_A_2,V_x_2))
% 80.71/80.76 => 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)) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_folding__image__simple_Oinsert,axiom,
% 80.71/80.76 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 80.71/80.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 80.71/80.76 => 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)) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 80.71/80.76 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 => 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)) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 80.71/80.76 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 80.71/80.76 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 => 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) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_le__supE,axiom,
% 80.71/80.76 ! [V_x,V_b,V_a,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => ( 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))
% 80.71/80.76 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 80.71/80.76 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__mono,axiom,
% 80.71/80.76 ! [V_d,V_b,V_c,V_a,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 80.71/80.76 => 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))) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__least,axiom,
% 80.71/80.76 ! [V_z,V_x,V_y,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 80.71/80.76 => 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)) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_le__supI,axiom,
% 80.71/80.76 ! [V_b,V_x,V_a,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 80.71/80.76 => 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)) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__absorb1,axiom,
% 80.71/80.76 ! [V_x,V_y,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 80.71/80.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__absorb2,axiom,
% 80.71/80.76 ! [V_y,V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 80.71/80.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_le__supI2,axiom,
% 80.71/80.76 ! [V_a,V_b,V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 80.71/80.76 => 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))) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_le__supI1,axiom,
% 80.71/80.76 ! [V_b,V_a,V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 80.71/80.76 => 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))) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_le__sup__iff,axiom,
% 80.71/80.76 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => ( 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))
% 80.71/80.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 80.71/80.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_le__iff__sup,axiom,
% 80.71/80.76 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 80.71/80.76 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__ge2,axiom,
% 80.71/80.76 ! [V_x,V_y,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => 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))) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_inf__sup__ord_I4_J,axiom,
% 80.71/80.76 ! [V_x,V_y,T_a] :
% 80.71/80.76 ( class_Lattices_Olattice(T_a)
% 80.71/80.76 => 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))) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__ge1,axiom,
% 80.71/80.76 ! [V_y,V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.76 => 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))) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_inf__sup__ord_I3_J,axiom,
% 80.71/80.76 ! [V_y,V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Olattice(T_a)
% 80.71/80.76 => 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))) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__bot__left,axiom,
% 80.71/80.76 ! [V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Obounded__lattice__bot(T_a)
% 80.71/80.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__bot__right,axiom,
% 80.71/80.76 ! [V_x,T_a] :
% 80.71/80.76 ( class_Lattices_Obounded__lattice__bot(T_a)
% 80.71/80.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_sup__eq__bot__iff,axiom,
% 80.71/80.76 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.76 ( class_Lattices_Obounded__lattice__bot(T_a)
% 80.71/80.76 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a)
% 80.71/80.76 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a)
% 80.71/80.76 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ).
% 80.71/80.76
% 80.71/80.76 fof(fact_Sup__fin_Oremove,axiom,
% 80.71/80.76 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.76 ( class_Lattices_Olattice(T_a)
% 80.71/80.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.76 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.76 => ( ( hAPP(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))
% 80.71/80.76 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 )
% 80.71/80.76 & ( hAPP(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))
% 80.71/80.77 => 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)))))) ) ) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__eq__diff__less__eq,axiom,
% 80.71/80.77 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__ab__group__add(T_a)
% 80.71/80.77 => ( 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)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 80.71/80.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_folding__one_Oclosed,axiom,
% 80.71/80.77 ! [V_A_2,V_F_2,V_f_2,T_a] :
% 80.71/80.77 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.77 => ( ! [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))))))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_finite__empty__induct,axiom,
% 80.71/80.77 ! [V_P_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 80.71/80.77 => ( ! [B_a,B_A] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A))
% 80.71/80.77 => ( hBOOL(hAPP(V_P_2,B_A))
% 80.71/80.77 => 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)))))) ) ) )
% 80.71/80.77 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_finite__subset__induct,axiom,
% 80.71/80.77 ! [V_P_2,V_A_2,V_F_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2))
% 80.71/80.77 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 80.71/80.77 => ( ! [B_a,B_F] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F))
% 80.71/80.77 => ( hBOOL(hAPP(V_P_2,B_F))
% 80.71/80.77 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) )
% 80.71/80.77 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( class_Lattices_Olattice(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.77 => 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) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( class_Lattices_Olattice(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( ( hAPP(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))
% 80.71/80.77 => 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 )
% 80.71/80.77 & ( hAPP(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))
% 80.71/80.77 => 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)))))) ) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__fold__sup,axiom,
% 80.71/80.77 ! [V_A_2,T_a] :
% 80.71/80.77 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => 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) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__fin_Oinsert,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( class_Lattices_Olattice(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.77 => 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)) ) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card__Suc__Diff1,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.77 => 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) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_evaln_OBody,axiom,
% 80.71/80.77 ! [V_s1,V_n,V_s0,V_pn] :
% 80.71/80.77 ( 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))
% 80.71/80.77 => 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)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_evaln_OSemi,axiom,
% 80.71/80.77 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2))
% 80.71/80.77 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_evaln_OSkip,axiom,
% 80.71/80.77 ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_evaln__elim__cases_I1_J,axiom,
% 80.71/80.77 ! [V_t,V_n,V_s] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_t))
% 80.71/80.77 => V_t = V_s ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_evaln__nonstrict,axiom,
% 80.71/80.77 ! [V_m,V_t,V_n,V_s,V_c] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 80.71/80.77 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_m),V_t)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_finite__UnionD,axiom,
% 80.71/80.77 ! [V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))
% 80.71/80.77 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_evaln__Suc,axiom,
% 80.71/80.77 ! [V_s_H,V_n,V_s,V_c] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H))
% 80.71/80.77 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__fin__Sup,axiom,
% 80.71/80.77 ! [V_A_2,T_a] :
% 80.71/80.77 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.77 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_eval__eq,axiom,
% 80.71/80.77 ! [V_t_2,V_s_2,V_ca_2] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),V_t_2))
% 80.71/80.77 <=> ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s_2),B_n),V_t_2)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_evaln__evalc,axiom,
% 80.71/80.77 ! [V_t,V_n,V_s,V_c] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_evaln_Oequations_I4_J,axiom,
% 80.71/80.77 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] :
% 80.71/80.77 ( 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))
% 80.71/80.77 <=> ? [B_s1] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1))
% 80.71/80.77 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_evaln_Oequations_I1_J,axiom,
% 80.71/80.77 ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_a1),V_a2),V_a1)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card__insert__le,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => 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)))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card__mono,axiom,
% 80.71/80.77 ! [V_A_2,V_B_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.77 => 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))) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card__seteq,axiom,
% 80.71/80.77 ! [V_A_2,V_B_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.77 => ( 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)))
% 80.71/80.77 => V_A_2 = V_B_2 ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__card__le__card__Diff,axiom,
% 80.71/80.77 ! [V_A_2,V_B_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.77 => 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)))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__fin_Osingleton,axiom,
% 80.71/80.77 ! [V_x_2,T_a] :
% 80.71/80.77 ( class_Lattices_Olattice(T_a)
% 80.71/80.77 => 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 ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_triple__valid__def2,axiom,
% 80.71/80.77 ! [V_Q_2,V_ca_2,V_P_2,V_n_2,T_a] :
% 80.71/80.77 ( 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))
% 80.71/80.77 <=> ! [B_Z,B_s] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 80.71/80.77 => ! [B_s_H] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),B_s),V_n_2),B_s_H))
% 80.71/80.77 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card__Diff__subset,axiom,
% 80.71/80.77 ! [V_A_2,V_B_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 80.71/80.77 => 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)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__eq__diff__eq,axiom,
% 80.71/80.77 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 80.71/80.77 ( class_Groups_Oab__group__add(T_a)
% 80.71/80.77 => ( 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)
% 80.71/80.77 => ( V_a_2 = V_b_2
% 80.71/80.77 <=> V_ca_2 = V_d_2 ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__fin_Oin__idem,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( class_Lattices_Olattice(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.77 => 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) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card__insert__disjoint,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.77 => 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)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card__insert__if,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.77 => 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) )
% 80.71/80.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.77 => 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)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card__Diff1__le,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => 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))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_sup__Sup__fold__sup,axiom,
% 80.71/80.77 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.77 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => 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) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_evaln_Oequations_I9_J,axiom,
% 80.71/80.77 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
% 80.71/80.77 ( 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))
% 80.71/80.77 <=> 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)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( class_Lattices_Olattice(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.77 => 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)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__fin_Osubset__idem,axiom,
% 80.71/80.77 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.77 ( class_Lattices_Olattice(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 80.71/80.77 => 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) ) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__fin_Ounion__idem,axiom,
% 80.71/80.77 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.77 ( class_Lattices_Olattice(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.77 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.77 => 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)) ) ) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card__insert,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => 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)))))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 80.71/80.77 ! [V_a_2,V_A_2,T_a] :
% 80.71/80.77 ( class_Lattices_Olattice(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => 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) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__binary,axiom,
% 80.71/80.77 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.77 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 80.71/80.77 => 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) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__insert,axiom,
% 80.71/80.77 ! [V_A_2,V_a_2,T_a] :
% 80.71/80.77 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 80.71/80.77 => 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)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__singleton,axiom,
% 80.71/80.77 ! [V_a_2,T_a] :
% 80.71/80.77 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 80.71/80.77 => 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 ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__empty,axiom,
% 80.71/80.77 ! [T_a] :
% 80.71/80.77 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 80.71/80.77 => 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) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__upper,axiom,
% 80.71/80.77 ! [V_A_2,V_x_2,T_a] :
% 80.71/80.77 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.77 => 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))) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_evaln__elim__cases_I6_J,axiom,
% 80.71/80.77 ! [V_s1,V_n,V_s,V_P] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_n),V_s1))
% 80.71/80.77 => ~ ! [B_n] :
% 80.71/80.77 ( V_n = hAPP(c_Nat_OSuc,B_n)
% 80.71/80.77 => ~ 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)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_UnionI,axiom,
% 80.71/80.77 ! [V_A_2,V_C_2,V_X_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2))
% 80.71/80.77 => 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))) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__fin_Oclosed,axiom,
% 80.71/80.77 ! [V_A_2,T_a] :
% 80.71/80.77 ( class_Lattices_Olattice(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.77 => ( ! [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))))))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Sup__le__iff,axiom,
% 80.71/80.77 ! [V_b_2,V_A_2,T_a] :
% 80.71/80.77 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 80.71/80.77 => ( 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))
% 80.71/80.77 <=> ! [B_x] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card__Diff__singleton__if,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.77 => 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)) )
% 80.71/80.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.77 => 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) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_one__reorient,axiom,
% 80.71/80.77 ! [V_x_2,T_a] :
% 80.71/80.77 ( class_Groups_Oone(T_a)
% 80.71/80.77 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 80.71/80.77 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 80.71/80.77 ! [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) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Union__empty,axiom,
% 80.71/80.77 ! [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)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Union__mono,axiom,
% 80.71/80.77 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.77 ( 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))
% 80.71/80.77 => 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))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Union__upper,axiom,
% 80.71/80.77 ! [V_A_2,V_B_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 80.71/80.77 => 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))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Union__insert,axiom,
% 80.71/80.77 ! [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)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Un__eq__Union,axiom,
% 80.71/80.77 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = 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))))) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Union__Un__distrib,axiom,
% 80.71/80.77 ! [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)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card__Diff__insert,axiom,
% 80.71/80.77 ! [V_B_2,V_a_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 80.71/80.77 => 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)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card__Diff__singleton,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.77 => 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)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__Suc__1,axiom,
% 80.71/80.77 ! [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 ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Suc__diff__le,axiom,
% 80.71/80.77 ! [V_m,V_n] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 80.71/80.77 => 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)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_finite__Union,axiom,
% 80.71/80.77 ! [V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2))
% 80.71/80.77 => ( ! [B_M] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2))
% 80.71/80.77 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) )
% 80.71/80.77 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_le__diff__iff,axiom,
% 80.71/80.77 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 80.71/80.77 => ( 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)))
% 80.71/80.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Nat_Odiff__diff__eq,axiom,
% 80.71/80.77 ! [V_n,V_m,V_k] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 80.71/80.77 => 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) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_eq__diff__iff,axiom,
% 80.71/80.77 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 80.71/80.77 => ( 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)
% 80.71/80.77 <=> V_m_2 = V_n_2 ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__diff__cancel,axiom,
% 80.71/80.77 ! [V_n,V_i] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 80.71/80.77 => 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 ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__le__mono,axiom,
% 80.71/80.77 ! [V_l,V_n,V_m] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 80.71/80.77 => 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))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__le__mono2,axiom,
% 80.71/80.77 ! [V_l,V_n,V_m] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 80.71/80.77 => 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))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__le__self,axiom,
% 80.71/80.77 ! [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)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_n__not__Suc__n,axiom,
% 80.71/80.77 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Suc__n__not__n,axiom,
% 80.71/80.77 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 80.71/80.77
% 80.71/80.77 fof(fact_nat_Oinject,axiom,
% 80.71/80.77 ! [V_nat_H_2,V_nat_2] :
% 80.71/80.77 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 80.71/80.77 <=> V_nat_2 = V_nat_H_2 ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Suc__inject,axiom,
% 80.71/80.77 ! [V_y,V_x] :
% 80.71/80.77 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 80.71/80.77 => V_x = V_y ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_le__refl,axiom,
% 80.71/80.77 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_nat__le__linear,axiom,
% 80.71/80.77 ! [V_n,V_m] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 80.71/80.77 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_eq__imp__le,axiom,
% 80.71/80.77 ! [V_n,V_m] :
% 80.71/80.77 ( V_m = V_n
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_le__trans,axiom,
% 80.71/80.77 ! [V_k,V_j,V_i] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_le__antisym,axiom,
% 80.71/80.77 ! [V_n,V_m] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 80.71/80.77 => V_m = V_n ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__commute,axiom,
% 80.71/80.77 ! [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) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Suc__n__not__le__n,axiom,
% 80.71/80.77 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_not__less__eq__eq,axiom,
% 80.71/80.77 ! [V_n_2,V_m_2] :
% 80.71/80.77 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 80.71/80.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_le__Suc__eq,axiom,
% 80.71/80.77 ! [V_n_2,V_m_2] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 80.71/80.77 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 80.71/80.77 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Suc__le__mono,axiom,
% 80.71/80.77 ! [V_m_2,V_n_2] :
% 80.71/80.77 ( 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)))
% 80.71/80.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_le__SucI,axiom,
% 80.71/80.77 ! [V_n,V_m] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_le__SucE,axiom,
% 80.71/80.77 ! [V_n,V_m] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 80.71/80.77 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Suc__leD,axiom,
% 80.71/80.77 ! [V_n,V_m] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__Suc__Suc,axiom,
% 80.71/80.77 ! [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) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Suc__diff__diff,axiom,
% 80.71/80.77 ! [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) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card_Oremove,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.77 => 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)))))) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Powp__mono,axiom,
% 80.71/80.77 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.77 => 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))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card_Oinsert__remove,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => 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)))))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card__Diff2__less,axiom,
% 80.71/80.77 ! [V_y_2,V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 80.71/80.77 => 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))) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card__Diff1__less,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.77 => 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))) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 80.71/80.77 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 80.71/80.77 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => 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) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 80.71/80.77 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 80.71/80.77 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => 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)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_setsum__diff1__ring,axiom,
% 80.71/80.77 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 80.71/80.77 ( class_Rings_Oring(T_b)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.77 => 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)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_setsum__diff1,axiom,
% 80.71/80.77 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 80.71/80.77 ( class_Groups_Oab__group__add(T_b)
% 80.71/80.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.77 => 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)) )
% 80.71/80.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.77 => 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) ) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_card_Oinsert,axiom,
% 80.71/80.77 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.77 => 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)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Suc__mono,axiom,
% 80.71/80.77 ! [V_n,V_m] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_lessI,axiom,
% 80.71/80.77 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__less__le__mono,axiom,
% 80.71/80.77 ! [V_d,V_c,V_b,V_a,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 80.71/80.77 => 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))) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__le__less__mono,axiom,
% 80.71/80.77 ! [V_d,V_c,V_b,V_a,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 80.71/80.77 => 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))) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__not__refl,axiom,
% 80.71/80.77 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_not__add__less1,axiom,
% 80.71/80.77 ! [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)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_not__add__less2,axiom,
% 80.71/80.77 ! [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)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_nat__neq__iff,axiom,
% 80.71/80.77 ! [V_n_2,V_m_2] :
% 80.71/80.77 ( V_m_2 != V_n_2
% 80.71/80.77 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 80.71/80.77 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_nat__add__commute,axiom,
% 80.71/80.77 ! [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) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_nat__add__left__commute,axiom,
% 80.71/80.77 ! [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)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_nat__add__assoc,axiom,
% 80.71/80.77 ! [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)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_nat__add__left__cancel,axiom,
% 80.71/80.77 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.77 ( 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)
% 80.71/80.77 <=> V_m_2 = V_n_2 ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_nat__add__right__cancel,axiom,
% 80.71/80.77 ! [V_n_2,V_k_2,V_m_2] :
% 80.71/80.77 ( 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)
% 80.71/80.77 <=> V_m_2 = V_n_2 ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_nat__add__left__cancel__less,axiom,
% 80.71/80.77 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.77 ( 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)))
% 80.71/80.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_linorder__neqE__nat,axiom,
% 80.71/80.77 ! [V_y,V_x] :
% 80.71/80.77 ( V_x != V_y
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__irrefl__nat,axiom,
% 80.71/80.77 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__not__refl2,axiom,
% 80.71/80.77 ! [V_m,V_n] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 80.71/80.77 => V_m != V_n ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__not__refl3,axiom,
% 80.71/80.77 ! [V_t,V_s] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 80.71/80.77 => V_s != V_t ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_trans__less__add1,axiom,
% 80.71/80.77 ! [V_m,V_j,V_i] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 80.71/80.77 => 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))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_trans__less__add2,axiom,
% 80.71/80.77 ! [V_m,V_j,V_i] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 80.71/80.77 => 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))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__less__mono1,axiom,
% 80.71/80.77 ! [V_k,V_j,V_i] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 80.71/80.77 => 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))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__less__mono,axiom,
% 80.71/80.77 ! [V_l,V_k,V_j,V_i] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 80.71/80.77 => 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))) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__add__eq__less,axiom,
% 80.71/80.77 ! [V_n,V_m,V_l,V_k] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 80.71/80.77 => ( 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)
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__lessD1,axiom,
% 80.71/80.77 ! [V_k,V_j,V_i] :
% 80.71/80.77 ( 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))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_nat__less__cases,axiom,
% 80.71/80.77 ! [V_P_2,V_n_2,V_m_2] :
% 80.71/80.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 80.71/80.77 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 80.71/80.77 => ( ( V_m_2 = V_n_2
% 80.71/80.77 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 80.71/80.77 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 80.71/80.77 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 80.71/80.77 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 80.71/80.77 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.77 ( class_Groups_Oab__semigroup__add(T_a)
% 80.71/80.77 => 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)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__left__cancel,axiom,
% 80.71/80.77 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 80.71/80.77 ( class_Groups_Ocancel__semigroup__add(T_a)
% 80.71/80.77 => ( 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)
% 80.71/80.77 <=> V_b_2 = V_ca_2 ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__right__cancel,axiom,
% 80.71/80.77 ! [V_ca_2,V_a_2,V_b_2,T_a] :
% 80.71/80.77 ( class_Groups_Ocancel__semigroup__add(T_a)
% 80.71/80.77 => ( 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)
% 80.71/80.77 <=> V_b_2 = V_ca_2 ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__less__cancel__right,axiom,
% 80.71/80.77 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 80.71/80.77 => ( 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)))
% 80.71/80.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__less__cancel__left,axiom,
% 80.71/80.77 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 80.71/80.77 => ( 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)))
% 80.71/80.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__strict__right__mono,axiom,
% 80.71/80.77 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 80.71/80.77 => 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))) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__strict__left__mono,axiom,
% 80.71/80.77 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 80.71/80.77 => 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))) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__strict__mono,axiom,
% 80.71/80.77 ! [V_d,V_c,V_b,V_a,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 80.71/80.77 => 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))) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__left__imp__eq,axiom,
% 80.71/80.77 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.77 ( class_Groups_Ocancel__semigroup__add(T_a)
% 80.71/80.77 => ( 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)
% 80.71/80.77 => V_b = V_c ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__imp__eq,axiom,
% 80.71/80.77 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.77 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 80.71/80.77 => ( 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)
% 80.71/80.77 => V_b = V_c ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__right__imp__eq,axiom,
% 80.71/80.77 ! [V_c,V_a,V_b,T_a] :
% 80.71/80.77 ( class_Groups_Ocancel__semigroup__add(T_a)
% 80.71/80.77 => ( 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)
% 80.71/80.77 => V_b = V_c ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__less__imp__less__right,axiom,
% 80.71/80.77 ! [V_b,V_c,V_a,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 80.71/80.77 => ( 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)))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__less__imp__less__left,axiom,
% 80.71/80.77 ! [V_b,V_a,V_c,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 80.71/80.77 => ( 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)))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__less__irrefl,axiom,
% 80.71/80.77 ! [V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Opreorder(T_a)
% 80.71/80.77 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_linorder__neq__iff,axiom,
% 80.71/80.77 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.77 ( class_Orderings_Olinorder(T_a)
% 80.71/80.77 => ( V_x_2 != V_y_2
% 80.71/80.77 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 80.71/80.77 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_not__less__iff__gr__or__eq,axiom,
% 80.71/80.77 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.77 ( class_Orderings_Olinorder(T_a)
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 80.71/80.77 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 80.71/80.77 | V_x_2 = V_y_2 ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_linorder__less__linear,axiom,
% 80.71/80.77 ! [V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Olinorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 80.71/80.77 | V_x = V_y
% 80.71/80.77 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_linorder__antisym__conv3,axiom,
% 80.71/80.77 ! [V_x_2,V_y_2,T_a] :
% 80.71/80.77 ( class_Orderings_Olinorder(T_a)
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 80.71/80.77 <=> V_x_2 = V_y_2 ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_linorder__neqE,axiom,
% 80.71/80.77 ! [V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Olinorder(T_a)
% 80.71/80.77 => ( V_x != V_y
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__imp__neq,axiom,
% 80.71/80.77 ! [V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 80.71/80.77 => V_x != V_y ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__less__not__sym,axiom,
% 80.71/80.77 ! [V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Opreorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 80.71/80.77 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__less__imp__not__less,axiom,
% 80.71/80.77 ! [V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Opreorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 80.71/80.77 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__less__imp__not__eq,axiom,
% 80.71/80.77 ! [V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 80.71/80.77 => V_x != V_y ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__less__imp__not__eq2,axiom,
% 80.71/80.77 ! [V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 80.71/80.77 => V_y != V_x ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__less__asym_H,axiom,
% 80.71/80.77 ! [V_b,V_a,T_a] :
% 80.71/80.77 ( class_Orderings_Opreorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 80.71/80.77 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_xt1_I9_J,axiom,
% 80.71/80.77 ! [V_a,V_b,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 80.71/80.77 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_ord__eq__less__trans,axiom,
% 80.71/80.77 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.77 ( class_Orderings_Oord(T_a)
% 80.71/80.77 => ( V_a = V_b
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_xt1_I1_J,axiom,
% 80.71/80.77 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( V_a = V_b
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_ord__less__eq__trans,axiom,
% 80.71/80.77 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.77 ( class_Orderings_Oord(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 80.71/80.77 => ( V_b = V_c
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_xt1_I2_J,axiom,
% 80.71/80.77 ! [V_c,V_a,V_b,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 80.71/80.77 => ( V_b = V_c
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__less__trans,axiom,
% 80.71/80.77 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Opreorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_xt1_I10_J,axiom,
% 80.71/80.77 ! [V_z,V_x,V_y,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__less__asym,axiom,
% 80.71/80.77 ! [V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Opreorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 80.71/80.77 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_linorder__cases,axiom,
% 80.71/80.77 ! [V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Olinorder(T_a)
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 80.71/80.77 => ( V_x != V_y
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 80.71/80.77 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] :
% 80.71/80.77 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 80.71/80.77 => 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) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__add__Suc1,axiom,
% 80.71/80.77 ! [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)))) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__add__Suc2,axiom,
% 80.71/80.77 ! [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)))) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__iff__Suc__add,axiom,
% 80.71/80.77 ! [V_n_2,V_m_2] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 80.71/80.77 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__diff__conv,axiom,
% 80.71/80.77 ! [V_k_2,V_j_2,V_i_2] :
% 80.71/80.77 ( 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)))
% 80.71/80.77 <=> 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)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__diff__inverse,axiom,
% 80.71/80.77 ! [V_n,V_m] :
% 80.71/80.77 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 80.71/80.77 => 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 ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__le__imp__le__left,axiom,
% 80.71/80.77 ! [V_b,V_a,V_c,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 80.71/80.77 => ( 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)))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__le__imp__le__right,axiom,
% 80.71/80.77 ! [V_b,V_c,V_a,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 80.71/80.77 => ( 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)))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__mono,axiom,
% 80.71/80.77 ! [V_d,V_c,V_b,V_a,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 80.71/80.77 => 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))) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__left__mono,axiom,
% 80.71/80.77 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.77 => 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))) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__right__mono,axiom,
% 80.71/80.77 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.77 => 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))) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__le__cancel__left,axiom,
% 80.71/80.77 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 80.71/80.77 => ( 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)))
% 80.71/80.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__le__cancel__right,axiom,
% 80.71/80.77 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 80.71/80.77 => ( 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)))
% 80.71/80.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__diff__cancel,axiom,
% 80.71/80.77 ! [V_b,V_a,T_a] :
% 80.71/80.77 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.77 => 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 ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__add__cancel,axiom,
% 80.71/80.77 ! [V_b,V_a,T_a] :
% 80.71/80.77 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.77 => 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 ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_linorder__not__less,axiom,
% 80.71/80.77 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.77 ( class_Orderings_Olinorder(T_a)
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 80.71/80.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_linorder__not__le,axiom,
% 80.71/80.77 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.77 ( class_Orderings_Olinorder(T_a)
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 80.71/80.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_linorder__le__less__linear,axiom,
% 80.71/80.77 ! [V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Olinorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 80.71/80.77 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__less__le,axiom,
% 80.71/80.77 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 80.71/80.77 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 80.71/80.77 & V_x_2 != V_y_2 ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__le__not__le,axiom,
% 80.71/80.77 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.77 ( class_Orderings_Opreorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 80.71/80.77 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 80.71/80.77 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__le__less,axiom,
% 80.71/80.77 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 80.71/80.77 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 80.71/80.77 | V_x_2 = V_y_2 ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_leI,axiom,
% 80.71/80.77 ! [V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Olinorder(T_a)
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_not__leE,axiom,
% 80.71/80.77 ! [V_x,V_y,T_a] :
% 80.71/80.77 ( class_Orderings_Olinorder(T_a)
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_linorder__antisym__conv1,axiom,
% 80.71/80.77 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.77 ( class_Orderings_Olinorder(T_a)
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 80.71/80.77 <=> V_x_2 = V_y_2 ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__neq__le__trans,axiom,
% 80.71/80.77 ! [V_b,V_a,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( V_a != V_b
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_xt1_I12_J,axiom,
% 80.71/80.77 ! [V_b,V_a,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( V_a != V_b
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_leD,axiom,
% 80.71/80.77 ! [V_x,V_y,T_a] :
% 80.71/80.77 ( class_Orderings_Olinorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 80.71/80.77 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__less__imp__le,axiom,
% 80.71/80.77 ! [V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Opreorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_linorder__antisym__conv2,axiom,
% 80.71/80.77 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.77 ( class_Orderings_Olinorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 80.71/80.77 <=> V_x_2 = V_y_2 ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__le__imp__less__or__eq,axiom,
% 80.71/80.77 ! [V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 80.71/80.77 | V_x = V_y ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__le__neq__trans,axiom,
% 80.71/80.77 ! [V_b,V_a,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.77 => ( V_a != V_b
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_xt1_I11_J,axiom,
% 80.71/80.77 ! [V_a,V_b,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 80.71/80.77 => ( V_a != V_b
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__less__le__trans,axiom,
% 80.71/80.77 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Opreorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_xt1_I7_J,axiom,
% 80.71/80.77 ! [V_z,V_x,V_y,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_order__le__less__trans,axiom,
% 80.71/80.77 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.77 ( class_Orderings_Opreorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_xt1_I8_J,axiom,
% 80.71/80.77 ! [V_z,V_x,V_y,T_a] :
% 80.71/80.77 ( class_Orderings_Oorder(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__eq__diff__less,axiom,
% 80.71/80.77 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 80.71/80.77 ( class_Groups_Oordered__ab__group__add(T_a)
% 80.71/80.77 => ( 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)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 80.71/80.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) ) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__supI2,axiom,
% 80.71/80.77 ! [V_a,V_b,V_x,T_a] :
% 80.71/80.77 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 80.71/80.77 => 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))) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__supI1,axiom,
% 80.71/80.77 ! [V_b,V_a,V_x,T_a] :
% 80.71/80.77 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 80.71/80.77 => 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))) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__Suc__shift,axiom,
% 80.71/80.77 ! [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)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__Suc,axiom,
% 80.71/80.77 ! [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)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__Suc__right,axiom,
% 80.71/80.77 ! [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)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Suc__less__SucD,axiom,
% 80.71/80.77 ! [V_n,V_m] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Suc__lessD,axiom,
% 80.71/80.77 ! [V_n,V_m] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__SucE,axiom,
% 80.71/80.77 ! [V_n,V_m] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 80.71/80.77 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 80.71/80.77 => V_m = V_n ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__trans__Suc,axiom,
% 80.71/80.77 ! [V_k,V_j,V_i] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Suc__lessI,axiom,
% 80.71/80.77 ! [V_n,V_m] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 80.71/80.77 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__SucI,axiom,
% 80.71/80.77 ! [V_n,V_m] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__antisym,axiom,
% 80.71/80.77 ! [V_m,V_n] :
% 80.71/80.77 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 80.71/80.77 => V_m = V_n ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_not__less__less__Suc__eq,axiom,
% 80.71/80.77 ! [V_m_2,V_n_2] :
% 80.71/80.77 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 80.71/80.77 <=> V_n_2 = V_m_2 ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_Suc__less__eq,axiom,
% 80.71/80.77 ! [V_n_2,V_m_2] :
% 80.71/80.77 ( 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)))
% 80.71/80.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__Suc__eq,axiom,
% 80.71/80.77 ! [V_n_2,V_m_2] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 80.71/80.77 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 80.71/80.77 | V_m_2 = V_n_2 ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_not__less__eq,axiom,
% 80.71/80.77 ! [V_n_2,V_m_2] :
% 80.71/80.77 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 80.71/80.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__leE,axiom,
% 80.71/80.77 ! [V_n,V_k,V_m] :
% 80.71/80.77 ( 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))
% 80.71/80.77 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 80.71/80.77 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__leD1,axiom,
% 80.71/80.77 ! [V_n,V_k,V_m] :
% 80.71/80.77 ( 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))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__leD2,axiom,
% 80.71/80.77 ! [V_n,V_k,V_m] :
% 80.71/80.77 ( 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))
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__le__mono,axiom,
% 80.71/80.77 ! [V_l,V_k,V_j,V_i] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 80.71/80.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 80.71/80.77 => 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))) ) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_add__le__mono1,axiom,
% 80.71/80.77 ! [V_k,V_j,V_i] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 80.71/80.77 => 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))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_trans__le__add2,axiom,
% 80.71/80.77 ! [V_m,V_j,V_i] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 80.71/80.77 => 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))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_trans__le__add1,axiom,
% 80.71/80.77 ! [V_m,V_j,V_i] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 80.71/80.77 => 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))) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_nat__add__left__cancel__le,axiom,
% 80.71/80.77 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.77 ( 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)))
% 80.71/80.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_le__iff__add,axiom,
% 80.71/80.77 ! [V_n_2,V_m_2] :
% 80.71/80.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 80.71/80.77 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_le__add1,axiom,
% 80.71/80.77 ! [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))) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_le__add2,axiom,
% 80.71/80.77 ! [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))) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__cancel2,axiom,
% 80.71/80.77 ! [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) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__cancel,axiom,
% 80.71/80.77 ! [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) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__diff__left,axiom,
% 80.71/80.77 ! [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)) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__add__inverse,axiom,
% 80.71/80.77 ! [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 ).
% 80.71/80.77
% 80.71/80.77 fof(fact_diff__add__inverse2,axiom,
% 80.71/80.77 ! [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 ).
% 80.71/80.77
% 80.71/80.77 fof(fact_less__or__eq__imp__le,axiom,
% 80.71/80.77 ! [V_n,V_m] :
% 80.71/80.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 80.71/80.77 | V_m = V_n )
% 80.71/80.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 80.71/80.77
% 80.71/80.77 fof(fact_le__neq__implies__less,axiom,
% 80.71/80.77 ! [V_n,V_m] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 80.71/80.78 => ( V_m != V_n
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__imp__le__nat,axiom,
% 80.71/80.78 ! [V_n,V_m] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__eq__less__or__eq,axiom,
% 80.71/80.78 ! [V_n_2,V_m_2] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 80.71/80.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 80.71/80.78 | V_m_2 = V_n_2 ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_nat__less__le,axiom,
% 80.71/80.78 ! [V_n_2,V_m_2] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 80.71/80.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 80.71/80.78 & V_m_2 != V_n_2 ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__less__mono2,axiom,
% 80.71/80.78 ! [V_l,V_n,V_m] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 80.71/80.78 => 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))) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__imp__diff__less,axiom,
% 80.71/80.78 ! [V_n,V_k,V_j] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__Sup__iff,axiom,
% 80.71/80.78 ! [V_S_2,V_a_2,T_a] :
% 80.71/80.78 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 80.71/80.78 & class_Orderings_Olinorder(T_a) )
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2)))
% 80.71/80.78 <=> ? [B_x] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 80.71/80.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum__insert,axiom,
% 80.71/80.78 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] :
% 80.71/80.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 80.71/80.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2))
% 80.71/80.78 => 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)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum_Oinsert,axiom,
% 80.71/80.78 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 80.71/80.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.78 => 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)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum_Oinsert__remove,axiom,
% 80.71/80.78 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
% 80.71/80.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => 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)))))) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_fun__left__comm__idem__insert,axiom,
% 80.71/80.78 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_fun__left__comm__idem__sup,axiom,
% 80.71/80.78 ! [T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.78 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__eq__Suc__le,axiom,
% 80.71/80.78 ! [V_m_2,V_n_2] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 80.71/80.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__Suc__eq__le,axiom,
% 80.71/80.78 ! [V_n_2,V_m_2] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 80.71/80.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Suc__le__eq,axiom,
% 80.71/80.78 ! [V_n_2,V_m_2] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 80.71/80.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__imp__less__Suc,axiom,
% 80.71/80.78 ! [V_n,V_m] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Suc__leI,axiom,
% 80.71/80.78 ! [V_n,V_m] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__less__Suc__eq,axiom,
% 80.71/80.78 ! [V_n_2,V_m_2] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 80.71/80.78 <=> V_n_2 = V_m_2 ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Suc__le__lessD,axiom,
% 80.71/80.78 ! [V_n,V_m] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__add__assoc2,axiom,
% 80.71/80.78 ! [V_i,V_j,V_k] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__diff__assoc2,axiom,
% 80.71/80.78 ! [V_i,V_j,V_k] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__add__assoc,axiom,
% 80.71/80.78 ! [V_i,V_j,V_k] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__imp__diff__is__add,axiom,
% 80.71/80.78 ! [V_k_2,V_j_2,V_i_2] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 80.71/80.78 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 80.71/80.78 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__add__diff__inverse2,axiom,
% 80.71/80.78 ! [V_m,V_n] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 80.71/80.78 => 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 ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__diff__conv2,axiom,
% 80.71/80.78 ! [V_i_2,V_j_2,V_k_2] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 80.71/80.78 => ( 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)))
% 80.71/80.78 <=> 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)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__diff__assoc,axiom,
% 80.71/80.78 ! [V_i,V_j,V_k] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__add__diff__inverse,axiom,
% 80.71/80.78 ! [V_m,V_n] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 80.71/80.78 => 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 ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__add__diff,axiom,
% 80.71/80.78 ! [V_m,V_n,V_k] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 80.71/80.78 => 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))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__diff__conv,axiom,
% 80.71/80.78 ! [V_i_2,V_k_2,V_j_2] :
% 80.71/80.78 ( 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))
% 80.71/80.78 <=> 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))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__diff__right,axiom,
% 80.71/80.78 ! [V_i,V_j,V_k] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__less__Suc,axiom,
% 80.71/80.78 ! [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))) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Suc__eq__plus1__left,axiom,
% 80.71/80.78 ! [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) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Suc__eq__plus1,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__diff__iff,axiom,
% 80.71/80.78 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 80.71/80.78 => ( 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)))
% 80.71/80.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__less__mono,axiom,
% 80.71/80.78 ! [V_c,V_b,V_a] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 80.71/80.78 => 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))) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum__diff1_H,axiom,
% 80.71/80.78 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 80.71/80.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.78 => 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)))))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum_Oremove,axiom,
% 80.71/80.78 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 80.71/80.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.78 => 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)))))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__Suc__diff__eq1,axiom,
% 80.71/80.78 ! [V_m,V_j,V_k] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__Suc__diff__eq2,axiom,
% 80.71/80.78 ! [V_m,V_j,V_k] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum__diff,axiom,
% 80.71/80.78 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 80.71/80.78 ( class_Groups_Oab__group__add(T_b)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 80.71/80.78 => 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)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum__diff__nat,axiom,
% 80.71/80.78 ! [V_f_2,V_A_2,V_B_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 80.71/80.78 => 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)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum__diff1__nat,axiom,
% 80.71/80.78 ! [V_f_2,V_A_2,V_a_2,T_a] :
% 80.71/80.78 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.78 => 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)) )
% 80.71/80.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.78 => 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) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__add__one,axiom,
% 80.71/80.78 ! [V_a,T_a] :
% 80.71/80.78 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.78 => 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)))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_termination__basic__simps_I4_J,axiom,
% 80.71/80.78 ! [V_y,V_z,V_x] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 80.71/80.78 => 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))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_termination__basic__simps_I3_J,axiom,
% 80.71/80.78 ! [V_z,V_y,V_x] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 80.71/80.78 => 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))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_termination__basic__simps_I5_J,axiom,
% 80.71/80.78 ! [V_y,V_x] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_termination__basic__simps_I2_J,axiom,
% 80.71/80.78 ! [V_y,V_z,V_x] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 80.71/80.78 => 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))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_termination__basic__simps_I1_J,axiom,
% 80.71/80.78 ! [V_z,V_y,V_x] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 80.71/80.78 => 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))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum__strict__mono,axiom,
% 80.71/80.78 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
% 80.71/80.78 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.78 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) )
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.78 => ( ! [B_x] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 80.71/80.78 => 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))) ) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_card__Plus,axiom,
% 80.71/80.78 ! [V_B_2,T_b,V_A_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 80.71/80.78 => 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)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.78 => ( 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))
% 80.71/80.78 => 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)) ) ) ) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Sup__fin_Ounion__inter,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => ( 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))
% 80.71/80.78 => 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)) ) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf1E,axiom,
% 80.71/80.78 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( 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))
% 80.71/80.78 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 80.71/80.78 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf1I,axiom,
% 80.71/80.78 ! [T_a,V_B_2,V_x_2,V_A_2] :
% 80.71/80.78 ( hBOOL(hAPP(V_A_2,V_x_2))
% 80.71/80.78 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 80.71/80.78 => 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)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_IntE,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 80.71/80.78 ( 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)))
% 80.71/80.78 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 80.71/80.78 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_IntI,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2))
% 80.71/80.78 => 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))) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_finite__Int,axiom,
% 80.71/80.78 ! [V_G_2,V_F_2,T_a] :
% 80.71/80.78 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 80.71/80.78 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) )
% 80.71/80.78 => 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))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf1D2,axiom,
% 80.71/80.78 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( 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))
% 80.71/80.78 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf1D1,axiom,
% 80.71/80.78 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( 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))
% 80.71/80.78 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__apply,axiom,
% 80.71/80.78 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__assoc,axiom,
% 80.71/80.78 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__sup__aci_I2_J,axiom,
% 80.71/80.78 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf_Oassoc,axiom,
% 80.71/80.78 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__left__commute,axiom,
% 80.71/80.78 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__sup__aci_I3_J,axiom,
% 80.71/80.78 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf_Oleft__commute,axiom,
% 80.71/80.78 ! [V_c,V_a,V_b,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__left__idem,axiom,
% 80.71/80.78 ! [V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__sup__aci_I4_J,axiom,
% 80.71/80.78 ! [V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf_Oleft__idem,axiom,
% 80.71/80.78 ! [V_b,V_a,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__commute,axiom,
% 80.71/80.78 ! [V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__sup__aci_I1_J,axiom,
% 80.71/80.78 ! [V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf_Ocommute,axiom,
% 80.71/80.78 ! [V_b,V_a,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__idem,axiom,
% 80.71/80.78 ! [V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Inf__fin_Oidem,axiom,
% 80.71/80.78 ! [V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf_Oidem,axiom,
% 80.71/80.78 ! [V_a,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__assoc,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__left__commute,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__left__absorb,axiom,
% 80.71/80.78 ! [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) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__commute,axiom,
% 80.71/80.78 ! [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) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__absorb,axiom,
% 80.71/80.78 ! [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 ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Union__Int__subset,axiom,
% 80.71/80.78 ! [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)))) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__sup__ord_I1_J,axiom,
% 80.71/80.78 ! [V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__le1,axiom,
% 80.71/80.78 ! [V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__sup__ord_I2_J,axiom,
% 80.71/80.78 ! [V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__le2,axiom,
% 80.71/80.78 ! [V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__iff__inf,axiom,
% 80.71/80.78 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 80.71/80.78 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__inf__iff,axiom,
% 80.71/80.78 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => ( 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)))
% 80.71/80.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 80.71/80.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__infI1,axiom,
% 80.71/80.78 ! [V_b,V_x,V_a,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 80.71/80.78 => 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)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__infI2,axiom,
% 80.71/80.78 ! [V_a,V_x,V_b,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 80.71/80.78 => 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)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__absorb1,axiom,
% 80.71/80.78 ! [V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 80.71/80.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__absorb2,axiom,
% 80.71/80.78 ! [V_x,V_y,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 80.71/80.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__infI,axiom,
% 80.71/80.78 ! [V_b,V_a,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__greatest,axiom,
% 80.71/80.78 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__mono,axiom,
% 80.71/80.78 ! [V_d,V_b,V_c,V_a,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__infE,axiom,
% 80.71/80.78 ! [V_b,V_a,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => ( 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)))
% 80.71/80.78 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 80.71/80.78 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__infI2,axiom,
% 80.71/80.78 ! [V_a,V_x,V_b,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 80.71/80.78 => 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)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__infI1,axiom,
% 80.71/80.78 ! [V_b,V_x,V_a,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 80.71/80.78 => 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)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__bot__right,axiom,
% 80.71/80.78 ! [V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Obounded__lattice__bot(T_a)
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__bot__left,axiom,
% 80.71/80.78 ! [V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Obounded__lattice__bot(T_a)
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__sup__absorb,axiom,
% 80.71/80.78 ! [V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => 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 ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_sup__inf__absorb,axiom,
% 80.71/80.78 ! [V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => 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 ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__sup__distrib1,axiom,
% 80.71/80.78 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Odistrib__lattice(T_a)
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_sup__inf__distrib1,axiom,
% 80.71/80.78 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Odistrib__lattice(T_a)
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__sup__distrib2,axiom,
% 80.71/80.78 ! [V_x,V_z,V_y,T_a] :
% 80.71/80.78 ( class_Lattices_Odistrib__lattice(T_a)
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_sup__inf__distrib2,axiom,
% 80.71/80.78 ! [V_x,V_z,V_y,T_a] :
% 80.71/80.78 ( class_Lattices_Odistrib__lattice(T_a)
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_IntD2,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 80.71/80.78 ( 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)))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_IntD1,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 80.71/80.78 ( 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)))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__iff,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,V_ca_2,T_a] :
% 80.71/80.78 ( 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)))
% 80.71/80.78 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 80.71/80.78 & hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__fun__def,axiom,
% 80.71/80.78 ! [V_g_2,V_f_2,T_a,T_b] :
% 80.71/80.78 ( class_Orderings_Oord(T_b)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 80.71/80.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 80.71/80.78 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_psubsetD,axiom,
% 80.71/80.78 ! [V_ca_2,V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_disjoint__iff__not__equal,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( 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))
% 80.71/80.78 <=> ! [B_x] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.78 => ! [B_xa] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2))
% 80.71/80.78 => B_x != B_xa ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__empty__right,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__empty__left,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_insert__inter__insert,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__mono,axiom,
% 80.71/80.78 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
% 80.71/80.78 => 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))) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__greatest,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,V_C_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2))
% 80.71/80.78 => 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))) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__absorb1,axiom,
% 80.71/80.78 ! [V_A_2,V_B_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 80.71/80.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__absorb2,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__lower2,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__lower1,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_not__psubset__empty,axiom,
% 80.71/80.78 ! [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)))) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Un__Int__crazy,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Un__Int__distrib2,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__Un__distrib2,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Un__Int__distrib,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__Un__distrib,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_subset__psubset__trans,axiom,
% 80.71/80.78 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_psubset__subset__trans,axiom,
% 80.71/80.78 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_psubset__imp__subset,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_subset__iff__psubset__eq,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.78 | V_A_2 = V_B_2 ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_psubset__eq,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.78 & V_A_2 != V_B_2 ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Diff__Int2,axiom,
% 80.71/80.78 ! [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) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Diff__Int__distrib2,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__Diff,axiom,
% 80.71/80.78 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Diff__Int__distrib,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_fun__left__comm__idem__inf,axiom,
% 80.71/80.78 ! [T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_finite__Plus__iff,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_b,T_a] :
% 80.71/80.78 ( 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)))
% 80.71/80.78 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_finite__Plus,axiom,
% 80.71/80.78 ! [V_B_2,T_b,V_A_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 80.71/80.78 => 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))) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_finite__PlusD_I1_J,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_b,T_a] :
% 80.71/80.78 ( 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)))
% 80.71/80.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_finite__PlusD_I2_J,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_b,T_a] :
% 80.71/80.78 ( 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)))
% 80.71/80.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_distrib__sup__le,axiom,
% 80.71/80.78 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => 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)))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_distrib__inf__le,axiom,
% 80.71/80.78 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => 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)))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__insert__right,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 80.71/80.78 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.78 => 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)) )
% 80.71/80.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.78 => 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) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__insert__left,axiom,
% 80.71/80.78 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 80.71/80.78 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 80.71/80.78 => 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)) )
% 80.71/80.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 80.71/80.78 => 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) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__insert__right__if0,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 80.71/80.78 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__insert__left__if0,axiom,
% 80.71/80.78 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 80.71/80.78 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__insert__right__if1,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Int__insert__left__if1,axiom,
% 80.71/80.78 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 80.71/80.78 => 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)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Diff__disjoint,axiom,
% 80.71/80.78 ! [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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Diff__triv,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( 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))
% 80.71/80.78 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Un__Int__assoc__eq,axiom,
% 80.71/80.78 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( 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))
% 80.71/80.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Un__Diff__Int,axiom,
% 80.71/80.78 ! [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 ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Diff__Un,axiom,
% 80.71/80.78 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Diff__Int,axiom,
% 80.71/80.78 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),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)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Union__disjoint,axiom,
% 80.71/80.78 ! [V_A_2,V_C_2,T_a] :
% 80.71/80.78 ( 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))
% 80.71/80.78 <=> ! [B_x] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2))
% 80.71/80.78 => 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)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_fold__inf__insert,axiom,
% 80.71/80.78 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => 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)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_inf__Sup__absorb,axiom,
% 80.71/80.78 ! [V_a_2,V_A_2,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.78 => 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 ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_psubset__card__mono,axiom,
% 80.71/80.78 ! [V_A_2,V_B_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.78 => 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))) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_linorder__neqE__linordered__idom,axiom,
% 80.71/80.78 ! [V_y,V_x,T_a] :
% 80.71/80.78 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.78 => ( V_x != V_y
% 80.71/80.78 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.78 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 80.71/80.78 => 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)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_fold__inf__le__inf,axiom,
% 80.71/80.78 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 80.71/80.78 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum__Un__Int,axiom,
% 80.71/80.78 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 80.71/80.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => 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)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum__Un__nat,axiom,
% 80.71/80.78 ! [V_f_2,V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => 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))) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_card__Un__Int,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => 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))) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_card_Ounion__inter,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => 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)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_card__Diff__subset__Int,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( 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)))
% 80.71/80.78 => 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))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_card__psubset,axiom,
% 80.71/80.78 ! [V_A_2,V_B_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.78 => ( 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)))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_folding__one_Ounion__disjoint,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 80.71/80.78 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.78 => ( 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))
% 80.71/80.78 => 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)) ) ) ) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_folding__one_Ounion__inter,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 80.71/80.78 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => ( 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))
% 80.71/80.78 => 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)) ) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.78 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 80.71/80.78 => ( 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))
% 80.71/80.78 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum__Un__disjoint,axiom,
% 80.71/80.78 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 80.71/80.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => ( 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))
% 80.71/80.78 => 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)) ) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum__Un,axiom,
% 80.71/80.78 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 80.71/80.78 ( class_Groups_Oab__group__add(T_b)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_card__Un__disjoint,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => ( 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))
% 80.71/80.78 => 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)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_psubset__insert__iff,axiom,
% 80.71/80.78 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 80.71/80.78 ( 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)))
% 80.71/80.78 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 80.71/80.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 80.71/80.78 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.78 => 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)) )
% 80.71/80.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Plus__eq__empty__conv,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_b,T_a] :
% 80.71/80.78 ( 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))
% 80.71/80.78 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.78 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_card__Plus__conv__if,axiom,
% 80.71/80.78 ! [V_B_2,T_b,V_A_2,T_a] :
% 80.71/80.78 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) )
% 80.71/80.78 => 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)) )
% 80.71/80.78 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) )
% 80.71/80.78 => 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) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Inf__fin_Oremove,axiom,
% 80.71/80.78 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.78 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.78 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 )
% 80.71/80.78 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.78 => 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)))))) ) ) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_insert__partition,axiom,
% 80.71/80.78 ! [V_F_2,V_x_2,T_a] :
% 80.71/80.78 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))
% 80.71/80.78 => ( ! [B_x] :
% 80.71/80.78 ( 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)))
% 80.71/80.78 => ! [B_xa] :
% 80.71/80.78 ( 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)))
% 80.71/80.78 => ( B_x != B_xa
% 80.71/80.78 => 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)) ) ) )
% 80.71/80.78 => 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)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 80.71/80.78 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.78 => 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) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.78 => ( 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))
% 80.71/80.78 => 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)) ) ) ) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Inf__fin_Ounion__inter,axiom,
% 80.71/80.78 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.78 => ( 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))
% 80.71/80.78 => 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)) ) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 80.71/80.78 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.78 => 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 )
% 80.71/80.78 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.78 => 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)))))) ) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Inf__fin_Oinsert,axiom,
% 80.71/80.78 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.78 => 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)) ) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__zeroE,axiom,
% 80.71/80.78 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le0,axiom,
% 80.71/80.78 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_zero__less__Suc,axiom,
% 80.71/80.78 ! [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))) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_psubset__trans,axiom,
% 80.71/80.78 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_bot__nat__def,axiom,
% 80.71/80.78 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_zero__reorient,axiom,
% 80.71/80.78 ! [V_x_2,T_a] :
% 80.71/80.78 ( class_Groups_Ozero(T_a)
% 80.71/80.78 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 80.71/80.78 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__0__left,axiom,
% 80.71/80.78 ! [V_a,T_a] :
% 80.71/80.78 ( class_Groups_Omonoid__add(T_a)
% 80.71/80.78 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__0,axiom,
% 80.71/80.78 ! [V_a,T_a] :
% 80.71/80.78 ( class_Groups_Ocomm__monoid__add(T_a)
% 80.71/80.78 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_double__zero__sym,axiom,
% 80.71/80.78 ! [V_a_2,T_a] :
% 80.71/80.78 ( class_Groups_Olinordered__ab__group__add(T_a)
% 80.71/80.78 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)
% 80.71/80.78 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__0__right,axiom,
% 80.71/80.78 ! [V_a,T_a] :
% 80.71/80.78 ( class_Groups_Omonoid__add(T_a)
% 80.71/80.78 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add_Ocomm__neutral,axiom,
% 80.71/80.78 ! [V_a,T_a] :
% 80.71/80.78 ( class_Groups_Ocomm__monoid__add(T_a)
% 80.71/80.78 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_right__minus__eq,axiom,
% 80.71/80.78 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.78 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.78 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.78 <=> V_a_2 = V_b_2 ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_eq__iff__diff__eq__0,axiom,
% 80.71/80.78 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.78 ( class_Groups_Oab__group__add(T_a)
% 80.71/80.78 => ( V_a_2 = V_b_2
% 80.71/80.78 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__self,axiom,
% 80.71/80.78 ! [V_a,T_a] :
% 80.71/80.78 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.78 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__0__right,axiom,
% 80.71/80.78 ! [V_a,T_a] :
% 80.71/80.78 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.78 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_zero__neq__one,axiom,
% 80.71/80.78 ! [T_a] :
% 80.71/80.78 ( class_Rings_Ozero__neq__one(T_a)
% 80.71/80.78 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_one__neq__zero,axiom,
% 80.71/80.78 ! [T_a] :
% 80.71/80.78 ( class_Rings_Ozero__neq__one(T_a)
% 80.71/80.78 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Suc__neq__Zero,axiom,
% 80.71/80.78 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Zero__neq__Suc,axiom,
% 80.71/80.78 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_nat_Osimps_I3_J,axiom,
% 80.71/80.78 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Suc__not__Zero,axiom,
% 80.71/80.78 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_nat_Osimps_I2_J,axiom,
% 80.71/80.78 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Zero__not__Suc,axiom,
% 80.71/80.78 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_not__less0,axiom,
% 80.71/80.78 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_neq0__conv,axiom,
% 80.71/80.78 ! [V_n_2] :
% 80.71/80.78 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__nat__zero__code,axiom,
% 80.71/80.78 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_gr__implies__not0,axiom,
% 80.71/80.78 ! [V_n,V_m] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 80.71/80.78 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_gr0I,axiom,
% 80.71/80.78 ! [V_n] :
% 80.71/80.78 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_plus__nat_Oadd__0,axiom,
% 80.71/80.78 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Nat_Oadd__0__right,axiom,
% 80.71/80.78 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__is__0,axiom,
% 80.71/80.78 ! [V_n_2,V_m_2] :
% 80.71/80.78 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.78 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.78 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__eq__self__zero,axiom,
% 80.71/80.78 ! [V_n,V_m] :
% 80.71/80.78 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 80.71/80.78 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__0__eq,axiom,
% 80.71/80.78 ! [V_n_2] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 80.71/80.78 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 80.71/80.78 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diffs0__imp__equal,axiom,
% 80.71/80.78 ! [V_n,V_m] :
% 80.71/80.78 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.78 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.78 => V_m = V_n ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__self__eq__0,axiom,
% 80.71/80.78 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_minus__nat_Odiff__0,axiom,
% 80.71/80.78 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__0__eq__0,axiom,
% 80.71/80.78 ! [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) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__nonpos__nonpos,axiom,
% 80.71/80.78 ! [V_b,V_a,T_a] :
% 80.71/80.78 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__increasing2,axiom,
% 80.71/80.78 ! [V_a,V_b,V_c,T_a] :
% 80.71/80.78 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__increasing,axiom,
% 80.71/80.78 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.78 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__nonneg__eq__0__iff,axiom,
% 80.71/80.78 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.78 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2))
% 80.71/80.78 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.78 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.78 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__nonneg__nonneg,axiom,
% 80.71/80.78 ! [V_b,V_a,T_a] :
% 80.71/80.78 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 80.71/80.78 ! [V_a_2,T_a] :
% 80.71/80.78 ( class_Groups_Olinordered__ab__group__add(T_a)
% 80.71/80.78 => ( 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)))
% 80.71/80.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 80.71/80.78 ! [V_a_2,T_a] :
% 80.71/80.78 ( class_Groups_Olinordered__ab__group__add(T_a)
% 80.71/80.78 => ( 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)))
% 80.71/80.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 80.71/80.78 ! [V_a_2,T_a] :
% 80.71/80.78 ( class_Groups_Olinordered__ab__group__add(T_a)
% 80.71/80.78 => ( 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)))
% 80.71/80.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 80.71/80.78 ! [V_a_2,T_a] :
% 80.71/80.78 ( class_Groups_Olinordered__ab__group__add(T_a)
% 80.71/80.78 => ( 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)))
% 80.71/80.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__pos__pos,axiom,
% 80.71/80.78 ! [V_b,V_a,T_a] :
% 80.71/80.78 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__neg__neg,axiom,
% 80.71/80.78 ! [V_b,V_a,T_a] :
% 80.71/80.78 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_pos__add__strict,axiom,
% 80.71/80.78 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.78 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_le__iff__diff__le__0,axiom,
% 80.71/80.78 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.78 ( class_Groups_Oordered__ab__group__add(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 80.71/80.78 <=> 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))) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__iff__diff__less__0,axiom,
% 80.71/80.78 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.78 ( class_Groups_Oordered__ab__group__add(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 80.71/80.78 <=> 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))) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_zero__le__one,axiom,
% 80.71/80.78 ! [T_a] :
% 80.71/80.78 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.78 => 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))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_not__one__le__zero,axiom,
% 80.71/80.78 ! [T_a] :
% 80.71/80.78 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.78 => ~ 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))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_zero__less__one,axiom,
% 80.71/80.78 ! [T_a] :
% 80.71/80.78 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_not__one__less__zero,axiom,
% 80.71/80.78 ! [T_a] :
% 80.71/80.78 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.78 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum__empty,axiom,
% 80.71/80.78 ! [V_f_2,T_b,T_a] :
% 80.71/80.78 ( class_Groups_Ocomm__monoid__add(T_a)
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum_Oempty,axiom,
% 80.71/80.78 ! [V_g_2,T_b,T_a] :
% 80.71/80.78 ( class_Groups_Ocomm__monoid__add(T_a)
% 80.71/80.78 => 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) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum_Oinfinite,axiom,
% 80.71/80.78 ! [V_g_2,V_A_2,T_a,T_b] :
% 80.71/80.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.78 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => 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) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum__infinite,axiom,
% 80.71/80.78 ! [V_f_2,V_A_2,T_a,T_b] :
% 80.71/80.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.78 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => 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) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_gr0__conv__Suc,axiom,
% 80.71/80.78 ! [V_n_2] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 80.71/80.78 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__Suc0,axiom,
% 80.71/80.78 ! [V_n_2] :
% 80.71/80.78 ( 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))))
% 80.71/80.78 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_less__Suc__eq__0__disj,axiom,
% 80.71/80.78 ! [V_n_2,V_m_2] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 80.71/80.78 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.78 | ? [B_j] :
% 80.71/80.78 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 80.71/80.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_one__is__add,axiom,
% 80.71/80.78 ! [V_n_2,V_m_2] :
% 80.71/80.78 ( 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)
% 80.71/80.78 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 80.71/80.78 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 80.71/80.78 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.78 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__is__1,axiom,
% 80.71/80.78 ! [V_n_2,V_m_2] :
% 80.71/80.78 ( 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))
% 80.71/80.78 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 80.71/80.78 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 80.71/80.78 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.78 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__gr__0,axiom,
% 80.71/80.78 ! [V_n_2,V_m_2] :
% 80.71/80.78 ( 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)))
% 80.71/80.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 80.71/80.78 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_card_Oempty,axiom,
% 80.71/80.78 ! [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) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_card__infinite,axiom,
% 80.71/80.78 ! [V_A_2,T_a] :
% 80.71/80.78 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.78 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_zero__less__diff,axiom,
% 80.71/80.78 ! [V_m_2,V_n_2] :
% 80.71/80.78 ( 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)))
% 80.71/80.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__less,axiom,
% 80.71/80.78 ! [V_m,V_n] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 80.71/80.78 => 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)) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__add__0,axiom,
% 80.71/80.78 ! [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) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__is__0__eq_H,axiom,
% 80.71/80.78 ! [V_n,V_m] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 80.71/80.78 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_diff__is__0__eq,axiom,
% 80.71/80.78 ! [V_n_2,V_m_2] :
% 80.71/80.78 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_One__nat__def,axiom,
% 80.71/80.78 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_Inf__fin_Osingleton,axiom,
% 80.71/80.78 ! [V_x_2,T_a] :
% 80.71/80.78 ( class_Lattices_Olattice(T_a)
% 80.71/80.78 => 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 ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_setsum__eq__0__iff,axiom,
% 80.71/80.78 ! [V_f_2,V_F_2,T_a] :
% 80.71/80.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 80.71/80.78 => ( 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)
% 80.71/80.78 <=> ! [B_x] :
% 80.71/80.78 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2))
% 80.71/80.78 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__pos__nonneg,axiom,
% 80.71/80.78 ! [V_b,V_a,T_a] :
% 80.71/80.78 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__nonneg__pos,axiom,
% 80.71/80.78 ! [V_b,V_a,T_a] :
% 80.71/80.78 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__strict__increasing,axiom,
% 80.71/80.78 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.78 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__strict__increasing2,axiom,
% 80.71/80.78 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.78 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__neg__nonpos,axiom,
% 80.71/80.78 ! [V_b,V_a,T_a] :
% 80.71/80.78 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_add__nonpos__neg,axiom,
% 80.71/80.78 ! [V_b,V_a,T_a] :
% 80.71/80.78 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.78 => 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))) ) ) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_zero__less__two,axiom,
% 80.71/80.78 ! [T_a] :
% 80.71/80.78 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.78 => 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)))) ) ).
% 80.71/80.78
% 80.71/80.78 fof(fact_card__eq__0__iff,axiom,
% 80.71/80.78 ! [V_A_2,T_a] :
% 80.71/80.79 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.79 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.79 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_card__ge__0__finite,axiom,
% 80.71/80.79 ! [V_A_2,T_a] :
% 80.71/80.79 ( 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)))
% 80.71/80.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_diff__Suc__less,axiom,
% 80.71/80.79 ! [V_i,V_n] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Suc__pred,axiom,
% 80.71/80.79 ! [V_n] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 80.71/80.79 => 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 ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_nat__diff__split,axiom,
% 80.71/80.79 ! [V_b_2,V_a_2,V_P_2] :
% 80.71/80.79 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 80.71/80.79 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 80.71/80.79 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 80.71/80.79 & ! [B_d] :
% 80.71/80.79 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 80.71/80.79 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_nat__diff__split__asm,axiom,
% 80.71/80.79 ! [V_b_2,V_a_2,V_P_2] :
% 80.71/80.79 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 80.71/80.79 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 80.71/80.79 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 80.71/80.79 | ? [B_d] :
% 80.71/80.79 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 80.71/80.79 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_sup__Inf__absorb,axiom,
% 80.71/80.79 ! [V_a_2,V_A_2,T_a] :
% 80.71/80.79 ( class_Lattices_Olattice(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.79 => 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 ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Inf__fin_Oin__idem,axiom,
% 80.71/80.79 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.79 ( class_Lattices_Olattice(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.79 => 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) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_setsum__eq__Suc0__iff,axiom,
% 80.71/80.79 ! [V_f_2,V_A_2,T_a] :
% 80.71/80.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => ( 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))
% 80.71/80.79 <=> ? [B_x] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.79 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 80.71/80.79 & ! [B_xa] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 80.71/80.79 => ( B_x != B_xa
% 80.71/80.79 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_setsum__eq__1__iff,axiom,
% 80.71/80.79 ! [V_f_2,V_A_2,T_a] :
% 80.71/80.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => ( 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)
% 80.71/80.79 <=> ? [B_x] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.79 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 80.71/80.79 & ! [B_xa] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 80.71/80.79 => ( B_x != B_xa
% 80.71/80.79 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Body__triple__valid__0,axiom,
% 80.71/80.79 ! [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)) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_card__gt__0__iff,axiom,
% 80.71/80.79 ! [V_A_2,T_a] :
% 80.71/80.79 ( 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)))
% 80.71/80.79 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.79 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Suc__pred_H,axiom,
% 80.71/80.79 ! [V_n] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 80.71/80.79 => 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))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Suc__diff__1,axiom,
% 80.71/80.79 ! [V_n] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 80.71/80.79 => 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 ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_add__eq__if,axiom,
% 80.71/80.79 ! [V_n,V_m] :
% 80.71/80.79 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.79 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 80.71/80.79 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.79 => 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)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 80.71/80.79 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.79 ( class_Lattices_Olattice(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.79 => 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)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Inf__fin_Osubset__idem,axiom,
% 80.71/80.79 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.79 ( class_Lattices_Olattice(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 80.71/80.79 => 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) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Inf__fin_Ounion__idem,axiom,
% 80.71/80.79 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.79 ( class_Lattices_Olattice(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.79 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.79 => 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)) ) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Inf__le__Sup,axiom,
% 80.71/80.79 ! [V_A_2,T_a] :
% 80.71/80.79 ( class_Lattices_Olattice(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 80.71/80.79 ! [V_a_2,V_A_2,T_a] :
% 80.71/80.79 ( class_Lattices_Olattice(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => 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) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_triple_Osize_I1_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_even__less__0__iff,axiom,
% 80.71/80.79 ! [V_a_2,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.79 => ( 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)))
% 80.71/80.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_triple_Osize_I2_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_card_Ounion__inter__neutral,axiom,
% 80.71/80.79 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.79 => ( ( ? [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)))
% 80.71/80.79 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 80.71/80.79 => 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)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_setsum__mono2,axiom,
% 80.71/80.79 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
% 80.71/80.79 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.79 => ( ! [B_b] :
% 80.71/80.79 ( 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)))
% 80.71/80.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) )
% 80.71/80.79 => 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))) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Inf__fin_Oclosed,axiom,
% 80.71/80.79 ! [V_A_2,T_a] :
% 80.71/80.79 ( class_Lattices_Olattice(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.79 => ( ! [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))))))
% 80.71/80.79 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_setsum__Un__zero,axiom,
% 80.71/80.79 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 80.71/80.79 ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 80.71/80.79 => ( ! [B_x] :
% 80.71/80.79 ( 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)))
% 80.71/80.79 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 80.71/80.79 => 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)) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 80.71/80.79 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 80.71/80.79 ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.79 => ( ! [B_x] :
% 80.71/80.79 ( 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)))
% 80.71/80.79 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 80.71/80.79 => 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)) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_card__Suc__eq,axiom,
% 80.71/80.79 ! [V_k_2,V_A_2,T_a] :
% 80.71/80.79 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 80.71/80.79 <=> ? [B_b,B_B] :
% 80.71/80.79 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B)
% 80.71/80.79 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B))
% 80.71/80.79 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2
% 80.71/80.79 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.79 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_double__eq__0__iff,axiom,
% 80.71/80.79 ! [V_a_2,T_a] :
% 80.71/80.79 ( class_Groups_Olinordered__ab__group__add(T_a)
% 80.71/80.79 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.79 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_setsum__mono3,axiom,
% 80.71/80.79 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
% 80.71/80.79 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.79 & class_Groups_Oordered__ab__semigroup__add(T_b) )
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.79 => ( ! [B_x] :
% 80.71/80.79 ( 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)))
% 80.71/80.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
% 80.71/80.79 => 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))) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_option_Osize_I2_J,axiom,
% 80.71/80.79 ! [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))) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Ints__odd__less__0,axiom,
% 80.71/80.79 ! [V_a_2,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 80.71/80.79 => ( 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)))
% 80.71/80.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osize_I4_J,axiom,
% 80.71/80.79 ! [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))) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 80.71/80.79 ! [V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 80.71/80.79 ! [V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_add__0__iff,axiom,
% 80.71/80.79 ! [V_a_2,V_b_2,T_a] :
% 80.71/80.79 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 80.71/80.79 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)
% 80.71/80.79 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osize_I12_J,axiom,
% 80.71/80.79 ! [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))) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Ints__0,axiom,
% 80.71/80.79 ! [T_a] :
% 80.71/80.79 ( class_Rings_Oring__1(T_a)
% 80.71/80.79 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Ints__add,axiom,
% 80.71/80.79 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.79 ( class_Rings_Oring__1(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Ints__diff,axiom,
% 80.71/80.79 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.79 ( class_Rings_Oring__1(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Ints__1,axiom,
% 80.71/80.79 ! [T_a] :
% 80.71/80.79 ( class_Rings_Oring__1(T_a)
% 80.71/80.79 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 80.71/80.79 ! [V_d,V_c,V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 80.71/80.79 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 80.71/80.79 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 80.71/80.79 ! [V_d,V_c,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 80.71/80.79 ! [V_d,V_c,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 80.71/80.79 ! [V_c,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_option_Osize_I1_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osize_I15_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osize_I7_J,axiom,
% 80.71/80.79 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osize_I16_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osize_I9_J,axiom,
% 80.71/80.79 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osize_I8_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osize_I1_J,axiom,
% 80.71/80.79 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Ints__double__eq__0__iff,axiom,
% 80.71/80.79 ! [V_a_2,T_a] :
% 80.71/80.79 ( class_Int_Oring__char__0(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 80.71/80.79 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.79 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Ints__odd__nonzero,axiom,
% 80.71/80.79 ! [V_a_2,T_a] :
% 80.71/80.79 ( class_Int_Oring__char__0(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 80.71/80.79 => 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) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_nat_Osize_I2_J,axiom,
% 80.71/80.79 ! [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))) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_nat_Osize_I4_J,axiom,
% 80.71/80.79 ! [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))) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_option_Osize_I4_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_option_Osize_I3_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_ex__least__nat__less,axiom,
% 80.71/80.79 ! [V_n_2,V_P_2] :
% 80.71/80.79 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 80.71/80.79 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 80.71/80.79 => ? [B_k] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 80.71/80.79 & ! [B_i] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 80.71/80.79 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 80.71/80.79 & 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)))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_setsum__mono__zero__right,axiom,
% 80.71/80.79 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 80.71/80.79 ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 80.71/80.79 => ( ! [B_x] :
% 80.71/80.79 ( 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)))
% 80.71/80.79 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 80.71/80.79 => 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) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_setsum__mono__zero__left,axiom,
% 80.71/80.79 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 80.71/80.79 ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 80.71/80.79 => ( ! [B_x] :
% 80.71/80.79 ( 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)))
% 80.71/80.79 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 80.71/80.79 => 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) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 80.71/80.79 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.79 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 80.71/80.79 => ( ! [B_x] :
% 80.71/80.79 ( 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)))
% 80.71/80.79 => hAPP(V_g_2,B_x) = V_z_2 )
% 80.71/80.79 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_nat__size,axiom,
% 80.71/80.79 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 80.71/80.79
% 80.71/80.79 fof(fact_nat_Osize_I3_J,axiom,
% 80.71/80.79 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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_nat_Osize_I1_J,axiom,
% 80.71/80.79 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_setsum__SucD,axiom,
% 80.71/80.79 ! [V_n_2,V_A_2,V_f_2,T_a] :
% 80.71/80.79 ( 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)
% 80.71/80.79 => ? [B_x] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.79 & 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))) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osize_I5_J,axiom,
% 80.71/80.79 ! [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))) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osize_I13_J,axiom,
% 80.71/80.79 ! [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))) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_card_Oneutral,axiom,
% 80.71/80.79 ! [V_A_2,T_a] :
% 80.71/80.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.79 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 80.71/80.79 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_inf__le__fold__inf,axiom,
% 80.71/80.79 ! [V_ca_2,V_b_2,V_A_2,T_a] :
% 80.71/80.79 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => ( ! [B_x] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) )
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_fold__sup__le__sup,axiom,
% 80.71/80.79 ! [V_ca_2,V_b_2,V_A_2,T_a] :
% 80.71/80.79 ( class_Lattices_Osemilattice__sup(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => ( ! [B_x] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) )
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_expand__Suc,axiom,
% 80.71/80.79 ! [V_v] :
% 80.71/80.79 ( 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)))
% 80.71/80.79 => 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))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_fold1Set_Ointros,axiom,
% 80.71/80.79 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] :
% 80.71/80.79 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2))
% 80.71/80.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.79 => 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)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_evaln_OIfFalse,axiom,
% 80.71/80.79 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] :
% 80.71/80.79 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2))
% 80.71/80.79 => 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)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_evaln_OIfTrue,axiom,
% 80.71/80.79 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] :
% 80.71/80.79 ( hBOOL(hAPP(V_b_2,V_s_2))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2))
% 80.71/80.79 => 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)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_evaln__elim__cases_I5_J,axiom,
% 80.71/80.79 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 80.71/80.79 ( 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))
% 80.71/80.79 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 80.71/80.79 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) )
% 80.71/80.79 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 80.71/80.79 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_evalc__elim__cases_I5_J,axiom,
% 80.71/80.79 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 80.71/80.79 ( 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))
% 80.71/80.79 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 80.71/80.79 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) )
% 80.71/80.79 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 80.71/80.79 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_evalc_OIfTrue,axiom,
% 80.71/80.79 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] :
% 80.71/80.79 ( hBOOL(hAPP(V_b_2,V_s_2))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2))
% 80.71/80.79 => 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)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_evalc_OIfFalse,axiom,
% 80.71/80.79 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] :
% 80.71/80.79 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2))
% 80.71/80.79 => 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)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_WTs__elim__cases_I5_J,axiom,
% 80.71/80.79 ! [V_c2_2,V_c1_2,V_b_2] :
% 80.71/80.79 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)))
% 80.71/80.79 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 80.71/80.79 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_number__of__reorient,axiom,
% 80.71/80.79 ! [V_x_2,V_w_2,T_a] :
% 80.71/80.79 ( class_Int_Onumber(T_a)
% 80.71/80.79 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2
% 80.71/80.79 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_eq__number__of,axiom,
% 80.71/80.79 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.79 ( ( class_Int_Onumber__ring(T_a)
% 80.71/80.79 & class_Int_Oring__char__0(T_a) )
% 80.71/80.79 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 80.71/80.79 <=> V_x_2 = V_y_2 ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I4_J,axiom,
% 80.71/80.79 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 80.71/80.79 ( 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)
% 80.71/80.79 <=> ( V_fun_2 = V_fun_H_2
% 80.71/80.79 & V_com1_2 = V_com1_H_2
% 80.71/80.79 & V_com2_2 = V_com2_H_2 ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_le__number__of,axiom,
% 80.71/80.79 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.79 ( ( class_Int_Onumber__ring(T_a)
% 80.71/80.79 & class_Rings_Olinordered__idom(T_a) )
% 80.71/80.79 => ( 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)))
% 80.71/80.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_less__number__of,axiom,
% 80.71/80.79 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.79 ( ( class_Int_Onumber__ring(T_a)
% 80.71/80.79 & class_Rings_Olinordered__idom(T_a) )
% 80.71/80.79 => ( 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)))
% 80.71/80.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_number__of__add,axiom,
% 80.71/80.79 ! [V_w,V_v,T_a] :
% 80.71/80.79 ( class_Int_Onumber__ring(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_add__number__of__eq,axiom,
% 80.71/80.79 ! [V_w,V_v,T_a] :
% 80.71/80.79 ( class_Int_Onumber__ring(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_add__number__of__left,axiom,
% 80.71/80.79 ! [V_z,V_w,V_v,T_a] :
% 80.71/80.79 ( class_Int_Onumber__ring(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_number__of__diff,axiom,
% 80.71/80.79 ! [V_w,V_v,T_a] :
% 80.71/80.79 ( class_Int_Onumber__ring(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 80.71/80.79 ! [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)) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_fold__graph_OemptyI,axiom,
% 80.71/80.79 ! [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)) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_empty__fold__graphE,axiom,
% 80.71/80.79 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.79 ( 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))
% 80.71/80.79 => V_x_2 = V_z_2 ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_fold__graph__imp__finite,axiom,
% 80.71/80.79 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.79 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2))
% 80.71/80.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_evaln_Oequations_I5_J,axiom,
% 80.71/80.79 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] :
% 80.71/80.79 ( 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))
% 80.71/80.79 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 80.71/80.79 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) )
% 80.71/80.79 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 80.71/80.79 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_evaln_Oequations_I6_J,axiom,
% 80.71/80.79 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] :
% 80.71/80.79 ( 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))
% 80.71/80.79 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 80.71/80.79 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) )
% 80.71/80.79 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 80.71/80.79 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_evalc_Oequations_I6_J,axiom,
% 80.71/80.79 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] :
% 80.71/80.79 ( 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))
% 80.71/80.79 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) )
% 80.71/80.79 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_evalc_Oequations_I5_J,axiom,
% 80.71/80.79 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
% 80.71/80.79 ( 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))
% 80.71/80.79 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) )
% 80.71/80.79 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I55_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I54_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_WT_Oequations_I5_J,axiom,
% 80.71/80.79 ! [V_a2_2,V_a1_2,V_a3_2] :
% 80.71/80.79 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2)))
% 80.71/80.79 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 80.71/80.79 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_WT_OIf,axiom,
% 80.71/80.79 ! [V_b_2,V_c1_2,V_c0_2] :
% 80.71/80.79 ( hBOOL(hAPP(c_Com_OWT,V_c0_2))
% 80.71/80.79 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 80.71/80.79 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I44_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I45_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I57_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I56_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I14_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I15_J,axiom,
% 80.71/80.79 ! [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 ).
% 80.71/80.79
% 80.71/80.79 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 80.71/80.79 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.79 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2))
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 80.71/80.79 => V_y_2 = V_x_2 ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_le__number__of__eq__not__less,axiom,
% 80.71/80.79 ! [V_w_2,V_v_2,T_a] :
% 80.71/80.79 ( ( class_Int_Onumber(T_a)
% 80.71/80.79 & class_Orderings_Olinorder(T_a) )
% 80.71/80.79 => ( 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)))
% 80.71/80.79 <=> ~ 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))) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_add__number__of__diff1,axiom,
% 80.71/80.79 ! [V_c,V_w,V_v,T_a] :
% 80.71/80.79 ( class_Int_Onumber__ring(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Ints__number__of,axiom,
% 80.71/80.79 ! [V_w_2,T_a] :
% 80.71/80.79 ( class_Int_Onumber__ring(T_a)
% 80.71/80.79 => 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))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_fold__graph_OinsertI,axiom,
% 80.71/80.79 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 80.71/80.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 80.71/80.79 => 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))) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 80.71/80.79 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.79 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 80.71/80.79 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 80.71/80.79 ! [V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 80.71/80.79 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.79 => 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))) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Diff1__fold__graph,axiom,
% 80.71/80.79 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.79 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_y_2))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.79 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 80.71/80.79 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.79 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.79 => ? [B_y_H] :
% 80.71/80.79 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 80.71/80.79 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_insert__fold1SetE,axiom,
% 80.71/80.79 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] :
% 80.71/80.79 ( 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))
% 80.71/80.79 => ~ ! [B_a,B_A] :
% 80.71/80.79 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A)
% 80.71/80.79 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2))
% 80.71/80.79 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_fold1Set_Oequations,axiom,
% 80.71/80.79 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] :
% 80.71/80.79 ( 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))
% 80.71/80.79 <=> ? [B_a,B_A] :
% 80.71/80.79 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A)
% 80.71/80.79 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2))
% 80.71/80.79 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 80.71/80.79 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.79 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 80.71/80.79 => ( 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))
% 80.71/80.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.79 => ~ ! [B_y] :
% 80.71/80.79 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 80.71/80.79 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_fold__graph__permute__diff,axiom,
% 80.71/80.79 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] :
% 80.71/80.79 ( class_Groups_Oab__semigroup__mult(T_a)
% 80.71/80.79 => ( 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))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.79 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 80.71/80.79 => 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)) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osize_I11_J,axiom,
% 80.71/80.79 ! [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))) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osize_I3_J,axiom,
% 80.71/80.79 ! [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))) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_dom__fun__upd,axiom,
% 80.71/80.79 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] :
% 80.71/80.79 ( ( V_y_2 = c_Option_Ooption_ONone(T_a)
% 80.71/80.79 => 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)))) )
% 80.71/80.79 & ( V_y_2 != c_Option_Ooption_ONone(T_a)
% 80.71/80.79 => 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)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_WTs__elim__cases_I3_J,axiom,
% 80.71/80.79 ! [V_ca_2,V_a_2,V_Y_2] :
% 80.71/80.79 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)))
% 80.71/80.79 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_less__number__of__int__code,axiom,
% 80.71/80.79 ! [V_l_2,V_k_2] :
% 80.71/80.79 ( 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)))
% 80.71/80.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_number__of__mult,axiom,
% 80.71/80.79 ! [V_w,V_v,T_a] :
% 80.71/80.79 ( class_Int_Onumber__ring(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_arith__simps_I32_J,axiom,
% 80.71/80.79 ! [V_w,V_v,T_a] :
% 80.71/80.79 ( class_Int_Onumber__ring(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__number__of__left,axiom,
% 80.71/80.79 ! [V_z,V_w,V_v,T_a] :
% 80.71/80.79 ( class_Int_Onumber__ring(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_less__eq__number__of__int__code,axiom,
% 80.71/80.79 ! [V_l_2,V_k_2] :
% 80.71/80.79 ( 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)))
% 80.71/80.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_plus__numeral__code_I9_J,axiom,
% 80.71/80.79 ! [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)) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 80.71/80.79 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 80.71/80.79 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 80.71/80.79 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 80.71/80.79 ! [V_rx,V_ly,V_lx,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 80.71/80.79 ! [V_rx,V_ly,V_lx,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 80.71/80.79 ! [V_ry,V_rx,V_lx,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 80.71/80.79 ! [V_ry,V_rx,V_lx,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__left__idem,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__idem,axiom,
% 80.71/80.79 ! [V_x,T_a] :
% 80.71/80.79 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 80.71/80.79 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_times_Oidem,axiom,
% 80.71/80.79 ! [V_a,T_a] :
% 80.71/80.79 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 80.71/80.79 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I2_J,axiom,
% 80.71/80.79 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 80.71/80.79 ( 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)
% 80.71/80.79 <=> ( V_loc_2 = V_loc_H_2
% 80.71/80.79 & V_fun_2 = V_fun_H_2
% 80.71/80.79 & V_com_2 = V_com_H_2 ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 80.71/80.79 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.79 ( class_Groups_Oab__semigroup__mult(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zadd__left__mono,axiom,
% 80.71/80.79 ! [V_k,V_j,V_i] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 80.71/80.79 => 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))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zadd__zmult__distrib,axiom,
% 80.71/80.79 ! [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)) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zadd__assoc,axiom,
% 80.71/80.79 ! [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)) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zadd__zmult__distrib2,axiom,
% 80.71/80.79 ! [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)) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zadd__left__commute,axiom,
% 80.71/80.79 ! [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)) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zadd__commute,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zle__antisym,axiom,
% 80.71/80.79 ! [V_w,V_z] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 80.71/80.79 => V_z = V_w ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zle__trans,axiom,
% 80.71/80.79 ! [V_k,V_j,V_i] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 80.71/80.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zle__linear,axiom,
% 80.71/80.79 ! [V_w,V_z] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 80.71/80.79 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zle__refl,axiom,
% 80.71/80.79 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zdiff__zmult__distrib2,axiom,
% 80.71/80.79 ! [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)) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zdiff__zmult__distrib,axiom,
% 80.71/80.79 ! [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)) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_less__bin__lemma,axiom,
% 80.71/80.79 ! [V_l_2,V_k_2] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 80.71/80.79 <=> 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))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zadd__0,axiom,
% 80.71/80.79 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zadd__0__right,axiom,
% 80.71/80.79 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zless__linear,axiom,
% 80.71/80.79 ! [V_y,V_x] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 80.71/80.79 | V_x = V_y
% 80.71/80.79 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zadd__strict__right__mono,axiom,
% 80.71/80.79 ! [V_k,V_j,V_i] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 80.71/80.79 => 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))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zmult__zless__mono2,axiom,
% 80.71/80.79 ! [V_k,V_j,V_i] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 80.71/80.79 => 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))) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_int__one__le__iff__zero__less,axiom,
% 80.71/80.79 ! [V_z_2] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 80.71/80.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zless__le,axiom,
% 80.71/80.79 ! [V_w_2,V_z_2] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 80.71/80.79 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 80.71/80.79 & V_z_2 != V_w_2 ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zle__add1__eq__le,axiom,
% 80.71/80.79 ! [V_z_2,V_w_2] :
% 80.71/80.79 ( 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))))
% 80.71/80.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zle__diff1__eq,axiom,
% 80.71/80.79 ! [V_z_2,V_w_2] :
% 80.71/80.79 ( 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))))
% 80.71/80.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_add1__zle__eq,axiom,
% 80.71/80.79 ! [V_z_2,V_w_2] :
% 80.71/80.79 ( 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))
% 80.71/80.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_le__imp__0__less,axiom,
% 80.71/80.79 ! [V_z] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 80.71/80.79 => 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))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zless__imp__add1__zle,axiom,
% 80.71/80.79 ! [V_z,V_w] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zadd__zless__mono,axiom,
% 80.71/80.79 ! [V_z,V_z_H,V_w,V_w_H] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 80.71/80.79 => 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))) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_odd__nonzero,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_int__0__less__1,axiom,
% 80.71/80.79 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))) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zless__add1__eq,axiom,
% 80.71/80.79 ! [V_z_2,V_w_2] :
% 80.71/80.79 ( 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))))
% 80.71/80.79 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 80.71/80.79 | V_w_2 = V_z_2 ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_odd__less__0,axiom,
% 80.71/80.79 ! [V_z_2] :
% 80.71/80.79 ( 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)))
% 80.71/80.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_pos__zmult__eq__1__iff,axiom,
% 80.71/80.79 ! [V_n_2,V_m_2] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 80.71/80.79 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 80.71/80.79 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 80.71/80.79 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_divisors__zero,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ono__zero__divisors(T_a)
% 80.71/80.79 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.79 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.79 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_no__zero__divisors,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ono__zero__divisors(T_a)
% 80.71/80.79 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.79 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.79 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__eq__0__iff,axiom,
% 80.71/80.79 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.79 ( class_Rings_Oring__no__zero__divisors(T_a)
% 80.71/80.79 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.79 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.79 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__zero__right,axiom,
% 80.71/80.79 ! [V_a,T_a] :
% 80.71/80.79 ( class_Rings_Omult__zero(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__zero__left,axiom,
% 80.71/80.79 ! [V_a,T_a] :
% 80.71/80.79 ( class_Rings_Omult__zero(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 80.71/80.79 ! [V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 80.71/80.79 ! [V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__class_Odistrib,axiom,
% 80.71/80.79 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_combine__common__factor,axiom,
% 80.71/80.79 ! [V_c,V_b,V_e,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Osemiring(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_crossproduct__eq,axiom,
% 80.71/80.79 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
% 80.71/80.79 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 80.71/80.79 => ( 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))
% 80.71/80.79 <=> ( V_w_2 = V_x_2
% 80.71/80.79 | V_y_2 = V_z_2 ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 80.71/80.79 ! [V_b,V_m,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 80.71/80.79 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_crossproduct__noteq,axiom,
% 80.71/80.79 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 80.71/80.79 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 80.71/80.79 => ( ( V_a_2 != V_b_2
% 80.71/80.79 & V_ca_2 != V_d_2 )
% 80.71/80.79 <=> 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)) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 80.71/80.79 ! [V_z,V_y,V_x,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => 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)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult_Ocomm__neutral,axiom,
% 80.71/80.79 ! [V_a,T_a] :
% 80.71/80.79 ( class_Groups_Ocomm__monoid__mult(T_a)
% 80.71/80.79 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__1__right,axiom,
% 80.71/80.79 ! [V_a,T_a] :
% 80.71/80.79 ( class_Groups_Omonoid__mult(T_a)
% 80.71/80.79 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__1,axiom,
% 80.71/80.79 ! [V_a,T_a] :
% 80.71/80.79 ( class_Groups_Ocomm__monoid__mult(T_a)
% 80.71/80.79 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__1__left,axiom,
% 80.71/80.79 ! [V_a,T_a] :
% 80.71/80.79 ( class_Groups_Omonoid__mult(T_a)
% 80.71/80.79 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 80.71/80.79 ! [V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 80.71/80.79 ! [V_a,T_a] :
% 80.71/80.79 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.79 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__cancel2,axiom,
% 80.71/80.79 ! [V_n_2,V_k_2,V_m_2] :
% 80.71/80.79 ( 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)
% 80.71/80.79 <=> ( V_m_2 = V_n_2
% 80.71/80.79 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__cancel1,axiom,
% 80.71/80.79 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.79 ( 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)
% 80.71/80.79 <=> ( V_m_2 = V_n_2
% 80.71/80.79 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__is__0,axiom,
% 80.71/80.79 ! [V_n_2,V_m_2] :
% 80.71/80.79 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.79 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.79 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__0__right,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__0,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_Suc__mult__cancel1,axiom,
% 80.71/80.79 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.79 ( 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)
% 80.71/80.79 <=> V_m_2 = V_n_2 ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_map__upd__Some__unfold,axiom,
% 80.71/80.79 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] :
% 80.71/80.79 ( 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)
% 80.71/80.79 <=> ( ( V_x_2 = V_a_2
% 80.71/80.79 & V_b_2 = V_y_2 )
% 80.71/80.79 | ( V_x_2 != V_a_2
% 80.71/80.79 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_map__upd__triv,axiom,
% 80.71/80.79 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] :
% 80.71/80.79 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 80.71/80.79 => 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 ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_map__upd__eqD1,axiom,
% 80.71/80.79 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] :
% 80.71/80.79 ( 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))
% 80.71/80.79 => V_x_2 = V_y_2 ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_add__mult__distrib,axiom,
% 80.71/80.79 ! [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)) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_add__mult__distrib2,axiom,
% 80.71/80.79 ! [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)) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_le__square,axiom,
% 80.71/80.79 ! [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))) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_le__cube,axiom,
% 80.71/80.79 ! [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)))) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__le__mono1,axiom,
% 80.71/80.79 ! [V_k,V_j,V_i] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 80.71/80.79 => 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))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__le__mono2,axiom,
% 80.71/80.79 ! [V_k,V_j,V_i] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 80.71/80.79 => 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))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__le__mono,axiom,
% 80.71/80.79 ! [V_l,V_k,V_j,V_i] :
% 80.71/80.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 80.71/80.79 => 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))) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_diff__mult__distrib2,axiom,
% 80.71/80.79 ! [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)) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_diff__mult__distrib,axiom,
% 80.71/80.79 ! [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)) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_nat__mult__1,axiom,
% 80.71/80.79 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 80.71/80.79
% 80.71/80.79 fof(fact_nat__1__eq__mult__iff,axiom,
% 80.71/80.79 ! [V_n_2,V_m_2] :
% 80.71/80.79 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 80.71/80.79 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 80.71/80.79 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_nat__mult__1__right,axiom,
% 80.71/80.79 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 80.71/80.79
% 80.71/80.79 fof(fact_nat__mult__eq__1__iff,axiom,
% 80.71/80.79 ! [V_n_2,V_m_2] :
% 80.71/80.79 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 80.71/80.79 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 80.71/80.79 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_fun__left__comm,axiom,
% 80.71/80.79 ! [T_a] :
% 80.71/80.79 ( class_Groups_Oab__semigroup__mult(T_a)
% 80.71/80.79 => c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_fun__left__comm__idem,axiom,
% 80.71/80.79 ! [T_a] :
% 80.71/80.79 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 80.71/80.79 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I40_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I41_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_WT_OLocal,axiom,
% 80.71/80.79 ! [V_a_2,V_Y_2,V_ca_2] :
% 80.71/80.79 ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
% 80.71/80.79 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_WT_Oequations_I3_J,axiom,
% 80.71/80.79 ! [V_a1_2,V_a3_2,V_a2_2] :
% 80.71/80.79 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2)))
% 80.71/80.79 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I36_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I37_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I42_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I43_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I34_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I35_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I11_J,axiom,
% 80.71/80.79 ! [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 ).
% 80.71/80.79
% 80.71/80.79 fof(fact_com_Osimps_I10_J,axiom,
% 80.71/80.79 ! [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) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_split__mult__neg__le,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Oordered__cancel__semiring(T_a)
% 80.71/80.79 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 80.71/80.79 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 80.71/80.79 => 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))) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_split__mult__pos__le,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Oordered__ring(T_a)
% 80.71/80.79 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 80.71/80.79 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 80.71/80.79 => 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))) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__mono,axiom,
% 80.71/80.79 ! [V_d,V_c,V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Oordered__semiring(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.79 => 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))) ) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__mono_H,axiom,
% 80.71/80.79 ! [V_d,V_c,V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Oordered__semiring(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.79 => 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))) ) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__left__mono__neg,axiom,
% 80.71/80.79 ! [V_c,V_a,V_b,T_a] :
% 80.71/80.79 ( class_Rings_Oordered__ring(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__right__mono__neg,axiom,
% 80.71/80.79 ! [V_c,V_a,V_b,T_a] :
% 80.71/80.79 ( class_Rings_Oordered__ring(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__mult__left__mono,axiom,
% 80.71/80.79 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Oordered__comm__semiring(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__left__mono,axiom,
% 80.71/80.79 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Oordered__semiring(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__right__mono,axiom,
% 80.71/80.79 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Oordered__semiring(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__nonpos__nonpos,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Oordered__ring(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__nonpos__nonneg,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Oordered__cancel__semiring(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__nonneg__nonpos2,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Oordered__cancel__semiring(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__nonneg__nonpos,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Oordered__cancel__semiring(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__nonneg__nonneg,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Oordered__cancel__semiring(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__le__0__iff,axiom,
% 80.71/80.79 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__ring__strict(T_a)
% 80.71/80.79 => ( 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)))
% 80.71/80.79 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 80.71/80.79 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zero__le__mult__iff,axiom,
% 80.71/80.79 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__ring__strict(T_a)
% 80.71/80.79 => ( 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)))
% 80.71/80.79 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 80.71/80.79 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zero__le__square,axiom,
% 80.71/80.79 ! [V_a,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__ring(T_a)
% 80.71/80.79 => 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))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_not__square__less__zero,axiom,
% 80.71/80.79 ! [V_a,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__ring(T_a)
% 80.71/80.79 => ~ 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))) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__less__cancel__right__disj,axiom,
% 80.71/80.79 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__ring__strict(T_a)
% 80.71/80.79 => ( 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)))
% 80.71/80.79 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
% 80.71/80.79 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__less__cancel__left__disj,axiom,
% 80.71/80.79 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__ring__strict(T_a)
% 80.71/80.79 => ( 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)))
% 80.71/80.79 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
% 80.71/80.79 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__less__cancel__left__pos,axiom,
% 80.71/80.79 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__ring__strict(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 80.71/80.79 => ( 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)))
% 80.71/80.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__pos__pos,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__pos__neg,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__pos__neg2,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zero__less__mult__pos,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.79 => ( 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)))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_zero__less__mult__pos2,axiom,
% 80.71/80.79 ! [V_a,V_b,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.79 => ( 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)))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__less__cancel__left__neg,axiom,
% 80.71/80.79 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__ring__strict(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 => ( 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)))
% 80.71/80.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__neg__pos,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__neg__neg,axiom,
% 80.71/80.79 ! [V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__ring__strict(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__strict__right__mono,axiom,
% 80.71/80.79 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__strict__left__mono,axiom,
% 80.71/80.79 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_comm__mult__strict__left__mono,axiom,
% 80.71/80.79 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__strict__right__mono__neg,axiom,
% 80.71/80.79 ! [V_c,V_a,V_b,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__ring__strict(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_mult__strict__left__mono__neg,axiom,
% 80.71/80.79 ! [V_c,V_a,V_b,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__ring__strict(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_sum__squares__eq__zero__iff,axiom,
% 80.71/80.79 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__ring__strict(T_a)
% 80.71/80.79 => ( 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)
% 80.71/80.79 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.79 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_add__scale__eq__noteq,axiom,
% 80.71/80.79 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 80.71/80.79 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 80.71/80.79 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.79 => ( ( V_a = V_b
% 80.71/80.79 & V_c != V_d )
% 80.71/80.79 => 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)) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_less__1__mult,axiom,
% 80.71/80.79 ! [V_n,V_m,T_a] :
% 80.71/80.79 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 80.71/80.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 80.71/80.79 => 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))) ) ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_eq__add__iff1,axiom,
% 80.71/80.79 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 80.71/80.79 ( class_Rings_Oring(T_a)
% 80.71/80.79 => ( 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)
% 80.71/80.79 <=> 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 ) ) ).
% 80.71/80.79
% 80.71/80.79 fof(fact_eq__add__iff2,axiom,
% 80.71/80.79 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 80.71/80.80 ( class_Rings_Oring(T_a)
% 80.71/80.80 => ( 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)
% 80.71/80.80 <=> 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) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_left__distrib__number__of,axiom,
% 80.71/80.80 ! [V_v,V_b,V_a,T_b] :
% 80.71/80.80 ( ( class_Int_Onumber(T_b)
% 80.71/80.80 & class_Rings_Osemiring(T_b) )
% 80.71/80.80 => 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))) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_right__distrib__number__of,axiom,
% 80.71/80.80 ! [V_c,V_b,V_v,T_b] :
% 80.71/80.80 ( ( class_Int_Onumber(T_b)
% 80.71/80.80 & class_Rings_Osemiring(T_b) )
% 80.71/80.80 => 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)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 80.71/80.80 ! [V_m,T_a] :
% 80.71/80.80 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.80 => 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) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 80.71/80.80 ! [V_a,V_m,T_a] :
% 80.71/80.80 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.80 => 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) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 80.71/80.80 ! [V_m,V_a,T_a] :
% 80.71/80.80 ( class_Rings_Ocomm__semiring__1(T_a)
% 80.71/80.80 => 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) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_right__diff__distrib__number__of,axiom,
% 80.71/80.80 ! [V_c,V_b,V_v,T_b] :
% 80.71/80.80 ( ( class_Int_Onumber(T_b)
% 80.71/80.80 & class_Rings_Oring(T_b) )
% 80.71/80.80 => 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)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_left__diff__distrib__number__of,axiom,
% 80.71/80.80 ! [V_v,V_b,V_a,T_b] :
% 80.71/80.80 ( ( class_Int_Onumber(T_b)
% 80.71/80.80 & class_Rings_Oring(T_b) )
% 80.71/80.80 => 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))) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__eq__1__iff,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2] :
% 80.71/80.80 ( 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))
% 80.71/80.80 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 80.71/80.80 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__0__less__mult__iff,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 80.71/80.80 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__less__cancel1,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 80.71/80.80 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__less__cancel2,axiom,
% 80.71/80.80 ! [V_n_2,V_k_2,V_m_2] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 80.71/80.80 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__less__mono1,axiom,
% 80.71/80.80 ! [V_k,V_j,V_i] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 80.71/80.80 => 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))) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__less__mono2,axiom,
% 80.71/80.80 ! [V_k,V_j,V_i] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 80.71/80.80 => 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))) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Suc__mult__less__cancel1,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__Suc__right,axiom,
% 80.71/80.80 ! [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)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__Suc,axiom,
% 80.71/80.80 ! [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)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Suc__mult__le__cancel1,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__eq__self__implies__10,axiom,
% 80.71/80.80 ! [V_n,V_m] :
% 80.71/80.80 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 80.71/80.80 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 80.71/80.80 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Ints__mult,axiom,
% 80.71/80.80 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.80 ( class_Rings_Oring__1(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 80.71/80.80 => 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))) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__le__cancel__left__pos,axiom,
% 80.71/80.80 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__ring__strict(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__le__cancel__left__neg,axiom,
% 80.71/80.80 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__ring__strict(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__strict__mono,axiom,
% 80.71/80.80 ! [V_d,V_c,V_b,V_a,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.80 => 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))) ) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__strict__mono_H,axiom,
% 80.71/80.80 ! [V_d,V_c,V_b,V_a,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.80 => 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))) ) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__less__le__imp__less,axiom,
% 80.71/80.80 ! [V_d,V_c,V_b,V_a,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.80 => 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))) ) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__le__less__imp__less,axiom,
% 80.71/80.80 ! [V_d,V_c,V_b,V_a,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.80 => 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))) ) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__right__less__imp__less,axiom,
% 80.71/80.80 ! [V_b,V_c,V_a,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semiring(T_a)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__less__imp__less__right,axiom,
% 80.71/80.80 ! [V_b,V_c,V_a,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__left__less__imp__less,axiom,
% 80.71/80.80 ! [V_b,V_a,V_c,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semiring(T_a)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__less__imp__less__left,axiom,
% 80.71/80.80 ! [V_b,V_a,V_c,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__right__le__imp__le,axiom,
% 80.71/80.80 ! [V_b,V_c,V_a,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__left__le__imp__le,axiom,
% 80.71/80.80 ! [V_b,V_a,V_c,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semiring__strict(T_a)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_sum__squares__ge__zero,axiom,
% 80.71/80.80 ! [V_y,V_x,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__ring(T_a)
% 80.71/80.80 => 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)))) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_sum__squares__le__zero__iff,axiom,
% 80.71/80.80 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__ring__strict(T_a)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.80 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_sum__squares__gt__zero__iff,axiom,
% 80.71/80.80 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__ring__strict(T_a)
% 80.71/80.80 => ( 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))))
% 80.71/80.80 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.80 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_not__sum__squares__lt__zero,axiom,
% 80.71/80.80 ! [V_y,V_x,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__ring(T_a)
% 80.71/80.80 => ~ 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))) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__right__le__one__le,axiom,
% 80.71/80.80 ! [V_y,V_x,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 80.71/80.80 => 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)) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__left__le__one__le,axiom,
% 80.71/80.80 ! [V_y,V_x,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 80.71/80.80 => 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)) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_le__add__iff2,axiom,
% 80.71/80.80 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 80.71/80.80 ( class_Rings_Oordered__ring(T_a)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> 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))) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_le__add__iff1,axiom,
% 80.71/80.80 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 80.71/80.80 ( class_Rings_Oordered__ring(T_a)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> 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)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_less__add__iff1,axiom,
% 80.71/80.80 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 80.71/80.80 ( class_Rings_Oordered__ring(T_a)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> 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)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_less__add__iff2,axiom,
% 80.71/80.80 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 80.71/80.80 ( class_Rings_Oordered__ring(T_a)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> 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))) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_n__less__m__mult__n,axiom,
% 80.71/80.80 ! [V_m,V_n] :
% 80.71/80.80 ( 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))
% 80.71/80.80 => ( 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))
% 80.71/80.80 => 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))) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_n__less__n__mult__m,axiom,
% 80.71/80.80 ! [V_m,V_n] :
% 80.71/80.80 ( 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))
% 80.71/80.80 => ( 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))
% 80.71/80.80 => 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))) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_one__less__mult,axiom,
% 80.71/80.80 ! [V_m,V_n] :
% 80.71/80.80 ( 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))
% 80.71/80.80 => ( 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))
% 80.71/80.80 => 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))) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_one__le__mult__iff,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 <=> ( 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))
% 80.71/80.80 & 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)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__le__cancel1,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__le__cancel2,axiom,
% 80.71/80.80 ! [V_n_2,V_k_2,V_m_2] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold__graph__insert__swap,axiom,
% 80.71/80.80 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] :
% 80.71/80.80 ( class_Groups_Oab__semigroup__mult(T_a)
% 80.71/80.80 => ( 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))
% 80.71/80.80 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 80.71/80.80 => 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))) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_convex__bound__le,axiom,
% 80.71/80.80 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semiring__1(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 80.71/80.80 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 80.71/80.80 => 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)) ) ) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_mult__eq__if,axiom,
% 80.71/80.80 ! [V_n,V_m] :
% 80.71/80.80 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.80 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 80.71/80.80 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.80 => 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)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_convex__bound__lt,axiom,
% 80.71/80.80 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 80.71/80.80 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 80.71/80.80 => 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)) ) ) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__less__add__iff2,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> 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))) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__less__add__iff1,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> 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)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__eq__add__iff2,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 80.71/80.80 => ( 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)
% 80.71/80.80 <=> 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) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__diff__add__eq2,axiom,
% 80.71/80.80 ! [V_n,V_m,V_u,V_j,V_i] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 80.71/80.80 => 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)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__le__add__iff2,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> 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))) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__eq__add__iff1,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 80.71/80.80 => ( 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)
% 80.71/80.80 <=> 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 ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__diff__add__eq1,axiom,
% 80.71/80.80 ! [V_n,V_m,V_u,V_i,V_j] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 80.71/80.80 => 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) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__le__add__iff1,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> 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)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_number__of__is__id,axiom,
% 80.71/80.80 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 80.71/80.80
% 80.71/80.80 fof(fact_times__numeral__code_I5_J,axiom,
% 80.71/80.80 ! [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)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__mult__assoc,axiom,
% 80.71/80.80 ! [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)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__mult__commute,axiom,
% 80.71/80.80 ! [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) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zmult__1__right,axiom,
% 80.71/80.80 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zmult__1,axiom,
% 80.71/80.80 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zmult__assoc,axiom,
% 80.71/80.80 ! [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)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zmult__commute,axiom,
% 80.71/80.80 ! [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) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_int__0__neq__1,axiom,
% 80.71/80.80 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.80 ( 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)
% 80.71/80.80 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.80 | V_m_2 = V_n_2 ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_left__add__mult__distrib,axiom,
% 80.71/80.80 ! [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) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__mult__less__cancel1,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__mult__eq__cancel1,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 80.71/80.80 => ( 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)
% 80.71/80.80 <=> V_m_2 = V_n_2 ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__mult__le__cancel1,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,V_k_2] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_self__quotient__aux1,axiom,
% 80.71/80.80 ! [V_q,V_r,V_a] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 80.71/80.80 => ( 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))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_self__quotient__aux2,axiom,
% 80.71/80.80 ! [V_q,V_r,V_a] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 80.71/80.80 => ( 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))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 80.71/80.80 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 80.71/80.80 ( 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)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_unique__quotient__lemma__neg,axiom,
% 80.71/80.80 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zdiv__mono2__lemma,axiom,
% 80.71/80.80 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 80.71/80.80 ( 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)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_unique__quotient__lemma,axiom,
% 80.71/80.80 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_q__neg__lemma,axiom,
% 80.71/80.80 ! [V_r_H,V_q_H,V_b_H] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_q__pos__lemma,axiom,
% 80.71/80.80 ! [V_r_H,V_q_H,V_b_H] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 80.71/80.80 ! [V_y,V_x] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 80.71/80.80 => 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))) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 80.71/80.80 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))) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 80.71/80.80 ! [V_y,V_x] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 80.71/80.80 => 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))) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fun__upd__triv,axiom,
% 80.71/80.80 ! [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 ).
% 80.71/80.80
% 80.71/80.80 fof(fact_ran__map__upd,axiom,
% 80.71/80.80 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] :
% 80.71/80.80 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a)
% 80.71/80.80 => 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)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fun__upd__None__restrict,axiom,
% 80.71/80.80 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 80.71/80.80 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 80.71/80.80 => 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))))) )
% 80.71/80.80 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 80.71/80.80 => 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) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 80.71/80.80 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))) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_restrict__in,axiom,
% 80.71/80.80 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.80 => 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) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_restrict__restrict,axiom,
% 80.71/80.80 ! [V_B_2,V_A_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_restrict__out,axiom,
% 80.71/80.80 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 80.71/80.80 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.80 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_restrict__map__insert,axiom,
% 80.71/80.80 ! [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)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_dom__restrict,axiom,
% 80.71/80.80 ! [V_A_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m_2)),V_A_2) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fun__upd__idem,axiom,
% 80.71/80.80 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] :
% 80.71/80.80 ( hAPP(V_f_2,V_x_2) = V_y_2
% 80.71/80.80 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fun__upd__other,axiom,
% 80.71/80.80 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
% 80.71/80.80 ( V_z_2 != V_x_2
% 80.71/80.80 => 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) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fun__upd__twist,axiom,
% 80.71/80.80 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_ca_2,V_a_2] :
% 80.71/80.80 ( V_a_2 != V_ca_2
% 80.71/80.80 => 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) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fun__upd__apply,axiom,
% 80.71/80.80 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
% 80.71/80.80 ( ( V_z_2 = V_x_2
% 80.71/80.80 => 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 )
% 80.71/80.80 & ( V_z_2 != V_x_2
% 80.71/80.80 => 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) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fun__upd__same,axiom,
% 80.71/80.80 ! [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 ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fun__upd__upd,axiom,
% 80.71/80.80 ! [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) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fun__upd__idem__iff,axiom,
% 80.71/80.80 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 80.71/80.80 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2
% 80.71/80.80 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_ranI,axiom,
% 80.71/80.80 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
% 80.71/80.80 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2)
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fun__upd__restrict,axiom,
% 80.71/80.80 ! [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) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_restrict__fun__upd,axiom,
% 80.71/80.80 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 80.71/80.80 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 80.71/80.80 => 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) )
% 80.71/80.80 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 80.71/80.80 => 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) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fun__upd__restrict__conv,axiom,
% 80.71/80.80 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 80.71/80.80 => 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) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_tsub__def,axiom,
% 80.71/80.80 ! [V_x,V_y] :
% 80.71/80.80 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 80.71/80.80 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 80.71/80.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 80.71/80.80 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold__Un__disjoint,axiom,
% 80.71/80.80 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 80.71/80.80 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.80 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.80 => 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)) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_of__nat__number__of__lemma,axiom,
% 80.71/80.80 ! [V_v,T_a] :
% 80.71/80.80 ( class_Int_Onumber__ring(T_a)
% 80.71/80.80 => ( ( 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)))
% 80.71/80.80 => 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) )
% 80.71/80.80 & ( ~ 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)))
% 80.71/80.80 => 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) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_ran__restrictD,axiom,
% 80.71/80.80 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] :
% 80.71/80.80 ( 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))))
% 80.71/80.80 => ? [B_x] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 80.71/80.80 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold1__eq__fold,axiom,
% 80.71/80.80 ! [V_a_2,V_A_2,T_a] :
% 80.71/80.80 ( class_Groups_Oab__semigroup__mult(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.80 => 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) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold1__Un,axiom,
% 80.71/80.80 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.80 ( class_Groups_Oab__semigroup__mult(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.80 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.80 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.80 => 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)) ) ) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold1__insert,axiom,
% 80.71/80.80 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.80 ( class_Groups_Oab__semigroup__mult(T_a)
% 80.71/80.80 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.80 => 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)) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 80.71/80.80 ! [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)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_of__nat__eq__iff,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,T_a] :
% 80.71/80.80 ( class_Nat_Osemiring__char__0(T_a)
% 80.71/80.80 => ( 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)
% 80.71/80.80 <=> V_m_2 = V_n_2 ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold__image__empty,axiom,
% 80.71/80.80 ! [V_z_2,V_g_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ).
% 80.71/80.80
% 80.71/80.80 fof(fact_int__eq__0__conv,axiom,
% 80.71/80.80 ! [V_n_2] :
% 80.71/80.80 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 80.71/80.80 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_int__0,axiom,
% 80.71/80.80 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) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 80.71/80.80 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)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zero__zle__int,axiom,
% 80.71/80.80 ! [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))) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 80.71/80.80 ! [V_P_2] :
% 80.71/80.80 ( ! [B_x] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 80.71/80.80 => hBOOL(hAPP(V_P_2,B_x)) )
% 80.71/80.80 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 80.71/80.80 ! [V_P_2] :
% 80.71/80.80 ( ? [B_x] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 80.71/80.80 & hBOOL(hAPP(V_P_2,B_x)) )
% 80.71/80.80 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 80.71/80.80 ! [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))) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_int__less__0__conv,axiom,
% 80.71/80.80 ! [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))) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zless__int,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 80.71/80.80 ! [V_y_2,V_x_2] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zle__int,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 80.71/80.80 ! [V_y_2,V_x_2] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zadd__int,axiom,
% 80.71/80.80 ! [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)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zadd__int__left,axiom,
% 80.71/80.80 ! [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) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 80.71/80.80 ! [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)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zle__iff__zadd,axiom,
% 80.71/80.80 ! [V_z_2,V_w_2] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 80.71/80.80 <=> ? [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)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zero__le__imp__of__nat,axiom,
% 80.71/80.80 ! [V_m,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.80 => 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))) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_of__nat__0__le__iff,axiom,
% 80.71/80.80 ! [V_n,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.80 => 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))) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_of__nat__less__0__iff,axiom,
% 80.71/80.80 ! [V_m,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.80 => ~ 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))) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_int__mult,axiom,
% 80.71/80.80 ! [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)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zmult__int,axiom,
% 80.71/80.80 ! [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)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 80.71/80.80 ! [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)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_of__nat__0,axiom,
% 80.71/80.80 ! [T_a] :
% 80.71/80.80 ( class_Rings_Osemiring__1(T_a)
% 80.71/80.80 => 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) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_of__nat__less__imp__less,axiom,
% 80.71/80.80 ! [V_n,V_m,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_less__imp__of__nat__less,axiom,
% 80.71/80.80 ! [V_n,V_m,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 80.71/80.80 => 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))) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_of__nat__less__iff,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_int__1,axiom,
% 80.71/80.80 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) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 80.71/80.80 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)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_of__nat__le__iff,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_of__nat__add,axiom,
% 80.71/80.80 ! [V_n,V_m,T_a] :
% 80.71/80.80 ( class_Rings_Osemiring__1(T_a)
% 80.71/80.80 => 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)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_of__nat__mult,axiom,
% 80.71/80.80 ! [V_n,V_m,T_a] :
% 80.71/80.80 ( class_Rings_Osemiring__1(T_a)
% 80.71/80.80 => 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)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_of__nat__1,axiom,
% 80.71/80.80 ! [T_a] :
% 80.71/80.80 ( class_Rings_Osemiring__1(T_a)
% 80.71/80.80 => 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) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold1__singleton__def,axiom,
% 80.71/80.80 ! [V_a_2,V_f_2,T_a,V_g_2] :
% 80.71/80.80 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2)
% 80.71/80.80 => 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 ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold1__singleton,axiom,
% 80.71/80.80 ! [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 ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Ints__of__nat,axiom,
% 80.71/80.80 ! [V_n_2,T_a] :
% 80.71/80.80 ( class_Rings_Oring__1(T_a)
% 80.71/80.80 => 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))) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 80.71/80.80 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.80 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 80.71/80.80 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_folding__one_Oeq__fold,axiom,
% 80.71/80.80 ! [V_A_2,V_F_2,V_f_2,T_a] :
% 80.71/80.80 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_int__le__0__conv,axiom,
% 80.71/80.80 ! [V_n_2] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_int__Suc0__eq__1,axiom,
% 80.71/80.80 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) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zless__iff__Suc__zadd,axiom,
% 80.71/80.80 ! [V_z_2,V_w_2] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 80.71/80.80 <=> ? [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))) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_int__Suc,axiom,
% 80.71/80.80 ! [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)) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zdiff__int,axiom,
% 80.71/80.80 ! [V_m,V_n] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 80.71/80.80 => 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)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_of__nat__Suc,axiom,
% 80.71/80.80 ! [V_m,T_a] :
% 80.71/80.80 ( class_Rings_Osemiring__1(T_a)
% 80.71/80.80 => 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)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_of__nat__diff,axiom,
% 80.71/80.80 ! [V_m,V_n,T_a] :
% 80.71/80.80 ( class_Rings_Oring__1(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 80.71/80.80 => 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)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Sup__fin_OF__eq,axiom,
% 80.71/80.80 ! [V_A_2,T_a] :
% 80.71/80.80 ( class_Lattices_Olattice(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => 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) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Inf__fin_OF__eq,axiom,
% 80.71/80.80 ! [V_A_2,T_a] :
% 80.71/80.80 ( class_Lattices_Olattice(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => 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) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zero__less__int__conv,axiom,
% 80.71/80.80 ! [V_n_2] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zmult__zless__mono2__lemma,axiom,
% 80.71/80.80 ! [V_k,V_j,V_i] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 80.71/80.80 => 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))) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_of__nat__0__less__iff,axiom,
% 80.71/80.80 ! [V_n_2,T_a] :
% 80.71/80.80 ( class_Rings_Olinordered__semidom(T_a)
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold__image__insert,axiom,
% 80.71/80.80 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] :
% 80.71/80.80 ( class_Groups_Oab__semigroup__mult(T_b)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.80 => 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)) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_setsum_OF__eq,axiom,
% 80.71/80.80 ! [V_g_2,V_A_2,T_a,T_b] :
% 80.71/80.80 ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.80 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => 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) )
% 80.71/80.80 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => 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) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_setsum_Oeq__fold,axiom,
% 80.71/80.80 ! [V_g_2,V_A_2,T_a,T_b] :
% 80.71/80.80 ( class_Groups_Ocomm__monoid__add(T_b)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => 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) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold1__belowI,axiom,
% 80.71/80.80 ! [V_a_2,V_A_2,T_a] :
% 80.71/80.80 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.80 => 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)) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_below__fold1__iff,axiom,
% 80.71/80.80 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.80 ( class_Lattices_Osemilattice__inf(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.80 => ( 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)))
% 80.71/80.80 <=> ! [B_x] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold1__insert__idem,axiom,
% 80.71/80.80 ! [V_x_2,V_A_2,T_a] :
% 80.71/80.80 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 80.71/80.80 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => 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)) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold1__Un2,axiom,
% 80.71/80.80 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.80 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.80 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.80 => 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)) ) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold1__eq__fold__idem,axiom,
% 80.71/80.80 ! [V_a_2,V_A_2,T_a] :
% 80.71/80.80 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => 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) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 80.71/80.80 ! [V_y,V_x] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 80.71/80.80 => 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))) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_tsub__eq,axiom,
% 80.71/80.80 ! [V_x,V_y] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 80.71/80.80 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold__image__Un__Int,axiom,
% 80.71/80.80 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 80.71/80.80 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.80 => 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))) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zdiff__int__split,axiom,
% 80.71/80.80 ! [V_y_2,V_x_2,V_P_2] :
% 80.71/80.80 ( 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))))
% 80.71/80.80 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 80.71/80.80 => 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)))) )
% 80.71/80.80 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 80.71/80.80 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_semilattice__big_OF__eq,axiom,
% 80.71/80.80 ! [V_A_2,V_F_2,V_f_2,T_a] :
% 80.71/80.80 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_comm__monoid__big_OF__eq,axiom,
% 80.71/80.80 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.80 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 80.71/80.80 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 80.71/80.80 => 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) )
% 80.71/80.80 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 80.71/80.80 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold__image__Un__one,axiom,
% 80.71/80.80 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 80.71/80.80 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 80.71/80.80 => ( ! [B_x] :
% 80.71/80.80 ( 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)))
% 80.71/80.80 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 80.71/80.80 => 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)) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_fold1__in,axiom,
% 80.71/80.80 ! [V_A_2,T_a] :
% 80.71/80.80 ( class_Groups_Oab__semigroup__mult(T_a)
% 80.71/80.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.80 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 80.71/80.80 => ( ! [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))))))
% 80.71/80.80 => 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)) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_setsum__bounded,axiom,
% 80.71/80.80 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] :
% 80.71/80.80 ( ( class_Groups_Oordered__ab__semigroup__add(T_b)
% 80.71/80.80 & class_Rings_Osemiring__1(T_b) )
% 80.71/80.80 => ( ! [B_i] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2))
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) )
% 80.71/80.80 => 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))) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_of__nat__number__of__eq,axiom,
% 80.71/80.80 ! [V_v,T_a] :
% 80.71/80.80 ( class_Int_Onumber__ring(T_a)
% 80.71/80.80 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 80.71/80.80 => 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) )
% 80.71/80.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 80.71/80.80 => 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) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 80.71/80.80 ! [V_y_2,V_x_2] :
% 80.71/80.80 ( 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)
% 80.71/80.80 <=> V_x_2 = V_y_2 ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_not__neg__int,axiom,
% 80.71/80.80 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_int__int__eq,axiom,
% 80.71/80.80 ! [V_n_2,V_m_2] :
% 80.71/80.80 ( 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)
% 80.71/80.80 <=> V_m_2 = V_n_2 ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_not__neg__0,axiom,
% 80.71/80.80 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_not__neg__1,axiom,
% 80.71/80.80 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_not__neg__eq__ge__0,axiom,
% 80.71/80.80 ! [V_x_2] :
% 80.71/80.80 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_neg__def,axiom,
% 80.71/80.80 ! [V_Z_2] :
% 80.71/80.80 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 80.71/80.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_neg__imp__number__of__eq__0,axiom,
% 80.71/80.80 ! [V_v] :
% 80.71/80.80 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 80.71/80.80 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_int__nat__number__of,axiom,
% 80.71/80.80 ! [V_v] :
% 80.71/80.80 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 80.71/80.80 => 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) )
% 80.71/80.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 80.71/80.80 => 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) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 80.71/80.80 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 80.71/80.80 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 80.71/80.80 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 80.71/80.80 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_eq__nat__number__of,axiom,
% 80.71/80.80 ! [V_v_H_2,V_v_2] :
% 80.71/80.80 ( 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)
% 80.71/80.80 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 80.71/80.80 => 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))) )
% 80.71/80.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 80.71/80.80 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 80.71/80.80 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 80.71/80.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 80.71/80.80 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_nat__number__of__add__left,axiom,
% 80.71/80.80 ! [V_k,V_v_H,V_v] :
% 80.71/80.80 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 80.71/80.80 => 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) )
% 80.71/80.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 80.71/80.80 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 80.71/80.80 => 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) )
% 80.71/80.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 80.71/80.80 => 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) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Suc__nat__number__of__add,axiom,
% 80.71/80.80 ! [V_n,V_v] :
% 80.71/80.80 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 80.71/80.80 => 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) )
% 80.71/80.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 80.71/80.80 => 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) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_Suc__nat__number__of,axiom,
% 80.71/80.80 ! [V_v] :
% 80.71/80.80 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 80.71/80.80 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 80.71/80.80 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 80.71/80.80 => 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)) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_decr__mult__lemma,axiom,
% 80.71/80.80 ! [V_k_2,V_P_2,V_d_2] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 80.71/80.80 => ( ! [B_x] :
% 80.71/80.80 ( hBOOL(hAPP(V_P_2,B_x))
% 80.71/80.80 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 80.71/80.80 => ! [B_x] :
% 80.71/80.80 ( hBOOL(hAPP(V_P_2,B_x))
% 80.71/80.80 => 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)))) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_incr__mult__lemma,axiom,
% 80.71/80.80 ! [V_k_2,V_P_2,V_d_2] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 80.71/80.80 => ( ! [B_x] :
% 80.71/80.80 ( hBOOL(hAPP(V_P_2,B_x))
% 80.71/80.80 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 80.71/80.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 80.71/80.80 => ! [B_x] :
% 80.71/80.80 ( hBOOL(hAPP(V_P_2,B_x))
% 80.71/80.80 => 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)))) ) ) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_zero__less__imp__eq__int,axiom,
% 80.71/80.80 ! [V_k] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 80.71/80.80 => ? [B_n] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 80.71/80.80 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_decr__lemma,axiom,
% 80.71/80.80 ! [V_z,V_x,V_d] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 80.71/80.80 => 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)) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_incr__lemma,axiom,
% 80.71/80.80 ! [V_x,V_z,V_d] :
% 80.71/80.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 80.71/80.80 => 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)))) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_abs__idempotent,axiom,
% 80.71/80.80 ! [V_a,T_a] :
% 80.71/80.80 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.80 => 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) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_abs__ge__self,axiom,
% 80.71/80.80 ! [V_a,T_a] :
% 80.71/80.80 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 80.71/80.80
% 80.71/80.80 fof(fact_abs__le__D1,axiom,
% 80.71/80.80 ! [V_b,V_a,T_a] :
% 80.71/80.80 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 80.71/80.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__eq__0,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__zero,axiom,
% 80.71/80.81 ! [T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__add__abs,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__mult__self,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__mult,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__minus__commute,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__one,axiom,
% 80.71/80.81 ! [T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__of__nat,axiom,
% 80.71/80.81 ! [V_n,T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__int__eq,axiom,
% 80.71/80.81 ! [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) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__of__nonneg,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.81 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__le__zero__iff,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__ge__zero,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => 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))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__of__pos,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.81 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_zero__less__abs__iff,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__not__less__zero,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => ~ 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))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__triangle__ineq,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => 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)))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__mult__less,axiom,
% 80.71/80.81 ! [V_d,V_b,V_c,V_a,T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 80.71/80.81 => 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))) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__triangle__ineq3,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => 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)))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__triangle__ineq2,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => 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)))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__triangle__ineq2__sym,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => 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)))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__zmult__eq__1,axiom,
% 80.71/80.81 ! [V_n,V_m] :
% 80.71/80.81 ( 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)
% 80.71/80.81 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__eq__mult,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Rings_Oordered__ring__abs(T_a)
% 80.71/80.81 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.81 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 80.71/80.81 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 80.71/80.81 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 80.71/80.81 => 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)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__mult__pos,axiom,
% 80.71/80.81 ! [V_y,V_x,T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 80.71/80.81 => 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)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__triangle__ineq4,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => 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)))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__diff__triangle__ineq,axiom,
% 80.71/80.81 ! [V_d,V_c,V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => 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))))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_zabs__less__one__iff,axiom,
% 80.71/80.81 ! [V_z_2] :
% 80.71/80.81 ( 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)))
% 80.71/80.81 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_succ__def,axiom,
% 80.71/80.81 ! [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)) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_number__of__succ,axiom,
% 80.71/80.81 ! [V_k,T_a] :
% 80.71/80.81 ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_int__val__lemma,axiom,
% 80.71/80.81 ! [V_k_2,V_f_2,V_n_2] :
% 80.71/80.81 ( ! [B_i] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 80.71/80.81 => 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))) )
% 80.71/80.81 => ( 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))
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 80.71/80.81 => ? [B_i] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 80.71/80.81 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_nat0__intermed__int__val,axiom,
% 80.71/80.81 ! [V_k_2,V_f_2,V_n_2] :
% 80.71/80.81 ( ! [B_i] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 80.71/80.81 => 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))) )
% 80.71/80.81 => ( 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))
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 80.71/80.81 => ? [B_i] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 80.71/80.81 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_nat__1__add__number__of,axiom,
% 80.71/80.81 ! [V_v] :
% 80.71/80.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 80.71/80.81 => 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) )
% 80.71/80.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 80.71/80.81 => 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)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_nat__number__of__add__1,axiom,
% 80.71/80.81 ! [V_v] :
% 80.71/80.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 80.71/80.81 => 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) )
% 80.71/80.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 80.71/80.81 => 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)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_neg__number__of__pred__iff__0,axiom,
% 80.71/80.81 ! [V_v_2] :
% 80.71/80.81 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 80.71/80.81 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_mult__nat__number__of,axiom,
% 80.71/80.81 ! [V_v_H,V_v] :
% 80.71/80.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 80.71/80.81 => 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) )
% 80.71/80.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 80.71/80.81 => 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)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_nat__number__of__mult__left,axiom,
% 80.71/80.81 ! [V_k,V_v_H,V_v] :
% 80.71/80.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 80.71/80.81 => 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) )
% 80.71/80.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 80.71/80.81 => 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) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Pls__def,axiom,
% 80.71/80.81 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_rel__simps_I19_J,axiom,
% 80.71/80.81 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_rel__simps_I2_J,axiom,
% 80.71/80.81 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_add__Pls,axiom,
% 80.71/80.81 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 80.71/80.81
% 80.71/80.81 fof(fact_add__Pls__right,axiom,
% 80.71/80.81 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 80.71/80.81
% 80.71/80.81 fof(fact_mult__Pls,axiom,
% 80.71/80.81 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 80.71/80.81
% 80.71/80.81 fof(fact_diff__bin__simps_I1_J,axiom,
% 80.71/80.81 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 80.71/80.81
% 80.71/80.81 fof(fact_succ__pred,axiom,
% 80.71/80.81 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 80.71/80.81
% 80.71/80.81 fof(fact_number__of__Pls,axiom,
% 80.71/80.81 ! [T_a] :
% 80.71/80.81 ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_semiring__norm_I112_J,axiom,
% 80.71/80.81 ! [T_a] :
% 80.71/80.81 ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_add__numeral__0__right,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 => 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 ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_add__numeral__0,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 => 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 ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_bin__less__0__simps_I1_J,axiom,
% 80.71/80.81 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_semiring__norm_I113_J,axiom,
% 80.71/80.81 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_nat__number__of__Pls,axiom,
% 80.71/80.81 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_zero__is__num__zero,axiom,
% 80.71/80.81 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Suc__diff__number__of,axiom,
% 80.71/80.81 ! [V_m,V_v] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 80.71/80.81 => 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))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_not__neg__number__of__Pls,axiom,
% 80.71/80.81 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_le__iff__pred__less,axiom,
% 80.71/80.81 ! [V_l_2,V_k_2] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_pred__def,axiom,
% 80.71/80.81 ! [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)) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_nat__number__of__diff__1,axiom,
% 80.71/80.81 ! [V_v] :
% 80.71/80.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 80.71/80.81 => 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) )
% 80.71/80.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 80.71/80.81 => 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)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_eq__number__of__0,axiom,
% 80.71/80.81 ! [V_v_2] :
% 80.71/80.81 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_eq__0__number__of,axiom,
% 80.71/80.81 ! [V_v_2] :
% 80.71/80.81 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_number__of2,axiom,
% 80.71/80.81 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))) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_less__nat__number__of,axiom,
% 80.71/80.81 ! [V_v_H_2,V_v_2] :
% 80.71/80.81 ( 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)))
% 80.71/80.81 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 80.71/80.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 80.71/80.81 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_le__nat__number__of,axiom,
% 80.71/80.81 ! [V_v_H_2,V_v_2] :
% 80.71/80.81 ( 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)))
% 80.71/80.81 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 80.71/80.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_le__special_I3_J,axiom,
% 80.71/80.81 ! [V_x_2,T_a] :
% 80.71/80.81 ( ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 & class_Rings_Olinordered__idom(T_a) )
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_le__special_I1_J,axiom,
% 80.71/80.81 ! [V_y_2,T_a] :
% 80.71/80.81 ( ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 & class_Rings_Olinordered__idom(T_a) )
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_less__special_I3_J,axiom,
% 80.71/80.81 ! [V_x_2,T_a] :
% 80.71/80.81 ( ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 & class_Rings_Olinordered__idom(T_a) )
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_less__special_I1_J,axiom,
% 80.71/80.81 ! [V_y_2,T_a] :
% 80.71/80.81 ( ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 & class_Rings_Olinordered__idom(T_a) )
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_less__0__number__of,axiom,
% 80.71/80.81 ! [V_v_2] :
% 80.71/80.81 ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_add__nat__number__of,axiom,
% 80.71/80.81 ! [V_v_H,V_v] :
% 80.71/80.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 80.71/80.81 => 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) )
% 80.71/80.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 80.71/80.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 80.71/80.81 => 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) )
% 80.71/80.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 80.71/80.81 => 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)) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Nats__number__of,axiom,
% 80.71/80.81 ! [V_w_2,T_a] :
% 80.71/80.81 ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 80.71/80.81 => 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))) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_restrict__upd__same,axiom,
% 80.71/80.81 ! [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))))) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_restrict__complement__singleton__eq,axiom,
% 80.71/80.81 ! [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)) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod_Oremove,axiom,
% 80.71/80.81 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.81 => 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)))))) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_card__partition,axiom,
% 80.71/80.81 ! [V_k_2,V_C_2,T_a] :
% 80.71/80.81 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2))
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
% 80.71/80.81 => ( ! [B_c] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2))
% 80.71/80.81 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 )
% 80.71/80.81 => ( ! [B_c1] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2))
% 80.71/80.81 => ! [B_c2] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2))
% 80.71/80.81 => ( B_c1 != B_c2
% 80.71/80.81 => 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)) ) ) )
% 80.71/80.81 => 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)) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_fold__image__1,axiom,
% 80.71/80.81 ! [V_f_2,V_S_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 80.71/80.81 => ( ! [B_x] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 80.71/80.81 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 80.71/80.81 => 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) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_fold__image__cong,axiom,
% 80.71/80.81 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Oab__semigroup__mult(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => ( ! [B_x] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.81 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 80.71/80.81 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),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) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_ComplI,axiom,
% 80.71/80.81 ! [V_A_2,V_ca_2,T_a] :
% 80.71/80.81 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 80.71/80.81 => 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))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_arith__simps_I30_J,axiom,
% 80.71/80.81 ! [V_w,T_a] :
% 80.71/80.81 ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_number__of__minus,axiom,
% 80.71/80.81 ! [V_w,T_a] :
% 80.71/80.81 ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_compl__eq__compl__iff,axiom,
% 80.71/80.81 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.81 ( class_Lattices_Oboolean__algebra(T_a)
% 80.71/80.81 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)
% 80.71/80.81 <=> V_x_2 = V_y_2 ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_uminus__apply,axiom,
% 80.71/80.81 ! [V_x_2,V_A_2,T_b,T_a] :
% 80.71/80.81 ( class_Groups_Ouminus(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_double__compl,axiom,
% 80.71/80.81 ! [V_x,T_a] :
% 80.71/80.81 ( class_Lattices_Oboolean__algebra(T_a)
% 80.71/80.81 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Compl__eq__Compl__iff,axiom,
% 80.71/80.81 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.81 ( 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)
% 80.71/80.81 <=> V_A_2 = V_B_2 ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_double__complement,axiom,
% 80.71/80.81 ! [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 ).
% 80.71/80.81
% 80.71/80.81 fof(fact_neg__equal__iff__equal,axiom,
% 80.71/80.81 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 80.71/80.81 <=> V_a_2 = V_b_2 ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__equation__iff,axiom,
% 80.71/80.81 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2
% 80.71/80.81 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_equation__minus__iff,axiom,
% 80.71/80.81 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 80.71/80.81 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__minus,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__number__of__mult,axiom,
% 80.71/80.81 ! [V_z,V_w,T_a] :
% 80.71/80.81 ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_le__minus__iff,axiom,
% 80.71/80.81 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add(T_a)
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> 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))) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__le__iff,axiom,
% 80.71/80.81 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add(T_a)
% 80.71/80.81 => ( 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))
% 80.71/80.81 <=> 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)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_neg__le__iff__le,axiom,
% 80.71/80.81 ! [V_a_2,V_b_2,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add(T_a)
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_le__imp__neg__le,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.81 => 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))) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_compl__le__compl__iff,axiom,
% 80.71/80.81 ! [V_y_2,V_x_2,T_a] :
% 80.71/80.81 ( class_Lattices_Oboolean__algebra(T_a)
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_compl__mono,axiom,
% 80.71/80.81 ! [V_y,V_x,T_a] :
% 80.71/80.81 ( class_Lattices_Oboolean__algebra(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 80.71/80.81 => 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))) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_neg__equal__zero,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Olinordered__ab__group__add(T_a)
% 80.71/80.81 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2
% 80.71/80.81 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_neg__equal__0__iff__equal,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_equal__neg__zero,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Olinordered__ab__group__add(T_a)
% 80.71/80.81 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)
% 80.71/80.81 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_neg__0__equal__iff__equal,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)
% 80.71/80.81 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__zero,axiom,
% 80.71/80.81 ! [T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_neg__less__iff__less,axiom,
% 80.71/80.81 ! [V_a_2,V_b_2,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add(T_a)
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__less__iff,axiom,
% 80.71/80.81 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_less__minus__iff,axiom,
% 80.71/80.81 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__add__cancel,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => 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 ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_add__minus__cancel,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => 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 ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__add,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__add__distrib,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oab__group__add(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_square__eq__iff,axiom,
% 80.71/80.81 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.81 ( class_Rings_Oidom(T_a)
% 80.71/80.81 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
% 80.71/80.81 <=> ( V_a_2 = V_b_2
% 80.71/80.81 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__mult__minus,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Rings_Oring(T_a)
% 80.71/80.81 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__mult__commute,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Rings_Oring(T_a)
% 80.71/80.81 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__mult__left,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Rings_Oring(T_a)
% 80.71/80.81 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__mult__right,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Rings_Oring(T_a)
% 80.71/80.81 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_ComplE,axiom,
% 80.71/80.81 ! [V_A_2,V_ca_2,T_a] :
% 80.71/80.81 ( 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)))
% 80.71/80.81 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_ComplD,axiom,
% 80.71/80.81 ! [V_A_2,V_ca_2,T_a] :
% 80.71/80.81 ( 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)))
% 80.71/80.81 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Compl__iff,axiom,
% 80.71/80.81 ! [V_A_2,V_ca_2,T_a] :
% 80.71/80.81 ( 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)))
% 80.71/80.81 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__diff__eq,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oab__group__add(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Compl__anti__mono,axiom,
% 80.71/80.81 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 80.71/80.81 => 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))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Compl__subset__Compl__iff,axiom,
% 80.71/80.81 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.81 ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__minus__cancel,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod__zero__iff,axiom,
% 80.71/80.81 ! [V_f_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( ( class_Rings_Ocomm__semiring__1(T_b)
% 80.71/80.81 & class_Rings_Ono__zero__divisors(T_b) )
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => ( 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)
% 80.71/80.81 <=> ? [B_x] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.81 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod__zero,axiom,
% 80.71/80.81 ! [V_f_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Rings_Ocomm__semiring__1(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => ( ? [B_x] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 80.71/80.81 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 80.71/80.81 => 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) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod__empty,axiom,
% 80.71/80.81 ! [V_f_2,T_b,T_a] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod_Oempty,axiom,
% 80.71/80.81 ! [V_g_2,T_b,T_a] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod_Oinfinite,axiom,
% 80.71/80.81 ! [V_g_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => 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) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod__infinite,axiom,
% 80.71/80.81 ! [V_f_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => 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) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod__eq__1__iff,axiom,
% 80.71/80.81 ! [V_f_2,V_F_2,T_a] :
% 80.71/80.81 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 80.71/80.81 => ( 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)
% 80.71/80.81 <=> ! [B_x] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2))
% 80.71/80.81 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__le__self__iff,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Olinordered__ab__group__add(T_a)
% 80.71/80.81 => ( 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))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_neg__le__0__iff__le,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add(T_a)
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_le__minus__self__iff,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Olinordered__ab__group__add(T_a)
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_neg__0__le__iff__le,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add(T_a)
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_less__minus__self__iff,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_neg__less__nonneg,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Olinordered__ab__group__add(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_neg__less__0__iff__less,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add(T_a)
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_neg__0__less__iff__less,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add(T_a)
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__unique,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_ab__left__minus,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oab__group__add(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_left__minus,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 80.71/80.81 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 80.71/80.81 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_right__minus,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_diff__0,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_diff__def,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_ab__diff__minus,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oab__group__add(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_diff__minus__eq__add,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Ogroup__add(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 80.71/80.81 ! [V_y,V_x,T_a] :
% 80.71/80.81 ( class_Rings_Ocomm__ring__1(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 80.71/80.81 ! [V_x,T_a] :
% 80.71/80.81 ( class_Rings_Ocomm__ring__1(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_square__eq__1__iff,axiom,
% 80.71/80.81 ! [V_x_2,T_a] :
% 80.71/80.81 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 80.71/80.81 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 80.71/80.81 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
% 80.71/80.81 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_compl__inf__bot,axiom,
% 80.71/80.81 ! [V_x,T_a] :
% 80.71/80.81 ( class_Lattices_Oboolean__algebra(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_inf__compl__bot,axiom,
% 80.71/80.81 ! [V_x,T_a] :
% 80.71/80.81 ( class_Lattices_Oboolean__algebra(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_diff__eq,axiom,
% 80.71/80.81 ! [V_y,V_x,T_a] :
% 80.71/80.81 ( class_Lattices_Oboolean__algebra(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_compl__sup,axiom,
% 80.71/80.81 ! [V_y,V_x,T_a] :
% 80.71/80.81 ( class_Lattices_Oboolean__algebra(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_compl__inf,axiom,
% 80.71/80.81 ! [V_y,V_x,T_a] :
% 80.71/80.81 ( class_Lattices_Oboolean__algebra(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__ge__minus__self,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => 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))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__le__iff,axiom,
% 80.71/80.81 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => ( 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))
% 80.71/80.81 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 80.71/80.81 & 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)) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__leI,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 80.71/80.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__le__D2,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 80.71/80.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__less__iff,axiom,
% 80.71/80.81 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2))
% 80.71/80.81 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 80.71/80.81 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_subset__Compl__self__eq,axiom,
% 80.71/80.81 ! [V_A_2,T_a] :
% 80.71/80.81 ( 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)))
% 80.71/80.81 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Compl__disjoint,axiom,
% 80.71/80.81 ! [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)) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Compl__disjoint2,axiom,
% 80.71/80.81 ! [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)) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Compl__Un,axiom,
% 80.71/80.81 ! [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)) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Compl__Int,axiom,
% 80.71/80.81 ! [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)) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Compl__Diff__eq,axiom,
% 80.71/80.81 ! [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) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Diff__eq,axiom,
% 80.71/80.81 ! [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)) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Diff__Compl,axiom,
% 80.71/80.81 ! [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) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Ints__minus,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Rings_Oring__1(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 80.71/80.81 => 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))) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod__pos__nat__iff,axiom,
% 80.71/80.81 ! [V_f_2,V_S_2,T_a] :
% 80.71/80.81 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> ! [B_x] :
% 80.71/80.81 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 80.71/80.81 => 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))) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__of__nonpos,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.81 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__minus__le__zero,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => 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))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__of__neg,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.81 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__if,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Groups_Oabs__if(T_a)
% 80.71/80.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.81 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 80.71/80.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.81 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_disjoint__eq__subset__Compl,axiom,
% 80.71/80.81 ! [V_B_2,V_A_2,T_a] :
% 80.71/80.81 ( 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))
% 80.71/80.81 <=> 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))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod__insert,axiom,
% 80.71/80.81 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.81 => 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)) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod_Oinsert,axiom,
% 80.71/80.81 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 80.71/80.81 => 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)) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod_Ounion__inter,axiom,
% 80.71/80.81 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.81 => 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)) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod__Un__Int,axiom,
% 80.71/80.81 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.81 => 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)) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod_Oeq__fold,axiom,
% 80.71/80.81 ! [V_g_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => 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) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod_OF__eq,axiom,
% 80.71/80.81 ! [V_g_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => 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) )
% 80.71/80.81 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => 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) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Nats__0,axiom,
% 80.71/80.81 ! [T_a] :
% 80.71/80.81 ( class_Rings_Osemiring__1(T_a)
% 80.71/80.81 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Nats__add,axiom,
% 80.71/80.81 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.81 ( class_Rings_Osemiring__1(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 80.71/80.81 => 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))) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Nats__mult,axiom,
% 80.71/80.81 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.81 ( class_Rings_Osemiring__1(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 80.71/80.81 => 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))) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_Nats__1,axiom,
% 80.71/80.81 ! [T_a] :
% 80.71/80.81 ( class_Rings_Osemiring__1(T_a)
% 80.71/80.81 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_of__nat__in__Nats,axiom,
% 80.71/80.81 ! [V_n_2,T_a] :
% 80.71/80.81 ( class_Rings_Osemiring__1(T_a)
% 80.71/80.81 => 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))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__number__of,axiom,
% 80.71/80.81 ! [V_x,T_a] :
% 80.71/80.81 ( ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 & class_Rings_Olinordered__idom(T_a) )
% 80.71/80.81 => ( ( 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)))
% 80.71/80.81 => 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)) )
% 80.71/80.81 & ( ~ 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)))
% 80.71/80.81 => 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) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_number__of__pred,axiom,
% 80.71/80.81 ! [V_w,T_a] :
% 80.71/80.81 ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod_Oinsert__remove,axiom,
% 80.71/80.81 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => 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)))))) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod_Ounion__disjoint,axiom,
% 80.71/80.81 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.81 => ( 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))
% 80.71/80.81 => 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)) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod__Un__disjoint,axiom,
% 80.71/80.81 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.81 => ( 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))
% 80.71/80.81 => 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)) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 80.71/80.81 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 80.71/80.81 => ( ! [B_x] :
% 80.71/80.81 ( 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)))
% 80.71/80.81 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 80.71/80.81 => 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)) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod__Un__one,axiom,
% 80.71/80.81 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 80.71/80.81 => ( ! [B_x] :
% 80.71/80.81 ( 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)))
% 80.71/80.81 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 80.71/80.81 => 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)) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod__diff1,axiom,
% 80.71/80.81 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] :
% 80.71/80.81 ( class_Fields_Ofield(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 80.71/80.81 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b)
% 80.71/80.81 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.81 => 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)) )
% 80.71/80.81 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 80.71/80.81 => 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) ) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod__mono__one__left,axiom,
% 80.71/80.81 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 80.71/80.81 => ( ! [B_x] :
% 80.71/80.81 ( 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)))
% 80.71/80.81 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 80.71/80.81 => 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) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_setprod__mono__one__right,axiom,
% 80.71/80.81 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 80.71/80.81 ( class_Groups_Ocomm__monoid__mult(T_b)
% 80.71/80.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 80.71/80.81 => ( ! [B_x] :
% 80.71/80.81 ( 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)))
% 80.71/80.81 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 80.71/80.81 => 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) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_sgn__neg,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.81 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_negative__zle,axiom,
% 80.71/80.81 ! [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))) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_negative__zless,axiom,
% 80.71/80.81 ! [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))) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_zminus__zminus,axiom,
% 80.71/80.81 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 80.71/80.81
% 80.71/80.81 fof(fact_sgn__sgn,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_divide__zero__left,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_divide__zero,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_add__divide__distrib,axiom,
% 80.71/80.81 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_times__divide__eq__right,axiom,
% 80.71/80.81 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_diff__divide__distrib,axiom,
% 80.71/80.81 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_divide__1,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring(T_a)
% 80.71/80.81 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__divide__left,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring(T_a)
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_zminus__0,axiom,
% 80.71/80.81 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) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__Pls,axiom,
% 80.71/80.81 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 80.71/80.81
% 80.71/80.81 fof(fact_zminus__zadd__distrib,axiom,
% 80.71/80.81 ! [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)) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__numeral__code_I5_J,axiom,
% 80.71/80.81 ! [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)) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_zmult__zminus,axiom,
% 80.71/80.81 ! [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)) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_zsgn__def,axiom,
% 80.71/80.81 ! [V_i] :
% 80.71/80.81 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 80.71/80.81 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 80.71/80.81 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 80.71/80.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 80.71/80.81 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 80.71/80.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 80.71/80.81 => 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)) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_sgn__0__0,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_sgn0,axiom,
% 80.71/80.81 ! [T_a] :
% 80.71/80.81 ( class_Groups_Osgn__if(T_a)
% 80.71/80.81 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_sgn__times,axiom,
% 80.71/80.81 ! [V_b,V_a,T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_nonzero__eq__divide__eq,axiom,
% 80.71/80.81 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring(T_a)
% 80.71/80.81 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)
% 80.71/80.81 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_nonzero__divide__eq__eq,axiom,
% 80.71/80.81 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring(T_a)
% 80.71/80.81 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2
% 80.71/80.81 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_divide__eq__imp,axiom,
% 80.71/80.81 ! [V_a,V_b,V_c,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring(T_a)
% 80.71/80.81 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 80.71/80.81 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_eq__divide__imp,axiom,
% 80.71/80.81 ! [V_b,V_a,V_c,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring(T_a)
% 80.71/80.81 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 80.71/80.81 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_divide__self__if,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 80.71/80.81 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 80.71/80.81 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_divide__self,axiom,
% 80.71/80.81 ! [V_a,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring(T_a)
% 80.71/80.81 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_right__inverse__eq,axiom,
% 80.71/80.81 ! [V_a_2,V_b_2,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring(T_a)
% 80.71/80.81 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a)
% 80.71/80.81 <=> V_a_2 = V_b_2 ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_nonzero__minus__divide__divide,axiom,
% 80.71/80.81 ! [V_a,V_b,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring(T_a)
% 80.71/80.81 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => 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) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_nonzero__minus__divide__right,axiom,
% 80.71/80.81 ! [V_a,V_b,T_a] :
% 80.71/80.81 ( class_Rings_Odivision__ring(T_a)
% 80.71/80.81 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => 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)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_zadd__zminus__inverse2,axiom,
% 80.71/80.81 ! [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) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_negative__eq__positive,axiom,
% 80.71/80.81 ! [V_m_2,V_n_2] :
% 80.71/80.81 ( 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)
% 80.71/80.81 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.81 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_not__int__zless__negative,axiom,
% 80.71/80.81 ! [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)))) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_diff__int__def__symmetric,axiom,
% 80.71/80.81 ! [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) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_diff__int__def,axiom,
% 80.71/80.81 ! [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)) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_divide__eq__eq__number__of1,axiom,
% 80.71/80.81 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 80.71/80.81 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 80.71/80.81 & class_Int_Onumber(T_a) )
% 80.71/80.81 => ( 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
% 80.71/80.81 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => 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)) )
% 80.71/80.81 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_divide__eq__eq__number__of,axiom,
% 80.71/80.81 ! [V_w_2,V_ca_2,V_b_2,T_a] :
% 80.71/80.81 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 80.71/80.81 & class_Int_Onumber(T_a) )
% 80.71/80.81 => ( 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)
% 80.71/80.81 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => 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) )
% 80.71/80.81 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_eq__divide__eq__number__of,axiom,
% 80.71/80.81 ! [V_ca_2,V_b_2,V_w_2,T_a] :
% 80.71/80.81 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 80.71/80.81 & class_Int_Onumber(T_a) )
% 80.71/80.81 => ( 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)
% 80.71/80.81 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => 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 )
% 80.71/80.81 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_eq__divide__eq__number__of1,axiom,
% 80.71/80.81 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 80.71/80.81 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 80.71/80.81 & class_Int_Onumber(T_a) )
% 80.71/80.81 => ( 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))
% 80.71/80.81 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => 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 )
% 80.71/80.81 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.81 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_divide__Numeral0,axiom,
% 80.71/80.81 ! [V_x,T_a] :
% 80.71/80.81 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 80.71/80.81 & class_Int_Onumber__ring(T_a) )
% 80.71/80.81 => 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) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_diff__number__of__eq,axiom,
% 80.71/80.81 ! [V_w,V_v,T_a] :
% 80.71/80.81 ( class_Int_Onumber__ring(T_a)
% 80.71/80.81 => 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))) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_int__zle__neg,axiom,
% 80.71/80.81 ! [V_m_2,V_n_2] :
% 80.71/80.81 ( 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))))
% 80.71/80.81 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 80.71/80.81 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_negative__zle__0,axiom,
% 80.71/80.81 ! [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))) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_sgn__greater,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_sgn__less,axiom,
% 80.71/80.81 ! [V_a_2,T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_minus__numeral__code_I6_J,axiom,
% 80.71/80.81 ! [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))) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_zabs__def,axiom,
% 80.71/80.81 ! [V_i] :
% 80.71/80.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 80.71/80.81 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 80.71/80.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 80.71/80.81 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_neg__zminus__int,axiom,
% 80.71/80.81 ! [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))))) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_abs__sgn,axiom,
% 80.71/80.81 ! [V_k,T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => 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)) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_mult__sgn__abs,axiom,
% 80.71/80.81 ! [V_x,T_a] :
% 80.71/80.81 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.81 => 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 ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_divide__less__eq__number__of1,axiom,
% 80.71/80.81 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 80.71/80.81 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.81 & class_Int_Onumber(T_a) )
% 80.71/80.81 => ( 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))
% 80.71/80.81 <=> ( ( 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)))
% 80.71/80.81 => 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)))) )
% 80.71/80.81 & ( ~ 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)))
% 80.71/80.81 => ( ( 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)))
% 80.71/80.81 => 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)) )
% 80.71/80.81 & ( ~ 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)))
% 80.71/80.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_divide__less__eq__number__of,axiom,
% 80.71/80.81 ! [V_w_2,V_ca_2,V_b_2,T_a] :
% 80.71/80.81 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.81 & class_Int_Onumber(T_a) )
% 80.71/80.81 => ( 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)))
% 80.71/80.81 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 80.71/80.81 => 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))) )
% 80.71/80.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 80.71/80.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.81 => 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)) )
% 80.71/80.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.81 => 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))) ) ) ) ) ) ) ).
% 80.71/80.81
% 80.71/80.81 fof(fact_less__divide__eq__number__of,axiom,
% 80.71/80.81 ! [V_ca_2,V_b_2,V_w_2,T_a] :
% 80.71/80.81 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.81 & class_Int_Onumber(T_a) )
% 80.71/80.82 => ( 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)))
% 80.71/80.82 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 80.71/80.82 => 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)) )
% 80.71/80.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 80.71/80.82 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 => 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))) )
% 80.71/80.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 => 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))) ) ) ) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_less__divide__eq__number__of1,axiom,
% 80.71/80.82 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 80.71/80.82 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.82 & class_Int_Onumber(T_a) )
% 80.71/80.82 => ( 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))))
% 80.71/80.82 <=> ( ( 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)))
% 80.71/80.82 => 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)) )
% 80.71/80.82 & ( ~ 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)))
% 80.71/80.82 => ( ( 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)))
% 80.71/80.82 => 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)))) )
% 80.71/80.82 & ( ~ 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)))
% 80.71/80.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_add__number__of__diff2,axiom,
% 80.71/80.82 ! [V_w,V_c,V_v,T_a] :
% 80.71/80.82 ( class_Int_Onumber__ring(T_a)
% 80.71/80.82 => 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) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_not__zle__0__negative,axiom,
% 80.71/80.82 ! [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))))) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_negative__zless__0,axiom,
% 80.71/80.82 ! [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))) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_sgn__pos,axiom,
% 80.71/80.82 ! [V_a,T_a] :
% 80.71/80.82 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 80.71/80.82 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_sgn__1__pos,axiom,
% 80.71/80.82 ! [V_a_2,T_a] :
% 80.71/80.82 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.82 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
% 80.71/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_divide__le__eq__number__of1,axiom,
% 80.71/80.82 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 80.71/80.82 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.82 & class_Int_Onumber(T_a) )
% 80.71/80.82 => ( 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))
% 80.71/80.82 <=> ( ( 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)))
% 80.71/80.82 => 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)))) )
% 80.71/80.82 & ( ~ 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)))
% 80.71/80.82 => ( ( 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)))
% 80.71/80.82 => 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)) )
% 80.71/80.82 & ( ~ 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)))
% 80.71/80.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_divide__le__eq__number__of,axiom,
% 80.71/80.82 ! [V_w_2,V_ca_2,V_b_2,T_a] :
% 80.71/80.82 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.82 & class_Int_Onumber(T_a) )
% 80.71/80.82 => ( 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)))
% 80.71/80.82 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 80.71/80.82 => 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))) )
% 80.71/80.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 80.71/80.82 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 => 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)) )
% 80.71/80.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 => 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))) ) ) ) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_le__divide__eq__number__of,axiom,
% 80.71/80.82 ! [V_ca_2,V_b_2,V_w_2,T_a] :
% 80.71/80.82 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.82 & class_Int_Onumber(T_a) )
% 80.71/80.82 => ( 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)))
% 80.71/80.82 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 80.71/80.82 => 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)) )
% 80.71/80.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 80.71/80.82 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 => 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))) )
% 80.71/80.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 => 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))) ) ) ) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_le__divide__eq__number__of1,axiom,
% 80.71/80.82 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 80.71/80.82 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.82 & class_Int_Onumber(T_a) )
% 80.71/80.82 => ( 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))))
% 80.71/80.82 <=> ( ( 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)))
% 80.71/80.82 => 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)) )
% 80.71/80.82 & ( ~ 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)))
% 80.71/80.82 => ( ( 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)))
% 80.71/80.82 => 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)))) )
% 80.71/80.82 & ( ~ 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)))
% 80.71/80.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_sgn__if,axiom,
% 80.71/80.82 ! [V_x,T_a] :
% 80.71/80.82 ( class_Groups_Osgn__if(T_a)
% 80.71/80.82 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.82 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 80.71/80.82 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.82 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 80.71/80.82 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 80.71/80.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 80.71/80.82 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_sgn__1__neg,axiom,
% 80.71/80.82 ! [V_a_2,T_a] :
% 80.71/80.82 ( class_Rings_Olinordered__idom(T_a)
% 80.71/80.82 => ( 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))
% 80.71/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_divide__left__mono__neg,axiom,
% 80.71/80.82 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 => ( 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)))
% 80.71/80.82 => 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))) ) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_divide__left__mono,axiom,
% 80.71/80.82 ! [V_c,V_a,V_b,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field(T_a)
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.82 => ( 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)))
% 80.71/80.82 => 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))) ) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_neg__divide__le__eq,axiom,
% 80.71/80.82 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field(T_a)
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 => ( 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))
% 80.71/80.82 <=> 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)) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_neg__le__divide__eq,axiom,
% 80.71/80.82 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field(T_a)
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 => ( 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)))
% 80.71/80.82 <=> 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))) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_mult__imp__le__div__pos,axiom,
% 80.71/80.82 ! [V_x,V_z,V_y,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field(T_a)
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 80.71/80.82 => ( 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))
% 80.71/80.82 => 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))) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_mult__imp__div__pos__le,axiom,
% 80.71/80.82 ! [V_z,V_x,V_y,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field(T_a)
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 80.71/80.82 => ( 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)))
% 80.71/80.82 => 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)) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_times__divide__times__eq,axiom,
% 80.71/80.82 ! [V_w,V_z,V_y,V_x,T_a] :
% 80.71/80.82 ( class_Fields_Ofield__inverse__zero(T_a)
% 80.71/80.82 => 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)) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_minus__divide__divide,axiom,
% 80.71/80.82 ! [V_b,V_a,T_a] :
% 80.71/80.82 ( class_Fields_Ofield__inverse__zero(T_a)
% 80.71/80.82 => 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) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_minus__divide__right,axiom,
% 80.71/80.82 ! [V_b,V_a,T_a] :
% 80.71/80.82 ( class_Fields_Ofield__inverse__zero(T_a)
% 80.71/80.82 => 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)) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_abs__divide,axiom,
% 80.71/80.82 ! [V_b,V_a,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.82 => 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)) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_zero__le__divide__iff,axiom,
% 80.71/80.82 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.82 => ( 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)))
% 80.71/80.82 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 80.71/80.82 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 80.71/80.82 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_divide__le__0__iff,axiom,
% 80.71/80.82 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.82 => ( 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)))
% 80.71/80.82 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 80.71/80.82 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 80.71/80.82 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_divide__right__mono,axiom,
% 80.71/80.82 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.82 => 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))) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_divide__right__mono__neg,axiom,
% 80.71/80.82 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 => 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))) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_zero__less__divide__iff,axiom,
% 80.71/80.82 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.82 => ( 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)))
% 80.71/80.82 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 80.71/80.82 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 80.71/80.82 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_divide__less__0__iff,axiom,
% 80.71/80.82 ! [V_b_2,V_a_2,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 80.71/80.82 => ( 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)))
% 80.71/80.82 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 80.71/80.82 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 80.71/80.82 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_divide__pos__pos,axiom,
% 80.71/80.82 ! [V_y,V_x,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field(T_a)
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 80.71/80.82 => 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))) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_divide__pos__neg,axiom,
% 80.71/80.82 ! [V_y,V_x,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field(T_a)
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 => 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))) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_divide__neg__pos,axiom,
% 80.71/80.82 ! [V_y,V_x,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field(T_a)
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 80.71/80.82 => 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))) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_divide__neg__neg,axiom,
% 80.71/80.82 ! [V_y,V_x,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field(T_a)
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 => 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))) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_divide__strict__right__mono,axiom,
% 80.71/80.82 ! [V_c,V_b,V_a,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field(T_a)
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 80.71/80.82 => 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))) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_divide__strict__right__mono__neg,axiom,
% 80.71/80.82 ! [V_c,V_a,V_b,T_a] :
% 80.71/80.82 ( class_Fields_Olinordered__field(T_a)
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 80.71/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 80.71/80.82 => 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))) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_eq__divide__eq,axiom,
% 80.71/80.82 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 80.71/80.82 ( class_Fields_Ofield__inverse__zero(T_a)
% 80.71/80.82 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)
% 80.71/80.82 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.82 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 )
% 80.71/80.82 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.82 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_divide__eq__eq,axiom,
% 80.71/80.82 ! [V_a_2,V_ca_2,V_b_2,T_a] :
% 80.71/80.82 ( class_Fields_Ofield__inverse__zero(T_a)
% 80.71/80.82 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2
% 80.71/80.82 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.82 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) )
% 80.71/80.82 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.82 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_mult__divide__mult__cancel__right,axiom,
% 80.71/80.82 ! [V_b,V_a,V_c,T_a] :
% 80.71/80.82 ( class_Fields_Ofield__inverse__zero(T_a)
% 80.71/80.82 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.82 => 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) ) ) ).
% 80.71/80.82
% 80.71/80.82 fof(fact_mult__divide__mult__cancel__left,axiom,
% 80.71/80.82 ! [V_b,V_a,V_c,T_a] :
% 80.71/80.82 ( class_Fields_Ofield__inverse__zero(T_a)
% 80.71/80.82 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 80.71/80.82 => 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) ) ) ).
% 80.71/80.82
% 81.03/80.82 fof(fact_frac__eq__eq,axiom,
% 81.03/80.82 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] :
% 81.03/80.82 ( class_Fields_Ofield(T_a)
% 81.03/80.82 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.82 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.82 => ( 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)
% 81.03/80.82 <=> 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) ) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_nonzero__abs__divide,axiom,
% 81.03/80.82 ! [V_a,V_b,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.82 => 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)) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_divide__nonneg__pos,axiom,
% 81.03/80.82 ! [V_y,V_x,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 81.03/80.82 => 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))) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_divide__nonneg__neg,axiom,
% 81.03/80.82 ! [V_y,V_x,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.82 => 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))) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_frac__less2,axiom,
% 81.03/80.82 ! [V_z,V_w,V_y,V_x,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 81.03/80.82 => 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))) ) ) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_frac__less,axiom,
% 81.03/80.82 ! [V_z,V_w,V_y,V_x,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 81.03/80.82 => 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))) ) ) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_frac__le,axiom,
% 81.03/80.82 ! [V_z,V_w,V_y,V_x,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 81.03/80.82 => 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))) ) ) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_divide__nonpos__pos,axiom,
% 81.03/80.82 ! [V_y,V_x,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 81.03/80.82 => 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))) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_divide__nonpos__neg,axiom,
% 81.03/80.82 ! [V_y,V_x,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.82 => 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))) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_less__divide__eq,axiom,
% 81.03/80.82 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 81.03/80.82 => ( 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)))
% 81.03/80.82 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 81.03/80.82 => 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)) )
% 81.03/80.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 81.03/80.82 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.82 => 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))) )
% 81.03/80.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_divide__less__eq,axiom,
% 81.03/80.82 ! [V_a_2,V_ca_2,V_b_2,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 81.03/80.82 => ( 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))
% 81.03/80.82 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 81.03/80.82 => 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))) )
% 81.03/80.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 81.03/80.82 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.82 => 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)) )
% 81.03/80.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_pos__less__divide__eq,axiom,
% 81.03/80.82 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 81.03/80.82 => ( 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)))
% 81.03/80.82 <=> 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)) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_pos__divide__less__eq,axiom,
% 81.03/80.82 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 81.03/80.82 => ( 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))
% 81.03/80.82 <=> 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))) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mult__imp__div__pos__less,axiom,
% 81.03/80.82 ! [V_z,V_x,V_y,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 81.03/80.82 => ( 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)))
% 81.03/80.82 => 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)) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mult__imp__less__div__pos,axiom,
% 81.03/80.82 ! [V_x,V_z,V_y,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 81.03/80.82 => ( 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))
% 81.03/80.82 => 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))) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_neg__less__divide__eq,axiom,
% 81.03/80.82 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.82 => ( 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)))
% 81.03/80.82 <=> 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))) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_neg__divide__less__eq,axiom,
% 81.03/80.82 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.82 => ( 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))
% 81.03/80.82 <=> 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)) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_divide__strict__left__mono,axiom,
% 81.03/80.82 ! [V_c,V_a,V_b,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 81.03/80.82 => ( 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)))
% 81.03/80.82 => 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))) ) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_divide__strict__left__mono__neg,axiom,
% 81.03/80.82 ! [V_c,V_b,V_a,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.82 => ( 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)))
% 81.03/80.82 => 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))) ) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_add__frac__eq,axiom,
% 81.03/80.82 ! [V_w,V_x,V_z,V_y,T_a] :
% 81.03/80.82 ( class_Fields_Ofield(T_a)
% 81.03/80.82 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.82 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.82 => 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)) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_divide__add__eq__iff,axiom,
% 81.03/80.82 ! [V_y,V_x,V_z,T_a] :
% 81.03/80.82 ( class_Fields_Ofield(T_a)
% 81.03/80.82 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.82 => 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) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_add__frac__num,axiom,
% 81.03/80.82 ! [V_z,V_x,V_y,T_a] :
% 81.03/80.82 ( class_Fields_Ofield__inverse__zero(T_a)
% 81.03/80.82 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.82 => 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) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_add__divide__eq__iff,axiom,
% 81.03/80.82 ! [V_y,V_x,V_z,T_a] :
% 81.03/80.82 ( class_Fields_Ofield(T_a)
% 81.03/80.82 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.82 => 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) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_add__num__frac,axiom,
% 81.03/80.82 ! [V_x,V_z,V_y,T_a] :
% 81.03/80.82 ( class_Fields_Ofield__inverse__zero(T_a)
% 81.03/80.82 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.82 => 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) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_diff__divide__eq__iff,axiom,
% 81.03/80.82 ! [V_y,V_x,V_z,T_a] :
% 81.03/80.82 ( class_Fields_Ofield(T_a)
% 81.03/80.82 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.82 => 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) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_divide__diff__eq__iff,axiom,
% 81.03/80.82 ! [V_y,V_x,V_z,T_a] :
% 81.03/80.82 ( class_Fields_Ofield(T_a)
% 81.03/80.82 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.82 => 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) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_diff__frac__eq,axiom,
% 81.03/80.82 ! [V_w,V_x,V_z,V_y,T_a] :
% 81.03/80.82 ( class_Fields_Ofield(T_a)
% 81.03/80.82 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.82 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.82 => 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)) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_less__half__sum,axiom,
% 81.03/80.82 ! [V_b,V_a,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 81.03/80.82 => 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))))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_gt__half__sum,axiom,
% 81.03/80.82 ! [V_b,V_a,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 81.03/80.82 => 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)) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_abs__div__pos,axiom,
% 81.03/80.82 ! [V_x,V_y,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 81.03/80.82 => 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)) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_le__divide__eq,axiom,
% 81.03/80.82 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 81.03/80.82 => ( 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)))
% 81.03/80.82 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 81.03/80.82 => 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)) )
% 81.03/80.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 81.03/80.82 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.82 => 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))) )
% 81.03/80.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_divide__le__eq,axiom,
% 81.03/80.82 ! [V_a_2,V_ca_2,V_b_2,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 81.03/80.82 => ( 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))
% 81.03/80.82 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 81.03/80.82 => 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))) )
% 81.03/80.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 81.03/80.82 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.82 => 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)) )
% 81.03/80.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_pos__le__divide__eq,axiom,
% 81.03/80.82 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 81.03/80.82 => ( 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)))
% 81.03/80.82 <=> 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)) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_pos__divide__le__eq,axiom,
% 81.03/80.82 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2))
% 81.03/80.82 => ( 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))
% 81.03/80.82 <=> 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))) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_setprod__Un,axiom,
% 81.03/80.82 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 81.03/80.82 ( class_Fields_Ofield(T_b)
% 81.03/80.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.82 => ( ! [B_x] :
% 81.03/80.82 ( 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)))
% 81.03/80.82 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) )
% 81.03/80.82 => 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))) ) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_eq__special_I3_J,axiom,
% 81.03/80.82 ! [V_x_2,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.82 <=> 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)))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_eq__special_I1_J,axiom,
% 81.03/80.82 ! [V_y_2,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 81.03/80.82 <=> 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)))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_negD,axiom,
% 81.03/80.82 ! [V_x] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.82 => ? [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))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_field__le__mult__one__interval,axiom,
% 81.03/80.82 ! [V_y,V_x,T_a] :
% 81.03/80.82 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 81.03/80.82 => ( ! [B_z] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 81.03/80.82 => 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)) ) )
% 81.03/80.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_diff__special_I2_J,axiom,
% 81.03/80.82 ! [V_v,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => 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)))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I51_J,axiom,
% 81.03/80.82 ! [V_l_2,V_k_2] :
% 81.03/80.82 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 81.03/80.82 <=> V_k_2 = V_l_2 ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_iszero__number__of__Bit1,axiom,
% 81.03/80.82 ! [V_w,T_a] :
% 81.03/80.82 ( ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 & class_Int_Oring__char__0(T_a) )
% 81.03/80.82 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I34_J,axiom,
% 81.03/80.82 ! [V_l_2,V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_less__eq__int__code_I16_J,axiom,
% 81.03/80.82 ! [V_k2_2,V_k1_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_less__int__code_I16_J,axiom,
% 81.03/80.82 ! [V_k2_2,V_k1_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I17_J,axiom,
% 81.03/80.82 ! [V_l_2,V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I39_J,axiom,
% 81.03/80.82 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I46_J,axiom,
% 81.03/80.82 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 81.03/80.82
% 81.03/80.82 fof(fact_not__iszero__Numeral1,axiom,
% 81.03/80.82 ! [T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_iszero__def,axiom,
% 81.03/80.82 ! [V_z_2,T_a] :
% 81.03/80.82 ( class_Rings_Osemiring__1(T_a)
% 81.03/80.82 => ( c_Int_Oiszero(T_a,V_z_2)
% 81.03/80.82 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_iszero__0,axiom,
% 81.03/80.82 ! [T_a] :
% 81.03/80.82 ( class_Rings_Osemiring__1(T_a)
% 81.03/80.82 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_not__iszero__1,axiom,
% 81.03/80.82 ! [T_a] :
% 81.03/80.82 ( class_Rings_Osemiring__1(T_a)
% 81.03/80.82 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_bin__less__0__simps_I4_J,axiom,
% 81.03/80.82 ! [V_w_2] :
% 81.03/80.82 ( 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)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I22_J,axiom,
% 81.03/80.82 ! [V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I12_J,axiom,
% 81.03/80.82 ! [V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Bit1__def,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_neg__number__of__Bit1,axiom,
% 81.03/80.82 ! [V_w_2] :
% 81.03/80.82 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 81.03/80.82 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_minus__Bit1,axiom,
% 81.03/80.82 ! [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))) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_succ__Pls,axiom,
% 81.03/80.82 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_number__of__Bit1,axiom,
% 81.03/80.82 ! [V_w,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => 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)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mult__numeral__1,axiom,
% 81.03/80.82 ! [V_a,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => 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 ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mult__numeral__1__right,axiom,
% 81.03/80.82 ! [V_a,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => 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 ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_numeral__1__eq__1,axiom,
% 81.03/80.82 ! [T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_semiring__norm_I110_J,axiom,
% 81.03/80.82 ! [T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I29_J,axiom,
% 81.03/80.82 ! [V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I5_J,axiom,
% 81.03/80.82 ! [V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_divide__Numeral1,axiom,
% 81.03/80.82 ! [V_x,T_a] :
% 81.03/80.82 ( ( class_Fields_Ofield(T_a)
% 81.03/80.82 & class_Int_Onumber__ring(T_a) )
% 81.03/80.82 => 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 ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_divide__numeral__1,axiom,
% 81.03/80.82 ! [V_a,T_a] :
% 81.03/80.82 ( ( class_Fields_Ofield(T_a)
% 81.03/80.82 & class_Int_Onumber__ring(T_a) )
% 81.03/80.82 => 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 ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_eq__special_I2_J,axiom,
% 81.03/80.82 ! [V_y_2,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 81.03/80.82 <=> 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)))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_eq__special_I4_J,axiom,
% 81.03/80.82 ! [V_x_2,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 81.03/80.82 <=> 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))))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_one__is__num__one,axiom,
% 81.03/80.82 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Numeral1__eq1__nat,axiom,
% 81.03/80.82 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_nat__numeral__1__eq__1,axiom,
% 81.03/80.82 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_iszero__Numeral0,axiom,
% 81.03/80.82 ! [T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_numeral__3__eq__3,axiom,
% 81.03/80.82 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)))) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_numeral__1__eq__Suc__0,axiom,
% 81.03/80.82 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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 81.03/80.82 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))))) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Suc3__eq__add__3,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 81.03/80.82 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)))) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_le__special_I2_J,axiom,
% 81.03/80.82 ! [V_y_2,T_a] :
% 81.03/80.82 ( ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 & class_Rings_Olinordered__idom(T_a) )
% 81.03/80.82 => ( 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)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_le__special_I4_J,axiom,
% 81.03/80.82 ! [V_x_2,T_a] :
% 81.03/80.82 ( ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 & class_Rings_Olinordered__idom(T_a) )
% 81.03/80.82 => ( 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)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_less__special_I4_J,axiom,
% 81.03/80.82 ! [V_x_2,T_a] :
% 81.03/80.82 ( ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 & class_Rings_Olinordered__idom(T_a) )
% 81.03/80.82 => ( 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)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_less__special_I2_J,axiom,
% 81.03/80.82 ! [V_y_2,T_a] :
% 81.03/80.82 ( ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 & class_Rings_Olinordered__idom(T_a) )
% 81.03/80.82 => ( 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)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_add__special_I2_J,axiom,
% 81.03/80.82 ! [V_w,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => 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)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_add__special_I3_J,axiom,
% 81.03/80.82 ! [V_v,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => 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))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 81.03/80.82 ! [V_m,V_n] :
% 81.03/80.82 ( 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))
% 81.03/80.82 => 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)))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_eq__number__of__eq,axiom,
% 81.03/80.82 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 81.03/80.82 <=> 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)))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_diff__special_I1_J,axiom,
% 81.03/80.82 ! [V_w,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => 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))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_one__code__numeral__code,axiom,
% 81.03/80.82 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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_less__2__cases,axiom,
% 81.03/80.82 ! [V_n] :
% 81.03/80.82 ( 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)))))
% 81.03/80.82 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.82 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_compl__unique,axiom,
% 81.03/80.82 ! [V_y,V_x,T_a] :
% 81.03/80.82 ( class_Lattices_Oboolean__algebra(T_a)
% 81.03/80.82 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 81.03/80.82 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 81.03/80.82 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_half__gt__zero__iff,axiom,
% 81.03/80.82 ! [V_r_2,T_a] :
% 81.03/80.82 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 81.03/80.82 & class_Int_Onumber__ring(T_a) )
% 81.03/80.82 => ( 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))))))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_half__gt__zero,axiom,
% 81.03/80.82 ! [V_r,T_a] :
% 81.03/80.82 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 81.03/80.82 & class_Int_Onumber__ring(T_a) )
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 81.03/80.82 => 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)))))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_setprod__pos__nat,axiom,
% 81.03/80.82 ! [V_f_2,V_S_2,T_a] :
% 81.03/80.82 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 81.03/80.82 => ( ! [B_x] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 81.03/80.82 => 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))) )
% 81.03/80.82 => 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))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_UNIV__I,axiom,
% 81.03/80.82 ! [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)))) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_code__numeral__zero__minus__one,axiom,
% 81.03/80.82 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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_finite__Prod__UNIV,axiom,
% 81.03/80.82 ! [T_b,T_a] :
% 81.03/80.82 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 81.03/80.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 81.03/80.82 => 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)))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_finite__option__UNIV,axiom,
% 81.03/80.82 ! [T_a] :
% 81.03/80.82 ( 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))))
% 81.03/80.82 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Union__UNIV,axiom,
% 81.03/80.82 ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_top__apply,axiom,
% 81.03/80.82 ! [V_x_2,T_b,T_a] :
% 81.03/80.82 ( class_Orderings_Otop(T_a)
% 81.03/80.82 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I48_J,axiom,
% 81.03/80.82 ! [V_l_2,V_k_2] :
% 81.03/80.82 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 81.03/80.82 <=> V_k_2 = V_l_2 ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Sup__UNIV,axiom,
% 81.03/80.82 ! [T_a] :
% 81.03/80.82 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.82 => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_UNIV__Plus__UNIV,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_less__eq__int__code_I13_J,axiom,
% 81.03/80.82 ! [V_k2_2,V_k1_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I31_J,axiom,
% 81.03/80.82 ! [V_l_2,V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I14_J,axiom,
% 81.03/80.82 ! [V_l_2,V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_less__int__code_I13_J,axiom,
% 81.03/80.82 ! [V_k2_2,V_k1_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I44_J,axiom,
% 81.03/80.82 ! [V_k_2] :
% 81.03/80.82 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 81.03/80.82 <=> V_k_2 = c_Int_OPls ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I38_J,axiom,
% 81.03/80.82 ! [V_l_2] :
% 81.03/80.82 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 81.03/80.82 <=> c_Int_OPls = V_l_2 ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Bit0__Pls,axiom,
% 81.03/80.82 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I50_J,axiom,
% 81.03/80.82 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I49_J,axiom,
% 81.03/80.82 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_add__Bit0__Bit0,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Bit0__def,axiom,
% 81.03/80.82 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mult__Bit0,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_finite__fun__UNIVD2,axiom,
% 81.03/80.82 ! [T_b,T_a] :
% 81.03/80.82 ( 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))))
% 81.03/80.82 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_diff__bin__simps_I7_J,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_minus__Bit0,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_UNIV__not__empty,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_finite__UNIV,axiom,
% 81.03/80.82 ! [T_a] :
% 81.03/80.82 ( class_Finite__Set_Ofinite(T_a)
% 81.03/80.82 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_subset__UNIV,axiom,
% 81.03/80.82 ! [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)))) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Un__UNIV__right,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Un__UNIV__left,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Int__UNIV__right,axiom,
% 81.03/80.82 ! [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 ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Int__UNIV__left,axiom,
% 81.03/80.82 ! [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 ).
% 81.03/80.82
% 81.03/80.82 fof(fact_card__UNIV__unit,axiom,
% 81.03/80.82 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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_finite__Plus__UNIV__iff,axiom,
% 81.03/80.82 ! [T_b,T_a] :
% 81.03/80.82 ( 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))))
% 81.03/80.82 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 81.03/80.82 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_card__UNIV__bool,axiom,
% 81.03/80.82 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))) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_top__greatest,axiom,
% 81.03/80.82 ! [V_x,T_a] :
% 81.03/80.82 ( class_Orderings_Otop(T_a)
% 81.03/80.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_sup__top__left,axiom,
% 81.03/80.82 ! [V_x,T_a] :
% 81.03/80.82 ( class_Lattices_Obounded__lattice__top(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_sup__top__right,axiom,
% 81.03/80.82 ! [V_x,T_a] :
% 81.03/80.82 ( class_Lattices_Obounded__lattice__top(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_inf__eq__top__iff,axiom,
% 81.03/80.82 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.82 ( class_Lattices_Obounded__lattice__top(T_a)
% 81.03/80.82 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a)
% 81.03/80.82 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a)
% 81.03/80.82 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_inf__top__right,axiom,
% 81.03/80.82 ! [V_x,T_a] :
% 81.03/80.82 ( class_Lattices_Obounded__lattice__top(T_a)
% 81.03/80.82 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_inf__top__left,axiom,
% 81.03/80.82 ! [V_x,T_a] :
% 81.03/80.82 ( class_Lattices_Obounded__lattice__top(T_a)
% 81.03/80.82 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_bin__less__0__simps_I3_J,axiom,
% 81.03/80.82 ! [V_w_2] :
% 81.03/80.82 ( 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)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I21_J,axiom,
% 81.03/80.82 ! [V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I27_J,axiom,
% 81.03/80.82 ! [V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I32_J,axiom,
% 81.03/80.82 ! [V_l_2,V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_less__eq__int__code_I14_J,axiom,
% 81.03/80.82 ! [V_k2_2,V_k1_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I10_J,axiom,
% 81.03/80.82 ! [V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I4_J,axiom,
% 81.03/80.82 ! [V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_less__int__code_I15_J,axiom,
% 81.03/80.82 ! [V_k2_2,V_k1_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I16_J,axiom,
% 81.03/80.82 ! [V_l_2,V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_add__Bit0__Bit1,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_add__Bit1__Bit0,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_diff__bin__simps_I3_J,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_diff__bin__simps_I10_J,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_diff__bin__simps_I9_J,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_neg__number__of__Bit0,axiom,
% 81.03/80.82 ! [V_w_2] :
% 81.03/80.82 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 81.03/80.82 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Diff__UNIV,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 81.03/80.82 ! [V_A_2,T_a] :
% 81.03/80.82 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 81.03/80.82 => ( 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)))
% 81.03/80.82 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_pred__Bit1,axiom,
% 81.03/80.82 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_pred__Bit0,axiom,
% 81.03/80.82 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Compl__empty__eq,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Compl__UNIV__eq,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_finite__compl,axiom,
% 81.03/80.82 ! [V_A_2,T_a] :
% 81.03/80.82 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 81.03/80.82 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_iszero__number__of__Bit0,axiom,
% 81.03/80.82 ! [V_w_2,T_a] :
% 81.03/80.82 ( ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 & class_Int_Oring__char__0(T_a) )
% 81.03/80.82 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2)))
% 81.03/80.82 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Compl__partition,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Compl__partition2,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_succ__Bit0,axiom,
% 81.03/80.82 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_succ__Bit1,axiom,
% 81.03/80.82 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_number__of__Bit0,axiom,
% 81.03/80.82 ! [V_w,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => 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)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_less__eq__int__code_I15_J,axiom,
% 81.03/80.82 ! [V_k2_2,V_k1_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I33_J,axiom,
% 81.03/80.82 ! [V_l_2,V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_less__int__code_I14_J,axiom,
% 81.03/80.82 ! [V_k2_2,V_k1_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_rel__simps_I15_J,axiom,
% 81.03/80.82 ! [V_l_2,V_k_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mult__Bit1,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_compl__bot__eq,axiom,
% 81.03/80.82 ! [T_a] :
% 81.03/80.82 ( class_Lattices_Oboolean__algebra(T_a)
% 81.03/80.82 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_compl__top__eq,axiom,
% 81.03/80.82 ! [T_a] :
% 81.03/80.82 ( class_Lattices_Oboolean__algebra(T_a)
% 81.03/80.82 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_sup__compl__top,axiom,
% 81.03/80.82 ! [V_x,T_a] :
% 81.03/80.82 ( class_Lattices_Oboolean__algebra(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_compl__sup__top,axiom,
% 81.03/80.82 ! [V_x,T_a] :
% 81.03/80.82 ( class_Lattices_Oboolean__algebra(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_diff__bin__simps_I8_J,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_add__Bit1__Bit1,axiom,
% 81.03/80.82 ! [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))) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zero__code__numeral__code,axiom,
% 81.03/80.82 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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_double__number__of__Bit0,axiom,
% 81.03/80.82 ! [V_w,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => 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)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_number__of1,axiom,
% 81.03/80.82 ! [V_n] :
% 81.03/80.82 ( 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)))
% 81.03/80.82 => ( 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))))
% 81.03/80.82 & 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)))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_finite__UNIV__card__ge__0,axiom,
% 81.03/80.82 ! [T_a] :
% 81.03/80.82 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 81.03/80.82 => 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))))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mult__2__right,axiom,
% 81.03/80.82 ! [V_z,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mult__2,axiom,
% 81.03/80.82 ! [V_z,T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_one__add__one__is__two,axiom,
% 81.03/80.82 ! [T_a] :
% 81.03/80.82 ( class_Int_Onumber__ring(T_a)
% 81.03/80.82 => 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))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_semiring__norm_I115_J,axiom,
% 81.03/80.82 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))) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_numeral__2__eq__2,axiom,
% 81.03/80.82 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))) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 81.03/80.82 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))))) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_add__2__eq__Suc_H,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_add__2__eq__Suc,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_nat__mult__2,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_nat__mult__2__right,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 81.03/80.82 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)))) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_nat__1__add__1,axiom,
% 81.03/80.82 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))) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_finite__fun__UNIVD1,axiom,
% 81.03/80.82 ! [T_b,T_a] :
% 81.03/80.82 ( 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))))
% 81.03/80.82 => ( 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))
% 81.03/80.82 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zmod__number__of__Bit1,axiom,
% 81.03/80.82 ! [V_v,V_w] :
% 81.03/80.82 ( ( 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)))
% 81.03/80.82 => 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)) )
% 81.03/80.82 & ( ~ 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)))
% 81.03/80.82 => 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)) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_neg__zmod__mult__2,axiom,
% 81.03/80.82 ! [V_b,V_a] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.82 => 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)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_pos__zmod__mult__2,axiom,
% 81.03/80.82 ! [V_b,V_a] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 81.03/80.82 => 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))) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_pos__zdiv__mult__2,axiom,
% 81.03/80.82 ! [V_b,V_a] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_neg__zdiv__mult__2,axiom,
% 81.03/80.82 ! [V_b,V_a] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_top1I,axiom,
% 81.03/80.82 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__self,axiom,
% 81.03/80.82 ! [V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__by__0,axiom,
% 81.03/80.82 ! [V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__0,axiom,
% 81.03/80.82 ! [V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 81.03/80.82 ! [V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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 ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__div__equality2,axiom,
% 81.03/80.82 ! [V_a,V_b,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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 ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__div__equality,axiom,
% 81.03/80.82 ! [V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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 ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_div__mod__equality2,axiom,
% 81.03/80.82 ! [V_c,V_a,V_b,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_div__mod__equality,axiom,
% 81.03/80.82 ! [V_c,V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zmod__zdiv__equality,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zdiv__zmult1__eq,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zdiv__zmod__equality,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zdiv__zmod__equality2,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zmult__div__cancel,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zmod__zdiv__equality_H,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zmod__zdiv__trivial,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__div__trivial,axiom,
% 81.03/80.82 ! [V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_DIVISION__BY__ZERO,axiom,
% 81.03/80.82 ! [V_a] :
% 81.03/80.82 ( 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)
% 81.03/80.82 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__mod__trivial,axiom,
% 81.03/80.82 ! [V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zdiv__zadd1__eq,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__add__cong,axiom,
% 81.03/80.82 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 81.03/80.82 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 81.03/80.82 => 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) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zmod__simps_I1_J,axiom,
% 81.03/80.82 ! [V_b,V_c,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zmod__simps_I2_J,axiom,
% 81.03/80.82 ! [V_c,V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__add__eq,axiom,
% 81.03/80.82 ! [V_c,V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__add__left__eq,axiom,
% 81.03/80.82 ! [V_c,V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__add__right__eq,axiom,
% 81.03/80.82 ! [V_c,V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__add__self1,axiom,
% 81.03/80.82 ! [V_a,V_b,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__add__self2,axiom,
% 81.03/80.82 ! [V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__mult__cong,axiom,
% 81.03/80.82 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 81.03/80.82 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 81.03/80.82 => 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) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zmod__simps_I4_J,axiom,
% 81.03/80.82 ! [V_b,V_c,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__mult__mult2,axiom,
% 81.03/80.82 ! [V_b,V_c,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__mult__mult1,axiom,
% 81.03/80.82 ! [V_b,V_a,V_c,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__mult__eq,axiom,
% 81.03/80.82 ! [V_c,V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__mult__left__eq,axiom,
% 81.03/80.82 ! [V_c,V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__mult__right__eq,axiom,
% 81.03/80.82 ! [V_c,V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__diff__cong,axiom,
% 81.03/80.82 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Oring__div(T_a)
% 81.03/80.82 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 81.03/80.82 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 81.03/80.82 => 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) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__diff__eq,axiom,
% 81.03/80.82 ! [V_c,V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Oring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__diff__left__eq,axiom,
% 81.03/80.82 ! [V_c,V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Oring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__diff__right__eq,axiom,
% 81.03/80.82 ! [V_c,V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Oring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__minus__eq,axiom,
% 81.03/80.82 ! [V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Oring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__minus__cong,axiom,
% 81.03/80.82 ! [V_a_H,V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Oring__div(T_a)
% 81.03/80.82 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 81.03/80.82 => 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) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zdiv__zero,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zmod__zero,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zmod__self,axiom,
% 81.03/80.82 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zdiv__zminus__zminus,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zdiv__zminus2,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zmod__simps_I3_J,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zmod__zmult1__eq,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zdiff__zmod__left,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zdiff__zmod__right,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zminus__zmod,axiom,
% 81.03/80.82 ! [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) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zmod__zminus__zminus,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zmod__zminus2,axiom,
% 81.03/80.82 ! [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)) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_div__0,axiom,
% 81.03/80.82 ! [V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_div__by__0,axiom,
% 81.03/80.82 ! [V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_div__by__1,axiom,
% 81.03/80.82 ! [V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__mult__self1__is__0,axiom,
% 81.03/80.82 ! [V_a,V_b,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__mult__self2__is__0,axiom,
% 81.03/80.82 ! [V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zmod__zmult2__eq,axiom,
% 81.03/80.82 ! [V_b,V_a,V_c] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 81.03/80.82 => 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)) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__mult__self1,axiom,
% 81.03/80.82 ! [V_b,V_c,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__mult__self2,axiom,
% 81.03/80.82 ! [V_c,V_b,V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => 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) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_mod__by__1,axiom,
% 81.03/80.82 ! [V_a,T_a] :
% 81.03/80.82 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.82 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zdiv__zminus1__eq__if,axiom,
% 81.03/80.82 ! [V_a,V_b] :
% 81.03/80.82 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.82 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.82 => 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)) )
% 81.03/80.82 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.82 => 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)) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zdiv__zminus2__eq__if,axiom,
% 81.03/80.82 ! [V_a,V_b] :
% 81.03/80.82 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.82 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.82 => 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)) )
% 81.03/80.82 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.82 => 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)) ) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 81.03/80.82 ! [V_y,V_x] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 81.03/80.82 => 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))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 81.03/80.82 ! [V_a_2,V_b_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 81.03/80.82 => ( 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)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 81.03/80.82 ! [V_a_2,V_b_2] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.82 => ( 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)))
% 81.03/80.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_div__neg__pos__less0,axiom,
% 81.03/80.82 ! [V_b,V_a] :
% 81.03/80.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.82 => 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))) ) ) ).
% 81.03/80.82
% 81.03/80.82 fof(fact_zdiv__self,axiom,
% 81.03/80.82 ! [V_a] :
% 81.03/80.82 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.83 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zmod__le__nonneg__dividend,axiom,
% 81.03/80.83 ! [V_k,V_m] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 81.03/80.83 ! [V_y,V_x] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_pos__mod__bound,axiom,
% 81.03/80.83 ! [V_a,V_b] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_neg__mod__bound,axiom,
% 81.03/80.83 ! [V_a,V_b] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => 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))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zdiv__number__of__Bit0,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zmod__eq__0__iff,axiom,
% 81.03/80.83 ! [V_d_2,V_m_2] :
% 81.03/80.83 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.83 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zmod__zminus2__not__zero,axiom,
% 81.03/80.83 ! [V_l,V_k] :
% 81.03/80.83 ( 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)
% 81.03/80.83 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zmod__zminus1__not__zero,axiom,
% 81.03/80.83 ! [V_l,V_k] :
% 81.03/80.83 ( 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)
% 81.03/80.83 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__mult__mult1,axiom,
% 81.03/80.83 ! [V_b,V_a,V_c,T_a] :
% 81.03/80.83 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.83 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 => 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) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__mult__mult2,axiom,
% 81.03/80.83 ! [V_b,V_a,V_c,T_a] :
% 81.03/80.83 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.83 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 => 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) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__mult__self1__is__id,axiom,
% 81.03/80.83 ! [V_a,V_b,T_a] :
% 81.03/80.83 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.83 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 => 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 ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__mult__self2__is__id,axiom,
% 81.03/80.83 ! [V_a,V_b,T_a] :
% 81.03/80.83 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.83 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 => 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 ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__mult__mult1__if,axiom,
% 81.03/80.83 ! [V_b,V_a,V_c,T_a] :
% 81.03/80.83 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.83 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 => 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) )
% 81.03/80.83 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 => 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) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__self,axiom,
% 81.03/80.83 ! [V_a,T_a] :
% 81.03/80.83 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.83 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_split__neg__lemma,axiom,
% 81.03/80.83 ! [V_n_2,V_P_2,V_k_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 <=> ! [B_i,B_j] :
% 81.03/80.83 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 81.03/80.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 & 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) )
% 81.03/80.83 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_split__pos__lemma,axiom,
% 81.03/80.83 ! [V_n_2,V_P_2,V_k_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 <=> ! [B_i,B_j] :
% 81.03/80.83 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 81.03/80.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 81.03/80.83 & 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) )
% 81.03/80.83 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zdiv__mono1__neg,axiom,
% 81.03/80.83 ! [V_b,V_a_H,V_a] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zdiv__mono1,axiom,
% 81.03/80.83 ! [V_b,V_a_H,V_a] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__neg__neg__trivial,axiom,
% 81.03/80.83 ! [V_b,V_a] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 81.03/80.83 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zdiv__mono2__neg,axiom,
% 81.03/80.83 ! [V_b,V_b_H,V_a] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 81.03/80.83 => 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))) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__nonpos__pos__le0,axiom,
% 81.03/80.83 ! [V_b,V_a] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 81.03/80.83 ! [V_a_2,V_b_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__pos__pos__trivial,axiom,
% 81.03/80.83 ! [V_b,V_a] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 81.03/80.83 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__nonneg__neg__le0,axiom,
% 81.03/80.83 ! [V_b,V_a] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zdiv__mono2,axiom,
% 81.03/80.83 ! [V_b,V_b_H,V_a] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 81.03/80.83 => 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))) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 81.03/80.83 ! [V_b_2,V_a_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 81.03/80.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 81.03/80.83 ! [V_i_2,V_k_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 81.03/80.83 ! [V_a_2,V_b_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zdiv__eq__0__iff,axiom,
% 81.03/80.83 ! [V_k_2,V_i_2] :
% 81.03/80.83 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.83 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.83 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 81.03/80.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 81.03/80.83 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_int__div__less__self,axiom,
% 81.03/80.83 ! [V_k,V_x] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zdiv__zmult2__eq,axiom,
% 81.03/80.83 ! [V_b,V_a,V_c] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__neg__neg__trivial,axiom,
% 81.03/80.83 ! [V_b,V_a] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 81.03/80.83 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_neg__mod__conj,axiom,
% 81.03/80.83 ! [V_a,V_b] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 & 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_neg__mod__sign,axiom,
% 81.03/80.83 ! [V_a,V_b] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => 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))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__pos__pos__trivial,axiom,
% 81.03/80.83 ! [V_b,V_a] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 81.03/80.83 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_pos__mod__conj,axiom,
% 81.03/80.83 ! [V_a,V_b] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 & 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_pos__mod__sign,axiom,
% 81.03/80.83 ! [V_a,V_b] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.83 => 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))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zmod__zminus2__eq__if,axiom,
% 81.03/80.83 ! [V_b,V_a] :
% 81.03/80.83 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.83 => 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) )
% 81.03/80.83 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.83 => 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) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zmod__zminus1__eq__if,axiom,
% 81.03/80.83 ! [V_b,V_a] :
% 81.03/80.83 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.83 => 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) )
% 81.03/80.83 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__mult__self2,axiom,
% 81.03/80.83 ! [V_c,V_a,V_b,T_a] :
% 81.03/80.83 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.83 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__mult__self1,axiom,
% 81.03/80.83 ! [V_c,V_a,V_b,T_a] :
% 81.03/80.83 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.83 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__add__self1,axiom,
% 81.03/80.83 ! [V_a,V_b,T_a] :
% 81.03/80.83 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.83 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__add__self2,axiom,
% 81.03/80.83 ! [V_a,V_b,T_a] :
% 81.03/80.83 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.83 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__pos__neg__trivial,axiom,
% 81.03/80.83 ! [V_b,V_a] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 => 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) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_divmod__int__rel__div__eq,axiom,
% 81.03/80.83 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 81.03/80.83 ( 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)
% 81.03/80.83 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 81.03/80.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 81.03/80.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 81.03/80.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 81.03/80.83 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.83 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_split__zdiv,axiom,
% 81.03/80.83 ! [V_k_2,V_n_2,V_P_2] :
% 81.03/80.83 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 81.03/80.83 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.83 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 81.03/80.83 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 81.03/80.83 => ! [B_i] :
% 81.03/80.83 ( ? [B_j] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 81.03/80.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 81.03/80.83 & 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) )
% 81.03/80.83 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 81.03/80.83 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => ! [B_i] :
% 81.03/80.83 ( ? [B_j] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 81.03/80.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 & 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) )
% 81.03/80.83 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_divmod__int__rel__mod__eq,axiom,
% 81.03/80.83 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 81.03/80.83 ( 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)
% 81.03/80.83 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 81.03/80.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 81.03/80.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 81.03/80.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 81.03/80.83 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.83 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zmult2__lemma__aux2,axiom,
% 81.03/80.83 ! [V_q,V_r,V_b,V_c] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => 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))) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zmult2__lemma__aux1,axiom,
% 81.03/80.83 ! [V_q,V_r,V_b,V_c] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => 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))) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zmult2__lemma__aux4,axiom,
% 81.03/80.83 ! [V_q,V_b,V_r,V_c] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 81.03/80.83 => 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))) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zmult2__lemma__aux3,axiom,
% 81.03/80.83 ! [V_q,V_b,V_r,V_c] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 81.03/80.83 => 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))) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_split__zmod,axiom,
% 81.03/80.83 ! [V_k_2,V_n_2,V_P_2] :
% 81.03/80.83 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 81.03/80.83 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.83 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 81.03/80.83 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 81.03/80.83 => ! [B_i,B_j] :
% 81.03/80.83 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 81.03/80.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 81.03/80.83 & 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) )
% 81.03/80.83 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 81.03/80.83 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => ! [B_i,B_j] :
% 81.03/80.83 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 81.03/80.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 & 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) )
% 81.03/80.83 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zmod__number__of__Bit0,axiom,
% 81.03/80.83 ! [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))) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zdiv__number__of__Bit1,axiom,
% 81.03/80.83 ! [V_v,V_w] :
% 81.03/80.83 ( ( 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)))
% 81.03/80.83 => 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)) )
% 81.03/80.83 & ( ~ 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)))
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__of__aux__code,axiom,
% 81.03/80.83 ! [V_n,V_i] :
% 81.03/80.83 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 81.03/80.83 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 81.03/80.83 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_z3div__def,axiom,
% 81.03/80.83 ! [V_k,V_l] :
% 81.03/80.83 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 81.03/80.83 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 81.03/80.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_z3mod__def,axiom,
% 81.03/80.83 ! [V_k,V_l] :
% 81.03/80.83 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 81.03/80.83 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 81.03/80.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_of__nat__double,axiom,
% 81.03/80.83 ! [V_x,T_a] :
% 81.03/80.83 ( class_Rings_Osemiring__1(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__minus1__odd,axiom,
% 81.03/80.83 ! [V_n,T_a] :
% 81.03/80.83 ( class_Rings_Oring__1(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__add1__eq,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__power__eq,axiom,
% 81.03/80.83 ! [V_n,V_z] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 81.03/80.83 ! [V_n,V_x] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__mod__equality_H,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mult__div__cancel,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Divides_Omod__div__equality_H,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__mult2__eq,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__mult1__eq,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 81.03/80.83 ! [V_q,V_y,V_x,T_a] :
% 81.03/80.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zpower__int,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_int__power,axiom,
% 81.03/80.83 ! [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) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__le__dividend,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__le__mono,axiom,
% 81.03/80.83 ! [V_k,V_n,V_m] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 81.03/80.83 => 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))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 81.03/80.83 ! [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) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__mult2__eq,axiom,
% 81.03/80.83 ! [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) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__less,axiom,
% 81.03/80.83 ! [V_n,V_m] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 81.03/80.83 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__less__eq__dividend,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__mult__distrib2,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__mult__distrib,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__int,axiom,
% 81.03/80.83 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 81.03/80.83
% 81.03/80.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 81.03/80.83 ! [V_q,V_p,V_x,T_a] :
% 81.03/80.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zpower__zpower,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 81.03/80.83 ! [V_x,T_a] :
% 81.03/80.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 81.03/80.83 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zpower__zmod,axiom,
% 81.03/80.83 ! [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) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__nat__number__of,axiom,
% 81.03/80.83 ! [V_n,V_v] :
% 81.03/80.83 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 81.03/80.83 => 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) )
% 81.03/80.83 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__nat__number__of__number__of,axiom,
% 81.03/80.83 ! [V_w,V_v] :
% 81.03/80.83 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 81.03/80.83 => 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)) )
% 81.03/80.83 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 81.03/80.83 ! [V_y,V_x] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__div__distrib,axiom,
% 81.03/80.83 ! [V_y,V_x] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 81.03/80.83 ! [V_y,V_x] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__mod__distrib,axiom,
% 81.03/80.83 ! [V_y,V_x] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__1,axiom,
% 81.03/80.83 ! [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 ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__less,axiom,
% 81.03/80.83 ! [V_n,V_m] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 81.03/80.83 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__mult__div__cancel__disj,axiom,
% 81.03/80.83 ! [V_n,V_m,V_k] :
% 81.03/80.83 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.83 => 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) )
% 81.03/80.83 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.83 => 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) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 81.03/80.83 ! [V_q,V_x,T_a] :
% 81.03/80.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 81.03/80.83 ! [V_q,V_x,T_a] :
% 81.03/80.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 81.03/80.83 ! [V_q,V_x,T_a] :
% 81.03/80.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__0,axiom,
% 81.03/80.83 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 81.03/80.83 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__Suc,axiom,
% 81.03/80.83 ! [V_n,V_m] :
% 81.03/80.83 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 81.03/80.83 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 81.03/80.83 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__1,axiom,
% 81.03/80.83 ! [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) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__less__divisor,axiom,
% 81.03/80.83 ! [V_m,V_n] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 81.03/80.83 ! [V_x,T_a] :
% 81.03/80.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 81.03/80.83 ! [V_q,V_p,V_x,T_a] :
% 81.03/80.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_eq__nat__nat__iff,axiom,
% 81.03/80.83 ! [V_z_H_2,V_z_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 81.03/80.83 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 81.03/80.83 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 81.03/80.83 ! [V_y_2,V_x_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 81.03/80.83 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 81.03/80.83 <=> V_x_2 = V_y_2 ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_all__nat,axiom,
% 81.03/80.83 ! [V_P_2] :
% 81.03/80.83 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 81.03/80.83 <=> ! [B_x] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 81.03/80.83 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_ex__nat,axiom,
% 81.03/80.83 ! [V_P_2] :
% 81.03/80.83 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 81.03/80.83 <=> ? [B_x] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 81.03/80.83 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__eq__0__iff,axiom,
% 81.03/80.83 ! [V_d_2,V_m_2] :
% 81.03/80.83 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.83 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 81.03/80.83 ! [V_n,V_x] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 81.03/80.83 => 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))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__geq,axiom,
% 81.03/80.83 ! [V_n,V_m] :
% 81.03/80.83 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__if,axiom,
% 81.03/80.83 ! [V_n,V_m] :
% 81.03/80.83 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 81.03/80.83 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 81.03/80.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 81.03/80.83 => 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) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__mult__self3,axiom,
% 81.03/80.83 ! [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) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_le__mod__geq,axiom,
% 81.03/80.83 ! [V_m,V_n] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zdiv__int,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__number__of__def,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__number__of,axiom,
% 81.03/80.83 ! [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) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zpower__zadd__distrib,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 81.03/80.83 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zmod__int,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_neg__nat,axiom,
% 81.03/80.83 ! [V_z] :
% 81.03/80.83 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 81.03/80.83 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_not__neg__nat,axiom,
% 81.03/80.83 ! [V_z] :
% 81.03/80.83 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 81.03/80.83 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Ints__power,axiom,
% 81.03/80.83 ! [V_n_2,V_a_2,T_a] :
% 81.03/80.83 ( class_Rings_Oring__1(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__nat__number__of,axiom,
% 81.03/80.83 ! [V_v_H,V_v] :
% 81.03/80.83 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 81.03/80.83 => 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) )
% 81.03/80.83 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__nat__number__of,axiom,
% 81.03/80.83 ! [V_v_H,V_v] :
% 81.03/80.83 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 81.03/80.83 => 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) )
% 81.03/80.83 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 81.03/80.83 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 81.03/80.83 => 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) )
% 81.03/80.83 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 81.03/80.83 => 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))) ) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_one__div__nat__number__of,axiom,
% 81.03/80.83 ! [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))) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__le__mono2,axiom,
% 81.03/80.83 ! [V_k,V_n,V_m] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__mult__self1__is__m,axiom,
% 81.03/80.83 ! [V_m,V_n] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 81.03/80.83 => 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 ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__mult__self__is__m,axiom,
% 81.03/80.83 ! [V_m,V_n] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 81.03/80.83 => 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 ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__mult__div__cancel1,axiom,
% 81.03/80.83 ! [V_n,V_m,V_k] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__less__dividend,axiom,
% 81.03/80.83 ! [V_m,V_n] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__le__0,axiom,
% 81.03/80.83 ! [V_z] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__0__iff,axiom,
% 81.03/80.83 ! [V_i_2] :
% 81.03/80.83 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__mono__iff,axiom,
% 81.03/80.83 ! [V_w_2,V_z_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zless__nat__conj,axiom,
% 81.03/80.83 ! [V_z_2,V_w_2] :
% 81.03/80.83 ( 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)))
% 81.03/80.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 81.03/80.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__le__divisor,axiom,
% 81.03/80.83 ! [V_m,V_n] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 81.03/80.83 ! [V_y_2,V_x_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__1,axiom,
% 81.03/80.83 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__mult__self4,axiom,
% 81.03/80.83 ! [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) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__0__le,axiom,
% 81.03/80.83 ! [V_z] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 81.03/80.83 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_int__eq__iff,axiom,
% 81.03/80.83 ! [V_z_2,V_m_2] :
% 81.03/80.83 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 81.03/80.83 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 81.03/80.83 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_int__nat__eq,axiom,
% 81.03/80.83 ! [V_z] :
% 81.03/80.83 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 81.03/80.83 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 81.03/80.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 81.03/80.83 => 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) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zless__nat__eq__int__zless,axiom,
% 81.03/80.83 ! [V_z_2,V_m_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 81.03/80.83 <=> 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__zminus__int,axiom,
% 81.03/80.83 ! [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) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zero__le__zpower__abs,axiom,
% 81.03/80.83 ! [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))) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__abs__mult__distrib,axiom,
% 81.03/80.83 ! [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))) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_one__mod__nat__number__of,axiom,
% 81.03/80.83 ! [V_v_H] :
% 81.03/80.83 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 81.03/80.83 => 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)) )
% 81.03/80.83 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__geq,axiom,
% 81.03/80.83 ! [V_m,V_n] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 81.03/80.83 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__if,axiom,
% 81.03/80.83 ! [V_m,V_n] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 81.03/80.83 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 81.03/80.83 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 81.03/80.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 81.03/80.83 => 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)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_split__div,axiom,
% 81.03/80.83 ! [V_k_2,V_n_2,V_P_2] :
% 81.03/80.83 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 81.03/80.83 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.83 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 81.03/80.83 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.83 => ! [B_i,B_j] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 81.03/80.83 => ( 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)
% 81.03/80.83 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zero__less__nat__eq,axiom,
% 81.03/80.83 ! [V_z_2] :
% 81.03/80.83 ( 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)))
% 81.03/80.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__less__eq__zless,axiom,
% 81.03/80.83 ! [V_z_2,V_w_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 81.03/80.83 ! [V_y_2,V_x_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__eq__iff2,axiom,
% 81.03/80.83 ! [V_w_2,V_m_2] :
% 81.03/80.83 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 81.03/80.83 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 81.03/80.83 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 81.03/80.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 81.03/80.83 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__eq__iff,axiom,
% 81.03/80.83 ! [V_m_2,V_w_2] :
% 81.03/80.83 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 81.03/80.83 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 81.03/80.83 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 81.03/80.83 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 81.03/80.83 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__le__eq__zle,axiom,
% 81.03/80.83 ! [V_z_2,V_w_2] :
% 81.03/80.83 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 81.03/80.83 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 81.03/80.83 => ( 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)))
% 81.03/80.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_split__nat,axiom,
% 81.03/80.83 ! [V_i_2,V_P_2] :
% 81.03/80.83 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 81.03/80.83 <=> ( ! [B_n] :
% 81.03/80.83 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 81.03/80.83 => hBOOL(hAPP(V_P_2,B_n)) )
% 81.03/80.83 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_split__mod,axiom,
% 81.03/80.83 ! [V_k_2,V_n_2,V_P_2] :
% 81.03/80.83 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 81.03/80.83 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.83 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 81.03/80.83 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.83 => ! [B_i,B_j] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 81.03/80.83 => ( 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)
% 81.03/80.83 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__lemma,axiom,
% 81.03/80.83 ! [V_q,V_b,V_r,V_c] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__add__distrib,axiom,
% 81.03/80.83 ! [V_z_H,V_z] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 81.03/80.83 ! [V_y,V_x] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power3__eq__cube,axiom,
% 81.03/80.83 ! [V_a,T_a] :
% 81.03/80.83 ( class_Groups_Omonoid__mult(T_a)
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_int__eq__iff__number__of,axiom,
% 81.03/80.83 ! [V_v_2,V_m_2] :
% 81.03/80.83 ( 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)
% 81.03/80.83 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 81.03/80.83 & 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__mult__distrib,axiom,
% 81.03/80.83 ! [V_z_H,V_z] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 81.03/80.83 ! [V_y,V_x] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__diff__distrib,axiom,
% 81.03/80.83 ! [V_z,V_z_H] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Suc__times__mod__eq,axiom,
% 81.03/80.83 ! [V_m,V_k] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 81.03/80.83 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)))) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__eq__if,axiom,
% 81.03/80.83 ! [V_p,V_m] :
% 81.03/80.83 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.83 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 81.03/80.83 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.83 => 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)))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zero__less__zpower__abs__iff,axiom,
% 81.03/80.83 ! [V_n_2,V_x_2] :
% 81.03/80.83 ( 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)))
% 81.03/80.83 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.83 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 81.03/80.83 ! [V_y,V_x] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_le__div__geq,axiom,
% 81.03/80.83 ! [V_m,V_n] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_split__div_H,axiom,
% 81.03/80.83 ! [V_n_2,V_m_2,V_P_2] :
% 81.03/80.83 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 81.03/80.83 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.83 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 81.03/80.83 | ? [B_q] :
% 81.03/80.83 ( 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))
% 81.03/80.83 & 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))))
% 81.03/80.83 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_split__div__lemma,axiom,
% 81.03/80.83 ! [V_m_2,V_q_2,V_n_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 81.03/80.83 => ( ( 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))
% 81.03/80.83 & 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)))) )
% 81.03/80.83 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Suc__div__eq__add3__div,axiom,
% 81.03/80.83 ! [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) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__Suc__eq__div__add3,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div2__Suc__Suc,axiom,
% 81.03/80.83 ! [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))))) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_add__self__div__2,axiom,
% 81.03/80.83 ! [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 ).
% 81.03/80.83
% 81.03/80.83 fof(fact_one__less__nat__eq,axiom,
% 81.03/80.83 ! [V_z_2] :
% 81.03/80.83 ( 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)))
% 81.03/80.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__less__iff,axiom,
% 81.03/80.83 ! [V_m_2,V_w_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 81.03/80.83 <=> 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 81.03/80.83 ! [V_z] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 81.03/80.83 ! [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) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zero__eq__power2,axiom,
% 81.03/80.83 ! [V_a_2,T_a] :
% 81.03/80.83 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 81.03/80.83 => ( 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)
% 81.03/80.83 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zero__power2,axiom,
% 81.03/80.83 ! [T_a] :
% 81.03/80.83 ( class_Rings_Osemiring__1(T_a)
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 81.03/80.83 ! [V_x,T_a] :
% 81.03/80.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 81.03/80.83 => 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)))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power2__eq__square,axiom,
% 81.03/80.83 ! [V_a,T_a] :
% 81.03/80.83 ( class_Groups_Omonoid__mult(T_a)
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod2__Suc__Suc,axiom,
% 81.03/80.83 ! [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)))) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_one__power2,axiom,
% 81.03/80.83 ! [T_a] :
% 81.03/80.83 ( class_Rings_Osemiring__1(T_a)
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 81.03/80.83 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)))) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power2__minus,axiom,
% 81.03/80.83 ! [V_a,T_a] :
% 81.03/80.83 ( class_Rings_Oring__1(T_a)
% 81.03/80.83 => 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)))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__mult__distrib__neg,axiom,
% 81.03/80.83 ! [V_z_H,V_z] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.83 => 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))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__even__eq,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Groups_Omonoid__mult(T_a)
% 81.03/80.83 => 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)))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_abs__power2,axiom,
% 81.03/80.83 ! [V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => 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)))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power2__abs,axiom,
% 81.03/80.83 ! [V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => 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)))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power2__eq__imp__eq,axiom,
% 81.03/80.83 ! [V_y,V_x,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( 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))))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 81.03/80.83 => V_x = V_y ) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power2__le__imp__le,axiom,
% 81.03/80.83 ! [V_y,V_x,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( 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))))))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 81.03/80.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zero__le__power2,axiom,
% 81.03/80.83 ! [V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => 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)))))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power2__less__0,axiom,
% 81.03/80.83 ! [V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => ~ 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))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zero__less__power2,axiom,
% 81.03/80.83 ! [V_a_2,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => ( 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))))))
% 81.03/80.83 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_sum__power2__eq__zero__iff,axiom,
% 81.03/80.83 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => ( 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)
% 81.03/80.83 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__2,axiom,
% 81.03/80.83 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))) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power2__eq__square__number__of,axiom,
% 81.03/80.83 ! [V_w,T_b] :
% 81.03/80.83 ( ( class_Groups_Omonoid__mult(T_b)
% 81.03/80.83 & class_Int_Onumber(T_b) )
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power2__eq__1__iff,axiom,
% 81.03/80.83 ! [V_a_2,T_a] :
% 81.03/80.83 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 81.03/80.83 => ( 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)
% 81.03/80.83 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a)
% 81.03/80.83 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 81.03/80.83 ! [V_n,V_x,T_a] :
% 81.03/80.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__minus__even,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Oring__1(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_div__2__gt__zero,axiom,
% 81.03/80.83 ! [V_n] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 81.03/80.83 => 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)))))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power2__less__imp__less,axiom,
% 81.03/80.83 ! [V_y,V_x,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( 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))))))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 81.03/80.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_sum__power2__le__zero__iff,axiom,
% 81.03/80.83 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => ( 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)))
% 81.03/80.83 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_sum__power2__ge__zero,axiom,
% 81.03/80.83 ! [V_y,V_x,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => 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))))))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_not__sum__power2__lt__zero,axiom,
% 81.03/80.83 ! [V_y,V_x,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => ~ 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))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_sum__power2__gt__zero__iff,axiom,
% 81.03/80.83 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => ( 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)))))))
% 81.03/80.83 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power2__sum,axiom,
% 81.03/80.83 ! [V_y,V_x,T_a] :
% 81.03/80.83 ( class_Int_Onumber__ring(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zero__le__even__power_H,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => 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)))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 81.03/80.83 ! [V_n,V_x,T_a] :
% 81.03/80.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 81.03/80.83 => 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))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__odd__eq,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Groups_Omonoid__mult(T_a)
% 81.03/80.83 => 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))))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_mod2__gr__0,axiom,
% 81.03/80.83 ! [V_m_2] :
% 81.03/80.83 ( 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))))))
% 81.03/80.83 <=> 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__minus1__even,axiom,
% 81.03/80.83 ! [V_n,T_a] :
% 81.03/80.83 ( class_Rings_Oring__1(T_a)
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_int__power__div__base,axiom,
% 81.03/80.83 ! [V_k,V_m] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 81.03/80.83 => 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)))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 81.03/80.83 ! [V_n] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 81.03/80.83 => 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)))))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power2__diff,axiom,
% 81.03/80.83 ! [V_y,V_x,T_a] :
% 81.03/80.83 ( class_Int_Onumber__ring(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => ( 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)))))
% 81.03/80.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_odd__power__less__zero,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_int__of__code,axiom,
% 81.03/80.83 ! [V_k] :
% 81.03/80.83 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 81.03/80.83 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 81.03/80.83 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 81.03/80.83 => ( ( 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)
% 81.03/80.83 => 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)))))) )
% 81.03/80.83 & ( 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)
% 81.03/80.83 => 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)) ) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__strict__mono,axiom,
% 81.03/80.83 ! [V_n,V_b,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 81.03/80.83 => 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))) ) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__diff,axiom,
% 81.03/80.83 ! [V_m,V_n,V_a,T_a] :
% 81.03/80.83 ( class_Fields_Ofield(T_a)
% 81.03/80.83 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 81.03/80.83 => 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)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_one__less__power,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 81.03/80.83 => 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))) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__increasing__iff,axiom,
% 81.03/80.83 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_field__power__not__zero,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 81.03/80.83 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__Suc__0,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 81.03/80.83 ! [V_m_2,V_x_2] :
% 81.03/80.83 ( 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))
% 81.03/80.83 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.83 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__power__less__imp__less,axiom,
% 81.03/80.83 ! [V_n,V_m,V_i] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__zero__less__power__iff,axiom,
% 81.03/80.83 ! [V_n_2,V_x_2] :
% 81.03/80.83 ( 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)))
% 81.03/80.83 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 81.03/80.83 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__mult__distrib,axiom,
% 81.03/80.83 ! [V_n,V_b,V_a,T_a] :
% 81.03/80.83 ( class_Groups_Ocomm__monoid__mult(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__commutes,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Groups_Omonoid__mult(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__one,axiom,
% 81.03/80.83 ! [V_n,T_a] :
% 81.03/80.83 ( class_Groups_Omonoid__mult(T_a)
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_of__nat__power,axiom,
% 81.03/80.83 ! [V_n,V_m,T_a] :
% 81.03/80.83 ( class_Rings_Osemiring__1(T_a)
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__mult,axiom,
% 81.03/80.83 ! [V_n,V_m,V_a,T_a] :
% 81.03/80.83 ( class_Groups_Omonoid__mult(T_a)
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__divide,axiom,
% 81.03/80.83 ! [V_n,V_b,V_a,T_a] :
% 81.03/80.83 ( class_Fields_Ofield__inverse__zero(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__abs,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__one__right,axiom,
% 81.03/80.83 ! [V_a,T_a] :
% 81.03/80.83 ( class_Groups_Omonoid__mult(T_a)
% 81.03/80.83 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__mono,axiom,
% 81.03/80.83 ! [V_n,V_b,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 81.03/80.83 => 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))) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zero__le__power,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zero__less__power,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__eq__0__iff,axiom,
% 81.03/80.83 ! [V_n_2,V_a_2,T_a] :
% 81.03/80.83 ( ( class_Power_Opower(T_a)
% 81.03/80.83 & class_Rings_Omult__zero(T_a)
% 81.03/80.83 & class_Rings_Ono__zero__divisors(T_a)
% 81.03/80.83 & class_Rings_Ozero__neq__one(T_a) )
% 81.03/80.83 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_one__le__power,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 81.03/80.83 => 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))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__0__Suc,axiom,
% 81.03/80.83 ! [V_n,T_a] :
% 81.03/80.83 ( ( class_Power_Opower(T_a)
% 81.03/80.83 & class_Rings_Osemiring__0(T_a) )
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__inject__exp,axiom,
% 81.03/80.83 ! [V_n_2,V_m_2,V_a_2,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2))
% 81.03/80.83 => ( 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)
% 81.03/80.83 <=> V_m_2 = V_n_2 ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__Suc,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Power_Opower(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__Suc2,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Groups_Omonoid__mult(T_a)
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__one__le__power,axiom,
% 81.03/80.83 ! [V_n,V_i] :
% 81.03/80.83 ( 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))
% 81.03/80.83 => 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))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__0,axiom,
% 81.03/80.83 ! [V_a,T_a] :
% 81.03/80.83 ( class_Power_Opower(T_a)
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__add,axiom,
% 81.03/80.83 ! [V_n,V_m,V_a,T_a] :
% 81.03/80.83 ( class_Groups_Omonoid__mult(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nonzero__power__divide,axiom,
% 81.03/80.83 ! [V_n,V_a,V_b,T_a] :
% 81.03/80.83 ( class_Fields_Ofield(T_a)
% 81.03/80.83 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.83 => 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)) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__one__over,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Fields_Ofield__inverse__zero(T_a)
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_abs__power__minus,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__less__imp__less__base,axiom,
% 81.03/80.83 ! [V_b,V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( 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)))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 81.03/80.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__inject__base,axiom,
% 81.03/80.83 ! [V_b,V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( 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))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 81.03/80.83 => V_a = V_b ) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__le__imp__le__base,axiom,
% 81.03/80.83 ! [V_b,V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( 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))))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 81.03/80.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__gt1__lemma,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 81.03/80.83 => 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)))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__less__power__Suc,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 81.03/80.83 => 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)))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__0__left,axiom,
% 81.03/80.83 ! [V_n,T_a] :
% 81.03/80.83 ( ( class_Power_Opower(T_a)
% 81.03/80.83 & class_Rings_Osemiring__0(T_a) )
% 81.03/80.83 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.83 => 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) )
% 81.03/80.83 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.83 => 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) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__gt1,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 81.03/80.83 => 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)))) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__strict__increasing,axiom,
% 81.03/80.83 ! [V_a,V_N,V_n,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 81.03/80.83 => 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))) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__less__imp__less__exp,axiom,
% 81.03/80.83 ! [V_n,V_m,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__strict__increasing__iff,axiom,
% 81.03/80.83 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_zero__le__power__abs,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.83 => 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))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__increasing,axiom,
% 81.03/80.83 ! [V_a,V_N,V_n,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 81.03/80.83 => 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))) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__minus,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Oring__1(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__Suc__less,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 81.03/80.83 => 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))) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__eq__imp__eq__base,axiom,
% 81.03/80.83 ! [V_b,V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( 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)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 81.03/80.83 => V_a = V_b ) ) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__Suc__less__one,axiom,
% 81.03/80.83 ! [V_n,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 81.03/80.83 => 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))) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__strict__decreasing,axiom,
% 81.03/80.83 ! [V_a,V_N,V_n,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 81.03/80.83 => 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))) ) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__decreasing,axiom,
% 81.03/80.83 ! [V_a,V_N,V_n,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 81.03/80.83 => 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))) ) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__le__imp__le__exp,axiom,
% 81.03/80.83 ! [V_n,V_m,V_a,T_a] :
% 81.03/80.83 ( class_Rings_Olinordered__semidom(T_a)
% 81.03/80.83 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 81.03/80.83 => ( 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)))
% 81.03/80.83 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_nat__aux__def,axiom,
% 81.03/80.83 ! [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) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_transfer__morphism__nat__int,axiom,
% 81.03/80.83 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))) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_card__Pow,axiom,
% 81.03/80.83 ! [V_A_2,T_a] :
% 81.03/80.83 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__power__power,axiom,
% 81.03/80.83 ! [T_a] :
% 81.03/80.83 ( class_Power_Opower(T_a)
% 81.03/80.83 => 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)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_power__m1__odd,axiom,
% 81.03/80.83 ! [V_n,T_a] :
% 81.03/80.83 ( class_Int_Onumber__ring(T_a)
% 81.03/80.83 => 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) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_PowI,axiom,
% 81.03/80.83 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.83 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_rel__simps_I40_J,axiom,
% 81.03/80.83 c_Int_OMin != c_Int_OPls ).
% 81.03/80.83
% 81.03/80.83 fof(fact_rel__simps_I37_J,axiom,
% 81.03/80.83 c_Int_OPls != c_Int_OMin ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Bit1__Min,axiom,
% 81.03/80.83 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 81.03/80.83
% 81.03/80.83 fof(fact_rel__simps_I43_J,axiom,
% 81.03/80.83 ! [V_l_2] :
% 81.03/80.83 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 81.03/80.83 <=> c_Int_OMin = V_l_2 ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_rel__simps_I47_J,axiom,
% 81.03/80.83 ! [V_k_2] :
% 81.03/80.83 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 81.03/80.83 <=> V_k_2 = c_Int_OMin ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_rel__simps_I42_J,axiom,
% 81.03/80.83 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_rel__simps_I45_J,axiom,
% 81.03/80.83 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 81.03/80.83
% 81.03/80.83 fof(fact_rel__simps_I7_J,axiom,
% 81.03/80.83 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_rel__simps_I24_J,axiom,
% 81.03/80.83 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Pow__top,axiom,
% 81.03/80.83 ! [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))) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Union__Pow__eq,axiom,
% 81.03/80.83 ! [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 ).
% 81.03/80.83
% 81.03/80.83 fof(fact_Pow__not__empty,axiom,
% 81.03/80.83 ! [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)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_bin__less__0__simps_I2_J,axiom,
% 81.03/80.83 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_rel__simps_I23_J,axiom,
% 81.03/80.83 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_rel__simps_I20_J,axiom,
% 81.03/80.83 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_rel__simps_I26_J,axiom,
% 81.03/80.83 ! [V_k_2] :
% 81.03/80.83 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 81.03/80.83 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 81.03/80.83
% 81.03/80.83 fof(fact_rel__simps_I30_J,axiom,
% 81.03/80.83 ! [V_k_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_rel__simps_I3_J,axiom,
% 81.03/80.84 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_rel__simps_I6_J,axiom,
% 81.03/80.84 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_rel__simps_I13_J,axiom,
% 81.03/80.84 ! [V_k_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_rel__simps_I9_J,axiom,
% 81.03/80.84 ! [V_k_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_rel__simps_I28_J,axiom,
% 81.03/80.84 ! [V_k_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_rel__simps_I8_J,axiom,
% 81.03/80.84 ! [V_k_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_eq__number__of__Pls__Min,axiom,
% 81.03/80.84 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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Int_OMin__def,axiom,
% 81.03/80.84 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_mult__Min,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_neg__number__of__Min,axiom,
% 81.03/80.84 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_pred__Pls,axiom,
% 81.03/80.84 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 81.03/80.84
% 81.03/80.84 fof(fact_add__Min,axiom,
% 81.03/80.84 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_add__Min__right,axiom,
% 81.03/80.84 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_pred__Min,axiom,
% 81.03/80.84 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_nonzero__number__of__Min,axiom,
% 81.03/80.84 ! [T_a] :
% 81.03/80.84 ( class_Int_Onumber__ring(T_a)
% 81.03/80.84 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_succ__Min,axiom,
% 81.03/80.84 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 81.03/80.84
% 81.03/80.84 fof(fact_diff__bin__simps_I2_J,axiom,
% 81.03/80.84 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Pow__bottom,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_PowD,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Pow__iff,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Pow__mono,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.84 => 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))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__Pow__iff,axiom,
% 81.03/80.84 ! [V_A_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)))
% 81.03/80.84 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_mult__minus1__right,axiom,
% 81.03/80.84 ! [V_z,T_a] :
% 81.03/80.84 ( class_Int_Onumber__ring(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_mult__minus1,axiom,
% 81.03/80.84 ! [V_z,T_a] :
% 81.03/80.84 ( class_Int_Onumber__ring(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_subset__Pow__Union,axiom,
% 81.03/80.84 ! [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)))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_number__of__Min,axiom,
% 81.03/80.84 ! [T_a] :
% 81.03/80.84 ( class_Int_Onumber__ring(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_arith__simps_I31_J,axiom,
% 81.03/80.84 ! [T_a] :
% 81.03/80.84 ( class_Int_Onumber__ring(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_abs__minus__one,axiom,
% 81.03/80.84 ! [T_a] :
% 81.03/80.84 ( ( class_Int_Onumber__ring(T_a)
% 81.03/80.84 & class_Rings_Olinordered__idom(T_a) )
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_divide__minus1,axiom,
% 81.03/80.84 ! [V_x,T_a] :
% 81.03/80.84 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 81.03/80.84 & class_Int_Onumber__ring(T_a) )
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_rel__simps_I11_J,axiom,
% 81.03/80.84 ! [V_k_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_rel__simps_I25_J,axiom,
% 81.03/80.84 ! [V_k_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_zmod__minus1__right,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_diff__bin__simps_I4_J,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_minus__Min,axiom,
% 81.03/80.84 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 81.03/80.84 ! [V_n,V_m] :
% 81.03/80.84 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 81.03/80.84 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 81.03/80.84 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_zmult__eq__1__iff,axiom,
% 81.03/80.84 ! [V_n_2,V_m_2] :
% 81.03/80.84 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 81.03/80.84 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 81.03/80.84 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 81.03/80.84 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 81.03/80.84 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_diff__bin__simps_I5_J,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_diff__bin__simps_I6_J,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_power_Opower_Opower__0,axiom,
% 81.03/80.84 ! [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 ).
% 81.03/80.84
% 81.03/80.84 fof(fact_power_Opower_Opower__Suc,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Pow__UNIV,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_zdiv__minus1__right,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Pow__Int__eq,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_minus1__divide,axiom,
% 81.03/80.84 ! [V_x,T_a] :
% 81.03/80.84 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 81.03/80.84 & class_Int_Onumber__ring(T_a) )
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_abs__power__minus__one,axiom,
% 81.03/80.84 ! [V_n,T_a] :
% 81.03/80.84 ( ( class_Int_Onumber__ring(T_a)
% 81.03/80.84 & class_Rings_Olinordered__idom(T_a) )
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_div__eq__minus1,axiom,
% 81.03/80.84 ! [V_b] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Pow__empty,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Un__Pow__subset,axiom,
% 81.03/80.84 ! [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)))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_div__pos__neg__trivial,axiom,
% 81.03/80.84 ! [V_b,V_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 81.03/80.84 => ( 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)))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_zmod__minus1,axiom,
% 81.03/80.84 ! [V_b] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_power__m1__even,axiom,
% 81.03/80.84 ! [V_n,T_a] :
% 81.03/80.84 ( class_Int_Onumber__ring(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_code__numeral_Osize_I1_J,axiom,
% 81.03/80.84 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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_iso__tuple__UNIV__I,axiom,
% 81.03/80.84 ! [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)))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__of__nat,axiom,
% 81.03/80.84 ! [V_k,T_a] :
% 81.03/80.84 ( class_Rings_Oring__1(T_a)
% 81.03/80.84 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.84 => 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)))) )
% 81.03/80.84 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.84 => 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)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_code__numeral_Osize_I3_J,axiom,
% 81.03/80.84 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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inf__fold__inf,axiom,
% 81.03/80.84 ! [V_A_2,T_a] :
% 81.03/80.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__Inter,axiom,
% 81.03/80.84 ! [V_M_2,T_a] :
% 81.03/80.84 ( ? [B_x] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2))
% 81.03/80.84 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) )
% 81.03/80.84 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_InterE,axiom,
% 81.03/80.84 ! [V_X_2,V_C_2,V_A_2,T_a] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_InterD,axiom,
% 81.03/80.84 ! [V_X_2,V_C_2,V_A_2,T_a] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__eq__iff,axiom,
% 81.03/80.84 ! [V_z_2,V_w_2,T_a] :
% 81.03/80.84 ( class_Int_Oring__char__0(T_a)
% 81.03/80.84 => ( 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)
% 81.03/80.84 <=> V_w_2 = V_z_2 ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_number__of__eq,axiom,
% 81.03/80.84 ! [V_k,T_a] :
% 81.03/80.84 ( class_Int_Onumber__ring(T_a)
% 81.03/80.84 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_int__number__of__def,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__int__eq,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_le__Inf__iff,axiom,
% 81.03/80.84 ! [V_A_2,V_b_2,T_a] :
% 81.03/80.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)))
% 81.03/80.84 <=> ! [B_x] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inf__less__iff,axiom,
% 81.03/80.84 ! [V_a_2,V_S_2,T_a] :
% 81.03/80.84 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.84 & class_Orderings_Olinorder(T_a) )
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2))
% 81.03/80.84 <=> ? [B_x] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 81.03/80.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__0,axiom,
% 81.03/80.84 ! [T_a] :
% 81.03/80.84 ( class_Rings_Oring__1(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__0__eq__iff,axiom,
% 81.03/80.84 ! [V_z_2,T_a] :
% 81.03/80.84 ( class_Int_Oring__char__0(T_a)
% 81.03/80.84 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)
% 81.03/80.84 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__eq__0__iff,axiom,
% 81.03/80.84 ! [V_z_2,T_a] :
% 81.03/80.84 ( class_Int_Oring__char__0(T_a)
% 81.03/80.84 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.84 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__le__iff,axiom,
% 81.03/80.84 ! [V_z_2,V_w_2,T_a] :
% 81.03/80.84 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inter__lower,axiom,
% 81.03/80.84 ! [V_A_2,V_B_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__less__iff,axiom,
% 81.03/80.84 ! [V_z_2,V_w_2,T_a] :
% 81.03/80.84 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__add,axiom,
% 81.03/80.84 ! [V_z,V_w,T_a] :
% 81.03/80.84 ( class_Rings_Oring__1(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__number__of__eq,axiom,
% 81.03/80.84 ! [V_v,T_a] :
% 81.03/80.84 ( class_Int_Onumber__ring(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__mult,axiom,
% 81.03/80.84 ! [V_z,V_w,T_a] :
% 81.03/80.84 ( class_Rings_Oring__1(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__1,axiom,
% 81.03/80.84 ! [T_a] :
% 81.03/80.84 ( class_Rings_Oring__1(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__diff,axiom,
% 81.03/80.84 ! [V_z,V_w,T_a] :
% 81.03/80.84 ( class_Rings_Oring__1(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__of__nat__eq,axiom,
% 81.03/80.84 ! [V_n,T_a] :
% 81.03/80.84 ( class_Rings_Oring__1(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__minus,axiom,
% 81.03/80.84 ! [V_z,T_a] :
% 81.03/80.84 ( class_Rings_Oring__1(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Ints__of__int,axiom,
% 81.03/80.84 ! [V_z_2,T_a] :
% 81.03/80.84 ( class_Rings_Oring__1(T_a)
% 81.03/80.84 => 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))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__power,axiom,
% 81.03/80.84 ! [V_n,V_z,T_a] :
% 81.03/80.84 ( class_Rings_Oring__1(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inter__anti__mono,axiom,
% 81.03/80.84 ! [V_A_2,V_B_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inter__empty,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inter__insert,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inter__UNIV,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inf__lower,axiom,
% 81.03/80.84 ! [V_A_2,V_x_2,T_a] :
% 81.03/80.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)),V_x_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inter__Un__distrib,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inf__singleton,axiom,
% 81.03/80.84 ! [V_a_2,T_a] :
% 81.03/80.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.84 => 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 ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inf__empty,axiom,
% 81.03/80.84 ! [T_a] :
% 81.03/80.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inf__UNIV,axiom,
% 81.03/80.84 ! [T_a] :
% 81.03/80.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inf__insert,axiom,
% 81.03/80.84 ! [V_A_2,V_a_2,T_a] :
% 81.03/80.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__m1,axiom,
% 81.03/80.84 ! [T_a] :
% 81.03/80.84 ( class_Int_Onumber__ring(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Int__eq__Inter,axiom,
% 81.03/80.84 ! [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))))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inter__Un__subset,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inf__binary,axiom,
% 81.03/80.84 ! [V_b_2,V_a_2,T_a] :
% 81.03/80.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__le__0__iff,axiom,
% 81.03/80.84 ! [V_z_2,T_a] :
% 81.03/80.84 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__0__le__iff,axiom,
% 81.03/80.84 ! [V_z_2,T_a] :
% 81.03/80.84 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__less__0__iff,axiom,
% 81.03/80.84 ! [V_z_2,T_a] :
% 81.03/80.84 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__int__0__less__iff,axiom,
% 81.03/80.84 ! [V_z_2,T_a] :
% 81.03/80.84 ( class_Rings_Olinordered__idom(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_inf__Inf__fold__inf,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inf__fin__Inf,axiom,
% 81.03/80.84 ! [V_A_2,T_a] :
% 81.03/80.84 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_of__nat__nat,axiom,
% 81.03/80.84 ! [V_z,T_a] :
% 81.03/80.84 ( class_Rings_Oring__1(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_code__numeral_Osize_I4_J,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_code__numeral_Osize_I2_J,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 81.03/80.84 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 81.03/80.84 ! [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 ).
% 81.03/80.84
% 81.03/80.84 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_code__numeral_Oinject,axiom,
% 81.03/80.84 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 81.03/80.84 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 81.03/80.84 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 81.03/80.84 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 81.03/80.84 ! [V_y,V_x] :
% 81.03/80.84 ( c_Nat__Transfer_Ois__nat(V_x)
% 81.03/80.84 => ( c_Nat__Transfer_Ois__nat(V_y)
% 81.03/80.84 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 81.03/80.84 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 81.03/80.84 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 81.03/80.84 ! [V_y,V_x] :
% 81.03/80.84 ( c_Nat__Transfer_Ois__nat(V_x)
% 81.03/80.84 => ( c_Nat__Transfer_Ois__nat(V_y)
% 81.03/80.84 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 81.03/80.84 ! [V_y,V_x] :
% 81.03/80.84 ( c_Nat__Transfer_Ois__nat(V_x)
% 81.03/80.84 => ( c_Nat__Transfer_Ois__nat(V_y)
% 81.03/80.84 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 81.03/80.84 ! [V_y,V_x] :
% 81.03/80.84 ( c_Nat__Transfer_Ois__nat(V_x)
% 81.03/80.84 => ( c_Nat__Transfer_Ois__nat(V_y)
% 81.03/80.84 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 81.03/80.84 ! [V_n,V_x] :
% 81.03/80.84 ( c_Nat__Transfer_Ois__nat(V_x)
% 81.03/80.84 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 81.03/80.84 ! [V_y,V_x] :
% 81.03/80.84 ( c_Nat__Transfer_Ois__nat(V_x)
% 81.03/80.84 => ( c_Nat__Transfer_Ois__nat(V_y)
% 81.03/80.84 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 81.03/80.84 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_is__nat__def,axiom,
% 81.03/80.84 ! [V_x_2] :
% 81.03/80.84 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 81.03/80.84 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Suc__code__numeral__minus__one,axiom,
% 81.03/80.84 ! [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 ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inter__subset,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.84 ( ! [B_X] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) )
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__map__freshness,axiom,
% 81.03/80.84 ! [V_f_2,T_b,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2)))
% 81.03/80.84 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 81.03/80.84 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_nat__mod__eq__lemma,axiom,
% 81.03/80.84 ! [V_y,V_n,V_x] :
% 81.03/80.84 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 81.03/80.84 => ? [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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_mod__induct__0,axiom,
% 81.03/80.84 ! [V_i_2,V_P_2,V_p_2] :
% 81.03/80.84 ( ! [B_i] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 81.03/80.84 => ( hBOOL(hAPP(V_P_2,B_i))
% 81.03/80.84 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 81.03/80.84 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 81.03/80.84 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_InterI,axiom,
% 81.03/80.84 ! [V_A_2,V_C_2,T_a] :
% 81.03/80.84 ( ! [B_X] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) )
% 81.03/80.84 => 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))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_nat__intermed__int__val,axiom,
% 81.03/80.84 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 81.03/80.84 ( ! [B_i] :
% 81.03/80.84 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 81.03/80.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 81.03/80.84 => 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))) )
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 81.03/80.84 => ? [B_i] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 81.03/80.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 81.03/80.84 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_log_Osimps,axiom,
% 81.03/80.84 ! [V_i,V_b] :
% 81.03/80.84 ( ( ( 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)))
% 81.03/80.84 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 81.03/80.84 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 81.03/80.84 & ( ~ ( 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)))
% 81.03/80.84 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 81.03/80.84 => 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))) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_mod__div__decomp,axiom,
% 81.03/80.84 ! [V_b,V_a,T_a] :
% 81.03/80.84 ( class_Divides_Osemiring__div(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_minus__shift__def,axiom,
% 81.03/80.84 ! [V_r,V_l,V_k] :
% 81.03/80.84 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 81.03/80.84 => 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) )
% 81.03/80.84 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_inc__shift__def,axiom,
% 81.03/80.84 ! [V_k,V_v] :
% 81.03/80.84 ( ( V_v = V_k
% 81.03/80.84 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 81.03/80.84 & ( V_v != V_k
% 81.03/80.84 => 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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_UnionE,axiom,
% 81.03/80.84 ! [V_C_2,V_A_2,T_a] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => ~ ! [B_X] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X))
% 81.03/80.84 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_map__add__upd__left,axiom,
% 81.03/80.84 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] :
% 81.03/80.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2)))
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_map__add__assoc,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_map__add__None,axiom,
% 81.03/80.84 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 81.03/80.84 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a)
% 81.03/80.84 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 81.03/80.84 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_map__add__find__right,axiom,
% 81.03/80.84 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] :
% 81.03/80.84 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_map__add__dom__app__simps_I1_J,axiom,
% 81.03/80.84 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2)))
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_map__add__dom__app__simps_I3_J,axiom,
% 81.03/80.84 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] :
% 81.03/80.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2)))
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_map__add__dom__app__simps_I2_J,axiom,
% 81.03/80.84 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] :
% 81.03/80.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2)))
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_map__add__SomeD,axiom,
% 81.03/80.84 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 81.03/80.84 ( 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)
% 81.03/80.84 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 81.03/80.84 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 81.03/80.84 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_map__add__Some__iff,axiom,
% 81.03/80.84 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 81.03/80.84 ( 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)
% 81.03/80.84 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 81.03/80.84 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 81.03/80.84 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_dom__map__add,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_map__add__upd,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_map__add__comm,axiom,
% 81.03/80.84 ! [V_m2_2,V_m1_2,T_b,T_a] :
% 81.03/80.84 ( 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))
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_setprod__pos,axiom,
% 81.03/80.84 ! [V_f_2,V_A_2,T_a,T_b] :
% 81.03/80.84 ( class_Rings_Olinordered__semidom(T_b)
% 81.03/80.84 => ( ! [B_x] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
% 81.03/80.84 => 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))) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_setprod__nonneg,axiom,
% 81.03/80.84 ! [V_f_2,V_A_2,T_a,T_b] :
% 81.03/80.84 ( class_Rings_Olinordered__semidom(T_b)
% 81.03/80.84 => ( ! [B_x] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
% 81.03/80.84 => 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))) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_bool_Osize_I2_J,axiom,
% 81.03/80.84 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_bool_Osize_I1_J,axiom,
% 81.03/80.84 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__induct,axiom,
% 81.03/80.84 ! [V_P_2,V_F_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 81.03/80.84 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 81.03/80.84 => ( ! [B_x,B_F] :
% 81.03/80.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F))
% 81.03/80.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F))
% 81.03/80.84 => ( hBOOL(hAPP(V_P_2,B_F))
% 81.03/80.84 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F))) ) ) )
% 81.03/80.84 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 81.03/80.84 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => ( 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)
% 81.03/80.84 => 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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_UNIV__option__conv,axiom,
% 81.03/80.84 ! [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)))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_fold1__antimono,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.84 => 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))) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__eqI,axiom,
% 81.03/80.84 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] :
% 81.03/80.84 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__imageI,axiom,
% 81.03/80.84 ! [V_h_2,T_b,V_F_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 81.03/80.84 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Ole__infE,axiom,
% 81.03/80.84 ! [V_b,V_a,V_x,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 81.03/80.84 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oinf__mono,axiom,
% 81.03/80.84 ! [V_d,V_b,V_c,V_a,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 81.03/80.84 => 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))) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oinf__greatest,axiom,
% 81.03/80.84 ! [V_z,V_y,V_x,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 81.03/80.84 => 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))) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Ole__infI,axiom,
% 81.03/80.84 ! [V_b,V_a,V_x,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 81.03/80.84 => 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))) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oinf__absorb2,axiom,
% 81.03/80.84 ! [V_x,V_y,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 81.03/80.84 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oinf__absorb1,axiom,
% 81.03/80.84 ! [V_y,V_x,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 81.03/80.84 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Ole__infI2,axiom,
% 81.03/80.84 ! [V_a,V_x,V_b,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 81.03/80.84 => 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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Ole__infI1,axiom,
% 81.03/80.84 ! [V_b,V_x,V_a,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 81.03/80.84 => 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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Ole__inf__iff,axiom,
% 81.03/80.84 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 81.03/80.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Ole__iff__inf,axiom,
% 81.03/80.84 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 81.03/80.84 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oinf__le2,axiom,
% 81.03/80.84 ! [V_y,V_x,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oinf__le1,axiom,
% 81.03/80.84 ! [V_y,V_x,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__le__iff__disj,axiom,
% 81.03/80.84 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( 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))
% 81.03/80.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 81.03/80.84 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_subset__image__iff,axiom,
% 81.03/80.84 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 81.03/80.84 <=> ? [B_AA] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2))
% 81.03/80.84 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__mono,axiom,
% 81.03/80.84 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__less__iff__conj,axiom,
% 81.03/80.84 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2))
% 81.03/80.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__less__iff__disj,axiom,
% 81.03/80.84 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( 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))
% 81.03/80.84 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2))
% 81.03/80.84 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oless__infI1,axiom,
% 81.03/80.84 ! [V_b,V_x,V_a,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 81.03/80.84 => 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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oless__infI2,axiom,
% 81.03/80.84 ! [V_a,V_x,V_b,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 81.03/80.84 => 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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__add__distrib__left,axiom,
% 81.03/80.84 ! [V_z,V_y,V_x,T_a] :
% 81.03/80.84 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__Pow__surj,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
% 81.03/80.84 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__diff__distrib__left,axiom,
% 81.03/80.84 ! [V_z,V_y,V_x,T_a] :
% 81.03/80.84 ( class_Groups_Oordered__ab__group__add(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_inf__min,axiom,
% 81.03/80.84 ! [T_a] :
% 81.03/80.84 ( ( class_Lattices_Osemilattice__inf(T_a)
% 81.03/80.84 & class_Orderings_Olinorder(T_a) )
% 81.03/80.84 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__0R,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__0L,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__Suc__Suc,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__diff,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_rev__image__eqI,axiom,
% 81.03/80.84 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_imageI,axiom,
% 81.03/80.84 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => 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))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__iff,axiom,
% 81.03/80.84 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 81.03/80.84 <=> ? [B_x] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 81.03/80.84 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oinf_Oidem,axiom,
% 81.03/80.84 ! [V_a,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min_Oidem,axiom,
% 81.03/80.84 ! [V_x,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oinf_Ocommute,axiom,
% 81.03/80.84 ! [V_b,V_a,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oinf__commute,axiom,
% 81.03/80.84 ! [V_y,V_x,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 81.03/80.84 ! [V_b,V_a,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oinf__left__idem,axiom,
% 81.03/80.84 ! [V_y,V_x,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 81.03/80.84 ! [V_c,V_a,V_b,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oinf__left__commute,axiom,
% 81.03/80.84 ! [V_z,V_y,V_x,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oinf_Oassoc,axiom,
% 81.03/80.84 ! [V_c,V_b,V_a,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Oinf__assoc,axiom,
% 81.03/80.84 ! [V_z,V_y,V_x,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__Un,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__insert,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__is__empty,axiom,
% 81.03/80.84 ! [V_A_2,V_f_2,T_a,T_b] :
% 81.03/80.84 ( 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))
% 81.03/80.84 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__empty,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_empty__is__image,axiom,
% 81.03/80.84 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.84 ( 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)
% 81.03/80.84 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 81.03/80.84 ! [T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__Pow__mono,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),V_B_2))
% 81.03/80.84 => 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))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_insert__image,axiom,
% 81.03/80.84 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_range__eqI,axiom,
% 81.03/80.84 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] :
% 81.03/80.84 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 81.03/80.84 => 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))))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_rangeI,axiom,
% 81.03/80.84 ! [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))))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__surj,axiom,
% 81.03/80.84 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 81.03/80.84 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__number__of,axiom,
% 81.03/80.84 ! [V_v,V_u,T_b] :
% 81.03/80.84 ( ( class_Int_Onumber(T_b)
% 81.03/80.84 & class_Orderings_Oord(T_b) )
% 81.03/80.84 => ( ( 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)))
% 81.03/80.84 => 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) )
% 81.03/80.84 & ( ~ 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)))
% 81.03/80.84 => 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) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__Int__subset,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__diff__subset,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_card__image__le,axiom,
% 81.03/80.84 ! [V_f_2,T_b,V_A_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_surj__Compl__image__subset,axiom,
% 81.03/80.84 ! [V_A_2,V_f_2,T_a,T_b] :
% 81.03/80.84 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__map__upd,axiom,
% 81.03/80.84 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 81.03/80.84 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Ofold__inf__insert,axiom,
% 81.03/80.84 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => 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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 81.03/80.84 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.84 => 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))) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Ofold1__belowI,axiom,
% 81.03/80.84 ! [V_a_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.84 => 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)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> ! [B_x] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_fold1__below__iff,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( 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))
% 81.03/80.84 <=> ? [B_x] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_strict__below__fold1__iff,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> ! [B_x] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_fold1__strict__below__iff,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( 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))
% 81.03/80.84 <=> ? [B_x] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__range__updI,axiom,
% 81.03/80.84 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
% 81.03/80.84 ( 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)))))
% 81.03/80.84 => 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))))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_fun__upd__image,axiom,
% 81.03/80.84 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 81.03/80.84 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => 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)))))) )
% 81.03/80.84 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__ord__min,axiom,
% 81.03/80.84 ! [T_a] :
% 81.03/80.84 ( class_Orderings_Oord(T_a)
% 81.03/80.84 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min_Oremove,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => ( ( hAPP(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))
% 81.03/80.84 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 )
% 81.03/80.84 & ( hAPP(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))
% 81.03/80.84 => 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)))))) ) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 81.03/80.84 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] :
% 81.03/80.84 ( 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))
% 81.03/80.84 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 81.03/80.84 | ? [B_x,B_y] :
% 81.03/80.84 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 81.03/80.84 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2))
% 81.03/80.84 & 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) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => ( ( hAPP(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))
% 81.03/80.84 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 )
% 81.03/80.84 & ( hAPP(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))
% 81.03/80.84 => 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)))))) ) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.84 <=> 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))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.84 <=> 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))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Cantors__paradox,axiom,
% 81.03/80.84 ! [V_A_2,T_a] :
% 81.03/80.84 ~ ? [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 81.03/80.84 ! [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 ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 81.03/80.84 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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 81.03/80.84 ! [V_A_2] :
% 81.03/80.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 81.03/80.84 <=> 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))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 81.03/80.84 ! [V_A_2,V_x_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 81.03/80.84 <=> 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))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2] :
% 81.03/80.84 ( V_A_2 = V_B_2
% 81.03/80.84 <=> 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 81.03/80.84 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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_inf__nat__def,axiom,
% 81.03/80.84 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min_Osingleton,axiom,
% 81.03/80.84 ! [V_x_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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 ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => 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) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min__le,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => 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)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 81.03/80.84 ! [V_x_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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 ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min__in,axiom,
% 81.03/80.84 ! [V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Pow__insert,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min_Oin__idem,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => 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) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 81.03/80.84 ! [V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min_OF__eq,axiom,
% 81.03/80.84 ! [V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => 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)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 81.03/80.84 => 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) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => 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)) ) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min__antimono,axiom,
% 81.03/80.84 ! [V_N_2,V_M_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
% 81.03/80.84 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 81.03/80.84 => 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))) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 81.03/80.84 ! [V_a_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min__insert,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => 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)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min_Osubset__idem,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 81.03/80.84 => 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) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min__Un,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => 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)) ) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 81.03/80.84 ! [V_a_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => 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)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( ( hAPP(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))
% 81.03/80.84 => 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 )
% 81.03/80.84 & ( hAPP(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))
% 81.03/80.84 => 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)))))) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => 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)) ) ) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.84 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => 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)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => 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) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min_Oinsert,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => 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)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min_Oinsert__remove,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( ( hAPP(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))
% 81.03/80.84 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 81.03/80.84 & ( hAPP(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))
% 81.03/80.84 => 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)))))) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min_Ounion__disjoint,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.84 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => 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)) ) ) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min_Ounion__inter,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.84 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => 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)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min_Oeq__fold_H,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.84 => 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) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 81.03/80.84 ! [V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( ! [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))))))
% 81.03/80.84 => 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)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min_Oclosed,axiom,
% 81.03/80.84 ! [V_A_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.84 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => ( ! [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))))))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 81.03/80.84 ! [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)))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 81.03/80.84 ! [V_N_2,V_h_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( ! [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))
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 81.03/80.84 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => 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)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_infinite__UNIV__int,axiom,
% 81.03/80.84 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_infinite__UNIV__nat,axiom,
% 81.03/80.84 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2] :
% 81.03/80.84 ( c_Nat__Transfer_Onat__set(V_A_2)
% 81.03/80.84 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 81.03/80.84 => 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))) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2] :
% 81.03/80.84 ( c_Nat__Transfer_Onat__set(V_A_2)
% 81.03/80.84 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 81.03/80.84 => 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))) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 81.03/80.84 ! [V_N_2] :
% 81.03/80.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 81.03/80.84 <=> ? [B_m] :
% 81.03/80.84 ! [B_x] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 81.03/80.84 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2] :
% 81.03/80.84 ( c_Nat__Transfer_Onat__set(V_A_2)
% 81.03/80.84 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 81.03/80.84 => 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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2] :
% 81.03/80.84 ( c_Nat__Transfer_Onat__set(V_A_2)
% 81.03/80.84 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 81.03/80.84 => 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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_nat__set__def,axiom,
% 81.03/80.84 ! [V_S_2] :
% 81.03/80.84 ( c_Nat__Transfer_Onat__set(V_S_2)
% 81.03/80.84 <=> ! [B_x] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2] :
% 81.03/80.84 ( c_Nat__Transfer_Onat__set(V_A_2)
% 81.03/80.84 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 81.03/80.84 => ( V_A_2 = V_B_2
% 81.03/80.84 <=> 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) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2] :
% 81.03/80.84 ( c_Nat__Transfer_Onat__set(V_A_2)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 81.03/80.84 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 81.03/80.84 ! [V_x_2,V_A_2] :
% 81.03/80.84 ( c_Nat__Transfer_Onat__set(V_A_2)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_nat__gcd_Osimps,axiom,
% 81.03/80.84 ! [V_x,V_y] :
% 81.03/80.84 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.84 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 81.03/80.84 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.84 => 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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 81.03/80.84 ! [V_A_2] :
% 81.03/80.84 ( c_Nat__Transfer_Onat__set(V_A_2)
% 81.03/80.84 => 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 ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 81.03/80.84 ! [V_A_2] :
% 81.03/80.84 ( c_Nat__Transfer_Onat__set(V_A_2)
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 81.03/80.84 <=> 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))) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 81.03/80.84 ! [V_A_2] :
% 81.03/80.84 ( c_Nat__Transfer_Onat__set(V_A_2)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 81.03/80.84 ! [V_A_2,V_x_2] :
% 81.03/80.84 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 81.03/80.84 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 81.03/80.84 <=> 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))) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2] :
% 81.03/80.84 ( c_Nat__Transfer_Onat__set(V_A_2)
% 81.03/80.84 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.84 <=> 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))) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 81.03/80.84 ! [V_B_2,V_A_2] :
% 81.03/80.84 ( c_Nat__Transfer_Onat__set(V_A_2)
% 81.03/80.84 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.84 <=> 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))) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__nat__set__iff__bounded,axiom,
% 81.03/80.84 ! [V_N_2] :
% 81.03/80.84 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 81.03/80.84 <=> ? [B_m] :
% 81.03/80.84 ! [B_x] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 81.03/80.84 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 81.03/80.84 ! [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)))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_card__greaterThanLessThan__int,axiom,
% 81.03/80.84 ! [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)))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ord_OatMost__iff,axiom,
% 81.03/80.84 ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ord_OatLeast__iff,axiom,
% 81.03/80.84 ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__greaterThanLessThan__int,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_greaterThanLessThan__empty,axiom,
% 81.03/80.84 ! [V_k_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
% 81.03/80.84 => 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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 81.03/80.84 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.84 ( class_Groups_Oordered__ab__group__add(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 81.03/80.84 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 81.03/80.84 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 81.03/80.84 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 81.03/80.84 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 81.03/80.84 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 81.03/80.84 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 81.03/80.84 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 81.03/80.84 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__greaterThanLessThan,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_card__greaterThanLessThan,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ord_OlessThan__iff,axiom,
% 81.03/80.84 ! [V_k_2,V_less_2,V_i_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ord_OgreaterThan__iff,axiom,
% 81.03/80.84 ! [V_k_2,V_less_2,V_i_2,T_a] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__un_I4_J,axiom,
% 81.03/80.84 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Min_Ohom__commute,axiom,
% 81.03/80.84 ! [V_N_2,V_h_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( ! [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))
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 81.03/80.84 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => 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)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__greaterThanAtMost,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__greaterThanAtMost__int,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_greaterThanAtMost__empty,axiom,
% 81.03/80.84 ! [V_k_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
% 81.03/80.84 => 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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 81.03/80.84 ! [V_l_2,V_k_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => ( 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))
% 81.03/80.84 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 81.03/80.84 ! [V_l_2,V_k_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => ( 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)
% 81.03/80.84 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__un_I20_J,axiom,
% 81.03/80.84 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 81.03/80.84 => 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) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__int_I14_J,axiom,
% 81.03/80.84 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_card__greaterThanAtMost,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__int_I10_J,axiom,
% 81.03/80.84 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_card__greaterThanAtMost__int,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__un_I16_J,axiom,
% 81.03/80.84 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
% 81.03/80.84 => 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) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Inf__fin_Ohom__commute,axiom,
% 81.03/80.84 ! [V_N_2,V_h_2,T_a] :
% 81.03/80.84 ( class_Lattices_Olattice(T_a)
% 81.03/80.84 => ( ! [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))
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 81.03/80.84 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => 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)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Sup__fin_Ohom__commute,axiom,
% 81.03/80.84 ! [V_N_2,V_h_2,T_a] :
% 81.03/80.84 ( class_Lattices_Olattice(T_a)
% 81.03/80.84 => ( ! [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))
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 81.03/80.84 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => 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)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_hom__fold1__commute,axiom,
% 81.03/80.84 ! [V_N_2,V_h_2,T_a] :
% 81.03/80.84 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 81.03/80.84 => ( ! [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))
% 81.03/80.84 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 81.03/80.84 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.84 => 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)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__un_I19_J,axiom,
% 81.03/80.84 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 81.03/80.84 => 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) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__atLeastAtMost,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__atLeastAtMost__int,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__Suc__atLeastAtMost,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 81.03/80.84 ! [V_k_2,V_f_2] :
% 81.03/80.84 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 81.03/80.84 ! [V_n_2,V_m_2] :
% 81.03/80.84 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 81.03/80.84 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 81.03/80.84 => 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))) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastAtMostSuc__conv,axiom,
% 81.03/80.84 ! [V_n_2,V_m_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 81.03/80.84 ! [V_y_2,V_x_2] :
% 81.03/80.84 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 81.03/80.84 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastatMost__empty__iff,axiom,
% 81.03/80.84 ! [V_b_2,V_a_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => ( 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))
% 81.03/80.84 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastatMost__empty__iff2,axiom,
% 81.03/80.84 ! [V_b_2,V_a_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => ( 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)
% 81.03/80.84 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastatMost__empty,axiom,
% 81.03/80.84 ! [V_a_2,V_b_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))
% 81.03/80.84 => 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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastatMost__subset__iff,axiom,
% 81.03/80.84 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 81.03/80.84 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2))
% 81.03/80.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastAtMost__singleton_H,axiom,
% 81.03/80.84 ! [V_b_2,V_a_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => ( V_a_2 = V_b_2
% 81.03/80.84 => 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))) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 81.03/80.84 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> ( V_a_2 = V_b_2
% 81.03/80.84 & V_b_2 = V_ca_2 ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastAtMost__singleton,axiom,
% 81.03/80.84 ! [V_a_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => 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))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__uminus__atLeastAtMost,axiom,
% 81.03/80.84 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.84 ( class_Groups_Oordered__ab__group__add(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_setsum__head__Suc,axiom,
% 81.03/80.84 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 81.03/80.84 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 81.03/80.84 => 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))) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 81.03/80.84 ! [V_y_2,V_x_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 81.03/80.84 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_card__atLeastAtMost,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastatMost__psubset__iff,axiom,
% 81.03/80.84 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 81.03/80.84 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2))
% 81.03/80.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2))
% 81.03/80.84 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_a_2))
% 81.03/80.84 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) )
% 81.03/80.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__un_I22_J,axiom,
% 81.03/80.84 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 81.03/80.84 => 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) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__int_I16_J,axiom,
% 81.03/80.84 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__int_I13_J,axiom,
% 81.03/80.84 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__int_I12_J,axiom,
% 81.03/80.84 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_setsum__cl__ivl__Suc,axiom,
% 81.03/80.84 ! [V_f_2,V_m_2,V_n_2,T_a] :
% 81.03/80.84 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.84 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 81.03/80.84 => 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) )
% 81.03/80.84 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 81.03/80.84 => 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))) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_setsum__ub__add__nat,axiom,
% 81.03/80.84 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] :
% 81.03/80.84 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
% 81.03/80.84 => 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)))) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_simp__from__to,axiom,
% 81.03/80.84 ! [V_i_2,V_j_2] :
% 81.03/80.84 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 81.03/80.84 => 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)) )
% 81.03/80.84 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 81.03/80.84 => 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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_card__atLeastAtMost__int,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__un_I5_J,axiom,
% 81.03/80.84 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_bset_I8_J,axiom,
% 81.03/80.84 ! [V_B_2,V_t_2,V_D_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 81.03/80.84 => ( 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))
% 81.03/80.84 => ! [B_x] :
% 81.03/80.84 ( ! [B_xa] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => ! [B_xb] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 81.03/80.84 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 81.03/80.84 => 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))) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_aset_I6_J,axiom,
% 81.03/80.84 ! [V_A_2,V_t_2,V_D_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 81.03/80.84 => ( 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))
% 81.03/80.84 => ! [B_x] :
% 81.03/80.84 ( ! [B_xa] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => ! [B_xb] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 81.03/80.84 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 81.03/80.84 => 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)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_aset_I4_J,axiom,
% 81.03/80.84 ! [V_A_2,V_t_2,V_D_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 81.03/80.84 => ! [B_x] :
% 81.03/80.84 ( ! [B_xa] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => ! [B_xb] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 81.03/80.84 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 81.03/80.84 => ( B_x != V_t_2
% 81.03/80.84 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_bset_I4_J,axiom,
% 81.03/80.84 ! [V_B_2,V_t_2,V_D_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 81.03/80.84 => ! [B_x] :
% 81.03/80.84 ( ! [B_xa] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => ! [B_xb] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 81.03/80.84 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 81.03/80.84 => ( B_x != V_t_2
% 81.03/80.84 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ex__nat__less,axiom,
% 81.03/80.84 ! [V_P_2,V_n_2] :
% 81.03/80.84 ( ? [B_m] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 81.03/80.84 & hBOOL(hAPP(V_P_2,B_m)) )
% 81.03/80.84 <=> ? [B_x] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_all__nat__less,axiom,
% 81.03/80.84 ! [V_P_2,V_n_2] :
% 81.03/80.84 ( ! [B_m] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 81.03/80.84 => hBOOL(hAPP(V_P_2,B_m)) )
% 81.03/80.84 <=> ! [B_x] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_bset_I3_J,axiom,
% 81.03/80.84 ! [V_B_2,V_t_2,V_D_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 81.03/80.84 => ( 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))
% 81.03/80.84 => ( ! [B_x] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => ! [B_xa] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 81.03/80.84 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 81.03/80.84 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_aset_I3_J,axiom,
% 81.03/80.84 ! [V_A_2,V_t_2,V_D_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 81.03/80.84 => ( 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))
% 81.03/80.84 => ( ! [B_x] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => ! [B_xa] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 81.03/80.84 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 81.03/80.84 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_bset_I7_J,axiom,
% 81.03/80.84 ! [V_B_2,V_t_2,V_D_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 81.03/80.84 => ! [B_x] :
% 81.03/80.84 ( ! [B_xa] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => ! [B_xb] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 81.03/80.84 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 81.03/80.84 => 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))) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_aset_I5_J,axiom,
% 81.03/80.84 ! [V_A_2,V_t_2,V_D_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 81.03/80.84 => ! [B_x] :
% 81.03/80.84 ( ! [B_xa] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => ! [B_xb] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 81.03/80.84 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 81.03/80.84 => 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)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_aset_I8_J,axiom,
% 81.03/80.84 ! [V_t_2,V_A_2,V_D_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 81.03/80.84 => ! [B_x] :
% 81.03/80.84 ( ! [B_xa] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => ! [B_xb] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 81.03/80.84 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 81.03/80.84 => 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))) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_bset_I6_J,axiom,
% 81.03/80.84 ! [V_t_2,V_B_2,V_D_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 81.03/80.84 => ! [B_x] :
% 81.03/80.84 ( ! [B_xa] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => ! [B_xb] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 81.03/80.84 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 81.03/80.84 => 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)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_periodic__finite__ex,axiom,
% 81.03/80.84 ! [V_P_2,V_d_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 81.03/80.84 => ( ! [B_x,B_k] :
% 81.03/80.84 ( hBOOL(hAPP(V_P_2,B_x))
% 81.03/80.84 <=> 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)))) )
% 81.03/80.84 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 81.03/80.84 <=> ? [B_x] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_bset_I5_J,axiom,
% 81.03/80.84 ! [V_t_2,V_B_2,V_D_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 81.03/80.84 => ! [B_x] :
% 81.03/80.84 ( ! [B_xa] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => ! [B_xb] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 81.03/80.84 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 81.03/80.84 => 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)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_aset_I7_J,axiom,
% 81.03/80.84 ! [V_t_2,V_A_2,V_D_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 81.03/80.84 => ! [B_x] :
% 81.03/80.84 ( ! [B_xa] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => ! [B_xb] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 81.03/80.84 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 81.03/80.84 => 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))) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__atMost,axiom,
% 81.03/80.84 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atMost__eq__iff,axiom,
% 81.03/80.84 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2)
% 81.03/80.84 <=> V_x_2 = V_y_2 ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeast0AtMost,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_card__atMost,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atMost__Suc,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atMost__iff,axiom,
% 81.03/80.84 ! [V_k_2,V_i_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oord(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atMost__subset__iff,axiom,
% 81.03/80.84 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atMost__0,axiom,
% 81.03/80.84 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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Int__atLeastAtMostR1,axiom,
% 81.03/80.84 ! [V_d_2,V_ca_2,V_b_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Int__atLeastAtMostL1,axiom,
% 81.03/80.84 ! [V_d_2,V_b_2,V_a_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__un_I9_J,axiom,
% 81.03/80.84 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__int_I3_J,axiom,
% 81.03/80.84 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__int_I1_J,axiom,
% 81.03/80.84 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_greaterThan__0,axiom,
% 81.03/80.84 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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__un_I7_J,axiom,
% 81.03/80.84 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__un_I10_J,axiom,
% 81.03/80.84 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__un_I18_J,axiom,
% 81.03/80.84 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
% 81.03/80.84 => 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) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__atLeastLessThan,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__lessThan,axiom,
% 81.03/80.84 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__atLeastLessThan__int,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__un_I8_J,axiom,
% 81.03/80.84 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastLessThan__eq__iff,axiom,
% 81.03/80.84 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2))
% 81.03/80.84 => ( 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)
% 81.03/80.84 <=> ( V_a_2 = V_ca_2
% 81.03/80.84 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 81.03/80.84 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( 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)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2))
% 81.03/80.84 => V_a_2 = V_ca_2 ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 81.03/80.84 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( 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)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2))
% 81.03/80.84 => V_b_2 = V_d_2 ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__int_I2_J,axiom,
% 81.03/80.84 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeast0LessThan,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_lessThan__eq__iff,axiom,
% 81.03/80.84 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2)
% 81.03/80.84 <=> V_x_2 = V_y_2 ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_greaterThan__eq__iff,axiom,
% 81.03/80.84 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2)
% 81.03/80.84 <=> V_x_2 = V_y_2 ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__uminus__lessThan,axiom,
% 81.03/80.84 ! [V_x_2,T_a] :
% 81.03/80.84 ( class_Groups_Oordered__ab__group__add(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__uminus__greaterThan,axiom,
% 81.03/80.84 ! [V_x_2,T_a] :
% 81.03/80.84 ( class_Groups_Oordered__ab__group__add(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_card__lessThan,axiom,
% 81.03/80.84 ! [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 ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ex__nat__less__eq,axiom,
% 81.03/80.84 ! [V_P_2,V_n_2] :
% 81.03/80.84 ( ? [B_m] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 81.03/80.84 & hBOOL(hAPP(V_P_2,B_m)) )
% 81.03/80.84 <=> ? [B_x] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_all__nat__less__eq,axiom,
% 81.03/80.84 ! [V_P_2,V_n_2] :
% 81.03/80.84 ( ! [B_m] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 81.03/80.84 => hBOOL(hAPP(V_P_2,B_m)) )
% 81.03/80.84 <=> ! [B_x] :
% 81.03/80.84 ( 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)))
% 81.03/80.84 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastLessThan0,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_card__atLeastLessThan,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__Suc__atLeastLessThan,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastLessThan__empty,axiom,
% 81.03/80.84 ! [V_a_2,V_b_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
% 81.03/80.84 => 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)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastLessThan__empty__iff,axiom,
% 81.03/80.84 ! [V_b_2,V_a_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => ( 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))
% 81.03/80.84 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 81.03/80.84 ! [V_b_2,V_a_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => ( 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)
% 81.03/80.84 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastLessThan__subset__iff,axiom,
% 81.03/80.84 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
% 81.03/80.84 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2))
% 81.03/80.84 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__un_I17_J,axiom,
% 81.03/80.84 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 81.03/80.84 => 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) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__diff,axiom,
% 81.03/80.84 ! [V_m_2,V_n_2,V_i_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2))
% 81.03/80.84 => 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) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__int_I11_J,axiom,
% 81.03/80.84 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_lessThan__0,axiom,
% 81.03/80.84 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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_lessThan__Suc,axiom,
% 81.03/80.84 ! [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)) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_lessThan__Suc__atMost,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 81.03/80.84 ! [V_u_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 81.03/80.84 => 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))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_lessThan__iff,axiom,
% 81.03/80.84 ! [V_k_2,V_i_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oord(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_lessThan__subset__iff,axiom,
% 81.03/80.84 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_setsum__add__nat__ivl,axiom,
% 81.03/80.84 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
% 81.03/80.84 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 81.03/80.84 => 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)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_setsum__diff__nat__ivl,axiom,
% 81.03/80.84 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
% 81.03/80.84 ( class_Groups_Oab__group__add(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 81.03/80.84 => 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)) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_greaterThan__iff,axiom,
% 81.03/80.84 ! [V_k_2,V_i_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oord(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_greaterThan__subset__iff,axiom,
% 81.03/80.84 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_lessThan__strict__subset__iff,axiom,
% 81.03/80.84 ! [V_n_2,V_m_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( 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)))
% 81.03/80.84 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastLessThan__singleton,axiom,
% 81.03/80.84 ! [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))) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 81.03/80.84 ! [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) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__un_I21_J,axiom,
% 81.03/80.84 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 81.03/80.84 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 81.03/80.84 => 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) ) ) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Compl__atMost,axiom,
% 81.03/80.84 ! [V_k_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_Compl__greaterThan,axiom,
% 81.03/80.84 ! [V_k_2,T_a] :
% 81.03/80.84 ( class_Orderings_Olinorder(T_a)
% 81.03/80.84 => 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) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_atLeastLessThan__add__Un,axiom,
% 81.03/80.84 ! [V_k_2,V_j_2,V_i_2] :
% 81.03/80.84 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 81.03/80.84 => 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))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__int_I15_J,axiom,
% 81.03/80.84 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_subset__card__intvl__is__intvl,axiom,
% 81.03/80.84 ! [V_k_2,V_A_2] :
% 81.03/80.84 ( 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)))))
% 81.03/80.84 => 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))) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_ivl__disj__int_I9_J,axiom,
% 81.03/80.84 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.84 ( class_Orderings_Oorder(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 81.03/80.84 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.84 ( class_Groups_Oordered__ab__group__add(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_image__uminus__atLeastLessThan,axiom,
% 81.03/80.84 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.84 ( class_Groups_Oordered__ab__group__add(T_a)
% 81.03/80.84 => 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)) ) ).
% 81.03/80.84
% 81.03/80.84 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 81.03/80.84 ! [V_k_2,V_f_2,T_a] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a)
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__head__upt__Suc,axiom,
% 81.03/80.85 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 81.03/80.85 => 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))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_card__atLeastLessThan__int,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_atLeastLessThanSuc,axiom,
% 81.03/80.85 ! [V_n_2,V_m_2] :
% 81.03/80.85 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_single__Diff__lessThan,axiom,
% 81.03/80.85 ! [V_k_2,T_a] :
% 81.03/80.85 ( class_Orderings_Oorder(T_a)
% 81.03/80.85 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_ivl__disj__int_I4_J,axiom,
% 81.03/80.85 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.85 ( class_Orderings_Oorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__op__ivl__Suc,axiom,
% 81.03/80.85 ! [V_f_2,V_m_2,V_n_2,T_a] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 81.03/80.85 => 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) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 81.03/80.85 => 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)) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_ivl__disj__int_I7_J,axiom,
% 81.03/80.85 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.85 ( class_Orderings_Oorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_ivl__disj__un_I15_J,axiom,
% 81.03/80.85 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 81.03/80.85 => 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) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_ivl__disj__un_I11_J,axiom,
% 81.03/80.85 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 81.03/80.85 => 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) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_ivl__disj__int_I5_J,axiom,
% 81.03/80.85 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.85 ( class_Orderings_Oorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_greaterThan__Suc,axiom,
% 81.03/80.85 ! [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)))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 81.03/80.85 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_ivl__disj__un_I6_J,axiom,
% 81.03/80.85 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 81.03/80.85 => 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) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_ivl__disj__un_I3_J,axiom,
% 81.03/80.85 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 81.03/80.85 => 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) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_ivl__disj__un_I2_J,axiom,
% 81.03/80.85 ! [V_u_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_ivl__disj__un_I12_J,axiom,
% 81.03/80.85 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 81.03/80.85 => 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) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_ivl__disj__un_I13_J,axiom,
% 81.03/80.85 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 81.03/80.85 => 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) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_ivl__disj__un_I1_J,axiom,
% 81.03/80.85 ! [V_l_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_atMost__Int__atLeast,axiom,
% 81.03/80.85 ! [V_n_2,T_a] :
% 81.03/80.85 ( class_Orderings_Oorder(T_a)
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_atLeast__eq__iff,axiom,
% 81.03/80.85 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2)
% 81.03/80.85 <=> V_x_2 = V_y_2 ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_atLeast__iff,axiom,
% 81.03/80.85 ! [V_k_2,V_i_2,T_a] :
% 81.03/80.85 ( class_Orderings_Oord(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)))
% 81.03/80.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_atLeast__subset__iff,axiom,
% 81.03/80.85 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.85 ( class_Orderings_Oorder(T_a)
% 81.03/80.85 => ( 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)))
% 81.03/80.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_atLeast__0,axiom,
% 81.03/80.85 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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Compl__lessThan,axiom,
% 81.03/80.85 ! [V_k_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Compl__atLeast,axiom,
% 81.03/80.85 ! [V_k_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_atLeast__Suc__greaterThan,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_ivl__disj__un_I14_J,axiom,
% 81.03/80.85 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 81.03/80.85 => 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) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_ivl__disj__int_I8_J,axiom,
% 81.03/80.85 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.85 ( class_Orderings_Oorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_ivl__disj__int_I6_J,axiom,
% 81.03/80.85 ! [V_u_2,V_l_2,T_a] :
% 81.03/80.85 ( class_Orderings_Oorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_image__uminus__atMost,axiom,
% 81.03/80.85 ! [V_x_2,T_a] :
% 81.03/80.85 ( class_Groups_Oordered__ab__group__add(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_image__uminus__atLeast,axiom,
% 81.03/80.85 ! [V_x_2,T_a] :
% 81.03/80.85 ( class_Groups_Oordered__ab__group__add(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_atLeast__Suc,axiom,
% 81.03/80.85 ! [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)))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_minus__Max__eq__Min,axiom,
% 81.03/80.85 ! [V_S_2,T_a] :
% 81.03/80.85 ( class_Groups_Olinordered__ab__group__add(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 81.03/80.85 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => 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)) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_minus__Min__eq__Max,axiom,
% 81.03/80.85 ! [V_S_2,T_a] :
% 81.03/80.85 ( class_Groups_Olinordered__ab__group__add(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 81.03/80.85 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => 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)) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 81.03/80.85 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] :
% 81.03/80.85 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 81.03/80.85 => ( ! [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))
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 81.03/80.85 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => 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)) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_finite__range__map__of__map__add,axiom,
% 81.03/80.85 ! [V_l_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( 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)))))
% 81.03/80.85 => 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))))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_finite__dom__map__of,axiom,
% 81.03/80.85 ! [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)))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max_Osingleton,axiom,
% 81.03/80.85 ! [V_x_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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 ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max__ge,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.85 => 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))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max__in,axiom,
% 81.03/80.85 ! [V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_finite__range__map__of,axiom,
% 81.03/80.85 ! [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))))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max__mono,axiom,
% 81.03/80.85 ! [V_N_2,V_M_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
% 81.03/80.85 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 81.03/80.85 => 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))) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_body__def,axiom,
% 81.03/80.85 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max_Oremove,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.85 => ( ( hAPP(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))
% 81.03/80.85 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 )
% 81.03/80.85 & ( hAPP(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))
% 81.03/80.85 => 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)))))) ) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 81.03/80.85 ! [V_ca_2,V_b_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( ! [B_x] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) )
% 81.03/80.85 => 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))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max__eqI,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( ! [B_y] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 81.03/80.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) )
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.85 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Ole__supE,axiom,
% 81.03/80.85 ! [V_x,V_b,V_a,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( 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))
% 81.03/80.85 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 81.03/80.85 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup__mono,axiom,
% 81.03/80.85 ! [V_d,V_b,V_c,V_a,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 81.03/80.85 => 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))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup__least,axiom,
% 81.03/80.85 ! [V_z,V_x,V_y,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 81.03/80.85 => 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)) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Ole__supI,axiom,
% 81.03/80.85 ! [V_b,V_x,V_a,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 81.03/80.85 => 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)) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup__absorb1,axiom,
% 81.03/80.85 ! [V_x,V_y,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 81.03/80.85 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup__absorb2,axiom,
% 81.03/80.85 ! [V_y,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 81.03/80.85 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Ole__supI2,axiom,
% 81.03/80.85 ! [V_a,V_b,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 81.03/80.85 => 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))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Ole__supI1,axiom,
% 81.03/80.85 ! [V_b,V_a,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 81.03/80.85 => 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))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Ole__sup__iff,axiom,
% 81.03/80.85 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( 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))
% 81.03/80.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 81.03/80.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Ole__iff__sup,axiom,
% 81.03/80.85 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 81.03/80.85 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_le__maxI2,axiom,
% 81.03/80.85 ! [V_x,V_y,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_le__maxI1,axiom,
% 81.03/80.85 ! [V_y,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_le__max__iff__disj,axiom,
% 81.03/80.85 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( 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)))
% 81.03/80.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2))
% 81.03/80.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_less__max__iff__disj,axiom,
% 81.03/80.85 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( 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)))
% 81.03/80.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2))
% 81.03/80.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_max__less__iff__conj,axiom,
% 81.03/80.85 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( 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))
% 81.03/80.85 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2))
% 81.03/80.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Oless__supI1,axiom,
% 81.03/80.85 ! [V_b,V_a,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 81.03/80.85 => 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))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Oless__supI2,axiom,
% 81.03/80.85 ! [V_a,V_b,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 81.03/80.85 => 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))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_sup__max,axiom,
% 81.03/80.85 ! [T_a] :
% 81.03/80.85 ( ( class_Lattices_Osemilattice__sup(T_a)
% 81.03/80.85 & class_Orderings_Olinorder(T_a) )
% 81.03/80.85 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup__assoc,axiom,
% 81.03/80.85 ! [V_z,V_y,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup_Oassoc,axiom,
% 81.03/80.85 ! [V_c,V_b,V_a,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup__left__commute,axiom,
% 81.03/80.85 ! [V_z,V_y,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 81.03/80.85 ! [V_c,V_a,V_b,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup__left__idem,axiom,
% 81.03/80.85 ! [V_y,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 81.03/80.85 ! [V_b,V_a,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup__commute,axiom,
% 81.03/80.85 ! [V_y,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup_Ocommute,axiom,
% 81.03/80.85 ! [V_b,V_a,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max_Oidem,axiom,
% 81.03/80.85 ! [V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup_Oidem,axiom,
% 81.03/80.85 ! [V_a,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_max__Suc__Suc,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_max__0L,axiom,
% 81.03/80.85 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 81.03/80.85
% 81.03/80.85 fof(fact_max__0R,axiom,
% 81.03/80.85 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 81.03/80.85
% 81.03/80.85 fof(fact_max__add__distrib__left,axiom,
% 81.03/80.85 ! [V_z,V_y,V_x,T_a] :
% 81.03/80.85 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 81.03/80.85 ! [T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 81.03/80.85 ! [V_x,V_z,V_y,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 81.03/80.85 ! [V_x,V_z,V_y,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 81.03/80.85 ! [V_z,V_y,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 81.03/80.85 ! [V_z,V_y,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 81.03/80.85 ! [V_y,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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 ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup__inf__absorb,axiom,
% 81.03/80.85 ! [V_y,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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 ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_max__diff__distrib__left,axiom,
% 81.03/80.85 ! [V_z,V_y,V_x,T_a] :
% 81.03/80.85 ( class_Groups_Oordered__ab__group__add(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_max__number__of,axiom,
% 81.03/80.85 ! [V_v,V_u,T_b] :
% 81.03/80.85 ( ( class_Int_Onumber(T_b)
% 81.03/80.85 & class_Orderings_Oord(T_b) )
% 81.03/80.85 => ( ( 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)))
% 81.03/80.85 => 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) )
% 81.03/80.85 & ( ~ 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)))
% 81.03/80.85 => 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) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Odistrib__sup__le,axiom,
% 81.03/80.85 ! [V_z,V_y,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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)))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Odistrib__inf__le,axiom,
% 81.03/80.85 ! [V_z,V_y,V_x,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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)))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_minus__min__eq__max,axiom,
% 81.03/80.85 ! [V_y,V_x,T_a] :
% 81.03/80.85 ( class_Groups_Olinordered__ab__group__add(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_minus__max__eq__min,axiom,
% 81.03/80.85 ! [V_y,V_x,T_a] :
% 81.03/80.85 ( class_Groups_Olinordered__ab__group__add(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_nat__minus__add__max,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Ofold__sup__insert,axiom,
% 81.03/80.85 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max_Oin__idem,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.85 => 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) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Int__atLeastAtMost,axiom,
% 81.03/80.85 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Int__atLeastLessThan,axiom,
% 81.03/80.85 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Int__greaterThanAtMost,axiom,
% 81.03/80.85 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Int__greaterThanLessThan,axiom,
% 81.03/80.85 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Int__atLeastAtMostR2,axiom,
% 81.03/80.85 ! [V_d_2,V_ca_2,V_a_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Int__atLeastAtMostL2,axiom,
% 81.03/80.85 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max_OF__eq,axiom,
% 81.03/80.85 ! [V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => 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) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 81.03/80.85 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.85 => 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))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max__insert,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => 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)) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max_Osubset__idem,axiom,
% 81.03/80.85 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 81.03/80.85 => 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) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 81.03/80.85 ! [V_a_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.85 => 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 ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max__Un,axiom,
% 81.03/80.85 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => 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)) ) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 81.03/80.85 ! [V_a_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => 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) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max_Oinsert,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => 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)) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max_Oinsert__remove,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( ( hAPP(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))
% 81.03/80.85 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 81.03/80.85 & ( hAPP(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))
% 81.03/80.85 => 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)))))) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max_Ounion__disjoint,axiom,
% 81.03/80.85 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => ( 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))
% 81.03/80.85 => 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)) ) ) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max_Ounion__inter,axiom,
% 81.03/80.85 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.85 => ( 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))
% 81.03/80.85 => 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)) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max_Oeq__fold_H,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.85 => 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) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_max__ord__max,axiom,
% 81.03/80.85 ! [T_a] :
% 81.03/80.85 ( class_Orderings_Oord(T_a)
% 81.03/80.85 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max_Oclosed,axiom,
% 81.03/80.85 ! [V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => ( ! [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))))))
% 81.03/80.85 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OInf__le__Sup,axiom,
% 81.03/80.85 ! [V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => 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))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.85 => ( ( hAPP(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))
% 81.03/80.85 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 )
% 81.03/80.85 & ( hAPP(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))
% 81.03/80.85 => 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)))))) ) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_sup__nat__def,axiom,
% 81.03/80.85 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.85 => 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) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 81.03/80.85 ! [V_x_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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 ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 81.03/80.85 ! [V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => 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) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => 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)) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 81.03/80.85 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 81.03/80.85 => 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) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 81.03/80.85 ! [V_a_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.85 => 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 ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 81.03/80.85 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => 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)) ) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 81.03/80.85 ! [V_a_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => 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) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => 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)) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( ( hAPP(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))
% 81.03/80.85 => 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 )
% 81.03/80.85 & ( hAPP(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))
% 81.03/80.85 => 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)))))) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 81.03/80.85 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.85 => ( 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))
% 81.03/80.85 => 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)) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 81.03/80.85 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.85 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => ( 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))
% 81.03/80.85 => 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)) ) ) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.85 => 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) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 81.03/80.85 ! [V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => ( ! [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))))))
% 81.03/80.85 => 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)) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 81.03/80.85 ! [V_N_2,V_h_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( ! [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))
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 81.03/80.85 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => 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)) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Max_Ohom__commute,axiom,
% 81.03/80.85 ! [V_N_2,V_h_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( ! [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))
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 81.03/80.85 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => 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)) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 81.03/80.85 ! [V_ca_2,V_b_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( ! [B_x] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) )
% 81.03/80.85 => 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))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Min__eqI,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => ( ! [B_y] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 81.03/80.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) )
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.85 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__ivl__cong,axiom,
% 81.03/80.85 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_a,T_b] :
% 81.03/80.85 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 81.03/80.85 & class_Orderings_Oord(T_a) )
% 81.03/80.85 => ( V_a_2 = V_ca_2
% 81.03/80.85 => ( V_b_2 = V_d_2
% 81.03/80.85 => ( ! [B_x] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),B_x))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2))
% 81.03/80.85 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 81.03/80.85 => 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)) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_MGF__lemma2__simult,axiom,
% 81.03/80.85 ! [V_F_2] :
% 81.03/80.85 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 81.03/80.85 => ( c_Com_OWT__bodies
% 81.03/80.85 => ( 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))))
% 81.03/80.85 => 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) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_field__le__epsilon,axiom,
% 81.03/80.85 ! [V_y,V_x,T_a] :
% 81.03/80.85 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.85 => ( ! [B_e] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 81.03/80.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))) )
% 81.03/80.85 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__abs,axiom,
% 81.03/80.85 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__abs__ge__zero,axiom,
% 81.03/80.85 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_sup__Un__eq,axiom,
% 81.03/80.85 ! [V_x_2,V_S_2,V_R_2,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 <=> 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_sup__fun__def,axiom,
% 81.03/80.85 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( class_Lattices_Olattice(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_image__add__atLeastLessThan,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 81.03/80.85 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 81.03/80.85 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__subtractf,axiom,
% 81.03/80.85 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( class_Groups_Oab__group__add(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_fun__diff__def,axiom,
% 81.03/80.85 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 81.03/80.85 ( class_Groups_Ominus(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_dom__const,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_restrict__map__def,axiom,
% 81.03/80.85 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 81.03/80.85 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.85 => 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) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.85 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_nat__number__of__Bit0,axiom,
% 81.03/80.85 ! [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))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_of__int__setprod,axiom,
% 81.03/80.85 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( ( class_Groups_Ocomm__monoid__mult(T_a)
% 81.03/80.85 & class_Rings_Oring__1(T_a) )
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_int__setprod,axiom,
% 81.03/80.85 ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_map__comp__def,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_map__comp__empty_I1_J,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_map__comp__empty_I2_J,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setprod__1,axiom,
% 81.03/80.85 ! [V_A_2,T_b,T_a] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__mult(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_restrict__map__empty,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 81.03/80.85 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 81.03/80.85 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 81.03/80.85 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 81.03/80.85 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_fun__upd__def,axiom,
% 81.03/80.85 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] :
% 81.03/80.85 ( ( V_x_2 = V_a_2
% 81.03/80.85 => 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 )
% 81.03/80.85 & ( V_x_2 != V_a_2
% 81.03/80.85 => 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) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_fun__Compl__def,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_b,T_a] :
% 81.03/80.85 ( class_Groups_Ouminus(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_abs__setprod,axiom,
% 81.03/80.85 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( class_Fields_Olinordered__field(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setprod__timesf,axiom,
% 81.03/80.85 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__mult(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_fold__image__def,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_empty__upd__none,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_map__add__def,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_map__add__empty,axiom,
% 81.03/80.85 ! [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 ).
% 81.03/80.85
% 81.03/80.85 fof(fact_empty__map__add,axiom,
% 81.03/80.85 ! [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 ).
% 81.03/80.85
% 81.03/80.85 fof(fact_dom__eq__empty__conv,axiom,
% 81.03/80.85 ! [V_f_2,T_b,T_a] :
% 81.03/80.85 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_dom__empty,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setprod_Odistrib,axiom,
% 81.03/80.85 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__mult(T_b)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_inf__fun__def,axiom,
% 81.03/80.85 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( class_Lattices_Olattice(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_bot__empty__eq,axiom,
% 81.03/80.85 ! [V_x_2,T_a] :
% 81.03/80.85 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2))
% 81.03/80.85 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_bot__fun__def,axiom,
% 81.03/80.85 ! [V_x_2,T_b,T_a] :
% 81.03/80.85 ( class_Orderings_Obot(T_a)
% 81.03/80.85 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_pred__equals__eq,axiom,
% 81.03/80.85 ! [V_S_2,V_R_2,T_a] :
% 81.03/80.85 ( 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)
% 81.03/80.85 <=> V_R_2 = V_S_2 ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_inf__Int__eq,axiom,
% 81.03/80.85 ! [V_x_2,V_S_2,V_R_2,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 <=> 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_pred__subset__eq,axiom,
% 81.03/80.85 ! [V_S_2,V_R_2,T_a] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_less__eq__Suc__le__raw,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setprod__dividef,axiom,
% 81.03/80.85 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
% 81.03/80.85 ( class_Fields_Ofield__inverse__zero(T_b)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_restrict__map__to__empty,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 81.03/80.85 ! [V_A_2,V_f_2,T_a] :
% 81.03/80.85 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 & class_Groups_Ocomm__monoid__mult(T_a) )
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_card__eq__setsum,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_map__upd__nonempty,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_of__nat__setsum,axiom,
% 81.03/80.85 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( class_Rings_Osemiring__1(T_a)
% 81.03/80.85 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_image__constant__conv,axiom,
% 81.03/80.85 ! [V_ca_2,T_b,T_a,V_A_2] :
% 81.03/80.85 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.85 => 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))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_image__image,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_image__ident,axiom,
% 81.03/80.85 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum_Odistrib,axiom,
% 81.03/80.85 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_b)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__0,axiom,
% 81.03/80.85 ! [V_A_2,T_b,T_a] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_A_2) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_int__setsum,axiom,
% 81.03/80.85 ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__divide__distrib,axiom,
% 81.03/80.85 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( class_Fields_Ofield(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__negf,axiom,
% 81.03/80.85 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( class_Groups_Oab__group__add(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_abs__setsum__abs,axiom,
% 81.03/80.85 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__commute,axiom,
% 81.03/80.85 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__right__distrib,axiom,
% 81.03/80.85 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] :
% 81.03/80.85 ( class_Rings_Osemiring__0(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__left__distrib,axiom,
% 81.03/80.85 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( class_Rings_Osemiring__0(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__product,axiom,
% 81.03/80.85 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( class_Rings_Osemiring__0(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_of__int__setsum,axiom,
% 81.03/80.85 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( class_Rings_Oring__1(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__addf,axiom,
% 81.03/80.85 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_finite__range__imageI,axiom,
% 81.03/80.85 ! [V_f_2,T_c,V_g_2,T_b,T_a] :
% 81.03/80.85 ( 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)))))
% 81.03/80.85 => 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))))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_range__composition,axiom,
% 81.03/80.85 ! [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)))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 81.03/80.85 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 81.03/80.85 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_of__nat__setprod,axiom,
% 81.03/80.85 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( ( class_Groups_Ocomm__monoid__mult(T_a)
% 81.03/80.85 & class_Rings_Osemiring__1(T_a) )
% 81.03/80.85 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_ran__empty,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_image__add__atLeastAtMost,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__delta_H,axiom,
% 81.03/80.85 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_b)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 81.03/80.85 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 81.03/80.85 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 81.03/80.85 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__delta,axiom,
% 81.03/80.85 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_b)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 81.03/80.85 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 81.03/80.85 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 81.03/80.85 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_image__constant,axiom,
% 81.03/80.85 ! [V_ca_2,T_b,V_A_2,V_x_2,T_a] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setprod__delta_H,axiom,
% 81.03/80.85 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__mult(T_b)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 81.03/80.85 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 81.03/80.85 => 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) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 81.03/80.85 => 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) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setprod__delta,axiom,
% 81.03/80.85 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__mult(T_b)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 81.03/80.85 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 81.03/80.85 => 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) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 81.03/80.85 => 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) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_MGT__def,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__constant,axiom,
% 81.03/80.85 ! [V_A_2,V_y_2,T_b,T_a] :
% 81.03/80.85 ( class_Rings_Osemiring__1(T_a)
% 81.03/80.85 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_y_2) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_power__number__of__even,axiom,
% 81.03/80.85 ! [V_w_2,V_z_2,T_a] :
% 81.03/80.85 ( class_Int_Onumber__ring(T_a)
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_fold__image__distrib,axiom,
% 81.03/80.85 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__mult(T_b)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_dual__max,axiom,
% 81.03/80.85 ! [T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_dual__min,axiom,
% 81.03/80.85 ! [T_a] :
% 81.03/80.85 ( class_Orderings_Olinorder(T_a)
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setprod__constant,axiom,
% 81.03/80.85 ! [V_y_2,V_A_2,T_a,T_b] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__mult(T_b)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_zpower__number__of__even,axiom,
% 81.03/80.85 ! [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))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__lessThan__Suc,axiom,
% 81.03/80.85 ! [V_n_2,V_f_2,T_a] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__atMost__Suc,axiom,
% 81.03/80.85 ! [V_n_2,V_f_2,T_a] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 81.03/80.85 ! [V_A_2,V_f_2,T_a] :
% 81.03/80.85 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 & class_Groups_Ocomm__monoid__mult(T_a) )
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_image__add__int__atLeastLessThan,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 81.03/80.85 ! [V_f_2,V_A_2,T_a] :
% 81.03/80.85 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 & class_Groups_Ocomm__monoid__mult(T_a) )
% 81.03/80.85 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Powp__Pow__eq,axiom,
% 81.03/80.85 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__restrict__set,axiom,
% 81.03/80.85 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_b)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_image__eq__fold__image,axiom,
% 81.03/80.85 ! [V_f_2,T_b,V_A_2,T_a] :
% 81.03/80.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_power__number__of__even__number__of,axiom,
% 81.03/80.85 ! [V_w_2,V_v_2,T_a] :
% 81.03/80.85 ( class_Int_Onumber__ring(T_a)
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_card_Oeq__fold__g,axiom,
% 81.03/80.85 ! [V_A_2,T_a] :
% 81.03/80.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_card__def,axiom,
% 81.03/80.85 ! [V_A_2,T_a] :
% 81.03/80.85 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_fun__left__comm__idem__remove,axiom,
% 81.03/80.85 ! [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))))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_diff__nat__eq__if,axiom,
% 81.03/80.85 ! [V_z_2,V_z_H_2] :
% 81.03/80.85 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 81.03/80.85 => 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) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 81.03/80.85 ! [V_f_2,V_A_2,T_a] :
% 81.03/80.85 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 & class_Groups_Ocomm__monoid__mult(T_a) )
% 81.03/80.85 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_hoare__derivs_OBody,axiom,
% 81.03/80.85 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__head,axiom,
% 81.03/80.85 ! [V_P_2,V_n_2,V_m_2,T_a] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 81.03/80.85 => 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))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_minus__fold__remove,axiom,
% 81.03/80.85 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Body__sound__lemma,axiom,
% 81.03/80.85 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_dom__eq__singleton__conv,axiom,
% 81.03/80.85 ! [V_x_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 <=> ? [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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Suc__eq__number__of,axiom,
% 81.03/80.85 ! [V_v_2,V_n_2] :
% 81.03/80.85 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 81.03/80.85 <=> 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))))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_eq__number__of__Suc,axiom,
% 81.03/80.85 ! [V_n_2,V_v_2] :
% 81.03/80.85 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 81.03/80.85 <=> 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))))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_nat__number__of__Bit1,axiom,
% 81.03/80.85 ! [V_w_2] :
% 81.03/80.85 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 81.03/80.85 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 81.03/80.85 => 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)))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_geometric__sum,axiom,
% 81.03/80.85 ! [V_n_2,V_x_2,T_a] :
% 81.03/80.85 ( class_Fields_Ofield(T_a)
% 81.03/80.85 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a)
% 81.03/80.85 => 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))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_gauss__sum,axiom,
% 81.03/80.85 ! [V_n_2,T_a] :
% 81.03/80.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 81.03/80.85 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setsum__natinterval__difff,axiom,
% 81.03/80.85 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 81.03/80.85 ( class_Groups_Oab__group__add(T_a)
% 81.03/80.85 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 81.03/80.85 => 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)))) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 81.03/80.85 => 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) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_less__number__of__Suc,axiom,
% 81.03/80.85 ! [V_n_2,V_v_2] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 <=> 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)))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_less__Suc__number__of,axiom,
% 81.03/80.85 ! [V_v_2,V_n_2] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 <=> 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))))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_le__Suc__number__of,axiom,
% 81.03/80.85 ! [V_v_2,V_n_2] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 <=> 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))))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_le__number__of__Suc,axiom,
% 81.03/80.85 ! [V_n_2,V_v_2] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 <=> 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)))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_max__Suc__number__of,axiom,
% 81.03/80.85 ! [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)))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_max__number__of__Suc,axiom,
% 81.03/80.85 ! [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)))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_MGT__Body,axiom,
% 81.03/80.85 ! [V_Procs_2,V_G_2] :
% 81.03/80.85 ( 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))
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),V_Procs_2))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Body1,axiom,
% 81.03/80.85 ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2))
% 81.03/80.85 => 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)))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_power__number__of__odd,axiom,
% 81.03/80.85 ! [V_z_2,V_w_2,T_a] :
% 81.03/80.85 ( class_Int_Onumber__ring(T_a)
% 81.03/80.85 => ( ( 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)))
% 81.03/80.85 => 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))) )
% 81.03/80.85 & ( ~ 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)))
% 81.03/80.85 => 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) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_setprod__gen__delta,axiom,
% 81.03/80.85 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 81.03/80.85 ( class_Groups_Ocomm__monoid__mult(T_b)
% 81.03/80.85 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 81.03/80.85 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 81.03/80.85 => 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)))) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 81.03/80.85 => 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)) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 81.03/80.85 ! [V_x_2,V_y_2,V_ca_2] :
% 81.03/80.85 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 81.03/80.85 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 81.03/80.85 => 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))) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 81.03/80.85 => 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)) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_zpower__number__of__odd,axiom,
% 81.03/80.85 ! [V_z_2,V_w_2] :
% 81.03/80.85 ( ( 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)))
% 81.03/80.85 => 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))) )
% 81.03/80.85 & ( ~ 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)))
% 81.03/80.85 => 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) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_arith__series__general,axiom,
% 81.03/80.85 ! [V_n_2,V_d_2,V_a_2,T_a] :
% 81.03/80.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 81.03/80.85 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_a)),c_Nat_Osemiring__1__class_Oof__nat(T_a))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__number__of__Suc,axiom,
% 81.03/80.85 ! [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)))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__Suc__number__of,axiom,
% 81.03/80.85 ! [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)))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_arith__series__nat,axiom,
% 81.03/80.85 ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_power__number__of__odd__number__of,axiom,
% 81.03/80.85 ! [V_v_2,V_w_2,T_a] :
% 81.03/80.85 ( class_Int_Onumber__ring(T_a)
% 81.03/80.85 => ( ( 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)))
% 81.03/80.85 => 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))) )
% 81.03/80.85 & ( ~ 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)))
% 81.03/80.85 => 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) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_diff__nat__number__of,axiom,
% 81.03/80.85 ! [V_v_2,V_v_H_2] :
% 81.03/80.85 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 81.03/80.85 => 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) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_arith__series__int,axiom,
% 81.03/80.85 ! [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)))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_nat__case__add__eq__if,axiom,
% 81.03/80.85 ! [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)))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_nat__case__number__of,axiom,
% 81.03/80.85 ! [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))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_nat__rec__add__eq__if,axiom,
% 81.03/80.85 ! [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))))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 81.03/80.85 ! [V_n_2,T_a] :
% 81.03/80.85 ( class_Rings_Osemiring__1(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_nat__rec__0,axiom,
% 81.03/80.85 ! [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 ).
% 81.03/80.85
% 81.03/80.85 fof(fact_nat__rec__Suc,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_nat__case__0,axiom,
% 81.03/80.85 ! [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 ).
% 81.03/80.85
% 81.03/80.85 fof(fact_nat__case__Suc,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 81.03/80.85 ! [V_i_2,V_inc_2,T_a] :
% 81.03/80.85 ( class_Rings_Osemiring__1(T_a)
% 81.03/80.85 => 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 ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 81.03/80.85 ! [V_i_2,V_n_2,V_inc_2,T_a] :
% 81.03/80.85 ( class_Rings_Osemiring__1(T_a)
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_max__Suc2,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_max__Suc1,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 81.03/80.85 ! [V_n_2,V_m_2] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 81.03/80.85 <=> 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_diff__Suc,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__Suc2,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_min__Suc1,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_nat__rec__number__of,axiom,
% 81.03/80.85 ! [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)))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_MGT__alternD,axiom,
% 81.03/80.85 ! [V_ca_2,V_G_2] :
% 81.03/80.85 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 81.03/80.85 => ( 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))))
% 81.03/80.85 => 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)))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 81.03/80.85 ! [V_f_2,V_A_2,T_a] :
% 81.03/80.85 ( ! [B_x] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.85 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 81.03/80.85 ! [V_f_2,V_A_2,T_a] :
% 81.03/80.85 ( ! [B_x] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.85 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_triple__valid__def,axiom,
% 81.03/80.85 ! [V_t_2,V_n_2,T_a] :
% 81.03/80.85 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2)
% 81.03/80.85 <=> 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_MGT__alternI,axiom,
% 81.03/80.85 ! [V_ca_2,V_G_2] :
% 81.03/80.85 ( 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))))
% 81.03/80.85 => 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)))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_of__int__num,axiom,
% 81.03/80.85 ! [V_k_2,T_a] :
% 81.03/80.85 ( class_Rings_Oring__1(T_a)
% 81.03/80.85 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) )
% 81.03/80.85 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => 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))) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => 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))))) ) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_finite__pointwise,axiom,
% 81.03/80.85 ! [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] :
% 81.03/80.85 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2))
% 81.03/80.85 => ( ! [B_p] :
% 81.03/80.85 ( 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))))
% 81.03/80.85 => 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)))) )
% 81.03/80.85 => ( 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))
% 81.03/80.85 => 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)) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_adjust__eq,axiom,
% 81.03/80.85 ! [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))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__int__mod__div,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_pred__subset__eq2,axiom,
% 81.03/80.85 ! [V_S_2,V_R_2,T_b,T_a] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 <=> 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_bot__empty__eq2,axiom,
% 81.03/80.85 ! [V_y_2,V_x_2,T_b,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 <=> 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)))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_pred__equals__eq2,axiom,
% 81.03/80.85 ! [V_S_2,V_R_2,T_b,T_a] :
% 81.03/80.85 ( 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)
% 81.03/80.85 <=> V_R_2 = V_S_2 ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_inf__Int__eq2,axiom,
% 81.03/80.85 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 <=> 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_sup__Un__eq2,axiom,
% 81.03/80.85 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 <=> 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_adjust__def,axiom,
% 81.03/80.85 ! [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))))))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Nitpick_OFrac__def,axiom,
% 81.03/80.85 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)))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_pair__imageI,axiom,
% 81.03/80.85 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_norm__frac_Osimps,axiom,
% 81.03/80.85 ! [V_a_2,V_b_2] :
% 81.03/80.85 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 81.03/80.85 => 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))) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_sup2CI,axiom,
% 81.03/80.85 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] :
% 81.03/80.85 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_sup2E,axiom,
% 81.03/80.85 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_inf2E,axiom,
% 81.03/80.85 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 81.03/80.85 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_inf2I,axiom,
% 81.03/80.85 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_mem__splitI,axiom,
% 81.03/80.85 ! [T_c,T_b,V_b_2,V_a_2,V_ca_2,V_z_2,T_a] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2)))
% 81.03/80.85 => 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)))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_splitI,axiom,
% 81.03/80.85 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_prod__caseI,axiom,
% 81.03/80.85 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_bot2E,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_splitD,axiom,
% 81.03/80.85 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_splitD_H,axiom,
% 81.03/80.85 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_sup2I2,axiom,
% 81.03/80.85 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_sup2I1,axiom,
% 81.03/80.85 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_inf2D2,axiom,
% 81.03/80.85 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_inf2D1,axiom,
% 81.03/80.85 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_less__by__empty,axiom,
% 81.03/80.85 ! [V_B_2,T_a,V_A_2] :
% 81.03/80.85 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 81.03/80.85 => 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_rev__predicate2D,axiom,
% 81.03/80.85 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 81.03/80.85 => ( 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))
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_predicate2D,axiom,
% 81.03/80.85 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Pair__inject,axiom,
% 81.03/80.85 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 81.03/80.85 ( 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)
% 81.03/80.85 => ~ ( V_a = V_a_H
% 81.03/80.85 => V_b != V_b_H ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Pair__eq,axiom,
% 81.03/80.85 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
% 81.03/80.85 ( 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)
% 81.03/80.85 <=> ( V_a_2 = V_a_H_2
% 81.03/80.85 & V_b_2 = V_b_H_2 ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_split__paired__All,axiom,
% 81.03/80.85 ! [T_b,T_a,V_P_2] :
% 81.03/80.85 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 81.03/80.85 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_split__weak__cong,axiom,
% 81.03/80.85 ! [V_ca_2,T_c,T_b,T_a,V_q_2,V_p_2] :
% 81.03/80.85 ( V_p_2 = V_q_2
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_split__twice,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_prod_Osimps_I2_J,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_split__conv,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_split__eta,axiom,
% 81.03/80.85 ! [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 ).
% 81.03/80.85
% 81.03/80.85 fof(fact_in__rel__def,axiom,
% 81.03/80.85 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2))
% 81.03/80.85 <=> 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_div__mod__code__numeral__def,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 81.03/80.85 ! [V_w] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ( 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))))
% 81.03/80.85 => 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))) )
% 81.03/80.85 & ( ~ 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))))
% 81.03/80.85 => 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)))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_negDivAlg__div__mod,axiom,
% 81.03/80.85 ! [V_l,V_k] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_negDivAlg__minus1,axiom,
% 81.03/80.85 ! [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))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_negDivAlg_Osimps,axiom,
% 81.03/80.85 ! [V_b,V_a] :
% 81.03/80.85 ( ( ( 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)))
% 81.03/80.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( ~ ( 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)))
% 81.03/80.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 81.03/80.85 => 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))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_negDivAlg__eqn,axiom,
% 81.03/80.85 ! [V_a,V_b] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.85 => ( ( 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)))
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( ~ 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)))
% 81.03/80.85 => 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))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_negDivAlg__eqn__number__of,axiom,
% 81.03/80.85 ! [V_w,V_v] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ( 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))))
% 81.03/80.85 => 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))) )
% 81.03/80.85 & ( ~ 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))))
% 81.03/80.85 => 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)))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Nitpick_Orefl_H__def,axiom,
% 81.03/80.85 ! [V_r_2,T_a] :
% 81.03/80.85 ( c_Nitpick_Orefl_H(T_a,V_r_2)
% 81.03/80.85 <=> ! [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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 81.03/80.85 ! [V_w] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ( 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)))
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( ~ 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)))
% 81.03/80.85 => 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)))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_posDivAlg_Osimps,axiom,
% 81.03/80.85 ! [V_b,V_a] :
% 81.03/80.85 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 81.03/80.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 81.03/80.85 => 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) )
% 81.03/80.85 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 81.03/80.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 81.03/80.85 => 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))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_posDivAlg__0,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_posDivAlg__div__mod,axiom,
% 81.03/80.85 ! [V_l,V_k] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_posDivAlg__eqn__number__of,axiom,
% 81.03/80.85 ! [V_w,V_v] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ( 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)))
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( ~ 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)))
% 81.03/80.85 => 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)))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_posDivAlg__eqn,axiom,
% 81.03/80.85 ! [V_a,V_b] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.85 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 81.03/80.85 => 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) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 81.03/80.85 => 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))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__int__def,axiom,
% 81.03/80.85 ! [V_b,V_a] :
% 81.03/80.85 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 81.03/80.85 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.85 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.85 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => 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))) ) ) ) ) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 81.03/80.85 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.85 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.85 => 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))) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__nat__step,axiom,
% 81.03/80.85 ! [V_m,V_n] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__int__pdivmod,axiom,
% 81.03/80.85 ! [V_l_2,V_k_2] :
% 81.03/80.85 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => 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) )
% 81.03/80.85 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => 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)))) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_negateSnd__def,axiom,
% 81.03/80.85 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_apsnd__conv,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__nat__zero,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__nat__base,axiom,
% 81.03/80.85 ! [V_n,V_m] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 81.03/80.85 => 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) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_negateSnd__eq,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__nat__div__mod,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__nat__if,axiom,
% 81.03/80.85 ! [V_m_2,V_n_2] :
% 81.03/80.85 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 81.03/80.85 => 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) )
% 81.03/80.85 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_pdivmod__def,axiom,
% 81.03/80.85 ! [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))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_pdivmod__posDivAlg,axiom,
% 81.03/80.85 ! [V_k,V_l] :
% 81.03/80.85 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__int__code,axiom,
% 81.03/80.85 ! [V_l_2,V_k_2] :
% 81.03/80.85 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => 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) )
% 81.03/80.85 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => 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)))) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 81.03/80.85 ! [V_a,V_r,V_q,V_c,V_b] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 81.03/80.85 => 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)))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 81.03/80.85 ! [V_c,V_r,V_q,V_b,V_a] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 81.03/80.85 => 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)))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_negDivAlg_Opsimps,axiom,
% 81.03/80.85 ! [V_b_2,V_a_2] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ( ( 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)))
% 81.03/80.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( ~ ( 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)))
% 81.03/80.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 81.03/80.85 => 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))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__nat__rel__unique,axiom,
% 81.03/80.85 ! [V_qr_H,V_qr,V_n,V_m] :
% 81.03/80.85 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 81.03/80.85 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 81.03/80.85 => V_qr = V_qr_H ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_accp_Osimps,axiom,
% 81.03/80.85 ! [V_a_2,V_r_2,T_a] :
% 81.03/80.85 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2))
% 81.03/80.85 <=> ! [B_x] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 81.03/80.85 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_accp_Oequations,axiom,
% 81.03/80.85 ! [V_a_2,V_r_2,T_a] :
% 81.03/80.85 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2))
% 81.03/80.85 <=> ! [B_x] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 81.03/80.85 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_accp__downward,axiom,
% 81.03/80.85 ! [V_a_2,V_b_2,V_r_2,T_a] :
% 81.03/80.85 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 81.03/80.85 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 81.03/80.85 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__nat__eq,axiom,
% 81.03/80.85 ! [V_qr,V_n,V_m] :
% 81.03/80.85 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 81.03/80.85 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_accp__subset,axiom,
% 81.03/80.85 ! [V_R2_2,V_R1_2,T_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_mod__eq,axiom,
% 81.03/80.85 ! [V_r,V_q,V_n,V_m] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_div__eq,axiom,
% 81.03/80.85 ! [V_r,V_q,V_n,V_m] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__nat__rel,axiom,
% 81.03/80.85 ! [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)))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 81.03/80.85 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( 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)))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 81.03/80.85 => 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)))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_posDivAlg_Opsimps,axiom,
% 81.03/80.85 ! [V_b_2,V_a_2] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 81.03/80.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 81.03/80.85 => 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) )
% 81.03/80.85 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 81.03/80.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 81.03/80.85 => 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))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_norm__frac_Opsimps,axiom,
% 81.03/80.85 ! [V_b_2,V_a_2] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 81.03/80.85 => 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)) )
% 81.03/80.85 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 81.03/80.85 => 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))) ) ) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_negDivAlg_Opinduct,axiom,
% 81.03/80.85 ! [V_P_2,V_a1_2,V_a0_2] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ! [B_a,B_b] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ( ~ ( 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)))
% 81.03/80.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 81.03/80.85 => 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))) )
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_posDivAlg_Opinduct,axiom,
% 81.03/80.85 ! [V_P_2,V_a1_2,V_a0_2] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ! [B_a,B_b] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 81.03/80.85 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 81.03/80.85 => 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))) )
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_nat__gcd_Opsimps,axiom,
% 81.03/80.85 ! [V_y_2,V_x_2] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.85 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 81.03/80.85 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.85 => 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)) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_zmult2__lemma,axiom,
% 81.03/80.85 ! [V_c,V_r,V_q,V_b,V_a] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 81.03/80.85 => 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)))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__int__rel__0,axiom,
% 81.03/80.85 ! [V_b] :
% 81.03/80.85 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => 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)))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_self__remainder,axiom,
% 81.03/80.85 ! [V_r,V_q,V_a] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_unique__quotient,axiom,
% 81.03/80.85 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( 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)))
% 81.03/80.85 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => V_q = V_q_H ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_unique__remainder,axiom,
% 81.03/80.85 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( 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)))
% 81.03/80.85 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => V_r = V_r_H ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__int__rel__neg,axiom,
% 81.03/80.85 ! [V_qr,V_b,V_a] :
% 81.03/80.85 ( 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))
% 81.03/80.85 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__int__correct,axiom,
% 81.03/80.85 ! [V_a,V_b] :
% 81.03/80.85 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_self__quotient,axiom,
% 81.03/80.85 ! [V_r,V_q,V_a] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__int__rel__mod,axiom,
% 81.03/80.85 ! [V_r,V_q,V_b,V_a] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__int__rel__div,axiom,
% 81.03/80.85 ! [V_r,V_q,V_b,V_a] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_negDivAlg__correct,axiom,
% 81.03/80.85 ! [V_b,V_a] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.85 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__int__rel__div__mod,axiom,
% 81.03/80.85 ! [V_a,V_b] :
% 81.03/80.85 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => 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)))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_posDivAlg__correct,axiom,
% 81.03/80.85 ! [V_b,V_a] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.85 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_zadd1__lemma,axiom,
% 81.03/80.85 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( 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)))
% 81.03/80.85 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => 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)))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_zminus1__lemma,axiom,
% 81.03/80.85 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => 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))))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__int__relI,axiom,
% 81.03/80.85 ! [V_r,V_q,V_b,V_a] :
% 81.03/80.85 ( 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)
% 81.03/80.85 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 81.03/80.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 81.03/80.85 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 81.03/80.85 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 81.03/80.85 => 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))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_zmult1__lemma,axiom,
% 81.03/80.85 ! [V_a,V_r,V_q,V_c,V_b] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 81.03/80.85 => 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)))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__int__rel__def,axiom,
% 81.03/80.85 ! [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))))))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_mod__pos__neg__1__number__of,axiom,
% 81.03/80.85 ! [V_w] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => 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))))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_in__measure,axiom,
% 81.03/80.85 ! [V_f_2,V_y_2,V_x_2,T_a] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 <=> 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_norm__frac_Opinduct,axiom,
% 81.03/80.85 ! [V_P_2,V_a1_2,V_a0_2] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ! [B_a,B_b] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => 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))) )
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_apsnd__eq__conv,axiom,
% 81.03/80.85 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] :
% 81.03/80.85 ( 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)
% 81.03/80.85 <=> 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)) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_snd__apsnd,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_snd__def,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_snd__conv,axiom,
% 81.03/80.85 ! [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 ).
% 81.03/80.85
% 81.03/80.85 fof(fact_snd__eqD,axiom,
% 81.03/80.85 ! [V_a,V_y,V_x,T_a,T_b] :
% 81.03/80.85 ( 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
% 81.03/80.85 => V_y = V_a ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_mod__int__def,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_mod__neg__pos,axiom,
% 81.03/80.85 ! [V_b,V_a] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_mod__pos__pos,axiom,
% 81.03/80.85 ! [V_b,V_a] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_mod__pos__pos__1__number__of,axiom,
% 81.03/80.85 ! [V_w] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_mod__pos__neg,axiom,
% 81.03/80.85 ! [V_b,V_a] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => 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)))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_mod__neg__neg,axiom,
% 81.03/80.85 ! [V_b,V_a] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => 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)))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_div__pos__neg__1__number__of,axiom,
% 81.03/80.85 ! [V_w] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => 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))))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_nat__gcd_Opinduct,axiom,
% 81.03/80.85 ! [V_P_2,V_a1_2,V_a0_2] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ! [B_x,B_y] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 81.03/80.85 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_mlex__leq,axiom,
% 81.03/80.85 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => ( 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))
% 81.03/80.85 => 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))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_prod__eqI,axiom,
% 81.03/80.85 ! [V_q,V_p,T_b,T_a] :
% 81.03/80.85 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 81.03/80.85 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 81.03/80.85 => V_p = V_q ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_Pair__fst__snd__eq,axiom,
% 81.03/80.85 ! [T_b,T_a,V_t_2,V_s_2] :
% 81.03/80.85 ( V_s_2 = V_t_2
% 81.03/80.85 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2)
% 81.03/80.85 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_fst__eqD,axiom,
% 81.03/80.85 ! [V_a,V_y,V_x,T_b,T_a] :
% 81.03/80.85 ( 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
% 81.03/80.85 => V_x = V_a ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_fst__conv,axiom,
% 81.03/80.85 ! [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 ).
% 81.03/80.85
% 81.03/80.85 fof(fact_fst__def,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_fst__apsnd,axiom,
% 81.03/80.85 ! [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) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_pair__collapse,axiom,
% 81.03/80.85 ! [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 ).
% 81.03/80.85
% 81.03/80.85 fof(fact_surjective__pairing,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_prod__case__beta,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_div__int__def,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_mod__nat__def,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_split__comp__eq,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_split__beta,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_split__def,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_div__neg__pos,axiom,
% 81.03/80.85 ! [V_b,V_a] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_div__pos__pos,axiom,
% 81.03/80.85 ! [V_b,V_a] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 81.03/80.85 => 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)) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_div__pos__pos__1__number__of,axiom,
% 81.03/80.85 ! [V_w] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_div__pos__neg,axiom,
% 81.03/80.85 ! [V_b,V_a] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => 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)))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_div__neg__neg,axiom,
% 81.03/80.85 ! [V_b,V_a] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 81.03/80.85 => 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)))) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_mlex__less,axiom,
% 81.03/80.85 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 81.03/80.85 ( 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)))
% 81.03/80.85 => 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))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_prod__size__simp,axiom,
% 81.03/80.85 ! [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))) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_conjI__realizer,axiom,
% 81.03/80.85 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] :
% 81.03/80.85 ( hBOOL(hAPP(V_P_2,V_p_2))
% 81.03/80.85 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 81.03/80.85 => ( 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))))
% 81.03/80.85 & 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)))) ) ) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_exI__realizer,axiom,
% 81.03/80.85 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] :
% 81.03/80.85 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 81.03/80.85 => 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)))) ) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_div__nat__def,axiom,
% 81.03/80.85 ! [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)) ).
% 81.03/80.85
% 81.03/80.85 fof(fact_divmod__nat__rel__def,axiom,
% 81.03/80.85 ! [V_qr_2,V_n_2,V_m_2] :
% 81.03/80.85 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 81.03/80.85 <=> ( 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))
% 81.03/80.85 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.85 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 81.03/80.85 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.85 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 81.03/80.85 => ( 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)))
% 81.03/80.85 & 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)) ) )
% 81.03/80.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 81.03/80.86 => ( 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)))
% 81.03/80.86 & 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))) ) ) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_range,axiom,
% 81.03/80.86 ! [V_s,V_k] :
% 81.03/80.86 ( 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))
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_prod_Orecs,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__add__map__of__foldr,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_in__lex__prod,axiom,
% 81.03/80.86 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 <=> ( 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))
% 81.03/80.86 | ( V_a_2 = V_a_H_2
% 81.03/80.86 & 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_in__finite__psubset,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.86 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_setsum__nonneg__0,axiom,
% 81.03/80.86 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] :
% 81.03/80.86 ( class_Groups_Oordered__ab__group__add(T_b)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 81.03/80.86 => ( ! [B_i] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) )
% 81.03/80.86 => ( 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)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
% 81.03/80.86 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_same__fstI,axiom,
% 81.03/80.86 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] :
% 81.03/80.86 ( hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => 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))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_setsum__nonneg__leq__bound,axiom,
% 81.03/80.86 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] :
% 81.03/80.86 ( class_Groups_Oordered__ab__group__add(T_b)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 81.03/80.86 => ( ! [B_i] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) )
% 81.03/80.86 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_full__small__int__def,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_small_H_Osimps,axiom,
% 81.03/80.86 ! [V_f_2,V_i_2,V_d_2] :
% 81.03/80.86 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 81.03/80.86 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 81.03/80.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 81.03/80.86 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_sum__diff__distrib,axiom,
% 81.03/80.86 ! [V_n_2,V_P_2,V_Q_2] :
% 81.03/80.86 ( ! [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)))
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_small_H_Opsimps,axiom,
% 81.03/80.86 ! [V_i_2,V_d_2,V_f_2] :
% 81.03/80.86 ( 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))))
% 81.03/80.86 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 81.03/80.86 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 81.03/80.86 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 81.03/80.86 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_small__int__def,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_apsnd__apfst,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_apfst__conv,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_fst__apfst,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_apfst__eq__conv,axiom,
% 81.03/80.86 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] :
% 81.03/80.86 ( 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)
% 81.03/80.86 <=> 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_snd__apfst,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_apsnd__apfst__commute,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_small__prod__def,axiom,
% 81.03/80.86 ! [V_d_2,V_f_2,T_a,T_b] :
% 81.03/80.86 ( ( class_Smallcheck_Osmall(T_b)
% 81.03/80.86 & class_Smallcheck_Osmall(T_a) )
% 81.03/80.86 => 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) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_apfst__apsnd,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_small_H_Opinduct,axiom,
% 81.03/80.86 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] :
% 81.03/80.86 ( 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))))
% 81.03/80.86 => ( ! [B_f,B_d,B_i] :
% 81.03/80.86 ( 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))))
% 81.03/80.86 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 81.03/80.86 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
% 81.03/80.86 => 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)))) ) )
% 81.03/80.86 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) )
% 81.03/80.86 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_pair__lessI2,axiom,
% 81.03/80.86 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INFI__fold__inf,axiom,
% 81.03/80.86 ! [V_f_2,V_A_2,T_a,T_b] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__D,axiom,
% 81.03/80.86 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__E,axiom,
% 81.03/80.86 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2)))
% 81.03/80.86 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INF1__E,axiom,
% 81.03/80.86 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 81.03/80.86 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INF1__D,axiom,
% 81.03/80.86 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INF2__D,axiom,
% 81.03/80.86 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INF2__E,axiom,
% 81.03/80.86 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 81.03/80.86 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__INT,axiom,
% 81.03/80.86 ! [V_A_2,T_b,V_I_2,T_a] :
% 81.03/80.86 ( ? [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2))
% 81.03/80.86 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) )
% 81.03/80.86 => 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INF__INT__eq2,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__Int__distrib,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__subset__iff,axiom,
% 81.03/80.86 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 81.03/80.86 => 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))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__simps_I10_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__extend__simps_I10_J,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__simps_I7_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__simps_I6_J,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__extend__simps_I7_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Un__INT__distrib,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__extend__simps_I6_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Un__INT__distrib2,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__extend__simps_I5_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__simps_I5_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__extend__simps_I8_J,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__simps_I8_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INFI__apply,axiom,
% 81.03/80.86 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INF__commute,axiom,
% 81.03/80.86 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.86 => 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Pow__INT__eq,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Inter__def,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,T_a] :
% 81.03/80.86 ( 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)
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 81.03/80.86 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_a,T_b] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 81.03/80.86 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__iff,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_le__INF__iff,axiom,
% 81.03/80.86 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.86 => ( 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)))
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INF__less__iff,axiom,
% 81.03/80.86 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] :
% 81.03/80.86 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.86 & class_Orderings_Olinorder(T_a) )
% 81.03/80.86 => ( 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))
% 81.03/80.86 <=> ? [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 81.03/80.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__insert__distrib,axiom,
% 81.03/80.86 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2))
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__lower,axiom,
% 81.03/80.86 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INF__INT__eq,axiom,
% 81.03/80.86 ! [V_x_2,V_r_2,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__absorb,axiom,
% 81.03/80.86 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2))
% 81.03/80.86 => 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) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INF__const,axiom,
% 81.03/80.86 ! [V_M_2,T_a,V_A_2,T_b] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 81.03/80.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__constant,axiom,
% 81.03/80.86 ! [V_ca_2,T_b,T_a,V_A_2] :
% 81.03/80.86 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) )
% 81.03/80.86 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__empty,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__extend__simps_I1_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 81.03/80.86 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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 )
% 81.03/80.86 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__extend__simps_I2_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 81.03/80.86 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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 )
% 81.03/80.86 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__insert,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__Un,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Un__Inter,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INTER__eq__Inter__image,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Inter__image__eq,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INF__subset,axiom,
% 81.03/80.86 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.86 => 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))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__simps_I2_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 81.03/80.86 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) )
% 81.03/80.86 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__simps_I1_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 81.03/80.86 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) )
% 81.03/80.86 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__extend__simps_I3_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 81.03/80.86 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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) )
% 81.03/80.86 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__simps_I3_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 81.03/80.86 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) )
% 81.03/80.86 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INF__leI,axiom,
% 81.03/80.86 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
% 81.03/80.86 => 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))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Int__Inter__image,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__greaterThan__UNIV,axiom,
% 81.03/80.86 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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_pair__lessI1,axiom,
% 81.03/80.86 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inf__INFI__fold__inf,axiom,
% 81.03/80.86 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_pair__leqI2,axiom,
% 81.03/80.86 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_smax__insertI,axiom,
% 81.03/80.86 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_smin__insertI,axiom,
% 81.03/80.86 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_smax__emptyI,axiom,
% 81.03/80.86 ! [V_Y_2] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 81.03/80.86 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_smin__emptyI,axiom,
% 81.03/80.86 ! [V_X_2] :
% 81.03/80.86 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INF2__iff,axiom,
% 81.03/80.86 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INF1__iff,axiom,
% 81.03/80.86 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_pair__leqI1,axiom,
% 81.03/80.86 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_wmin__insertI,axiom,
% 81.03/80.86 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_wmax__insertI,axiom,
% 81.03/80.86 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_wmax__emptyI,axiom,
% 81.03/80.86 ! [V_X_2] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_wmin__emptyI,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_min__weak__def,axiom,
% 81.03/80.86 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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_max__weak__def,axiom,
% 81.03/80.86 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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_max__rpair__set,axiom,
% 81.03/80.86 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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_max__strict__def,axiom,
% 81.03/80.86 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_max__ext__additive,axiom,
% 81.03/80.86 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => 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))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_min__strict__def,axiom,
% 81.03/80.86 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_min__rpair__set,axiom,
% 81.03/80.86 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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_max__extp__max__ext__eq,axiom,
% 81.03/80.86 ! [V_xa_2,V_x_2,V_R_2,T_a] :
% 81.03/80.86 ( 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)
% 81.03/80.86 <=> 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_less__than__iff,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_intrel__iff,axiom,
% 81.03/80.86 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> 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) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_pair__less__def,axiom,
% 81.03/80.86 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_mlex__prod__def,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_rp__inv__image__rp,axiom,
% 81.03/80.86 ! [V_f_2,T_b,V_P_2,T_a] :
% 81.03/80.86 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 81.03/80.86 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_SUPR__fold__sup,axiom,
% 81.03/80.86 ! [V_f_2,V_A_2,T_a,T_b] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_SUP1__I,axiom,
% 81.03/80.86 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__I,axiom,
% 81.03/80.86 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 81.03/80.86 => 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))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_SUP2__I,axiom,
% 81.03/80.86 ! [T_c,T_b,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__UN,axiom,
% 81.03/80.86 ! [V_B_2,T_b,V_A_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( 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)))
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__extend__simps_I6_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__simps_I6_J,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_SUP__commute,axiom,
% 81.03/80.86 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.86 => 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_SUPR__apply,axiom,
% 81.03/80.86 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__simps_I8_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__extend__simps_I8_J,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Union__def,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__extend__simps_I10_J,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_image__UN,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__simps_I10_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__subset__iff,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__Pow__subset,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__simps_I5_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__simps_I4_J,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__extend__simps_I5_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Int__UN__distrib,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__extend__simps_I4_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Int__UN__distrib2,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__iff,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 <=> ? [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 81.03/80.86 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__extend__simps_I9_J,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__simps_I9_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_SUP__UN__eq2,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__Un__distrib,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__Un,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UNION__empty__conv_I1_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,T_a] :
% 81.03/80.86 ( 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)
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 81.03/80.86 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__empty2,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__constant,axiom,
% 81.03/80.86 ! [V_ca_2,T_b,T_a,V_A_2] :
% 81.03/80.86 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) )
% 81.03/80.86 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UNION__empty__conv_I2_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_a,T_b] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 81.03/80.86 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_SUP__le__iff,axiom,
% 81.03/80.86 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.86 => ( 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))
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_less__SUP__iff,axiom,
% 81.03/80.86 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] :
% 81.03/80.86 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.86 & class_Orderings_Olinorder(T_a) )
% 81.03/80.86 => ( 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)))
% 81.03/80.86 <=> ? [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 81.03/80.86 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_SUP__const,axiom,
% 81.03/80.86 ! [V_M_2,T_a,V_A_2,T_b] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 81.03/80.86 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__insert__distrib,axiom,
% 81.03/80.86 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2))
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__upper,axiom,
% 81.03/80.86 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_SUP__UN__eq,axiom,
% 81.03/80.86 ! [V_x_2,V_r_2,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__absorb,axiom,
% 81.03/80.86 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2))
% 81.03/80.86 => 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) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__simps_I1_J,axiom,
% 81.03/80.86 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] :
% 81.03/80.86 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) )
% 81.03/80.86 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__singleton,axiom,
% 81.03/80.86 ! [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 ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__extend__simps_I1_J,axiom,
% 81.03/80.86 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] :
% 81.03/80.86 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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))) )
% 81.03/80.86 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__extend__simps_I2_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 81.03/80.86 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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 )
% 81.03/80.86 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__extend__simps_I3_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 81.03/80.86 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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 )
% 81.03/80.86 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__simps_I2_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 81.03/80.86 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) )
% 81.03/80.86 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__simps_I3_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 81.03/80.86 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) )
% 81.03/80.86 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__insert,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__simps_I7_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__extend__simps_I7_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_image__Union,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Int__Union,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Int__Union2,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Compl__UN,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Compl__INT,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UNION__eq__Union__image,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Union__image__eq,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_rp__inv__image__def,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__lessThan__UNIV,axiom,
% 81.03/80.86 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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__atMost__UNIV,axiom,
% 81.03/80.86 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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__atLeast__UNIV,axiom,
% 81.03/80.86 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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_SUP__subset,axiom,
% 81.03/80.86 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.86 => 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))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_image__eq__UN,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__extend__simps_I4_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 81.03/80.86 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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 )
% 81.03/80.86 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__UN__finite__eq,axiom,
% 81.03/80.86 ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_le__SUPI,axiom,
% 81.03/80.86 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
% 81.03/80.86 => 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))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Un__Union__image,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__le__add__shift,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_INT__simps_I4_J,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 81.03/80.86 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) )
% 81.03/80.86 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_sup__SUPR__fold__sup,axiom,
% 81.03/80.86 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 81.03/80.86 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__le__eq__Un0,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_in__inv__image,axiom,
% 81.03/80.86 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 <=> 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_nat__def,axiom,
% 81.03/80.86 ! [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)))))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__finite2__subset,axiom,
% 81.03/80.86 ! [V_B_2,V_k_2,V_A_2,T_a] :
% 81.03/80.86 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_SUP1__iff,axiom,
% 81.03/80.86 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> ? [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.86 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_SUP2__iff,axiom,
% 81.03/80.86 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> ? [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.86 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__extend__simps_I9_J,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__simps_I9_J,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__UN__flatten,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_ball__UN,axiom,
% 81.03/80.86 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] :
% 81.03/80.86 ( ! [B_x] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => hBOOL(hAPP(V_P_2,B_x)) )
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 81.03/80.86 => ! [B_xa] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x)))
% 81.03/80.86 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Rep__Integ__inject,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2] :
% 81.03/80.86 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 81.03/80.86 <=> V_x_2 = V_y_2 ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_measure__def,axiom,
% 81.03/80.86 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_irrefl__def,axiom,
% 81.03/80.86 ! [V_r_2,T_a] :
% 81.03/80.86 ( c_Relation_Oirrefl(T_a,V_r_2)
% 81.03/80.86 <=> ! [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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Field__insert,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__finite2__eq,axiom,
% 81.03/80.86 ! [V_B_2,V_k_2,V_A_2,T_a] :
% 81.03/80.86 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)
% 81.03/80.86 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Field__Union,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Field__empty,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_mono__Field,axiom,
% 81.03/80.86 ! [V_s_2,V_r_2,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 => 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Field__Un,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__Field,axiom,
% 81.03/80.86 ! [V_r_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 81.03/80.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__finite__subset,axiom,
% 81.03/80.86 ! [V_C_2,V_A_2,T_a] :
% 81.03/80.86 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Id__on__def,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_equiv__intrel__iff,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2] :
% 81.03/80.86 ( 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))))
% 81.03/80.86 <=> 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Image__Id__on,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Image__Un,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Image__empty,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Image__UN,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Image__Int__subset,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Image__mono,axiom,
% 81.03/80.86 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 81.03/80.86 => 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))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Un__Image,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Id__on__def_H,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Image__INT__subset,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_rev__ImageI,axiom,
% 81.03/80.86 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Image__iff,axiom,
% 81.03/80.86 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)))
% 81.03/80.86 <=> ? [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 81.03/80.86 & 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Id__on__empty,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Image__eq__UN,axiom,
% 81.03/80.86 ! [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))))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Id__on__iff,axiom,
% 81.03/80.86 ! [V_A_2,V_y_2,V_x_2,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 <=> ( V_x_2 = V_y_2
% 81.03/80.86 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Id__on__eqI,axiom,
% 81.03/80.86 ! [V_A_2,T_a,V_b_2,V_a_2] :
% 81.03/80.86 ( V_a_2 = V_b_2
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => 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))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Image__singleton__iff,axiom,
% 81.03/80.86 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] :
% 81.03/80.86 ( 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))))))
% 81.03/80.86 <=> 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_of__int,axiom,
% 81.03/80.86 ! [V_j_2,V_i_2,T_a] :
% 81.03/80.86 ( class_Rings_Oring__1(T_a)
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_One__int__def,axiom,
% 81.03/80.86 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))))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_mult,axiom,
% 81.03/80.86 ! [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))))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Rep__Integ__inverse,axiom,
% 81.03/80.86 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 81.03/80.86
% 81.03/80.86 fof(fact_minus,axiom,
% 81.03/80.86 ! [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))))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Zero__int__def,axiom,
% 81.03/80.86 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))))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_int__def,axiom,
% 81.03/80.86 ! [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))))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_add,axiom,
% 81.03/80.86 ! [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))))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_nat,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_minus__int__def,axiom,
% 81.03/80.86 ! [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))))))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_less,axiom,
% 81.03/80.86 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 81.03/80.86 ( 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)))))))
% 81.03/80.86 <=> 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_le,axiom,
% 81.03/80.86 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 81.03/80.86 ( 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)))))))
% 81.03/80.86 <=> 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_eq__Abs__Integ,axiom,
% 81.03/80.86 ! [V_z_2] :
% 81.03/80.86 ~ ! [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))))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_quotient__def,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Id__onE,axiom,
% 81.03/80.86 ! [V_A_2,V_ca_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_ca_2),c_Relation_OId__on(T_a,V_A_2)))
% 81.03/80.86 => ~ ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.86 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_quotient__is__empty,axiom,
% 81.03/80.86 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_quotient__is__empty2,axiom,
% 81.03/80.86 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( 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)
% 81.03/80.86 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_quotient__empty,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_quotientI,axiom,
% 81.03/80.86 ! [V_r_2,V_A_2,V_x_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.86 => 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_singleton__quotient,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_equiv__class__nondisjoint,axiom,
% 81.03/80.86 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => ( 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)))))))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_subset__equiv__class,axiom,
% 81.03/80.86 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => ( 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))))))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 81.03/80.86 => 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_quotientE,axiom,
% 81.03/80.86 ! [V_r_2,V_A_2,V_X_2,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => ~ ! [B_x] :
% 81.03/80.86 ( 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))))
% 81.03/80.86 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_equiv__intrel,axiom,
% 81.03/80.86 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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Union__quotient,axiom,
% 81.03/80.86 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => 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 ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_equiv__class__self,axiom,
% 81.03/80.86 ! [V_a_2,V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => 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)))))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_quotient__disj,axiom,
% 81.03/80.86 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => ( V_X_2 = V_Y_2
% 81.03/80.86 | 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)) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_equiv__class__eq,axiom,
% 81.03/80.86 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => ( 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))
% 81.03/80.86 => 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)))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_quotient__eq__iff,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
% 81.03/80.86 => ( V_X_2 = V_Y_2
% 81.03/80.86 <=> 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)) ) ) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_quotient__eqI,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_equiv__class__eq__iff,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => ( 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))
% 81.03/80.86 <=> ( 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))))
% 81.03/80.86 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.86 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_eq__equiv__class__iff,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 81.03/80.86 => ( 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))))
% 81.03/80.86 <=> 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)) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_eq__equiv__class,axiom,
% 81.03/80.86 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] :
% 81.03/80.86 ( 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))))
% 81.03/80.86 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 81.03/80.86 => 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_equiv__class__subset,axiom,
% 81.03/80.86 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => ( 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))
% 81.03/80.86 => 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)))))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_eq__equiv__class__iff2,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 81.03/80.86 => ( 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)
% 81.03/80.86 <=> 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)) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__equiv__class,axiom,
% 81.03/80.86 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => 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) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__equiv__class2,axiom,
% 81.03/80.86 ! [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] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 81.03/80.86 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 81.03/80.86 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2))
% 81.03/80.86 => 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) ) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_equivp__equiv,axiom,
% 81.03/80.86 ! [V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2)
% 81.03/80.86 <=> 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_equivp__transp,axiom,
% 81.03/80.86 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_equivp__symp,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_R_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_equivp__reflp,axiom,
% 81.03/80.86 ! [V_x_2,V_R_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 81.03/80.86 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_equivp__def,axiom,
% 81.03/80.86 ! [V_R_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 81.03/80.86 <=> ! [B_x,B_y] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 81.03/80.86 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_identity__equivp,axiom,
% 81.03/80.86 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_congruent2__implies__congruent,axiom,
% 81.03/80.86 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2)
% 81.03/80.86 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_congruent2D,axiom,
% 81.03/80.86 ! [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] :
% 81.03/80.86 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2)
% 81.03/80.86 => ( 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))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_congruentD,axiom,
% 81.03/80.86 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2)
% 81.03/80.86 => ( 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))
% 81.03/80.86 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_congruent2__implies__congruent__UN,axiom,
% 81.03/80.86 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 81.03/80.86 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 81.03/80.86 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2))
% 81.03/80.86 => 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)) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__equiv__class__inject,axiom,
% 81.03/80.86 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 81.03/80.86 => ( 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)
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => ( ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.86 => ! [B_y] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 81.03/80.86 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 81.03/80.86 => 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)) ) ) )
% 81.03/80.86 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__equiv__class__type2,axiom,
% 81.03/80.86 ! [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] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 81.03/80.86 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 81.03/80.86 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => ( ! [B_x1] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2))
% 81.03/80.86 => ! [B_x2] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 81.03/80.86 => 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)) ) ) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__equiv__class__type,axiom,
% 81.03/80.86 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.86 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => ( ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 81.03/80.86 => 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)) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Integ__def,axiom,
% 81.03/80.86 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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_card__quotient__disjoint,axiom,
% 81.03/80.86 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( 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)
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_ImageE,axiom,
% 81.03/80.86 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)))
% 81.03/80.86 => ~ ! [B_x] :
% 81.03/80.86 ( 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))
% 81.03/80.86 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__empty,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__uminus,axiom,
% 81.03/80.86 ! [V_A_2,T_a] :
% 81.03/80.86 ( class_Groups_Oordered__ab__group__add(T_a)
% 81.03/80.86 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__contraD,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => ( V_x_2 != V_y_2
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 81.03/80.86 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__iff,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 81.03/80.86 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 81.03/80.86 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__onD,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 81.03/80.86 => V_x_2 = V_y_2 ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__Int,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_subset__inj__on,axiom,
% 81.03/80.86 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.86 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__def,axiom,
% 81.03/80.86 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.86 => ! [B_xa] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 81.03/80.86 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 81.03/80.86 => B_x = B_xa ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__diff,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__id2,axiom,
% 81.03/80.86 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 => ( 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)
% 81.03/80.86 <=> V_A_2 = V_B_2 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_card__image,axiom,
% 81.03/80.86 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => 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) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__imageD,axiom,
% 81.03/80.86 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 81.03/80.86 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)
% 81.03/80.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__image__eq__iff,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => ( 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)
% 81.03/80.86 <=> V_A_2 = V_B_2 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__fun,axiom,
% 81.03/80.86 ! [T_c,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_injD,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 81.03/80.86 => V_x_2 = V_y_2 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__eq,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 81.03/80.86 <=> V_x_2 = V_y_2 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__strict__subset,axiom,
% 81.03/80.86 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.86 => 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))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__image__mem__iff,axiom,
% 81.03/80.86 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => ( 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)))
% 81.03/80.86 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_range__ex1__eq,axiom,
% 81.03/80.86 ! [V_b_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => ( 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)))))
% 81.03/80.86 <=> ? [B_x] :
% 81.03/80.86 ( V_b_2 = hAPP(V_f_2,B_x)
% 81.03/80.86 & ! [B_y] :
% 81.03/80.86 ( V_b_2 = hAPP(V_f_2,B_y)
% 81.03/80.86 => B_y = B_x ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__iff__surj,axiom,
% 81.03/80.86 ! [V_A_H_2,T_b,T_a,V_A_2] :
% 81.03/80.86 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 => ( ? [B_f] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 81.03/80.86 & 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)) )
% 81.03/80.86 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_endo__inj__surj,axiom,
% 81.03/80.86 ! [V_f_2,V_A_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2)
% 81.03/80.86 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__surj__inj,axiom,
% 81.03/80.86 ! [V_f_2,V_A_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__UNIV__inj__surj,axiom,
% 81.03/80.86 ! [V_f_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 81.03/80.86 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__UNIV__surj__inj,axiom,
% 81.03/80.86 ! [V_f_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__image__subset__iff,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => ( 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)))
% 81.03/80.86 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__image__Int,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 81.03/80.86 => 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_image__Int,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__iff__eq__card,axiom,
% 81.03/80.86 ! [V_f_2,T_b,V_A_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 <=> 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_eq__card__imp__inj__on,axiom,
% 81.03/80.86 ! [V_f_2,T_b,V_A_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( 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)
% 81.03/80.86 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__image__set__diff,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 81.03/80.86 => 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_image__set__diff,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_pigeonhole,axiom,
% 81.03/80.86 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__fun__updI,axiom,
% 81.03/80.86 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__singleton,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Rep__Integ,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_card__bij__eq,axiom,
% 81.03/80.86 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => ( 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))
% 81.03/80.86 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2)
% 81.03/80.86 => ( 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))
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 81.03/80.86 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__image__Compl__subset,axiom,
% 81.03/80.86 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => 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)))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__insert,axiom,
% 81.03/80.86 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))
% 81.03/80.86 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 & ~ 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))))))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__Un,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 81.03/80.86 & 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__iff__card__le,axiom,
% 81.03/80.86 ! [V_B_2,T_b,V_A_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 81.03/80.86 => ( ? [B_f] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 81.03/80.86 & 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)) )
% 81.03/80.86 <=> 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))) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_card__inj__on__le,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => ( 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))
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 81.03/80.86 => 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))) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_quotient__diff1,axiom,
% 81.03/80.86 ! [V_a_2,V_A_2,V_r_2,T_a] :
% 81.03/80.86 ( 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)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_image__INT,axiom,
% 81.03/80.86 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 81.03/80.86 => ( ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2))
% 81.03/80.86 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Oimage(T_a,T_b,V_f_2)),V_B_2)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_type__definition__Integ,axiom,
% 81.03/80.86 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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_the__inv__into__into,axiom,
% 81.03/80.86 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__Suc,axiom,
% 81.03/80.86 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__add__nat,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__Some,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__of__nat,axiom,
% 81.03/80.86 ! [T_a] :
% 81.03/80.86 ( class_Nat_Osemiring__char__0(T_a)
% 81.03/80.86 => 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__int,axiom,
% 81.03/80.86 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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__map__add__dom,axiom,
% 81.03/80.86 ! [V_m_H_2,V_m_2,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_swap__inj__on,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_the__inv__into__f__f,axiom,
% 81.03/80.86 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.86 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_the__inv__into__f__eq,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.86 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_the__inv__into__onto,axiom,
% 81.03/80.86 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => hAPP(c_Set_Oimage(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__the__inv__into,axiom,
% 81.03/80.86 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => c_Fun_Oinj__on(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_the__inv__f__f,axiom,
% 81.03/80.86 ! [V_x_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_f__the__inv__into__f,axiom,
% 81.03/80.86 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 81.03/80.86 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_type__definition_OAbs__image,axiom,
% 81.03/80.86 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 81.03/80.86 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_type__definition_ORep__range,axiom,
% 81.03/80.86 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 81.03/80.86 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 81.03/80.86 => 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 ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_type__definition_ORep,axiom,
% 81.03/80.86 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 81.03/80.86 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_type__definition_ORep__inverse,axiom,
% 81.03/80.86 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 81.03/80.86 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 81.03/80.86 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_type__definition_ORep__inject,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 81.03/80.86 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 81.03/80.86 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 81.03/80.86 <=> V_x_2 = V_y_2 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_type__definition_OAbs__inject,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 81.03/80.86 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 81.03/80.86 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 81.03/80.86 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_type__definition_OAbs__inverse,axiom,
% 81.03/80.86 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 81.03/80.86 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 81.03/80.86 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__of__mapk__SomeI,axiom,
% 81.03/80.86 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => ( 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)
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_escape,axiom,
% 81.03/80.86 ! [V_Q_2,V_ca_2,V_G_2,T_a,V_P_2] :
% 81.03/80.86 ( ! [B_Z,B_s] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 81.03/80.86 => 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)))) )
% 81.03/80.86 => 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)))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 81.03/80.86 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
% 81.03/80.86 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.86 & class_Groups_Ocomm__monoid__mult(T_a) )
% 81.03/80.86 => ( V_A_2 = V_B_2
% 81.03/80.86 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 81.03/80.86 => ( ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 81.03/80.86 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 81.03/80.86 => 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) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__mapI,axiom,
% 81.03/80.86 ! [V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__injective,axiom,
% 81.03/80.86 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 81.03/80.86 ( 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)
% 81.03/80.86 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 81.03/80.86 => V_xs_2 = V_ys_2 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__mapD,axiom,
% 81.03/80.86 ! [V_f_2,T_b,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__map__eq__map,axiom,
% 81.03/80.86 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => ( 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)
% 81.03/80.86 <=> V_xs_2 = V_ys_2 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__map,axiom,
% 81.03/80.86 ! [V_f_2,T_b,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__ident,axiom,
% 81.03/80.86 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__of__map__keys,axiom,
% 81.03/80.86 ! [V_m_2,T_b,V_xs_2,T_a] :
% 81.03/80.86 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2)
% 81.03/80.86 => 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 ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 81.03/80.86 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
% 81.03/80.86 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.86 & class_Groups_Ocomm__monoid__mult(T_a) )
% 81.03/80.86 => ( V_A_2 = V_B_2
% 81.03/80.86 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 81.03/80.86 => ( ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 81.03/80.86 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 81.03/80.86 => 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) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_accp__acc__eq,axiom,
% 81.03/80.86 ! [V_x_2,V_r_2,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__set,axiom,
% 81.03/80.86 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__eq__conv,axiom,
% 81.03/80.86 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] :
% 81.03/80.86 ( 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)
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 81.03/80.86 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_infinite__UNIV__listI,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_set__map,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_acc__subset,axiom,
% 81.03/80.86 ! [V_R2_2,V_R1_2,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 => 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__map__eq__map,axiom,
% 81.03/80.86 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => ( 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)
% 81.03/80.86 <=> V_xs_2 = V_ys_2 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__inj__on,axiom,
% 81.03/80.86 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 81.03/80.86 ( 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)
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => V_xs_2 = V_ys_2 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__fun__upd,axiom,
% 81.03/80.86 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] :
% 81.03/80.86 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.86 => 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) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__mapI,axiom,
% 81.03/80.86 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => 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) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__of__eq__dom,axiom,
% 81.03/80.86 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 81.03/80.86 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_acc__downward,axiom,
% 81.03/80.86 ! [V_a_2,V_r_2,V_b_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_acc_Osimps,axiom,
% 81.03/80.86 ! [V_r_2,V_a_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 81.03/80.86 <=> ! [B_x] :
% 81.03/80.86 ( 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))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__of__SomeD,axiom,
% 81.03/80.86 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] :
% 81.03/80.86 ( 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)
% 81.03/80.86 => 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__of__is__SomeD,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] :
% 81.03/80.86 ( 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)
% 81.03/80.86 => 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))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_dom__map__of__conv__image__fst,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__of__eq__None__iff,axiom,
% 81.03/80.86 ! [V_x_2,V_xys_2,T_a,T_b] :
% 81.03/80.86 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a)
% 81.03/80.86 <=> ~ 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)))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_ran__distinct,axiom,
% 81.03/80.86 ! [V_al_2,T_b,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_greaterThanLessThan__upto,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__of__map__restrict,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__map,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_List_Omap_Ocompositionality,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__comp__map,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_List_Omap_Ocomp,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_atLeastAtMost__upto,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_set__upto,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_comp__surj,axiom,
% 81.03/80.86 ! [V_g_2,T_c,V_f_2,T_a,T_b] :
% 81.03/80.86 ( 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))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__comp,axiom,
% 81.03/80.86 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.86 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 81.03/80.86 => 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))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__imageI,axiom,
% 81.03/80.86 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] :
% 81.03/80.86 ( 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)
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_comp__inj__on,axiom,
% 81.03/80.86 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => ( 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))
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_comp__inj__on__iff,axiom,
% 81.03/80.86 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => ( 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))
% 81.03/80.86 <=> 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__on__imageI2,axiom,
% 81.03/80.86 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] :
% 81.03/80.86 ( 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)
% 81.03/80.86 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_image__compose,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_o__def,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_K__record__comp,axiom,
% 81.03/80.86 ! [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 ).
% 81.03/80.86
% 81.03/80.86 fof(fact_distinct__upto,axiom,
% 81.03/80.86 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 81.03/80.86 ! [V_x_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 81.03/80.86 => 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) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_fun__upd__comp,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_comp__cong,axiom,
% 81.03/80.86 ! [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] :
% 81.03/80.86 ( 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))
% 81.03/80.86 => 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) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_o__assoc,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_o__apply,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_o__eq__dest,axiom,
% 81.03/80.86 ! [V_v_2,V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
% 81.03/80.86 ( 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)
% 81.03/80.86 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_o__eq__elim,axiom,
% 81.03/80.86 ! [V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
% 81.03/80.86 ( 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)
% 81.03/80.86 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_o__eq__dest__lhs,axiom,
% 81.03/80.86 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] :
% 81.03/80.86 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_ca_2
% 81.03/80.86 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_apsnd__compose,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_apfst__compose,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_setsum__reindex,axiom,
% 81.03/80.86 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
% 81.03/80.86 ( class_Groups_Ocomm__monoid__add(T_c)
% 81.03/80.86 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_setprod__reindex__cong,axiom,
% 81.03/80.86 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 81.03/80.86 ( class_Groups_Ocomm__monoid__mult(T_c)
% 81.03/80.86 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.86 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 81.03/80.86 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)
% 81.03/80.86 => 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) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_setprod__reindex,axiom,
% 81.03/80.86 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
% 81.03/80.86 ( class_Groups_Ocomm__monoid__mult(T_c)
% 81.03/80.86 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_distinct__map,axiom,
% 81.03/80.86 ! [V_xs_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)))
% 81.03/80.86 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 81.03/80.86 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__of__inject__set,axiom,
% 81.03/80.86 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
% 81.03/80.86 <=> 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) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_setsum_Oreindex,axiom,
% 81.03/80.86 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
% 81.03/80.86 ( class_Groups_Ocomm__monoid__add(T_b)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
% 81.03/80.86 => 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) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_setprod_Oreindex,axiom,
% 81.03/80.86 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
% 81.03/80.86 ( class_Groups_Ocomm__monoid__mult(T_b)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
% 81.03/80.86 => 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) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_the__inv__into__comp,axiom,
% 81.03/80.86 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] :
% 81.03/80.86 ( 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))
% 81.03/80.86 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2)
% 81.03/80.86 => ( 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))))
% 81.03/80.86 => 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) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_fold__image__reindex,axiom,
% 81.03/80.86 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] :
% 81.03/80.86 ( class_Groups_Oab__semigroup__mult(T_c)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2)
% 81.03/80.86 => 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) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_atLeastLessThan__upto,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_greaterThanAtMost__upto,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__of__is__SomeI,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => ( 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)))
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_map__of__eq__Some__iff,axiom,
% 81.03/80.86 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => ( 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)
% 81.03/80.86 <=> 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))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Some__eq__map__of__iff,axiom,
% 81.03/80.86 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => ( 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)
% 81.03/80.86 <=> 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))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_nat__list__def,axiom,
% 81.03/80.86 ! [V_l_2] :
% 81.03/80.86 ( c_List_Onat__list(V_l_2)
% 81.03/80.86 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_folding_Oremove,axiom,
% 81.03/80.86 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.86 => 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_set__map__of__compr,axiom,
% 81.03/80.86 ! [V_xs_2,T_b,T_a] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => 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)))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_CollectI,axiom,
% 81.03/80.86 ! [T_a,V_a_2,V_P_2] :
% 81.03/80.86 ( hBOOL(hAPP(V_P_2,V_a_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__Collect__conjI,axiom,
% 81.03/80.86 ! [V_Q_2,V_P_2,T_a] :
% 81.03/80.86 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 81.03/80.86 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) )
% 81.03/80.86 => 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)))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UN__o,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__Collect__disjI,axiom,
% 81.03/80.86 ! [V_Q_2,V_P_2,T_a] :
% 81.03/80.86 ( 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))))
% 81.03/80.86 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 81.03/80.86 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 81.03/80.86 ! [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] :
% 81.03/80.86 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2)
% 81.03/80.86 => 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) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_folding_Ocommute__comp,axiom,
% 81.03/80.86 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_folding_Ocommute__left__comp,axiom,
% 81.03/80.86 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Collect__mem__eq,axiom,
% 81.03/80.86 ! [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 ).
% 81.03/80.86
% 81.03/80.86 fof(fact_mem__Collect__eq,axiom,
% 81.03/80.86 ! [V_P_2,V_a_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 81.03/80.86 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_CollectD,axiom,
% 81.03/80.86 ! [V_P_2,V_a_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 81.03/80.86 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_CollectE,axiom,
% 81.03/80.86 ! [V_P_2,V_a_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 81.03/80.86 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_insert__Collect,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_empty__def,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_empty__Collect__eq,axiom,
% 81.03/80.86 ! [V_P_2,T_a] :
% 81.03/80.86 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2)
% 81.03/80.86 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Collect__empty__eq,axiom,
% 81.03/80.86 ! [V_P_2,T_a] :
% 81.03/80.86 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.86 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Collect__disj__eq,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Collect__conj__eq,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Collect__def,axiom,
% 81.03/80.86 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Collect__neg__eq,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_UNIV__def,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_foldr__map,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_insert__compr__raw,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_insert__compr,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Un__def,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Int__def,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Int__Collect,axiom,
% 81.03/80.86 ! [V_P_2,V_A_2,V_x_2,T_a] :
% 81.03/80.86 ( 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))))
% 81.03/80.86 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.86 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_singleton__conv2,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_singleton__conv,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Collect__conv__if2,axiom,
% 81.03/80.86 ! [T_a,V_a_2,V_P_2] :
% 81.03/80.86 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 81.03/80.86 => 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))) )
% 81.03/80.86 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Collect__conv__if,axiom,
% 81.03/80.86 ! [T_a,V_a_2,V_P_2] :
% 81.03/80.86 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 81.03/80.86 => 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))) )
% 81.03/80.86 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_set__diff__eq,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__Collect__not,axiom,
% 81.03/80.86 ! [V_P_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 81.03/80.86 => ( 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))))
% 81.03/80.86 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_insert__def,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Compl__eq,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Collect__imp__eq,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_dom__def,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_split__comp,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_setsum__setsum__restrict,axiom,
% 81.03/80.86 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] :
% 81.03/80.86 ( class_Groups_Ocomm__monoid__add(T_c)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 81.03/80.86 => 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) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inj__graph,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_if__image__distrib,axiom,
% 81.03/80.86 ! [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))))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_folding_Ocommute__comp_H,axiom,
% 81.03/80.86 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 81.03/80.86 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.86 => 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 81.03/80.86 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.86 => 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Collect__all__eq,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_dom__if,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_folding_Oeq__fold,axiom,
% 81.03/80.86 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__psubset__def,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_setsum__restrict__set_H,axiom,
% 81.03/80.86 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
% 81.03/80.86 ( class_Groups_Ocomm__monoid__add(T_b)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_setsum__image__gen,axiom,
% 81.03/80.86 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] :
% 81.03/80.86 ( class_Groups_Ocomm__monoid__add(T_b)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_inv__image__def,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Image__singleton,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_setsum__cases,axiom,
% 81.03/80.86 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] :
% 81.03/80.86 ( class_Groups_Ocomm__monoid__add(T_b)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => 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))))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_folding_Oinsert,axiom,
% 81.03/80.86 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.86 => 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_folding_Ounion__inter,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.86 => 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_folding_Oinsert__remove,axiom,
% 81.03/80.86 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => 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)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_folding_Ounion,axiom,
% 81.03/80.86 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => 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)) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Nitpick_Oprod__def,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_int__ge__less__than__def,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_int__ge__less__than2__def,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__Collect__less__nat,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__Collect__le__nat,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__Collect__subsets,axiom,
% 81.03/80.86 ! [V_A_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.86 => 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)))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 81.03/80.86 ! [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)))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Pow__def,axiom,
% 81.03/80.86 ! [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)) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_finite__M__bounded__by__nat,axiom,
% 81.03/80.86 ! [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))))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 81.03/80.86 ! [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))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_nat__seg__image__imp__finite,axiom,
% 81.03/80.86 ! [V_n_2,V_f_2,T_a,V_A_2] :
% 81.03/80.86 ( 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)))
% 81.03/80.86 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_card__less__Suc2,axiom,
% 81.03/80.86 ! [V_i_2,V_M_2] :
% 81.03/80.86 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 81.03/80.86 => 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))))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_card__less,axiom,
% 81.03/80.86 ! [V_i_2,V_M_2] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 81.03/80.86 => 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) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_card__less__Suc,axiom,
% 81.03/80.86 ! [V_i_2,V_M_2] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 81.03/80.86 => 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))))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_dom__override__on,axiom,
% 81.03/80.86 ! [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))))) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_hoare__derivs_OIf,axiom,
% 81.03/80.86 ! [V_d_2,V_Q_2,V_ca_2,V_b_2,V_P_2,V_G_2,T_a] :
% 81.03/80.86 ( 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))))
% 81.03/80.86 => ( 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))))
% 81.03/80.86 => 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)))) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_setsum__multicount,axiom,
% 81.03/80.86 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 81.03/80.86 => ( ! [B_x] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2))
% 81.03/80.86 => 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 )
% 81.03/80.86 => 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_peek__and__def,axiom,
% 81.03/80.86 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2))
% 81.03/80.86 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2))
% 81.03/80.86 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_override__on__apply__notin,axiom,
% 81.03/80.86 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 81.03/80.86 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => 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) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_override__on__apply__in,axiom,
% 81.03/80.86 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => 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) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_override__on__emptyset,axiom,
% 81.03/80.86 ! [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 ).
% 81.03/80.86
% 81.03/80.86 fof(fact_override__on__def,axiom,
% 81.03/80.86 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 81.03/80.86 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => 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) )
% 81.03/80.86 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.86 => 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) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Loop__sound__lemma,axiom,
% 81.03/80.86 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] :
% 81.03/80.86 ( 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))))
% 81.03/80.86 => 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)))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_Loop,axiom,
% 81.03/80.86 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] :
% 81.03/80.86 ( 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))))
% 81.03/80.86 => 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)))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_folding__image_Oreindex,axiom,
% 81.03/80.86 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 81.03/80.86 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 81.03/80.86 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 81.03/80.86 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 81.03/80.86 => 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) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_evaln_OWhileTrue,axiom,
% 81.03/80.86 ! [V_s2_2,V_s1_2,V_n_2,V_ca_2,V_s0_2,V_b_2] :
% 81.03/80.86 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s0_2),V_n_2),V_s1_2))
% 81.03/80.86 => ( 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))
% 81.03/80.86 => 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_evaln_OWhileFalse,axiom,
% 81.03/80.86 ! [V_n_2,V_ca_2,V_s_2,V_b_2] :
% 81.03/80.86 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 81.03/80.86 => 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)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_evalc_OWhileFalse,axiom,
% 81.03/80.86 ! [V_ca_2,V_s_2,V_b_2] :
% 81.03/80.86 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_s_2)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_evalc_OWhileTrue,axiom,
% 81.03/80.86 ! [V_s2_2,V_s1_2,V_ca_2,V_s0_2,V_b_2] :
% 81.03/80.86 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s0_2),V_s1_2))
% 81.03/80.86 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_s2_2))
% 81.03/80.86 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_s2_2)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_WTs__elim__cases_I6_J,axiom,
% 81.03/80.86 ! [V_ca_2,V_b_2] :
% 81.03/80.86 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2)))
% 81.03/80.86 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_com_Osimps_I5_J,axiom,
% 81.03/80.86 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 81.03/80.86 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 81.03/80.86 <=> ( V_fun_2 = V_fun_H_2
% 81.03/80.86 & V_com_2 = V_com_H_2 ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_While,axiom,
% 81.03/80.86 ! [V_b_2,V_ca_2] :
% 81.03/80.86 ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
% 81.03/80.86 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2))) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_WT_Oequations_I6_J,axiom,
% 81.03/80.86 ! [V_a1_2,V_a2_2] :
% 81.03/80.86 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2)))
% 81.03/80.86 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_com_Osimps_I58_J,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_com_Osimps_I59_J,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_evalc_Oequations_I7_J,axiom,
% 81.03/80.86 ! [V_a2_2,V_a3_2,V_a1_2] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2))
% 81.03/80.86 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 81.03/80.86 => ? [B_s1] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 81.03/80.86 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_evalc_Oequations_I8_J,axiom,
% 81.03/80.86 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2))
% 81.03/80.86 <=> ( ( V_a5_2 = V_a2_2
% 81.03/80.86 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 81.03/80.86 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 81.03/80.86 & ? [B_s1] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 81.03/80.86 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_evaln_Oequations_I8_J,axiom,
% 81.03/80.86 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> ( ( V_a6_2 = V_a2_2
% 81.03/80.86 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 81.03/80.86 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 81.03/80.86 & ? [B_s1] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1))
% 81.03/80.86 & 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)) ) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_evaln_Oequations_I7_J,axiom,
% 81.03/80.86 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 81.03/80.86 ( 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))
% 81.03/80.86 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 81.03/80.86 => ? [B_s1] :
% 81.03/80.86 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1))
% 81.03/80.86 & 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)) ) ) ) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_com_Osimps_I52_J,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_com_Osimps_I53_J,axiom,
% 81.03/80.86 ! [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) ).
% 81.03/80.86
% 81.03/80.86 fof(fact_com_Osimps_I17_J,axiom,
% 81.03/80.86 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 81.03/80.86
% 81.03/80.86 fof(fact_com_Osimps_I16_J,axiom,
% 81.03/80.87 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_com_Osimps_I38_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_com_Osimps_I39_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_com_Osimps_I61_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_com_Osimps_I60_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_com_Osimps_I47_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_com_Osimps_I46_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_folding__image_Odistrib,axiom,
% 81.03/80.87 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_folding__image_Oeq__fold,axiom,
% 81.03/80.87 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 81.03/80.87 => 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_com_Osize_I14_J,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_com_Osize_I6_J,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_LoopF,axiom,
% 81.03/80.87 ! [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)))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 81.03/80.87 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 => 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))))) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 81.03/80.87 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 => 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))))) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 81.03/80.87 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.87 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 => 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))))))) ) ) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_finite__image__set,axiom,
% 81.03/80.87 ! [V_f_2,T_b,V_P_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 81.03/80.87 => 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))))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_finite__Collect__bounded__ex,axiom,
% 81.03/80.87 ! [V_Q_2,T_b,V_P_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 81.03/80.87 => ( 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)))))
% 81.03/80.87 <=> ! [B_y] :
% 81.03/80.87 ( hBOOL(hAPP(V_P_2,B_y))
% 81.03/80.87 => 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)))) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_ran__def,axiom,
% 81.03/80.87 ! [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)))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Pow__Compl,axiom,
% 81.03/80.87 ! [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))))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_add__Max__commute,axiom,
% 81.03/80.87 ! [V_k_2,V_N_2,T_a] :
% 81.03/80.87 ( class_Groups_Olinordered__ab__semigroup__add(T_a)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 81.03/80.87 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 => 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))))) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_add__Min__commute,axiom,
% 81.03/80.87 ! [V_k_2,V_N_2,T_a] :
% 81.03/80.87 ( class_Groups_Olinordered__ab__semigroup__add(T_a)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 81.03/80.87 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 => 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))))) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_sup__Inf1__distrib,axiom,
% 81.03/80.87 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.87 ( class_Lattices_Odistrib__lattice(T_a)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 => 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))))) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_sup__Inf2__distrib,axiom,
% 81.03/80.87 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.87 ( class_Lattices_Odistrib__lattice(T_a)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.87 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 => 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))))))) ) ) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_inf__Sup2__distrib,axiom,
% 81.03/80.87 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.87 ( class_Lattices_Odistrib__lattice(T_a)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.87 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 => 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))))))) ) ) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_inf__Sup1__distrib,axiom,
% 81.03/80.87 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.87 ( class_Lattices_Odistrib__lattice(T_a)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 => 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))))) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 81.03/80.87 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.87 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 => 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))))))) ) ) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_setsum__reindex__nonzero,axiom,
% 81.03/80.87 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] :
% 81.03/80.87 ( class_Groups_Ocomm__monoid__add(T_c)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 81.03/80.87 => ( ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 81.03/80.87 => ! [B_y] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2))
% 81.03/80.87 => ( B_x != B_y
% 81.03/80.87 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 81.03/80.87 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) )
% 81.03/80.87 => 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) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_setsum__multicount__gen,axiom,
% 81.03/80.87 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2))
% 81.03/80.87 => ( ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2))
% 81.03/80.87 => 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) )
% 81.03/80.87 => 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) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__of__map,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_option__map__o__empty,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_option__map__comp,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Option_Omap_Ocompositionality,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Option_Omap_Ocomp,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_dom__option__map,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_option__map__is__None,axiom,
% 81.03/80.87 ! [V_opt_2,V_f_2,T_a,T_b] :
% 81.03/80.87 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a)
% 81.03/80.87 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_option__map__None,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_option__map__eq__Some,axiom,
% 81.03/80.87 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] :
% 81.03/80.87 ( 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)
% 81.03/80.87 <=> ? [B_z] :
% 81.03/80.87 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z)
% 81.03/80.87 & hAPP(V_f_2,B_z) = V_y_2 ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_option__map__Some,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_option__map__o__map__upd,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Option_Omap__def,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_weak__map__of__SomeI,axiom,
% 81.03/80.87 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => ? [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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_folding__idem_Ounion__idem,axiom,
% 81.03/80.87 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 81.03/80.87 => 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)) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 81.03/80.87 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 81.03/80.87 => 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) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 81.03/80.87 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_folding__idem_Oidem__comp,axiom,
% 81.03/80.87 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 81.03/80.87 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.87 => 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) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_folding__idem_Oinsert__idem,axiom,
% 81.03/80.87 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__remove1__eq,axiom,
% 81.03/80.87 ! [V_x_2,V_xs_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.87 => 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)))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__of__zip__map,axiom,
% 81.03/80.87 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => 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)) )
% 81.03/80.87 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_strong__setprod__reindex__cong,axiom,
% 81.03/80.87 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 81.03/80.87 ( class_Groups_Ocomm__monoid__mult(T_c)
% 81.03/80.87 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.87 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 81.03/80.87 => ( ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.87 => 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) )
% 81.03/80.87 => 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) ) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__zipI1,axiom,
% 81.03/80.87 ! [V_ys,T_b,V_xs,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 81.03/80.87 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__remove1,axiom,
% 81.03/80.87 ! [V_x,V_xs,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 81.03/80.87 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__zipI2,axiom,
% 81.03/80.87 ! [V_xs,T_b,V_ys,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 81.03/80.87 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_remove1__commute,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_remove1__idem,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_notin__set__remove1,axiom,
% 81.03/80.87 ! [V_y_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => ~ 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)))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_in__set__remove1,axiom,
% 81.03/80.87 ! [V_xs_2,T_a,V_b_2,V_a_2] :
% 81.03/80.87 ( V_a_2 != V_b_2
% 81.03/80.87 => ( 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))))
% 81.03/80.87 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip__same__conv__map,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__remove1__subset,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip__map__fst__snd,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__zip__map,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__zip__map2,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip__same,axiom,
% 81.03/80.87 ! [V_xs_2,V_b_2,V_a_2,T_a] :
% 81.03/80.87 ( 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))))
% 81.03/80.87 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 & V_a_2 = V_b_2 ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__zip__leftD,axiom,
% 81.03/80.87 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 81.03/80.87 ( 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))))
% 81.03/80.87 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__zip__rightD,axiom,
% 81.03/80.87 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 81.03/80.87 ( 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))))
% 81.03/80.87 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_in__set__zipE,axiom,
% 81.03/80.87 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 81.03/80.87 ( 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))))
% 81.03/80.87 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip__map__map,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip__map1,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip__map2,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_sorted__list__of__set__remove,axiom,
% 81.03/80.87 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__of__zip__upd,axiom,
% 81.03/80.87 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => ( 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)
% 81.03/80.87 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 81.03/80.87 => ( 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))
% 81.03/80.87 => 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)) ) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__removeAll__inj__on,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_length__zip,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_length__map,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__eq__imp__length__eq,axiom,
% 81.03/80.87 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_neq__if__length__neq,axiom,
% 81.03/80.87 ! [V_ys,V_xs,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => V_xs != V_ys ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__removeAll,axiom,
% 81.03/80.87 ! [V_x,V_xs,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 81.03/80.87 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_card__length,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_removeAll__id,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_card__distinct,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__card,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__of__zip__inject,axiom,
% 81.03/80.87 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => ( 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)
% 81.03/80.87 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 81.03/80.87 => ( 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))
% 81.03/80.87 => V_ys_2 = V_zs_2 ) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__fst__zip,axiom,
% 81.03/80.87 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => 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 ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__snd__zip,axiom,
% 81.03/80.87 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => 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 ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__remove1__removeAll,axiom,
% 81.03/80.87 ! [V_x,V_xs,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 81.03/80.87 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_length__pos__if__in__set,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip__eq__conv,axiom,
% 81.03/80.87 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2
% 81.03/80.87 <=> ( 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
% 81.03/80.87 & 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 ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__removeAll__inj,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_finite__lists__length__eq,axiom,
% 81.03/80.87 ! [V_n_2,V_A_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => 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))))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__of__zip__is__None,axiom,
% 81.03/80.87 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => ( 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)
% 81.03/80.87 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__of__zip__is__Some,axiom,
% 81.03/80.87 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 <=> ? [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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_length__remove1,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => 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)) )
% 81.03/80.87 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_dom__map__of__zip,axiom,
% 81.03/80.87 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.87 => 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_finite__lists__length__le,axiom,
% 81.03/80.87 ! [V_n_2,V_A_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => 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))))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__removeAll,axiom,
% 81.03/80.87 ! [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)))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_length__sublist,axiom,
% 81.03/80.87 ! [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)))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__zip,axiom,
% 81.03/80.87 ! [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)))))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_sorted__list__of__set__insert,axiom,
% 81.03/80.87 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => 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)))))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__zip,axiom,
% 81.03/80.87 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => ( 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)))
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__eq__iff__nth__eq,axiom,
% 81.03/80.87 ! [T_a,V_ys_2,V_xs_2] :
% 81.03/80.87 ( V_xs_2 = V_ys_2
% 81.03/80.87 <=> ( 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)
% 81.03/80.87 & ! [B_i] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__sublistI,axiom,
% 81.03/80.87 ! [V_I_2,V_xs_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.87 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_fun__left__comm__insort,axiom,
% 81.03/80.87 ! [T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_insort__left__comm,axiom,
% 81.03/80.87 ! [V_xs_2,V_y_2,V_x_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_insort__key__left__comm,axiom,
% 81.03/80.87 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_remove1__insort,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => 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 ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__insort,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_b)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_length__insort,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_b)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_all__set__conv__all__nth,axiom,
% 81.03/80.87 ! [V_P_2,V_xs_2,T_a] :
% 81.03/80.87 ( ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => hBOOL(hAPP(V_P_2,B_x)) )
% 81.03/80.87 <=> ! [B_i] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__map,axiom,
% 81.03/80.87 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__conv__nth,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.87 <=> ! [B_i] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => ! [B_j] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => ( B_i != B_j
% 81.03/80.87 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__eq__iff__index__eq,axiom,
% 81.03/80.87 ! [V_j_2,V_i_2,V_xs_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.87 => ( 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)))
% 81.03/80.87 => ( 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)))
% 81.03/80.87 => ( 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)
% 81.03/80.87 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__sublist,axiom,
% 81.03/80.87 ! [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))))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_in__set__sublistD,axiom,
% 81.03/80.87 ! [V_I_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( 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))))
% 81.03/80.87 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_notin__set__sublistI,axiom,
% 81.03/80.87 ! [V_I_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => ~ 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)))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__sublist__subset,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_in__set__conv__nth,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 <=> ? [B_i] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__mem,axiom,
% 81.03/80.87 ! [V_xs_2,T_a,V_n_2] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__insort,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_b)
% 81.03/80.87 => ( 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)))
% 81.03/80.87 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__conv__nth,axiom,
% 81.03/80.87 ! [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))))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_insort__insert__insort__key,axiom,
% 81.03/80.87 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => ( ~ 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))))
% 81.03/80.87 => 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__list__update,axiom,
% 81.03/80.87 ! [V_i_2,V_a_2,V_xs_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.87 => ( ~ 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))))))
% 81.03/80.87 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_length__list__update,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__update__id,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__list__update__neq,axiom,
% 81.03/80.87 ! [V_x,V_xs,T_a,V_j,V_i] :
% 81.03/80.87 ( V_i != V_j
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip__update,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_update__zip,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__update,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__update__swap,axiom,
% 81.03/80.87 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 81.03/80.87 ( V_i != V_i_H
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__update__overwrite,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__update__beyond,axiom,
% 81.03/80.87 ! [V_x,V_i,V_xs,T_a] :
% 81.03/80.87 ( 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))
% 81.03/80.87 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__insort__insert,axiom,
% 81.03/80.87 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_b)
% 81.03/80.87 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.87 => 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))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__update__subsetI,axiom,
% 81.03/80.87 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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))
% 81.03/80.87 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__update__subset__insert,axiom,
% 81.03/80.87 ! [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)))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__list__update__eq,axiom,
% 81.03/80.87 ! [V_x,V_xs,T_a,V_i] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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 ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__update__same__conv,axiom,
% 81.03/80.87 ! [V_x_2,V_xs_2,T_a,V_i_2] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 81.03/80.87 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__list__update,axiom,
% 81.03/80.87 ! [V_x,V_j,V_xs,T_a,V_i] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => ( ( V_i = V_j
% 81.03/80.87 => 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 )
% 81.03/80.87 & ( V_i != V_j
% 81.03/80.87 => 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) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__update__memI,axiom,
% 81.03/80.87 ! [V_x_2,V_xs_2,T_a,V_n_2] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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)))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_insort__insert__triv,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__insort__insert,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_insort__insert__key__triv,axiom,
% 81.03/80.87 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => ( 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))))
% 81.03/80.87 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_insort__insert__insort,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__setsum__nth,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_restrict__map__upds,axiom,
% 81.03/80.87 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => ( 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))
% 81.03/80.87 => 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__add__upds,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 81.03/80.87 ! [V_ns_2] :
% 81.03/80.87 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 <=> ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 81.03/80.87 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_elem__le__listsum__nat,axiom,
% 81.03/80.87 ! [V_ns,V_k] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__upds__apply__nontin,axiom,
% 81.03/80.87 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__0,axiom,
% 81.03/80.87 ! [V_xs_2,T_b,T_a] :
% 81.03/80.87 ( class_Groups_Omonoid__add(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__addf,axiom,
% 81.03/80.87 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__const__mult,axiom,
% 81.03/80.87 ! [V_xs_2,V_f_2,V_ca_2,T_b,T_a] :
% 81.03/80.87 ( class_Rings_Osemiring__0(T_a)
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__mult__const,axiom,
% 81.03/80.87 ! [V_xs_2,V_ca_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( class_Rings_Osemiring__0(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__subtractf,axiom,
% 81.03/80.87 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( class_Groups_Oab__group__add(T_a)
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__update__nat,axiom,
% 81.03/80.87 ! [V_n,V_ns,V_k] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__abs,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 81.03/80.87 => 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)))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_uminus__listsum__map,axiom,
% 81.03/80.87 ! [V_xs_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( class_Groups_Oab__group__add(T_a)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.87 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 81.03/80.87 ! [V_f_2,V_xs_2,T_a,T_b] :
% 81.03/80.87 ( class_Groups_Ocomm__monoid__add(T_b)
% 81.03/80.87 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 81.03/80.87 ! [V_l_2,V_k_2,V_f_2,T_a] :
% 81.03/80.87 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 81.03/80.87 ! [V_j_2,V_i_2,V_f_2,T_a] :
% 81.03/80.87 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__upds__list__update2__drop,axiom,
% 81.03/80.87 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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))
% 81.03/80.87 => ( 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)))
% 81.03/80.87 => 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__triv,axiom,
% 81.03/80.87 ! [V_xs_2,V_r_2,T_b,T_a] :
% 81.03/80.87 ( class_Rings_Osemiring__1(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__upds__twist,axiom,
% 81.03/80.87 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] :
% 81.03/80.87 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2)))
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__map__remove1,axiom,
% 81.03/80.87 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] :
% 81.03/80.87 ( class_Groups_Ocomm__monoid__add(T_b)
% 81.03/80.87 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => 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)))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_select__weight__member,axiom,
% 81.03/80.87 ! [V_s_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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))))
% 81.03/80.87 => 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)))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_pick__member,axiom,
% 81.03/80.87 ! [V_xs_2,T_a,V_i_2] :
% 81.03/80.87 ( 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))))
% 81.03/80.87 => 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)))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_select__weight__def,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_pick__same,axiom,
% 81.03/80.87 ! [V_xs_2,T_a,V_l_2] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_scomp__Pair,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Pair__scomp,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_times__code__numeral__code,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 81.03/80.87 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 81.03/80.87 ! [V_m_2,V_n_2] :
% 81.03/80.87 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 81.03/80.87 <=> V_n_2 = V_m_2 ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_scomp__scomp,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_scomp__apply,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zero__code__numeral__def,axiom,
% 81.03/80.87 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_scomp__def,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_one__code__numeral__def,axiom,
% 81.03/80.87 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_less__code__numeral__code,axiom,
% 81.03/80.87 ! [V_m_2,V_n_2] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 81.03/80.87 ! [V_y_2,V_x_2] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 81.03/80.87 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 81.03/80.87 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 81.03/80.87 <=> V_x_2 = V_y_2 ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_number__of__code__numeral__def,axiom,
% 81.03/80.87 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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_plus__code__numeral__code,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_less__eq__code__numeral__code,axiom,
% 81.03/80.87 ! [V_m_2,V_n_2] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_code__numeral__not__eq__zero,axiom,
% 81.03/80.87 ! [V_i_2] :
% 81.03/80.87 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 81.03/80.87 <=> 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_scomp__unfold,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_iterate_Osimps,axiom,
% 81.03/80.87 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
% 81.03/80.87 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 81.03/80.87 => 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) )
% 81.03/80.87 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 81.03/80.87 ! [V_f_2,V_A_2,T_a,T_b] :
% 81.03/80.87 ( class_Groups_Ocomm__monoid__add(T_b)
% 81.03/80.87 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => 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))))) )
% 81.03/80.87 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_exE__some,axiom,
% 81.03/80.87 ! [T_a,V_ca_2,V_P_2] :
% 81.03/80.87 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 81.03/80.87 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_a,V_P_2)
% 81.03/80.87 => hBOOL(hAPP(V_P_2,V_ca_2)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_someI,axiom,
% 81.03/80.87 ! [T_a,V_x_2,V_P_2] :
% 81.03/80.87 ( hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.87 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_tfl__some,axiom,
% 81.03/80.87 ! [T_a,B_P] :
% 81.03/80.87 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 81.03/80.87 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_someI__ex,axiom,
% 81.03/80.87 ! [T_a,V_P_2] :
% 81.03/80.87 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 81.03/80.87 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_some__eq__ex,axiom,
% 81.03/80.87 ! [T_a,V_P_2] :
% 81.03/80.87 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2)))
% 81.03/80.87 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_some__eq__trivial,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_some__sym__eq__trivial,axiom,
% 81.03/80.87 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Nitpick_Ocard_H__def,axiom,
% 81.03/80.87 ! [V_A_2,T_a] :
% 81.03/80.87 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => 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)))) )
% 81.03/80.87 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.87 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_LeastM__def,axiom,
% 81.03/80.87 ! [V_P_2,V_m_2,T_a,T_b] :
% 81.03/80.87 ( class_Orderings_Oord(T_b)
% 81.03/80.87 => 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))))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_LeastM__nat__le,axiom,
% 81.03/80.87 ! [T_a,V_m_2,V_x_2,V_P_2] :
% 81.03/80.87 ( hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_LeastM__nat__lemma,axiom,
% 81.03/80.87 ! [V_m_2,T_a,V_k_2,V_P_2] :
% 81.03/80.87 ( hBOOL(hAPP(V_P_2,V_k_2))
% 81.03/80.87 => ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2)))
% 81.03/80.87 & ! [B_y] :
% 81.03/80.87 ( hBOOL(hAPP(V_P_2,B_y))
% 81.03/80.87 => 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))) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_split__paired__Eps,axiom,
% 81.03/80.87 ! [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)))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Eps__split__eq,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Eps__split,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_GreatestM__def,axiom,
% 81.03/80.87 ! [V_P_2,V_m_2,T_a,T_b] :
% 81.03/80.87 ( class_Orderings_Oord(T_b)
% 81.03/80.87 => 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))))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_select__def,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_LeastM__natI,axiom,
% 81.03/80.87 ! [V_m_2,T_a,V_k_2,V_P_2] :
% 81.03/80.87 ( hBOOL(hAPP(V_P_2,V_k_2))
% 81.03/80.87 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nat__of__of__nat,axiom,
% 81.03/80.87 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 81.03/80.87
% 81.03/80.87 fof(fact_of__nat__nat__of,axiom,
% 81.03/80.87 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nat__of__inverse,axiom,
% 81.03/80.87 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 81.03/80.87
% 81.03/80.87 fof(fact_code__numeral_Onat__of__inject,axiom,
% 81.03/80.87 ! [V_y_2,V_x_2] :
% 81.03/80.87 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 81.03/80.87 <=> V_x_2 = V_y_2 ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 81.03/80.87 ! [V_l_2,V_k_2] :
% 81.03/80.87 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 81.03/80.87 <=> V_k_2 = V_l_2 ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_type__definition__code__numeral,axiom,
% 81.03/80.87 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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_less__code__numeral__def,axiom,
% 81.03/80.87 ! [V_m_2,V_n_2] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 81.03/80.87 <=> 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nat__of,axiom,
% 81.03/80.87 ! [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)))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nat__of__number,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_int__of__def,axiom,
% 81.03/80.87 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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_less__eq__code__numeral__def,axiom,
% 81.03/80.87 ! [V_m_2,V_n_2] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 81.03/80.87 <=> 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nat__of__code,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nat__of__aux__def,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Suc__code__numeral__def,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_minus__code__numeral__def,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_of__nat__inverse,axiom,
% 81.03/80.87 ! [V_y_2] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 81.03/80.87 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_plus__code__numeral__def,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_div__code__numeral__def,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_times__code__numeral__def,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_mod__code__numeral__def,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_code__numeral__decr,axiom,
% 81.03/80.87 ! [V_k] :
% 81.03/80.87 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_select__weigth__select,axiom,
% 81.03/80.87 ! [T_a,V_xs_2] :
% 81.03/80.87 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Greatest__def,axiom,
% 81.03/80.87 ! [T_a] :
% 81.03/80.87 ( class_Orderings_Oord(T_a)
% 81.03/80.87 => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__update__code_I1_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__update_Osimps_I1_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__update__nonempty,axiom,
% 81.03/80.87 ! [V_x_2,V_k_2,V_xs_2,T_a] :
% 81.03/80.87 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a)
% 81.03/80.87 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__simps_I1_J,axiom,
% 81.03/80.87 ! [T_a] :
% 81.03/80.87 ( class_Groups_Omonoid__add(T_a)
% 81.03/80.87 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list_Osize_I3_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_length__0__conv,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__empty2,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2)
% 81.03/80.87 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__empty,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_removeAll_Osimps_I1_J,axiom,
% 81.03/80.87 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct_Osimps_I1_J,axiom,
% 81.03/80.87 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_foldr_Osimps_I1_J,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_remove1_Osimps_I1_J,axiom,
% 81.03/80.87 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip_Osimps_I1_J,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip__Nil,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_sublist__nil,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_insort__not__Nil,axiom,
% 81.03/80.87 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_b)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__upds__Nil2,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__upds__Nil1,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__is__Nil__conv,axiom,
% 81.03/80.87 ! [V_xs_2,V_f_2,T_a,T_b] :
% 81.03/80.87 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 81.03/80.87 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map_Osimps_I1_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Nil__is__map__conv,axiom,
% 81.03/80.87 ! [V_xs_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)
% 81.03/80.87 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__of__Cons__code_I1_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_upto__empty,axiom,
% 81.03/80.87 ! [V_i,V_j] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 81.03/80.87 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_sorted__list__of__set__empty,axiom,
% 81.03/80.87 ! [T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_sublist__empty,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__of_Osimps_I1_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_length__greater__0__conv,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_select,axiom,
% 81.03/80.87 ! [V_s_2,T_a,V_xs_2] :
% 81.03/80.87 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_subtract__code__numeral__code,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_pick_Osimps,axiom,
% 81.03/80.87 ! [V_xs,V_x,T_a,V_i] :
% 81.03/80.87 ( ( 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)))
% 81.03/80.87 => 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) )
% 81.03/80.87 & ( ~ 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)))
% 81.03/80.87 => 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))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list_Osimps_I2_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list_Osimps_I3_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_insort__key_Osimps_I1_J,axiom,
% 81.03/80.87 ! [V_x_2,V_f_2,T_a,T_b] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_b)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map_Osimps_I2_J,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip__Cons__Cons,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_insort__key_Osimps_I2_J,axiom,
% 81.03/80.87 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => ( ( 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)))
% 81.03/80.87 => 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)) )
% 81.03/80.87 & ( ~ 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)))
% 81.03/80.87 => 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)) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_remove1_Osimps_I2_J,axiom,
% 81.03/80.87 ! [V_xs,T_a,V_y,V_x] :
% 81.03/80.87 ( ( V_x = V_y
% 81.03/80.87 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 81.03/80.87 & ( V_x != V_y
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_foldr_Osimps_I2_J,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list_Oinject,axiom,
% 81.03/80.87 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 <=> ( V_a_2 = V_a_H_2
% 81.03/80.87 & V_list_2 = V_list_H_2 ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_not__Cons__self2,axiom,
% 81.03/80.87 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 81.03/80.87
% 81.03/80.87 fof(fact_not__Cons__self,axiom,
% 81.03/80.87 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_removeAll_Osimps_I2_J,axiom,
% 81.03/80.87 ! [V_xs,T_a,V_y,V_x] :
% 81.03/80.87 ( ( V_x = V_y
% 81.03/80.87 => 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) )
% 81.03/80.87 & ( V_x != V_y
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__Cons__0,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__Cons__Suc,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__subset__Cons,axiom,
% 81.03/80.87 ! [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)))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__ConsD,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,V_y_2,T_a] :
% 81.03/80.87 ( 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))))
% 81.03/80.87 => ( V_y_2 = V_x_2
% 81.03/80.87 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_impossible__Cons,axiom,
% 81.03/80.87 ! [V_x,V_ys,V_xs,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__simps_I2_J,axiom,
% 81.03/80.87 ! [V_xs,V_x,T_a] :
% 81.03/80.87 ( class_Groups_Omonoid__add(T_a)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__update_Osimps_I2_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__update__code_I2_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__update__code_I3_J,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth_Osimps,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct_Osimps_I2_J,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))
% 81.03/80.87 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__of__Cons__code_I2_J,axiom,
% 81.03/80.87 ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
% 81.03/80.87 ( ( V_l = V_k
% 81.03/80.87 => 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) )
% 81.03/80.87 & ( V_l != V_k
% 81.03/80.87 => 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__upds__Cons,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list_Osize_I4_J,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__Cons_H,axiom,
% 81.03/80.87 ! [V_xs,V_x,T_a,V_n] :
% 81.03/80.87 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 81.03/80.87 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 => 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))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_select__weight__cons__zero,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_sublist__singleton,axiom,
% 81.03/80.87 ! [V_x_2,T_a,V_A_2] :
% 81.03/80.87 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 81.03/80.87 => 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)) )
% 81.03/80.87 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 81.03/80.87 => 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_minus__code__numeral__code,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_subtract__code__numeral__def,axiom,
% 81.03/80.87 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__Cons__number__of,axiom,
% 81.03/80.87 ! [V_xs,V_x,T_a,V_v] :
% 81.03/80.87 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 => 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 )
% 81.03/80.87 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 => 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))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__of_Osimps_I2_J,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__Cons__def,axiom,
% 81.03/80.87 ! [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)))))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip__Cons,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list_Osimps_I5_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list_Osimps_I4_J,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_upto_Osimps,axiom,
% 81.03/80.87 ! [V_j,V_i] :
% 81.03/80.87 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 81.03/80.87 => 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)) )
% 81.03/80.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 81.03/80.87 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_upto__rec__number__of,axiom,
% 81.03/80.87 ! [V_n,V_m] :
% 81.03/80.87 ( ( 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)))
% 81.03/80.87 => 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))) )
% 81.03/80.87 & ( ~ 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)))
% 81.03/80.87 => 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__Cons__sing__Nil,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip__Cons1,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_upto_Opsimps,axiom,
% 81.03/80.87 ! [V_j_2,V_i_2] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 81.03/80.87 => 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)) )
% 81.03/80.87 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 81.03/80.87 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_anamorph_Osimps,axiom,
% 81.03/80.87 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
% 81.03/80.87 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 81.03/80.87 => 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) )
% 81.03/80.87 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listset_Osimps_I1_J,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel__Cons,axiom,
% 81.03/80.87 ! [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))))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel__Nil2,axiom,
% 81.03/80.87 ! [V_r_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel__Nil1,axiom,
% 81.03/80.87 ! [V_r_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel_ONil,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel__eq__len,axiom,
% 81.03/80.87 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel__mono,axiom,
% 81.03/80.87 ! [V_s_2,V_r_2,T_a] :
% 81.03/80.87 ( 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))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel_OCons,axiom,
% 81.03/80.87 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 81.03/80.87 ( 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))
% 81.03/80.87 => ( 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)))
% 81.03/80.87 => 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))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel__Nil,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listset_Osimps_I2_J,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel__iff__nth,axiom,
% 81.03/80.87 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> ( 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)
% 81.03/80.87 & ! [B_n] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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)) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_upto_Opinduct,axiom,
% 81.03/80.87 ! [V_P_2,V_a1_2,V_a0_2] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => ( ! [B_i,B_j] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 81.03/80.87 => 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)) )
% 81.03/80.87 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 81.03/80.87 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__upds__append1,axiom,
% 81.03/80.87 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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)))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__eq__Cons__conv,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a)
% 81.03/80.87 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) )
% 81.03/80.87 | ? [B_ys_H] :
% 81.03/80.87 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H)
% 81.03/80.87 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Cons__eq__append__conv,axiom,
% 81.03/80.87 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a)
% 81.03/80.87 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 )
% 81.03/80.87 | ? [B_ys_H] :
% 81.03/80.87 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2
% 81.03/80.87 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append1__eq__conv,axiom,
% 81.03/80.87 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> ( V_xs_2 = V_ys_2
% 81.03/80.87 & V_x_2 = V_y_2 ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__Nil,axiom,
% 81.03/80.87 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Nil__is__append__conv,axiom,
% 81.03/80.87 ! [V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 81.03/80.87 <=> ( V_xs_2 = c_List_Olist_ONil(T_a)
% 81.03/80.87 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__Nil2,axiom,
% 81.03/80.87 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 81.03/80.87
% 81.03/80.87 fof(fact_self__append__conv,axiom,
% 81.03/80.87 ! [V_ys_2,T_a,V_xs_2] :
% 81.03/80.87 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 81.03/80.87 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_self__append__conv2,axiom,
% 81.03/80.87 ! [V_xs_2,T_a,V_ys_2] :
% 81.03/80.87 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 81.03/80.87 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__is__Nil__conv,axiom,
% 81.03/80.87 ! [V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a)
% 81.03/80.87 <=> ( V_xs_2 = c_List_Olist_ONil(T_a)
% 81.03/80.87 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__self__conv,axiom,
% 81.03/80.87 ! [V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2
% 81.03/80.87 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__self__conv2,axiom,
% 81.03/80.87 ! [V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2
% 81.03/80.87 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_eq__Nil__appendI,axiom,
% 81.03/80.87 ! [T_a,V_ys,V_xs] :
% 81.03/80.87 ( V_xs = V_ys
% 81.03/80.87 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__append,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__of__append,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_foldr__append,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__eq__appendI,axiom,
% 81.03/80.87 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 81.03/80.87 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 81.03/80.87 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 81.03/80.87 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__same__eq,axiom,
% 81.03/80.87 ! [V_zs_2,V_xs_2,V_ys_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 <=> V_ys_2 = V_zs_2 ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_same__append__eq,axiom,
% 81.03/80.87 ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 <=> V_ys_2 = V_zs_2 ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__eq__append__conv2,axiom,
% 81.03/80.87 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 <=> ? [B_us] :
% 81.03/80.87 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us)
% 81.03/80.87 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 )
% 81.03/80.87 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2
% 81.03/80.87 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__assoc,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_removeAll__append,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__append,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_length__append,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip__append,axiom,
% 81.03/80.87 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => ( 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)
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_fun__upds__append__drop,axiom,
% 81.03/80.87 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_fun__upds__append2__drop,axiom,
% 81.03/80.87 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__append,axiom,
% 81.03/80.87 ! [V_ys,V_xs,T_a] :
% 81.03/80.87 ( class_Groups_Omonoid__add(T_a)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__Cons,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Cons__eq__appendI,axiom,
% 81.03/80.87 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 81.03/80.87 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 81.03/80.87 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 81.03/80.87 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__append__length,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__append__length__plus,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__update__append1,axiom,
% 81.03/80.87 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__update__length,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_remove1__append,axiom,
% 81.03/80.87 ! [V_ys_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => 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) )
% 81.03/80.87 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__append,axiom,
% 81.03/80.87 ! [V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
% 81.03/80.87 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.87 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
% 81.03/80.87 & 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__append,axiom,
% 81.03/80.87 ! [V_ys,V_xs,T_a,V_n] :
% 81.03/80.87 ( ( 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)))
% 81.03/80.87 => 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) )
% 81.03/80.87 & ( ~ 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)))
% 81.03/80.87 => 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))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__update__append,axiom,
% 81.03/80.87 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 81.03/80.87 ( ( 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)))
% 81.03/80.87 => 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) )
% 81.03/80.87 & ( ~ 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)))
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_sublist__append,axiom,
% 81.03/80.87 ! [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)))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_sublist__Cons,axiom,
% 81.03/80.87 ! [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)))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Cons__in__lex,axiom,
% 81.03/80.87 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> ( ( 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))
% 81.03/80.87 & 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) )
% 81.03/80.87 | ( V_x_2 = V_y_2
% 81.03/80.87 & 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))) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrelp__listrel__eq,axiom,
% 81.03/80.87 ! [V_xa_2,V_x_2,V_r_2,T_a] :
% 81.03/80.87 ( 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)
% 81.03/80.87 <=> 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrelp_Oequations_I2_J,axiom,
% 81.03/80.87 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] :
% 81.03/80.87 ( 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))
% 81.03/80.87 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 81.03/80.87 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrelp_OCons,axiom,
% 81.03/80.87 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 81.03/80.87 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2)
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrelp_ONil,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrelp_Oequations_I1_J,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Nil__notin__lex,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Nil2__notin__lex,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lenlex__conv,axiom,
% 81.03/80.87 ! [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)))))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lenlex__def,axiom,
% 81.03/80.87 ! [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)))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel__Cons1,axiom,
% 81.03/80.87 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => ~ ! [B_y,B_ys] :
% 81.03/80.87 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys)
% 81.03/80.87 => ( 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))
% 81.03/80.87 => ~ 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))) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel__Cons2,axiom,
% 81.03/80.87 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => ~ ! [B_x,B_xs] :
% 81.03/80.87 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs)
% 81.03/80.87 => ( 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))
% 81.03/80.87 => ~ 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))) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel__iff__zip,axiom,
% 81.03/80.87 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> ( 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)
% 81.03/80.87 & ! [B_x] :
% 81.03/80.87 ( 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))))
% 81.03/80.87 => 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)) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lexord__append__left__rightI,axiom,
% 81.03/80.87 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] :
% 81.03/80.87 ( 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))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_INFI__bool__eq,axiom,
% 81.03/80.87 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_ball__UNIV,axiom,
% 81.03/80.87 ! [V_P_2,T_a] :
% 81.03/80.87 ( ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 81.03/80.87 => hBOOL(hAPP(V_P_2,B_x)) )
% 81.03/80.87 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Powp__def,axiom,
% 81.03/80.87 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2))
% 81.03/80.87 <=> ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 81.03/80.87 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_ball__empty,axiom,
% 81.03/80.87 ! [V_P_2,T_a,B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 81.03/80.87 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Collect__ball__eq,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_congruent__def,axiom,
% 81.03/80.87 ! [V_f_2,V_r_2,T_b,T_a] :
% 81.03/80.87 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2)
% 81.03/80.87 <=> ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2))
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_INTER__def,axiom,
% 81.03/80.87 ! [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)))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Inf__Sup,axiom,
% 81.03/80.87 ! [V_A_2,T_a] :
% 81.03/80.87 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.87 => 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))))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Sup__Inf,axiom,
% 81.03/80.87 ! [V_A_2,T_a] :
% 81.03/80.87 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.87 => 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)))))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__eq__iff__zip__eq,axiom,
% 81.03/80.87 ! [T_a,V_ys_2,V_xs_2] :
% 81.03/80.87 ( V_xs_2 = V_ys_2
% 81.03/80.87 <=> ( 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)
% 81.03/80.87 & ! [B_x] :
% 81.03/80.87 ( 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))))
% 81.03/80.87 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lexord__Nil__right,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lexord__append__leftI,axiom,
% 81.03/80.87 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_WT__bodies__def,axiom,
% 81.03/80.87 ( c_Com_OWT__bodies
% 81.03/80.87 <=> ! [B_x] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lexord__lex,axiom,
% 81.03/80.87 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> ( 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)))
% 81.03/80.87 & 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lexord__cons__cons,axiom,
% 81.03/80.87 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> ( 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))
% 81.03/80.87 | ( V_a_2 = V_b_2
% 81.03/80.87 & 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))) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lexord__take__index__conv,axiom,
% 81.03/80.87 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> ( ( 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)))
% 81.03/80.87 & 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 )
% 81.03/80.87 | ? [B_i] :
% 81.03/80.87 ( 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))))
% 81.03/80.87 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2)
% 81.03/80.87 & 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)) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 81.03/80.87 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> ( ( 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)))
% 81.03/80.87 & V_x_2 = V_y_2 )
% 81.03/80.87 | ( V_xs_2 = V_ys_2
% 81.03/80.87 & 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)) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Cons__acc__listrel1I,axiom,
% 81.03/80.87 ! [V_xs_2,V_r_2,V_x_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 81.03/80.87 => ( 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))))
% 81.03/80.87 => 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)))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_triples__valid__Suc,axiom,
% 81.03/80.87 ! [V_n_2,V_ts_2,T_a] :
% 81.03/80.87 ( ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 81.03/80.87 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) )
% 81.03/80.87 => ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 81.03/80.87 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_in__set__takeD,axiom,
% 81.03/80.87 ! [V_xs_2,V_n_2,V_x_2,T_a] :
% 81.03/80.87 ( 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))))
% 81.03/80.87 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__take__subset,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__all,axiom,
% 81.03/80.87 ! [V_n,V_xs,T_a] :
% 81.03/80.87 ( 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))
% 81.03/80.87 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__Suc__Cons,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_length__take,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__take,axiom,
% 81.03/80.87 ! [V_xs,T_a,V_n,V_i] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__take,axiom,
% 81.03/80.87 ! [V_i,V_xs,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 81.03/80.87 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__take,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__zip,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__map,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__Nil,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__eq__Nil,axiom,
% 81.03/80.87 ! [V_xs_2,V_n_2,T_a] :
% 81.03/80.87 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 81.03/80.87 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__0,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_sublist__upt__eq__take,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_hoare__valids__def,axiom,
% 81.03/80.87 ! [V_ts_2,V_G_2,T_a] :
% 81.03/80.87 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2)
% 81.03/80.87 <=> ! [B_n] :
% 81.03/80.87 ( ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_G_2))
% 81.03/80.87 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) )
% 81.03/80.87 => ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 81.03/80.87 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__take__subset__set__take,axiom,
% 81.03/80.87 ! [V_xs_2,T_a,V_n_2,V_m_2] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 81.03/80.87 => 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)))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__append,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__1__Cons,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel1__mono,axiom,
% 81.03/80.87 ! [V_s_2,V_r_2,T_a] :
% 81.03/80.87 ( 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))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Inter__eq,axiom,
% 81.03/80.87 ! [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)))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel1I2,axiom,
% 81.03/80.87 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel1__eq__len,axiom,
% 81.03/80.87 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_not__Nil__listrel1,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_not__listrel1__Nil,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__listrel1I,axiom,
% 81.03/80.87 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( ( ( 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)))
% 81.03/80.87 & V_us_2 = V_vs_2 )
% 81.03/80.87 | ( V_xs_2 = V_ys_2
% 81.03/80.87 & 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))) ) )
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__Cons,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__Cons_H,axiom,
% 81.03/80.87 ! [V_xs,V_x,T_a,V_n] :
% 81.03/80.87 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 => 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) )
% 81.03/80.87 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_dom__map__upds,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel1I1,axiom,
% 81.03/80.87 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 81.03/80.87 ( 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))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Cons__listrel1__Cons,axiom,
% 81.03/80.87 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> ( ( 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))
% 81.03/80.87 & V_xs_2 = V_ys_2 )
% 81.03/80.87 | ( V_x_2 = V_y_2
% 81.03/80.87 & 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))) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__Cons__number__of,axiom,
% 81.03/80.87 ! [V_xs,V_x,T_a,V_v] :
% 81.03/80.87 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 => 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) )
% 81.03/80.87 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__upd__upds__conv__if,axiom,
% 81.03/80.87 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] :
% 81.03/80.87 ( ( 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))))
% 81.03/80.87 => 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) )
% 81.03/80.87 & ( ~ 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))))
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__Suc__conv__app__nth,axiom,
% 81.03/80.87 ! [V_xs,T_a,V_i] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel1I,axiom,
% 81.03/80.87 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 81.03/80.87 ( 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))
% 81.03/80.87 => ( 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))
% 81.03/80.87 => ( 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))
% 81.03/80.87 => 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))) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel1__iff__update,axiom,
% 81.03/80.87 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> ? [B_y,B_n] :
% 81.03/80.87 ( 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))
% 81.03/80.87 & 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)))
% 81.03/80.87 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel1E,axiom,
% 81.03/80.87 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => ~ ! [B_x,B_y] :
% 81.03/80.87 ( 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))
% 81.03/80.87 => ! [B_us,B_vs] :
% 81.03/80.87 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs))
% 81.03/80.87 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lexord__append__leftD,axiom,
% 81.03/80.87 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => ( ! [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))
% 81.03/80.87 => 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))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_rotate1__def,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_length__rotate1,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct1__rotate,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)))
% 81.03/80.87 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_rotate1__is__Nil__conv,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
% 81.03/80.87 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__rotate1,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_rotate__simps,axiom,
% 81.03/80.87 ! [V_xs,V_x,T_b,T_a] :
% 81.03/80.87 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 81.03/80.87 & 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_rotate1__length01,axiom,
% 81.03/80.87 ! [V_xs,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel1__subset__listrel,axiom,
% 81.03/80.87 ! [V_r_H_2,V_r_2,T_a] :
% 81.03/80.87 ( 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))
% 81.03/80.87 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2)
% 81.03/80.87 => 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))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lexn__length,axiom,
% 81.03/80.87 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2
% 81.03/80.87 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_refl__on__Id__on,axiom,
% 81.03/80.87 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lexn_Osimps_I1_J,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_refl__on__empty,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_refl__on__Un,axiom,
% 81.03/80.87 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
% 81.03/80.87 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 81.03/80.87 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_refl__on__Int,axiom,
% 81.03/80.87 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
% 81.03/80.87 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 81.03/80.87 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_refl__onD2,axiom,
% 81.03/80.87 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 81.03/80.87 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 81.03/80.87 => ( 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))
% 81.03/80.87 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_refl__onD1,axiom,
% 81.03/80.87 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 81.03/80.87 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 81.03/80.87 => ( 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))
% 81.03/80.87 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_refl__onD,axiom,
% 81.03/80.87 ! [V_a_2,V_r_2,V_A_2,T_a] :
% 81.03/80.87 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 81.03/80.87 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lex__def,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_refl__on__def_H,axiom,
% 81.03/80.87 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.87 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 81.03/80.87 <=> ( ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2))
% 81.03/80.87 => 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)) )
% 81.03/80.87 & ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.87 => 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)) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lexn_Osimps_I2_J,axiom,
% 81.03/80.87 ! [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)))))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_reflp__def,axiom,
% 81.03/80.87 ! [V_r_2,T_a] :
% 81.03/80.87 ( c_Predicate_Oreflp(T_a,V_r_2)
% 81.03/80.87 <=> 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__pair__imageI,axiom,
% 81.03/80.87 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] :
% 81.03/80.87 ( 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))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__pair__simp,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_fst__map__pair,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_snd__prod__fun,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_reflpE,axiom,
% 81.03/80.87 ! [V_x_2,V_r_2,T_a] :
% 81.03/80.87 ( c_Predicate_Oreflp(T_a,V_r_2)
% 81.03/80.87 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__pair__ident,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_fst__comp__map__pair,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_snd__comp__map__pair,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__pair_Ocomp,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__pair__compose,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__pair_Ocompositionality,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__pair__def,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__pair__surj,axiom,
% 81.03/80.87 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] :
% 81.03/80.87 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.87 => ( 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))
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_prod__fun__imageE,axiom,
% 81.03/80.87 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_ca_2,T_b,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => ~ ! [B_x,B_y] :
% 81.03/80.87 ( 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))
% 81.03/80.87 => ~ 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_upd__conv__take__nth__drop,axiom,
% 81.03/80.87 ! [V_a,V_xs,T_a,V_i] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_in__set__dropD,axiom,
% 81.03/80.87 ! [V_xs_2,V_n_2,V_x_2,T_a] :
% 81.03/80.87 ( 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))))
% 81.03/80.87 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__drop__subset,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__Nil,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__map,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__zip,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__drop,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__0,axiom,
% 81.03/80.87 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__drop,axiom,
% 81.03/80.87 ! [V_i,V_xs,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 81.03/80.87 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_length__drop,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__1__Cons,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__Suc__Cons,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__via__drop,axiom,
% 81.03/80.87 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 81.03/80.87 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 81.03/80.87 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__take__drop__id,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__take,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__drop,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__drop__subset__set__drop,axiom,
% 81.03/80.87 ! [V_xs_2,T_a,V_m_2,V_n_2] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 81.03/80.87 => 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)))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__all,axiom,
% 81.03/80.87 ! [V_n,V_xs,T_a] :
% 81.03/80.87 ( 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))
% 81.03/80.87 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__eq__Nil,axiom,
% 81.03/80.87 ! [V_xs_2,V_n_2,T_a] :
% 81.03/80.87 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 81.03/80.87 <=> 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__append,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__eq__conv__conj,axiom,
% 81.03/80.87 ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2
% 81.03/80.87 <=> ( 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)
% 81.03/80.87 & 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__Cons,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__Cons_H,axiom,
% 81.03/80.87 ! [V_xs,V_x,T_a,V_n] :
% 81.03/80.87 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 => 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) )
% 81.03/80.87 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 => 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__drop,axiom,
% 81.03/80.87 ! [V_xs,T_a,V_i,V_n] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__eq__append__conv__if,axiom,
% 81.03/80.87 ! [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] :
% 81.03/80.87 ( 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)
% 81.03/80.87 <=> ( ( 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)))
% 81.03/80.87 => ( 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)
% 81.03/80.87 & 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) ) )
% 81.03/80.87 & ( ~ 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)))
% 81.03/80.87 => ( 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
% 81.03/80.87 & 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 ) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_nth__drop_H,axiom,
% 81.03/80.87 ! [V_xs,T_a,V_i] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__Cons__number__of,axiom,
% 81.03/80.87 ! [V_xs,V_x,T_a,V_v] :
% 81.03/80.87 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 => 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) )
% 81.03/80.87 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 => 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__add,axiom,
% 81.03/80.87 ! [V_xs,T_a,V_j,V_i] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip__append1,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_zip__append2,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_id__take__nth__drop,axiom,
% 81.03/80.87 ! [V_xs,T_a,V_i] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__hd__drop,axiom,
% 81.03/80.87 ! [V_xs,T_a,V_n] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_hd__drop__conv__nth,axiom,
% 81.03/80.87 ! [V_n,T_a,V_xs] :
% 81.03/80.87 ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.87 => ( 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)))
% 81.03/80.87 => 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_hd_Osimps,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_hd__map,axiom,
% 81.03/80.87 ! [V_f_2,T_b,T_a,V_xs_2] :
% 81.03/80.87 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_hd__append2,axiom,
% 81.03/80.87 ! [V_ys,T_a,V_xs] :
% 81.03/80.87 ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_hd__append,axiom,
% 81.03/80.87 ! [V_ys,T_a,V_xs] :
% 81.03/80.87 ( ( V_xs = c_List_Olist_ONil(T_a)
% 81.03/80.87 => 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) )
% 81.03/80.87 & ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.87 => 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) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_hd__in__set,axiom,
% 81.03/80.87 ! [T_a,V_xs_2] :
% 81.03/80.87 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_hd__conv__nth,axiom,
% 81.03/80.87 ! [T_a,V_xs] :
% 81.03/80.87 ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_rotate1__hd__tl,axiom,
% 81.03/80.87 ! [T_a,V_xs] :
% 81.03/80.87 ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_hd__rotate__conv__nth,axiom,
% 81.03/80.87 ! [V_n,T_a,V_xs] :
% 81.03/80.87 ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__tl,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_tl__drop,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_rotate1__rotate__swap,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_set__rotate,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_tl_Osimps_I1_J,axiom,
% 81.03/80.87 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_rotate__is__Nil__conv,axiom,
% 81.03/80.87 ! [V_xs_2,V_n_2,T_a] :
% 81.03/80.87 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 81.03/80.87 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__tl,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_rotate__map,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_rotate__rotate,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__rotate,axiom,
% 81.03/80.87 ! [V_xs_2,V_n_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)))
% 81.03/80.87 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_distinct__tl,axiom,
% 81.03/80.87 ! [V_xs,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 81.03/80.87 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_length__rotate,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_tl_Osimps_I2_J,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_tl__append2,axiom,
% 81.03/80.87 ! [V_ys,T_a,V_xs] :
% 81.03/80.87 ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__tl,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_rotate__conv__mod,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_drop__Suc,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_rotate__Suc,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_tl__append,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_rotate__add,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_rotate__id,axiom,
% 81.03/80.87 ! [V_xs,T_a,V_n] :
% 81.03/80.87 ( 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)
% 81.03/80.87 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_rotate__length01,axiom,
% 81.03/80.87 ! [V_n,V_xs,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_length__tl,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_tl__take,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_take__Suc,axiom,
% 81.03/80.87 ! [V_n,T_a,V_xs] :
% 81.03/80.87 ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_rotate__drop__take,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_fold1__set,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 81.03/80.87 => ( V_xs_2 != c_List_Olist_ONil(T_a)
% 81.03/80.87 => 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)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list_Osize_I2_J,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__size__map,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_foldr__conv__foldl,axiom,
% 81.03/80.87 ! [V_a_2,V_xs_2,T_a] :
% 81.03/80.87 ( class_Groups_Oab__semigroup__add(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_start__le__sum,axiom,
% 81.03/80.87 ! [V_ns_2,V_n_2,V_m_2] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_foldl__Cons,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_foldl__absorb0,axiom,
% 81.03/80.87 ! [V_zs_2,V_x_2,T_a] :
% 81.03/80.87 ( class_Groups_Omonoid__add(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_foldl__assoc,axiom,
% 81.03/80.87 ! [V_zs_2,V_y_2,V_x_2,T_a] :
% 81.03/80.87 ( class_Groups_Osemigroup__add(T_a)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_foldl__map,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_foldl__Nil,axiom,
% 81.03/80.87 ! [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 ).
% 81.03/80.87
% 81.03/80.87 fof(fact_foldl__append,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__foldl,axiom,
% 81.03/80.87 ! [T_a] :
% 81.03/80.87 ( class_Groups_Omonoid__add(T_a)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_foldl__foldr1__lemma,axiom,
% 81.03/80.87 ! [V_xs_2,V_a_2,T_a] :
% 81.03/80.87 ( class_Groups_Omonoid__add(T_a)
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_foldl__foldr1,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( class_Groups_Omonoid__add(T_a)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_sum__eq__0__conv,axiom,
% 81.03/80.87 ! [V_ns_2,V_m_2] :
% 81.03/80.87 ( 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)
% 81.03/80.87 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.87 & ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 81.03/80.87 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list_Osize_I1_J,axiom,
% 81.03/80.87 ! [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) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 81.03/80.87 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] :
% 81.03/80.87 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Sup__set__fold,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Inf__set__fold,axiom,
% 81.03/80.87 ! [V_xs_2,T_a] :
% 81.03/80.87 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Sup__fin__set__fold,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( class_Lattices_Olattice(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Inf__fin__set__fold,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( class_Lattices_Olattice(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Min__fin__set__fold,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Max__fin__set__fold,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 81.03/80.87 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( class_Orderings_Olinorder(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_SUPR__set__fold,axiom,
% 81.03/80.87 ! [V_f_2,V_xs_2,T_b,T_a] :
% 81.03/80.87 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_INFI__set__fold,axiom,
% 81.03/80.87 ! [V_f_2,V_xs_2,T_b,T_a] :
% 81.03/80.87 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 81.03/80.87 => 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) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__size__estimation,axiom,
% 81.03/80.87 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 81.03/80.87 => 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))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__size__estimation_H,axiom,
% 81.03/80.87 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 81.03/80.87 => 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))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_map__upds__fold__map__upd,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_elem__le__sum,axiom,
% 81.03/80.87 ! [V_ns_2,V_n_2] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_list__size__conv__listsum,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lists__accD,axiom,
% 81.03/80.87 ! [V_r_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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))))
% 81.03/80.87 => 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)))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lists__accI,axiom,
% 81.03/80.87 ! [V_r_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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))))
% 81.03/80.87 => 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)))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lists_ONil,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lists__mono,axiom,
% 81.03/80.87 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_append__in__lists__conv,axiom,
% 81.03/80.87 ! [V_A_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
% 81.03/80.87 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lists__UNIV,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_equiv__listrel,axiom,
% 81.03/80.87 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.87 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listrel__refl__on,axiom,
% 81.03/80.87 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.87 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_Cons__in__lists__iff,axiom,
% 81.03/80.87 ! [V_A_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 81.03/80.87 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_in__lists__conv__set,axiom,
% 81.03/80.87 ! [V_A_2,V_xs_2,T_a] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
% 81.03/80.87 <=> ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lists__eq__set,axiom,
% 81.03/80.87 ! [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)) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lists__empty,axiom,
% 81.03/80.87 ! [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))) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lexord__append__rightI,axiom,
% 81.03/80.87 ! [V_r_2,V_x_2,T_a,V_y_2] :
% 81.03/80.87 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z)
% 81.03/80.87 => 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))) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_lexord__Nil__left,axiom,
% 81.03/80.87 ! [V_r_2,V_y_2,T_a] :
% 81.03/80.87 ( 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)))
% 81.03/80.87 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_last__list__update,axiom,
% 81.03/80.87 ! [V_x,V_k,T_a,V_xs] :
% 81.03/80.87 ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.87 => ( ( 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))
% 81.03/80.87 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 81.03/80.87 & ( 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))
% 81.03/80.87 => 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) ) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_listsum__mono,axiom,
% 81.03/80.87 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] :
% 81.03/80.87 ( ( class_Groups_Omonoid__add(T_b)
% 81.03/80.87 & class_Groups_Oordered__ab__semigroup__add(T_b) )
% 81.03/80.87 => ( ! [B_x] :
% 81.03/80.87 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.87 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 81.03/80.87 => 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)))) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_last_Osimps,axiom,
% 81.03/80.87 ! [V_x,T_a,V_xs] :
% 81.03/80.87 ( ( V_xs = c_List_Olist_ONil(T_a)
% 81.03/80.87 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 81.03/80.87 & ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.87 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_last__ConsR,axiom,
% 81.03/80.87 ! [V_x,T_a,V_xs] :
% 81.03/80.87 ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.87 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_last__ConsL,axiom,
% 81.03/80.87 ! [V_x,T_a,V_xs] :
% 81.03/80.87 ( V_xs = c_List_Olist_ONil(T_a)
% 81.03/80.87 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 81.03/80.87
% 81.03/80.87 fof(fact_last__map,axiom,
% 81.03/80.87 ! [V_f_2,T_b,T_a,V_xs_2] :
% 81.03/80.87 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 81.03/80.87 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_last__append,axiom,
% 81.03/80.88 ! [V_xs,T_a,V_ys] :
% 81.03/80.88 ( ( V_ys = c_List_Olist_ONil(T_a)
% 81.03/80.88 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 81.03/80.88 & ( V_ys != c_List_Olist_ONil(T_a)
% 81.03/80.88 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_last__appendR,axiom,
% 81.03/80.88 ! [V_xs,T_a,V_ys] :
% 81.03/80.88 ( V_ys != c_List_Olist_ONil(T_a)
% 81.03/80.88 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_last__appendL,axiom,
% 81.03/80.88 ! [V_xs,T_a,V_ys] :
% 81.03/80.88 ( V_ys = c_List_Olist_ONil(T_a)
% 81.03/80.88 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_last__in__set,axiom,
% 81.03/80.88 ! [T_a,V_as_2] :
% 81.03/80.88 ( V_as_2 != c_List_Olist_ONil(T_a)
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_last__snoc,axiom,
% 81.03/80.88 ! [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 ).
% 81.03/80.88
% 81.03/80.88 fof(fact_last__drop,axiom,
% 81.03/80.88 ! [V_xs,T_a,V_n] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_last__conv__nth,axiom,
% 81.03/80.88 ! [T_a,V_xs] :
% 81.03/80.88 ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_lexord__linear,axiom,
% 81.03/80.88 ! [V_y_2,V_x_2,V_r_2,T_a] :
% 81.03/80.88 ( ! [B_a,B_b] :
% 81.03/80.88 ( 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))
% 81.03/80.88 | B_a = B_b
% 81.03/80.88 | 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)) )
% 81.03/80.88 => ( 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)))
% 81.03/80.88 | V_x_2 = V_y_2
% 81.03/80.88 | 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_lexord__irreflexive,axiom,
% 81.03/80.88 ! [V_y_2,V_r_2,T_a] :
% 81.03/80.88 ( ! [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))
% 81.03/80.88 => ~ 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_lists_Osimps,axiom,
% 81.03/80.88 ! [V_A_2,V_a_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2)))
% 81.03/80.88 <=> ( V_a_2 = c_List_Olist_ONil(T_a)
% 81.03/80.88 | ? [B_a,B_l] :
% 81.03/80.88 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l)
% 81.03/80.88 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 81.03/80.88 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__size__pointwise,axiom,
% 81.03/80.88 ! [V_g_2,V_f_2,V_xs_2,T_a] :
% 81.03/80.88 ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_butlast__take,axiom,
% 81.03/80.88 ! [V_xs,T_a,V_n] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__butlast,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_in__set__butlastD,axiom,
% 81.03/80.88 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2))))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_butlast_Osimps_I1_J,axiom,
% 81.03/80.88 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_butlast__drop,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_drop__butlast,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_butlast_Osimps_I2_J,axiom,
% 81.03/80.88 ! [V_x,T_a,V_xs] :
% 81.03/80.88 ( ( V_xs = c_List_Olist_ONil(T_a)
% 81.03/80.88 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 81.03/80.88 & ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_butlast__append,axiom,
% 81.03/80.88 ! [V_xs,T_a,V_ys] :
% 81.03/80.88 ( ( V_ys = c_List_Olist_ONil(T_a)
% 81.03/80.88 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 81.03/80.88 & ( V_ys != c_List_Olist_ONil(T_a)
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_distinct__butlast,axiom,
% 81.03/80.88 ! [T_a,V_xs] :
% 81.03/80.88 ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.88 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 81.03/80.88 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_in__set__butlast__appendI,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.88 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2))))
% 81.03/80.88 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) )
% 81.03/80.88 => 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))))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_butlast__snoc,axiom,
% 81.03/80.88 ! [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 ).
% 81.03/80.88
% 81.03/80.88 fof(fact_take__butlast,axiom,
% 81.03/80.88 ! [V_xs,T_a,V_n] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__butlast,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_butlast__conv__take,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_butlast__list__update,axiom,
% 81.03/80.88 ! [V_x,V_xs,T_a,V_k] :
% 81.03/80.88 ( ( 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))
% 81.03/80.88 => 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) )
% 81.03/80.88 & ( 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))
% 81.03/80.88 => 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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_append__butlast__last__id,axiom,
% 81.03/80.88 ! [T_a,V_xs] :
% 81.03/80.88 ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.88 => 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 ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_snoc__eq__iff__butlast,axiom,
% 81.03/80.88 ! [V_ys_2,V_x_2,V_xs_2,T_a] :
% 81.03/80.88 ( 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
% 81.03/80.88 <=> ( V_ys_2 != c_List_Olist_ONil(T_a)
% 81.03/80.88 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2
% 81.03/80.88 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_nth__take__lemma,axiom,
% 81.03/80.88 ! [V_ys,V_xs,T_a,V_k] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => ( ! [B_i] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 81.03/80.88 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 81.03/80.88 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose__aux__max,axiom,
% 81.03/80.88 ! [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)))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__filter__le,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter__is__subset,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter__id__conv,axiom,
% 81.03/80.88 ! [V_xs_2,V_P_2,T_a] :
% 81.03/80.88 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2
% 81.03/80.88 <=> ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter__empty__conv,axiom,
% 81.03/80.88 ! [V_xs_2,V_P_2,T_a] :
% 81.03/80.88 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 81.03/80.88 <=> ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter__append,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sum__length__filter__compl,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter_Osimps_I1_J,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter__insort__triv,axiom,
% 81.03/80.88 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_b)
% 81.03/80.88 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.88 => 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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter__remove1,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_remove1__filter__not,axiom,
% 81.03/80.88 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 81.03/80.88 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter__filter,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_distinct__filter,axiom,
% 81.03/80.88 ! [V_P_2,V_xs_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.88 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_removeAll__filter__not__eq,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_removeAll__filter__not,axiom,
% 81.03/80.88 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 81.03/80.88 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter_Osimps_I2_J,axiom,
% 81.03/80.88 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 81.03/80.88 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.88 => 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)) )
% 81.03/80.88 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.88 => 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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter__map,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_set__filter,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__filter__map,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__filter__less,axiom,
% 81.03/80.88 ! [V_P_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_set__minus__filter__out,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter__in__sublist,axiom,
% 81.03/80.88 ! [V_s_2,V_xs_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__filter__conv__card,axiom,
% 81.03/80.88 ! [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))))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__filter__def,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose__max__length,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose__map__map,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose_Osimps_I2_J,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose_Osimps_I1_J,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose__empty,axiom,
% 81.03/80.88 ! [V_xs_2,T_a] :
% 81.03/80.88 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a))
% 81.03/80.88 <=> ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 81.03/80.88 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__filter__simps_I2_J,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__of__filter__in,axiom,
% 81.03/80.88 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] :
% 81.03/80.88 ( 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)
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2))
% 81.03/80.88 => 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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__filter__simps_I1_J,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sublist__shift__lemma__Suc,axiom,
% 81.03/80.88 ! [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)))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_select__weigth__drop__zero,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_pick__drop__zero,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_nth__transpose,axiom,
% 81.03/80.88 ! [V_xs_2,T_a,V_i_2] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__transpose,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__filter__map__filter,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_insort__key__remove1,axiom,
% 81.03/80.88 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_b)
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
% 81.03/80.88 => ( 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
% 81.03/80.88 => 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 ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sublist__def,axiom,
% 81.03/80.88 ! [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))))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted_ONil,axiom,
% 81.03/80.88 ! [T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__single,axiom,
% 81.03/80.88 ! [V_x,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__same,axiom,
% 81.03/80.88 ! [V_xs_2,V_g_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__filter,axiom,
% 81.03/80.88 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__butlast,axiom,
% 81.03/80.88 ! [V_xs,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 81.03/80.88 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_take__upt,axiom,
% 81.03/80.88 ! [V_n,V_m,V_i] :
% 81.03/80.88 ( 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))
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_upt__eq__Nil__conv,axiom,
% 81.03/80.88 ! [V_j_2,V_i_2] :
% 81.03/80.88 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 81.03/80.88 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.88 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_upt__conv__Nil,axiom,
% 81.03/80.88 ! [V_i,V_j] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 81.03/80.88 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__many,axiom,
% 81.03/80.88 ! [V_zs,V_y,V_x,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 81.03/80.88 => 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))) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__many__eq,axiom,
% 81.03/80.88 ! [V_zs_2,V_y_2,V_x_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( 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)))
% 81.03/80.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 81.03/80.88 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_upt__add__eq__append,axiom,
% 81.03/80.88 ! [V_k,V_j,V_i] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_upt__Suc,axiom,
% 81.03/80.88 ! [V_j,V_i] :
% 81.03/80.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 81.03/80.88 => 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))) )
% 81.03/80.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 81.03/80.88 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_upt__Suc__append,axiom,
% 81.03/80.88 ! [V_j,V_i] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_drop__upt,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__drop,axiom,
% 81.03/80.88 ! [V_n,V_xs,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 81.03/80.88 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_hd__upt,axiom,
% 81.03/80.88 ! [V_j,V_i] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 81.03/80.88 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__distinct__set__unique,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 81.03/80.88 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2)
% 81.03/80.88 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
% 81.03/80.88 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2)
% 81.03/80.88 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_upt__0,axiom,
% 81.03/80.88 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted_Oequations_I1_J,axiom,
% 81.03/80.88 ! [T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__insort,axiom,
% 81.03/80.88 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( 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))
% 81.03/80.88 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__remove1,axiom,
% 81.03/80.88 ! [V_a,V_xs,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 81.03/80.88 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__upto,axiom,
% 81.03/80.88 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__upt,axiom,
% 81.03/80.88 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_distinct__upt,axiom,
% 81.03/80.88 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__list__of__set__range,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__insort__insert,axiom,
% 81.03/80.88 ! [V_x_2,V_xs_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_upt__conv__Cons,axiom,
% 81.03/80.88 ! [V_j,V_i] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_upt__rec,axiom,
% 81.03/80.88 ! [V_j,V_i] :
% 81.03/80.88 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 81.03/80.88 => 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)) )
% 81.03/80.88 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 81.03/80.88 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__take,axiom,
% 81.03/80.88 ! [V_n,V_xs,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 81.03/80.88 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__tl,axiom,
% 81.03/80.88 ! [V_xs,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 81.03/80.88 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__Suc__upt,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__map__remove1,axiom,
% 81.03/80.88 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__insort__key,axiom,
% 81.03/80.88 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( 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)))
% 81.03/80.88 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__insort__insert__key,axiom,
% 81.03/80.88 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_atLeastLessThan__upt,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_set__upt,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__map__same,axiom,
% 81.03/80.88 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__upt,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__Cons,axiom,
% 81.03/80.88 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 81.03/80.88 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 81.03/80.88 & ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__append,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 81.03/80.88 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 81.03/80.88 & c_List_Olinorder__class_Osorted(T_a,V_ys_2)
% 81.03/80.88 & ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => ! [B_xa] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2)))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_upt__rec__number__of,axiom,
% 81.03/80.88 ! [V_n,V_m] :
% 81.03/80.88 ( ( 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)))
% 81.03/80.88 => 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))) )
% 81.03/80.88 & ( ~ 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)))
% 81.03/80.88 => 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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_upt__eq__Cons__conv,axiom,
% 81.03/80.88 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 81.03/80.88 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 81.03/80.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 81.03/80.88 & V_i_2 = V_x_2
% 81.03/80.88 & 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 ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_last__upt,axiom,
% 81.03/80.88 ! [V_j,V_i] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter__insort,axiom,
% 81.03/80.88 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 81.03/80.88 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.88 => 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)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__nth,axiom,
% 81.03/80.88 ! [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 ).
% 81.03/80.88
% 81.03/80.88 fof(fact_atLeastAtMost__upt,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_atLeast__upt,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 81.03/80.88 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 81.03/80.88 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 81.03/80.88 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 81.03/80.88 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_nth__upt,axiom,
% 81.03/80.88 ! [V_j,V_k,V_i] :
% 81.03/80.88 ( 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))
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_greaterThanAtMost__upt,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted_Oequations_I2_J,axiom,
% 81.03/80.88 ! [V_a1_2,V_a2_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2))
% 81.03/80.88 <=> ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2)))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) )
% 81.03/80.88 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_greaterThanLessThan__upt,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_nth__map__upt,axiom,
% 81.03/80.88 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__list__of__set,axiom,
% 81.03/80.88 ! [V_A_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.88 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2
% 81.03/80.88 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))
% 81.03/80.88 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_atMost__upto,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_insort__remove1,axiom,
% 81.03/80.88 ! [V_xs_2,V_a_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 81.03/80.88 => 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 ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__equals__nth__mono,axiom,
% 81.03/80.88 ! [V_xs_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 81.03/80.88 <=> ! [B_j] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => ! [B_i] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 81.03/80.88 => 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))) ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__nth__mono,axiom,
% 81.03/80.88 ! [V_j,V_i,V_xs,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => 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))) ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__sorted__distinct__set__unique,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_b)
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
% 81.03/80.88 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)))
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))
% 81.03/80.88 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)))
% 81.03/80.88 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2)
% 81.03/80.88 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sublist__shift__lemma,axiom,
% 81.03/80.88 ! [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))))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose__rectangle,axiom,
% 81.03/80.88 ! [V_n_2,T_a,V_xs_2] :
% 81.03/80.88 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a))
% 81.03/80.88 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 81.03/80.88 => ( ! [B_i] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => 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 )
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose_Opsimps_I2_J,axiom,
% 81.03/80.88 ! [V_xss_2,T_a] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose_Opsimps_I1_J,axiom,
% 81.03/80.88 ! [T_a] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose__column,axiom,
% 81.03/80.88 ! [V_i_2,V_xs_2,T_a] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => 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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose__aux__filter__head,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_inj__on__rev,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev_Osimps_I1_J,axiom,
% 81.03/80.88 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Nil__is__rev__conv,axiom,
% 81.03/80.88 ! [V_xs_2,T_a] :
% 81.03/80.88 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2)
% 81.03/80.88 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev__is__Nil__conv,axiom,
% 81.03/80.88 ! [V_xs_2,T_a] :
% 81.03/80.88 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
% 81.03/80.88 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_singleton__rev__conv,axiom,
% 81.03/80.88 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.88 ( 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)
% 81.03/80.88 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev__singleton__conv,axiom,
% 81.03/80.88 ! [V_x_2,V_xs_2,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev__map,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev__concat,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev__foldl__cons,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_concat__conv__foldl,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_foldl__conv__concat,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_distinct__rev,axiom,
% 81.03/80.88 ! [V_xs_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2)))
% 81.03/80.88 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev__append,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_concat__append,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__rev,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev__is__rev__conv,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,T_a] :
% 81.03/80.88 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2)
% 81.03/80.88 <=> V_xs_2 = V_ys_2 ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev__swap,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,T_a] :
% 81.03/80.88 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2
% 81.03/80.88 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev__rev__ident,axiom,
% 81.03/80.88 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 81.03/80.88
% 81.03/80.88 fof(fact_listsum__rev,axiom,
% 81.03/80.88 ! [V_xs,T_a] :
% 81.03/80.88 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_set__rev,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_zip__rev,axiom,
% 81.03/80.88 ! [V_ys,T_b,V_xs,T_a] :
% 81.03/80.88 ( 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)
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev__filter,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_foldl__foldr,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_foldr__foldl,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_concat_Osimps_I1_J,axiom,
% 81.03/80.88 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_concat_Osimps_I2_J,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Nil__eq__concat__conv,axiom,
% 81.03/80.88 ! [V_xss_2,T_a] :
% 81.03/80.88 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2)
% 81.03/80.88 <=> ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)))
% 81.03/80.88 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_concat__eq__Nil__conv,axiom,
% 81.03/80.88 ! [V_xss_2,T_a] :
% 81.03/80.88 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a)
% 81.03/80.88 <=> ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)))
% 81.03/80.88 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__concat,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter__concat,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev_Osimps_I2_J,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev__eq__Cons__iff,axiom,
% 81.03/80.88 ! [V_ys_2,V_y_2,V_xs_2,T_a] :
% 81.03/80.88 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)
% 81.03/80.88 <=> 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__concat,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_set__concat,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_last__rev,axiom,
% 81.03/80.88 ! [T_a,V_xs] :
% 81.03/80.88 ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.88 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_hd__rev,axiom,
% 81.03/80.88 ! [T_a,V_xs] :
% 81.03/80.88 ( V_xs != c_List_Olist_ONil(T_a)
% 81.03/80.88 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__transpose,axiom,
% 81.03/80.88 ! [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)))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev__take,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev__drop,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rotate__rev,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose_Osimps_I3_J,axiom,
% 81.03/80.88 ! [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))))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev__nth,axiom,
% 81.03/80.88 ! [V_xs,T_a,V_n] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_concat__injective,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,T_a] :
% 81.03/80.88 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2)
% 81.03/80.88 => ( 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)
% 81.03/80.88 => ( ! [B_x] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => 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)) )
% 81.03/80.88 => V_xs_2 = V_ys_2 ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_concat__eq__concat__iff,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,T_a] :
% 81.03/80.88 ( ! [B_x] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => 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)) )
% 81.03/80.88 => ( 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)
% 81.03/80.88 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2)
% 81.03/80.88 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rev__update,axiom,
% 81.03/80.88 ! [V_y,V_xs,T_a,V_k] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_concat__map__singleton,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__rev__nth__mono,axiom,
% 81.03/80.88 ! [V_j,V_i,V_xs,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => 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))) ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_foldr__max__sorted,axiom,
% 81.03/80.88 ! [V_y_2,V_xs_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2))
% 81.03/80.88 => ( ( V_xs_2 = c_List_Olist_ONil(T_a)
% 81.03/80.88 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 )
% 81.03/80.88 & ( V_xs_2 != c_List_Olist_ONil(T_a)
% 81.03/80.88 => 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) ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose_Opsimps_I3_J,axiom,
% 81.03/80.88 ! [V_xss_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => 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))))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__transpose__sorted,axiom,
% 81.03/80.88 ! [V_xs_2,T_a] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a))
% 81.03/80.88 => 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) )
% 81.03/80.88 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a))
% 81.03/80.88 => 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))) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose__column__length,axiom,
% 81.03/80.88 ! [V_i_2,V_xs_2,T_a] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose__aux__filter__tail,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_nth__nth__transpose__sorted,axiom,
% 81.03/80.88 ! [V_j_2,V_i_2,V_xs_2,T_a] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => ( 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))))
% 81.03/80.88 => ( 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))))
% 81.03/80.88 => 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) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transpose__transpose,axiom,
% 81.03/80.88 ! [V_xs_2,T_a] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 81.03/80.88 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_zip__takeWhile__snd,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_zip__takeWhile__fst,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_takeWhile__eq__all__conv,axiom,
% 81.03/80.88 ! [V_xs_2,V_P_2,T_a] :
% 81.03/80.88 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2
% 81.03/80.88 <=> ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_set__takeWhileD,axiom,
% 81.03/80.88 ! [V_xs_2,V_P_2,V_x_2,T_a] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__takeWhile__le,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_takeWhile__eq__take,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_distinct__takeWhile,axiom,
% 81.03/80.88 ! [V_P_2,V_xs_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.88 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 81.03/80.88 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 81.03/80.88 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.88 => 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)) )
% 81.03/80.88 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.88 => 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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__takeWhile,axiom,
% 81.03/80.88 ! [V_P_2,V_xs_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 81.03/80.88 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_takeWhile__tail,axiom,
% 81.03/80.88 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] :
% 81.03/80.88 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_takeWhile__map,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_return__list__def,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_takeWhile__append1,axiom,
% 81.03/80.88 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.88 => 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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_nth__length__takeWhile,axiom,
% 81.03/80.88 ! [V_xs_2,V_P_2,T_a] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => ~ 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))))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_takeWhile__nth,axiom,
% 81.03/80.88 ! [V_xs_2,V_P_2,T_a,V_j_2] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__upds__def,axiom,
% 81.03/80.88 ! [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)))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_takeWhile__not__last,axiom,
% 81.03/80.88 ! [T_a,V_xs_2] :
% 81.03/80.88 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 81.03/80.88 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.88 => 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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 81.03/80.88 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => 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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 81.03/80.88 ! [V_l] :
% 81.03/80.88 ( c_List_Onat__list(V_l)
% 81.03/80.88 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__remdups__concat,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_distinct__remdups,axiom,
% 81.03/80.88 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__remdups__leq,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_remdups__map__remdups,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_set__remdups,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_remdups_Osimps_I1_J,axiom,
% 81.03/80.88 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_remdups__eq__nil__right__iff,axiom,
% 81.03/80.88 ! [V_x_2,T_a] :
% 81.03/80.88 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2)
% 81.03/80.88 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_remdups__eq__nil__iff,axiom,
% 81.03/80.88 ! [V_x_2,T_a] :
% 81.03/80.88 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a)
% 81.03/80.88 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__remdups,axiom,
% 81.03/80.88 ! [V_l,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 81.03/80.88 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_distinct__remdups__id,axiom,
% 81.03/80.88 ! [V_xs,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 81.03/80.88 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_remdups__id__iff__distinct,axiom,
% 81.03/80.88 ! [V_xs_2,T_a] :
% 81.03/80.88 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2
% 81.03/80.88 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__remdups__eq,axiom,
% 81.03/80.88 ! [V_xs_2,T_a] :
% 81.03/80.88 ( 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)
% 81.03/80.88 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_remdups__remdups,axiom,
% 81.03/80.88 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_remdups__filter,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_remove1__remdups,axiom,
% 81.03/80.88 ! [V_x,V_xs,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_embed__list__def,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_remdups_Osimps_I2_J,axiom,
% 81.03/80.88 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.88 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => 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) )
% 81.03/80.88 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__remdups__card__conv,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 81.03/80.88 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] :
% 81.03/80.88 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_takeWhile__neq__rev,axiom,
% 81.03/80.88 ! [V_x_2,V_xs_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_dropWhile__neq__rev,axiom,
% 81.03/80.88 ! [V_x_2,V_xs_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_distinct__dropWhile,axiom,
% 81.03/80.88 ! [V_P_2,V_xs_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.88 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 81.03/80.88 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 81.03/80.88 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.88 => 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) )
% 81.03/80.88 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.88 => 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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__dropWhile,axiom,
% 81.03/80.88 ! [V_P_2,V_xs_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 81.03/80.88 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__dropWhile__le,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 81.03/80.88 ! [V_xs_2,V_P_2,T_a] :
% 81.03/80.88 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a)
% 81.03/80.88 <=> ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_takeWhile__dropWhile__id,axiom,
% 81.03/80.88 ! [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 ).
% 81.03/80.88
% 81.03/80.88 fof(fact_hd__dropWhile,axiom,
% 81.03/80.88 ! [V_xs_2,V_P_2,T_a] :
% 81.03/80.88 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a)
% 81.03/80.88 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_dropWhile__map,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_dropWhile__append1,axiom,
% 81.03/80.88 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.88 => 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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 81.03/80.88 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] :
% 81.03/80.88 ( 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)
% 81.03/80.88 <=> ( 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))
% 81.03/80.88 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_dropWhile__eq__drop,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_dropWhile__nth,axiom,
% 81.03/80.88 ! [V_xs_2,V_P_2,T_a,V_j_2] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => 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)))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_listsum__map__filter,axiom,
% 81.03/80.88 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] :
% 81.03/80.88 ( class_Groups_Omonoid__add(T_b)
% 81.03/80.88 => ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => ( ~ hBOOL(hAPP(V_P_2,B_x))
% 81.03/80.88 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) )
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__nth__monoI,axiom,
% 81.03/80.88 ! [V_xs,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( ! [B_i,B_j] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => 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))) ) )
% 81.03/80.88 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_n__lists_Osimps_I2_J,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_partition__filter__conv,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_partition__filter1,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_distinct__n__lists,axiom,
% 81.03/80.88 ! [V_n,V_xs,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 81.03/80.88 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__n__lists,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__n__lists__elem,axiom,
% 81.03/80.88 ! [V_xs_2,V_n_2,V_ys_2,T_a] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_partition__P,axiom,
% 81.03/80.88 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
% 81.03/80.88 ( 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)
% 81.03/80.88 => ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2)))
% 81.03/80.88 => hBOOL(hAPP(V_P_2,B_x)) )
% 81.03/80.88 & ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2)))
% 81.03/80.88 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_partition_Osimps_I1_J,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_n__lists__Nil,axiom,
% 81.03/80.88 ! [T_a,V_n] :
% 81.03/80.88 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.88 => 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))) )
% 81.03/80.88 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.88 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_n__lists_Osimps_I1_J,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_partition_Osimps_I2_J,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_partition__filter2,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_partition__set,axiom,
% 81.03/80.88 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
% 81.03/80.88 ( 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)
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_set__n__lists,axiom,
% 81.03/80.88 ! [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)))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sublists__powset,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__sublists,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_distinct__set__sublists,axiom,
% 81.03/80.88 ! [V_xs_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 81.03/80.88 => 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)))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sublists_Osimps_I1_J,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sublists_Osimps_I2_J,axiom,
% 81.03/80.88 ! [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))))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_product_Osimps_I2_J,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__of__zip__enum__inject,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,T_a,T_b] :
% 81.03/80.88 ( ( class_Enum_Oenum(T_b)
% 81.03/80.88 & class_Enum_Oenum(T_a) )
% 81.03/80.88 => ( 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))
% 81.03/80.88 => ( 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))
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => V_xs_2 = V_ys_2 ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__distinct,axiom,
% 81.03/80.88 ! [T_a] :
% 81.03/80.88 ( class_Enum_Oenum(T_a)
% 81.03/80.88 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__option__def,axiom,
% 81.03/80.88 ! [T_a] :
% 81.03/80.88 ( class_Enum_Oenum(T_a)
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_in__enum,axiom,
% 81.03/80.88 ! [V_x_2,T_a] :
% 81.03/80.88 ( class_Enum_Oenum(T_a)
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_UNIV__enum,axiom,
% 81.03/80.88 ! [T_a] :
% 81.03/80.88 ( class_Enum_Oenum(T_a)
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__UNIV,axiom,
% 81.03/80.88 ! [T_a] :
% 81.03/80.88 ( class_Enum_Oenum(T_a)
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__prod__def,axiom,
% 81.03/80.88 ! [T_b,T_a] :
% 81.03/80.88 ( ( class_Enum_Oenum(T_a)
% 81.03/80.88 & class_Enum_Oenum(T_b) )
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__fun__def,axiom,
% 81.03/80.88 ! [T_b,T_a] :
% 81.03/80.88 ( ( class_Enum_Oenum(T_a)
% 81.03/80.88 & class_Enum_Oenum(T_b) )
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__fun__code,axiom,
% 81.03/80.88 ! [T_b,T_a] :
% 81.03/80.88 ( ( class_Enum_Oenum(T_a)
% 81.03/80.88 & class_HOL_Oequal(T_a)
% 81.03/80.88 & class_Enum_Oenum(T_b) )
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_product_Osimps_I1_J,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_distinct__product,axiom,
% 81.03/80.88 ! [V_ys,T_b,V_xs,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 81.03/80.88 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 81.03/80.88 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_ex__n__lists__def,axiom,
% 81.03/80.88 ! [V_n_2,V_P_2,T_a] :
% 81.03/80.88 ( class_Enum_Oenum(T_a)
% 81.03/80.88 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2)
% 81.03/80.88 <=> ? [B_x] :
% 81.03/80.88 ( 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)))))
% 81.03/80.88 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_all__n__lists__def,axiom,
% 81.03/80.88 ! [V_n_2,V_P_2,T_a] :
% 81.03/80.88 ( class_Enum_Oenum(T_a)
% 81.03/80.88 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2)
% 81.03/80.88 <=> ! [B_x] :
% 81.03/80.88 ( 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)))))
% 81.03/80.88 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__all__fun__def,axiom,
% 81.03/80.88 ! [V_P_2,T_a,T_b] :
% 81.03/80.88 ( ( class_Enum_Oenum(T_b)
% 81.03/80.88 & class_Enum_Oenum(T_a) )
% 81.03/80.88 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
% 81.03/80.88 <=> 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__ex__fun__def,axiom,
% 81.03/80.88 ! [V_P_2,T_a,T_b] :
% 81.03/80.88 ( ( class_Enum_Oenum(T_b)
% 81.03/80.88 & class_Enum_Oenum(T_a) )
% 81.03/80.88 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
% 81.03/80.88 <=> 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__ex,axiom,
% 81.03/80.88 ! [V_P_2,T_a] :
% 81.03/80.88 ( class_Enum_Oenum(T_a)
% 81.03/80.88 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2))
% 81.03/80.88 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__all,axiom,
% 81.03/80.88 ! [V_P_2,T_a] :
% 81.03/80.88 ( class_Enum_Oenum(T_a)
% 81.03/80.88 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2))
% 81.03/80.88 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_exists__code,axiom,
% 81.03/80.88 ! [V_P_2,T_a] :
% 81.03/80.88 ( class_Enum_Oenum(T_a)
% 81.03/80.88 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 81.03/80.88 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_all__code,axiom,
% 81.03/80.88 ! [V_P_2,T_a] :
% 81.03/80.88 ( class_Enum_Oenum(T_a)
% 81.03/80.88 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 81.03/80.88 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__all__option__def,axiom,
% 81.03/80.88 ! [V_P_2,T_a] :
% 81.03/80.88 ( class_Enum_Oenum(T_a)
% 81.03/80.88 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2))
% 81.03/80.88 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a)))
% 81.03/80.88 & 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)))) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__ex__option__def,axiom,
% 81.03/80.88 ! [V_P_2,T_a] :
% 81.03/80.88 ( class_Enum_Oenum(T_a)
% 81.03/80.88 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2))
% 81.03/80.88 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a)))
% 81.03/80.88 | 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)))) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__ex__prod__def,axiom,
% 81.03/80.88 ! [V_P_2,T_a,T_b] :
% 81.03/80.88 ( ( class_Enum_Oenum(T_b)
% 81.03/80.88 & class_Enum_Oenum(T_a) )
% 81.03/80.88 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2))
% 81.03/80.88 <=> 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))))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__all__prod__def,axiom,
% 81.03/80.88 ! [V_P_2,T_a,T_b] :
% 81.03/80.88 ( ( class_Enum_Oenum(T_b)
% 81.03/80.88 & class_Enum_Oenum(T_a) )
% 81.03/80.88 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2))
% 81.03/80.88 <=> 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))))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_order__fun_I1_J,axiom,
% 81.03/80.88 ! [V_g_2,V_f_2,T_a,T_b] :
% 81.03/80.88 ( ( class_Orderings_Oorder(T_b)
% 81.03/80.88 & class_Enum_Oenum(T_a) )
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 81.03/80.88 <=> 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_order__fun_I2_J,axiom,
% 81.03/80.88 ! [V_g_2,V_f_2,T_a,T_b] :
% 81.03/80.88 ( ( class_Orderings_Oorder(T_b)
% 81.03/80.88 & class_Enum_Oenum(T_a) )
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 81.03/80.88 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 81.03/80.88 & 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)))) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__ex__fun__code,axiom,
% 81.03/80.88 ! [V_P_2,T_a,T_b] :
% 81.03/80.88 ( ( class_Enum_Oenum(T_b)
% 81.03/80.88 & class_Enum_Oenum(T_a)
% 81.03/80.88 & class_HOL_Oequal(T_a) )
% 81.03/80.88 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
% 81.03/80.88 <=> 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__all__fun__code,axiom,
% 81.03/80.88 ! [V_P_2,T_a,T_b] :
% 81.03/80.88 ( ( class_Enum_Oenum(T_b)
% 81.03/80.88 & class_Enum_Oenum(T_a)
% 81.03/80.88 & class_HOL_Oequal(T_a) )
% 81.03/80.88 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
% 81.03/80.88 <=> 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sort__foldl__insort,axiom,
% 81.03/80.88 ! [V_xs_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__of__zip__enum__is__Some,axiom,
% 81.03/80.88 ! [V_x,V_ys,T_b,T_a] :
% 81.03/80.88 ( class_Enum_Oenum(T_a)
% 81.03/80.88 => ( 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))
% 81.03/80.88 => ? [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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_distinct__sort,axiom,
% 81.03/80.88 ! [V_xs_2,V_f_2,T_a,T_b] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_b)
% 81.03/80.88 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)))
% 81.03/80.88 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_set__sort,axiom,
% 81.03/80.88 ! [V_xs_2,V_f_2,T_a,T_b] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_b)
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sort__key__simps_I1_J,axiom,
% 81.03/80.88 ! [V_f_2,T_a,T_b] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_b)
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__sort,axiom,
% 81.03/80.88 ! [V_xs_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__sort,axiom,
% 81.03/80.88 ! [V_xs_2,V_f_2,T_a,T_b] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_b)
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter__sort,axiom,
% 81.03/80.88 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_b)
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__sort__key,axiom,
% 81.03/80.88 ! [V_xs_2,V_f_2,T_b,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sort__key__simps_I2_J,axiom,
% 81.03/80.88 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_b)
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 81.03/80.88 ! [V_xs_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_takeWhile__eq__filter,axiom,
% 81.03/80.88 ! [V_xs_2,V_P_2,T_a] :
% 81.03/80.88 ( ! [B_x] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 81.03/80.88 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 81.03/80.88 ! [V_P_2,V_xs_2,T_a,V_n_2] :
% 81.03/80.88 ( ! [B_i] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) )
% 81.03/80.88 => ( ( 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)))
% 81.03/80.88 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) )
% 81.03/80.88 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_length__takeWhile__less__P__nth,axiom,
% 81.03/80.88 ! [V_xs_2,T_a,V_P_2,V_j_2] :
% 81.03/80.88 ( ! [B_i] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 81.03/80.88 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) )
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => 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)))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_lists__Int__eq,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_listsp_ONil,axiom,
% 81.03/80.88 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_append__in__listsp__conv,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,V_A_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
% 81.03/80.88 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2))
% 81.03/80.88 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_in__listsp__conv__set,axiom,
% 81.03/80.88 ! [V_xs_2,V_A_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2))
% 81.03/80.88 <=> ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_listsp_Oequations_I1_J,axiom,
% 81.03/80.88 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_listsp__infI,axiom,
% 81.03/80.88 ! [V_B_2,V_l_2,V_A_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2))
% 81.03/80.88 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2))
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_listsp__inf__eq,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_listsp__conj__eq,axiom,
% 81.03/80.88 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2))
% 81.03/80.88 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_listsp_Oequations_I2_J,axiom,
% 81.03/80.88 ! [V_a2_2,V_a1_2,V_A_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2)))
% 81.03/80.88 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 81.03/80.88 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_listsp__mono,axiom,
% 81.03/80.88 ! [V_B_2,V_A_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_listsp__lists__eq,axiom,
% 81.03/80.88 ! [V_x_2,V_A_2,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_lists__IntI,axiom,
% 81.03/80.88 ! [V_B_2,V_A_2,V_l_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2)))
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2)))
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__def,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 81.03/80.88 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 81.03/80.88 <=> ( 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)
% 81.03/80.88 & ! [B_x] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_sorted_Osimps,axiom,
% 81.03/80.88 ! [V_a_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2)
% 81.03/80.88 <=> ( V_a_2 = c_List_Olist_ONil(T_a)
% 81.03/80.88 | ? [B_xs,B_x] :
% 81.03/80.88 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs)
% 81.03/80.88 & ! [B_xa] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs)))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) )
% 81.03/80.88 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__map2,axiom,
% 81.03/80.88 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 <=> 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__map1,axiom,
% 81.03/80.88 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] :
% 81.03/80.88 ( 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)
% 81.03/80.88 <=> 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__Cons,axiom,
% 81.03/80.88 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 81.03/80.88 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__eq,axiom,
% 81.03/80.88 ! [T_a,V_ys_2,V_xs_2] :
% 81.03/80.88 ( V_xs_2 = V_ys_2
% 81.03/80.88 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__lengthD,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 81.03/80.88 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__dropI,axiom,
% 81.03/80.88 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] :
% 81.03/80.88 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2)
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__takeI,axiom,
% 81.03/80.88 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 81.03/80.88 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__Nil2,axiom,
% 81.03/80.88 ! [V_xs_2,V_P_2,T_b,T_a] :
% 81.03/80.88 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b))
% 81.03/80.88 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__Nil,axiom,
% 81.03/80.88 ! [V_ys_2,V_P_2,T_b,T_a] :
% 81.03/80.88 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2)
% 81.03/80.88 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__rev1,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 81.03/80.88 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2)
% 81.03/80.88 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__rev,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__append,axiom,
% 81.03/80.88 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
% 81.03/80.88 ( 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)
% 81.03/80.88 => ( 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))
% 81.03/80.88 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 81.03/80.88 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__appendI,axiom,
% 81.03/80.88 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_P_2,T_b,T_a] :
% 81.03/80.88 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2)
% 81.03/80.88 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_ca_2,V_d_2)
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__nthD2,axiom,
% 81.03/80.88 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 81.03/80.88 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__nthD,axiom,
% 81.03/80.88 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 81.03/80.88 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__conv__all__nth,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 81.03/80.88 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 81.03/80.88 <=> ( 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)
% 81.03/80.88 & ! [B_i] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => 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))) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__update__cong,axiom,
% 81.03/80.88 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 81.03/80.88 => 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)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__update__cong2,axiom,
% 81.03/80.88 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 81.03/80.88 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => 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)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2I,axiom,
% 81.03/80.88 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] :
% 81.03/80.88 ( ! [B_x] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) )
% 81.03/80.88 => ( 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)
% 81.03/80.88 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_all__nth__imp__all__set,axiom,
% 81.03/80.88 ! [V_x_2,V_P_2,V_xs_2,T_a] :
% 81.03/80.88 ( ! [B_i] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) )
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_not__in__set__insert,axiom,
% 81.03/80.88 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.88 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_List_Oinsert__def,axiom,
% 81.03/80.88 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.88 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 )
% 81.03/80.88 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => 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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_insert__remdups,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_distinct__insert,axiom,
% 81.03/80.88 ! [V_x,V_xs,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 81.03/80.88 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_in__set__insert,axiom,
% 81.03/80.88 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_List_Oset__insert,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_insert__Nil,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_concat__map__maps,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_maps__def,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_maps__simps_I2_J,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_maps__simps_I1_J,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_finite__conv__nat__seg__image,axiom,
% 81.03/80.88 ! [V_A_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.88 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_distinct__concat,axiom,
% 81.03/80.88 ! [V_xs_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2))
% 81.03/80.88 => ( ! [B_ys] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 81.03/80.88 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) )
% 81.03/80.88 => ( ! [B_ys] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 81.03/80.88 => ! [B_zs] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 81.03/80.88 => ( B_ys != B_zs
% 81.03/80.88 => 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)) ) ) )
% 81.03/80.88 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_measures__lesseq,axiom,
% 81.03/80.88 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => 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)))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rel__comp__def,axiom,
% 81.03/80.88 ! [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))))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rel__compI,axiom,
% 81.03/80.88 ! [V_s_2,V_ca_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 => ( 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))
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rel__comp__UNION__distrib2,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rel__comp__UNION__distrib,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rel__comp__mono,axiom,
% 81.03/80.88 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 81.03/80.88 => ( 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))
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_union__comp__emptyL,axiom,
% 81.03/80.88 ! [V_B_2,V_C_2,V_A_2,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 => ( 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))
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_union__comp__emptyR,axiom,
% 81.03/80.88 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 => ( 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))
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rel__comp__empty2,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rel__comp__empty1,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_O__assoc,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rel__comp__distrib2,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rel__comp__distrib,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_in__measures_I1_J,axiom,
% 81.03/80.88 ! [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))))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_measures__def,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_max__ext__compat,axiom,
% 81.03/80.88 ! [V_S_2,V_R_2,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_min__ext__compat,axiom,
% 81.03/80.88 ! [V_S_2,V_R_2,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_measures__less,axiom,
% 81.03/80.88 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => 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)))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_in__measures_I2_J,axiom,
% 81.03/80.88 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 <=> ( 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)))
% 81.03/80.88 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 81.03/80.88 & 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))) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_pred__comp__rel__comp__eq,axiom,
% 81.03/80.88 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] :
% 81.03/80.88 ( 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)
% 81.03/80.88 <=> 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_reduction__pairI,axiom,
% 81.03/80.88 ! [V_S_2,V_R_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_R_2)
% 81.03/80.88 => ( 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))
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__less__than,axiom,
% 81.03/80.88 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_pred__comp_Ointros,axiom,
% 81.03/80.88 ! [T_c,T_b,T_a,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2))
% 81.03/80.88 => c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2,V_a_2,V_ca_2) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__empty,axiom,
% 81.03/80.88 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__inv__image,axiom,
% 81.03/80.88 ! [V_f_2,T_b,V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__lex,axiom,
% 81.03/80.88 ! [V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__lex__prod,axiom,
% 81.03/80.88 ! [V_rb_2,T_b,V_ra_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_ra_2)
% 81.03/80.88 => ( c_Wellfounded_Owf(T_b,V_rb_2)
% 81.03/80.88 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__lenlex,axiom,
% 81.03/80.88 ! [V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__measure,axiom,
% 81.03/80.88 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__no__loop,axiom,
% 81.03/80.88 ! [V_R_2,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__union__merge,axiom,
% 81.03/80.88 ! [V_S_2,V_R_2,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 <=> 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__comp__self,axiom,
% 81.03/80.88 ! [V_R_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_R_2)
% 81.03/80.88 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__measures,axiom,
% 81.03/80.88 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__Int1,axiom,
% 81.03/80.88 ! [V_r_H_2,V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__Int2,axiom,
% 81.03/80.88 ! [V_r_H_2,V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__less,axiom,
% 81.03/80.88 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)))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__lexn,axiom,
% 81.03/80.88 ! [V_n_2,V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_acc__wfD,axiom,
% 81.03/80.88 ! [V_x_2,V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__acc__iff,axiom,
% 81.03/80.88 ! [V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__irrefl,axiom,
% 81.03/80.88 ! [V_a_2,V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => ~ 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__asym,axiom,
% 81.03/80.88 ! [V_x_2,V_a_2,V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => ( 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))
% 81.03/80.88 => ~ 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__not__sym,axiom,
% 81.03/80.88 ! [V_x_2,V_a_2,V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => ( 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))
% 81.03/80.88 => ~ 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__not__refl,axiom,
% 81.03/80.88 ! [V_a_2,V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => ~ 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_max__ext__wf,axiom,
% 81.03/80.88 ! [V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__pair__less,axiom,
% 81.03/80.88 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__finite__psubset,axiom,
% 81.03/80.88 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_pred__comp_Oequations,axiom,
% 81.03/80.88 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] :
% 81.03/80.88 ( c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2,V_a1_2,V_a3_2)
% 81.03/80.88 <=> ? [B_b] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 81.03/80.88 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__mlex,axiom,
% 81.03/80.88 ! [V_f_2,V_R_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_R_2)
% 81.03/80.88 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_min__ext__wf,axiom,
% 81.03/80.88 ! [V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__int__ge__less__than2,axiom,
% 81.03/80.88 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__int__ge__less__than,axiom,
% 81.03/80.88 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__subset,axiom,
% 81.03/80.88 ! [V_p_2,V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => ( 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))
% 81.03/80.88 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 81.03/80.88 ! [V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 <=> ~ ? [B_f] :
% 81.03/80.88 ! [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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wfE__pf,axiom,
% 81.03/80.88 ! [V_A_2,V_R_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_R_2)
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__union__compatible,axiom,
% 81.03/80.88 ! [V_S_2,V_R_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_R_2)
% 81.03/80.88 => ( c_Wellfounded_Owf(T_a,V_S_2)
% 81.03/80.88 => ( 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))
% 81.03/80.88 => 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)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf,axiom,
% 81.03/80.88 ! [T_a] :
% 81.03/80.88 ( class_Orderings_Owellorder(T_a)
% 81.03/80.88 => 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)))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_reduction__pair__def,axiom,
% 81.03/80.88 ! [V_P_2,T_a] :
% 81.03/80.88 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 81.03/80.88 <=> ( 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))
% 81.03/80.88 & 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_reduction__pair__lemma,axiom,
% 81.03/80.88 ! [V_S_2,V_R_2,V_P_2,T_a] :
% 81.03/80.88 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => ( c_Wellfounded_Owf(T_a,V_S_2)
% 81.03/80.88 => 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)) ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__map__pair__image,axiom,
% 81.03/80.88 ! [V_f_2,T_b,V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__if__measure,axiom,
% 81.03/80.88 ! [T_a,V_g_2,V_f_2,V_P_2] :
% 81.03/80.88 ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(V_P_2,B_x))
% 81.03/80.88 => 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))) )
% 81.03/80.88 => 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))))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_max__extp_Oequations,axiom,
% 81.03/80.88 ! [V_a2_2,V_a1_2,V_R_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2)
% 81.03/80.88 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2))
% 81.03/80.88 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
% 81.03/80.88 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.88 & ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2))
% 81.03/80.88 => ? [B_xa] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2))
% 81.03/80.88 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_pred__nat__def,axiom,
% 81.03/80.88 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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__same__fst,axiom,
% 81.03/80.88 ! [T_a,V_R_2,T_b,V_P_2] :
% 81.03/80.88 ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(V_P_2,B_x))
% 81.03/80.88 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) )
% 81.03/80.88 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__pred__nat,axiom,
% 81.03/80.88 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_max__ext_Ointros,axiom,
% 81.03/80.88 ! [V_R_2,V_Y_2,V_X_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2))
% 81.03/80.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2))
% 81.03/80.88 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.88 => ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2))
% 81.03/80.88 => ? [B_xa] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2))
% 81.03/80.88 & 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)) ) )
% 81.03/80.88 => 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))) ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Nitpick_Oone__frac__def,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Nitpick_Ofrac__def,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_inj__on__Inter,axiom,
% 81.03/80.88 ! [V_f_2,T_b,T_a,V_S_2] :
% 81.03/80.88 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
% 81.03/80.88 => ( ! [B_A] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2))
% 81.03/80.88 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) )
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Range__Collect__split,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_the__elem__def,axiom,
% 81.03/80.88 ! [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))))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_RangeI,axiom,
% 81.03/80.88 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_snd__eq__Range,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Range__Id__on,axiom,
% 81.03/80.88 ! [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 ).
% 81.03/80.88
% 81.03/80.88 fof(fact_finite__Range,axiom,
% 81.03/80.88 ! [V_r_2,T_b,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2))
% 81.03/80.88 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Range__Union,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Range__Diff__subset,axiom,
% 81.03/80.88 ! [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)))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Range__empty__iff,axiom,
% 81.03/80.88 ! [V_r_2,T_a,T_b] :
% 81.03/80.88 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.88 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Range__empty,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Range__Un__eq,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_The__split__eq,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_split__paired__The,axiom,
% 81.03/80.88 ! [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)))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Range__iff,axiom,
% 81.03/80.88 ! [V_r_2,T_b,V_a_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)))
% 81.03/80.88 <=> ? [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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_the__inv__into__def,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_fold__def,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Range__insert,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_divmod__nat__def,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Range__Int__subset,axiom,
% 81.03/80.88 ! [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)))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_fold1__def,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_The__split,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_RangeP__Range__eq,axiom,
% 81.03/80.88 ! [V_x_2,V_r_2,T_b,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_enum__the__def,axiom,
% 81.03/80.88 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_RangeP_Ointros,axiom,
% 81.03/80.88 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 81.03/80.88 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_RangeP_Oequations,axiom,
% 81.03/80.88 ! [V_a2_2,V_r_2,T_b,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2))
% 81.03/80.88 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_flat__lub__def,axiom,
% 81.03/80.88 ! [V_b_2,V_A_2,T_a] :
% 81.03/80.88 ( ( 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)))))
% 81.03/80.88 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 )
% 81.03/80.88 & ( ~ 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)))))
% 81.03/80.88 => 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)))))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_RangeE,axiom,
% 81.03/80.88 ! [V_r_2,T_b,V_b_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)))
% 81.03/80.88 => ~ ! [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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_inj__vimage__singleton,axiom,
% 81.03/80.88 ! [V_a_2,V_f_2,T_b,T_a] :
% 81.03/80.88 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.88 => 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))))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__Un,axiom,
% 81.03/80.88 ! [V_s_2,V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => ( c_Wellfounded_Owf(T_a,V_s_2)
% 81.03/80.88 => ( 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))
% 81.03/80.88 => 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)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimageI,axiom,
% 81.03/80.88 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] :
% 81.03/80.88 ( hAPP(V_f_2,V_a_2) = V_b_2
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_DomainI,axiom,
% 81.03/80.88 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_inj__vimage__image__eq,axiom,
% 81.03/80.88 ! [V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.88 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.88 => 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 ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__insert,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Domain__Un__eq,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__Un,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__empty,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Domain__empty,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Domain__empty__iff,axiom,
% 81.03/80.88 ! [V_r_2,T_b,T_a] :
% 81.03/80.88 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.88 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Domain__mono,axiom,
% 81.03/80.88 ! [V_s_2,V_r_2,T_b,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__mono,axiom,
% 81.03/80.88 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_image__vimage__subset,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__singleton__eq,axiom,
% 81.03/80.88 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] :
% 81.03/80.88 ( 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))))))
% 81.03/80.88 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_finite__vimageD,axiom,
% 81.03/80.88 ! [V_F_2,V_h_2,T_b,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2)))
% 81.03/80.88 => ( 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))
% 81.03/80.88 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__compose,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_finite__Domain,axiom,
% 81.03/80.88 ! [V_r_2,T_b,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2))
% 81.03/80.88 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__INT,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__code,axiom,
% 81.03/80.88 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2))
% 81.03/80.88 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__Compl,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__ident,axiom,
% 81.03/80.88 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Domain__Id__on,axiom,
% 81.03/80.88 ! [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 ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__UNIV,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimageI2,axiom,
% 81.03/80.88 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimageD,axiom,
% 81.03/80.88 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__eq,axiom,
% 81.03/80.88 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)))
% 81.03/80.88 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_surj__image__vimage__eq,axiom,
% 81.03/80.88 ! [V_A_2,V_f_2,T_a,T_b] :
% 81.03/80.88 ( 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))
% 81.03/80.88 => 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 ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__Int,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_finite__vimageI,axiom,
% 81.03/80.88 ! [V_h_2,T_b,V_F_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 81.03/80.88 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 81.03/80.88 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_image__vimage__eq,axiom,
% 81.03/80.88 ! [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)))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__subsetD,axiom,
% 81.03/80.88 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] :
% 81.03/80.88 ( 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))
% 81.03/80.88 => ( 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))
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_fst__eq__Domain,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__Collect__eq,axiom,
% 81.03/80.88 ! [V_P_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),V_P_2),V_f_2)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__def,axiom,
% 81.03/80.88 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(T_b)),V_f_2)),V_B_2)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__Diff,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__UN,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__Union,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__const,axiom,
% 81.03/80.88 ! [T_b,V_A_2,V_ca_2,T_a] :
% 81.03/80.88 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 81.03/80.88 => 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)) )
% 81.03/80.88 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__eq__UN,axiom,
% 81.03/80.88 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(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))))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Domain__iff,axiom,
% 81.03/80.88 ! [V_r_2,T_b,V_a_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
% 81.03/80.88 <=> ? [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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Domain__insert,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Domain__Int__subset,axiom,
% 81.03/80.88 ! [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)))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__subsetI,axiom,
% 81.03/80.88 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 81.03/80.88 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Domain__Diff__subset,axiom,
% 81.03/80.88 ! [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)))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Field__def,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__if,axiom,
% 81.03/80.88 ! [V_B_2,T_b,V_d_2,V_A_2,V_ca_2,T_a] :
% 81.03/80.88 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 81.03/80.88 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 81.03/80.88 => 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)) )
% 81.03/80.88 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 81.03/80.88 => 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 ) ) )
% 81.03/80.88 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 81.03/80.88 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 81.03/80.88 => 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) )
% 81.03/80.88 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 81.03/80.88 => 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)) ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Domain__Union,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Domain__Collect__split,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_DomainP__Domain__eq,axiom,
% 81.03/80.88 ! [V_x_2,V_r_2,T_b,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_image__split__eq__Sigma,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_DomainP_Ointros,axiom,
% 81.03/80.88 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 81.03/80.88 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_SigmaI,axiom,
% 81.03/80.88 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Sigma__Union,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Sigma__Diff__distrib2,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Times__Diff__distrib1,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Sigma__Diff__distrib1,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_setsum__cartesian__product,axiom,
% 81.03/80.88 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 81.03/80.88 ( class_Groups_Ocomm__monoid__add(T_a)
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_setprod__cartesian__product,axiom,
% 81.03/80.88 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 81.03/80.88 ( class_Groups_Ocomm__monoid__mult(T_a)
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Times__subset__cancel2,axiom,
% 81.03/80.88 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2))
% 81.03/80.88 => ( 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))))
% 81.03/80.88 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Sigma__Int__distrib1,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Times__Int__distrib1,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Sigma__Int__distrib2,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Times__eq__cancel2,axiom,
% 81.03/80.88 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2))
% 81.03/80.88 => ( 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))
% 81.03/80.88 <=> V_A_2 = V_B_2 ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_finite__cartesian__product,axiom,
% 81.03/80.88 ! [V_B_2,T_b,V_A_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 81.03/80.88 => 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)))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_card__cartesian__product,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Compl__Times__UNIV2,axiom,
% 81.03/80.88 ! [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)))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Compl__Times__UNIV1,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_DomainP_Oequations,axiom,
% 81.03/80.88 ! [V_a1_2,V_r_2,T_b,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2))
% 81.03/80.88 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_SigmaE2,axiom,
% 81.03/80.88 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.88 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_SigmaD2,axiom,
% 81.03/80.88 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_SigmaD1,axiom,
% 81.03/80.88 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_mem__Sigma__iff,axiom,
% 81.03/80.88 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 81.03/80.88 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_UNIV__Times__UNIV,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_card__cartesian__product__singleton,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_listrel__subset,axiom,
% 81.03/80.88 ! [V_A_2,V_r_2,T_a] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => 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))))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_equiv__type,axiom,
% 81.03/80.88 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.88 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.88 => 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)))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Id__on__subset__Times,axiom,
% 81.03/80.88 ! [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)))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Sigma__empty1,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Sigma__empty2,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Times__empty,axiom,
% 81.03/80.88 ! [V_B_2,V_A_2,T_b,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.88 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Sigma__Un__distrib1,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Times__Un__distrib1,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Sigma__Un__distrib2,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rel__comp__subset__Sigma,axiom,
% 81.03/80.88 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => ( 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))))
% 81.03/80.88 => 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)))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Image__subset,axiom,
% 81.03/80.88 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_C_2)),V_B_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_finite__cartesian__productD2,axiom,
% 81.03/80.88 ! [V_B_2,V_A_2,T_b,T_a] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.88 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_finite__cartesian__productD1,axiom,
% 81.03/80.88 ! [V_B_2,V_A_2,T_b,T_a] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 81.03/80.88 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_SetCompr__Sigma__eq,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Collect__split,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_fst__image__times,axiom,
% 81.03/80.88 ! [V_A_2,T_b,T_a,V_B_2] :
% 81.03/80.88 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.88 => 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)) )
% 81.03/80.88 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.88 => 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 ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_snd__image__times,axiom,
% 81.03/80.88 ! [V_B_2,T_b,T_a,V_A_2] :
% 81.03/80.88 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.88 => 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)) )
% 81.03/80.88 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.88 => 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 ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__pair__surj__on,axiom,
% 81.03/80.88 ! [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] :
% 81.03/80.88 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2
% 81.03/80.88 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_product__list__set,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_swap__product,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_refl__on__def,axiom,
% 81.03/80.88 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.88 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 81.03/80.88 <=> ( 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))))
% 81.03/80.88 & ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.88 => 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)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_insert__times__insert,axiom,
% 81.03/80.88 ! [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)))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_finite__equiv__class,axiom,
% 81.03/80.88 ! [V_X_2,V_r_2,V_A_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.88 => ( 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))))
% 81.03/80.88 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)))
% 81.03/80.88 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__pair__inj__on,axiom,
% 81.03/80.88 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] :
% 81.03/80.88 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.88 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2)
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_UN__Times__distrib,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Sigma__def,axiom,
% 81.03/80.88 ! [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))))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_finite__quotient,axiom,
% 81.03/80.88 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.88 => ( 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))))
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__Times,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 81.03/80.88 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] :
% 81.03/80.88 ( class_Rings_Osemiring__0(T_c)
% 81.03/80.88 => ( 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)))
% 81.03/80.88 => 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))))))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 81.03/80.88 ! [V_A_2,V_I_2,T_b,T_a] :
% 81.03/80.88 ? [B_f] :
% 81.03/80.88 ( 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))
% 81.03/80.88 & 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_image__id,axiom,
% 81.03/80.88 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ).
% 81.03/80.88
% 81.03/80.88 fof(fact_surj__id,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_List_Omap_Oidentity,axiom,
% 81.03/80.88 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_List_Omap_Oid,axiom,
% 81.03/80.88 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_folding_Oempty,axiom,
% 81.03/80.88 ! [V_F_2,V_f_2,T_b,T_a] :
% 81.03/80.88 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 81.03/80.88 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_id__o,axiom,
% 81.03/80.88 ! [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 ).
% 81.03/80.88
% 81.03/80.88 fof(fact_o__id,axiom,
% 81.03/80.88 ! [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 ).
% 81.03/80.88
% 81.03/80.88 fof(fact_o__eq__id__dest,axiom,
% 81.03/80.88 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] :
% 81.03/80.88 ( 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)
% 81.03/80.88 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Option_Omap_Oidentity,axiom,
% 81.03/80.88 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Option_Omap_Oid,axiom,
% 81.03/80.88 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_inj__on__id,axiom,
% 81.03/80.88 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_apfst__id,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_apsnd__id,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_id__apply,axiom,
% 81.03/80.88 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 81.03/80.88
% 81.03/80.88 fof(fact_id__def,axiom,
% 81.03/80.88 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 81.03/80.88
% 81.03/80.88 fof(fact_of__int__eq__id,axiom,
% 81.03/80.88 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__pair_Oidentity,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__pair_Oid,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_rotate0,axiom,
% 81.03/80.88 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_apsnd__def,axiom,
% 81.03/80.88 ! [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) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_apfst__def,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_split__Pair,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_vimage__id,axiom,
% 81.03/80.88 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ).
% 81.03/80.88
% 81.03/80.88 fof(fact_setsum__reindex__id,axiom,
% 81.03/80.88 ! [V_B_2,V_f_2,T_a,T_b] :
% 81.03/80.88 ( class_Groups_Ocomm__monoid__add(T_b)
% 81.03/80.88 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_setprod__reindex__id,axiom,
% 81.03/80.88 ! [V_B_2,V_f_2,T_a,T_b] :
% 81.03/80.88 ( class_Groups_Ocomm__monoid__mult(T_b)
% 81.03/80.88 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_setprod__Sigma,axiom,
% 81.03/80.88 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 81.03/80.88 ( class_Groups_Ocomm__monoid__mult(T_c)
% 81.03/80.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.88 => ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.88 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 81.03/80.88 => 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)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_refl__onI,axiom,
% 81.03/80.88 ! [V_A_2,V_r_2,T_a] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.88 => 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)) )
% 81.03/80.88 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_setsum__Sigma,axiom,
% 81.03/80.88 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 81.03/80.88 ( class_Groups_Ocomm__monoid__add(T_c)
% 81.03/80.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.88 => ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.88 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 81.03/80.88 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),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)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_fold__image__Sigma,axiom,
% 81.03/80.88 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 81.03/80.88 ( class_Groups_Ocomm__monoid__mult(T_c)
% 81.03/80.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.88 => ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.88 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 81.03/80.88 => 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)) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_card__SigmaI,axiom,
% 81.03/80.88 ! [V_B_2,T_b,V_A_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.88 => ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.88 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 81.03/80.88 => 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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_finite__SigmaI,axiom,
% 81.03/80.88 ! [V_B_2,T_b,V_A_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.88 => ( ! [B_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 81.03/80.88 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) )
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_DomainE,axiom,
% 81.03/80.88 ! [V_r_2,T_b,V_a_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
% 81.03/80.88 => ~ ! [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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_SigmaE,axiom,
% 81.03/80.88 ! [V_B_2,V_A_2,V_ca_2,T_b,T_a] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => ~ ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.88 => ! [B_y] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x)))
% 81.03/80.88 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_foldl__apply,axiom,
% 81.03/80.88 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] :
% 81.03/80.88 ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => 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)) )
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wfP__def,axiom,
% 81.03/80.88 ! [V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 81.03/80.88 <=> 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wfP__empty,axiom,
% 81.03/80.88 ! [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))) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wfP__accp__iff,axiom,
% 81.03/80.88 ! [V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 81.03/80.88 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_accp__wfPD,axiom,
% 81.03/80.88 ! [V_x_2,V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 81.03/80.88 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wfP__subset,axiom,
% 81.03/80.88 ! [V_p_2,V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 81.03/80.88 => ( 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))
% 81.03/80.88 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__in__rel,axiom,
% 81.03/80.88 ! [V_R_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_R_2)
% 81.03/80.88 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wfP__wf__eq,axiom,
% 81.03/80.88 ! [V_r_2,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wfP__acyclicP,axiom,
% 81.03/80.88 ! [V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Rep__Integ__cases,axiom,
% 81.03/80.88 ! [V_y_2] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 81.03/80.88 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_acyclic__subset,axiom,
% 81.03/80.88 ! [V_r_2,V_s_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Oacyclic(T_a,V_s_2)
% 81.03/80.88 => ( 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))
% 81.03/80.88 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__acyclic,axiom,
% 81.03/80.88 ! [V_r_2,T_a] :
% 81.03/80.88 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_finite__acyclic__wf,axiom,
% 81.03/80.88 ! [V_r_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 81.03/80.88 => ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 81.03/80.88 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 81.03/80.88 ! [V_r_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 81.03/80.88 => ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.88 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Nitpick_Owf_H__def,axiom,
% 81.03/80.88 ! [V_r_2,T_a] :
% 81.03/80.88 ( c_Nitpick_Owf_H(T_a,V_r_2)
% 81.03/80.88 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 81.03/80.88 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 81.03/80.88 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Rep__Integ__induct,axiom,
% 81.03/80.88 ! [V_P_2,V_y_2] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 81.03/80.88 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 81.03/80.88 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_inj__on__INTER,axiom,
% 81.03/80.88 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] :
% 81.03/80.88 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.88 => ( ! [B_i] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2))
% 81.03/80.88 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) )
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_zip__obtain__same__length,axiom,
% 81.03/80.88 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
% 81.03/80.88 ( ( 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))
% 81.03/80.88 => 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)))) )
% 81.03/80.88 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_map__of__eqI,axiom,
% 81.03/80.88 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 81.03/80.88 ( 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))
% 81.03/80.88 => ( ! [B_x] :
% 81.03/80.88 ( 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))))
% 81.03/80.88 => 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) )
% 81.03/80.88 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_the__sym__eq__trivial,axiom,
% 81.03/80.88 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 81.03/80.88
% 81.03/80.88 fof(fact_the__eq__trivial,axiom,
% 81.03/80.88 ! [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 ).
% 81.03/80.88
% 81.03/80.88 fof(fact_pigeonhole__infinite,axiom,
% 81.03/80.88 ! [V_f_2,T_b,V_A_2,T_a] :
% 81.03/80.88 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 81.03/80.88 => ? [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.88 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Abs__Integ__induct,axiom,
% 81.03/80.88 ! [V_x_2,V_P_2] :
% 81.03/80.88 ( ! [B_y] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 81.03/80.88 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 81.03/80.88 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_Abs__Integ__cases,axiom,
% 81.03/80.88 ! [V_x_2] :
% 81.03/80.88 ~ ! [B_y] :
% 81.03/80.88 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 81.03/80.88 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_finite__UN__I,axiom,
% 81.03/80.88 ! [V_B_2,T_b,V_A_2,T_a] :
% 81.03/80.88 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.88 => ( ! [B_a] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 81.03/80.88 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) )
% 81.03/80.88 => 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))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_inj__on__diff__nat,axiom,
% 81.03/80.88 ! [V_k_2,V_N_2] :
% 81.03/80.88 ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 81.03/80.88 => c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wfP__SUP,axiom,
% 81.03/80.88 ! [T_a,V_r_2,T_b] :
% 81.03/80.88 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i))
% 81.03/80.88 => ( ! [B_i,B_j] :
% 81.03/80.88 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 81.03/80.88 => 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)) )
% 81.03/80.88 => 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)) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_pos__not__random__dseq__def,axiom,
% 81.03/80.88 ! [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)) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_dropWhile__append2,axiom,
% 81.03/80.88 ! [V_ys_2,V_P_2,V_xs_2,T_a] :
% 81.03/80.88 ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => hBOOL(hAPP(V_P_2,B_x)) )
% 81.03/80.88 => 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) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_list__all2__all__nthI,axiom,
% 81.03/80.88 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] :
% 81.03/80.88 ( 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)
% 81.03/80.88 => ( ! [B_n] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => 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))) )
% 81.03/80.88 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_mem__splitI2,axiom,
% 81.03/80.88 ! [V_ca_2,V_z_2,T_c,T_b,T_a,V_p_2] :
% 81.03/80.88 ( ! [B_a,B_b] :
% 81.03/80.88 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) )
% 81.03/80.88 => 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))) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_mem__splitE,axiom,
% 81.03/80.88 ! [V_p_2,V_ca_2,T_c,T_b,V_z_2,T_a] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => ~ ! [B_x,B_y] :
% 81.03/80.88 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)
% 81.03/80.88 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_finite__sorted__distinct__unique,axiom,
% 81.03/80.88 ! [V_A_2,T_a] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_a)
% 81.03/80.88 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 81.03/80.88 => ? [B_x] :
% 81.03/80.88 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2
% 81.03/80.88 & c_List_Olinorder__class_Osorted(T_a,B_x)
% 81.03/80.88 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x))
% 81.03/80.88 & ! [B_y] :
% 81.03/80.88 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2
% 81.03/80.88 & c_List_Olinorder__class_Osorted(T_a,B_y)
% 81.03/80.88 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) )
% 81.03/80.88 => B_y = B_x ) ) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_takeWhile__append2,axiom,
% 81.03/80.88 ! [V_ys_2,V_P_2,V_xs_2,T_a] :
% 81.03/80.88 ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => hBOOL(hAPP(V_P_2,B_x)) )
% 81.03/80.88 => 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)) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_insort__is__Cons,axiom,
% 81.03/80.88 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] :
% 81.03/80.88 ( class_Orderings_Olinorder(T_b)
% 81.03/80.88 => ( ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.88 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 81.03/80.88 => 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) ) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_wfI__pf,axiom,
% 81.03/80.88 ! [V_R_2,T_a] :
% 81.03/80.88 ( ! [B_A] :
% 81.03/80.88 ( 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)))
% 81.03/80.88 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
% 81.03/80.88 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 81.03/80.88
% 81.03/80.88 fof(fact_filter__eq__Cons__iff,axiom,
% 81.03/80.88 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] :
% 81.03/80.88 ( 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)
% 81.03/80.88 <=> ? [B_us,B_vs] :
% 81.03/80.88 ( 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))
% 81.03/80.88 & ! [B_x] :
% 81.03/80.88 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us)))
% 81.03/80.89 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 81.03/80.89 & hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.89 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Cons__eq__filter__iff,axiom,
% 81.03/80.89 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 81.03/80.89 ( 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)
% 81.03/80.89 <=> ? [B_us,B_vs] :
% 81.03/80.89 ( 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))
% 81.03/80.89 & ! [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us)))
% 81.03/80.89 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 81.03/80.89 & hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.89 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Sigma__mono,axiom,
% 81.03/80.89 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 81.03/80.89 => ( ! [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.89 => 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))) )
% 81.03/80.89 => 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))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_acc_OaccI,axiom,
% 81.03/80.89 ! [V_r_2,V_x_2,T_a] :
% 81.03/80.89 ( ! [B_y] :
% 81.03/80.89 ( 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))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) )
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_not__acc__down,axiom,
% 81.03/80.89 ! [V_R_2,V_x_2,T_a] :
% 81.03/80.89 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2)))
% 81.03/80.89 => ~ ! [B_z] :
% 81.03/80.89 ( 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))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__ball__nth,axiom,
% 81.03/80.89 ! [V_P_2,V_xs_2,T_a,V_n_2] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))
% 81.03/80.89 => ( ! [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.89 => hBOOL(hAPP(V_P_2,B_x)) )
% 81.03/80.89 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_max__ext_Osimps,axiom,
% 81.03/80.89 ! [V_R_2,V_a2_2,V_a1_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_a,V_R_2)))
% 81.03/80.89 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2))
% 81.03/80.89 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
% 81.03/80.89 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 81.03/80.89 & ! [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2))
% 81.03/80.89 => ? [B_xa] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2))
% 81.03/80.89 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2)) ) ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_sorted_OCons,axiom,
% 81.03/80.89 ! [V_x_2,V_xs_2,T_a] :
% 81.03/80.89 ( class_Orderings_Olinorder(T_a)
% 81.03/80.89 => ( ! [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) )
% 81.03/80.89 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 81.03/80.89 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_wf__no__infinite__down__chainE,axiom,
% 81.03/80.89 ! [V_f_2,V_r_2,T_a] :
% 81.03/80.89 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.89 => ~ ! [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)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__ex__length,axiom,
% 81.03/80.89 ! [V_xs_2,V_P_2,T_a] :
% 81.03/80.89 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 81.03/80.89 <=> ? [B_n] :
% 81.03/80.89 ( 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)))
% 81.03/80.89 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_setsum__reindex__cong,axiom,
% 81.03/80.89 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 81.03/80.89 ( class_Groups_Ocomm__monoid__add(T_c)
% 81.03/80.89 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 81.03/80.89 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 81.03/80.89 => ( ! [B_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 81.03/80.89 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 81.03/80.89 => 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) ) ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__ex__simps_I2_J,axiom,
% 81.03/80.89 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__ex__append,axiom,
% 81.03/80.89 ! [V_ys_2,V_xs_2,V_P_2,T_a] :
% 81.03/80.89 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 81.03/80.89 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 81.03/80.89 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__ex__rev,axiom,
% 81.03/80.89 ! [V_xs_2,V_P_2,T_a] :
% 81.03/80.89 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2))
% 81.03/80.89 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__ex__iff,axiom,
% 81.03/80.89 ! [V_xs_2,V_P_2,T_a] :
% 81.03/80.89 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 81.03/80.89 <=> ? [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.89 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__ex__simps_I1_J,axiom,
% 81.03/80.89 ! [V_xs_2,V_x_2,V_P_2,T_a] :
% 81.03/80.89 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 81.03/80.89 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.89 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_less__eq,axiom,
% 81.03/80.89 ! [V_n_2,V_m_2] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
% 81.03/80.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_in__set__conv__decomp,axiom,
% 81.03/80.89 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.89 <=> ? [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)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_acyclic__def,axiom,
% 81.03/80.89 ! [V_r_2,T_a] :
% 81.03/80.89 ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 81.03/80.89 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_wf__trancl,axiom,
% 81.03/80.89 ! [V_r_2,T_a] :
% 81.03/80.89 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.89 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_less__than__def,axiom,
% 81.03/80.89 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl_Or__into__trancl,axiom,
% 81.03/80.89 ! [V_r_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__subset__Field2,axiom,
% 81.03/80.89 ! [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))))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_r__into__trancl_H,axiom,
% 81.03/80.89 ! [V_r_2,V_p_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__empty,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__domain,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__range,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_finite__trancl,axiom,
% 81.03/80.89 ! [V_r_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 81.03/80.89 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__trans,axiom,
% 81.03/80.89 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 81.03/80.89 => ( 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)))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 81.03/80.89 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 81.03/80.89 => ( 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))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__into__trancl2,axiom,
% 81.03/80.89 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 81.03/80.89 => ( 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)))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_r__r__into__trancl,axiom,
% 81.03/80.89 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_R_2))
% 81.03/80.89 => ( 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))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__mono,axiom,
% 81.03/80.89 ! [V_s_2,V_r_2,V_p_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__unfold,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__subset__Sigma,axiom,
% 81.03/80.89 ! [V_A_2,V_r_2,T_a] :
% 81.03/80.89 ( 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))))
% 81.03/80.89 => 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)))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__Int__subset,axiom,
% 81.03/80.89 ! [V_s_2,V_r_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 81.03/80.89 => ( 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))
% 81.03/80.89 => 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)) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__insert,axiom,
% 81.03/80.89 ! [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)))))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_reflcl__set__eq,axiom,
% 81.03/80.89 ! [V_y_2,V_x_2,V_r_2,T_a] :
% 81.03/80.89 ( 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))
% 81.03/80.89 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a)))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_r__into__rtrancl,axiom,
% 81.03/80.89 ! [V_r_2,V_p_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 81.03/80.89 ! [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))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_IdI,axiom,
% 81.03/80.89 ! [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))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__into__rtrancl,axiom,
% 81.03/80.89 ! [V_r_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_listrel__rtrancl__refl,axiom,
% 81.03/80.89 ! [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)))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__eq__or__trancl,axiom,
% 81.03/80.89 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 81.03/80.89 <=> ( V_x_2 = V_y_2
% 81.03/80.89 | ( V_x_2 != V_y_2
% 81.03/80.89 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__into__trancl2,axiom,
% 81.03/80.89 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 81.03/80.89 => ( 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)))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtranclD,axiom,
% 81.03/80.89 ! [V_R_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 81.03/80.89 => ( V_a_2 = V_b_2
% 81.03/80.89 | ( V_a_2 != V_b_2
% 81.03/80.89 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__into__trancl1,axiom,
% 81.03/80.89 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 81.03/80.89 => ( 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))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__rtrancl__trancl,axiom,
% 81.03/80.89 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 81.03/80.89 => ( 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)))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__trancl__trancl,axiom,
% 81.03/80.89 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__rtrancl__absorb,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__trancl__absorb,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__reflcl,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_reflcl__trancl,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__unfold__right,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__unfold__left,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Range__rtrancl,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__unfold,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_r__comp__rtrancl__eq,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__idemp__self__comp,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__Int__subset,axiom,
% 81.03/80.89 ! [V_r_2,V_s_2,T_a] :
% 81.03/80.89 ( 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))
% 81.03/80.89 => ( 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))
% 81.03/80.89 => 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)) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_in__rtrancl__UnI,axiom,
% 81.03/80.89 ! [V_S_2,V_R_2,V_x_2,T_a] :
% 81.03/80.89 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 81.03/80.89 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) )
% 81.03/80.89 => 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)))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__reflcl__absorb,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__Un__rtrancl,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__reflcl,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__empty,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__mono,axiom,
% 81.03/80.89 ! [V_s_2,V_r_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2))
% 81.03/80.89 => 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))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__subset,axiom,
% 81.03/80.89 ! [V_S_2,V_R_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2))
% 81.03/80.89 => ( 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)))
% 81.03/80.89 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__subset__rtrancl,axiom,
% 81.03/80.89 ! [V_s_2,V_r_2,T_a] :
% 81.03/80.89 ( 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)))
% 81.03/80.89 => 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))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__Un__subset,axiom,
% 81.03/80.89 ! [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)))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Image__closed__trancl,axiom,
% 81.03/80.89 ! [V_X_2,V_r_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),V_X_2)),V_X_2))
% 81.03/80.89 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_refl__rtrancl,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__idemp,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__trans,axiom,
% 81.03/80.89 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 81.03/80.89 => ( 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)))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 81.03/80.89 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 81.03/80.89 => ( 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))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 81.03/80.89 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2))
% 81.03/80.89 => ( 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)))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__r__diff__Id,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Domain__rtrancl,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_listrel__rtrancl__trans,axiom,
% 81.03/80.89 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.89 ( 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))))
% 81.03/80.89 => ( 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))))
% 81.03/80.89 => 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)))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Domain__Id,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 81.03/80.89 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 81.03/80.89 => ( 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))))
% 81.03/80.89 => 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)))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_refl__Id,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_pair__in__Id__conv,axiom,
% 81.03/80.89 ! [V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId(T_a)))
% 81.03/80.89 <=> V_a_2 = V_b_2 ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Image__Id,axiom,
% 81.03/80.89 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ).
% 81.03/80.89
% 81.03/80.89 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 81.03/80.89 ! [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)))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Id__O__R,axiom,
% 81.03/80.89 ! [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 ).
% 81.03/80.89
% 81.03/80.89 fof(fact_R__O__Id,axiom,
% 81.03/80.89 ! [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 ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Range__Id,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 81.03/80.89 ! [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)))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_pair__leq__def,axiom,
% 81.03/80.89 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))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Not__Domain__rtrancl,axiom,
% 81.03/80.89 ! [V_y_2,V_R_2,V_x_2,T_a] :
% 81.03/80.89 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2)))
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 81.03/80.89 <=> V_x_2 = V_y_2 ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_acc__downwards,axiom,
% 81.03/80.89 ! [V_b_2,V_r_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 81.03/80.89 => ( 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)))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_acc__downwards__aux,axiom,
% 81.03/80.89 ! [V_r_2,V_a_2,V_b_2,T_a] :
% 81.03/80.89 ( 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)))
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_wf__insert,axiom,
% 81.03/80.89 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 81.03/80.89 ( 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))
% 81.03/80.89 <=> ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.89 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 81.03/80.89 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.89 ( 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))))
% 81.03/80.89 => 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)))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 81.03/80.89 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 81.03/80.89 ( 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))))
% 81.03/80.89 => 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) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_acyclic__insert,axiom,
% 81.03/80.89 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 81.03/80.89 ( 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))
% 81.03/80.89 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 81.03/80.89 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 81.03/80.89 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.89 ( 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)))
% 81.03/80.89 => 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)))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 81.03/80.89 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 81.03/80.89 ( 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)))
% 81.03/80.89 => 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)))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_refl__reflcl,axiom,
% 81.03/80.89 ! [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))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Id__def,axiom,
% 81.03/80.89 ! [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))))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_irrefl__diff__Id,axiom,
% 81.03/80.89 ! [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))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_pred__nat__trancl__eq__le,axiom,
% 81.03/80.89 ! [V_n_2,V_m_2] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
% 81.03/80.89 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__subset__Sigma__aux,axiom,
% 81.03/80.89 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 81.03/80.89 => ( 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))))
% 81.03/80.89 => ( V_a_2 = V_b_2
% 81.03/80.89 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_irrefl__tranclI,axiom,
% 81.03/80.89 ! [V_x_2,V_r_2,T_a] :
% 81.03/80.89 ( 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))
% 81.03/80.89 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_sequence__trans,axiom,
% 81.03/80.89 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] :
% 81.03/80.89 ( ! [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)))
% 81.03/80.89 => 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))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__converse,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__converseD,axiom,
% 81.03/80.89 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__converseI,axiom,
% 81.03/80.89 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converse__Id,axiom,
% 81.03/80.89 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_equiv__comp__eq,axiom,
% 81.03/80.89 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.89 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 81.03/80.89 => 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 ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converse__rel__comp,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converse__inv__image,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converse__Un,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_refl__on__converse,axiom,
% 81.03/80.89 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.89 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 81.03/80.89 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_in__listrel1__converse,axiom,
% 81.03/80.89 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 81.03/80.89 ( 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))))
% 81.03/80.89 <=> 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)))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converse__INTER,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_listrel1__converse,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_finite__converse,axiom,
% 81.03/80.89 ! [V_r_2,T_b,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
% 81.03/80.89 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Field__converse,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converse__converse,axiom,
% 81.03/80.89 ! [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 ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converse__Id__on,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converse__iff,axiom,
% 81.03/80.89 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
% 81.03/80.89 <=> 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)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converseI,axiom,
% 81.03/80.89 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2))
% 81.03/80.89 => 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))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converseD,axiom,
% 81.03/80.89 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
% 81.03/80.89 => 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)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converse__Int,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Range__def,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Domain__converse,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Range__converse,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converse__UNION,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_acyclic__converse,axiom,
% 81.03/80.89 ! [V_r_2,T_a] :
% 81.03/80.89 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 81.03/80.89 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__converse,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__converseD,axiom,
% 81.03/80.89 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__converseI,axiom,
% 81.03/80.89 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_wf__converse__trancl,axiom,
% 81.03/80.89 ! [V_r_2,T_a] :
% 81.03/80.89 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 81.03/80.89 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Image__subset__eq,axiom,
% 81.03/80.89 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 81.03/80.89 ( 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))
% 81.03/80.89 <=> 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))))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_refl__on__comp__subset,axiom,
% 81.03/80.89 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.89 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 81.03/80.89 => 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))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_comp__equivI,axiom,
% 81.03/80.89 ! [V_A_2,V_r_2,T_a] :
% 81.03/80.89 ( 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
% 81.03/80.89 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2
% 81.03/80.89 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_finite__acyclic__wf__converse,axiom,
% 81.03/80.89 ! [V_r_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 81.03/80.89 => ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 81.03/80.89 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converse__def,axiom,
% 81.03/80.89 ! [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))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Image__INT__eq,axiom,
% 81.03/80.89 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] :
% 81.03/80.89 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))
% 81.03/80.89 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 81.03/80.89 => 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)) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_total__on__diff__Id,axiom,
% 81.03/80.89 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.89 ( 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)))
% 81.03/80.89 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_single__valued__Id,axiom,
% 81.03/80.89 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_total__on__converse,axiom,
% 81.03/80.89 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.89 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 81.03/80.89 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_single__valued__Id__on,axiom,
% 81.03/80.89 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_total__on__empty,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_single__valued__subset,axiom,
% 81.03/80.89 ! [V_s_2,V_r_2,T_b,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 81.03/80.89 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2)
% 81.03/80.89 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_single__valued__rel__comp,axiom,
% 81.03/80.89 ! [V_s_2,T_c,V_r_2,T_b,T_a] :
% 81.03/80.89 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 81.03/80.89 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 81.03/80.89 => 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)) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_single__valued__def,axiom,
% 81.03/80.89 ! [V_r_2,T_b,T_a] :
% 81.03/80.89 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 81.03/80.89 <=> ! [B_x,B_y] :
% 81.03/80.89 ( 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))
% 81.03/80.89 => ! [B_z] :
% 81.03/80.89 ( 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))
% 81.03/80.89 => B_y = B_z ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_single__valuedD,axiom,
% 81.03/80.89 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] :
% 81.03/80.89 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_r_2))
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_z_2)),V_r_2))
% 81.03/80.89 => V_y_2 = V_z_2 ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_total__on__def,axiom,
% 81.03/80.89 ! [V_r_2,V_A_2,T_a] :
% 81.03/80.89 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2)
% 81.03/80.89 <=> ! [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.89 => ! [B_xa] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 81.03/80.89 => ( B_x != B_xa
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_r_2))
% 81.03/80.89 | 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)) ) ) ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_single__valued__confluent,axiom,
% 81.03/80.89 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
% 81.03/80.89 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2)
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 81.03/80.89 | 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))) ) ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Image__Int__eq,axiom,
% 81.03/80.89 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] :
% 81.03/80.89 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2))
% 81.03/80.89 => 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)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 81.03/80.89 ! [V_R_2,V_p_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 81.03/80.89 => 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)))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_acyclicI,axiom,
% 81.03/80.89 ! [V_r_2,T_a] :
% 81.03/80.89 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 81.03/80.89 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_single__valued__rel__pow,axiom,
% 81.03/80.89 ! [V_n_2,V_R_2,T_a] :
% 81.03/80.89 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2)
% 81.03/80.89 => 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)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rel__pow__0__I,axiom,
% 81.03/80.89 ! [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))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rel__pow__0__E,axiom,
% 81.03/80.89 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2)))
% 81.03/80.89 => V_x_2 = V_y_2 ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rel__pow__Suc__I2,axiom,
% 81.03/80.89 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2))
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_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))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rel__pow__Suc__I,axiom,
% 81.03/80.89 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_R_2))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_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))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_funpow__swap1,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_funpow__mult,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_wf__exp,axiom,
% 81.03/80.89 ! [V_R_2,V_n_2,T_a] :
% 81.03/80.89 ( 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))
% 81.03/80.89 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_comp__funpow,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rel__pow__1,axiom,
% 81.03/80.89 ! [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 ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rel__pow__add,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_relpow_Osimps_I2_J,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rel__pow__commute,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_funpow__add,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_funpow_Osimps_I2_J,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__power,axiom,
% 81.03/80.89 ! [V_R_2,V_p_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 81.03/80.89 <=> ? [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))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rel__pow__imp__rtrancl,axiom,
% 81.03/80.89 ! [V_R_2,V_n_2,V_p_2,T_a] :
% 81.03/80.89 ( 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)))
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_relpow_Osimps_I1_J,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_funpow_Osimps_I1_J,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_trancl__power,axiom,
% 81.03/80.89 ! [V_R_2,V_p_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
% 81.03/80.89 <=> ? [B_n] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 81.03/80.89 & 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))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_funpow__code__def,axiom,
% 81.03/80.89 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rel__pow__E,axiom,
% 81.03/80.89 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 81.03/80.89 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.89 => V_x_2 != V_z_2 )
% 81.03/80.89 => ~ ! [B_y,B_m] :
% 81.03/80.89 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2)))
% 81.03/80.89 => ~ 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)) ) ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rotate__def,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rel__pow__E2,axiom,
% 81.03/80.89 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 81.03/80.89 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 81.03/80.89 => V_x_2 != V_z_2 )
% 81.03/80.89 => ~ ! [B_y,B_m] :
% 81.03/80.89 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2))
% 81.03/80.89 => ~ 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))) ) ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 81.03/80.89 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_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))))
% 81.03/80.89 => ( ! [B_x] :
% 81.03/80.89 ( 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)))
% 81.03/80.89 => ! [B_y] :
% 81.03/80.89 ( 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))
% 81.03/80.89 => B_y = B_x ) )
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rtrancl__Un__separatorE,axiom,
% 81.03/80.89 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_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))))
% 81.03/80.89 => ( ! [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_a,V_P_2)))
% 81.03/80.89 => ! [B_y] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_Q_2))
% 81.03/80.89 => B_x = B_y ) )
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rel__pow__Suc__D2,axiom,
% 81.03/80.89 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_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)))
% 81.03/80.89 => ? [B_y] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2))
% 81.03/80.89 & 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))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rel__pow__Suc__E,axiom,
% 81.03/80.89 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_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)))
% 81.03/80.89 => ~ ! [B_y] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)))
% 81.03/80.89 => ~ 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)) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rel__pow__Suc__E2,axiom,
% 81.03/80.89 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_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)))
% 81.03/80.89 => ~ ! [B_y] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2))
% 81.03/80.89 => ~ 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))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_tranclD2,axiom,
% 81.03/80.89 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
% 81.03/80.89 => ? [B_z] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 81.03/80.89 & 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)) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_tranclD,axiom,
% 81.03/80.89 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
% 81.03/80.89 => ? [B_z] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),V_R_2))
% 81.03/80.89 & 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))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_IdE,axiom,
% 81.03/80.89 ! [V_p_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a)))
% 81.03/80.89 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_in__set__conv__decomp__first,axiom,
% 81.03/80.89 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.89 <=> ? [B_ys] :
% 81.03/80.89 ( ? [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))
% 81.03/80.89 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_in__set__conv__decomp__last,axiom,
% 81.03/80.89 ! [V_xs_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.89 <=> ? [B_ys,B_zs] :
% 81.03/80.89 ( 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))
% 81.03/80.89 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_wf__eq__minimal,axiom,
% 81.03/80.89 ! [V_r_2,T_a] :
% 81.03/80.89 ( c_Wellfounded_Owf(T_a,V_r_2)
% 81.03/80.89 <=> ! [B_Q] :
% 81.03/80.89 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q))
% 81.03/80.89 => ? [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q))
% 81.03/80.89 & ! [B_y] :
% 81.03/80.89 ( 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))
% 81.03/80.89 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) ) ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_transfer__nat__int__set__cong,axiom,
% 81.03/80.89 ! [V_P_H_2,V_P_2] :
% 81.03/80.89 ( ! [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 81.03/80.89 => ( hBOOL(hAPP(V_P_2,B_x))
% 81.03/80.89 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 81.03/80.89 => 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)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Int__Collect__mono,axiom,
% 81.03/80.89 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 81.03/80.89 => ( ! [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 81.03/80.89 => ( hBOOL(hAPP(V_P_2,B_x))
% 81.03/80.89 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 81.03/80.89 => 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)))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converseE,axiom,
% 81.03/80.89 ! [V_r_2,V_yx_2,T_b,T_a] :
% 81.03/80.89 ( 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)))
% 81.03/80.89 => ~ ! [B_x,B_y] :
% 81.03/80.89 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x)
% 81.03/80.89 => ~ 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)) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_rel__compE,axiom,
% 81.03/80.89 ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] :
% 81.03/80.89 ( 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)))
% 81.03/80.89 => ~ ! [B_x,B_y,B_z] :
% 81.03/80.89 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)
% 81.03/80.89 => ( 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))
% 81.03/80.89 => ~ 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)) ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 81.03/80.89 ! [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))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__all__length,axiom,
% 81.03/80.89 ! [V_xs_2,V_P_2,T_a] :
% 81.03/80.89 ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 81.03/80.89 <=> ! [B_n] :
% 81.03/80.89 ( 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)))
% 81.03/80.89 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__all__simps_I2_J,axiom,
% 81.03/80.89 ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__all__append,axiom,
% 81.03/80.89 ! [V_ys_2,V_xs_2,V_P_2,T_a] :
% 81.03/80.89 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 81.03/80.89 <=> ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 81.03/80.89 & c_List_Olist__all(T_a,V_P_2,V_ys_2) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__all__rev,axiom,
% 81.03/80.89 ! [V_xs_2,V_P_2,T_a] :
% 81.03/80.89 ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2))
% 81.03/80.89 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__all__iff,axiom,
% 81.03/80.89 ! [V_xs_2,V_P_2,T_a] :
% 81.03/80.89 ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 81.03/80.89 <=> ! [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.89 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__all__simps_I1_J,axiom,
% 81.03/80.89 ! [V_xs_2,V_x_2,V_P_2,T_a] :
% 81.03/80.89 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 81.03/80.89 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.89 & c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Ball__set__list__all,axiom,
% 81.03/80.89 ! [V_P_2,V_xs_2,T_a] :
% 81.03/80.89 ( ! [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.89 => hBOOL(hAPP(V_P_2,B_x)) )
% 81.03/80.89 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__all__iff__raw,axiom,
% 81.03/80.89 ! [V_xs_2,V_P_2,T_a] :
% 81.03/80.89 ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 81.03/80.89 <=> ! [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.89 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 81.03/80.89 ! [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))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Nitpick_Oof__frac__def,axiom,
% 81.03/80.89 ! [V_q,T_a,T_b] :
% 81.03/80.89 ( ( class_Rings_Oinverse(T_b)
% 81.03/80.89 & class_Rings_Oring__1(T_b) )
% 81.03/80.89 => 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))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 81.03/80.89 ! [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))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Nitpick_Oless__frac__def,axiom,
% 81.03/80.89 ! [V_r_2,V_q_2,T_a] :
% 81.03/80.89 ( c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2)
% 81.03/80.89 <=> 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))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 81.03/80.89 ! [V_r_2,V_q_2,T_a] :
% 81.03/80.89 ( c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2)
% 81.03/80.89 <=> 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))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Nitpick_Odenom__def,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_Nitpick_Onum__def,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__ex1__simps_I2_J,axiom,
% 81.03/80.89 ! [V_xs_2,V_x_2,V_P_2,T_a] :
% 81.03/80.89 ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 81.03/80.89 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.89 => 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) )
% 81.03/80.89 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 81.03/80.89 => c_List_Olist__ex1(T_a,V_P_2,V_xs_2) ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_internal__split__def,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_exists1__code,axiom,
% 81.03/80.89 ! [V_P_2,T_a] :
% 81.03/80.89 ( class_Enum_Oenum(T_a)
% 81.03/80.89 => ( ? [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(V_P_2,B_x))
% 81.03/80.89 & ! [B_y] :
% 81.03/80.89 ( hBOOL(hAPP(V_P_2,B_y))
% 81.03/80.89 => B_y = B_x ) )
% 81.03/80.89 <=> c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a)) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__ex1__simps_I1_J,axiom,
% 81.03/80.89 ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_internal__split__conv,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_list__ex1__iff,axiom,
% 81.03/80.89 ! [V_xs_2,V_P_2,T_a] :
% 81.03/80.89 ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2)
% 81.03/80.89 <=> ? [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.89 & hBOOL(hAPP(V_P_2,B_x))
% 81.03/80.89 & ! [B_y] :
% 81.03/80.89 ( ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2)))
% 81.03/80.89 & hBOOL(hAPP(V_P_2,B_y)) )
% 81.03/80.89 => B_y = B_x ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_finite__less__ub,axiom,
% 81.03/80.89 ! [V_u_2,V_f_2] :
% 81.03/80.89 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 81.03/80.89 => 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)))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_measure__function__int,axiom,
% 81.03/80.89 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))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_measure__size,axiom,
% 81.03/80.89 ! [T_a] :
% 81.03/80.89 ( class_Nat_Osize(T_a)
% 81.03/80.89 => c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_is__measure_Osimps,axiom,
% 81.03/80.89 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_is__measure_Oequations,axiom,
% 81.03/80.89 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_is__measure_Ointros,axiom,
% 81.03/80.89 ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_measure__fst,axiom,
% 81.03/80.89 ! [T_b,V_f_2,T_a] :
% 81.03/80.89 ( c_FunDef_Ois__measure(T_a,V_f_2)
% 81.03/80.89 => 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))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_measure__snd,axiom,
% 81.03/80.89 ! [T_b,V_f_2,T_a] :
% 81.03/80.89 ( c_FunDef_Ois__measure(T_a,V_f_2)
% 81.03/80.89 => 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))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_equal__fun__def,axiom,
% 81.03/80.89 ! [V_g_2,V_f_2,T_a,T_b] :
% 81.03/80.89 ( ( class_HOL_Oequal(T_b)
% 81.03/80.89 & class_Enum_Oenum(T_a) )
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 81.03/80.89 <=> ! [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a))))
% 81.03/80.89 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_transfer__morphism__int__nat,axiom,
% 81.03/80.89 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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_equal,axiom,
% 81.03/80.89 ! [T_a] :
% 81.03/80.89 ( class_HOL_Oequal(T_a)
% 81.03/80.89 => c_HOL_Oequal__class_Oequal(T_a) = c_fequal ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_equal__refl,axiom,
% 81.03/80.89 ! [V_x,T_a] :
% 81.03/80.89 ( class_HOL_Oequal(T_a)
% 81.03/80.89 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_equal__eq,axiom,
% 81.03/80.89 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.89 ( class_HOL_Oequal(T_a)
% 81.03/80.89 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2))
% 81.03/80.89 <=> V_x_2 = V_y_2 ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__equal,axiom,
% 81.03/80.89 ! [T_a] :
% 81.03/80.89 ( class_HOL_Oequal(T_a)
% 81.03/80.89 => c_fequal = c_HOL_Oequal__class_Oequal(T_a) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_bool_Osize_I4_J,axiom,
% 81.03/80.89 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_bool_Osize_I3_J,axiom,
% 81.03/80.89 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_size__code,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 81.03/80.89 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] :
% 81.03/80.89 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 81.03/80.89 => 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) )
% 81.03/80.89 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 81.03/80.89 => 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)) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_equal__int__def,axiom,
% 81.03/80.89 ! [V_l_2,V_k_2] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2))
% 81.03/80.89 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I4_J,axiom,
% 81.03/80.89 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I10_J,axiom,
% 81.03/80.89 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I6_J,axiom,
% 81.03/80.89 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I16_J,axiom,
% 81.03/80.89 ! [V_k2_2,V_k1_2] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 81.03/80.89 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I1_J,axiom,
% 81.03/80.89 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I13_J,axiom,
% 81.03/80.89 ! [V_k2_2,V_k1_2] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 81.03/80.89 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__number__of__int__code,axiom,
% 81.03/80.89 ! [V_l_2,V_k_2] :
% 81.03/80.89 ( 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)))
% 81.03/80.89 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I14_J,axiom,
% 81.03/80.89 ! [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))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I15_J,axiom,
% 81.03/80.89 ! [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))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I3_J,axiom,
% 81.03/80.89 ! [V_k2_2] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2)))
% 81.03/80.89 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I9_J,axiom,
% 81.03/80.89 ! [V_k1_2] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls))
% 81.03/80.89 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I7_J,axiom,
% 81.03/80.89 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I11_J,axiom,
% 81.03/80.89 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I8_J,axiom,
% 81.03/80.89 ! [V_k2_2] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2)))
% 81.03/80.89 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I12_J,axiom,
% 81.03/80.89 ! [V_k1_2] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin))
% 81.03/80.89 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I5_J,axiom,
% 81.03/80.89 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__code_I2_J,axiom,
% 81.03/80.89 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_lazy__sequence__size__code,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_eq__int__refl,axiom,
% 81.03/80.89 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_seq__case,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_yieldn__def,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 81.03/80.89 ! [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))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact__01,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_lazy__sequence_Oinject,axiom,
% 81.03/80.89 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_a] :
% 81.03/80.89 ( 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)
% 81.03/80.89 <=> ( V_a_2 = V_a_H_2
% 81.03/80.89 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 81.03/80.89 ! [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))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_neg__bind__def,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 81.03/80.89 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] :
% 81.03/80.89 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 81.03/80.89 => 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) )
% 81.03/80.89 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 81.03/80.89 => 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)) ) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 81.03/80.89 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_pos__empty__def,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_pos__bind__def,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_neg__map__def,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_neg__single__def,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_pos__map__def,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_pos__single__def,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_New__DSequence_Opos__single__def,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_length__splice,axiom,
% 81.03/80.89 ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(T_a,V_xs,V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_splice__Nil2,axiom,
% 81.03/80.89 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 81.03/80.89
% 81.03/80.89 fof(fact_splice_Osimps_I1_J,axiom,
% 81.03/80.89 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 81.03/80.89
% 81.03/80.89 fof(fact_splice_Osimps_I3_J,axiom,
% 81.03/80.89 ! [V_ys,V_y,V_xs,V_x,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_splice_Osimps_I2_J,axiom,
% 81.03/80.89 ! [V_va,V_v,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va) ).
% 81.03/80.89
% 81.03/80.89 fof(fact__02,axiom,
% 81.03/80.89 ! [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)))) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_acyclicP__converse,axiom,
% 81.03/80.89 ! [V_r_2,T_a] :
% 81.03/80.89 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Predicate_Oconversep(T_a,T_a,V_r_2))))
% 81.03/80.89 <=> 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))) ) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converse__join,axiom,
% 81.03/80.89 ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_converse__meet,axiom,
% 81.03/80.89 ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)) ).
% 81.03/80.89
% 81.03/80.89 fof(fact_conversep__noteq,axiom,
% 81.03/80.89 ! [V_y_2,V_x_2,T_a] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot)),c_fequal)),V_x_2),V_y_2))
% 81.03/80.89 <=> V_x_2 != V_y_2 ) ).
% 81.03/80.89
% 81.03/80.89 %----Arity declarations (233)
% 81.03/80.89 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 81.03/80.89 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Lattices_Obounded__lattice(T_1)
% 81.03/80.89 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 81.03/80.89 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Lattices_Obounded__lattice(T_1)
% 81.03/80.89 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Lattices_Obounded__lattice(T_1)
% 81.03/80.89 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Lattices_Olattice(T_1)
% 81.03/80.89 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Lattices_Olattice(T_1)
% 81.03/80.89 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Lattices_Odistrib__lattice(T_1)
% 81.03/80.89 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Lattices_Oboolean__algebra(T_1)
% 81.03/80.89 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Orderings_Opreorder,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Orderings_Opreorder(T_1)
% 81.03/80.89 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 81.03/80.89 ! [T_1,T_2] :
% 81.03/80.89 ( ( class_Finite__Set_Ofinite(T_2)
% 81.03/80.89 & class_Finite__Set_Ofinite(T_1) )
% 81.03/80.89 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Lattices_Olattice,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Lattices_Olattice(T_1)
% 81.03/80.89 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Orderings_Oorder,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Orderings_Oorder(T_1)
% 81.03/80.89 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Orderings_Otop,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Orderings_Otop(T_1)
% 81.03/80.89 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Orderings_Oord,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Orderings_Oord(T_1)
% 81.03/80.89 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Orderings_Obot,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Orderings_Obot(T_1)
% 81.03/80.89 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Groups_Ouminus,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Groups_Ouminus(T_1)
% 81.03/80.89 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Groups_Ominus,axiom,
% 81.03/80.89 ! [T_2,T_1] :
% 81.03/80.89 ( class_Groups_Ominus(T_1)
% 81.03/80.89 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__HOL_Oequal,axiom,
% 81.03/80.89 ! [T_1,T_2] :
% 81.03/80.89 ( ( class_Enum_Oenum(T_2)
% 81.03/80.89 & class_HOL_Oequal(T_1) )
% 81.03/80.89 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_fun__Enum_Oenum,axiom,
% 81.03/80.89 ! [T_1,T_2] :
% 81.03/80.89 ( ( class_Enum_Oenum(T_2)
% 81.03/80.89 & class_Enum_Oenum(T_1) )
% 81.03/80.89 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Com__Ocom__HOL_Oequal,axiom,
% 81.03/80.89 class_HOL_Oequal(tc_Com_Ocom) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Com__Ocom__Nat_Osize,axiom,
% 81.03/80.89 class_Nat_Osize(tc_Com_Ocom) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 81.03/80.89 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 81.03/80.89 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 81.03/80.89 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 81.03/80.89 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 81.03/80.89 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 81.03/80.89 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 81.03/80.89 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 81.03/80.89 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 81.03/80.89 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 81.03/80.89 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 81.03/80.89 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 81.03/80.89 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 81.03/80.89 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 81.03/80.89 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 81.03/80.89 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 81.03/80.89 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 81.03/80.89 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 81.03/80.89 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 81.03/80.89 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 81.03/80.89 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 81.03/80.89 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 81.03/80.89 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 81.03/80.89 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 81.03/80.89 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 81.03/80.89 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 81.03/80.89 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 81.03/80.89 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 81.03/80.89 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 81.03/80.89 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 81.03/80.89 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 81.03/80.89 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 81.03/80.89 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 81.03/80.89 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 81.03/80.89 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 81.03/80.89 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 81.03/80.89 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 81.03/80.89 class_Orderings_Opreorder(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 81.03/80.89 class_Orderings_Olinorder(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 81.03/80.89 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 81.03/80.89 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 81.03/80.89 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
% 81.03/80.89 class_Smallcheck_Osmall(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 81.03/80.89 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 81.03/80.89 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 81.03/80.89 class_Lattices_Olattice(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 81.03/80.89 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 81.03/80.89 class_Divides_Oring__div(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 81.03/80.89 class_Rings_Omult__zero(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 81.03/80.89 class_Orderings_Oorder(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 81.03/80.89 class_Int_Oring__char__0(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 81.03/80.89 class_Int_Onumber__ring(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 81.03/80.89 class_Rings_Osemiring(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 81.03/80.89 class_Orderings_Oord(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 81.03/80.89 class_Groups_Ouminus(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 81.03/80.89 class_Groups_Osgn__if(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 81.03/80.89 class_Groups_Oabs__if(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 81.03/80.89 class_Rings_Oring__1(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 81.03/80.89 class_Groups_Ominus(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Power_Opower,axiom,
% 81.03/80.89 class_Power_Opower(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 81.03/80.89 class_Groups_Ozero(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Oring,axiom,
% 81.03/80.89 class_Rings_Oring(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 81.03/80.89 class_Rings_Oidom(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Int_Onumber,axiom,
% 81.03/80.89 class_Int_Onumber(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__Groups_Oone,axiom,
% 81.03/80.89 class_Groups_Oone(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Int__Oint__HOL_Oequal,axiom,
% 81.03/80.89 class_HOL_Oequal(tc_Int_Oint) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 81.03/80.89 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 81.03/80.89 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 81.03/80.89 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 81.03/80.89 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 81.03/80.89 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 81.03/80.89 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 81.03/80.89 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 81.03/80.89 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 81.03/80.89 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 81.03/80.89 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 81.03/80.89 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 81.03/80.89 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 81.03/80.89 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 81.03/80.89 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 81.03/80.89 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 81.03/80.89 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 81.03/80.89 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 81.03/80.89 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 81.03/80.89 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 81.03/80.89 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 81.03/80.89 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 81.03/80.89 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 81.03/80.89 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 81.03/80.89 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 81.03/80.89 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 81.03/80.89 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 81.03/80.89 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 81.03/80.89 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 81.03/80.89 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 81.03/80.89 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 81.03/80.89 class_Lattices_Olattice(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 81.03/80.89 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 81.03/80.89 class_Orderings_Oorder(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 81.03/80.89 class_Rings_Osemiring(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 81.03/80.89 class_Orderings_Oord(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 81.03/80.89 class_Orderings_Obot(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 81.03/80.89 class_Groups_Ominus(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Power_Opower,axiom,
% 81.03/80.89 class_Power_Opower(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 81.03/80.89 class_Groups_Ozero(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 81.03/80.89 class_Int_Onumber(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 81.03/80.89 class_Groups_Oone(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__HOL_Oequal,axiom,
% 81.03/80.89 class_HOL_Oequal(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 81.03/80.89 class_Nat_Osize(tc_Nat_Onat) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 81.03/80.89 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 81.03/80.89 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 81.03/80.89 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 81.03/80.89 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 81.03/80.89 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 81.03/80.89 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 81.03/80.89 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 81.03/80.89 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 81.03/80.89 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 81.03/80.89 class_Lattices_Olattice(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 81.03/80.89 class_Orderings_Oorder(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 81.03/80.89 class_Orderings_Otop(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 81.03/80.89 class_Orderings_Oord(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 81.03/80.89 class_Orderings_Obot(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 81.03/80.89 class_Groups_Ouminus(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 81.03/80.89 class_Groups_Ominus(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__HOL_Oequal,axiom,
% 81.03/80.89 class_HOL_Oequal(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 81.03/80.89 class_Enum_Oenum(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 81.03/80.89 class_Nat_Osize(tc_HOL_Obool) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Com__Ostate__HOL_Oequal,axiom,
% 81.03/80.89 class_HOL_Oequal(tc_Com_Ostate) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Com__Ostate__Nat_Osize,axiom,
% 81.03/80.89 class_Nat_Osize(tc_Com_Ostate) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Com__Ovname__HOL_Oequal,axiom,
% 81.03/80.89 class_HOL_Oequal(tc_Com_Ovname) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Com__Ovname__Nat_Osize,axiom,
% 81.03/80.89 class_Nat_Osize(tc_Com_Ovname) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_List__Olist__HOL_Oequal,axiom,
% 81.03/80.89 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_List__Olist__Nat_Osize,axiom,
% 81.03/80.89 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 81.03/80.89 ! [T_1,T_2] :
% 81.03/80.89 ( ( class_Finite__Set_Ofinite(T_2)
% 81.03/80.89 & class_Finite__Set_Ofinite(T_1) )
% 81.03/80.89 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_sum__HOL_Oequal,axiom,
% 81.03/80.89 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_sum__Enum_Oenum,axiom,
% 81.03/80.89 ! [T_1,T_2] :
% 81.03/80.89 ( ( class_Enum_Oenum(T_2)
% 81.03/80.89 & class_Enum_Oenum(T_1) )
% 81.03/80.89 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_sum__Nat_Osize,axiom,
% 81.03/80.89 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 81.03/80.89 ! [T_1] :
% 81.03/80.89 ( class_Finite__Set_Ofinite(T_1)
% 81.03/80.89 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Option__Ooption__HOL_Oequal,axiom,
% 81.03/80.89 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 81.03/80.89 ! [T_1] :
% 81.03/80.89 ( class_Enum_Oenum(T_1)
% 81.03/80.89 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 81.03/80.89 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 81.03/80.89 ! [T_1,T_2] :
% 81.03/80.89 ( ( class_Finite__Set_Ofinite(T_2)
% 81.03/80.89 & class_Finite__Set_Ofinite(T_1) )
% 81.03/80.89 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_prod__Smallcheck_Osmall,axiom,
% 81.03/80.89 ! [T_1,T_2] :
% 81.03/80.89 ( ( class_Smallcheck_Osmall(T_2)
% 81.03/80.89 & class_Smallcheck_Osmall(T_1) )
% 81.03/80.89 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_prod__HOL_Oequal,axiom,
% 81.03/80.89 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_prod__Enum_Oenum,axiom,
% 81.03/80.89 ! [T_1,T_2] :
% 81.03/80.89 ( ( class_Enum_Oenum(T_2)
% 81.03/80.89 & class_Enum_Oenum(T_1) )
% 81.03/80.89 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_prod__Nat_Osize,axiom,
% 81.03/80.89 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 81.03/80.89 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
% 81.03/80.89 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom,
% 81.03/80.89 class_HOL_Oequal(tc_Product__Type_Ounit) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 81.03/80.89 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 81.03/80.89 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom,
% 81.03/80.89 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 81.03/80.89 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom,
% 81.03/80.89 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 81.03/80.89 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 81.03/80.89 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 81.03/80.89 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 81.03/80.89 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 81.03/80.89 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 81.03/80.89 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 81.03/80.89 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 81.03/80.89 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 81.03/80.89 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 81.03/80.89 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 81.03/80.89 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 81.03/80.89 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 81.03/80.89 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 81.03/80.89 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 81.03/80.89 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 81.03/80.89 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 81.03/80.89 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 81.03/80.89 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 81.03/80.89 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 81.03/80.89 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 81.03/80.89 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 81.03/80.89 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 81.03/80.89 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 81.03/80.89 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 81.03/80.89 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 81.03/80.89 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 81.03/80.89 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 81.03/80.89 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 81.03/80.89 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 81.03/80.89 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 81.03/80.89 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 81.03/80.89 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 81.03/80.89 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 81.03/80.89 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 81.03/80.89 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 81.03/80.89 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom,
% 81.03/80.89 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 81.03/80.89 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom,
% 81.03/80.89 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 81.03/80.89
% 81.03/80.89 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 81.03/80.89 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 81.03/80.89
% 81.03/80.89 %----Helper facts (20)
% 81.03/80.89 fof(help_c__COMBI__1,axiom,
% 81.03/80.89 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__COMBK__1,axiom,
% 81.03/80.89 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__COMBB__1,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__COMBC__1,axiom,
% 81.03/80.89 ! [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) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__COMBS__1,axiom,
% 81.03/80.89 ! [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)) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__fequal__1,axiom,
% 81.03/80.89 ! [V_y_2,V_x_2] :
% 81.03/80.89 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 81.03/80.89 | V_x_2 = V_y_2 ) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__fequal__2,axiom,
% 81.03/80.89 ! [V_y_2,V_x_2] :
% 81.03/80.89 ( V_x_2 != V_y_2
% 81.03/80.89 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__fFalse__1,axiom,
% 81.03/80.89 ~ hBOOL(c_fFalse) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__fTrue__1,axiom,
% 81.03/80.89 hBOOL(c_fTrue) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__fNot__1,axiom,
% 81.03/80.89 ! [V_P_2] :
% 81.03/80.89 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 81.03/80.89 | ~ hBOOL(V_P_2) ) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__fNot__2,axiom,
% 81.03/80.89 ! [V_P_2] :
% 81.03/80.89 ( ~ ~ hBOOL(V_P_2)
% 81.03/80.89 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__fconj__1,axiom,
% 81.03/80.89 ! [V_Q_2,V_P_2] :
% 81.03/80.89 ( ~ hBOOL(V_P_2)
% 81.03/80.89 | ~ hBOOL(V_Q_2)
% 81.03/80.89 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__fconj__2,axiom,
% 81.03/80.89 ! [V_Q_2,V_P_2] :
% 81.03/80.89 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 81.03/80.89 | hBOOL(V_P_2) ) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__fconj__3,axiom,
% 81.03/80.89 ! [V_Q_2,V_P_2] :
% 81.03/80.89 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 81.03/80.89 | hBOOL(V_Q_2) ) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__fdisj__1,axiom,
% 81.03/80.89 ! [V_Q_2,V_P_2] :
% 81.03/80.89 ( ~ hBOOL(V_P_2)
% 81.03/80.89 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__fdisj__2,axiom,
% 81.03/80.89 ! [V_P_2,V_Q_2] :
% 81.03/80.89 ( ~ hBOOL(V_Q_2)
% 81.03/80.89 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__fdisj__3,axiom,
% 81.03/80.89 ! [V_Q_2,V_P_2] :
% 81.03/80.89 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
% 81.03/80.89 | hBOOL(V_P_2)
% 81.03/80.89 | hBOOL(V_Q_2) ) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__fimplies__1,axiom,
% 81.03/80.89 ! [V_Q_2,V_P_2] :
% 81.03/80.89 ( hBOOL(V_P_2)
% 81.03/80.89 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__fimplies__2,axiom,
% 81.03/80.89 ! [V_P_2,V_Q_2] :
% 81.03/80.89 ( ~ hBOOL(V_Q_2)
% 81.03/80.89 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 81.03/80.89
% 81.03/80.89 fof(help_c__fimplies__3,axiom,
% 81.03/80.89 ! [V_Q_2,V_P_2] :
% 81.03/80.89 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
% 81.03/80.89 | ~ hBOOL(V_P_2)
% 81.03/80.89 | hBOOL(V_Q_2) ) ).
% 81.03/80.89
% 81.03/80.89 %----Conjectures (4)
% 81.03/80.89 fof(conj_0,hypothesis,
% 81.03/80.89 c_Hoare__Mirabelle_Ostate__not__singleton ).
% 81.03/80.89
% 81.03/80.89 fof(conj_1,hypothesis,
% 81.03/80.89 c_Com_OWT__bodies ).
% 81.03/80.89
% 81.03/80.89 fof(conj_2,hypothesis,
% 81.03/80.89 hBOOL(hAPP(c_Com_OWT,v_c)) ).
% 81.03/80.89
% 81.03/80.89 fof(conj_3,conjecture,
% 81.03/80.89 ! [B_x] :
% 81.03/80.89 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))
% 81.03/80.89 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,B_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ).
% 81.03/80.89
% 81.03/80.89 %------------------------------------------------------------------------------
% 81.03/80.89 %-------------------------------------------
% 81.03/80.89 % Proof found
% 81.03/80.89 % SZS status Theorem for theBenchmark
% 81.03/80.89 % SZS output start Proof
% 81.29/80.90 %ClaNum:10204(EqnAxiom:2870)
% 81.29/80.90 %VarNum:69979(SingletonVarNum:20430)
% 81.29/80.90 %MaxLitNum:8
% 81.29/80.90 %MaxfuncDepth:15
% 81.29/80.90 %SharedTerms:1110
% 81.29/80.90 %goalClause: 3567 4561
% 81.29/80.90 %singleGoalClaCount:2
% 81.29/80.90 [2871]P1(a5000)
% 81.29/80.90 [2872]P2(a5000)
% 81.29/80.90 [2876]P24(a192)
% 81.29/80.90 [2877]P25(a871)
% 81.29/80.90 [2878]P25(a877)
% 81.29/80.90 [2879]P26(a871)
% 81.29/80.90 [2880]P26(a880)
% 81.29/80.90 [2881]P105(a871)
% 81.29/80.90 [2882]P105(a877)
% 81.29/80.90 [2883]P105(a1)
% 81.29/80.90 [2884]P105(a105)
% 81.29/80.90 [2885]P106(a877)
% 81.29/80.90 [2886]P106(a1)
% 81.29/80.90 [2887]P106(a105)
% 81.29/80.90 [2888]P107(a871)
% 81.29/80.90 [2889]P107(a877)
% 81.29/80.90 [2890]P107(a1)
% 81.29/80.90 [2891]P107(a105)
% 81.29/80.90 [2892]P108(a871)
% 81.29/80.90 [2893]P108(a877)
% 81.29/80.90 [2894]P108(a1)
% 81.29/80.90 [2895]P108(a105)
% 81.29/80.90 [2896]P65(a871)
% 81.29/80.90 [2897]P65(a877)
% 81.29/80.90 [2898]P65(a1)
% 81.29/80.90 [2899]P66(a871)
% 81.29/80.90 [2900]P66(a877)
% 81.29/80.90 [2901]P66(a1)
% 81.29/80.90 [2902]P66(a105)
% 81.29/80.90 [2903]P78(a871)
% 81.29/80.90 [2904]P78(a877)
% 81.29/80.90 [2905]P78(a1)
% 81.29/80.90 [2906]P79(a871)
% 81.29/80.90 [2907]P80(a1)
% 81.29/80.90 [2908]P27(a871)
% 81.29/80.90 [2909]P67(a1)
% 81.29/80.90 [2910]P81(a877)
% 81.29/80.90 [2911]P81(a1)
% 81.29/80.90 [2912]P81(a105)
% 81.29/80.90 [2913]P109(a1)
% 81.29/80.90 [2914]P84(a877)
% 81.29/80.90 [2915]P84(a1)
% 81.29/80.90 [2916]P84(a105)
% 81.29/80.90 [2917]P68(a877)
% 81.29/80.90 [2918]P68(a1)
% 81.29/80.90 [2919]P68(a105)
% 81.29/80.90 [2920]P69(a877)
% 81.29/80.90 [2921]P69(a1)
% 81.29/80.90 [2922]P69(a105)
% 81.29/80.90 [2923]P85(a877)
% 81.29/80.90 [2924]P85(a1)
% 81.29/80.90 [2925]P85(a105)
% 81.29/80.90 [2926]P70(a877)
% 81.29/80.90 [2927]P70(a1)
% 81.29/80.90 [2928]P70(a105)
% 81.29/80.90 [2929]P86(a877)
% 81.29/80.90 [2930]P86(a1)
% 81.29/80.90 [2931]P86(a105)
% 81.29/80.90 [2932]P73(a1)
% 81.29/80.90 [2933]P74(a877)
% 81.29/80.90 [2934]P74(a1)
% 81.29/80.90 [2935]P74(a105)
% 81.29/80.90 [2936]P110(a877)
% 81.29/80.90 [2937]P110(a1)
% 81.29/80.90 [2938]P110(a105)
% 81.29/80.90 [2939]P102(a871)
% 81.29/80.90 [2940]P102(a877)
% 81.29/80.90 [2941]P102(a1)
% 81.29/80.90 [2942]P100(a871)
% 81.29/80.90 [2943]P100(a877)
% 81.29/80.90 [2944]P100(a1)
% 81.29/80.90 [2945]P111(a1)
% 81.29/80.90 [2946]P88(a877)
% 81.29/80.90 [2947]P88(a1)
% 81.29/80.90 [2948]P88(a105)
% 81.29/80.90 [2949]P82(a877)
% 81.29/80.90 [2950]P82(a1)
% 81.29/80.90 [2951]P82(a105)
% 81.29/80.90 [2952]P76(a1)
% 81.29/80.90 [2953]P136(a877)
% 81.29/80.90 [2954]P136(a1)
% 81.29/80.90 [2955]P136(a105)
% 81.29/80.90 [2956]P89(a877)
% 81.29/80.90 [2957]P89(a1)
% 81.29/80.90 [2958]P89(a105)
% 81.29/80.90 [2959]P112(a877)
% 81.29/80.90 [2960]P112(a1)
% 81.29/80.90 [2961]P112(a105)
% 81.29/80.90 [2962]P143(a877)
% 81.29/80.90 [2963]P143(a1)
% 81.29/80.90 [2964]P137(a1)
% 81.29/80.90 [2965]P93(a1)
% 81.29/80.90 [2966]P94(a877)
% 81.29/80.90 [2967]P94(a1)
% 81.29/80.90 [2968]P94(a105)
% 81.29/80.90 [2969]P96(a1)
% 81.29/80.90 [2970]P71(a877)
% 81.29/80.90 [2971]P71(a1)
% 81.29/80.90 [2972]P71(a105)
% 81.29/80.90 [2973]P125(a877)
% 81.29/80.90 [2974]P125(a1)
% 81.29/80.90 [2975]P125(a105)
% 81.29/80.90 [2976]P138(a1)
% 81.29/80.90 [2977]P126(a877)
% 81.29/80.90 [2978]P126(a1)
% 81.29/80.90 [2979]P126(a105)
% 81.29/80.90 [2980]P113(a877)
% 81.29/80.90 [2981]P113(a1)
% 81.29/80.90 [2982]P113(a105)
% 81.29/80.90 [2983]P140(a877)
% 81.29/80.90 [2984]P140(a1)
% 81.29/80.90 [2985]P140(a105)
% 81.29/80.90 [2986]P75(a877)
% 81.29/80.90 [2987]P75(a1)
% 81.29/80.90 [2988]P75(a105)
% 81.29/80.90 [2989]P83(a877)
% 81.29/80.90 [2990]P83(a1)
% 81.29/80.90 [2991]P83(a105)
% 81.29/80.90 [2992]P131(a877)
% 81.29/80.90 [2993]P131(a1)
% 81.29/80.90 [2994]P131(a105)
% 81.29/80.90 [2995]P132(a1)
% 81.29/80.90 [2996]P134(a877)
% 81.29/80.90 [2997]P134(a1)
% 81.29/80.90 [2998]P134(a105)
% 81.29/80.90 [2999]P133(a877)
% 81.29/80.90 [3000]P133(a1)
% 81.29/80.90 [3001]P133(a105)
% 81.29/80.90 [3002]P123(a1)
% 81.29/80.90 [3003]P124(a1)
% 81.29/80.90 [3004]P127(a877)
% 81.29/80.90 [3005]P127(a1)
% 81.29/80.90 [3006]P127(a105)
% 81.29/80.90 [3007]P118(a877)
% 81.29/80.90 [3008]P118(a1)
% 81.29/80.90 [3009]P118(a105)
% 81.29/80.90 [3010]P128(a877)
% 81.29/80.90 [3011]P128(a1)
% 81.29/80.90 [3012]P128(a105)
% 81.29/80.90 [3013]P129(a1)
% 81.29/80.90 [3014]P130(a1)
% 81.29/80.90 [3015]P103(a877)
% 81.29/80.90 [3016]P103(a1)
% 81.29/80.90 [3017]P103(a105)
% 81.29/80.90 [3018]P141(a877)
% 81.29/80.90 [3019]P141(a1)
% 81.29/80.90 [3020]P141(a105)
% 81.29/80.90 [3021]P87(a1)
% 81.29/80.90 [3022]P135(a1)
% 81.29/80.90 [3023]P97(a871)
% 81.29/80.90 [3024]P90(a871)
% 81.29/80.90 [3025]P90(a1)
% 81.29/80.90 [3026]P119(a1)
% 81.29/80.90 [3027]P114(a1)
% 81.29/80.90 [3028]P139(a1)
% 81.29/80.90 [3029]P72(a1)
% 81.29/80.90 [3030]P91(a1)
% 81.29/80.90 [3031]P115(a871)
% 81.29/80.90 [3032]P101(a871)
% 81.29/80.90 [3033]P58(a877)
% 81.29/80.90 [3034]P58(a1)
% 81.29/80.90 [3035]P58(a105)
% 81.29/80.90 [3036]P59(a1)
% 81.29/80.90 [3037]P116(a877)
% 81.29/80.90 [3038]P116(a1)
% 81.29/80.90 [3039]P116(a105)
% 81.29/80.90 [3040]P142(a877)
% 81.29/80.90 [3041]P142(a1)
% 81.29/80.90 [3042]P142(a105)
% 81.29/80.90 [3043]P144(a1)
% 81.29/80.90 [3044]P144(a880)
% 81.29/80.90 [3045]P77(a877)
% 81.29/80.90 [3046]P77(a1)
% 81.29/80.90 [3047]P77(a105)
% 81.29/80.90 [3048]P92(a877)
% 81.29/80.90 [3049]P92(a1)
% 81.29/80.90 [3050]P92(a105)
% 81.29/80.90 [3051]P60(a871)
% 81.29/80.90 [3052]P60(a880)
% 81.29/80.90 [3053]P95(a871)
% 81.29/80.90 [3054]P95(a872)
% 81.29/80.90 [3055]P95(a873)
% 81.29/80.90 [3056]P95(a877)
% 81.29/80.90 [3057]P95(a1)
% 81.29/80.90 [3058]P95(a105)
% 81.29/80.90 [3059]P95(a880)
% 81.29/80.90 [3060]P95(a324)
% 81.29/80.90 [3061]P95(a875)
% 81.29/80.90 [3062]P117(a877)
% 81.29/80.90 [3063]P104(a871)
% 81.29/80.90 [3064]P104(a872)
% 81.29/80.90 [3065]P104(a873)
% 81.29/80.90 [3066]P104(a877)
% 81.29/80.90 [3067]P104(a105)
% 81.29/80.90 [3068]P104(a880)
% 81.29/80.90 [3069]P104(a324)
% 81.29/80.90 [3070]P104(a875)
% 81.29/80.90 [3071]P99(a871)
% 81.29/80.90 [3091]P38(a877,a248)
% 81.29/80.90 [3092]P38(a877,a318)
% 81.29/80.90 [4452]~E(a103,a84)
% 81.29/80.90 [4453]~P24(a241)
% 81.29/80.90 [2873]E(f2(a1),a84)
% 81.29/80.90 [2874]E(f106(a105),a3)
% 81.29/80.90 [2875]E(f22(a105),a23)
% 81.29/80.90 [3072]E(f193(a877),f2(a877))
% 81.29/80.90 [3073]E(f32(a24),f2(a877))
% 81.29/80.90 [3074]E(f85(a241),f2(a877))
% 81.29/80.90 [3075]E(f85(a192),f2(a877))
% 81.29/80.90 [3076]E(f107(a877),f242(a877))
% 81.29/80.90 [3077]E(f116(a877),f243(a877))
% 81.29/80.90 [3078]E(f108(a1),f35(a1))
% 81.29/80.90 [3079]P28(f79(a1))
% 81.29/80.90 [3080]P28(f2(a1))
% 81.29/80.90 [3130]P24(f328(a25,a24))
% 81.29/80.90 [3131]P24(f328(a25,a882))
% 81.29/80.90 [3144]P38(f884(a877,a877),a36)
% 81.29/80.90 [3495]E(f320(a877,a877,a248,a248),a36)
% 81.29/80.90 [4454]~E(f79(a1),f2(a1))
% 81.29/80.90 [3081]E(f117(f2(a877)),f2(a877))
% 81.29/80.90 [3082]E(f4(f2(a105)),f2(a877))
% 81.29/80.90 [3094]E(f328(f80(a1),a84),a84)
% 81.29/80.90 [3097]E(f328(a118,f2(a877)),f79(a877))
% 81.29/80.90 [3098]E(f328(a110,f79(a1)),f79(a877))
% 81.29/80.90 [3099]E(f328(a3,f79(a877)),f79(a105))
% 81.29/80.90 [3101]E(f328(a3,f2(a877)),f2(a105))
% 81.29/80.90 [3103]E(f328(f109(a1),a84),f2(a1))
% 81.29/80.90 [3104]E(f328(f109(a105),a84),f2(a105))
% 81.29/80.90 [3105]E(f328(a110,f2(a1)),f2(a877))
% 81.29/80.90 [3106]E(f328(f194(a871),a241),f2(a877))
% 81.29/80.90 [3107]E(f328(f194(a871),a192),f2(a877))
% 81.29/80.90 [3108]E(f328(f194(a873),a24),f2(a877))
% 81.29/80.90 [3109]E(f328(f109(a877),a84),f2(a877))
% 81.29/80.90 [3114]E(f328(f80(a1),f79(a1)),a103)
% 81.29/80.90 [3122]E(f328(f194(a105),f2(a105)),f2(a877))
% 81.29/80.90 [3123]E(f328(f106(a1),f79(a877)),f79(a1))
% 81.29/80.90 [3124]E(f328(f106(a1),f2(a877)),f2(a1))
% 81.29/80.90 [3125]E(f328(f80(a1),f2(a1)),f2(a1))
% 81.29/80.90 [3140]E(f328(a110,f79(a1)),f328(a118,f2(a877)))
% 81.29/80.90 [3141]E(f328(f177(a874,a873),a27),a28)
% 81.29/80.90 [3142]E(f319(f884(a877,a877),a36),a37)
% 81.29/80.90 [3143]E(f321(f884(a877,a877),a36),a69)
% 81.29/80.90 [3165]E(f328(f250(a877),f2(a877)),f193(f885(a877,a871)))
% 81.29/80.90 [3166]E(f328(f251(a877),f2(a877)),f252(f885(a877,a871)))
% 81.29/80.90 [3174]P40(f193(f885(a1,a871)))
% 81.29/80.90 [3209]E(f328(f328(f22(a105),f2(a105)),f79(a105)),f2(a105))
% 81.29/80.90 [3288]P24(f328(f328(f245(a1),a103),f2(a1)))
% 81.29/80.90 [3313]P24(f328(f328(f244(a1),f2(a1)),f79(a1)))
% 81.29/80.90 [3315]P24(f328(f328(f245(a1),f2(a1)),f79(a1)))
% 81.29/80.90 [3488]P24(f328(f62(a874),f183(a874,a873,a28)))
% 81.29/80.90 [3525]E(f328(f328(f285(a877,a877,a877),a318),f304(a877,a318)),a248)
% 81.29/80.90 [3563]P41(a1,a877,a110,f328(f244(a1),f2(a1)))
% 81.29/80.90 [3567]P24(f328(f328(f330(a874),a717),f183(a874,a873,a28)))
% 81.29/80.90 [3568]E(f328(f328(f42(a877,f885(a877,a871)),f252(f885(a877,a871))),f300(a877)),f193(f885(a877,a871)))
% 81.29/80.90 [3569]E(f328(f328(f43(a877,f885(a877,a871)),f252(f885(a877,a871))),f297(a877)),f252(f885(a877,a871)))
% 81.29/80.90 [3570]E(f328(f328(f43(a877,f885(a877,a871)),f252(f885(a877,a871))),f250(a877)),f252(f885(a877,a871)))
% 81.29/80.90 [3571]E(f328(f328(f43(a877,f885(a877,a871)),f252(f885(a877,a871))),f251(a877)),f252(f885(a877,a871)))
% 81.29/80.90 [3587]P21(a877,a1,f106(a1),f252(f885(a877,a871)))
% 81.29/80.90 [3598]P41(a877,a1,f106(a1),f328(f16(a871,a877),a192))
% 81.29/80.90 [3733]E(f328(f74(a877,a105,a1,a3),a110),f109(a105))
% 81.29/80.90 [3954]P54(a105,a877,a19,a3,f252(f885(a877,a871)))
% 81.29/80.90 [3963]P54(a1,f885(f884(a877,a877),a871),a112,a90,a104)
% 81.29/80.90 [4227]E(f268(a1,a1,a1,a1,f35(a1),f80(a1)),a51)
% 81.29/80.90 [4477]~E(f328(f109(a1),a103),f328(f109(a1),a84))
% 81.29/80.90 [4478]~P24(f328(a199,f79(a1)))
% 81.29/80.90 [4479]~P24(f328(a199,f2(a1)))
% 81.29/80.90 [4529]~P24(f328(f328(f245(a1),a84),f2(a1)))
% 81.29/80.90 [3157]E(f328(f328(f22(a1),a103),a103),a84)
% 81.29/80.90 [3172]E(f328(f106(a1),f328(a118,f2(a877))),f79(a1))
% 81.29/80.90 [3237]E(f328(f38(a880),f252(f885(a880,a871))),f79(a877))
% 81.29/80.90 [3258]P24(f328(a199,f328(f109(a1),a103)))
% 81.29/80.90 [3260]P24(f328(f328(f244(a1),a103),a84))
% 81.29/80.90 [3262]P24(f328(f328(f245(a1),a103),a84))
% 81.29/80.90 [3326]E(f328(f328(f306(a877),f2(a877)),f193(f885(a877,a871))),f328(f297(a877),f2(a877)))
% 81.29/80.90 [3381]P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),a84)))
% 81.29/80.90 [3393]E(f328(f307(a877,a877,a118),f252(f885(a877,a871))),f328(f300(a877),f2(a877)))
% 81.29/80.90 [3432]P6(f884(a877,a877),f252(f885(f884(a877,a877),a871)),a114)
% 81.29/80.90 [3741]E(f328(f74(a877,a1,a105,f106(a1)),a19),a20)
% 81.29/80.90 [3800]P38(a877,f328(f249(f884(a877,a877)),f328(f267(a877,a877,a871),f245(a877))))
% 81.29/80.90 [4518]~P24(f328(a199,f328(f109(a1),a84)))
% 81.29/80.90 [4519]~P24(f328(f328(f244(a1),a84),a103))
% 81.29/80.90 [4520]~P24(f328(f328(f245(a1),a84),a84))
% 81.29/80.90 [4521]~P24(f328(f328(f245(a1),a84),a103))
% 81.29/80.90 [4522]~P24(f328(f328(f245(a1),a103),a103))
% 81.29/80.90 [4523]~P24(f328(f328(f92(a1),a84),a103))
% 81.29/80.90 [4524]~P24(f328(f328(f92(a1),a103),a84))
% 81.29/80.90 [4539]~P24(f328(f62(a877),f252(f885(a877,a871))))
% 81.29/80.90 [4540]~P24(f328(f62(a1),f252(f885(a1,a871))))
% 81.29/80.90 [4398]E(f328(f267(a1,a1,a871),f328(f328(f8(f885(a1,a871),f885(a1,a871),a1),f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f245(a1),f2(a1))))),f328(f328(f7(a1,a1,f885(a1,a871)),f328(f328(f8(f885(a1,f885(a1,a871)),f885(a1,f885(a1,a871)),a1),f7(a1,a1,a871)),f328(f328(f8(f885(a1,a1),f885(a1,f885(a1,a871)),a1),f328(f8(a1,f885(a1,a871),a1),a325)),a225))),f79(a1)))),a221)
% 81.29/80.90 [4561]~P20(a872,f193(f885(f876(a872),a871)),f328(f328(f306(f876(a872)),f328(a94,f328(a26,a717))),f193(f885(f876(a872),a871))))
% 81.29/80.90 [3470]E(f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103),f328(f80(a1),a103))
% 81.29/80.90 [3508]E(f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103),f328(f328(f22(a1),a84),a103))
% 81.29/80.90 [3667]E(f328(f328(f61(f884(a877,a877)),f252(f885(f884(a877,a877),a871))),a114),a104)
% 81.29/80.90 [3696]E(f328(f109(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f79(a1))
% 81.29/80.90 [3697]E(f328(f109(a105),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f79(a105))
% 81.29/80.90 [3698]E(f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f79(a877))
% 81.29/80.90 [3702]E(f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(a118,f2(a877)))
% 81.29/80.90 [4088]E(f328(f328(f116(f885(f884(f884(a877,a877),f884(a877,a877)),a871)),a36),f304(f884(a877,a877),f193(f885(f884(f884(a877,a877),f884(a877,a877)),a871)))),a71)
% 81.29/80.90 [4159]E(f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),f79(a877)),f2(a877))),f193(f885(f884(a877,a877),a871))))),f79(a1))
% 81.29/80.90 [4160]E(f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),f2(a877)),f2(a877))),f193(f885(f884(a877,a877),a871))))),f2(a1))
% 81.29/80.90 [4175]E(f328(f249(f884(a877,a877)),f328(f267(a877,a877,a871),f328(f328(f8(a877,f885(a877,a871),a877),f328(f7(a877,a877,a871),a325)),a118))),a318)
% 81.29/80.90 [4145]E(f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),f328(a118,f328(a118,f2(a877))))
% 81.29/80.90 [4148]E(f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),f328(f328(f81(a877),f79(a877)),f79(a877)))
% 81.29/80.90 [4149]E(f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),f328(f38(a871),f252(f885(a871,a871))))
% 81.29/80.90 [4213]P28(f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))
% 81.29/80.90 [4285]P22(f885(f884(a877,a877),a871),f328(f328(f257(f885(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),a871),f885(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),a871)),a37),a70))
% 81.29/80.90 [4286]P22(f885(f884(a877,a877),a871),f328(f328(f257(f885(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),a871),f885(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),a871)),a69),a72))
% 81.29/80.90 [4326]E(f328(f328(f116(f885(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),a871)),f321(f884(a877,a877),a71)),f328(f328(f306(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f328(f328(f257(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),f193(f885(f884(a877,a877),a871))),f193(f885(f884(a877,a877),a871)))),f193(f885(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),a871)))),a72)
% 81.29/80.90 [4327]E(f328(f328(f116(f885(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),a871)),f319(f884(a877,a877),a71)),f328(f328(f306(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f328(f328(f257(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),f193(f885(f884(a877,a877),a871))),f193(f885(f884(a877,a877),a871)))),f193(f885(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),a871)))),a70)
% 81.29/80.90 [4215]E(f328(a110,f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f328(a118,f328(a118,f2(a877))))
% 81.29/80.90 [4262]E(f328(f106(a1),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))
% 81.29/80.90 [4297]P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))
% 81.29/80.90 [4298]E(f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),a103)),f328(a118,f328(a118,f328(a118,f2(a877)))))
% 81.29/80.90 [4340]P28(f328(f109(a1),f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),a103)))
% 81.29/80.90 [4368]E(f328(f106(a1),f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),a103))),f328(f109(a1),f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),a103)))
% 81.29/80.90 [4383]P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),a103))))
% 81.29/80.90 [3093]P5(x30931,a325)
% 81.29/80.90 [3496]P21(a877,a877,a118,x34961)
% 81.29/80.90 [3083]P95(f876(x30831))
% 81.29/80.90 [3084]P95(f881(x30841))
% 81.29/80.90 [3085]P95(f878(x30851))
% 81.29/80.90 [3086]P95(f879(x30861))
% 81.29/80.90 [3087]P104(f876(x30871))
% 81.29/80.90 [3088]P104(f881(x30881))
% 81.29/80.90 [3089]P104(f878(x30891))
% 81.29/80.90 [3090]P104(f879(x30901))
% 81.29/80.90 [3110]P38(a1,f111(x31101))
% 81.29/80.90 [3111]P38(a1,f113(x31111))
% 81.29/80.90 [3113]P39(x31131,f196(x31131))
% 81.29/80.90 [3162]P38(f885(x31621,a871),f303(x31621))
% 81.29/80.90 [3200]E(f45(a1,x32001,x32001),f2(a1))
% 81.29/80.90 [3255]P11(x32551,f885(x32551,a871),f306(x32551))
% 81.29/80.90 [4456]~E(f328(a26,x44561),a24)
% 81.29/80.90 [4458]~E(f328(a118,x44581),x44581)
% 81.29/80.90 [4468]~E(f328(a118,x44681),f2(a877))
% 81.29/80.90 [3095]E(f328(f194(a877),x30951),x30951)
% 81.29/80.90 [3096]E(f328(f109(a1),x30961),x30961)
% 81.29/80.90 [3112]E(f328(a90,f329(x31121)),x31121)
% 81.29/80.90 [3126]E(f120(x31261,f119(x31261)),f119(x31261))
% 81.29/80.90 [3127]E(f151(x31271,f119(x31271)),f119(x31271))
% 81.29/80.90 [3132]E(f32(f328(a26,x31321)),f2(a877))
% 81.29/80.90 [3137]E(f328(f167(x31371),f119(x31371)),f119(x31371))
% 81.29/80.90 [3138]E(f328(f170(x31381),f119(x31381)),f119(x31381))
% 81.29/80.90 [3139]E(f328(f168(x31391),f119(x31391)),f119(x31391))
% 81.29/80.90 [3145]E(f328(f109(a1),x31451),f328(f108(a1),x31451))
% 81.29/80.90 [3146]E(f328(a90,f328(a112,x31461)),x31461)
% 81.29/80.90 [3148]E(f328(a3,f328(a19,x31481)),x31481)
% 81.29/80.90 [3149]E(f328(a19,f328(a3,x31491)),x31491)
% 81.29/80.90 [3150]P28(f328(f106(a1),x31501))
% 81.29/80.90 [3155]E(f328(f194(f881(x31551)),f196(x31551)),f2(a877))
% 81.29/80.90 [3156]E(f328(f194(f878(x31561)),f119(x31561)),f2(a877))
% 81.29/80.90 [3161]E(f328(f194(a873),f328(a26,x31611)),f2(a877))
% 81.29/80.90 [3170]E(f235(x31701,f196(x31701)),f193(f885(x31701,a871)))
% 81.29/80.90 [3177]E(f328(f328(f22(a877),x31771),f2(a877)),x31771)
% 81.29/80.90 [3178]E(f328(f328(f81(a877),x31781),f2(a877)),x31781)
% 81.29/80.90 [3179]E(f328(f328(f81(a1),x31791),f2(a1)),x31791)
% 81.29/80.90 [3180]E(f328(f328(f82(a877),x31801),f79(a877)),x31801)
% 81.29/80.90 [3181]E(f328(f328(f82(a1),x31811),f79(a1)),x31811)
% 81.29/80.90 [3182]E(f328(f328(f243(a877),x31821),f2(a877)),x31821)
% 81.29/80.90 [3183]E(f328(f328(f82(a877),x31831),f2(a877)),f2(a877))
% 81.29/80.90 [3184]E(f328(f328(f39(a1),x31841),f2(a1)),f2(a1))
% 81.29/80.90 [3185]E(f328(f328(f242(a877),x31851),f2(a877)),f2(a877))
% 81.29/80.90 [3191]E(f328(f171(x31911),f119(x31911)),f193(f885(x31911,a871)))
% 81.29/80.90 [3195]P24(f328(f136(x31951),f119(x31951)))
% 81.29/80.90 [3201]E(f328(f153(x32011,x32011),f5(x32011)),f35(f878(x32011)))
% 81.29/80.90 [3202]E(f328(f153(x32021,x32021),f35(x32021)),f35(f878(x32021)))
% 81.29/80.90 [3203]E(f328(f207(x32031,x32031),f5(x32031)),f35(f881(x32031)))
% 81.29/80.90 [3204]E(f328(f207(x32041,x32041),f35(x32041)),f35(f881(x32041)))
% 81.29/80.90 [3205]E(f45(a1,x32051,f2(a1)),x32051)
% 81.29/80.90 [3206]E(f328(f244(a877),f328(a118,x32061)),f328(f245(a877),x32061))
% 81.29/80.90 [3207]E(f328(f250(a877),f328(a118,x32071)),f328(f297(a877),x32071))
% 81.29/80.90 [3208]E(f328(f251(a877),f328(a118,x32081)),f328(f300(a877),x32081))
% 81.29/80.90 [3210]E(f45(a1,f2(a1),x32101),f2(a1))
% 81.29/80.90 [3221]E(f328(f328(f81(a877),x32211),f79(a877)),f328(a118,x32211))
% 81.29/80.90 [3231]E(f328(f298(a877,x32311),f2(a877)),f193(f885(a877,a871)))
% 81.29/80.90 [3243]E(f299(a877,f2(a877),x32431),f328(f297(a877),x32431))
% 81.29/80.90 [3291]E(f328(f328(f22(a877),f328(a118,x32911)),f79(a877)),x32911)
% 81.29/80.90 [3304]E(f47(f2(a1),x33041),f328(f328(f257(a1,a1),f2(a1)),f2(a1)))
% 81.29/80.90 [3321]E(f328(f328(f328(f93(a872),a325),x33211),f200(x33211)),f328(a94,x33211))
% 81.29/80.90 [3356]P24(f328(f328(f245(a877),x33561),f328(a118,x33561)))
% 81.29/80.90 [3368]P24(f328(f328(f245(a877),f2(a877)),f328(a118,x33681)))
% 81.29/80.90 [3653]E(f328(f328(f22(a105),f328(a3,f328(a118,f328(a19,x36531)))),f79(a105)),x36531)
% 81.29/80.90 [3725]P24(f328(f328(f244(a1),f328(f80(a1),f328(f106(a1),x37251))),f2(a1)))
% 81.29/80.90 [3871]P24(f328(f328(f245(a1),f328(f80(a1),f328(f106(a1),f328(a118,x38711)))),f2(a1)))
% 81.29/80.90 [4485]~E(f252(f885(x44851,a871)),f193(f885(x44851,a871)))
% 81.29/80.90 [4532]~P24(f328(f328(f245(a877),x45321),f2(a877)))
% 81.29/80.90 [4548]~P24(f328(f328(f245(a1),f328(f106(a1),x45481)),f2(a1)))
% 81.29/80.90 [3160]E(f179(x31601,f119(f878(x31601))),f119(f878(x31601)))
% 81.29/80.90 [3163]E(f328(f328(f82(a1),a84),x31631),a84)
% 81.29/80.90 [3164]E(f328(f328(f81(a1),a84),x31641),x31641)
% 81.29/80.90 [3167]E(f328(a110,f328(f106(a1),x31671)),x31671)
% 81.29/80.90 [3168]E(f328(f328(f22(a1),x31681),a84),x31681)
% 81.29/80.90 [3169]E(f328(f328(f81(a1),x31691),a84),x31691)
% 81.29/80.90 [3171]E(f328(f328(f22(a877),x31711),x31711),f2(a877))
% 81.29/80.90 [3175]E(f328(f38(a877),f328(f250(a877),x31751)),x31751)
% 81.29/80.90 [3176]E(f328(f80(a1),f328(f80(a1),x31761)),x31761)
% 81.29/80.90 [3186]E(f328(f328(f81(a877),f2(a877)),x31861),x31861)
% 81.29/80.90 [3187]E(f328(f328(f81(a1),f2(a1)),x31871),x31871)
% 81.29/80.90 [3188]E(f328(f328(f82(a877),f79(a877)),x31881),x31881)
% 81.29/80.90 [3189]E(f328(f328(f82(a1),f79(a1)),x31891),x31891)
% 81.29/80.90 [3190]E(f328(f328(f243(a877),f2(a877)),x31901),x31901)
% 81.29/80.90 [3196]E(f328(f328(f22(a877),f2(a877)),x31961),f2(a877))
% 81.29/80.90 [3197]E(f328(f328(f82(a877),f2(a877)),x31971),f2(a877))
% 81.29/80.90 [3198]E(f328(f328(f39(a1),f2(a1)),x31981),f2(a1))
% 81.29/80.90 [3199]E(f328(f328(f242(a877),f2(a877)),x31991),f2(a877))
% 81.29/80.90 [3216]E(f328(f298(a877,f2(a877)),x32161),f328(f250(a877),x32161))
% 81.29/80.90 [3217]E(f328(f328(f82(a1),a103),x32171),f328(f80(a1),x32171))
% 81.29/80.90 [3223]E(f328(a110,f328(f109(a1),x32231)),f328(f109(a877),x32231))
% 81.29/80.90 [3224]E(f328(a19,f328(f109(a105),x32241)),f328(f109(a877),x32241))
% 81.29/80.90 [3225]E(f328(f38(a877),f328(f297(a877),x32251)),f328(a118,x32251))
% 81.29/80.90 [3235]E(f328(f328(f81(a877),f79(a877)),x32351),f328(a118,x32351))
% 81.29/80.90 [3239]E(f328(f76(a1),f328(f106(a1),x32391)),f328(f106(a1),x32391))
% 81.29/80.90 [3240]E(f328(f108(a1),f328(f106(a1),x32401)),f328(f106(a1),x32401))
% 81.29/80.90 [3245]E(f328(f38(x32451),f193(f885(x32451,a871))),f2(a877))
% 81.29/80.90 [3247]E(f328(f328(f39(a877),x32471),f328(a118,f2(a877))),x32471)
% 81.29/80.90 [3256]E(f45(a877,x32561,f328(a118,f2(a877))),f2(a877))
% 81.29/80.90 [3257]E(f45(a1,x32571,f328(f109(a1),a103)),f2(a1))
% 81.29/80.90 [3273]E(f328(f328(f39(a1),x32731),f328(f109(a1),a103)),f328(f80(a1),x32731))
% 81.29/80.90 [3277]E(f138(a877,f328(f298(a877,x32771),f2(a877))),f119(a877))
% 81.29/80.90 [3278]E(f328(f328(f81(a1),x32781),f79(a1)),f328(f328(f22(a1),x32781),a103))
% 81.29/80.90 [3279]E(f328(f328(f22(a1),x32791),f79(a1)),f328(f328(f81(a1),x32791),a103))
% 81.29/80.90 [3283]P24(f328(f328(f244(a877),x32831),x32831))
% 81.29/80.90 [3284]P24(f328(f328(f244(a1),x32841),x32841))
% 81.29/80.90 [3286]P24(f328(f328(f200(a24),x32861),x32861))
% 81.29/80.90 [3287]P24(f328(f328(f92(a1),x32871),x32871))
% 81.29/80.90 [3292]E(f328(f80(a1),f328(f109(a1),x32921)),f328(f109(a1),f328(f80(a1),x32921)))
% 81.29/80.90 [3293]P24(f328(f62(a877),f328(f297(a877),x32931)))
% 81.29/80.90 [3294]P24(f328(f62(a877),f328(f250(a877),x32941)))
% 81.29/80.90 [3302]E(f160(x33021,f252(f885(x33021,a871))),f252(f885(f878(x33021),a871)))
% 81.29/80.90 [3307]P24(f328(f328(f244(a877),f2(a877)),x33071))
% 81.29/80.90 [3318]E(f328(f328(f81(a877),f117(x33181)),f328(a118,f2(a877))),f117(f328(a118,x33181)))
% 81.29/80.90 [3319]E(f328(f249(x33191),f328(f16(a871,x33191),a241)),f193(f885(x33191,a871)))
% 81.29/80.90 [3320]E(f328(f249(x33201),f328(f16(a871,x33201),a192)),f252(f885(x33201,a871)))
% 81.29/80.90 [3325]E(f328(f328(f306(a877),x33251),f328(f250(a877),x33251)),f328(f250(a877),f328(a118,x33251)))
% 81.29/80.90 [3337]E(f328(f328(f81(a1),f79(a1)),f328(f106(a1),x33371)),f328(f106(a1),f328(a118,x33371)))
% 81.29/80.90 [3340]E(f328(f328(f150(f878(x33401)),f119(x33401)),f119(f878(x33401))),f54(x33401,f119(x33401)))
% 81.29/80.90 [3359]E(f193(f885(f884(x33591,x33591),a871)),f254(x33591,f193(f885(x33591,a871))))
% 81.29/80.90 [3360]E(f328(f305(x33601),f252(f885(x33601,a871))),f252(f885(f885(x33601,a871),a871)))
% 81.29/80.90 [3361]E(f328(f80(f885(x33611,a871)),f193(f885(x33611,a871))),f252(f885(x33611,a871)))
% 81.29/80.90 [3362]E(f328(f80(f885(x33621,a871)),f252(f885(x33621,a871))),f193(f885(x33621,a871)))
% 81.29/80.90 [3364]P24(f328(f62(x33641),f193(f885(x33641,a871))))
% 81.29/80.90 [3366]E(f328(f298(a877,x33661),f328(a118,x33661)),f328(f328(f306(a877),x33661),f193(f885(a877,a871))))
% 81.29/80.90 [3367]E(f86(f884(a877,a877),f48(x33671,f2(a877))),f328(f328(f257(a877,a877),f2(a877)),x33671))
% 81.29/80.90 [3380]E(f328(f328(f306(a877),f328(a118,x33801)),f328(f297(a877),x33801)),f328(f297(a877),f328(a118,x33801)))
% 81.29/80.90 [3384]P38(x33841,f193(f885(f884(x33841,x33841),a871)))
% 81.29/80.90 [3387]P24(f328(f328(f244(a1),f2(a1)),f328(f106(a1),x33871)))
% 81.29/80.90 [3395]E(f328(f328(f81(a877),f328(f194(a877),x33951)),f328(a118,f2(a877))),f328(f194(a877),f328(a118,x33951)))
% 81.29/80.90 [3503]P40(f328(f307(a877,a1,f106(a1)),x35031))
% 81.29/80.90 [3541]P48(x35411,f193(f885(x35411,a871)),f193(f885(f884(x35411,x35411),a871)))
% 81.29/80.90 [3560]E(f328(f328(f257(a1,a1),f328(f109(a1),a103)),f328(f328(f22(a1),x35601),f79(a1))),f50(f328(f109(a1),a103),x35601))
% 81.29/80.90 [3610]P57(x36101,f328(f16(f885(x36101,a871),x36101),f328(f16(a871,x36101),a241)))
% 81.29/80.90 [3812]P24(f328(f328(f330(f885(f884(a877,a877),a871)),f329(x38121)),a104))
% 81.29/80.90 [3837]P24(f328(f328(f330(f885(f884(a877,a877),a871)),f328(a112,x38371)),a104))
% 81.29/80.90 [3972]P21(x39721,f885(x39721,a871),f328(f328(f7(x39721,f885(x39721,a871),f885(x39721,a871)),f306(x39721)),f193(f885(x39721,a871))),f252(f885(x39721,a871)))
% 81.29/80.90 [4481]~E(f328(f328(f81(a1),x44811),x44811),a103)
% 81.29/80.90 [4517]~E(f328(a3,f328(a118,f328(a19,x45171))),f2(a105))
% 81.29/80.90 [4525]~P24(f328(a199,f328(f106(a1),x45251)))
% 81.29/80.90 [4528]~P24(f328(f328(f245(a877),x45281),x45281))
% 81.29/80.90 [4541]~P24(f328(f328(f244(a877),f328(a118,x45411)),x45411))
% 81.29/80.90 [3309]E(f328(a110,f328(f80(a1),f328(f106(a1),x33091))),f2(a877))
% 81.29/80.90 [3312]E(f328(f328(f81(a1),f328(f80(a1),x33121)),x33121),f2(a1))
% 81.29/80.90 [3317]E(f328(f38(a1),f328(f298(a1,f2(a1)),x33171)),f328(a110,x33171))
% 81.29/80.90 [3330]E(f328(f328(f258(a877),f328(a118,f2(a877))),x33301),f328(a118,f2(a877)))
% 81.29/80.90 [3429]E(f328(f281(x34291),f193(f885(f884(x34291,x34291),a871))),f193(f885(x34291,a871)))
% 81.29/80.90 [3437]E(f40(f885(x34371,a871),f193(f885(f885(x34371,a871),a871))),f193(f885(x34371,a871)))
% 81.29/80.90 [3438]E(f40(f885(x34381,a871),f252(f885(f885(x34381,a871),a871))),f252(f885(x34381,a871)))
% 81.29/80.90 [3439]E(f41(f885(x34391,a871),f193(f885(f885(x34391,a871),a871))),f252(f885(x34391,a871)))
% 81.29/80.90 [3440]E(f41(f885(x34401,a871),f252(f885(f885(x34401,a871),a871))),f193(f885(x34401,a871)))
% 81.29/80.90 [3486]E(f328(f328(f306(f878(x34861)),f119(x34861)),f193(f885(f878(x34861),a871))),f161(x34861,f119(f885(x34861,a871))))
% 81.29/80.90 [3487]E(f328(f328(f306(f878(x34871)),f119(x34871)),f193(f885(f878(x34871),a871))),f160(x34871,f193(f885(x34871,a871))))
% 81.29/80.90 [3524]E(f328(f328(f81(a877),f4(x35241)),f328(a118,f2(a877))),f4(f328(a3,f328(a118,f328(a19,x35241)))))
% 81.29/80.90 [3552]E(f328(f38(a1),f328(f307(a877,a1,f106(a1)),x35521)),f328(f38(a877),x35521))
% 81.29/80.90 [3555]P24(f328(f328(f244(a877),x35551),f328(f328(f82(a877),x35551),x35551)))
% 81.29/80.90 [3591]E(f328(f307(a1,a877,a110),f299(a1,f2(a1),f328(f106(a1),x35911))),f328(f297(a877),x35911))
% 81.29/80.90 [3605]E(f328(f328(f39(a877),f328(a118,f2(a877))),f328(f109(a877),x36051)),f328(a110,f328(f328(f39(a1),f79(a1)),f328(f109(a1),x36051))))
% 81.29/80.90 [3607]E(f328(f171(a877),f138(a877,f328(f298(a877,f2(a877)),f328(a118,x36071)))),f328(f297(a877),x36071))
% 81.29/80.90 [3608]E(f328(f328(f81(a877),f328(f194(a105),x36081)),f328(a118,f2(a877))),f328(f194(a105),f328(a3,f328(a118,f328(a19,x36081)))))
% 81.29/80.90 [3627]E(f328(f307(a1,a877,a110),f328(f307(a877,a1,f106(a1)),x36271)),x36271)
% 81.29/80.90 [3659]E(f328(f328(f306(a877),f2(a877)),f328(f307(a877,a877,a118),f328(f250(a877),x36591))),f328(f250(a877),f328(a118,x36591)))
% 81.29/80.90 [3666]P52(x36661,x36661,f304(x36661,f193(f885(f884(x36661,x36661),a871))))
% 81.29/80.90 [3672]P24(f328(a199,f328(f80(a1),f328(f106(a1),f328(a118,x36721)))))
% 81.29/80.90 [3683]E(f328(f328(f22(f885(a877,a871)),f328(f251(a877),x36831)),f328(f328(f306(a877),x36831),f193(f885(a877,a871)))),f328(f251(a877),f328(a118,x36831)))
% 81.29/80.90 [3699]E(f328(f328(f81(a1),f328(f328(f22(a1),a84),x36991)),f328(f328(f22(a1),a84),x36991)),f328(f328(f22(a1),a84),f328(f328(f81(a1),x36991),x36991)))
% 81.29/80.90 [3715]E(f328(f328(f306(f885(x37151,a871)),f193(f885(x37151,a871))),f193(f885(f885(x37151,a871),a871))),f328(f305(x37151),f193(f885(x37151,a871))))
% 81.29/80.90 [3742]E(f328(f328(f22(f885(a877,a871)),f328(f300(a877),x37421)),f328(f328(f306(a877),f328(a118,x37421)),f193(f885(a877,a871)))),f328(f300(a877),f328(a118,x37421)))
% 81.29/80.90 [3750]E(f328(f328(f306(f881(x37501)),f196(x37501)),f328(f307(x37501,f881(x37501),f236(x37501)),f252(f885(x37501,a871)))),f252(f885(f881(x37501),a871)))
% 81.29/80.90 [3849]E(f328(f109(a877),f328(f328(f81(a1),x38491),x38491)),f328(f328(f87(a877,a877),f328(f109(a877),x38491)),f328(f328(f18(a877,a877,a877),f81(a877)),f5(a877))))
% 81.29/80.90 [4236]P11(x42361,f885(x42361,a871),f328(f328(f8(f885(x42361,a871),f885(f885(x42361,a871),f885(x42361,a871)),x42361),f328(f7(f885(x42361,a871),f885(x42361,a871),f885(x42361,a871)),f22(f885(x42361,a871)))),f328(f328(f7(x42361,f885(x42361,a871),f885(x42361,a871)),f306(x42361)),f193(f885(x42361,a871)))))
% 81.29/80.90 [4325]E(f328(f249(f884(a1,a1)),f328(f267(a1,a1,a871),f328(f328(f8(f885(a1,a871),f885(a1,a871),a1),f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f244(a1),x43251)))),f245(a1)))),f113(x43251))
% 81.29/80.90 [4358]E(f328(f249(f884(a1,a1)),f328(f267(a1,a1,a871),f328(f328(f18(a1,f885(a1,a871),f885(a1,a871)),f328(f328(f8(f885(a871,a871),f885(f885(a1,a871),f885(a1,a871)),a1),f8(a871,a871,a1)),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f244(a1),x43581)))),f245(a1)))),f111(x43581))
% 81.29/80.90 [4413]E(f328(f249(f884(f885(x44131,a871),f885(x44131,a871))),f328(f267(f885(x44131,a871),f885(x44131,a871),a871),f328(f328(f7(f885(x44131,a871),f885(f885(x44131,a871),a871),f885(f885(x44131,a871),a871)),f328(f328(f8(f885(f885(x44131,a871),f885(a871,a871)),f885(f885(f885(x44131,a871),a871),f885(f885(x44131,a871),a871)),f885(x44131,a871)),f18(f885(x44131,a871),a871,a871)),f328(f328(f8(f885(f885(x44131,a871),a871),f885(f885(x44131,a871),f885(a871,a871)),f885(x44131,a871)),f328(f8(a871,f885(a871,a871),f885(x44131,a871)),a326)),f245(f885(x44131,a871))))),f62(x44131)))),f303(x44131))
% 81.29/80.90 [4545]~P24(f328(f62(f878(x45451)),f252(f885(f878(x45451),a871))))
% 81.29/80.90 [4550]~P24(f328(f328(f92(a1),a103),f328(f328(f81(a1),x45501),x45501)))
% 81.29/80.90 [4560]~P24(f328(f328(f244(a1),f2(a1)),f328(f80(a1),f328(f106(a1),f328(a118,x45601)))))
% 81.29/80.90 [3464]E(f328(f328(f22(a1),f328(f328(f81(a1),x34641),a103)),a103),x34641)
% 81.29/80.90 [3480]E(f328(f171(a877),f138(a877,f328(f298(a877,f2(a877)),x34801))),f328(f250(a877),x34801))
% 81.29/80.90 [3721]E(f328(f328(f81(a1),f328(f328(f81(a1),f79(a1)),x37211)),x37211),f328(f328(f22(a1),f328(f328(f81(a1),x37211),x37211)),a103))
% 81.29/80.90 [3767]E(f328(f283(x37671,x37671),f304(x37671,f193(f885(f884(x37671,x37671),a871)))),f304(x37671,f193(f885(f884(x37671,x37671),a871))))
% 81.29/80.90 [3815]P24(f328(f328(f244(a877),x38151),f328(f328(f82(a877),x38151),f328(f328(f82(a877),x38151),x38151))))
% 81.29/80.90 [4092]P24(f328(f62(a877),f328(f249(a877),f328(f328(f7(a877,a877,a871),f244(a877)),x40921))))
% 81.29/80.90 [4093]P24(f328(f62(a877),f328(f249(a877),f328(f328(f7(a877,a877,a871),f245(a877)),x40931))))
% 81.29/80.90 [4378]E(f328(f249(f884(x43781,x43781)),f328(f328(f8(f885(x43781,a871),a871,f884(x43781,x43781)),f88(x43781)),f328(f328(f7(f884(x43781,x43781),f885(x43781,f884(x43781,x43781)),f885(x43781,a871)),f328(f328(f8(f885(f884(x43781,x43781),a871),f885(f885(x43781,f884(x43781,x43781)),f885(x43781,a871)),f884(x43781,x43781)),f8(f884(x43781,x43781),a871,x43781)),a325)),f328(f328(f18(x43781,x43781,f884(x43781,x43781)),f257(x43781,x43781)),f5(x43781))))),f304(x43781,f193(f885(f884(x43781,x43781),a871))))
% 81.29/80.90 [4547]~E(f328(f328(f22(a1),f328(f328(f81(a1),x45471),x45471)),a103),a84)
% 81.29/80.90 [4549]~E(f328(f328(f81(a1),f328(f328(f81(a1),f79(a1)),x45491)),x45491),f2(a1))
% 81.29/80.90 [4557]~P24(f328(f328(f92(a1),f328(f328(f81(a1),x45571),x45571)),a103))
% 81.29/80.90 [3860]E(f328(f328(f81(a1),f328(f328(f22(a1),a103),x38601)),f328(f328(f22(a1),a103),x38601)),f328(f328(f22(a1),a103),f328(f328(f22(a1),f328(f328(f81(a1),x38601),x38601)),a103)))
% 81.29/80.90 [3981]E(f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),a103),x39811)),f328(f328(f22(a1),a103),x39811))),a103),f328(f328(f22(a1),a103),f328(f328(f81(a1),x39811),x39811)))
% 81.29/80.90 [4016]E(f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f81(a1),x40161),a103)),f328(f328(f81(a1),x40161),a103))),a103),f328(f328(f81(a1),f328(f328(f81(a1),x40161),x40161)),a103))
% 81.29/80.90 [4054]E(f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),a103),x40541)),f328(f328(f22(a1),a103),x40541))),a103),f328(f328(f22(a1),a84),f328(f328(f22(a1),f328(f328(f81(a1),x40541),x40541)),a103)))
% 81.29/80.90 [4155]E(f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x41551),f2(a877))),f193(f885(f884(a877,a877),a871))))),f328(f106(a1),x41551))
% 81.29/80.90 [4165]E(f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),f333(x41651)),f529(x41651))),f193(f885(f884(a877,a877),a871))))),x41651)
% 81.29/80.90 [4198]E(f328(f249(a1),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f244(a1),f2(a1)))),x41981)),f328(f307(a877,a1,f106(a1)),f328(f249(a877),f328(f328(f8(a1,a871,a877),x41981),f106(a1)))))
% 81.29/80.90 [4244]P40(f328(f249(a1),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f244(a1),f2(a1)))),x42441)))
% 81.29/80.90 [4265]P24(f328(f328(f330(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f328(f328(f257(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),x42651),f193(f885(f884(a877,a877),a871)))),a72))
% 81.29/80.90 [4271]E(f328(f307(a1,a877,a110),f328(f249(a1),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f244(a1),f2(a1)))),f328(f328(f8(a877,a871,a1),x42711),a110)))),f328(f249(a877),x42711))
% 81.29/80.90 [4427]E(f309(a877,f328(f328(f43(f884(a877,a877),f885(a877,a871)),f328(a112,x44271)),f328(f267(a877,a877,f885(a877,a871)),f328(f328(f7(a877,f885(a877,a871),f885(a877,f885(a877,a871))),f328(f328(f8(f885(a877,f885(f885(a877,a871),f885(a877,a871))),f885(f885(a877,a871),f885(a877,f885(a877,a871))),a877),f7(a877,f885(a877,a871),f885(a877,a871))),f328(f328(f8(f885(a877,a877),f885(a877,f885(f885(a877,a871),f885(a877,a871))),a877),f328(f8(a877,f885(f885(a877,a871),f885(a877,a871)),a877),f306(a877))),f22(a877)))),f193(f885(a877,a871)))))),f328(a110,x44271))
% 81.29/80.90 [4563]~P24(f328(f328(f92(a1),a84),f328(f328(f22(a1),f328(f328(f81(a1),x45631),x45631)),a103)))
% 81.29/80.90 [3904]E(f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),x39041),x39041)),a103)),a103),f328(f328(f81(a1),x39041),x39041))
% 81.29/80.90 [3955]E(f328(f328(f22(a1),f328(f328(f22(a1),f328(f328(f81(a1),x39551),x39551)),a103)),a103),f328(f328(f81(a1),f328(f328(f22(a1),x39551),a103)),f328(f328(f22(a1),x39551),a103)))
% 81.29/80.90 [4173]E(f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f81(a1),f328(f80(a1),x41731)),a103)),f328(f328(f81(a1),f328(f80(a1),x41731)),a103))),a103),f328(f80(a1),f328(f328(f22(a1),f328(f328(f81(a1),x41731),x41731)),a103)))
% 81.29/80.90 [4571]~P24(f328(f328(f92(a1),f328(f328(f22(a1),f328(f328(f81(a1),x45711),x45711)),a103)),a84))
% 81.29/80.90 [4216]E(f328(f328(f81(a877),x42161),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f328(a118,f328(a118,x42161)))
% 81.29/80.90 [4217]E(f328(f328(f82(a877),x42171),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f328(f328(f81(a877),x42171),x42171))
% 81.29/80.90 [4218]E(f328(f328(f39(a877),f328(f328(f81(a877),x42181),x42181)),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x42181)
% 81.29/80.90 [4300]E(f45(a877,f328(a118,f328(a118,x43001)),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f45(a877,x43001,f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))
% 81.29/80.90 [4442]E(f328(a90,f328(f328(f43(f884(a877,a877),f885(f884(a877,a877),a871)),f328(a112,x44421)),f328(f267(a877,a877,f885(f884(a877,a877),a871)),f328(f328(f8(f885(a877,f885(f884(a877,a877),a871)),f885(a877,f885(f884(a877,a877),a871)),a877),f328(f8(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871),a877),f282(f884(a877,a877),f884(a877,a877),a114))),f328(f328(f7(a877,f885(f884(a877,a877),a871),f885(a877,f885(f884(a877,a877),a871))),f328(f328(f8(f885(a877,f885(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f885(f885(f884(a877,a877),a871),f885(a877,f885(f884(a877,a877),a871))),a877),f7(a877,f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f328(f328(f8(f885(a877,f884(a877,a877)),f885(a877,f885(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),a877),f328(f8(f884(a877,a877),f885(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),a877),f306(f884(a877,a877)))),f328(f7(a877,a877,f884(a877,a877)),f257(a877,a877))))),f193(f885(f884(a877,a877),a871))))))),f328(f80(a1),x44421))
% 81.29/80.90 [4295]E(f328(f328(f81(a877),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x42951),f328(a118,f328(a118,x42951)))
% 81.29/80.90 [4296]E(f328(f328(f82(a877),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x42961),f328(f328(f81(a877),x42961),x42961))
% 81.29/80.90 [4330]E(f328(f328(f39(a877),f328(a118,f328(a118,x43301))),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f328(a118,f328(f328(f39(a877),x43301),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))))
% 81.29/80.90 [4384]E(f328(f328(f81(a877),f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),a103))),x43841),f328(a118,f328(a118,f328(a118,x43841))))
% 81.29/80.90 [4450]E(f328(f267(a1,a1,f884(a1,a1)),f328(f328(f18(a1,f885(a1,f884(a1,a1)),f885(a1,f884(a1,a1))),f328(f328(f8(f885(a1,f885(f884(a1,a1),f884(a1,a1))),f885(f885(a1,f884(a1,a1)),f885(a1,f884(a1,a1))),a1),f18(a1,f884(a1,a1),f884(a1,a1))),f328(f328(f8(f885(a1,f884(a1,a1)),f885(a1,f885(f884(a1,a1),f884(a1,a1))),a1),f328(f18(a1,f884(a1,a1),f885(f884(a1,a1),f884(a1,a1))),f328(f328(f8(a871,f885(f884(a1,a1),f885(f884(a1,a1),f884(a1,a1))),a1),f102(f884(a1,a1))),f328(f328(f8(a1,a871,a1),f328(f244(a1),f2(a1))),f328(f328(f7(a1,a1,a1),f22(a1)),x44501))))),f328(f328(f7(a1,f885(a1,a1),f885(a1,f884(a1,a1))),f328(f328(f8(f885(a1,f884(a1,a1)),f885(f885(a1,a1),f885(a1,f884(a1,a1))),a1),f8(a1,f884(a1,a1),a1)),f328(f328(f8(a1,f885(a1,f884(a1,a1)),a1),f257(a1,a1)),f328(f328(f7(a1,a1,a1),f328(f328(f8(a1,f885(a1,a1),a1),f81(a1)),f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))),f79(a1))))),f328(f328(f7(a1,a1,a1),f22(a1)),x44501))))),f328(f328(f8(a1,f885(a1,f884(a1,a1)),a1),f257(a1,a1)),f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))))),f44(x44501))
% 81.29/80.90 [3133]P95(f883(x31331,x31332))
% 81.29/80.90 [3134]P95(f884(x31341,x31342))
% 81.29/80.90 [3135]P104(f883(x31351,x31352))
% 81.29/80.90 [3136]P104(f884(x31361,x31362))
% 81.29/80.90 [3153]P29(a1,f178(x31531,x31532))
% 81.29/80.90 [3154]P38(x31541,f152(x31541,x31542))
% 81.29/80.90 [3218]P32(x32181,x32182,f119(x32181))
% 81.29/80.90 [3251]P48(x32511,x32512,f254(x32511,x32512))
% 81.29/80.90 [3252]P52(x32521,x32521,f254(x32521,x32522))
% 81.29/80.90 [3527]P21(x35271,x35271,f5(x35271),x35272)
% 81.29/80.90 [3528]P21(x35281,x35281,f35(x35281),x35282)
% 81.29/80.90 [3536]P33(x35361,x35362,f119(x35361),f119(x35361))
% 81.29/80.90 [3537]P21(x35371,f881(x35371),f236(x35371),x35372)
% 81.29/80.90 [3546]P21(f878(x35461),f878(x35461),f168(x35461),x35462)
% 81.29/80.90 [4461]~E(f34(x44611,x44612),a24)
% 81.29/80.90 [4462]~E(f33(x44621,x44622),a24)
% 81.29/80.90 [4494]~P34(x44941,x44942,f119(x44941))
% 81.29/80.90 [4495]~P36(x44951,x44952,f119(x44951))
% 81.29/80.90 [3115]E(f328(f5(x31151),x31152),x31152)
% 81.29/80.90 [3116]E(f328(f249(x31161),x31162),x31162)
% 81.29/80.90 [3118]E(f328(f35(x31181),x31182),x31182)
% 81.29/80.90 [3128]E(f328(f197(x31281),x31282),f121(x31281))
% 81.29/80.90 [3151]E(f91(x31511,f328(a325,x31512)),x31512)
% 81.29/80.90 [3152]E(f86(x31521,f328(a325,x31522)),x31522)
% 81.29/80.90 [3173]E(f328(f135(x31731,x31732),f119(x31731)),f119(x31731))
% 81.29/80.90 [3192]E(f151(x31921,f151(x31921,x31922)),f151(x31921,x31922))
% 81.29/80.90 [3193]E(f304(x31931,f304(x31931,x31932)),f304(x31931,x31932))
% 81.29/80.90 [3213]E(f328(f328(f127(x32131),x32132),f119(x32131)),x32132)
% 81.29/80.90 [3219]E(f172(x32191,x32192,f119(x32191)),x32192)
% 81.29/80.90 [3220]E(f172(x32201,f119(x32201),x32202),x32202)
% 81.29/80.90 [3226]E(f328(f328(f174(x32261),x32262),f119(x32261)),f119(x32261))
% 81.29/80.90 [3227]E(f328(f328(f137(x32271),x32272),f119(x32271)),f119(x32271))
% 81.29/80.90 [3229]E(f237(x32291,x32292,f196(x32291)),f2(a877))
% 81.29/80.90 [3230]E(f154(x32301,x32302,f119(x32301)),f2(a877))
% 81.29/80.90 [3232]E(f169(x32321,x32322,f119(x32321)),f119(x32321))
% 81.29/80.90 [3233]E(f176(x32331,x32332,f119(x32331)),f119(x32331))
% 81.29/80.90 [3234]E(f175(x32341,f119(x32341),x32342),f119(x32341))
% 81.29/80.90 [3238]E(f328(f171(x32381),f151(x32381,x32382)),f328(f171(x32381),x32382))
% 81.29/80.90 [3241]E(f328(f253(x32411,x32411),f254(x32411,x32412)),x32412)
% 81.29/80.90 [3242]E(f328(f255(x32421,x32421),f254(x32421,x32422)),x32422)
% 81.29/80.90 [3250]E(f328(f283(x32501,x32501),f254(x32501,x32502)),f254(x32501,x32502))
% 81.29/80.90 [3265]E(f304(f878(x32651),f156(x32651,x32652)),f157(x32651,f304(x32651,x32652)))
% 81.29/80.90 [3267]P24(f328(f136(a1),f178(x32671,x32672)))
% 81.29/80.90 [3275]E(f328(f253(x32751,x32751),f304(x32751,x32752)),f252(f885(x32751,a871)))
% 81.29/80.90 [3276]E(f328(f255(x32761,x32761),f304(x32761,x32762)),f252(f885(x32761,a871)))
% 81.29/80.90 [3280]P24(f328(f136(x32801),f151(x32801,x32802)))
% 81.29/80.90 [3282]P24(f328(f159(x32821,x32822),f119(x32821)))
% 81.29/80.90 [3290]E(f328(f171(a1),f178(x32901,x32902)),f299(a1,x32901,x32902))
% 81.29/80.90 [3305]P53(x33051,f193(f885(x33051,a871)),x33052)
% 81.29/80.90 [3310]E(f328(f266(a1,a1),f46(x33101,x33102)),f45(a1,x33101,x33102))
% 81.29/80.90 [3311]E(f328(f298(a877,x33111),f328(a118,x33112)),f299(a877,x33111,x33112))
% 81.29/80.90 [3329]E(f328(f328(f150(x33291),x33292),f119(x33291)),f139(x33291,x33292,f119(x33291)))
% 81.29/80.90 [3342]E(f299(a877,f328(a118,x33421),x33422),f301(a877,x33421,x33422))
% 81.29/80.90 [3345]P48(x33451,f252(f885(x33451,a871)),f304(x33451,x33452))
% 81.29/80.90 [3406]E(f328(f328(f22(a877),x34061),f328(a118,x34062)),f328(f38(a877),f302(a877,x34062,x34061)))
% 81.29/80.90 [3465]E(f166(x34651,x34652,f119(x34651)),f328(f328(f257(f878(x34651),f878(x34651)),f119(x34651)),f119(x34651)))
% 81.29/80.90 [3484]E(f328(f267(x34841,x34842,f884(x34841,x34842)),f257(x34841,x34842)),f35(f884(x34841,x34842)))
% 81.29/80.90 [3489]P24(f328(f328(f330(f878(x34891)),f119(x34891)),f160(x34891,x34892)))
% 81.29/80.90 [3490]E(f328(f194(f878(x34901)),f120(x34901,x34902)),f328(f328(f22(a877),f328(f194(f878(x34901)),x34902)),f79(a877)))
% 81.29/80.90 [3497]P24(f328(f62(a877),f302(a877,x34971,x34972)))
% 81.29/80.90 [3498]P24(f328(f62(a877),f301(a877,x34981,x34982)))
% 81.29/80.90 [3499]P24(f328(f62(a877),f299(a877,x34991,x34992)))
% 81.29/80.90 [3500]P24(f328(f62(a1),f302(a1,x35001,x35002)))
% 81.29/80.90 [3501]P24(f328(f62(a1),f301(a1,x35011,x35012)))
% 81.29/80.90 [3502]P24(f328(f62(a1),f299(a1,x35021,x35022)))
% 81.29/80.90 [3604]E(f328(f307(a877,a877,a118),f299(a877,x36041,x36042)),f299(a877,f328(a118,x36041),f328(a118,x36042)))
% 81.29/80.90 [3624]E(f328(f328(f285(x36241,x36241,x36241),f304(x36241,x36242)),f304(x36241,x36242)),f304(x36241,x36242))
% 81.29/80.90 [3657]E(f328(f328(f257(a1,a1),f328(f328(f39(a1),x36571),x36572)),f45(a1,x36571,x36572)),f46(x36571,x36572))
% 81.29/80.90 [3658]E(f328(f328(f257(a105,a105),f328(f328(f39(a105),x36581),x36582)),f45(a105,x36581,x36582)),f21(x36581,x36582))
% 81.29/80.90 [3687]E(f328(f328(f257(a877,a877),f328(f328(f39(a877),x36871),x36872)),f45(a877,x36871,x36872)),f86(f884(a877,a877),f48(x36871,x36872)))
% 81.29/80.90 [3738]P24(f328(f328(f245(a877),f328(f328(f22(a877),x37381),x37382)),f328(a118,x37381)))
% 81.29/80.90 [3836]E(f328(f328(f81(a1),f328(f328(f82(a1),x38361),f328(f328(f39(a1),x38362),x38361))),f45(a1,x38362,x38361)),x38362)
% 81.29/80.90 [3840]E(f328(f328(f43(a877,f885(f884(f878(x38401),f878(x38401)),a871)),f252(f885(a877,a871))),f142(x38401,x38402)),f144(x38401,x38402))
% 81.29/80.90 [4067]P24(f328(f328(f330(f884(f878(x40671),f878(x40671))),f328(f328(f257(f878(x40671),f878(x40671)),f119(x40671)),f119(x40671))),f157(x40671,x40672)))
% 81.29/80.90 [4229]E(f268(x42291,x42291,x42292,x42292,f5(x42291),f5(x42292)),f35(f884(x42291,x42292)))
% 81.29/80.90 [4231]E(f268(x42311,x42311,x42312,x42312,f35(x42311),f35(x42312)),f35(f884(x42311,x42312)))
% 81.29/80.90 [4470]~E(f328(f236(x44701),x44702),f196(x44701))
% 81.29/80.90 [4482]~P39(x44821,f328(f236(x44821),x44822))
% 81.29/80.90 [3211]E(f328(f240(x32111),f328(f236(x32111),x32112)),x32112)
% 81.29/80.90 [3212]E(f328(f168(x32121),f328(f168(x32121),x32122)),x32122)
% 81.29/80.90 [3214]E(f328(f328(f137(x32141),f2(a877)),x32142),x32142)
% 81.29/80.90 [3228]E(f328(f328(f174(x32281),f2(a877)),x32282),f119(x32281))
% 81.29/80.90 [3236]E(f328(f328(f127(x32361),f119(x32361)),x32362),x32362)
% 81.29/80.90 [3244]E(f328(f194(f881(x32441)),f328(f236(x32441),x32442)),f2(a877))
% 81.29/80.90 [3246]E(f40(f885(x32461,a871),f328(f305(x32461),x32462)),x32462)
% 81.29/80.90 [3248]E(f328(f171(x32481),f328(f167(x32481),x32482)),f328(f171(x32481),x32482))
% 81.29/80.90 [3249]E(f328(f171(x32491),f328(f168(x32491),x32492)),f328(f171(x32491),x32492))
% 81.29/80.90 [3254]E(f328(f328(f22(a105),x32541),x32542),f328(f328(a23,x32541),x32542))
% 81.29/80.90 [3269]E(f328(f328(f81(a877),x32691),x32692),f328(f328(f81(a877),x32692),x32691))
% 81.29/80.90 [3270]E(f328(f328(f81(a1),x32701),x32702),f328(f328(f81(a1),x32702),x32701))
% 81.29/80.90 [3271]E(f328(f328(f82(a877),x32711),x32712),f328(f328(f82(a877),x32712),x32711))
% 81.29/80.90 [3272]E(f328(f328(f82(a1),x32721),x32722),f328(f328(f82(a1),x32722),x32721))
% 81.29/80.90 [3297]E(f328(f328(f188(x32971,x32971),f2(a877)),x32972),f35(x32971))
% 81.29/80.90 [3298]E(f328(f194(f878(x32981)),f328(f167(x32981),x32982)),f328(f194(f878(x32981)),x32982))
% 81.29/80.90 [3299]E(f328(f194(f878(x32991)),f328(f168(x32991),x32992)),f328(f194(f878(x32991)),x32992))
% 81.29/80.90 [3300]E(f175(x33001,x33002,f193(f885(a877,a871))),f119(x33001))
% 81.29/80.90 [3301]E(f328(f328(f153(x33011,x33011),f5(x33011)),x33012),x33012)
% 81.29/80.90 [3303]E(f328(f256(a1,a1),f46(x33031,x33032)),f328(f328(f39(a1),x33031),x33032))
% 81.29/80.90 [3322]E(f328(f194(f878(x33221)),f151(x33221,x33222)),f328(f38(x33221),f328(f171(x33221),x33222)))
% 81.29/80.90 [3323]E(f32(f33(x33231,x33232)),f328(f328(f81(a877),f32(x33232)),f328(a118,f2(a877))))
% 81.29/80.90 [3324]E(f328(f281(x33241),f328(f283(x33241,x33241),x33242)),f328(f281(x33241),x33242))
% 81.29/80.90 [3328]P24(f328(f62(x33281),f328(f171(x33281),x33282)))
% 81.29/80.90 [3336]E(f328(f328(f81(a1),x33361),f328(f80(a1),x33362)),f328(f328(f22(a1),x33361),x33362))
% 81.29/80.90 [3344]P20(x33441,x33442,f193(f885(f876(x33441),a871)))
% 81.29/80.90 [3346]E(f328(f307(x33461,x33461,f5(x33461)),x33462),x33462)
% 81.29/80.90 [3347]E(f328(f307(x33471,x33471,f35(x33471)),x33472),x33472)
% 81.29/80.90 [3348]E(f328(f308(x33481,x33481,f5(x33481)),x33482),x33482)
% 81.29/80.90 [3349]E(f328(f308(x33491,x33491,f35(x33491)),x33492),x33492)
% 81.29/80.90 [3350]P24(f328(f252(f885(x33501,a871)),x33502))
% 81.29/80.90 [3352]E(f328(f38(a877),f328(f298(a877,x33521),x33522)),f328(f328(f22(a877),x33522),x33521))
% 81.29/80.90 [3353]E(f328(f298(a877,f328(a118,x33531)),x33532),f302(a877,x33531,x33532))
% 81.29/80.90 [3365]E(f328(f328(f306(x33651),x33652),f193(f885(x33651,a871))),f328(f249(x33651),f328(a325,x33652)))
% 81.29/80.90 [3369]E(f328(f328(f306(x33691),x33692),f193(f885(x33691,a871))),f235(x33691,f328(f236(x33691),x33692)))
% 81.29/80.90 [3372]E(f304(x33721,f328(f283(x33721,x33721),x33722)),f328(f283(x33721,x33721),f304(x33721,x33722)))
% 81.29/80.90 [3376]E(f328(f328(f81(a877),f328(a118,x33761)),x33762),f328(f328(f81(a877),x33761),f328(a118,x33762)))
% 81.29/80.90 [3377]E(f328(f328(f22(a877),f328(a118,x33771)),f328(a118,x33772)),f328(f328(f22(a877),x33771),x33772))
% 81.29/80.90 [3382]E(f55(x33821,f2(a877),x33822),f328(f328(f150(f878(x33821)),f119(x33821)),f119(f878(x33821))))
% 81.29/80.90 [3383]E(f328(f38(a877),f301(a877,x33831,x33832)),f328(f328(f22(a877),x33832),x33831))
% 81.29/80.90 [3392]P38(x33921,f328(f328(f284(a877,x33921),a248),x33922))
% 81.29/80.90 [3394]P29(a877,f138(a877,f328(f298(a877,x33941),x33942)))
% 81.29/80.90 [3396]P24(f328(f62(a877),f328(f298(a877,x33961),x33962)))
% 81.29/80.90 [3397]P24(f328(f62(a1),f328(f298(a1,x33971),x33972)))
% 81.29/80.90 [3399]E(f328(f283(f878(x33991),f878(x33991)),f156(x33991,x33992)),f156(x33991,f328(f283(x33991,x33991),x33992)))
% 81.29/80.90 [3400]E(f328(f194(a873),f33(x34001,x34002)),f328(f328(f81(a877),f328(f194(a873),x34002)),f328(a118,f2(a877))))
% 81.29/80.90 [3402]E(f328(f298(a1,x34021),f328(f328(f81(a1),x34022),f79(a1))),f299(a1,x34021,x34022))
% 81.29/80.90 [3405]E(f328(f328(f39(a1),f328(f80(a1),x34051)),f328(f80(a1),x34052)),f328(f328(f39(a1),x34051),x34052))
% 81.29/80.90 [3413]E(f183(x34131,x34132,f328(f16(f881(x34132),x34131),f196(x34132))),f193(f885(x34131,a871)))
% 81.29/80.90 [3414]E(f185(x34141,x34142,f328(f16(f881(x34142),x34141),f196(x34142))),f193(f885(x34142,a871)))
% 81.29/80.90 [3415]E(f328(f328(f188(f884(x34151,x34151),a871),f79(a877)),x34152),x34152)
% 81.29/80.90 [3417]E(f328(f328(f22(f885(x34171,a871)),x34172),f193(f885(x34171,a871))),x34172)
% 81.29/80.90 [3418]E(f328(f328(f116(f885(x34181,a871)),x34182),f193(f885(x34181,a871))),x34182)
% 81.29/80.90 [3419]E(f328(f328(f107(f885(x34191,a871)),x34192),f252(f885(x34191,a871))),x34192)
% 81.29/80.90 [3420]E(f328(f256(a877,a877),f86(f884(a877,a877),f48(x34201,x34202))),f328(f328(f39(a877),x34201),x34202))
% 81.29/80.90 [3427]E(f310(x34271,f328(a20,x34272),f328(f80(a1),f328(a20,x34272))),f328(f328(f313(a1),x34271),x34272))
% 81.29/80.90 [3428]E(f299(a1,f328(f328(f81(a1),x34281),f79(a1)),x34282),f301(a1,x34281,x34282))
% 81.29/80.90 [3433]E(f328(f266(a877,a877),f86(f884(a877,a877),f48(x34331,x34332))),f45(a877,x34331,x34332))
% 81.29/80.90 [3441]E(f311(x34411,f328(a20,x34412),f328(f80(a1),f328(a20,x34412))),f312(a1,x34411,x34412))
% 81.29/80.90 [3444]P24(f328(f328(f330(x34441),x34442),f252(f885(x34441,a871))))
% 81.29/80.90 [3449]E(f328(f328(f22(a877),f328(a118,x34491)),x34492),f328(f38(a877),f299(a877,x34492,x34491)))
% 81.29/80.90 [3476]E(f328(f328(f22(f885(x34761,a871)),x34762),f252(f885(x34761,a871))),f193(f885(x34761,a871)))
% 81.29/80.90 [3477]E(f328(f328(f116(f885(x34771,a871)),x34772),f252(f885(x34771,a871))),f252(f885(x34771,a871)))
% 81.29/80.90 [3478]E(f328(f328(f107(f885(x34781,a871)),x34782),f193(f885(x34781,a871))),f193(f885(x34781,a871)))
% 81.29/80.90 [3492]E(f45(a1,f328(f106(a1),x34921),f328(f106(a1),x34922)),f328(f106(a1),f45(a877,x34921,x34922)))
% 81.29/80.90 [3493]E(f45(a1,f328(f80(a1),x34931),f328(f80(a1),x34932)),f328(f80(a1),f45(a1,x34931,x34932)))
% 81.29/80.90 [3504]E(f328(f194(f878(x35041)),f328(f170(x35041),x35042)),f328(f328(f22(a877),f328(f194(f878(x35041)),x35042)),f79(a877)))
% 81.29/80.90 [3529]E(f328(f328(f39(a1),f45(a1,x35291,x35292)),x35292),f2(a1))
% 81.29/80.90 [3539]E(f328(a3,f45(a877,f328(a19,x35391),f328(a19,x35392))),f45(a105,x35391,x35392))
% 81.29/80.90 [3573]E(f328(a3,f328(f328(f22(a877),f328(a19,x35731)),f328(a19,x35732))),f328(f328(f22(a105),x35731),x35732))
% 81.29/80.90 [3574]E(f328(a3,f328(f328(f81(a877),f328(a19,x35741)),f328(a19,x35742))),f328(f328(f81(a105),x35741),x35742))
% 81.29/80.90 [3575]E(f328(a3,f328(f328(f82(a877),f328(a19,x35751)),f328(a19,x35752))),f328(f328(f82(a105),x35751),x35752))
% 81.29/80.90 [3576]E(f328(a3,f328(f328(f39(a877),f328(a19,x35761)),f328(a19,x35762))),f328(f328(f39(a105),x35761),x35762))
% 81.29/80.90 [3585]E(f328(f307(a877,a877,a118),f328(f298(a877,x35851),x35852)),f328(f298(a877,f328(a118,x35851)),f328(a118,x35852)))
% 81.29/80.90 [3609]P24(f328(f48(x36091,x36092),f86(f884(a877,a877),f48(x36091,x36092))))
% 81.29/80.90 [3630]E(f328(f328(f81(a877),f328(f328(f81(a877),f32(x36301)),f32(x36302))),f328(a118,f2(a877))),f32(f34(x36301,x36302)))
% 81.29/80.90 [3631]E(f45(a877,f328(a118,f45(a877,x36311,x36312)),x36312),f45(a877,f328(a118,x36311),x36312))
% 81.29/80.90 [3645]E(f328(f328(f43(f885(x36451,a871),f885(x36451,a871)),x36452),f5(f885(x36451,a871))),f40(f885(x36451,a871),x36452))
% 81.29/80.90 [3646]E(f328(f328(f42(f885(x36461,a871),f885(x36461,a871)),x36462),f5(f885(x36461,a871))),f41(f885(x36461,a871),x36462))
% 81.29/80.90 [3647]E(f328(f307(f878(x36471),f885(x36471,a871),f171(x36471)),f328(f171(f878(x36471)),f54(x36471,x36472))),f328(f305(x36471),f328(f171(x36471),x36472)))
% 81.29/80.90 [3650]P24(f328(f328(f330(f885(x36501,a871)),x36502),f328(f305(x36501),x36502)))
% 81.29/80.90 [3656]E(f45(a1,f328(f80(a1),f45(a1,x36561,x36562)),x36562),f45(a1,f328(f80(a1),x36561),x36562))
% 81.29/80.90 [3668]P24(f328(f328(f244(f885(x36681,a871)),x36682),f252(f885(x36681,a871))))
% 81.29/80.90 [3670]E(f328(f328(f285(x36701,x36701,x36701),f304(x36701,x36702)),f304(x36701,f304(x36701,x36702))),f304(x36701,x36702))
% 81.29/80.90 [3671]E(f328(f328(f116(f885(x36711,a871)),f328(f255(x36711,x36711),x36712)),f328(f253(x36711,x36711),x36712)),f328(f281(x36711),x36712))
% 81.29/80.90 [3692]E(f315(x36921,x36922,f252(f885(x36921,a871)),f252(f885(x36922,a871))),f252(f885(f883(x36921,x36922),a871)))
% 81.29/80.90 [3743]P24(f328(f328(f244(a877),f45(a877,x37431,x37432)),x37431))
% 81.29/80.90 [3765]P24(f328(f328(f244(a1),f328(f80(a1),f328(f106(a1),x37651))),f328(f106(a1),x37652)))
% 81.29/80.90 [3791]P24(f328(f328(f330(f885(x37911,a871)),f193(f885(x37911,a871))),f328(f305(x37911),x37912)))
% 81.29/80.90 [3796]E(f304(x37961,f328(f328(f285(x37961,x37961,x37961),x37962),f304(x37961,x37962))),f304(x37961,x37962))
% 81.29/80.90 [3799]E(f328(f328(f285(x37991,x37991,x37991),f304(x37991,x37992)),x37992),f328(f328(f285(x37991,x37991,x37991),x37992),f304(x37991,x37992)))
% 81.29/80.90 [3801]E(f328(a110,f328(f328(f81(a1),f328(f328(f22(a1),x38011),x38012)),f79(a1))),f328(f38(a1),f299(a1,x38012,x38011)))
% 81.29/80.90 [3816]E(f328(f253(x38161,x38161),f328(f328(f285(x38161,x38161,x38161),x38162),f304(x38161,x38162))),f328(f253(x38161,x38161),x38162))
% 81.29/80.90 [3817]E(f328(f255(x38171,x38171),f328(f328(f285(x38171,x38171,x38171),x38172),f304(x38171,x38172))),f328(f255(x38171,x38171),x38172))
% 81.29/80.90 [3833]E(f328(f328(f81(a877),f328(f328(f81(a877),f328(f194(a873),x38331)),f328(f194(a873),x38332))),f328(a118,f2(a877))),f328(f194(a873),f34(x38331,x38332)))
% 81.29/80.90 [3844]P21(a877,a877,f328(f328(f7(a877,a877,a877),f81(a877)),x38441),x38442)
% 81.29/80.90 [3846]P29(a877,f328(f168(a877),f328(f328(f153(f878(x38461),a877),f194(f878(x38461))),f179(x38461,x38462))))
% 81.29/80.90 [3891]P24(f328(f328(f245(a1),f328(f80(a1),f328(f106(a1),f328(a118,x38911)))),f328(f106(a1),x38912)))
% 81.29/80.90 [3936]E(f328(f141(f878(x39361),x39361,f328(f7(x39361,f878(x39361),f878(x39361)),f150(x39361)),f119(x39361)),x39362),f328(f168(x39361),x39362))
% 81.29/80.90 [3988]P24(f328(f328(f244(f885(f884(f878(x39881),f878(x39881)),a871)),f157(x39881,x39882)),f304(f878(x39881),f156(x39881,x39882))))
% 81.29/80.90 [4020]P24(f328(f48(x40201,x40202),f328(f328(f257(a877,a877),f328(f328(f39(a877),x40201),x40202)),f45(a877,x40201,x40202))))
% 81.29/80.90 [4031]P24(f328(f328(f244(f885(f884(f878(x40311),f878(x40311)),a871)),f156(x40311,f304(x40311,x40312))),f304(f878(x40311),f156(x40311,x40312))))
% 81.29/80.90 [4255]E(f328(f328(f269(f884(a105,a105),a105,f884(a105,a105),f884(x42551,f884(a105,a105))),f273(f328(f165(a105),f328(f328(f153(f884(a105,x42551),a105),f256(a105,x42551)),x42552)))),f328(f328(f8(x42551,f885(f884(a105,a105),f884(x42551,f884(a105,a105))),a105),f257(x42551,f884(a105,a105))),f274(x42551,x42552))),f272(x42551,x42552))
% 81.29/80.90 [4366]E(f328(f238(a877,f884(x43661,f879(x43661)),f2(a877),f328(f267(x43661,f879(x43661),a877),f328(f16(f885(f879(x43661),a877),x43661),f328(f328(f7(f879(x43661),a877,a877),f328(f328(f8(a877,f885(a877,a877),f879(x43661)),f81(a877)),f194(f879(x43661)))),f79(a877))))),f328(f134(x43661),x43662)),f328(f194(f879(x43661)),x43662))
% 81.29/80.90 [4441]E(f328(f267(f885(f884(x44411,x44411),a871),f885(f884(x44411,x44411),a871),f885(f885(x44412,x44411),f884(f885(f884(x44412,x44412),a871),f885(f884(x44412,x44412),a871)))),f328(f328(f7(f885(f884(x44411,x44411),a871),f885(f885(f884(x44411,x44411),a871),f885(f885(x44412,x44411),f885(f884(x44412,x44412),a871))),f885(f885(f884(x44411,x44411),a871),f885(f885(x44412,x44411),f884(f885(f884(x44412,x44412),a871),f885(f884(x44412,x44412),a871))))),f328(f328(f8(f885(f885(f885(x44412,x44411),f885(f884(x44412,x44412),a871)),f885(f885(x44412,x44411),f884(f885(f884(x44412,x44412),a871),f885(f884(x44412,x44412),a871)))),f885(f885(f885(f884(x44411,x44411),a871),f885(f885(x44412,x44411),f885(f884(x44412,x44412),a871))),f885(f885(f884(x44411,x44411),a871),f885(f885(x44412,x44411),f884(f885(f884(x44412,x44412),a871),f885(f884(x44412,x44412),a871))))),f885(f884(x44411,x44411),a871)),f8(f885(f885(x44412,x44411),f885(f884(x44412,x44412),a871)),f885(f885(x44412,x44411),f884(f885(f884(x44412,x44412),a871),f885(f884(x44412,x44412),a871))),f885(f884(x44411,x44411),a871))),f328(f328(f8(f885(f885(x44412,x44411),f885(f885(f884(x44412,x44412),a871),f884(f885(f884(x44412,x44412),a871),f885(f884(x44412,x44412),a871)))),f885(f885(f885(x44412,x44411),f885(f884(x44412,x44412),a871)),f885(f885(x44412,x44411),f884(f885(f884(x44412,x44412),a871),f885(f884(x44412,x44412),a871)))),f885(f884(x44411,x44411),a871)),f18(f885(x44412,x44411),f885(f884(x44412,x44412),a871),f884(f885(f884(x44412,x44412),a871),f885(f884(x44412,x44412),a871)))),f328(f328(f8(f885(f885(x44412,x44411),f885(f884(x44412,x44412),a871)),f885(f885(x44412,x44411),f885(f885(f884(x44412,x44412),a871),f884(f885(f884(x44412,x44412),a871),f885(f884(x44412,x44412),a871)))),f885(f884(x44411,x44411),a871)),f328(f8(f885(f884(x44412,x44412),a871),f885(f885(f884(x44412,x44412),a871),f884(f885(f884(x44412,x44412),a871),f885(f884(x44412,x44412),a871))),f885(x44412,x44411)),f257(f885(f884(x44412,x44412),a871),f885(f884(x44412,x44412),a871)))),f284(x44411,x44412))))),f284(x44411,x44412))),f75(x44411,x44412))
% 81.29/80.90 [4526]~E(f328(f305(x45261),x45262),f193(f885(f885(x45261,a871),a871)))
% 81.29/80.90 [4544]~P24(f328(f328(f330(x45441),x45442),f193(f885(x45441,a871))))
% 81.29/80.90 [4554]~P24(f328(f328(f245(f885(x45541,a871)),x45542),f193(f885(x45541,a871))))
% 81.29/80.90 [3355]E(f328(f328(f22(a877),x33551),f328(f328(f81(a877),x33551),x33552)),f2(a877))
% 81.29/80.90 [3357]E(f328(f328(f116(f885(x33571,a871)),x33572),x33572),x33572)
% 81.29/80.90 [3358]E(f328(f328(f107(f885(x33581,a871)),x33582),x33582),x33582)
% 81.29/80.90 [3385]E(f328(f328(f22(f885(x33851,a871)),x33852),x33852),f193(f885(x33851,a871)))
% 81.29/80.90 [3388]E(f328(f142(x33881,x33882),f2(a877)),f193(f885(f884(f878(x33881),f878(x33881)),a871)))
% 81.29/80.90 [3389]E(f328(f328(f81(a877),x33891),f328(a118,x33892)),f328(a118,f328(f328(f81(a877),x33891),x33892)))
% 81.29/80.90 [3401]E(f201(f328(f106(a1),x34011),f328(f106(a1),x34012)),f328(f106(a1),f328(f328(f22(a877),x34011),x34012)))
% 81.29/80.90 [3404]E(f328(f328(f39(a1),f328(f80(a1),x34041)),x34042),f328(f328(f39(a1),x34041),f328(f80(a1),x34042)))
% 81.29/80.90 [3408]E(f328(f38(a1),f328(f298(a1,x34081),x34082)),f328(a110,f328(f328(f22(a1),x34082),x34081)))
% 81.29/80.90 [3411]E(f328(f328(f81(a877),f328(a118,x34111)),x34112),f328(a118,f328(f328(f81(a877),x34111),x34112)))
% 81.29/80.90 [3416]E(f328(f80(f885(x34161,a871)),f328(f80(f885(x34161,a871)),x34162)),x34162)
% 81.29/80.90 [3430]E(f179(x34301,f328(f328(f150(f878(x34301)),f119(x34301)),x34302)),f179(x34301,x34302))
% 81.29/80.90 [3434]E(f328(f328(f81(a877),x34341),f328(f328(f82(a877),x34341),x34342)),f328(f328(f82(a877),x34341),f328(a118,x34342)))
% 81.29/80.90 [3442]E(f328(f328(a23,f328(a3,x34421)),f328(a3,x34422)),f328(a3,f328(f328(f22(a877),x34421),x34422)))
% 81.29/80.90 [3456]E(f328(f328(f82(a1),f328(f80(a1),x34561)),x34562),f328(f80(a1),f328(f328(f82(a1),x34561),x34562)))
% 81.29/80.90 [3458]E(f328(f328(f258(a1),f328(f106(a1),x34581)),x34582),f328(f106(a1),f328(f328(f258(a877),x34581),x34582)))
% 81.29/80.90 [3459]E(f328(f328(f81(a105),f328(a3,x34591)),f328(a3,x34592)),f328(a3,f328(f328(f81(a877),x34591),x34592)))
% 81.29/80.90 [3460]E(f328(f328(f82(a105),f328(a3,x34601)),f328(a3,x34602)),f328(a3,f328(f328(f82(a877),x34601),x34602)))
% 81.29/80.90 [3461]E(f328(f328(f242(a877),f328(a118,x34611)),f328(a118,x34612)),f328(a118,f328(f328(f242(a877),x34611),x34612)))
% 81.29/80.90 [3462]E(f328(f328(f243(a877),f328(a118,x34621)),f328(a118,x34622)),f328(a118,f328(f328(f243(a877),x34621),x34622)))
% 81.29/80.90 [3468]E(f328(f171(a877),f138(a877,f328(f298(a877,x34681),x34682))),f328(f298(a877,x34681),x34682))
% 81.29/80.90 [3469]E(f309(x34691,f328(f328(f306(x34691),x34692),f193(f885(x34691,a871)))),x34692)
% 81.29/80.90 [3474]E(f328(f253(x34741,x34742),f193(f885(f884(x34741,x34742),a871))),f193(f885(x34742,a871)))
% 81.29/80.90 [3475]E(f328(f255(x34751,x34752),f193(f885(f884(x34751,x34752),a871))),f193(f885(x34751,a871)))
% 81.29/80.90 [3479]E(f328(a110,f328(f328(f22(a1),x34791),x34792)),f328(f38(a1),f301(a1,x34792,x34791)))
% 81.29/80.90 [3483]E(f328(f328(f81(a877),x34831),f328(f328(f82(a877),x34832),x34831)),f328(f328(f82(a877),f328(a118,x34832)),x34831))
% 81.29/80.90 [3485]E(f328(f328(f61(x34851),f193(f885(x34851,a871))),x34852),f193(f885(f885(x34851,a871),a871)))
% 81.29/80.90 [3494]E(f328(f194(f878(a877)),f138(a877,f328(f298(a877,x34941),x34942))),f328(f328(f22(a877),x34942),x34941))
% 81.29/80.90 [3509]E(f328(f328(f116(f885(x35091,a871)),f193(f885(x35091,a871))),x35092),x35092)
% 81.29/80.90 [3510]E(f328(f328(f107(f885(x35101,a871)),f252(f885(x35101,a871))),x35102),x35102)
% 81.29/80.90 [3513]E(f328(f328(f81(a1),f328(f80(a1),x35131)),f328(f80(a1),x35132)),f328(f80(a1),f328(f328(f81(a1),x35131),x35132)))
% 81.29/80.90 [3515]E(f328(f328(f81(a1),f328(f109(a1),x35151)),f328(f109(a1),x35152)),f328(f109(a1),f328(f328(f81(a1),x35151),x35152)))
% 81.29/80.90 [3517]E(f328(f328(f81(a1),f328(f106(a1),x35171)),f328(f106(a1),x35172)),f328(f106(a1),f328(f328(f81(a877),x35171),x35172)))
% 81.29/80.90 [3518]E(f328(f328(f82(a1),f328(f109(a1),x35181)),f328(f109(a1),x35182)),f328(f109(a1),f328(f328(f82(a1),x35181),x35182)))
% 81.29/80.90 [3520]E(f328(f328(f82(a1),f328(f106(a1),x35201)),f328(f106(a1),x35202)),f328(f106(a1),f328(f328(f82(a877),x35201),x35202)))
% 81.29/80.90 [3521]E(f328(f328(f39(a1),f328(f106(a1),x35211)),f328(f106(a1),x35212)),f328(f106(a1),f328(f328(f39(a877),x35211),x35212)))
% 81.29/80.90 [3540]E(f328(f328(f6(x35401,a877),f328(f16(a877,x35401),f79(a877))),x35402),f328(f38(x35401),x35402))
% 81.29/80.90 [3547]E(f328(f80(a1),f45(a1,f328(f80(a1),x35471),x35472)),f45(a1,x35471,f328(f80(a1),x35472)))
% 81.29/80.90 [3549]E(f328(f171(a1),f178(x35491,f328(f328(f22(a1),x35492),f79(a1)))),f328(f298(a1,x35491),x35492))
% 81.29/80.90 [3553]P24(f328(f328(f244(a877),x35531),f328(f328(f81(a877),x35532),x35531)))
% 81.29/80.90 [3554]P24(f328(f328(f244(a877),x35541),f328(f328(f81(a877),x35541),x35542)))
% 81.29/80.90 [3557]E(f328(f328(f22(f885(x35571,a871)),f193(f885(x35571,a871))),x35572),f193(f885(x35571,a871)))
% 81.29/80.90 [3558]E(f328(f328(f116(f885(x35581,a871)),f252(f885(x35581,a871))),x35582),f252(f885(x35581,a871)))
% 81.29/80.90 [3559]E(f328(f328(f107(f885(x35591,a871)),f193(f885(x35591,a871))),x35592),f193(f885(x35591,a871)))
% 81.29/80.90 [3564]E(f328(f328(f257(a1,a1),x35641),f328(f80(a1),x35642)),f328(a51,f328(f328(f257(a1,a1),x35641),x35642)))
% 81.29/80.90 [3565]E(f328(f298(a1,f328(f328(f81(a1),x35651),f79(a1))),x35652),f302(a1,x35651,x35652))
% 81.29/80.90 [3577]E(f328(f328(f82(a877),x35771),f328(f328(f39(a877),x35772),x35771)),f328(f328(f22(a877),x35772),f45(a877,x35772,x35771)))
% 81.29/80.90 [3578]E(f328(f328(f82(a1),x35781),f328(f328(f39(a1),x35782),x35781)),f328(f328(f22(a1),x35782),f45(a1,x35782,x35781)))
% 81.29/80.90 [3582]E(f328(f171(a1),f178(f328(f328(f81(a1),x35821),f79(a1)),x35822)),f301(a1,x35821,x35822))
% 81.29/80.90 [3586]P24(f328(f328(f244(f885(x35861,a871)),x35862),x35862))
% 81.29/80.90 [3589]E(f328(f328(f116(f885(x35891,a871)),x35892),f328(f80(f885(x35891,a871)),x35892)),f252(f885(x35891,a871)))
% 81.29/80.90 [3590]E(f328(f328(f107(f885(x35901,a871)),x35902),f328(f80(f885(x35901,a871)),x35902)),f193(f885(x35901,a871)))
% 81.29/80.90 [3596]E(f328(f328(f22(a877),f328(f328(f22(a877),x35961),f79(a877))),x35962),f328(f328(f22(a877),x35961),f328(a118,x35962)))
% 81.29/80.90 [3601]E(f328(f328(f22(f885(x36011,a871)),f252(f885(x36011,a871))),x36012),f328(f80(f885(x36011,a871)),x36012))
% 81.29/80.90 [3602]E(f328(f328(f22(a1),f328(f109(a1),x36021)),f328(f109(a1),x36022)),f328(f109(a1),f328(f328(f81(a1),x36021),f328(f80(a1),x36022))))
% 81.29/80.90 [3614]E(f328(f171(a877),f138(a877,f328(f298(a877,x36141),f328(a118,x36142)))),f299(a877,x36141,x36142))
% 81.29/80.90 [3622]P24(f328(f328(f328(f328(a202,a24),x36221),x36222),x36221))
% 81.29/80.90 [3628]E(f328(f194(f878(f878(x36281))),f54(x36281,x36282)),f328(f328(f258(a877),f328(a118,f328(a118,f2(a877)))),f328(f194(f878(x36281)),x36282)))
% 81.29/80.90 [3648]E(f328(f328(f188(f884(x36481,x36481),a871),f2(a877)),x36482),f304(x36481,f193(f885(f884(x36481,x36481),a871))))
% 81.29/80.90 [3652]P24(f328(f136(a877),f138(a877,f328(f298(a877,x36521),x36522))))
% 81.29/80.90 [3669]E(f328(f307(a1,a877,a110),f299(a1,f328(f106(a1),x36691),f328(f106(a1),x36692))),f299(a877,x36691,x36692))
% 81.29/80.90 [3679]E(f190(a877,f2(a877),f5(a877),f328(f328(f22(a877),x36791),x36792)),f328(f328(f22(a877),x36791),f328(a118,x36792)))
% 81.29/80.90 [3680]E(f328(a110,f328(f328(f22(a1),x36801),f328(f328(f81(a1),x36802),f79(a1)))),f328(f38(a1),f302(a1,x36802,x36801)))
% 81.29/80.90 [3716]E(f328(f328(f153(a877,a877),a118),f138(a877,f328(f298(a877,x37161),x37162))),f138(a877,f328(f298(a877,f328(a118,x37161)),f328(a118,x37162))))
% 81.29/80.90 [3723]E(f328(f171(a1),f178(f328(f328(f81(a1),x37231),f79(a1)),f328(f328(f22(a1),x37232),f79(a1)))),f302(a1,x37231,x37232))
% 81.29/80.90 [3734]P24(f328(f328(f244(f885(x37341,a871)),f193(f885(x37341,a871))),x37342))
% 81.29/80.90 [3739]E(f91(x37391,f328(f328(f7(x37391,x37391,a871),a325),x37392)),x37392)
% 81.29/80.90 [3740]E(f86(x37401,f328(f328(f7(x37401,x37401,a871),a325),x37402)),x37402)
% 81.29/80.90 [3744]E(f328(f171(a877),f138(a877,f328(f298(a877,f328(a118,x37441)),f328(a118,x37442)))),f301(a877,x37441,x37442))
% 81.29/80.90 [3768]E(f328(f328(f265(x37681,x37682),f252(f885(x37681,a871))),f328(f16(f885(x37682,a871),x37681),f252(f885(x37682,a871)))),f252(f885(f884(x37681,x37682),a871)))
% 81.29/80.90 [3803]E(f328(f249(x38031),f328(f328(f8(a871,a871,x38031),a323),x38032)),f328(f80(f885(x38031,a871)),f328(f249(x38031),x38032)))
% 81.29/80.90 [3806]E(f328(f249(x38061),f328(f328(f7(x38061,x38061,a871),a325),x38062)),f328(f328(f306(x38061),x38062),f193(f885(x38061,a871))))
% 81.29/80.90 [3813]E(f328(f328(f81(a1),f328(f328(f22(a1),x38131),x38132)),f328(f328(f22(a1),x38131),x38132)),f328(f328(f22(a1),f328(f328(f81(a1),x38131),x38131)),f328(f328(f81(a1),x38132),x38132)))
% 81.29/80.90 [3814]E(f328(f328(f81(a1),f328(f328(f81(a1),x38141),x38141)),f328(f328(f81(a1),x38142),x38142)),f328(f328(f81(a1),f328(f328(f81(a1),x38141),x38142)),f328(f328(f81(a1),x38141),x38142)))
% 81.29/80.90 [3830]P24(f328(f328(f244(a877),f328(f38(x38301),f328(f171(x38301),x38302))),f328(f194(f878(x38301)),x38302)))
% 81.29/80.90 [3831]P24(f328(f328(f244(a877),f328(f194(f878(x38311)),f151(x38311,x38312))),f328(f194(f878(x38311)),x38312)))
% 81.29/80.90 [3841]E(f328(f249(x38411),f328(f328(f7(x38411,f885(x38411,a871),a871),f330(x38411)),x38412)),x38412)
% 81.29/80.90 [3856]E(f328(f328(f174(x38561),f328(f328(f22(a877),f328(f194(f878(x38561)),x38562)),f79(a877))),x38562),f120(x38561,x38562))
% 81.29/80.90 [3878]E(f190(a877,f2(a877),f328(f328(f8(a877,a877,a877),a118),f328(f242(a877),x38781)),x38782),f328(f328(f242(a877),f328(a118,x38781)),x38782))
% 81.29/80.90 [3882]E(f40(f885(x38821,a871),f328(f307(f885(f884(x38821,x38821),a871),f885(x38821,a871),f281(x38821)),x38822)),f328(f281(x38821),f40(f885(f884(x38821,x38821),a871),x38822)))
% 81.29/80.90 [3883]E(f190(a877,f328(a118,x38831),f328(f328(f8(a877,a877,a877),a118),f328(f243(a877),x38831)),x38832),f328(f328(f243(a877),f328(a118,x38831)),x38832))
% 81.29/80.90 [3885]E(f328(f328(f257(a1,a1),f328(f328(f39(a1),f328(f76(a1),x38851)),f328(f76(a1),x38852))),f45(a1,f328(f76(a1),x38851),f328(f76(a1),x38852))),f53(x38851,x38852))
% 81.29/80.90 [3907]P24(f328(f328(f244(f885(f885(x39071,a871),a871)),x39072),f328(f305(x39071),f40(f885(x39071,a871),x39072))))
% 81.29/80.90 [3941]E(f328(f328(f43(x39411,f885(x39411,a871)),x39412),f328(f328(f7(x39411,f885(x39411,a871),f885(x39411,a871)),f306(x39411)),f193(f885(x39411,a871)))),x39412)
% 81.29/80.90 [3942]E(f328(f328(f285(x39421,x39421,x39421),f328(f283(x39421,x39421),x39422)),f304(x39421,f328(f283(x39421,x39421),x39422))),f328(f283(x39421,x39421),f328(f328(f285(x39421,x39421,x39421),x39422),f304(x39421,x39422))))
% 81.29/80.90 [4011]E(f328(f171(x40111),f328(f141(f878(x40111),f878(x40111),f127(x40111),f119(x40111)),x40112)),f328(f328(f43(f878(x40111),f885(x40111,a871)),f328(f171(f878(x40111)),x40112)),f171(x40111)))
% 81.29/80.90 [4043]E(f328(f328(f116(f885(f884(x40431,x40431),a871)),f304(x40431,f193(f885(f884(x40431,x40431),a871)))),f328(f328(f285(x40431,x40431,x40431),f304(x40431,x40432)),x40432)),f304(x40431,x40432))
% 81.29/80.90 [4077]E(f328(f328(f181(x40771,x40771),x40772),x40772),f328(f328(f153(x40771,f884(x40771,x40771)),f328(f328(f18(x40771,x40771,f884(x40771,x40771)),f257(x40771,x40771)),f5(x40771))),x40772))
% 81.29/80.90 [4192]E(f328(f141(a877,f878(x41921),f328(f7(f878(x41921),a877,a877),f328(f328(f8(a877,f885(a877,a877),f878(x41921)),f243(a877)),f194(f878(x41921)))),f2(a877)),f328(f168(f878(x41921)),x41922)),f328(f194(f878(f878(x41921))),f179(x41921,x41922)))
% 81.29/80.90 [4270]E(f328(f328(f284(f884(a877,f878(x42701)),f878(x42701)),f320(a877,f878(x42701),a248,f144(x42701,x42702))),f328(f328(f18(f878(x42701),f878(x42701),f884(a877,f878(x42701))),f328(f328(f8(a877,f885(f878(x42701),f884(a877,f878(x42701))),f878(x42701)),f257(a877,f878(x42701))),f194(f878(x42701)))),f5(f878(x42701)))),f145(x42701,x42702))
% 81.29/80.90 [4400]E(f328(f249(x44001),f328(f328(f8(f885(f885(x44001,a871),a871),a871,x44001),f89(f885(x44001,a871))),f328(f328(f8(f885(f885(x44001,a871),a871),f885(f885(x44001,a871),a871),x44001),f328(f18(f885(x44001,a871),a871,a871),f328(f328(f8(a871,f885(a871,a871),f885(x44001,a871)),a331),f328(f328(f7(f885(x44001,a871),f885(f885(x44001,a871),a871),a871),f330(f885(x44001,a871))),x44002)))),f330(x44001)))),f41(f885(x44001,a871),x44002))
% 81.29/80.90 [4555]~P24(f328(f328(f245(a1),f328(f106(a1),x45551)),f328(f80(a1),f328(f106(a1),x45552))))
% 81.29/80.90 [4572]~P24(f328(f328(f92(a1),f328(f328(f22(a1),f328(f328(f81(a1),x45721),x45721)),a103)),f328(f328(f81(a1),x45722),x45722)))
% 81.29/80.90 [3481]E(f328(f328(f22(a877),f328(f328(f81(a877),x34811),x34812)),x34812),x34811)
% 81.29/80.90 [3482]E(f328(f328(f22(a877),f328(f328(f81(a877),x34821),x34822)),x34821),x34822)
% 81.29/80.90 [3548]E(f328(f328(f81(a877),f328(f328(f22(a877),x35481),x35482)),x35482),f328(f328(f243(a877),x35481),x35482))
% 81.29/80.90 [3655]E(f328(f328(f82(a877),f328(f328(f39(a877),x36551),x36552)),x36552),f328(f328(f22(a877),x36551),f45(a877,x36551,x36552)))
% 81.29/80.90 [3684]E(f328(f171(a877),f138(a877,f328(f298(a877,f328(a118,x36841)),x36842))),f302(a877,x36841,x36842))
% 81.29/80.90 [3691]E(f328(f106(a1),f224(f328(a110,f328(f76(a1),x36911)),f328(a110,f328(f76(a1),x36912)))),f328(f328(a225,x36911),x36912))
% 81.29/80.90 [3693]E(f328(f328(f116(f885(x36931,a871)),f328(f80(f885(x36931,a871)),x36932)),x36932),f252(f885(x36931,a871)))
% 81.29/80.90 [3694]E(f328(f328(f107(f885(x36941,a871)),f328(f80(f885(x36941,a871)),x36942)),x36942),f193(f885(x36941,a871)))
% 81.29/80.90 [3712]P24(f328(f328(f244(a877),f328(f328(f22(a877),x37121),x37122)),x37121))
% 81.29/80.90 [3713]P24(f328(f328(f244(a877),f328(f328(f39(a877),x37131),x37132)),x37131))
% 81.29/80.90 [3736]P24(f328(f328(f245(a877),x37361),f328(a118,f328(f328(f81(a877),x37362),x37361))))
% 81.29/80.90 [3737]P24(f328(f328(f245(a877),x37371),f328(a118,f328(f328(f81(a877),x37371),x37372))))
% 81.29/80.90 [3754]E(f328(f328(f82(a877),f328(a110,f328(f76(a1),x37541))),f328(a110,f328(f76(a1),x37542))),f328(a110,f328(f76(a1),f328(f328(f82(a1),x37541),x37542))))
% 81.29/80.90 [3764]P24(f328(f328(f244(a1),f2(a1)),f328(f328(f258(a1),f328(f76(a1),x37641)),x37642)))
% 81.29/80.90 [3835]E(f328(f282(f878(x38351),f878(x38351),f157(x38351,x38352)),f328(f328(f306(f878(x38351)),f119(x38351)),f193(f885(f878(x38351),a871)))),f328(f328(f306(f878(x38351)),f119(x38351)),f193(f885(f878(x38351),a871))))
% 81.29/80.90 [3854]E(f328(f328(f116(f885(f884(x38541,x38541),a871)),f304(x38541,x38542)),f304(x38541,f193(f885(f884(x38541,x38541),a871)))),f304(x38541,x38542))
% 81.29/80.90 [3868]E(f328(f328(f39(a1),f328(f109(a1),f328(f328(f81(a1),x38681),x38681))),f328(f109(a1),f328(f328(f81(a1),x38682),x38682))),f328(f328(f39(a1),f328(f109(a1),x38681)),f328(f109(a1),x38682)))
% 81.29/80.90 [3931]E(f328(f328(f258(a1),x39311),f328(f109(a877),f328(f328(f81(a1),x39312),x39312))),f328(f328(f87(a1,a1),f328(f328(f258(a1),x39311),f328(f109(a877),x39312))),f328(f328(f18(a1,a1,a1),f82(a1)),f5(a1))))
% 81.29/80.90 [3937]E(f328(f249(f885(x39371,a871)),f328(f328(f7(f885(x39371,a871),f885(x39371,a871),a871),f244(f885(x39371,a871))),x39372)),f328(f305(x39371),x39372))
% 81.29/80.90 [3952]E(f328(f328(f153(a1,a877),a110),f328(f328(f127(a1),f328(f328(f153(a877,a1),f106(a1)),x39521)),f328(f328(f153(a877,a1),f106(a1)),x39522))),f328(f328(f127(a877),x39521),x39522))
% 81.29/80.90 [3987]E(f328(f307(a1,a1,f328(f328(f7(a1,a1,a1),f81(a1)),x39871)),f328(f298(a1,f2(a1)),f328(f328(f22(a1),x39872),x39871))),f328(f298(a1,x39871),x39872))
% 81.29/80.90 [3989]P49(x39891,f328(f328(f22(f885(f884(x39891,x39891),a871)),x39892),f304(x39891,f193(f885(f884(x39891,x39891),a871)))))
% 81.29/80.90 [4009]E(f328(f194(f878(x40091)),f328(f141(f878(x40091),f878(x40091),f127(x40091),f119(x40091)),x40092)),f328(f165(a877),f328(f328(f153(f878(x40091),a877),f194(f878(x40091))),x40092)))
% 81.29/80.90 [4014]P48(x40141,f252(f885(x40141,a871)),f328(f328(f116(f885(f884(x40141,x40141),a871)),x40142),f304(x40141,f193(f885(f884(x40141,x40141),a871)))))
% 81.29/80.90 [4057]E(f190(a877,f2(a877),f328(f328(f8(a877,a877,a877),a118),f328(f328(f7(a877,a877,a877),f242(a877)),x40571)),x40572),f328(f328(f242(a877),x40572),f328(a118,x40571)))
% 81.29/80.90 [4060]E(f190(a877,f328(a118,x40601),f328(f328(f8(a877,a877,a877),a118),f328(f328(f7(a877,a877,a877),f243(a877)),x40601)),x40602),f328(f328(f243(a877),x40602),f328(a118,x40601)))
% 81.29/80.90 [4063]E(f328(f307(x40631,f878(x40631),f328(f328(f7(x40631,f878(x40631),f878(x40631)),f150(x40631)),f119(x40631))),x40632),f173(x40631,x40632,f328(f328(f306(f878(x40631)),f119(x40631)),f193(f885(f878(x40631),a871)))))
% 81.29/80.90 [4064]E(f328(f328(f116(f885(f884(x40641,x40641),a871)),f328(f328(f285(x40641,x40641,x40641),x40642),f304(x40641,x40642))),f304(x40641,f193(f885(f884(x40641,x40641),a871)))),f304(x40641,x40642))
% 81.29/80.90 [4072]P24(f328(f328(f244(f885(f884(x40721,x40721),a871)),f254(x40721,x40722)),f328(f328(f265(x40721,x40721),x40722),f328(f16(f885(x40721,a871),x40721),x40722))))
% 81.29/80.90 [4075]E(f328(f307(a1,a877,a110),f328(f328(f116(f885(a1,a871)),f328(f307(a877,a1,f106(a1)),x40751)),f328(f307(a877,a1,f106(a1)),x40752))),f328(f328(f116(f885(a877,a871)),x40751),x40752))
% 81.29/80.90 [4076]E(f328(f307(a1,a877,a110),f328(f328(f107(f885(a1,a871)),f328(f307(a877,a1,f106(a1)),x40761)),f328(f307(a877,a1,f106(a1)),x40762))),f328(f328(f107(f885(a877,a871)),x40761),x40762))
% 81.29/80.90 [4080]E(f328(f249(x40801),f328(f328(f8(a871,a871,x40801),a323),f328(f328(f7(x40801,f885(x40801,a871),a871),f330(x40801)),x40802))),f328(f80(f885(x40801,a871)),x40802))
% 81.29/80.90 [4107]E(f328(f141(f878(x41071),f878(x41071),f127(x41071),f119(x41071)),f328(f328(f153(f878(x41071),f878(x41071)),f168(x41071)),f328(f168(f878(x41071)),x41072))),f328(f168(x41071),f328(f141(f878(x41071),f878(x41071),f127(x41071),f119(x41071)),x41072)))
% 81.29/80.90 [4136]E(f328(f328(f43(a877,f885(f884(x41361,x41361),a871)),f252(f885(a877,a871))),f328(f328(f7(a877,f885(f884(x41361,x41361),a871),f885(f884(x41361,x41361),a871)),f188(f884(x41361,x41361),a871)),x41362)),f304(x41361,x41362))
% 81.29/80.90 [4156]E(f86(x41561,f328(f328(f8(f885(x41561,a871),a871,x41561),f328(a325,x41562)),f328(f328(f7(x41561,f885(x41561,a871),f885(x41561,a871)),f306(x41561)),f193(f885(x41561,a871))))),f309(x41561,x41562))
% 81.29/80.90 [4164]E(f328(f194(f878(x41641)),f151(x41641,f328(f141(f878(x41641),f878(x41641),f127(x41641),f119(x41641)),x41642))),f328(f38(x41641),f328(f328(f43(f878(x41641),f885(x41641,a871)),f328(f171(f878(x41641)),x41642)),f171(x41641))))
% 81.29/80.90 [4180]E(f328(f328(f116(f885(f884(x41801,x41801),a871)),x41802),f328(f328(f285(x41801,x41801,x41801),f328(f328(f285(x41801,x41801,x41801),x41802),f304(x41801,x41802))),x41802)),f328(f328(f285(x41801,x41801,x41801),x41802),f304(x41801,x41802)))
% 81.29/80.90 [4202]P24(f328(f328(f244(f885(f884(x42021,x42021),a871)),f328(f328(f285(x42021,x42021,x42021),x42022),f304(x42021,x42022))),f328(f328(f265(x42021,x42021),f328(f281(x42021),x42022)),f328(f16(f885(x42021,a871),x42021),f328(f281(x42021),x42022)))))
% 81.29/80.90 [4245]E(f328(f249(f878(x42451)),f328(f328(f7(f878(x42451),f885(x42451,a871),a871),f328(f328(f8(f885(x42451,a871),f885(f885(x42451,a871),a871),f878(x42451)),f244(f885(x42451,a871))),f171(x42451))),x42452)),f160(x42451,x42452))
% 81.29/80.90 [4257]E(f328(f155(f878(x42571),x42571,f119(x42571),f328(f328(f8(f878(x42571),f885(f878(x42571),f878(x42571)),x42571),f328(f7(f878(x42571),f878(x42571),f878(x42571)),f127(x42571))),f328(f328(f7(x42571,f878(x42571),f878(x42571)),f150(x42571)),f119(x42571)))),x42572),f328(f167(x42571),x42572))
% 81.29/80.90 [4299]P21(f885(x42991,x42992),f885(f884(x42991,x42992),a871),f328(f328(f8(f885(f884(x42991,x42992),a871),f885(f884(x42991,x42992),a871),f885(x42991,x42992)),f249(f884(x42991,x42992))),f328(f328(f8(f885(x42991,f885(x42992,a871)),f885(f884(x42991,x42992),a871),f885(x42991,x42992)),f267(x42991,x42992,a871)),f328(f8(x42992,f885(x42992,a871),x42991),f328(f7(x42992,x42992,a871),a325)))),f252(f885(f885(x42991,x42992),a871)))
% 81.29/80.90 [4304]E(f45(a1,f328(f109(a1),f328(f328(f81(a1),x43041),x43041)),f328(f109(a1),f328(f328(f81(a1),x43042),x43042))),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f45(a1,f328(f109(a1),x43041),f328(f109(a1),x43042))))
% 81.29/80.90 [4347]E(f328(f328(f43(x43471,f885(f884(x43471,x43471),a871)),x43472),f328(f328(f7(x43471,f885(f884(x43471,x43471),a871),f885(f884(x43471,x43471),a871)),f328(f328(f8(f884(x43471,x43471),f885(f885(f884(x43471,x43471),a871),f885(f884(x43471,x43471),a871)),x43471),f306(f884(x43471,x43471))),f328(f328(f18(x43471,x43471,f884(x43471,x43471)),f257(x43471,x43471)),f5(x43471)))),f193(f885(f884(x43471,x43471),a871)))),f254(x43471,x43472))
% 81.29/80.90 [4355]E(f211(x43551,f328(f328(f257(a1,a1),f328(f80(a1),f328(f328(f74(f884(a1,a1),a1,x43551,f256(a1,a1)),f220(x43551)),x43552))),f328(f328(f74(f884(a1,a1),a1,x43551,f266(a1,a1)),f220(x43551)),x43552))),f228(x43551,x43552))
% 81.29/80.90 [4436]E(f328(f249(f885(x44361,a871)),f328(f328(f8(f885(f885(x44361,a871),a871),a871,f885(x44361,a871)),f88(f885(x44361,a871))),f328(f328(f7(f885(x44361,a871),f885(f885(x44361,a871),a871),f885(f885(x44361,a871),a871)),f328(f328(f8(f885(f885(x44361,a871),f885(a871,a871)),f885(f885(f885(x44361,a871),a871),f885(f885(x44361,a871),a871)),f885(x44361,a871)),f18(f885(x44361,a871),a871,a871)),f328(f328(f8(f885(f885(x44361,a871),a871),f885(f885(x44361,a871),f885(a871,a871)),f885(x44361,a871)),f328(f8(a871,f885(a871,a871),f885(x44361,a871)),a326)),f328(f328(f7(f885(x44361,a871),f885(f885(x44361,a871),f885(x44361,a871)),f885(f885(x44361,a871),a871)),f328(f328(f8(f885(f885(x44361,a871),a871),f885(f885(f885(x44361,a871),f885(x44361,a871)),f885(f885(x44361,a871),a871)),f885(x44361,a871)),f8(f885(x44361,a871),a871,f885(x44361,a871))),a325)),f80(f885(x44361,a871)))))),f328(f328(f8(f885(f885(x44361,a871),a871),a871,f885(x44361,a871)),f328(f330(f885(x44361,a871)),x44362)),f305(x44361))))),f328(f305(x44361),f328(f80(f885(x44361,a871)),x44362)))
% 81.29/80.90 [4552]~E(f328(f328(f81(a1),x45521),x45521),f328(f328(f22(a1),f328(f328(f81(a1),x45522),x45522)),a103))
% 81.29/80.90 [4558]~P24(f328(f328(f245(a877),f328(f328(f81(a877),x45581),x45582)),x45582))
% 81.29/80.90 [4559]~P24(f328(f328(f245(a877),f328(f328(f81(a877),x45591),x45592)),x45591))
% 81.29/80.90 [3769]E(f328(f328(f22(a877),x37691),f328(f328(f82(a877),f328(f328(f39(a877),x37691),x37692)),x37692)),f45(a877,x37691,x37692))
% 81.29/80.90 [3770]E(f328(f328(f22(a1),x37701),f328(f328(f82(a1),f328(f328(f39(a1),x37701),x37702)),x37702)),f45(a1,x37701,x37702))
% 81.29/80.90 [3804]E(f328(f328(f153(a877,x38041),f328(f164(x38041),x38042)),f138(a877,f328(f298(a877,f2(a877)),f328(f194(f878(x38041)),x38042)))),x38042)
% 81.29/80.90 [3864]E(f328(f282(x38641,x38641,f304(x38641,f193(f885(f884(x38641,x38641),a871)))),x38642),x38642)
% 81.29/80.90 [3992]E(f304(x39921,f328(f328(f22(f885(f884(x39921,x39921),a871)),x39922),f304(x39921,f193(f885(f884(x39921,x39921),a871))))),f304(x39921,x39922))
% 81.29/80.90 [3993]E(f304(x39931,f328(f328(f116(f885(f884(x39931,x39931),a871)),x39932),f304(x39931,f193(f885(f884(x39931,x39931),a871))))),f304(x39931,x39932))
% 81.29/80.90 [4046]E(f328(f328(f22(a1),f328(f328(f22(a1),f328(f328(f81(a1),x40461),x40461)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),x40462),x40462)),a103)),f328(f328(f81(a1),f328(f328(f22(a1),x40461),x40462)),f328(f328(f22(a1),x40461),x40462)))
% 81.29/80.90 [4085]E(f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f81(a1),x40851),x40852)),f328(f328(f81(a1),x40851),x40852))),a103),f328(f328(f81(a1),f328(f328(f81(a1),x40851),x40851)),f328(f328(f22(a1),f328(f328(f81(a1),x40852),x40852)),a103)))
% 81.29/80.90 [4111]E(f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),x41111),x41111)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),x41112),x41112)),a103)),f328(f328(f81(a1),f328(f328(f81(a1),x41111),f328(f328(f22(a1),x41112),a103))),f328(f328(f81(a1),x41111),f328(f328(f22(a1),x41112),a103))))
% 81.29/80.90 [4121]E(f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),x41211),x41212)),f328(f328(f22(a1),x41211),x41212))),a103),f328(f328(f22(a1),f328(f328(f22(a1),f328(f328(f81(a1),x41211),x41211)),a103)),f328(f328(f81(a1),x41212),x41212)))
% 81.29/80.90 [4122]E(f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f81(a1),x41221),x41222)),f328(f328(f81(a1),x41221),x41222))),a103),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),x41221),x41221)),a103)),f328(f328(f81(a1),x41222),x41222)))
% 81.29/80.90 [4177]E(f328(f106(a1),f328(f328(f39(a877),f328(f328(f82(a877),f328(a110,f328(f76(a1),x41771))),f328(a110,f328(f76(a1),x41772)))),f224(f328(a110,f328(f76(a1),x41771)),f328(a110,f328(f76(a1),x41772))))),f226(x41771,x41772))
% 81.29/80.90 [4222]E(f328(f328(f269(f884(a105,a105),a105,f884(a105,a105),f884(x42221,f884(a105,a105))),f273(f328(a3,f328(f194(f878(x42221)),x42222)))),f328(f328(f8(x42221,f885(f884(a105,a105),f884(x42221,f884(a105,a105))),a105),f257(x42221,f884(a105,a105))),f328(f328(f8(a877,x42221,a105),f328(f164(x42221),x42222)),a19))),f279(x42221,x42222))
% 81.29/80.90 [4305]E(f328(f141(a877,f878(x43051),f328(f7(f878(x43051),a877,a877),f328(f328(f8(a877,f885(a877,a877),f878(x43051)),f243(a877)),f194(f878(x43051)))),f2(a877)),f328(f168(f878(x43051)),f179(x43051,x43052))),f328(f194(f878(f878(x43051))),f328(f135(f878(x43051),f328(f328(f8(a871,a871,f878(x43051)),a323),f328(f328(f7(f878(x43051),f878(x43051),a871),a325),f119(x43051)))),x43052)))
% 81.29/80.90 [4311]E(f328(f328(f43(a877,f885(x43111,a871)),f252(f885(a877,a871))),f328(f328(f7(a877,f885(a877,f885(x43111,a871)),f885(x43111,a871)),f328(f328(f8(f885(a877,a871),f885(f885(a877,f885(x43111,a871)),f885(x43111,a871)),a877),f43(a877,f885(x43111,a871))),f298(a877,f2(a877)))),x43112)),f328(f328(f43(a877,f885(x43111,a871)),f252(f885(a877,a871))),x43112))
% 81.29/80.90 [4331]P24(f328(f62(a877),f328(f249(a877),f328(f328(f18(a877,a871,a871),f328(f328(f8(a871,f885(a871,a871),a877),a326),x43311)),f328(f328(f7(a877,a877,a871),f245(a877)),x43312)))))
% 81.29/80.90 [4447]E(f328(f249(f884(f878(x44471),f878(x44471))),f328(f267(f878(x44471),f878(x44471),a871),f328(f328(f18(f878(x44471),f885(f878(x44471),a871),f885(f878(x44471),a871)),f328(f328(f8(f885(f878(x44471),f885(a871,a871)),f885(f885(f878(x44471),a871),f885(f878(x44471),a871)),f878(x44471)),f18(f878(x44471),a871,a871)),f328(f328(f8(f885(f878(x44471),a871),f885(f878(x44471),f885(a871,a871)),f878(x44471)),f328(f8(a871,f885(a871,a871),f878(x44471)),a327)),f328(f328(f7(f878(x44471),f885(f878(x44471),a877),f885(f878(x44471),a871)),f328(f328(f8(f885(a877,a871),f885(f885(f878(x44471),a877),f885(f878(x44471),a871)),f878(x44471)),f8(a877,a871,f878(x44471))),f328(f328(f8(a877,f885(a877,a871),f878(x44471)),f245(a877)),f194(f878(x44471))))),f194(f878(x44471)))))),f328(f328(f18(f878(x44471),f885(f878(x44471),a871),f885(f878(x44471),a871)),f328(f328(f8(f885(f878(x44471),f885(a871,a871)),f885(f885(f878(x44471),a871),f885(f878(x44471),a871)),f878(x44471)),f18(f878(x44471),a871,a871)),f328(f328(f8(f885(f878(x44471),a871),f885(f878(x44471),f885(a871,a871)),f878(x44471)),f328(f8(a871,f885(a871,a871),f878(x44471)),a326)),f328(f328(f7(f878(x44471),f885(f878(x44471),a877),f885(f878(x44471),a871)),f328(f328(f8(f885(a877,a871),f885(f885(f878(x44471),a877),f885(f878(x44471),a871)),f878(x44471)),f8(a877,a871,f878(x44471))),f328(f328(f8(a877,f885(a877,a871),f878(x44471)),a325),f194(f878(x44471))))),f194(f878(x44471)))))),f328(f328(f7(f878(x44471),f885(f884(f878(x44471),f878(x44471)),a871),f885(f878(x44471),a871)),f328(f328(f8(f885(f878(x44471),f885(f885(f884(f878(x44471),f878(x44471)),a871),a871)),f885(f885(f884(f878(x44471),f878(x44471)),a871),f885(f878(x44471),a871)),f878(x44471)),f7(f878(x44471),f885(f884(f878(x44471),f878(x44471)),a871),a871)),f328(f328(f8(f885(f878(x44471),f884(f878(x44471),f878(x44471))),f885(f878(x44471),f885(f885(f884(f878(x44471),f878(x44471)),a871),a871)),f878(x44471)),f328(f8(f884(f878(x44471),f878(x44471)),f885(f885(f884(f878(x44471),f878(x44471)),a871),a871),f878(x44471)),f330(f884(f878(x44471),f878(x44471))))),f257(f878(x44471),f878(x44471))))),f144(x44471,x44472)))))),f145(x44471,x44472))
% 81.29/80.90 [4565]~P24(f328(f328(f92(a1),f328(f328(f81(a1),x45651),x45651)),f328(f328(f22(a1),f328(f328(f81(a1),x45652),x45652)),a103)))
% 81.29/80.90 [4114]E(f328(f328(f81(a1),f328(f328(f81(a1),f328(f328(f82(a1),x41141),x41142)),f328(f328(f82(a1),x41141),x41142))),x41142),f328(f328(f82(a1),f328(f328(f22(a1),f328(f328(f81(a1),x41141),x41141)),a103)),x41142))
% 81.29/80.90 [4220]E(f328(a110,f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x42201),x42202)),f193(f885(f884(a877,a877),a871)))))),f328(f328(f22(a877),x42201),x42202))
% 81.29/80.90 [4225]E(f328(f328(f285(x42251,x42251,x42251),f328(f328(f116(f885(f884(x42251,x42251),a871)),x42252),f304(x42251,f193(f885(f884(x42251,x42251),a871))))),f304(x42251,f328(f328(f116(f885(f884(x42251,x42251),a871)),x42252),f304(x42251,f193(f885(f884(x42251,x42251),a871)))))),f304(x42251,x42252))
% 81.29/80.90 [4263]E(f272(x42631,f328(f135(f884(a105,x42631),f328(f267(a105,x42631,a871),f328(f328(f8(a871,f885(x42631,a871),a105),f16(a871,x42631)),f328(f245(a105),f2(a105))))),x42632)),f272(x42631,x42632))
% 81.29/80.90 [4264]E(f274(x42641,f328(f135(f884(a105,x42641),f328(f267(a105,x42641,a871),f328(f328(f8(a871,f885(x42641,a871),a105),f16(a871,x42641)),f328(f245(a105),f2(a105))))),x42642)),f274(x42641,x42642))
% 81.29/80.90 [4266]E(f328(f80(a1),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x42661),x42662)),f193(f885(f884(a877,a877),a871)))))),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x42662),x42661)),f193(f885(f884(a877,a877),a871))))))
% 81.29/80.90 [4323]E(f328(f328(f284(f878(a877),x43231),f144(a877,a248)),f328(f328(f7(x43231,f878(f885(x43231,a877)),f878(a877)),f328(f328(f8(f885(f885(x43231,a877),a877),f885(f878(f885(x43231,a877)),f878(a877)),x43231),f153(f885(x43231,a877),a877)),f328(f7(f885(x43231,a877),x43231,a877),f5(f885(x43231,a877))))),x43232)),f152(x43231,x43232))
% 81.29/80.90 [4344]E(f328(f328(f87(a1,a877),f328(f109(a1),f328(f328(f81(a1),x43441),a103))),f328(f328(f18(a1,a877,a877),f328(f328(f7(a1,a877,f885(a877,a877)),f328(f328(f8(a871,f885(a877,f885(a877,a877)),a1),f102(a877)),a199)),f2(a877))),f328(f328(f8(a877,a877,a1),a118),f328(f328(f8(a877,a877,a1),f328(f242(a877),x43442)),a110)))),f328(f328(f242(a877),f328(a118,x43442)),f328(f109(a877),x43441)))
% 81.29/80.90 [4345]E(f328(f328(f87(a1,a877),f328(f109(a1),f328(f328(f81(a1),x43451),a103))),f328(f328(f18(a1,a877,a877),f328(f328(f7(a1,a877,f885(a877,a877)),f328(f328(f8(a871,f885(a877,f885(a877,a877)),a1),f102(a877)),a199)),f328(a118,x43452))),f328(f328(f8(a877,a877,a1),a118),f328(f328(f8(a877,a877,a1),f328(f243(a877),x43452)),a110)))),f328(f328(f243(a877),f328(a118,x43452)),f328(f109(a877),x43451)))
% 81.29/80.90 [4365]E(f328(f141(f878(x43651),f878(x43651),f127(x43651),f119(x43651)),f328(f328(f153(f878(x43651),f878(x43651)),f155(f878(x43651),x43651,f119(x43651),f328(f328(f8(f878(x43651),f885(f878(x43651),f878(x43651)),x43651),f16(f878(x43651),f878(x43651))),f328(f328(f7(x43651,f878(x43651),f878(x43651)),f150(x43651)),f119(x43651))))),x43652)),f328(f328(f153(f878(x43651),x43651),f140(x43651)),f328(f135(f878(x43651),f328(f328(f8(a871,a871,f878(x43651)),a323),f328(f328(f7(f878(x43651),f878(x43651),a871),a325),f119(x43651)))),x43652)))
% 81.29/80.90 [4428]E(f328(f267(a1,a1,a871),f328(f328(f7(a1,f885(a1,a871),f885(a1,a871)),f328(f328(f8(f885(a1,f885(a871,a871)),f885(f885(a1,a871),f885(a1,a871)),a1),f18(a1,a871,a871)),f328(f328(f8(f885(a1,a871),f885(a1,f885(a871,a871)),a1),f328(f8(a871,f885(a871,a871),a1),a326)),f328(f328(f8(f885(a1,a1),f885(a1,a871),a1),f328(f8(a1,a871,a1),f328(a325,x44281))),f328(f328(f8(a1,f885(a1,a1),a1),f81(a1)),f328(f82(a1),x44282)))))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f328(f8(a871,a871,a1),f328(a331,f328(f328(f245(a1),f2(a1)),x44282))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f244(a1),f2(a1)))),f328(f328(f7(a1,a1,a871),f245(a1)),x44282))))),f328(f328(f8(a871,a871,a1),f328(a331,f328(a323,f328(f328(f245(a1),f2(a1)),x44282)))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f245(a1),x44282))),f328(f328(f7(a1,a1,a871),f244(a1)),f2(a1))))))),f49(x44281,x44282))
% 81.29/80.90 [4430]E(f328(f249(x44301),f328(f328(f8(f885(a877,a871),a871,x44301),f88(a877)),f328(f328(f7(x44301,f885(a877,a871),f885(a877,a871)),f328(f328(f8(f885(a877,f885(a871,a871)),f885(f885(a877,a871),f885(a877,a871)),x44301),f18(a877,a871,a871)),f328(f328(f8(f885(a877,a871),f885(a877,f885(a871,a871)),x44301),f328(f8(a871,f885(a871,a871),a877),a326)),f328(f328(f7(x44301,f885(a877,x44301),f885(a877,a871)),f328(f328(f8(f885(x44301,a871),f885(f885(a877,x44301),f885(a877,a871)),x44301),f8(x44301,a871,a877)),a325)),f328(f164(x44301),x44302))))),f328(f328(f7(a877,a877,a871),f245(a877)),f328(f194(f878(x44301)),x44302))))),f328(f171(x44301),x44302))
% 81.29/80.90 [4235]E(f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),x42351),a103)),x42352)),f328(f328(f22(a1),f328(f328(f81(a1),x42351),a103)),x42352))),a103),f328(f328(f22(a1),f328(f328(f81(a1),x42351),x42351)),f328(f328(f22(a1),f328(f328(f81(a1),x42352),x42352)),a103)))
% 81.29/80.90 [4360]E(f328(f141(f878(f878(x43601)),f878(f878(x43601)),f127(f878(x43601)),f119(f878(x43601))),f328(f328(f153(f878(x43601),f878(f878(x43601))),f155(f878(f878(x43601)),x43601,f119(f878(x43601)),f328(f16(f885(f878(x43601),f878(f878(x43601))),x43601),f328(f328(f7(f878(x43601),f878(f878(x43601)),f878(f878(x43601))),f150(f878(x43601))),f119(f878(x43601)))))),x43602)),f328(f328(f153(f878(x43601),f878(x43601)),f170(x43601)),f328(f135(f878(x43601),f328(f328(f8(a871,a871,f878(x43601)),a323),f328(f328(f7(f878(x43601),f878(x43601),a871),a325),f119(x43601)))),x43602)))
% 81.29/80.90 [4371]E(f328(f328(f87(a1,a877),f328(f109(a1),f328(f328(f81(a1),x43711),a103))),f328(f328(f18(a1,a877,a877),f328(f328(f7(a1,a877,f885(a877,a877)),f328(f328(f8(a871,f885(a877,f885(a877,a877)),a1),f102(a877)),a199)),f2(a877))),f328(f328(f8(a877,a877,a1),a118),f328(f328(f7(a1,a877,a877),f328(f328(f8(a877,f885(a877,a877),a1),f242(a877)),a110)),x43712)))),f328(f328(f242(a877),f328(f109(a877),x43711)),f328(a118,x43712)))
% 81.29/80.90 [4372]E(f328(f328(f87(a1,a877),f328(f109(a1),f328(f328(f81(a1),x43721),a103))),f328(f328(f18(a1,a877,a877),f328(f328(f7(a1,a877,f885(a877,a877)),f328(f328(f8(a871,f885(a877,f885(a877,a877)),a1),f102(a877)),a199)),f328(a118,x43722))),f328(f328(f8(a877,a877,a1),a118),f328(f328(f7(a1,a877,a877),f328(f328(f8(a877,f885(a877,a877),a1),f243(a877)),a110)),x43722)))),f328(f328(f243(a877),f328(f109(a877),x43721)),f328(a118,x43722)))
% 81.29/80.90 [4359]E(f328(f267(x43591,x43591,a871),f328(f328(f18(x43591,a871,f885(x43591,a871)),f328(f328(f8(f885(x43591,f885(a871,a871)),f885(a871,f885(x43591,a871)),x43591),f7(x43591,a871,a871)),f328(f328(f8(f885(x43591,a871),f885(x43591,f885(a871,a871)),x43591),f328(f8(a871,f885(a871,a871),x43591),a326)),a325))),x43592)),f254(x43591,x43592))
% 81.29/80.90 [4406]E(f328(f328(f39(a877),x44061),f328(f328(f81(a877),f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),a103))),x44062)),f328(f328(f39(a877),x44061),f328(a118,f328(a118,f328(a118,x44062)))))
% 81.29/80.90 [4407]E(f45(a877,x44071,f328(f328(f81(a877),f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),a103))),x44072)),f45(a877,x44071,f328(a118,f328(a118,f328(a118,x44072)))))
% 81.29/80.90 [4408]E(f45(a877,f328(f328(f81(a877),f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),a103))),x44081),x44082),f45(a877,f328(a118,f328(a118,f328(a118,x44081))),x44082))
% 81.29/80.90 [4421]E(f126(f328(x44211,f328(f328(f82(a105),f328(f109(a105),f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),a103))),x44212))),f328(f209(x44211),x44212))
% 81.29/80.90 [4422]E(f328(f328(f39(a877),f328(f328(f81(a877),f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),a103))),x44221)),x44222),f328(f328(f39(a877),f328(a118,f328(a118,f328(a118,x44221)))),x44222))
% 81.29/80.90 [4471]~E(f34(x44711,x44712),f328(a26,x44713))
% 81.29/80.90 [4472]~E(f33(x44721,x44722),f328(a26,x44723))
% 81.29/80.90 [4473]~E(f328(a26,x44731),f34(x44732,x44733))
% 81.29/80.90 [4474]~E(f328(a26,x44741),f33(x44742,x44743))
% 81.29/80.90 [4489]~E(f29(x44891,x44892,x44893),a24)
% 81.29/80.90 [4490]~E(f31(x44901,x44902,x44903),a24)
% 81.29/80.90 [4491]~E(f30(x44911,x44912,x44913),a24)
% 81.29/80.90 [3194]E(f328(f198(x31941,x31942),x31943),f124(x31941,x31942))
% 81.29/80.90 [3215]E(f328(f208(x32151,x32152),x32153),f328(f128(x32151),x32152))
% 81.29/80.90 [3295]E(f328(f328(f153(x32951,x32952),x32953),f119(x32951)),f119(x32952))
% 81.29/80.90 [3296]E(f328(f328(f207(x32961,x32962),x32963),f196(x32961)),f196(x32962))
% 81.29/80.90 [3316]E(f32(f29(x33161,x33162,x33163)),f2(a877))
% 81.29/80.90 [3338]E(f328(f189(x33381,x33382,x33383),f2(a877)),x33382)
% 81.29/80.90 [3339]E(f328(f194(a873),f29(x33391,x33392,x33393)),f2(a877))
% 81.29/80.90 [3341]E(f328(f328(f181(x33411,x33412),x33413),f119(x33412)),f119(f884(x33411,x33412)))
% 81.29/80.90 [3375]E(f86(x33751,f63(x33751,x33752,x33753)),f328(f64(x33751,x33752),x33753))
% 81.29/80.90 [3426]E(f139(x34261,x34262,f151(x34261,x34263)),f151(x34261,f139(x34261,x34262,x34263)))
% 81.29/80.90 [3445]E(f328(f256(f878(x34451),f878(x34451)),f166(x34451,x34452,x34453)),f328(f135(x34451,x34452),x34453))
% 81.29/80.90 [3522]E(f17(x35221,x35222,x35223,f2(a105)),x35222)
% 81.29/80.90 [3523]E(f190(x35231,x35232,x35233,f2(a877)),x35232)
% 81.29/80.90 [3530]E(f162(x35301,x35302,x35303,f119(x35301)),f119(x35302))
% 81.29/80.90 [3531]E(f163(x35311,x35312,x35313,f119(x35311)),f119(x35312))
% 81.29/80.90 [3538]E(f328(f328(f164(x35381),f328(f328(f150(x35381),x35382),x35383)),f2(a877)),x35382)
% 81.29/80.90 [3566]E(f60(x35661,x35662,f119(x35661),x35663),f119(f884(x35661,x35662)))
% 81.29/80.90 [3588]P21(x35881,x35882,x35883,f193(f885(x35881,a871)))
% 81.29/80.90 [3746]E(f328(f74(x37461,x37462,x37461,x37463),f35(x37461)),x37463)
% 81.29/80.90 [3922]P24(f328(f328(f330(f884(x39221,x39221)),f328(f328(f257(x39221,x39221),x39222),x39222)),f304(x39221,x39223)))
% 81.29/80.90 [4566]~P24(f328(f328(f330(f884(f878(x45661),f878(x45661))),f328(f328(f257(f878(x45661),f878(x45661)),x45662),f119(x45661))),f144(x45661,x45663)))
% 81.29/80.90 [4567]~P24(f328(f328(f330(f884(f878(x45671),f878(x45671))),f328(f328(f257(f878(x45671),f878(x45671)),x45672),f119(x45671))),f146(x45671,x45673)))
% 81.29/80.90 [4568]~P24(f328(f328(f330(f884(f878(x45681),f878(x45681))),f328(f328(f257(f878(x45681),f878(x45681)),x45682),f119(x45681))),f156(x45681,x45683)))
% 81.29/80.90 [4569]~P24(f328(f328(f330(f884(f878(x45691),f878(x45691))),f328(f328(f257(f878(x45691),f878(x45691)),f119(x45691)),x45692)),f144(x45691,x45693)))
% 81.29/80.90 [4570]~P24(f328(f328(f330(f884(f878(x45701),f878(x45701))),f328(f328(f257(f878(x45701),f878(x45701)),f119(x45701)),x45702)),f156(x45701,x45703)))
% 81.29/80.90 [3268]E(f328(f328(f210(x32681),x32682),x32683),f211(x32681,f223(x32682,x32683)))
% 81.29/80.90 [3327]E(f328(f283(x33271,x33272),f328(f283(x33272,x33271),x33273)),x33273)
% 81.29/80.90 [3351]E(f328(f328(f181(x33511,x33512),f119(x33511)),x33513),f119(f884(x33511,x33512)))
% 81.29/80.90 [3354]E(f175(x33541,x33542,f328(f250(a877),x33543)),f328(f328(f174(x33541),x33543),x33542))
% 81.29/80.90 [3371]E(f151(x33711,f328(f135(x33711,x33712),x33713)),f328(f135(x33711,x33712),f151(x33711,x33713)))
% 81.29/80.90 [3373]E(f328(f253(x33731,x33732),f328(f283(x33732,x33731),x33733)),f328(f255(x33732,x33731),x33733))
% 81.29/80.90 [3374]E(f328(f255(x33741,x33742),f328(f283(x33742,x33741),x33743)),f328(f253(x33742,x33741),x33743))
% 81.29/80.90 [3390]E(f328(f135(x33901,x33902),f328(f168(x33901),x33903)),f328(f168(x33901),f328(f135(x33901,x33902),x33903)))
% 81.29/80.90 [3403]E(f328(f328(f137(x34031),x34032),f328(f170(x34031),x34033)),f328(f328(f137(x34031),f328(a118,x34032)),x34033))
% 81.29/80.90 [3421]E(f32(f30(x34211,x34212,x34213)),f328(f328(f81(a877),f32(x34213)),f328(a118,f2(a877))))
% 81.29/80.90 [3422]E(f328(f307(x34221,x34222,x34223),f193(f885(x34221,a871))),f193(f885(x34222,a871)))
% 81.29/80.90 [3423]E(f328(f282(x34231,x34232,x34233),f193(f885(x34231,a871))),f193(f885(x34232,a871)))
% 81.29/80.90 [3424]E(f328(f308(x34241,x34242,x34243),f193(f885(x34242,a871))),f193(f885(x34241,a871)))
% 81.29/80.90 [3425]E(f328(f308(x34251,x34252,x34253),f252(f885(x34252,a871))),f252(f885(x34251,a871)))
% 81.29/80.90 [3454]E(f328(f328(f306(x34541),x34542),f328(f171(x34541),x34543)),f328(f171(x34541),f139(x34541,x34542,x34543)))
% 81.29/80.90 [3466]E(f237(x34661,x34662,f328(f236(x34661),x34663)),f328(f328(f81(a877),f328(x34662,x34663)),f328(a118,f2(a877))))
% 81.29/80.90 [3542]E(f328(f194(a873),f30(x35421,x35422,x35423)),f328(f328(f81(a877),f328(f194(a873),x35423)),f328(a118,f2(a877))))
% 81.29/80.90 [3543]E(f328(f307(f884(x35431,x35432),x35432,f266(x35431,x35432)),x35433),f328(f253(x35431,x35432),x35433))
% 81.29/80.90 [3544]E(f328(f307(f884(x35441,x35442),x35441,f256(x35441,x35442)),x35443),f328(f255(x35441,x35442),x35443))
% 81.29/80.90 [3613]E(f328(f328(f257(x36131,x36132),f328(f256(x36131,x36132),x36133)),f328(f266(x36131,x36132),x36133)),x36133)
% 81.29/80.90 [3620]E(f328(f194(f879(x36201)),f129(x36201,x36202,x36203)),f328(f328(f81(a877),f328(f194(f879(x36201)),x36203)),f328(a118,f2(a877))))
% 81.29/80.90 [3623]E(f328(f328(f267(x36231,x36232,x36231),f16(x36231,x36232)),x36233),f328(f256(x36231,x36232),x36233))
% 81.29/80.90 [3643]E(f184(x36431,x36432,x36433,f328(f16(f881(x36432),x36431),f196(x36432))),x36433)
% 81.29/80.90 [3644]E(f184(x36441,x36442,f328(f16(f881(x36442),x36441),f196(x36442)),x36443),x36443)
% 81.29/80.90 [3700]E(f32(f31(x37001,x37002,x37003)),f328(f328(f81(a877),f328(f328(f81(a877),f32(x37002)),f32(x37003))),f328(a118,f2(a877))))
% 81.29/80.90 [3749]E(f328(f74(x37491,x37491,x37492,f35(x37491)),x37493),x37493)
% 81.29/80.90 [3857]E(f328(f194(a873),f31(x38571,x38572,x38573)),f328(f328(f81(a877),f328(f328(f81(a877),f328(f194(a873),x38572)),f328(f194(a873),x38573))),f328(a118,f2(a877))))
% 81.29/80.90 [3932]P24(f328(f328(f244(f885(x39321,a871)),f328(f171(x39321),f328(f135(x39321,x39322),x39323))),f328(f171(x39321),x39323)))
% 81.29/80.90 [3977]P24(f328(f328(f244(f885(x39771,a871)),f328(f171(x39771),f328(f328(f174(x39771),x39772),x39773))),f328(f171(x39771),x39773)))
% 81.29/80.90 [3978]P24(f328(f328(f244(f885(x39781,a871)),f328(f171(x39781),f328(f328(f137(x39781),x39782),x39783))),f328(f171(x39781),x39783)))
% 81.29/80.90 [3983]P24(f328(f328(f244(f885(x39831,a871)),f328(f171(x39831),f169(x39831,x39832,x39833))),f328(f171(x39831),x39833)))
% 81.29/80.90 [3984]P24(f328(f328(f244(f885(x39841,a871)),f328(f171(x39841),f175(x39841,x39842,x39843))),f328(f171(x39841),x39842)))
% 81.29/80.90 [4007]P21(f884(x40071,x40072),f884(x40072,x40071),f328(f267(x40071,x40072,f884(x40072,x40071)),f328(f7(x40072,x40071,f884(x40072,x40071)),f257(x40072,x40071))),x40073)
% 81.29/80.90 [4019]E(f328(f328(f328(f188(f878(x40191),f878(x40191)),f45(a877,x40192,f328(f194(f878(x40191)),x40193))),f167(x40191)),x40193),f328(f328(f328(f188(f878(x40191),f878(x40191)),x40192),f167(x40191)),x40193))
% 81.29/80.90 [4061]P24(f328(f328(f330(f884(f878(x40611),f878(x40611))),f328(f328(f257(f878(x40611),f878(x40611)),x40612),x40612)),f157(x40611,f304(x40611,x40613))))
% 81.29/80.90 [4205]E(f91(f884(x42051,x42052),f328(f328(f18(f884(x42051,x42052),x42052,a871),f328(f328(f8(x42051,f885(x42052,a871),f884(x42051,x42052)),x42053),f256(x42051,x42052))),f266(x42051,x42052))),f91(f884(x42051,x42052),f328(f267(x42051,x42052,a871),x42053)))
% 81.29/80.90 [4206]E(f86(f884(x42061,x42062),f328(f328(f18(f884(x42061,x42062),x42062,a871),f328(f328(f8(x42061,f885(x42062,a871),f884(x42061,x42062)),x42063),f256(x42061,x42062))),f266(x42061,x42062))),f86(f884(x42061,x42062),f328(f267(x42061,x42062,a871),x42063)))
% 81.29/80.90 [4242]E(f328(f328(f284(f884(a877,x42421),x42421),f320(a877,x42421,a248,x42422)),f328(f328(f18(x42421,x42421,f884(a877,x42421)),f328(f328(f8(a877,f885(x42421,f884(a877,x42421)),x42421),f257(a877,x42421)),x42423)),f5(x42421))),f322(x42421,x42423,x42422))
% 81.29/80.90 [4307]E(f328(f268(x43071,x43071,x43072,x43072,f5(x43071),f5(x43072)),x43073),x43073)
% 81.29/80.90 [4382]E(f328(f141(f878(f878(x43821)),f878(f878(x43821)),f127(f878(x43821)),f119(f878(x43821))),f328(f328(f153(f878(x43821),f878(f878(x43821))),f328(f328(f7(f878(x43821),f878(x43821),f878(f878(x43821))),f328(f328(f8(f885(x43821,f878(x43821)),f885(f878(x43821),f878(f878(x43821))),f878(x43821)),f153(x43821,f878(x43821))),f328(f7(x43821,f878(x43821),f878(x43821)),f150(x43821)))),x43822)),f55(x43821,x43823,x43822))),f55(x43821,f328(a118,x43823),x43822))
% 81.29/80.90 [4443]E(f328(f238(a877,f884(x44431,f879(x44431)),f2(a877),f328(f267(x44431,f879(x44431),a877),f328(f328(f7(x44431,a877,f885(f879(x44431),a877)),f328(f328(f8(f885(f879(x44431),f885(a877,a877)),f885(a877,f885(f879(x44431),a877)),x44431),f7(f879(x44431),a877,a877)),f328(f328(f8(f885(f879(x44431),a877),f885(f879(x44431),f885(a877,a877)),x44431),f328(f8(a877,f885(a877,a877),f879(x44431)),f81(a877))),f328(f328(f7(x44431,f885(f879(x44431),a877),f885(f879(x44431),a877)),f328(f328(f8(f885(a877,a877),f885(f885(f879(x44431),a877),f885(f879(x44431),a877)),x44431),f8(a877,a877,f879(x44431))),f328(f328(f8(a877,f885(a877,a877),x44431),f81(a877)),x44432))),f131(x44431,x44432))))),f79(a877)))),f328(f134(x44431),x44433)),f328(f131(x44431,x44432),x44433))
% 81.29/80.90 [4446]E(f328(f328(f87(a1,x44461),f226(f328(f328(f74(f884(a1,a1),a1,x44461,f266(a1,a1)),f220(x44461)),x44462),f328(f328(f74(f884(a1,a1),a1,x44461,f266(a1,a1)),f220(x44461)),x44463))),f328(f328(f18(a1,a1,x44461),f328(f328(f8(a1,f885(a1,x44461),a1),f210(x44461)),f328(f328(f18(a1,a1,a1),f328(f328(f8(a1,f885(a1,a1),a1),f81(a1)),f328(f328(f8(a1,a1,a1),f328(f82(a1),f328(f328(f74(f884(a1,a1),a1,x44461,f256(a1,a1)),f220(x44461)),x44462))),f328(f328(f7(a1,a1,a1),f39(a1)),f328(f328(f74(f884(a1,a1),a1,x44461,f266(a1,a1)),f220(x44461)),x44462))))),f328(f328(f8(a1,a1,a1),f328(f82(a1),f328(f328(f74(f884(a1,a1),a1,x44461,f256(a1,a1)),f220(x44461)),x44463))),f328(f328(f7(a1,a1,a1),f39(a1)),f328(f328(f74(f884(a1,a1),a1,x44461,f266(a1,a1)),f220(x44461)),x44463)))))),f5(a1))),f231(x44461,x44462,x44463))
% 81.29/80.90 [4484]~E(f328(f328(f150(x44841),x44842),x44843),x44843)
% 81.29/80.90 [4493]~E(f328(f328(f150(x44931),x44932),x44933),f119(x44931))
% 81.29/80.90 [4515]~E(f328(f328(f306(x45151),x45152),x45153),f193(f885(x45151,a871)))
% 81.29/80.90 [4542]~E(f328(f307(x45421,f885(x45421,a871),x45422),x45423),f328(f305(x45421),x45423))
% 81.29/80.90 [3332]E(f328(f328(f158(x33321,f119(x33321)),x33322),x33323),f119(x33321))
% 81.29/80.90 [3333]E(f328(f140(x33331),f328(f328(f150(x33331),x33332),x33333)),x33332)
% 81.29/80.90 [3334]E(f328(f170(x33341),f328(f328(f150(x33341),x33342),x33343)),x33343)
% 81.29/80.90 [3378]E(f328(f328(f137(x33781),f79(a877)),f328(f328(f150(x33781),x33782),x33783)),x33783)
% 81.29/80.90 [3410]E(f120(x34101,f328(f328(f137(x34101),x34102),x34103)),f328(f328(f137(x34101),x34102),f120(x34101,x34103)))
% 81.29/80.90 [3412]E(f328(f328(f158(x34121,x34122),x34123),f328(f328(f164(x34121),x34122),x34123)),x34122)
% 81.29/80.90 [3436]E(f328(f328(f306(x34361),x34362),f328(f328(f306(x34361),x34362),x34363)),f328(f328(f306(x34361),x34362),x34363))
% 81.29/80.90 [3447]E(f328(f328(f177(x34471,x34472),f119(f884(x34471,x34472))),x34473),f196(x34472))
% 81.29/80.90 [3450]E(f328(f328(f306(x34501),x34502),f328(f171(x34501),x34503)),f328(f171(x34501),f328(f328(f150(x34501),x34502),x34503)))
% 81.29/80.90 [3452]E(f328(f328(f137(x34521),x34522),f328(f170(x34521),x34523)),f328(f170(x34521),f328(f328(f137(x34521),x34522),x34523)))
% 81.29/80.90 [3463]E(f328(f328(f174(x34631),f79(a877)),f328(f328(f150(x34631),x34632),x34633)),f328(f328(f150(x34631),x34632),f119(x34631)))
% 81.29/80.90 [3507]E(f328(f64(x35071,x35072),f328(f328(f306(x35071),x35073),f193(f885(x35071,a871)))),x35073)
% 81.29/80.90 [3550]E(f328(f328(f81(a877),x35501),f328(f328(f81(a877),x35502),x35503)),f328(f328(f81(a877),x35502),f328(f328(f81(a877),x35501),x35503)))
% 81.29/80.90 [3551]E(f328(f328(f81(a1),x35511),f328(f328(f81(a1),x35512),x35513)),f328(f328(f81(a1),x35512),f328(f328(f81(a1),x35511),x35513)))
% 81.29/80.90 [3556]E(f328(f328(f265(x35561,x35562),f193(f885(x35561,a871))),x35563),f193(f885(f884(x35561,x35562),a871)))
% 81.29/80.90 [3580]E(f328(f328(f116(f885(x35801,a871)),x35802),x35803),f328(f328(f116(f885(x35801,a871)),x35803),x35802))
% 81.29/80.90 [3581]E(f328(f328(f107(f885(x35811,a871)),x35812),x35813),f328(f328(f107(f885(x35811,a871)),x35813),x35812))
% 81.29/80.90 [3583]E(f328(f328(f127(x35831),x35832),f328(f328(f150(x35831),x35833),f119(x35831))),f328(f167(x35831),f328(f328(f150(x35831),x35833),x35832)))
% 81.29/80.90 [3584]E(f328(f328(f127(x35841),f328(f168(x35841),x35842)),f328(f168(x35841),x35843)),f328(f168(x35841),f328(f328(f127(x35841),x35843),x35842)))
% 81.29/80.90 [3592]E(f328(f170(x35921),f328(f328(f174(x35921),f328(a118,x35922)),x35923)),f328(f328(f174(x35921),x35922),f328(f170(x35921),x35923)))
% 81.29/80.90 [3599]P24(f328(f328(f330(x35991),x35992),f328(f328(f306(x35991),x35992),x35993)))
% 81.29/80.90 [3603]E(f328(f328(f42(x36031,f885(x36032,a871)),f193(f885(x36031,a871))),x36033),f252(f885(x36032,a871)))
% 81.29/80.90 [3606]E(f328(f282(x36061,x36061,f254(x36061,x36062)),x36063),f328(f328(f107(f885(x36061,a871)),x36062),x36063))
% 81.29/80.90 [3619]E(f328(f194(f878(x36191)),f328(f328(f150(x36191),x36192),x36193)),f328(f328(f81(a877),f328(f194(f878(x36191)),x36193)),f328(a118,f2(a877))))
% 81.29/80.90 [3625]E(f143(x36251,f328(f328(f127(x36251),x36252),f328(f328(f150(x36251),x36253),f119(x36251)))),x36253)
% 81.29/80.90 [3626]E(f120(x36261,f328(f328(f127(x36261),x36262),f328(f328(f150(x36261),x36263),f119(x36261)))),x36262)
% 81.29/80.90 [3632]E(f328(f328(f127(x36321),f328(f328(f174(x36321),x36322),x36323)),f328(f328(f137(x36321),x36322),x36323)),x36323)
% 81.29/80.90 [3641]E(f328(f328(f22(a877),f328(f328(f81(a877),x36411),x36412)),f328(f328(f81(a877),x36413),x36412)),f328(f328(f22(a877),x36411),x36413))
% 81.29/80.90 [3642]E(f328(f328(f22(a877),f328(f328(f81(a877),x36421),x36422)),f328(f328(f81(a877),x36421),x36423)),f328(f328(f22(a877),x36422),x36423))
% 81.29/80.90 [3649]E(f328(f328(f127(x36491),f328(f168(x36491),x36492)),f328(f328(f150(x36491),x36493),f119(x36491))),f328(f168(x36491),f328(f328(f150(x36491),x36493),x36492)))
% 81.29/80.90 [3651]E(f328(f328(f81(a877),f328(f194(f878(x36511)),x36512)),f328(f194(f878(x36511)),x36513)),f328(f194(f878(x36511)),f328(f328(f127(x36511),x36512),x36513)))
% 81.29/80.90 [3654]E(f328(f328(f81(a877),f328(f194(f878(x36541)),x36542)),f328(f194(f878(x36541)),x36543)),f328(f194(f878(x36541)),f172(x36541,x36542,x36543)))
% 81.29/80.90 [3662]E(f328(f328(f116(f885(x36621,a871)),f328(f171(x36621),x36622)),f328(f171(x36621),x36623)),f328(f171(x36621),f328(f328(f127(x36621),x36622),x36623)))
% 81.29/80.90 [3663]E(f45(a877,f328(f328(f82(a877),x36631),x36632),f328(f328(f82(a877),x36631),x36633)),f328(f328(f82(a877),x36631),f45(a877,x36632,x36633)))
% 81.29/80.90 [3676]E(f328(f328(f174(x36761),f328(f328(f22(a877),x36762),f79(a877))),f328(f170(x36761),x36763)),f328(f170(x36761),f328(f328(f174(x36761),x36762),x36763)))
% 81.29/80.90 [3681]E(f328(f328(f107(f885(x36811,a871)),x36812),f328(f80(f885(x36811,a871)),x36813)),f328(f328(f22(f885(x36811,a871)),x36812),x36813))
% 81.29/80.90 [3682]E(f328(f328(f22(f885(x36821,a871)),x36822),f328(f80(f885(x36821,a871)),x36823)),f328(f328(f107(f885(x36821,a871)),x36822),x36823))
% 81.29/80.90 [3704]E(f328(f328(f265(x37041,x37042),x37043),f328(f16(f885(x37042,a871),x37041),f193(f885(x37042,a871)))),f193(f885(f884(x37041,x37042),a871)))
% 81.29/80.90 [3706]E(f328(f328(f22(a877),f328(f328(f82(a877),x37061),x37062)),f328(f328(f82(a877),x37061),x37063)),f328(f328(f82(a877),x37061),f328(f328(f22(a877),x37062),x37063)))
% 81.29/80.90 [3707]E(f328(f328(f81(a877),f328(f328(f82(a877),x37071),x37072)),f328(f328(f82(a877),x37071),x37073)),f328(f328(f82(a877),x37071),f328(f328(f81(a877),x37072),x37073)))
% 81.29/80.90 [3708]E(f328(f328(f22(a1),f328(f328(f82(a1),x37081),x37082)),f328(f328(f82(a1),x37081),x37083)),f328(f328(f82(a1),x37081),f328(f328(f22(a1),x37082),x37083)))
% 81.29/80.90 [3709]E(f328(f328(f81(a1),f328(f328(f82(a1),x37091),x37092)),f328(f328(f82(a1),x37091),x37093)),f328(f328(f82(a1),x37091),f328(f328(f81(a1),x37092),x37093)))
% 81.29/80.90 [3710]E(f328(f328(f82(a1),f328(f328(f258(a1),x37101),x37102)),f328(f328(f258(a1),x37101),x37103)),f328(f328(f258(a1),x37101),f328(f328(f81(a877),x37102),x37103)))
% 81.29/80.90 [3724]E(f328(f328(f43(x37241,f885(x37242,a871)),x37243),f328(f16(f885(x37242,a871),x37241),f193(f885(x37242,a871)))),f193(f885(x37242,a871)))
% 81.29/80.90 [3726]E(f45(a877,f328(f328(f82(a877),x37261),x37262),f328(f328(f82(a877),x37263),x37262)),f328(f328(f82(a877),f45(a877,x37261,x37263)),x37262))
% 81.29/80.90 [3730]E(f45(a1,f328(f328(f22(a1),x37301),f45(a1,x37302,x37303)),x37303),f45(a1,f328(f328(f22(a1),x37301),x37302),x37303))
% 81.29/80.90 [3731]E(f45(a1,f328(f328(f82(a1),x37311),f45(a1,x37312,x37313)),x37313),f45(a1,f328(f328(f82(a1),x37311),x37312),x37313))
% 81.29/80.90 [3732]P24(f328(f328(f244(f885(x37321,a871)),x37322),f328(f328(f306(x37321),x37323),x37322)))
% 81.29/80.90 [3735]E(f328(f307(f884(x37351,x37352),x37351,f256(x37351,x37352)),f328(f171(f884(x37351,x37352)),x37353)),f183(x37351,x37352,f328(f177(x37351,x37352),x37353)))
% 81.29/80.90 [3783]P24(f328(f62(x37831),f183(x37831,x37832,f328(f177(x37831,x37832),x37833))))
% 81.29/80.90 [3808]E(f328(f328(f42(f885(x38081,a871),f885(x38081,a871)),x38082),f328(f116(f885(x38081,a871)),x38083)),f328(f328(f116(f885(x38081,a871)),x38083),f41(f885(x38081,a871),x38082)))
% 81.29/80.90 [3809]E(f328(f328(f43(f885(x38091,a871),f885(x38091,a871)),x38092),f328(f107(f885(x38091,a871)),x38093)),f328(f328(f107(f885(x38091,a871)),x38093),f40(f885(x38091,a871),x38092)))
% 81.29/80.90 [3820]E(f328(f171(x38201),f328(f328(f328(f188(f878(x38201),f878(x38201)),x38202),f167(x38201)),x38203)),f328(f171(x38201),x38203))
% 81.29/80.90 [3824]E(f328(f328(f174(x38241),f328(f194(f878(x38241)),f176(x38241,x38242,x38243))),x38243),f176(x38241,x38242,x38243))
% 81.29/80.90 [3825]E(f183(x38251,x38252,f328(f328(f8(x38252,f881(x38252),x38251),f236(x38252)),x38253)),f252(f885(x38251,a871)))
% 81.29/80.90 [3829]E(f328(f194(f878(x38291)),f328(f328(f328(f188(f878(x38291),f878(x38291)),x38292),f167(x38291)),x38293)),f328(f194(f878(x38291)),x38293))
% 81.29/80.90 [3832]E(f328(f328(f267(x38321,x38322,x38322),f328(f16(f885(x38322,x38322),x38321),f5(x38322))),x38323),f328(f266(x38321,x38322),x38323))
% 81.29/80.90 [3838]E(f45(a1,f328(f328(f22(a1),f45(a1,x38381,x38382)),x38383),x38382),f45(a1,f328(f328(f22(a1),x38381),x38383),x38382))
% 81.29/80.90 [3839]E(f45(a1,f328(f328(f258(a1),f45(a1,x38391,x38392)),x38393),x38392),f45(a1,f328(f328(f258(a1),x38391),x38393),x38392))
% 81.29/80.90 [3842]E(f328(f328(f43(f885(f884(x38421,x38422),a871),f885(x38422,a871)),x38423),f253(x38421,x38422)),f328(f253(x38421,x38422),f40(f885(f884(x38421,x38422),a871),x38423)))
% 81.29/80.90 [3843]E(f328(f328(f43(f885(f884(x38431,x38432),a871),f885(x38431,a871)),x38433),f255(x38431,x38432)),f328(f255(x38431,x38432),f40(f885(f884(x38431,x38432),a871),x38433)))
% 81.29/80.90 [3869]E(f328(f74(x38691,x38691,x38691,x38692),f328(f328(f188(x38691,x38691),x38693),x38692)),f328(f328(f188(x38691,x38691),f328(a118,x38693)),x38692))
% 81.29/80.90 [3879]E(f238(f881(x38791),x38792,f196(x38791),f328(f328(f8(x38791,f881(x38791),x38792),f236(x38791)),x38793)),f328(f207(x38792,x38791),x38793))
% 81.29/80.90 [3886]E(f328(f328(f137(x38861),f328(f328(f22(a877),f328(f194(f878(x38861)),x38862)),x38863)),f328(f168(x38861),x38862)),f328(f168(x38861),f328(f328(f174(x38861),x38863),x38862)))
% 81.29/80.90 [3887]E(f328(f328(f174(x38871),f328(f328(f22(a877),f328(f194(f878(x38871)),x38872)),x38873)),f328(f168(x38871),x38872)),f328(f168(x38871),f328(f328(f137(x38871),x38873),x38872)))
% 81.29/80.90 [3890]E(f328(f328(f81(a877),f328(f165(a877),f328(f328(f153(x38901,a877),x38902),x38903))),f328(f194(f878(x38901)),x38903)),f154(x38901,x38902,x38903))
% 81.29/80.90 [3908]E(f328(f167(x39081),f328(f328(f328(f188(f878(x39081),f878(x39081)),x39082),f167(x39081)),x39083)),f328(f328(f328(f188(f878(x39081),f878(x39081)),f328(a118,x39082)),f167(x39081)),x39083))
% 81.29/80.90 [3923]P24(f328(f328(f244(a877),f328(f194(f878(x39231)),f328(f135(x39231,x39232),x39233))),f328(f194(f878(x39231)),x39233)))
% 81.29/80.90 [3940]E(f328(f328(f116(f885(f885(x39401,a871),a871)),f328(f305(x39401),x39402)),f328(f307(f885(x39401,a871),f885(x39401,a871),f328(f306(x39401),x39403)),f328(f305(x39401),x39402))),f328(f305(x39401),f328(f328(f306(x39401),x39403),x39402)))
% 81.29/80.90 [3959]P20(x39591,x39592,f328(f328(f306(f876(x39591)),f328(f328(f328(f93(x39591),x39593),a24),x39593)),f193(f885(f876(x39591),a871))))
% 81.29/80.90 [3974]P24(f328(f328(f244(a877),f328(f194(f878(x39741)),f176(x39741,x39742,x39743))),f328(f194(f878(x39741)),x39743)))
% 81.29/80.90 [3982]E(f328(f255(x39821,x39822),f328(f249(f884(x39821,x39822)),f328(f267(x39821,x39822,a871),x39823))),f328(f249(x39821),f328(f328(f8(f885(x39822,a871),a871,x39821),f88(x39822)),x39823)))
% 81.29/80.90 [3994]E(f328(f307(a877,a877,f328(f328(f7(a877,a877,a877),f81(a877)),x39941)),f299(a877,x39942,x39943)),f299(a877,f328(f328(f81(a877),x39942),x39941),f328(f328(f81(a877),x39943),x39941)))
% 81.29/80.90 [3997]P24(f328(f62(f881(x39971)),f328(f307(x39972,f881(x39971),f328(f177(x39972,x39971),x39973)),f252(f885(x39972,a871)))))
% 81.29/80.90 [4010]E(f328(f307(a877,a877,f328(f328(f7(a877,a877,a877),f81(a877)),x40101)),f328(f298(a877,x40102),x40103)),f328(f298(a877,f328(f328(f81(a877),x40102),x40101)),f328(f328(f81(a877),x40103),x40101)))
% 81.29/80.90 [4028]E(f328(f328(f181(x40281,x40282),f328(f328(f153(f884(x40281,x40282),x40281),f256(x40281,x40282)),x40283)),f328(f328(f153(f884(x40281,x40282),x40282),f266(x40281,x40282)),x40283)),x40283)
% 81.29/80.90 [4033]E(f328(f328(f81(a877),f328(f328(f82(a877),x40331),f45(a877,f328(f328(f39(a877),x40332),x40331),x40333))),f45(a877,x40332,x40331)),f45(a877,x40332,f328(f328(f82(a877),x40331),x40333)))
% 81.29/80.90 [4047]E(f328(f328(f127(x40471),x40472),f328(f141(f878(x40471),f878(x40471),f127(x40471),f119(x40471)),x40473)),f328(f141(f878(x40471),f878(x40471),f127(x40471),x40472),x40473))
% 81.29/80.90 [4065]P24(f328(f328(f330(f884(x40651,x40651)),f328(f328(f257(x40651,x40651),x40652),x40652)),f328(f328(f188(f884(x40651,x40651),a871),f2(a877)),x40653)))
% 81.29/80.90 [4071]E(f328(f249(x40711),f328(f328(f8(f885(x40712,a871),a871,x40711),f88(x40712)),f328(f7(x40712,x40711,a871),x40713))),f328(f253(x40712,x40711),f328(f249(f884(x40712,x40711)),f328(f267(x40712,x40711,a871),x40713))))
% 81.29/80.90 [4089]E(f328(f328(f116(f885(x40891,a871)),f328(f328(f43(a877,f885(x40891,a871)),f299(a877,f79(a877),x40892)),x40893)),f328(x40893,f2(a877))),f328(f328(f43(a877,f885(x40891,a871)),f328(f297(a877),x40892)),x40893))
% 81.29/80.90 [4104]E(f328(f141(f878(x41041),f878(x41041),f127(x41041),f119(x41041)),f328(f328(f153(f878(x41041),f878(x41041)),f135(x41041,x41042)),x41043)),f328(f135(x41041,x41042),f328(f141(f878(x41041),f878(x41041),f127(x41041),f119(x41041)),x41043)))
% 81.29/80.90 [4109]E(f328(f266(f878(x41091),f878(x41091)),f166(x41091,x41092,x41093)),f328(f135(x41091,f328(f74(a871,a871,x41091,a323),x41092)),x41093))
% 81.29/80.90 [4127]E(f328(f328(f42(x41271,f885(x41272,a871)),f252(f885(x41271,a871))),f328(f328(f8(f885(x41272,a871),f885(x41272,a871),x41271),f249(x41272)),f328(f7(x41272,x41271,a871),x41273))),f328(f249(x41272),f328(f328(f8(f885(x41271,a871),a871,x41272),f89(x41271)),x41273)))
% 81.29/80.90 [4158]E(f328(f328(f81(a1),f328(f328(f81(a1),f328(f328(f82(a1),x41581),f328(f328(f39(a1),x41582),x41581))),f45(a1,x41582,x41581))),x41583),f328(f328(f81(a1),x41582),x41583))
% 81.29/80.90 [4194]E(f328(f328(f81(a1),f328(f328(f81(a1),f328(f328(f82(a1),f328(f328(f39(a1),x41941),x41942)),x41942)),f45(a1,x41941,x41942))),x41943),f328(f328(f81(a1),x41941),x41943))
% 81.29/80.90 [4223]E(f91(f884(x42231,x42232),f328(f267(x42231,x42232,a871),f328(f328(f8(f885(x42232,f884(x42231,x42232)),f885(x42232,a871),x42231),f328(f8(f884(x42231,x42232),a871,x42232),x42233)),f257(x42231,x42232)))),f91(f884(x42231,x42232),x42233))
% 81.29/80.90 [4224]E(f86(f884(x42241,x42242),f328(f267(x42241,x42242,a871),f328(f328(f8(f885(x42242,f884(x42241,x42242)),f885(x42242,a871),x42241),f328(f8(f884(x42241,x42242),a871,x42242),x42243)),f257(x42241,x42242)))),f86(f884(x42241,x42242),x42243))
% 81.29/80.90 [4252]P24(f328(f328(f244(f885(x42521,a871)),f40(f885(x42521,a871),f328(f328(f107(f885(f885(x42521,a871),a871)),x42522),x42523))),f328(f328(f107(f885(x42521,a871)),f40(f885(x42521,a871),x42522)),f40(f885(x42521,a871),x42523))))
% 81.29/80.90 [4253]E(f328(f168(x42531),f328(f328(f328(f188(f878(x42531),f878(x42531)),f328(f328(f22(a877),f328(f194(f878(x42531)),x42532)),f45(a877,x42533,f328(f194(f878(x42531)),x42532)))),f167(x42531)),x42532)),f328(f328(f328(f188(f878(x42531),f878(x42531)),x42533),f167(x42531)),f328(f168(x42531),x42532)))
% 81.29/80.90 [4267]E(f328(f249(x42671),f328(f328(f8(a871,a871,x42671),a323),f328(f328(f7(x42671,f881(x42672),a871),f328(f328(f8(f881(x42672),f885(f881(x42672),a871),x42671),a325),x42673)),f196(x42672)))),f183(x42671,x42672,x42673))
% 81.29/80.90 [4292]P24(f328(f328(f244(a877),f328(f194(f878(x42921)),f328(f328(f137(x42921),f328(f194(f878(x42921)),f176(x42921,x42922,x42923))),x42923))),f328(f194(f878(x42921)),x42923)))
% 81.29/80.90 [4333]E(f328(f249(x43331),f328(f328(f8(f885(x43332,a871),a871,x43331),f88(x43332)),f328(f328(f8(f881(x43331),f885(x43332,a871),x43331),f328(f7(x43332,f881(x43331),a871),f328(f328(f8(f881(x43331),f885(f881(x43331),a871),x43332),a325),x43333))),f236(x43331)))),f185(x43332,x43331,x43333))
% 81.29/80.90 [4556]~P24(f328(f63(x45561,x45562,f193(f885(x45561,a871))),x45563))
% 81.29/80.90 [4564]~P24(f328(f328(f330(f884(x45641,x45641)),f328(f328(f257(x45641,x45641),x45642),x45643)),f152(x45641,f119(f885(x45641,a877)))))
% 81.29/80.90 [3593]E(f328(f194(f878(x35931)),f328(f328(f174(x35931),x35932),x35933)),f328(f328(f242(a877),f328(f194(f878(x35931)),x35933)),x35932))
% 81.29/80.90 [3594]E(f328(f194(f878(x35941)),f328(f328(f137(x35941),x35942),x35943)),f328(f328(f22(a877),f328(f194(f878(x35941)),x35943)),x35942))
% 81.29/80.90 [3618]E(f328(f194(f878(f878(x36181))),f55(x36181,x36182,x36183)),f328(f328(f258(a877),f328(f194(f878(x36181)),x36183)),x36182))
% 81.29/80.90 [3634]E(f328(f328(f39(a877),f328(f328(f39(a877),x36341),x36342)),x36343),f328(f328(f39(a877),x36341),f328(f328(f82(a877),x36342),x36343)))
% 81.29/80.90 [3635]E(f328(f328(f22(a877),f328(f328(f22(a877),x36351),x36352)),x36353),f328(f328(f22(a877),x36351),f328(f328(f81(a877),x36352),x36353)))
% 81.29/80.90 [3636]E(f328(f328(f81(a877),f328(f328(f81(a877),x36361),x36362)),x36363),f328(f328(f81(a877),x36361),f328(f328(f81(a877),x36362),x36363)))
% 81.29/80.90 [3637]E(f328(f328(f81(a1),f328(f328(f81(a1),x36371),x36372)),x36373),f328(f328(f81(a1),x36371),f328(f328(f81(a1),x36372),x36373)))
% 81.29/80.90 [3638]E(f328(f328(f82(a877),f328(f328(f82(a877),x36381),x36382)),x36383),f328(f328(f82(a877),x36381),f328(f328(f82(a877),x36382),x36383)))
% 81.29/80.90 [3639]E(f328(f328(f82(a1),f328(f328(f82(a1),x36391),x36392)),x36393),f328(f328(f82(a1),x36391),f328(f328(f82(a1),x36392),x36393)))
% 81.29/80.90 [3640]E(f328(f328(f258(a1),f328(f328(f258(a1),x36401),x36402)),x36403),f328(f328(f258(a1),x36401),f328(f328(f82(a877),x36402),x36403)))
% 81.29/80.90 [3660]E(f161(x36601,f328(f328(f150(f885(x36601,a871)),x36602),x36603)),f173(x36601,x36602,f161(x36601,x36603)))
% 81.29/80.90 [3705]E(f328(f328(f22(a877),f328(f328(f22(a877),x37051),x37052)),x37053),f328(f328(f22(a877),f328(f328(f22(a877),x37051),x37053)),x37052))
% 81.29/80.90 [3711]E(f328(f236(f884(x37111,f879(x37111))),f328(f328(f257(x37111,f879(x37111)),x37112),x37113)),f328(f134(x37111),f129(x37111,x37112,x37113)))
% 81.29/80.90 [3714]E(f328(f328(f107(f885(x37141,a871)),x37142),f328(f328(f22(f885(x37141,a871)),x37143),x37142)),f193(f885(x37141,a871)))
% 81.29/80.90 [3755]E(f40(f885(x37551,a871),f328(f328(f306(f885(x37551,a871)),x37552),x37553)),f328(f328(f116(f885(x37551,a871)),x37552),f40(f885(x37551,a871),x37553)))
% 81.29/80.90 [3756]E(f41(f885(x37561,a871),f328(f328(f306(f885(x37561,a871)),x37562),x37563)),f328(f328(f107(f885(x37561,a871)),x37562),f41(f885(x37561,a871),x37563)))
% 81.29/80.90 [3758]E(f328(f328(f22(a877),f328(f328(f82(a877),x37581),x37582)),f328(f328(f82(a877),x37583),x37582)),f328(f328(f82(a877),f328(f328(f22(a877),x37581),x37583)),x37582))
% 81.29/80.90 [3759]E(f328(f328(f81(a877),f328(f328(f82(a877),x37591),x37592)),f328(f328(f82(a877),x37593),x37592)),f328(f328(f82(a877),f328(f328(f81(a877),x37591),x37593)),x37592))
% 81.29/80.90 [3760]E(f328(f328(f22(a1),f328(f328(f82(a1),x37601),x37602)),f328(f328(f82(a1),x37603),x37602)),f328(f328(f82(a1),f328(f328(f22(a1),x37601),x37603)),x37602))
% 81.29/80.90 [3761]E(f328(f328(f81(a1),f328(f328(f82(a1),x37611),x37612)),f328(f328(f82(a1),x37613),x37612)),f328(f328(f82(a1),f328(f328(f81(a1),x37611),x37613)),x37612))
% 81.29/80.90 [3763]E(f328(f328(f242(a877),f328(f328(f22(a877),x37631),x37632)),f328(f328(f22(a877),x37633),x37632)),f328(f328(f22(a877),f328(f328(f242(a877),x37631),x37633)),x37632))
% 81.29/80.90 [3786]E(f328(f328(f107(f885(f878(x37861),a871)),f159(x37861,x37862)),f159(x37861,x37863)),f159(x37861,f328(f328(f107(f885(x37861,a871)),x37862),x37863)))
% 81.29/80.90 [3788]E(f328(f328(f116(f885(x37881,a871)),x37882),f328(f328(f22(f885(x37881,a871)),x37883),x37882)),f328(f328(f116(f885(x37881,a871)),x37882),x37883))
% 81.29/80.90 [3789]E(f328(f328(f116(f885(x37891,a871)),x37892),f328(f328(f116(f885(x37891,a871)),x37892),x37893)),f328(f328(f116(f885(x37891,a871)),x37892),x37893))
% 81.29/80.90 [3790]E(f328(f328(f107(f885(x37901,a871)),x37902),f328(f328(f107(f885(x37901,a871)),x37902),x37903)),f328(f328(f107(f885(x37901,a871)),x37902),x37903))
% 81.29/80.90 [3802]E(f328(f328(f285(x38021,x38022,x38022),x38023),f304(x38022,f193(f885(f884(x38022,x38022),a871)))),x38023)
% 81.29/80.90 [3805]E(f328(f328(f116(f885(x38051,a871)),f328(f328(f306(x38051),x38052),f193(f885(x38051,a871)))),x38053),f328(f328(f306(x38051),x38052),x38053))
% 81.29/80.90 [3823]E(f328(f328(f22(a877),f328(f328(f22(a877),f328(a118,x38231)),x38232)),f328(a118,x38233)),f328(f328(f22(a877),f328(f328(f22(a877),x38231),x38232)),x38233))
% 81.29/80.90 [3851]E(f328(f328(f107(f885(f885(x38511,a871),a871)),f328(f305(x38511),x38512)),f328(f305(x38511),x38513)),f328(f305(x38511),f328(f328(f107(f885(x38511,a871)),x38512),x38513)))
% 81.29/80.90 [3855]E(f328(f328(f116(f885(x38551,a871)),f328(f80(f885(x38551,a871)),x38552)),x38553),f328(f80(f885(x38551,a871)),f328(f328(f22(f885(x38551,a871)),x38552),x38553)))
% 81.29/80.90 [3866]E(f328(f328(f306(x38661),x38662),f328(f328(f22(f885(x38661,a871)),x38663),f328(f328(f306(x38661),x38662),f193(f885(x38661,a871))))),f328(f328(f306(x38661),x38662),x38663))
% 81.29/80.90 [3876]P24(f328(f328(f244(f885(x38761,a871)),x38762),f328(f328(f116(f885(x38761,a871)),x38763),x38762)))
% 81.29/80.90 [3877]P24(f328(f328(f244(f885(x38771,a871)),x38772),f328(f328(f116(f885(x38771,a871)),x38772),x38773)))
% 81.29/80.90 [3880]E(f328(f328(f107(f885(x38801,a871)),f328(f80(f885(x38801,a871)),x38802)),f328(f80(f885(x38801,a871)),x38803)),f328(f80(f885(x38801,a871)),f328(f328(f116(f885(x38801,a871)),x38802),x38803)))
% 81.29/80.90 [3881]E(f328(f328(f116(f885(x38811,a871)),f328(f80(f885(x38811,a871)),x38812)),f328(f80(f885(x38811,a871)),x38813)),f328(f80(f885(x38811,a871)),f328(f328(f107(f885(x38811,a871)),x38812),x38813)))
% 81.29/80.90 [3895]P24(f328(f328(f244(f885(x38951,a871)),f328(f171(x38951),x38952)),f328(f171(x38951),f328(f328(f150(x38951),x38953),x38952))))
% 81.29/80.90 [3905]E(f328(f328(f116(f885(x39051,a871)),f328(f328(f22(f885(x39051,a871)),x39052),x39053)),f328(f328(f107(f885(x39051,a871)),x39052),x39053)),x39052)
% 81.29/80.90 [3961]E(f328(f328(f6(x39611,a1),f328(f328(f8(a877,a1,x39611),f106(a1)),x39612)),x39613),f328(f106(a1),f328(f328(f6(x39611,a877),x39612),x39613)))
% 81.29/80.90 [3962]E(f328(f328(f9(x39621,a1),f328(f328(f8(a877,a1,x39621),f106(a1)),x39622)),x39623),f328(f106(a1),f328(f328(f9(x39621,a877),x39622),x39623)))
% 81.29/80.90 [4012]E(f328(f328(f127(x40121),f176(x40121,x40122,x40123)),f328(f328(f137(x40121),f328(f194(f878(x40121)),f176(x40121,x40122,x40123))),x40123)),x40123)
% 81.29/80.90 [4017]E(f328(f80(f885(f884(x40171,x40172),a871)),f328(f328(f265(x40171,x40172),x40173),f328(f16(f885(x40172,a871),x40171),f252(f885(x40172,a871))))),f328(f328(f265(x40171,x40172),f328(f80(f885(x40171,a871)),x40173)),f328(f16(f885(x40172,a871),x40171),f252(f885(x40172,a871)))))
% 81.29/80.90 [4018]E(f328(f80(f885(f884(x40181,x40182),a871)),f328(f328(f265(x40181,x40182),f252(f885(x40181,a871))),f328(f16(f885(x40182,a871),x40181),x40183))),f328(f328(f265(x40181,x40182),f252(f885(x40181,a871))),f328(f16(f885(x40182,a871),x40181),f328(f80(f885(x40182,a871)),x40183))))
% 81.29/80.90 [4066]E(f328(f328(f43(f885(x40661,a871),f885(x40661,a871)),x40662),f328(f328(f7(f885(x40661,a871),f885(x40661,a871),f885(x40661,a871)),f107(f885(x40661,a871))),x40663)),f328(f328(f107(f885(x40661,a871)),f40(f885(x40661,a871),x40662)),x40663))
% 81.29/80.90 [4073]E(f328(f141(f878(x40731),f878(x40731),f127(x40731),f119(x40731)),f328(f328(f150(f878(x40731)),x40732),x40733)),f328(f328(f127(x40731),x40732),f328(f141(f878(x40731),f878(x40731),f127(x40731),f119(x40731)),x40733)))
% 81.29/80.90 [4095]E(f328(f328(f306(f885(x40951,a871)),f328(f282(x40951,x40951,x40952),f328(f328(f306(x40951),x40953),f193(f885(x40951,a871))))),f193(f885(f885(x40951,a871),a871))),f328(f328(f61(x40951),f328(f328(f306(x40951),x40953),f193(f885(x40951,a871)))),x40952))
% 81.29/80.90 [4105]E(f328(f328(f81(a877),f328(f328(f82(a877),x41051),f328(f328(f39(a877),x41052),x41053))),f328(f328(f39(a877),f328(f328(f82(a877),x41051),f45(a877,x41052,x41053))),x41053)),f328(f328(f39(a877),f328(f328(f82(a877),x41051),x41052)),x41053))
% 81.29/80.90 [4106]E(f328(f328(f81(a1),f328(f328(f82(a1),x41061),f328(f328(f39(a1),x41062),x41063))),f328(f328(f39(a1),f328(f328(f82(a1),x41061),f45(a1,x41062,x41063))),x41063)),f328(f328(f39(a1),f328(f328(f82(a1),x41061),x41062)),x41063))
% 81.29/80.90 [4143]E(f328(f328(f22(f885(x41431,a871)),f328(f171(x41431),x41432)),f328(f328(f306(x41431),x41433),f193(f885(x41431,a871)))),f328(f171(x41431),f328(f135(x41431,f328(f328(f8(a871,a871,x41431),a323),f328(a325,x41433))),x41432)))
% 81.29/80.90 [4191]E(f328(f328(f127(x41911),f328(f141(f878(x41911),f878(x41911),f127(x41911),f119(x41911)),x41912)),f328(f141(f878(x41911),f878(x41911),f127(x41911),f119(x41911)),x41913)),f328(f141(f878(x41911),f878(x41911),f127(x41911),f119(x41911)),f328(f328(f127(f878(x41911)),x41912),x41913)))
% 81.29/80.90 [4196]E(f328(f328(f257(f878(x41961),f878(x41961)),f328(f135(x41961,x41962),x41963)),f328(f135(x41961,f328(f74(a871,a871,x41961,a323),x41962)),x41963)),f166(x41961,x41962,x41963))
% 81.29/80.90 [4199]E(f328(f328(f81(a877),f328(f328(f81(a877),f328(f328(f39(a877),x41991),x41992)),f328(f328(f39(a877),x41993),x41992))),f328(f328(f39(a877),f328(f328(f81(a877),f45(a877,x41991,x41992)),f45(a877,x41993,x41992))),x41992)),f328(f328(f39(a877),f328(f328(f81(a877),x41991),x41993)),x41992))
% 81.29/80.90 [4200]E(f328(f328(f81(a1),f328(f328(f81(a1),f328(f328(f39(a1),x42001),x42002)),f328(f328(f39(a1),x42003),x42002))),f328(f328(f39(a1),f328(f328(f81(a1),f45(a1,x42001,x42002)),f45(a1,x42003,x42002))),x42002)),f328(f328(f39(a1),f328(f328(f81(a1),x42001),x42003)),x42002))
% 81.29/80.90 [4256]E(f328(f328(f107(f885(f878(x42561),a871)),f328(f328(f7(f878(x42561),f885(f878(x42561),a871),a871),f330(f878(x42561))),f160(x42561,x42562))),f328(f328(f7(f878(x42561),f885(f878(x42561),a871),a871),f330(f878(x42561))),f160(x42561,x42563))),f159(x42561,f328(f328(f107(f885(x42561,a871)),f328(f328(f7(x42561,f885(x42561,a871),a871),f330(x42561)),x42562)),f328(f328(f7(x42561,f885(x42561,a871),a871),f330(x42561)),x42563))))
% 81.29/80.90 [4269]E(f328(f249(x42691),f328(f328(f18(x42691,a871,a871),f328(f328(f8(a871,f885(a871,a871),x42691),a327),f328(f328(f7(x42691,x42691,a871),a325),x42692))),f328(f328(f7(x42691,f885(x42691,a871),a871),f330(x42691)),x42693))),f328(f328(f306(x42691),x42692),x42693))
% 81.29/80.90 [4289]E(f328(f328(f87(f878(f878(x42891)),f878(f878(x42891))),f54(x42891,x42892)),f328(f328(f18(f878(f878(x42891)),f878(f878(x42891)),f878(f878(x42891))),f328(f328(f8(f878(f878(x42891)),f885(f878(f878(x42891)),f878(f878(x42891))),f878(f878(x42891))),f127(f878(x42891))),f328(f153(f878(x42891),f878(x42891)),f328(f150(x42891),x42893)))),f5(f878(f878(x42891))))),f54(x42891,f328(f328(f150(x42891),x42893),x42892)))
% 81.29/80.90 [4293]E(f328(f249(x42931),f328(f328(f18(x42931,a871,a871),f328(f328(f8(a871,f885(a871,a871),x42931),a327),f328(f328(f7(x42931,f885(x42931,a871),a871),f330(x42931)),x42932))),f328(f328(f7(x42931,f885(x42931,a871),a871),f330(x42931)),x42933))),f328(f328(f116(f885(x42931,a871)),x42932),x42933))
% 81.29/80.90 [4294]E(f328(f249(x42941),f328(f328(f18(x42941,a871,a871),f328(f328(f8(a871,f885(a871,a871),x42941),a326),f328(f328(f7(x42941,f885(x42941,a871),a871),f330(x42941)),x42942))),f328(f328(f7(x42941,f885(x42941,a871),a871),f330(x42941)),x42943))),f328(f328(f107(f885(x42941,a871)),x42942),x42943))
% 81.29/80.90 [4385]E(f328(f328(f43(x43851,f885(f885(x43851,a871),a871)),x43852),f328(f328(f7(x43851,f885(f885(x43851,a871),a871),f885(f885(x43851,a871),a871)),f328(f328(f8(f885(x43851,a871),f885(f885(f885(x43851,a871),a871),f885(f885(x43851,a871),a871)),x43851),f306(f885(x43851,a871))),f328(f328(f8(f885(x43851,a871),f885(x43851,a871),x43851),f282(x43851,x43851,x43853)),f328(f328(f7(x43851,f885(x43851,a871),f885(x43851,a871)),f306(x43851)),f193(f885(x43851,a871)))))),f193(f885(f885(x43851,a871),a871)))),f328(f328(f61(x43851),x43852),x43853))
% 81.29/80.90 [4387]E(f328(f328(f210(x43871),f328(f328(f82(a1),f328(f328(f74(f884(a1,a1),a1,x43871,f256(a1,a1)),f220(x43871)),x43872)),f328(f328(f74(f884(a1,a1),a1,x43871,f256(a1,a1)),f220(x43871)),x43873))),f328(f328(f82(a1),f328(f328(f74(f884(a1,a1),a1,x43871,f266(a1,a1)),f220(x43871)),x43872)),f328(f328(f74(f884(a1,a1),a1,x43871,f266(a1,a1)),f220(x43871)),x43873))),f229(x43871,x43872,x43873))
% 81.29/80.90 [4390]E(f328(f249(f878(x43901)),f328(f328(f18(f878(x43901),a871,a871),f328(f328(f8(a871,f885(a871,a871),f878(x43901)),a326),f328(f328(f7(f878(x43901),a877,a871),f328(f328(f8(a877,f885(a877,a871),f878(x43901)),a325),f194(f878(x43901)))),x43902))),f328(f328(f7(f878(x43901),f885(x43901,a871),a871),f328(f328(f8(f885(x43901,a871),f885(f885(x43901,a871),a871),f878(x43901)),f244(f885(x43901,a871))),f171(x43901))),f328(f171(x43901),x43903)))),f328(f171(f878(x43901)),f55(x43901,x43902,x43903)))
% 81.29/80.90 [3776]E(f45(a877,f328(f328(f81(a877),f328(f328(f82(a877),x37761),x37762)),x37763),x37762),f45(a877,x37763,x37762))
% 81.29/80.90 [3822]E(f138(a877,f328(f298(a877,f328(f328(f81(a877),x38221),x38222)),x38223)),f328(f328(f137(a877),x38222),f138(a877,f328(f298(a877,x38221),x38223))))
% 81.29/80.90 [3865]E(f328(f328(f81(a1),f328(f106(a1),x38651)),f328(f328(f81(a1),f328(f106(a1),x38652)),x38653)),f328(f328(f81(a1),f328(f106(a1),f328(f328(f81(a877),x38651),x38652))),x38653))
% 81.29/80.90 [3872]E(f328(f328(f22(f885(x38721,a871)),f328(f328(f22(f885(x38721,a871)),x38722),x38723)),x38723),f328(f328(f22(f885(x38721,a871)),x38722),x38723))
% 81.29/80.90 [3873]E(f328(f328(f116(f885(x38731,a871)),f328(f328(f22(f885(x38731,a871)),x38732),x38733)),x38733),f328(f328(f116(f885(x38731,a871)),x38732),x38733))
% 81.29/80.90 [3896]E(f328(f328(f285(x38961,x38961,x38962),f304(x38961,f193(f885(f884(x38961,x38961),a871)))),x38963),x38963)
% 81.29/80.90 [3902]E(f328(f328(f116(f885(x39021,a871)),f328(f281(x39021),x39022)),f328(f281(x39021),x39023)),f328(f281(x39021),f328(f328(f116(f885(f884(x39021,x39021),a871)),x39022),x39023)))
% 81.29/80.90 [3913]E(f272(x39131,f328(f328(f150(f884(a105,x39131)),f328(f328(f257(a105,x39131),f2(a105)),x39132)),x39133)),f272(x39131,x39133))
% 81.29/80.90 [3916]E(f328(f328(f116(f885(x39161,a871)),f40(f885(x39161,a871),x39162)),f40(f885(x39161,a871),x39163)),f40(f885(x39161,a871),f328(f328(f116(f885(f885(x39161,a871),a871)),x39162),x39163)))
% 81.29/80.90 [3917]E(f328(f328(f107(f885(x39171,a871)),f41(f885(x39171,a871),x39172)),f41(f885(x39171,a871),x39173)),f41(f885(x39171,a871),f328(f328(f116(f885(f885(x39171,a871),a871)),x39172),x39173)))
% 81.29/80.90 [3953]E(f328(f328(f285(x39531,x39531,x39531),f328(f328(f188(f884(x39531,x39531),a871),x39532),x39533)),x39533),f328(f328(f188(f884(x39531,x39531),a871),f328(a118,x39532)),x39533))
% 81.29/80.90 [4003]P24(f328(f328(f244(f885(x40031,a871)),f328(f328(f22(f885(x40031,a871)),x40032),x40033)),x40032))
% 81.29/80.90 [4004]P24(f328(f328(f244(f885(x40041,a871)),f328(f328(f107(f885(x40041,a871)),x40042),x40043)),x40043))
% 81.29/80.90 [4005]P24(f328(f328(f244(f885(x40051,a871)),f328(f328(f107(f885(x40051,a871)),x40052),x40053)),x40052))
% 81.29/80.90 [4030]E(f304(x40301,f328(f328(f116(f885(f884(x40301,x40301),a871)),f304(x40301,x40302)),f304(x40301,x40303))),f304(x40301,f328(f328(f116(f885(f884(x40301,x40301),a871)),x40302),x40303)))
% 81.29/80.90 [4034]E(f40(f885(x40341,a871),f328(f328(f306(f885(x40341,a871)),x40342),f328(f328(f306(f885(x40341,a871)),x40343),f193(f885(f885(x40341,a871),a871))))),f328(f328(f116(f885(x40341,a871)),x40342),x40343))
% 81.29/80.90 [4035]E(f41(f885(x40351,a871),f328(f328(f306(f885(x40351,a871)),x40352),f328(f328(f306(f885(x40351,a871)),x40353),f193(f885(f885(x40351,a871),a871))))),f328(f328(f107(f885(x40351,a871)),x40352),x40353))
% 81.29/80.90 [4041]E(f328(f328(f285(x40411,x40411,x40411),f328(f328(f188(f884(x40411,x40411),a871),x40412),x40413)),x40413),f328(f328(f285(x40411,x40411,x40411),x40413),f328(f328(f188(f884(x40411,x40411),a871),x40412),x40413)))
% 81.29/80.90 [4110]E(f328(f328(f116(f885(x41101,a871)),f328(f249(x41101),f328(f328(f7(x41101,x41101,a871),a325),x41102))),x41103),f328(f328(f306(x41101),x41102),x41103))
% 81.29/80.90 [4112]E(f328(a110,f328(f328(f6(x41121,a1),f328(f328(f8(a877,a1,x41121),f106(a1)),x41122)),x41123)),f328(f328(f6(x41121,a877),x41122),x41123))
% 81.29/80.90 [4113]E(f328(a110,f328(f328(f9(x41131,a1),f328(f328(f8(a877,a1,x41131),f106(a1)),x41132)),x41133)),f328(f328(f9(x41131,a877),x41132),x41133))
% 81.29/80.90 [4188]E(f328(f155(f878(x41881),x41881,f328(f170(x41881),x41882),f328(f16(f885(f878(x41881),f878(x41881)),x41881),f328(f328(f7(f878(x41881),f878(x41881),f878(x41881)),f127(x41881)),x41882))),x41883),f328(f170(x41881),f328(f328(f127(x41881),x41883),x41882)))
% 81.29/80.90 [4219]P24(f328(f328(f244(f885(f885(x42191,a871),a871)),f328(f328(f116(f885(f885(x42191,a871),a871)),f328(f305(x42191),x42192)),f328(f305(x42191),x42193))),f328(f305(x42191),f328(f328(f116(f885(x42191,a871)),x42192),x42193))))
% 81.29/80.90 [4312]E(f328(f249(x43121),f328(f328(f18(x43121,a871,a871),f328(f328(f8(a871,f885(a871,a871),x43121),a326),f328(f328(f7(x43121,f885(x43121,a871),a871),f330(x43121)),x43122))),f328(f328(f8(a871,a871,x43121),a323),f328(f328(f7(x43121,f885(x43121,a871),a871),f330(x43121)),x43123)))),f328(f328(f22(f885(x43121,a871)),x43122),x43123))
% 81.29/80.90 [4334]E(f328(f38(a877),f328(f249(a877),f328(f328(f18(a877,a871,a871),f328(f328(f8(a871,f885(a871,a871),a877),a326),f328(f328(f7(a877,a877,a871),f245(a877)),f328(f194(f878(x43341)),x43342)))),f328(f328(f8(x43341,a871,a877),x43343),f328(f164(x43341),x43342))))),f328(f194(f878(x43341)),f328(f135(x43341,x43343),x43342)))
% 81.29/80.90 [4336]E(f328(f194(f878(x43361)),f175(x43361,x43362,x43363)),f328(f38(a877),f328(f249(a877),f328(f328(f18(a877,a871,a871),f328(f328(f8(a871,f885(a871,a871),a877),a326),f328(f328(f7(a877,a877,a871),f245(a877)),f328(f194(f878(x43361)),x43362)))),f328(f328(f7(a877,f885(a877,a871),a871),f330(a877)),x43363)))))
% 81.29/80.90 [4433]E(f328(f328(f107(f885(f884(f878(x44331),f878(x44331)),a871)),f328(f307(f884(f884(x44331,f878(x44331)),f884(x44331,f878(x44331))),f884(f878(x44331),f878(x44331)),f268(f884(x44331,f878(x44331)),f878(x44331),f884(x44331,f878(x44331)),f878(x44331),f328(f267(x44331,f878(x44331),f878(x44331)),f150(x44331)),f328(f267(x44331,f878(x44331),f878(x44331)),f150(x44331)))),f320(x44331,f878(x44331),x44332,f328(f142(x44331,x44332),x44333)))),f328(f249(f884(f878(x44331),f878(x44331))),f328(f267(f878(x44331),f878(x44331),a871),f328(f328(f7(f878(x44331),f885(f878(x44331),a871),f885(f878(x44331),a871)),f328(f328(f8(f885(a871,a871),f885(f885(f878(x44331),a871),f885(f878(x44331),a871)),f878(x44331)),f8(a871,a871,f878(x44331))),f328(f328(f8(a871,f885(a871,a871),f878(x44331)),a326),f328(f328(f7(f878(x44331),a877,a871),f328(f328(f8(a877,f885(a877,a871),f878(x44331)),a325),f194(f878(x44331)))),f328(a118,x44333))))),f328(f328(f7(f878(x44331),a877,a871),f328(f328(f8(a877,f885(a877,a871),f878(x44331)),a325),f194(f878(x44331)))),f328(a118,x44333)))))),f328(f142(x44331,x44332),f328(a118,x44333)))
% 81.29/80.90 [3918]E(f45(a877,f328(a118,f328(f328(f81(a877),f328(f328(f82(a877),x39181),x39182)),x39183)),x39182),f45(a877,f328(a118,x39183),x39182))
% 81.29/80.90 [4178]E(f328(f249(x41781),f328(f328(f18(x41781,a871,a871),f328(f328(f8(a871,f885(a871,a871),x41781),a326),x41782)),x41783)),f328(f328(f107(f885(x41781,a871)),f328(f249(x41781),x41782)),f328(f249(x41781),x41783)))
% 81.29/80.90 [4179]E(f328(f249(x41791),f328(f328(f18(x41791,a871,a871),f328(f328(f8(a871,f885(a871,a871),x41791),a327),x41792)),x41793)),f328(f328(f116(f885(x41791,a871)),f328(f249(x41791),x41792)),f328(f249(x41791),x41793)))
% 81.29/80.90 [4181]E(f328(f328(f127(x41811),f328(f328(f137(x41811),f45(a877,x41812,f328(f194(f878(x41811)),x41813))),x41813)),f328(f328(f174(x41811),f45(a877,x41812,f328(f194(f878(x41811)),x41813))),x41813)),f328(f328(f328(f188(f878(x41811),f878(x41811)),x41812),f167(x41811)),x41813))
% 81.29/80.90 [4186]E(f328(f249(x41861),f328(f328(f18(x41861,a871,a871),f328(f328(f8(a871,f885(a871,a871),x41861),a331),x41862)),x41863)),f328(f328(f116(f885(x41861,a871)),f328(f80(f885(x41861,a871)),f328(f249(x41861),x41862))),f328(f249(x41861),x41863)))
% 81.29/80.90 [4201]E(f328(f328(f81(a877),f328(f194(f878(x42011)),f328(f135(x42011,x42012),x42013))),f328(f194(f878(x42011)),f328(f135(x42011,f328(f328(f8(a871,a871,x42011),a323),x42012)),x42013))),f328(f194(f878(x42011)),x42013))
% 81.29/80.90 [4226]P24(f328(f328(f244(f885(x42261,a871)),f328(f328(f116(f885(x42261,a871)),f41(f885(x42261,a871),x42262)),f41(f885(x42261,a871),x42263))),f41(f885(x42261,a871),f328(f328(f107(f885(f885(x42261,a871),a871)),x42262),x42263))))
% 81.29/80.90 [4240]E(f328(f171(x42401),f328(f135(x42401,f328(f328(f8(a871,a871,x42401),a323),f328(f328(f7(x42401,x42401,a871),a325),x42402))),x42403)),f328(f328(f22(f885(x42401,a871)),f328(f171(x42401),x42403)),f328(f328(f306(x42401),x42402),f193(f885(x42401,a871)))))
% 81.29/80.90 [4249]P24(f328(f328(f244(f885(f884(x42491,x42491),a871)),f328(f328(f116(f885(f884(x42491,x42491),a871)),f304(x42491,x42492)),f304(x42491,x42493))),f304(x42491,f328(f328(f116(f885(f884(x42491,x42491),a871)),x42492),x42493))))
% 81.29/80.90 [4274]E(f328(f328(f82(a877),f328(a118,f328(a118,f2(a877)))),f328(f328(f6(a877,a877),f328(f328(f8(a877,a877,a877),f328(f81(a877),x42741)),f328(f328(f7(a877,a877,a877),f82(a877)),x42742))),f328(f250(a877),x42743))),f328(f328(f82(a877),x42743),f328(f328(f81(a877),x42741),f328(f328(f81(a877),x42741),f328(f328(f82(a877),f328(f328(f22(a877),x42743),f79(a877))),x42742)))))
% 81.29/80.90 [4284]E(f328(f249(x42841),f328(f328(f18(x42841,a871,a871),f328(f328(f8(a871,f885(a871,a871),x42841),a326),f328(f328(f7(x42841,f885(x42841,a871),a871),f330(x42841)),f328(f171(x42841),x42842)))),x42843)),f328(f171(x42841),f328(f135(x42841,x42843),x42842)))
% 81.29/80.90 [4432]E(f328(f249(x44321),f328(f328(f8(f885(a877,a871),a871,x44321),f88(a877)),f328(f328(f7(x44321,f885(a877,a871),f885(a877,a871)),f328(f328(f8(f885(a877,f885(a871,a871)),f885(f885(a877,a871),f885(a877,a871)),x44321),f18(a877,a871,a871)),f328(f328(f8(f885(a877,a871),f885(a877,f885(a871,a871)),x44321),f328(f8(a871,f885(a871,a871),a877),a326)),f328(f328(f7(x44321,f885(a877,x44321),f885(a877,a871)),f328(f328(f8(f885(x44321,a871),f885(f885(a877,x44321),f885(a877,a871)),x44321),f8(x44321,a871,a877)),a325)),f328(f164(x44321),x44322))))),f328(f328(f18(a877,a871,a871),f328(f328(f8(a871,f885(a871,a871),a877),a326),f328(f328(f7(a877,a877,a871),f245(a877)),f328(f194(f878(x44321)),x44322)))),f328(f328(f7(a877,f885(a877,a871),a871),f330(a877)),x44323))))),f328(f171(x44321),f175(x44321,x44322,x44323)))
% 81.29/80.90 [4324]E(f328(f249(x43241),f328(f328(f18(x43241,a871,a871),f328(f328(f8(a871,f885(a871,a871),x43241),a331),f328(f328(f8(a871,a871,x43241),a323),f328(f328(f7(x43241,x43241,a871),a325),x43242)))),x43243)),f328(f328(f306(x43241),x43242),f328(f249(x43241),x43243)))
% 81.29/80.90 [4356]E(f328(f328(f153(f884(x43561,a877),x43561),f256(x43561,a877)),f328(f135(f884(x43561,a877),f328(f328(f7(f884(x43561,a877),f885(a877,a871),a871),f328(f328(f8(a877,f885(f885(a877,a871),a871),f884(x43561,a877)),f330(a877)),f266(x43561,a877))),x43562)),f328(f328(f181(x43561,a877),x43563),f138(a877,f328(f298(a877,f2(a877)),f328(f194(f878(x43561)),x43563)))))),f175(x43561,x43563,x43562))
% 81.29/80.90 [4386]E(f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f328(f328(f6(a877,a1),f328(f328(f8(a1,a1,a877),f328(f81(a1),x43861)),f328(f328(f7(a877,a1,a1),f328(f328(f8(a1,f885(a1,a1),a877),f82(a1)),f106(a1))),x43862))),f328(f250(a877),x43863))),f328(f328(f82(a1),f328(f106(a1),x43863)),f328(f328(f81(a1),x43861),f328(f328(f81(a1),x43861),f328(f328(f82(a1),f328(f106(a1),f328(f328(f22(a877),x43863),f79(a877)))),x43862)))))
% 81.29/80.90 [4426]E(f328(f249(f884(x44261,x44262)),f328(f267(x44261,x44262,a871),f328(f328(f7(x44261,f885(f884(x44262,x44261),a871),f885(x44262,a871)),f328(f328(f8(f885(x44262,f885(f885(f884(x44262,x44261),a871),a871)),f885(f885(f884(x44262,x44261),a871),f885(x44262,a871)),x44261),f7(x44262,f885(f884(x44262,x44261),a871),a871)),f328(f328(f8(f885(x44262,f884(x44262,x44261)),f885(x44262,f885(f885(f884(x44262,x44261),a871),a871)),x44261),f328(f8(f884(x44262,x44261),f885(f885(f884(x44262,x44261),a871),a871),x44262),f330(f884(x44262,x44261)))),f328(f7(x44262,x44261,f884(x44262,x44261)),f257(x44262,x44261))))),x44263))),f328(f283(x44262,x44261),x44263))
% 81.29/80.90 [4448]E(f328(f249(f878(x44481)),f328(f328(f8(f885(x44481,a871),a871,f878(x44481)),f88(x44481)),f328(f328(f8(f885(x44481,f885(f878(x44481),a871)),f885(x44481,a871),f878(x44481)),f328(f8(f885(f878(x44481),a871),a871,x44481),f88(f878(x44481)))),f328(f328(f7(f878(x44481),f885(x44481,f885(f878(x44481),a871)),f885(x44481,f885(f878(x44481),a871))),f328(f328(f8(f885(x44481,f885(f885(f878(x44481),a871),f885(f878(x44481),a871))),f885(f885(x44481,f885(f878(x44481),a871)),f885(x44481,f885(f878(x44481),a871))),f878(x44481)),f18(x44481,f885(f878(x44481),a871),f885(f878(x44481),a871))),f328(f328(f8(f885(x44481,f885(f878(x44481),f885(a871,a871))),f885(x44481,f885(f885(f878(x44481),a871),f885(f878(x44481),a871))),f878(x44481)),f328(f8(f885(f878(x44481),f885(a871,a871)),f885(f885(f878(x44481),a871),f885(f878(x44481),a871)),x44481),f18(f878(x44481),a871,a871))),f328(f328(f8(f885(x44481,f885(f878(x44481),a871)),f885(x44481,f885(f878(x44481),f885(a871,a871))),f878(x44481)),f328(f8(f885(f878(x44481),a871),f885(f878(x44481),f885(a871,a871)),x44481),f328(f8(a871,f885(a871,a871),f878(x44481)),a326))),f328(f328(f7(f878(x44481),f885(x44481,f885(f878(x44481),f878(x44481))),f885(x44481,f885(f878(x44481),a871))),f328(f328(f8(f885(f885(f878(x44481),f878(x44481)),f885(f878(x44481),a871)),f885(f885(x44481,f885(f878(x44481),f878(x44481))),f885(x44481,f885(f878(x44481),a871))),f878(x44481)),f8(f885(f878(x44481),f878(x44481)),f885(f878(x44481),a871),x44481)),f328(f328(f8(f885(f878(x44481),a871),f885(f885(f878(x44481),f878(x44481)),f885(f878(x44481),a871)),f878(x44481)),f8(f878(x44481),a871,f878(x44481))),a325))),f150(x44481)))))),f328(f328(f7(x44481,f885(f878(x44481),a871),f885(f878(x44481),a871)),f328(f328(f8(f885(a871,a871),f885(f885(f878(x44481),a871),f885(f878(x44481),a871)),x44481),f8(a871,a871,f878(x44481))),f328(f328(f8(a871,f885(a871,a871),x44481),a326),f328(f328(f7(x44481,f885(x44481,a871),a871),f330(x44481)),x44482)))),f328(f328(f7(f878(x44481),f885(f878(x44481),a871),a871),f330(f878(x44481))),x44483)))))),f173(x44481,x44482,x44483))
% 81.29/80.90 [4445]E(f328(f328(f87(a1,f884(a1,a1)),f328(f328(f22(a1),x44451),x44452)),f328(f328(f7(a1,f884(a1,a1),f884(a1,a1)),f328(f328(f18(a1,f884(a1,a1),f885(f884(a1,a1),f884(a1,a1))),f328(f328(f8(a871,f885(f884(a1,a1),f885(f884(a1,a1),f884(a1,a1))),a1),f102(f884(a1,a1))),f328(f244(a1),f2(a1)))),f328(f257(a1,a1),f328(f328(f81(a1),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x44453)),f79(a1))))),f328(f328(f257(a1,a1),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x44453)),x44451))),f328(f44(x44452),f328(f328(f257(a1,a1),x44453),x44451)))
% 81.29/80.90 [4476]~E(f33(x44761,x44762),f34(x44763,x44764))
% 81.29/80.90 [4496]~E(f328(a26,x44961),f29(x44962,x44963,x44964))
% 81.29/80.90 [4497]~E(f328(a26,x44971),f31(x44972,x44973,x44974))
% 81.29/80.90 [4498]~E(f328(a26,x44981),f30(x44982,x44983,x44984))
% 81.29/80.90 [4499]~E(f29(x44991,x44992,x44993),f328(a26,x44994))
% 81.29/80.90 [4500]~E(f31(x45001,x45002,x45003),f328(a26,x45004))
% 81.29/80.90 [4501]~E(f30(x45011,x45012,x45013),f328(a26,x45014))
% 81.29/80.90 [3473]E(f328(f328(f328(f73(x34731,x34732),x34733),x34734),f328(x34733,x34734)),x34733)
% 81.29/80.90 [3532]E(f328(f328(f259(x35321,x35322,x35323),x35324),f2(a877)),x35322)
% 81.29/80.90 [3572]E(f190(x35721,x35722,x35723,f328(a118,x35724)),f328(x35723,x35724))
% 81.29/80.90 [3611]E(f169(x36111,x36112,f169(x36111,x36113,x36114)),f169(x36111,x36113,f169(x36111,x36112,x36114)))
% 81.29/80.90 [3745]E(f328(f238(x37451,x37452,x37453,x37454),f196(x37452)),x37453)
% 81.29/80.90 [3747]E(f328(f155(x37471,x37472,x37473,x37474),f119(x37472)),x37473)
% 81.29/80.90 [3748]E(f328(f141(x37481,x37482,x37483,x37484),f119(x37482)),x37484)
% 81.29/80.90 [3862]E(f328(f238(f881(x38621),x38622,f196(x38621),f328(f16(f881(x38621),x38622),f196(x38621))),f328(x38623,x38624)),f196(x38621))
% 81.29/80.90 [3906]E(f328(f328(f116(f885(x39061,a871)),f183(x39061,x39062,x39063)),f183(x39061,x39062,x39064)),f183(x39061,x39062,f184(x39061,x39062,x39064,x39063)))
% 81.29/80.90 [3938]E(f328(f328(f269(x39381,x39382,x39383,f884(x39382,x39383)),x39384),f257(x39382,x39383)),x39384)
% 81.29/80.90 [3947]E(f239(x39471,x39472,x39473,x39474,f196(x39472)),x39473)
% 81.29/80.90 [3948]E(f186(x39481,x39482,x39483,x39484,f119(x39482)),x39483)
% 81.29/80.90 [3949]E(f186(x39491,x39492,x39493,f119(x39491),x39494),x39493)
% 81.29/80.90 [4233]P42(x42331,x42332,x42333,x42334,f193(f885(x42331,a871)),x42334)
% 81.29/80.90 [3274]E(f328(f328(f16(x32741,x32742),x32743),x32744),x32743)
% 81.29/80.90 [3391]E(f328(f328(f207(x33911,x33912),x33913),f328(f236(x33911),x33914)),f328(f236(x33912),f328(x33913,x33914)))
% 81.29/80.90 [3562]E(f169(x35621,x35622,f328(f135(x35621,x35623),x35624)),f328(f135(x35621,x35623),f169(x35621,x35622,x35624)))
% 81.29/80.90 [3595]E(f328(f328(f65(x35951,x35952,x35953),x35954),f193(f885(x35951,a871))),x35954)
% 81.29/80.90 [3617]E(f328(f328(f164(x36171),f328(f328(f150(x36171),x36172),x36173)),f328(a118,x36174)),f328(f328(f164(x36171),x36173),x36174))
% 81.29/80.90 [3661]P30(x36611,f2(a877),f328(f328(f328(f93(x36611),x36612),f328(a26,x36613)),x36614))
% 81.29/80.90 [3686]E(f328(f328(x36861,x36862),f328(f189(x36863,x36864,x36861),x36862)),f328(f189(x36863,x36864,x36861),f328(a118,x36862)))
% 81.29/80.90 [3781]E(f328(f328(f158(x37811,f328(f328(f150(x37811),x37812),x37813)),f2(a877)),x37814),f328(f328(f150(x37811),x37814),x37813))
% 81.29/80.90 [3792]E(f328(f328(f43(f885(x37921,a871),f885(x37922,a871)),x37923),f307(x37921,x37922,x37924)),f328(f307(x37921,x37922,x37924),f40(f885(x37921,a871),x37923)))
% 81.29/80.90 [3793]E(f328(f328(f43(f885(x37931,a871),f885(x37932,a871)),x37933),f308(x37932,x37931,x37934)),f328(f308(x37932,x37931,x37934),f40(f885(x37931,a871),x37933)))
% 81.29/80.90 [3889]E(f183(x38891,x38892,f187(x38891,x38892,x38893,x38894)),f328(f328(f107(f885(x38891,a871)),f183(x38891,x38892,x38893)),x38894))
% 81.29/80.90 [3893]E(f328(f131(x38931,x38932),f129(x38931,x38933,x38934)),f328(f328(f81(a877),f328(f328(f81(a877),f328(x38932,x38933)),f328(f131(x38931,x38932),x38934))),f328(a118,f2(a877))))
% 81.29/80.90 [3912]E(f328(f141(x39121,x39122,f328(f7(x39122,x39121,x39121),x39123),x39124),f328(f168(x39122),f119(x39122))),x39124)
% 81.29/80.90 [3960]E(f77(x39601,x39602,x39603,x39604,f193(f885(x39601,a871))),x39603)
% 81.29/80.90 [4006]E(f328(f328(f328(f328(f73(x40061,f881(x40062)),f328(f16(f881(x40062),x40061),f196(x40062))),x40063),f196(x40062)),x40064),f196(x40062))
% 81.29/80.90 [4161]E(f328(f267(x41611,x41612,x41613),f328(f328(f8(f885(x41612,f884(x41611,x41612)),f885(x41612,x41613),x41611),f328(f8(f884(x41611,x41612),x41613,x41612),x41614)),f257(x41611,x41612))),x41614)
% 81.29/80.90 [3471]E(f328(f266(x34711,x34712),f328(f328(f257(x34711,x34712),x34713),x34714)),x34714)
% 81.29/80.90 [3472]E(f328(f256(x34721,x34722),f328(f328(f257(x34721,x34722),x34723),x34724)),x34723)
% 81.29/80.90 [3505]E(f328(f194(f878(x35051)),f328(f328(f153(x35052,x35051),x35053),x35054)),f328(f194(f878(x35052)),x35054))
% 81.29/80.90 [3506]E(f328(f194(f878(x35061)),f328(f328(f158(x35061,x35062),x35063),x35064)),f328(f194(f878(x35061)),x35062))
% 81.29/80.90 [3526]E(f328(f328(f137(x35261),f328(a118,x35262)),f328(f328(f150(x35261),x35263),x35264)),f328(f328(f137(x35261),x35262),x35264))
% 81.29/80.90 [3597]E(f328(f328(f306(x35971),x35972),f328(f328(f306(x35971),x35973),x35974)),f328(f328(f306(x35971),x35973),f328(f328(f306(x35971),x35972),x35974)))
% 81.29/80.90 [3600]E(f328(f328(f153(x36001,x36002),x36003),f120(x36001,x36004)),f120(x36002,f328(f328(f153(x36001,x36002),x36003),x36004)))
% 81.29/80.90 [3615]E(f328(f168(x36151),f328(f328(f153(x36152,x36151),x36153),x36154)),f328(f328(f153(x36152,x36151),x36153),f328(f168(x36152),x36154)))
% 81.29/80.90 [3616]E(f328(f328(f153(x36161,x36162),x36163),f328(f170(x36161),x36164)),f328(f170(x36162),f328(f328(f153(x36161,x36162),x36163),x36164)))
% 81.29/80.90 [3629]E(f328(f328(f174(x36291),f328(a118,x36292)),f328(f328(f150(x36291),x36293),x36294)),f328(f328(f150(x36291),x36293),f328(f328(f174(x36291),x36292),x36294)))
% 81.29/80.90 [3633]E(f328(f171(x36331),f328(f328(f153(x36332,x36331),x36333),x36334)),f328(f307(x36332,x36331,x36333),f328(f171(x36332),x36334)))
% 81.29/80.90 [3685]E(f17(x36851,x36852,x36853,f328(a3,f328(a118,f328(a19,x36854)))),f328(x36853,x36854))
% 81.29/80.90 [3688]E(f328(f328(f127(x36881),f328(f135(x36881,x36882),x36883)),f328(f135(x36881,x36882),x36884)),f328(f135(x36881,x36882),f328(f328(f127(x36881),x36883),x36884)))
% 81.29/80.90 [3701]E(f151(x37011,f328(f328(f153(x37012,x37011),x37013),f151(x37012,x37014))),f151(x37011,f328(f328(f153(x37012,x37011),x37013),x37014)))
% 81.29/80.90 [3717]E(f328(f283(x37171,x37171),f328(f328(f284(x37172,x37171),x37173),x37174)),f328(f328(f284(x37172,x37171),f328(f283(x37172,x37172),x37173)),x37174))
% 81.29/80.90 [3727]E(f328(f328(f285(x37271,x37272,x37273),x37274),f193(f885(f884(x37272,x37273),a871))),f193(f885(f884(x37271,x37273),a871)))
% 81.29/80.90 [3728]E(f328(f328(f174(x37281),f328(f328(f22(a877),x37282),x37283)),f328(f328(f137(x37281),x37283),x37284)),f328(f328(f137(x37281),x37283),f328(f328(f174(x37281),x37282),x37284)))
% 81.29/80.90 [3773]E(f40(f885(x37731,a871),f328(f307(x37732,f885(x37731,a871),x37733),x37734)),f328(f328(f43(x37732,f885(x37731,a871)),x37734),x37733))
% 81.29/80.90 [3774]E(f41(f885(x37741,a871),f328(f307(x37742,f885(x37741,a871),x37743),x37744)),f328(f328(f42(x37742,f885(x37741,a871)),x37744),x37743))
% 81.29/80.90 [3775]E(f328(f194(f878(f884(x37751,x37752))),f328(f328(f181(x37751,x37752),x37753),x37754)),f328(f328(f242(a877),f328(f194(f878(x37751)),x37753)),f328(f194(f878(x37752)),x37754)))
% 81.29/80.90 [3777]E(f328(f308(x37771,x37772,x37773),f328(f80(f885(x37772,a871)),x37774)),f328(f80(f885(x37771,a871)),f328(f308(x37771,x37772,x37773),x37774)))
% 81.29/80.90 [3807]E(f328(f187(x38071,x38072,x38073,f193(f885(x38071,a871))),x38074),f196(x38072))
% 81.29/80.90 [3828]E(f328(f308(x38281,x38282,x38283),f328(f249(x38282),x38284)),f328(f249(x38281),f328(f328(f8(x38282,a871,x38281),x38284),x38283)))
% 81.29/80.90 [3845]E(f328(f328(f164(x38451),f328(f328(f127(x38451),x38452),f328(f328(f150(x38451),x38453),x38454))),f328(f194(f878(x38451)),x38452)),x38453)
% 81.29/80.90 [3850]E(f328(f187(x38501,x38502,f328(f16(f881(x38502),x38501),f196(x38502)),x38503),x38504),f196(x38502))
% 81.29/80.90 [3870]E(f328(f307(x38701,x38702,x38703),f328(f308(x38701,x38702,x38703),x38704)),f328(f328(f107(f885(x38702,a871)),x38704),f328(f307(x38701,x38702,x38703),f252(f885(x38701,a871)))))
% 81.29/80.90 [3888]P24(f328(f328(f330(x38881),f328(x38882,x38883)),f328(f307(x38884,x38881,x38882),f252(f885(x38884,a871)))))
% 81.29/80.90 [3901]E(f328(f328(f265(x39011,x39012),f328(f171(x39011),x39013)),f328(f16(f885(x39012,a871),x39011),f328(f171(x39012),x39014))),f328(f171(f884(x39011,x39012)),f60(x39011,x39012,x39013,x39014)))
% 81.29/80.90 [3915]E(f154(x39151,x39152,f328(f328(f150(x39151),x39153),x39154)),f328(f328(f81(a877),f328(f328(f81(a877),f328(x39152,x39153)),f154(x39151,x39152,x39154))),f328(a118,f2(a877))))
% 81.29/80.90 [3929]E(f190(f878(x39291),f328(f328(f150(x39291),x39292),x39293),f328(f328(f7(a877,f878(x39291),f878(x39291)),f137(x39291)),x39293),x39294),f328(f328(f137(x39291),x39294),f328(f328(f150(x39291),x39292),x39293)))
% 81.29/80.90 [3930]P21(x39301,f884(x39302,x39301),f332(x39303,x39304,x39302,x39301),f328(f328(f43(x39302,f885(x39301,a871)),x39304),x39303))
% 81.29/80.90 [3939]E(f328(f328(f22(f885(x39391,a871)),f328(f328(f22(f885(x39391,a871)),x39392),x39393)),f328(f328(f306(x39391),x39394),f193(f885(x39391,a871)))),f328(f328(f22(f885(x39391,a871)),x39392),f328(f328(f306(x39391),x39394),x39393)))
% 81.29/80.90 [3951]E(f328(f328(f188(f885(x39511,x39512),f885(x39511,x39512)),x39513),f74(x39512,x39512,x39511,x39514)),f74(x39512,x39512,x39511,f328(f328(f188(x39512,x39512),x39513),x39514)))
% 81.29/80.90 [4029]E(f328(f328(f328(f188(f878(x40291),f878(x40291)),x40292),f167(x40291)),f328(f328(f328(f188(f878(x40291),f878(x40291)),x40293),f167(x40291)),x40294)),f328(f328(f328(f188(f878(x40291),f878(x40291)),f328(f328(f81(a877),x40292),x40293)),f167(x40291)),x40294))
% 81.29/80.90 [4115]P24(f328(f328(f244(f885(x41151,a871)),f328(f171(x41151),f328(f328(f158(x41151,x41152),x41153),x41154))),f328(f328(f306(x41151),x41154),f328(f171(x41151),x41152))))
% 81.29/80.90 [4151]E(f328(f328(f43(f885(x41511,a871),f885(f884(x41511,x41512),a871)),x41513),f328(f328(f7(f885(x41511,a871),f885(x41511,f885(x41512,a871)),f885(f884(x41511,x41512),a871)),f265(x41511,x41512)),x41514)),f328(f328(f265(x41511,x41512),f40(f885(x41511,a871),x41513)),x41514))
% 81.29/80.90 [4187]E(f217(x41871,x41872,x41873,f328(f74(x41872,f885(a105,f885(a105,f885(f884(a105,a105),f885(a105,f879(x41872))))),x41871,f216(x41872)),x41874)),f218(x41871,x41872,x41874,x41873))
% 81.29/80.90 [4204]E(f213(x42041,x42042,x42043,f328(f74(x42042,f885(a105,f885(a105,f885(f884(a105,a105),f885(a105,f879(f881(x42042)))))),x42041,f212(x42042)),x42044)),f214(x42041,x42042,x42044,x42043))
% 81.29/80.90 [4209]P24(f328(f67(x42091,x42092,x42093,x42094,f193(f885(x42091,a871))),x42094))
% 81.29/80.90 [4251]E(f328(f328(f43(x42511,f885(x42512,a871)),x42513),f328(f328(f7(x42511,f885(x42512,a871),f885(x42512,a871)),f328(f328(f8(x42512,f885(f885(x42512,a871),f885(x42512,a871)),x42511),f306(x42512)),x42514)),f193(f885(x42512,a871)))),f328(f307(x42511,x42512,x42514),x42513))
% 81.29/80.90 [4258]P24(f328(f328(f244(f885(x42581,a871)),f328(f253(x42582,x42581),f328(f328(f107(f885(f884(x42582,x42581),a871)),x42583),x42584))),f328(f328(f107(f885(x42581,a871)),f328(f253(x42582,x42581),x42583)),f328(f253(x42582,x42581),x42584))))
% 81.29/80.90 [4259]P24(f328(f328(f244(f885(x42591,a871)),f328(f255(x42591,x42592),f328(f328(f107(f885(f884(x42591,x42592),a871)),x42593),x42594))),f328(f328(f107(f885(x42591,a871)),f328(f255(x42591,x42592),x42593)),f328(f255(x42591,x42592),x42594))))
% 81.29/80.90 [4321]P24(f328(f328(f244(f885(f884(x43211,x43212),a871)),f328(f307(x43212,f884(x43211,x43212),f332(x43213,x43214,x43211,x43212)),f328(f328(f43(x43211,f885(x43212,a871)),x43214),x43213))),f328(f328(f265(x43211,x43212),x43214),x43213)))
% 81.29/80.90 [4322]E(f328(f122(x43221,f884(x43221,x43222),x43223),f328(f328(f8(f885(x43222,f879(f884(x43221,x43222))),f879(f884(x43221,x43222)),x43221),f122(x43222,f884(x43221,x43222),x43224)),f328(f328(f8(f885(x43222,f884(x43221,x43222)),f885(x43222,f879(f884(x43221,x43222))),x43221),f328(f8(f884(x43221,x43222),f879(f884(x43221,x43222)),x43222),f128(f884(x43221,x43222)))),f257(x43221,x43222)))),f133(x43221,x43222,x43223,x43224))
% 81.29/80.90 [4362]E(f91(f884(x43621,x43622),f328(f267(x43621,x43622,a871),f328(f328(f7(x43621,f885(x43622,a871),f885(x43622,a871)),f328(f328(f8(f885(a871,a871),f885(f885(x43622,a871),f885(x43622,a871)),x43621),f8(a871,a871,x43622)),f328(f328(f8(a871,f885(a871,a871),x43621),a326),f328(a325,x43623)))),f328(a325,x43624)))),f328(f328(f257(x43621,x43622),x43623),x43624))
% 81.29/80.90 [4363]E(f86(f884(x43631,x43632),f328(f267(x43631,x43632,a871),f328(f328(f7(x43631,f885(x43632,a871),f885(x43632,a871)),f328(f328(f8(f885(a871,a871),f885(f885(x43632,a871),f885(x43632,a871)),x43631),f8(a871,a871,x43632)),f328(f328(f8(a871,f885(a871,a871),x43631),a326),f328(a325,x43633)))),f328(a325,x43634)))),f328(f328(f257(x43631,x43632),x43633),x43634))
% 81.29/80.90 [4434]E(f328(f328(f267(f878(x44341),f878(x44341),f884(f878(x44341),f878(x44341))),f328(f328(f18(f878(x44341),f885(f878(x44341),f884(f878(x44341),f878(x44341))),f885(f878(x44341),f884(f878(x44341),f878(x44341)))),f328(f328(f8(f885(f878(x44341),f885(f884(f878(x44341),f878(x44341)),f884(f878(x44341),f878(x44341)))),f885(f885(f878(x44341),f884(f878(x44341),f878(x44341))),f885(f878(x44341),f884(f878(x44341),f878(x44341)))),f878(x44341)),f18(f878(x44341),f884(f878(x44341),f878(x44341)),f884(f878(x44341),f878(x44341)))),f328(f328(f8(f885(f878(x44341),f884(f878(x44341),f878(x44341))),f885(f878(x44341),f885(f884(f878(x44341),f878(x44341)),f884(f878(x44341),f878(x44341)))),f878(x44341)),f328(f8(f884(f878(x44341),f878(x44341)),f885(f884(f878(x44341),f878(x44341)),f884(f878(x44341),f878(x44341))),f878(x44341)),f328(f102(f884(f878(x44341),f878(x44341))),f328(x44342,x44343)))),f328(f328(f8(f878(x44341),f885(f878(x44341),f884(f878(x44341),f878(x44341))),f878(x44341)),f257(f878(x44341),f878(x44341))),f328(f150(x44341),x44343))))),f328(f328(f7(f878(x44341),f885(f878(x44341),f878(x44341)),f885(f878(x44341),f884(f878(x44341),f878(x44341)))),f328(f328(f8(f885(f878(x44341),f884(f878(x44341),f878(x44341))),f885(f885(f878(x44341),f878(x44341)),f885(f878(x44341),f884(f878(x44341),f878(x44341)))),f878(x44341)),f8(f878(x44341),f884(f878(x44341),f878(x44341)),f878(x44341))),f257(f878(x44341),f878(x44341)))),f328(f150(x44341),x44343)))),f166(x44341,x44342,x44344)),f166(x44341,x44342,f328(f328(f150(x44341),x44343),x44344)))
% 81.29/80.90 [4440]E(f328(f141(f885(x44401,f881(x44402)),f884(x44401,x44402),f328(f7(f884(x44401,x44402),f885(x44401,f881(x44402)),f885(x44401,f881(x44402))),f328(f267(x44401,x44402,f885(f885(x44401,f881(x44402)),f885(x44401,f881(x44402)))),f328(f328(f7(x44401,f885(x44402,f881(x44402)),f885(x44402,f885(f885(x44401,f881(x44402)),f885(x44401,f881(x44402))))),f328(f328(f8(f885(f881(x44402),f885(f885(x44401,f881(x44402)),f885(x44401,f881(x44402)))),f885(f885(x44402,f881(x44402)),f885(x44402,f885(f885(x44401,f881(x44402)),f885(x44401,f881(x44402))))),x44401),f8(f881(x44402),f885(f885(x44401,f881(x44402)),f885(x44401,f881(x44402))),x44402)),f328(f328(f8(f885(f885(x44401,f881(x44402)),f885(f881(x44402),f885(x44401,f881(x44402)))),f885(f881(x44402),f885(f885(x44401,f881(x44402)),f885(x44401,f881(x44402)))),x44401),f7(f885(x44401,f881(x44402)),f881(x44402),f885(x44401,f881(x44402)))),f328(f7(f885(x44401,f881(x44402)),x44401,f885(f881(x44402),f885(x44401,f881(x44402)))),f73(x44401,f881(x44402)))))),f236(x44402)))),x44403),f328(f168(f884(x44401,x44402)),x44404)),f184(x44401,x44402,x44403,f328(f177(x44401,x44402),x44404)))
% 81.29/80.90 [3545]E(f328(f194(f876(x35451)),f328(f328(f328(f93(x35451),x35452),x35453),x35454)),f2(a877))
% 81.29/80.90 [3664]E(f328(f328(f174(x36641),x36642),f328(f328(f174(x36641),x36643),x36644)),f328(f328(f174(x36641),f328(f328(f242(a877),x36642),x36643)),x36644))
% 81.29/80.90 [3665]E(f328(f328(f137(x36651),x36652),f328(f328(f137(x36651),x36653),x36654)),f328(f328(f137(x36651),f328(f328(f81(a877),x36652),x36653)),x36654))
% 81.29/80.90 [3677]E(f328(f328(f127(x36771),f328(f328(f150(x36771),x36772),x36773)),x36774),f328(f328(f150(x36771),x36772),f328(f328(f127(x36771),x36773),x36774)))
% 81.29/80.90 [3678]E(f328(f328(f127(x36781),f328(f328(f127(x36781),x36782),x36783)),x36784),f328(f328(f127(x36781),x36782),f328(f328(f127(x36781),x36783),x36784)))
% 81.29/80.90 [3757]E(f328(f328(f164(x37571),f328(f328(f150(x37571),x37572),x37573)),x37574),f190(x37571,x37572,f328(f164(x37571),x37573),x37574))
% 81.29/80.90 [3766]E(f328(f328(f188(x37661,x37661),x37662),f328(f328(f188(x37661,x37661),x37663),x37664)),f328(f328(f188(x37661,x37661),f328(f328(f82(a877),x37663),x37662)),x37664))
% 81.29/80.90 [3795]E(f328(f328(f116(f885(x37951,a871)),x37952),f328(f328(f306(x37951),x37953),x37954)),f328(f328(f306(x37951),x37953),f328(f328(f116(f885(x37951,a871)),x37952),x37954)))
% 81.29/80.90 [3810]E(f328(f328(f328(f188(x38101,x38101),x38102),x38103),f328(x38103,x38104)),f328(x38103,f328(f328(f328(f188(x38101,x38101),x38102),x38103),x38104)))
% 81.29/80.90 [3818]E(f328(f328(f285(x38181,x38182,x38183),f193(f885(f884(x38181,x38182),a871))),x38184),f193(f885(f884(x38181,x38183),a871)))
% 81.29/80.90 [3834]E(f328(f328(f116(f885(x38341,a871)),f328(f328(f306(x38341),x38342),x38343)),x38344),f328(f328(f306(x38341),x38342),f328(f328(f116(f885(x38341,a871)),x38343),x38344)))
% 81.29/80.90 [3852]E(f184(x38521,x38522,f328(f177(x38521,x38522),x38523),f328(f177(x38521,x38522),x38524)),f328(f177(x38521,x38522),f328(f328(f127(f884(x38521,x38522)),x38524),x38523)))
% 81.29/80.90 [3853]E(f328(f38(f884(x38531,x38532)),f328(f328(f265(x38531,x38532),x38533),f328(f16(f885(x38532,a871),x38531),x38534))),f328(f328(f82(a877),f328(f38(x38531),x38533)),f328(f38(x38532),x38534)))
% 81.29/80.90 [3859]E(f328(f328(f107(f885(x38591,a871)),f328(f328(f306(x38591),x38592),x38593)),f328(f328(f306(x38591),x38592),x38594)),f328(f328(f306(x38591),x38592),f328(f328(f107(f885(x38591,a871)),x38593),x38594)))
% 81.29/80.90 [3874]E(f328(f328(f116(f885(x38741,a871)),x38742),f328(f328(f116(f885(x38741,a871)),x38743),x38744)),f328(f328(f116(f885(x38741,a871)),x38743),f328(f328(f116(f885(x38741,a871)),x38742),x38744)))
% 81.29/80.90 [3875]E(f328(f328(f107(f885(x38751,a871)),x38752),f328(f328(f107(f885(x38751,a871)),x38753),x38754)),f328(f328(f107(f885(x38751,a871)),x38753),f328(f328(f107(f885(x38751,a871)),x38752),x38754)))
% 81.29/80.90 [3884]E(f65(x38841,x38842,f328(f328(f8(x38842,f885(x38842,x38842),x38841),x38843),x38844)),f328(f66(x38842,x38841,x38843),x38844))
% 81.29/80.90 [3894]E(f179(x38941,f328(f328(f153(f878(x38942),f878(x38941)),f328(f153(x38942,x38941),x38943)),x38944)),f328(f328(f153(f878(x38942),f878(x38941)),f328(f153(x38942,x38941),x38943)),f179(x38942,x38944)))
% 81.29/80.90 [3911]E(f328(f141(f878(x39111),f878(x39111),f127(x39111),f119(x39111)),f328(f328(f153(x39112,f878(x39111)),x39113),x39114)),f163(x39112,x39111,x39113,x39114))
% 81.29/80.90 [3914]E(f187(x39141,x39142,x39143,f328(f80(f885(x39141,a871)),f328(f328(f306(x39141),x39144),f193(f885(x39141,a871))))),f328(f328(f328(f73(x39141,f881(x39142)),x39143),x39144),f196(x39142)))
% 81.29/80.90 [3956]E(f328(f328(f328(f73(x39561,f881(x39562)),f328(f177(x39561,x39562),x39563)),f328(f256(x39561,x39562),x39564)),f328(f236(x39562),f328(f266(x39561,x39562),x39564))),f328(f177(x39561,x39562),f328(f328(f150(f884(x39561,x39562)),x39564),x39563)))
% 81.29/80.90 [3973]E(f328(f74(x39731,x39731,x39731,f328(f328(f188(x39731,x39731),x39732),x39733)),f328(f328(f188(x39731,x39731),x39734),x39733)),f328(f328(f188(x39731,x39731),f328(f328(f81(a877),x39732),x39734)),x39733))
% 81.29/80.90 [3998]E(f328(f328(f107(f885(x39981,a871)),f328(f328(f22(f885(x39981,a871)),x39982),x39983)),f328(f328(f22(f885(x39981,a871)),x39982),x39984)),f328(f328(f22(f885(x39981,a871)),x39982),f328(f328(f116(f885(x39981,a871)),x39983),x39984)))
% 81.29/80.90 [3999]E(f328(f328(f116(f885(x39991,a871)),f328(f328(f22(f885(x39991,a871)),x39992),x39993)),f328(f328(f22(f885(x39991,a871)),x39992),x39994)),f328(f328(f22(f885(x39991,a871)),x39992),f328(f328(f107(f885(x39991,a871)),x39993),x39994)))
% 81.29/80.90 [4000]E(f328(f328(f107(f885(x40001,a871)),f328(f328(f116(f885(x40001,a871)),x40002),x40003)),f328(f328(f116(f885(x40001,a871)),x40002),x40004)),f328(f328(f116(f885(x40001,a871)),x40002),f328(f328(f107(f885(x40001,a871)),x40003),x40004)))
% 81.29/80.90 [4001]E(f328(f328(f22(f885(x40011,a871)),f328(f328(f107(f885(x40011,a871)),x40012),x40013)),f328(f328(f107(f885(x40011,a871)),x40012),x40014)),f328(f328(f107(f885(x40011,a871)),x40012),f328(f328(f22(f885(x40011,a871)),x40013),x40014)))
% 81.29/80.90 [4002]E(f328(f328(f116(f885(x40021,a871)),f328(f328(f107(f885(x40021,a871)),x40022),x40023)),f328(f328(f107(f885(x40021,a871)),x40022),x40024)),f328(f328(f107(f885(x40021,a871)),x40022),f328(f328(f116(f885(x40021,a871)),x40023),x40024)))
% 81.29/80.90 [4008]E(f328(f38(f884(x40081,x40082)),f328(f328(f265(x40081,x40082),f328(f328(f306(x40081),x40083),f193(f885(x40081,a871)))),f328(f16(f885(x40082,a871),x40081),x40084))),f328(f38(x40082),x40084))
% 81.29/80.90 [4044]E(f328(f328(f43(x40441,f885(x40442,a871)),x40443),f328(f328(f8(f885(x40442,a871),f885(x40442,a871),x40441),f80(f885(x40442,a871))),x40444)),f328(f80(f885(x40442,a871)),f328(f328(f42(x40441,f885(x40442,a871)),x40443),x40444)))
% 81.29/80.90 [4045]E(f328(f328(f42(x40451,f885(x40452,a871)),x40453),f328(f328(f8(f885(x40452,a871),f885(x40452,a871),x40451),f80(f885(x40452,a871))),x40454)),f328(f80(f885(x40452,a871)),f328(f328(f43(x40451,f885(x40452,a871)),x40453),x40454)))
% 81.29/80.90 [4059]E(f328(f328(f285(x40591,x40591,x40591),f328(f328(f188(f884(x40591,x40591),a871),x40592),x40593)),f328(f328(f188(f884(x40591,x40591),a871),x40594),x40593)),f328(f328(f188(f884(x40591,x40591),a871),f328(f328(f81(a877),x40592),x40594)),x40593))
% 81.29/80.90 [4090]E(f328(f328(f42(x40901,f885(f885(x40902,a871),a871)),x40903),f328(f328(f8(f885(x40902,a871),f885(f885(x40902,a871),a871),x40901),f305(x40902)),x40904)),f328(f305(x40902),f328(f328(f42(x40901,f885(x40902,a871)),x40903),x40904)))
% 81.29/80.90 [4119]E(f328(f328(f42(f885(x41191,a871),f885(x41192,a871)),x41193),f328(f328(f7(f885(x41191,a871),f885(x41191,f885(x41192,a871)),f885(x41192,a871)),f42(x41191,f885(x41192,a871))),x41194)),f328(f328(f42(x41191,f885(x41192,a871)),f40(f885(x41191,a871),x41193)),x41194))
% 81.29/80.90 [4120]E(f328(f328(f43(f885(x41201,a871),f885(x41202,a871)),x41203),f328(f328(f7(f885(x41201,a871),f885(x41201,f885(x41202,a871)),f885(x41202,a871)),f43(x41201,f885(x41202,a871))),x41204)),f328(f328(f43(x41201,f885(x41202,a871)),f40(f885(x41201,a871),x41203)),x41204))
% 81.29/80.90 [4125]E(f328(f328(f153(x41251,x41252),x41253),f328(f141(f878(x41251),f878(x41251),f127(x41251),f119(x41251)),x41254)),f328(f141(f878(x41252),f878(x41252),f127(x41252),f119(x41252)),f328(f328(f153(f878(x41251),f878(x41252)),f328(f153(x41251,x41252),x41253)),x41254)))
% 81.29/80.90 [4129]E(f190(f878(x41291),f119(x41291),f328(f328(f8(f878(x41291),f878(x41291),a877),f328(f150(x41291),x41292)),f328(f328(f7(a877,f878(x41291),f878(x41291)),f174(x41291)),x41293)),x41294),f328(f328(f174(x41291),x41294),f328(f328(f150(x41291),x41292),x41293)))
% 81.29/80.90 [4171]P24(f328(f328(f244(f885(x41711,a871)),f328(f307(x41712,x41711,x41713),f328(f308(x41712,x41711,x41713),x41714))),x41714))
% 81.29/80.90 [4174]E(f328(f307(f884(x41741,x41742),f884(x41742,x41741),f328(f267(x41741,x41742,f884(x41742,x41741)),f328(f7(x41742,x41741,f884(x41742,x41741)),f257(x41742,x41741)))),f328(f328(f265(x41741,x41742),x41743),f328(f16(f885(x41742,a871),x41741),x41744))),f328(f328(f265(x41742,x41741),x41744),f328(f16(f885(x41741,a871),x41742),x41743)))
% 81.29/80.90 [4183]E(f328(f328(f43(x41831,f885(x41832,a871)),x41833),f328(f328(f8(f885(x41831,a871),f885(x41832,a871),x41831),f282(x41831,x41832,x41834)),f328(f328(f7(x41831,f885(x41831,a871),f885(x41831,a871)),f306(x41831)),f193(f885(x41831,a871))))),f328(f282(x41831,x41832,x41834),x41833))
% 81.29/80.90 [4184]E(f328(f328(f43(x41841,f885(x41842,a871)),x41843),f328(f328(f8(f885(x41841,a871),f885(x41842,a871),x41841),f308(x41842,x41841,x41844)),f328(f328(f7(x41841,f885(x41841,a871),f885(x41841,a871)),f306(x41841)),f193(f885(x41841,a871))))),f328(f308(x41842,x41841,x41844),x41843))
% 81.29/80.90 [4273]E(f328(f328(f116(f885(x42731,a871)),f328(f328(f116(f885(x42731,a871)),f328(f328(f107(f885(x42731,a871)),x42732),x42733)),f328(f328(f107(f885(x42731,a871)),x42733),x42734))),f328(f328(f107(f885(x42731,a871)),x42734),x42732)),f328(f328(f107(f885(x42731,a871)),f328(f328(f107(f885(x42731,a871)),f328(f328(f116(f885(x42731,a871)),x42732),x42733)),f328(f328(f116(f885(x42731,a871)),x42733),x42734))),f328(f328(f116(f885(x42731,a871)),x42734),x42732)))
% 81.29/80.90 [4335]E(f328(f141(f878(x43351),f878(x43351),f127(x43351),f119(x43351)),f328(f328(f153(x43352,f878(x43351)),f328(f328(f7(x43352,f878(x43351),f878(x43351)),f328(f328(f8(x43351,f885(f878(x43351),f878(x43351)),x43352),f150(x43351)),x43353)),f119(x43351))),x43354)),f328(f328(f153(x43352,x43351),x43353),x43354))
% 81.29/80.90 [4346]E(f328(f328(f87(a1,x43461),f328(f109(a1),f328(f328(f81(a1),x43462),a103))),f328(f328(f18(a1,x43461,x43461),f328(f328(f7(a1,x43461,f885(x43461,x43461)),f328(f328(f8(a871,f885(x43461,f885(x43461,x43461)),a1),f102(x43461)),a199)),x43463)),f328(f328(f8(a877,x43461,a1),x43464),a110))),f190(x43461,x43463,x43464,f328(f109(a877),x43462)))
% 81.29/80.90 [4562]~P24(f328(f328(f193(f885(x45621,f885(x45622,a871))),x45623),x45624))
% 81.29/80.90 [3821]E(f328(f328(f164(x38211),f328(f328(f127(x38211),x38212),x38213)),f328(f328(f81(a877),f328(f194(f878(x38211)),x38212)),x38214)),f328(f328(f164(x38211),x38213),x38214))
% 81.29/80.90 [3827]E(f328(f328(f137(x38271),x38272),f328(f328(f174(x38271),f328(f328(f81(a877),x38273),x38272)),x38274)),f328(f328(f174(x38271),x38273),f328(f328(f137(x38271),x38272),x38274)))
% 81.29/80.90 [3927]E(f328(f328(f116(f885(x39271,a871)),f328(f253(x39272,x39271),x39273)),f328(f253(x39272,x39271),x39274)),f328(f253(x39272,x39271),f328(f328(f116(f885(f884(x39272,x39271),a871)),x39273),x39274)))
% 81.29/80.90 [3928]E(f328(f328(f116(f885(x39281,a871)),f328(f255(x39281,x39282),x39283)),f328(f255(x39281,x39282),x39284)),f328(f255(x39281,x39282),f328(f328(f116(f885(f884(x39281,x39282),a871)),x39283),x39284)))
% 81.29/80.90 [3933]E(f328(f328(f22(f885(x39331,a871)),f328(f328(f107(f885(x39331,a871)),x39332),x39333)),x39334),f328(f328(f107(f885(x39331,a871)),x39332),f328(f328(f22(f885(x39331,a871)),x39333),x39334)))
% 81.29/80.90 [3934]E(f328(f328(f116(f885(x39341,a871)),f328(f328(f116(f885(x39341,a871)),x39342),x39343)),x39344),f328(f328(f116(f885(x39341,a871)),x39342),f328(f328(f116(f885(x39341,a871)),x39343),x39344)))
% 81.29/80.90 [3935]E(f328(f328(f107(f885(x39351,a871)),f328(f328(f107(f885(x39351,a871)),x39352),x39353)),x39354),f328(f328(f107(f885(x39351,a871)),x39352),f328(f328(f107(f885(x39351,a871)),x39353),x39354)))
% 81.29/80.90 [3975]E(f328(f328(f116(f885(f884(x39751,x39752),a871)),f328(f283(x39752,x39751),x39753)),f328(f283(x39752,x39751),x39754)),f328(f283(x39752,x39751),f328(f328(f116(f885(f884(x39752,x39751),a871)),x39753),x39754)))
% 81.29/80.90 [3976]E(f328(f328(f107(f885(f884(x39761,x39762),a871)),f328(f283(x39762,x39761),x39763)),f328(f283(x39762,x39761),x39764)),f328(f283(x39762,x39761),f328(f328(f107(f885(f884(x39762,x39761),a871)),x39763),x39764)))
% 81.29/80.90 [3990]E(f328(f328(f116(f885(x39901,f885(x39902,a871))),f261(x39902,x39901,x39903)),f261(x39902,x39901,x39904)),f261(x39902,x39901,f328(f328(f116(f885(x39902,f885(x39901,a871))),x39903),x39904)))
% 81.29/80.90 [3991]E(f328(f328(f107(f885(x39911,f885(x39912,a871))),f261(x39912,x39911,x39913)),f261(x39912,x39911,x39914)),f261(x39912,x39911,f328(f328(f107(f885(x39912,f885(x39911,a871))),x39913),x39914)))
% 81.29/80.90 [4048]E(f328(f328(f116(f885(x40481,a871)),f328(f328(f22(f885(x40481,a871)),x40482),x40483)),f328(f328(f22(f885(x40481,a871)),x40484),x40483)),f328(f328(f22(f885(x40481,a871)),f328(f328(f116(f885(x40481,a871)),x40482),x40484)),x40483))
% 81.29/80.90 [4049]E(f328(f328(f107(f885(x40491,a871)),f328(f328(f116(f885(x40491,a871)),x40492),x40493)),f328(f328(f116(f885(x40491,a871)),x40494),x40493)),f328(f328(f116(f885(x40491,a871)),f328(f328(f107(f885(x40491,a871)),x40492),x40494)),x40493))
% 81.29/80.90 [4050]E(f328(f328(f22(f885(x40501,a871)),f328(f328(f107(f885(x40501,a871)),x40502),x40503)),f328(f328(f107(f885(x40501,a871)),x40504),x40503)),f328(f328(f107(f885(x40501,a871)),f328(f328(f22(f885(x40501,a871)),x40502),x40504)),x40503))
% 81.29/80.90 [4051]E(f328(f328(f116(f885(x40511,a871)),f328(f328(f107(f885(x40511,a871)),x40512),x40513)),f328(f328(f107(f885(x40511,a871)),x40514),x40513)),f328(f328(f107(f885(x40511,a871)),f328(f328(f116(f885(x40511,a871)),x40512),x40514)),x40513))
% 81.29/80.90 [4052]E(f328(f328(f22(f885(x40521,a871)),f328(f328(f107(f885(x40521,a871)),x40522),x40523)),f328(f328(f107(f885(x40521,a871)),x40524),x40523)),f328(f328(f22(f885(x40521,a871)),f328(f328(f107(f885(x40521,a871)),x40522),x40523)),x40524))
% 81.29/80.90 [4062]E(f328(f328(f22(f885(x40621,a871)),f328(f328(f22(f885(x40621,a871)),x40622),f328(f328(f306(x40621),x40623),f193(f885(x40621,a871))))),x40624),f328(f328(f22(f885(x40621,a871)),x40622),f328(f328(f306(x40621),x40623),x40624)))
% 81.29/80.90 [4116]E(f328(f328(f116(f885(x41161,a871)),f328(f328(f306(x41161),x41162),f328(f328(f306(x41161),x41163),f193(f885(x41161,a871))))),f328(f281(x41161),x41164)),f328(f281(x41161),f328(f328(f306(f884(x41161,x41161)),f328(f328(f257(x41161,x41161),x41162),x41163)),x41164)))
% 81.29/80.90 [4146]E(f328(f328(f43(a877,f885(x41461,a871)),f328(f297(a877),x41462)),f328(f328(f8(a877,f885(x41461,a871),a877),x41463),f328(f328(f7(a877,a877,a877),f81(a877)),x41464))),f328(f328(f43(a877,f885(x41461,a871)),f299(a877,x41464,f328(f328(f81(a877),x41462),x41464))),x41463))
% 81.29/80.90 [4147]E(f173(x41471,f328(f282(x41471,x41471,x41472),f328(f328(f306(x41471),x41473),f193(f885(x41471,a871)))),f328(f282(f878(x41471),f878(x41471),f157(x41471,x41472)),f328(f328(f306(f878(x41471)),x41474),f193(f885(f878(x41471),a871))))),f328(f282(f878(x41471),f878(x41471),f157(x41471,x41472)),f328(f328(f306(f878(x41471)),f328(f328(f150(x41471),x41473),x41474)),f193(f885(f878(x41471),a871)))))
% 81.29/80.90 [4207]E(f328(f177(x42071,x42072),f328(f328(f153(x42071,f884(x42071,x42072)),f328(f328(f18(x42071,x42072,f884(x42071,x42072)),f257(x42071,x42072)),x42073)),x42074)),f187(x42071,x42072,f328(f74(x42072,f881(x42072),x42071,f236(x42072)),x42073),f328(f171(x42071),x42074)))
% 81.29/80.90 [4212]E(f328(f249(x42121),f328(f328(f7(x42121,f885(x42122,a871),a871),f328(f328(f8(x42122,f885(f885(x42122,a871),a871),x42121),f330(x42122)),x42123)),x42124)),f328(f308(x42121,x42122,x42123),x42124))
% 81.29/80.90 [4306]E(f328(f249(x43061),f328(f328(f7(x43061,f885(f884(x43062,x43061),a871),a871),f328(f328(f8(f884(x43062,x43061),f885(f885(f884(x43062,x43061),a871),a871),x43061),f330(f884(x43062,x43061))),f328(f257(x43062,x43061),x43063))),x43064)),f328(f282(x43062,x43061,x43064),f328(f328(f306(x43062),x43063),f193(f885(x43062,a871)))))
% 81.29/80.90 [4320]E(f328(f328(f153(f884(x43201,a877),x43201),f256(x43201,a877)),f328(f135(f884(x43201,a877),f328(f328(f8(a877,a871,f884(x43201,a877)),x43202),f328(f328(f8(a877,a877,f884(x43201,a877)),a118),f266(x43201,a877)))),f328(f328(f181(x43201,a877),x43203),x43204))),f328(f328(f153(f884(x43201,a877),x43201),f256(x43201,a877)),f328(f135(f884(x43201,a877),f328(f328(f8(a877,a871,f884(x43201,a877)),x43202),f266(x43201,a877))),f328(f328(f181(x43201,a877),x43203),f328(f328(f153(a877,a877),a118),x43204)))))
% 81.29/80.90 [4328]P24(f328(f328(f244(f885(f885(x43281,a871),a871)),f328(f328(f43(x43282,f885(f885(x43281,a871),a871)),x43283),f328(f328(f8(f885(x43281,a871),f885(f885(x43281,a871),a871),x43282),f305(x43281)),x43284))),f328(f305(x43281),f328(f328(f43(x43282,f885(x43281,a871)),x43283),x43284))))
% 81.29/80.90 [4370]E(f328(f328(f87(a1,x43701),f328(f109(a1),f328(f328(f81(a1),x43702),a103))),f328(f328(f18(a1,x43701,x43701),f328(f328(f7(a1,x43701,f885(x43701,x43701)),f328(f328(f8(a871,f885(x43701,f885(x43701,x43701)),a1),f102(x43701)),a199)),x43703)),f328(f328(f18(a1,x43701,x43701),f328(f328(f8(a877,f885(x43701,x43701),a1),x43704),a110)),f328(f328(f8(a877,x43701,a1),f189(x43701,x43703,x43704)),a110)))),f328(f189(x43701,x43703,x43704),f328(f109(a877),x43702)))
% 81.29/80.90 [4373]E(f328(f328(f153(x43731,x43732),f328(f74(f881(x43732),x43732,x43731,f240(x43732)),x43733)),f328(f135(x43731,f328(f328(f8(a871,a871,x43731),a323),f328(f328(f7(x43731,f881(x43732),a871),f328(f328(f8(f881(x43732),f885(f881(x43732),a871),x43731),a325),x43733)),f196(x43732)))),x43734)),f162(x43731,x43732,x43733,x43734))
% 81.29/80.90 [4396]E(f328(f249(f884(x43961,x43962)),f328(f267(x43961,x43962,a871),f328(f328(f7(x43961,f885(x43962,a871),f885(x43962,a871)),f328(f328(f8(f885(a871,a871),f885(f885(x43962,a871),f885(x43962,a871)),x43961),f8(a871,a871,x43962)),f328(f328(f8(a871,f885(a871,a871),x43961),a326),f328(f328(f7(x43961,f885(x43961,a871),a871),f330(x43961)),x43963)))),f328(f328(f7(x43962,f885(x43962,a871),a871),f330(x43962)),x43964)))),f230(x43961,x43962,x43963,x43964))
% 81.29/80.90 [4429]E(f328(f328(f43(x44291,f885(f884(x44291,x44292),a871)),x44293),f328(f328(f18(x44291,f885(x44292,f885(f884(x44291,x44292),a871)),f885(f884(x44291,x44292),a871)),f328(f328(f8(f885(x44292,a871),f885(f885(x44292,f885(f884(x44291,x44292),a871)),f885(f884(x44291,x44292),a871)),x44291),f43(x44292,f885(f884(x44291,x44292),a871))),x44294)),f328(f328(f7(x44291,f885(f884(x44291,x44292),a871),f885(x44292,f885(f884(x44291,x44292),a871))),f328(f328(f8(f885(x44292,f885(f885(f884(x44291,x44292),a871),f885(f884(x44291,x44292),a871))),f885(f885(f884(x44291,x44292),a871),f885(x44292,f885(f884(x44291,x44292),a871))),x44291),f7(x44292,f885(f884(x44291,x44292),a871),f885(f884(x44291,x44292),a871))),f328(f328(f8(f885(x44292,f884(x44291,x44292)),f885(x44292,f885(f885(f884(x44291,x44292),a871),f885(f884(x44291,x44292),a871))),x44291),f328(f8(f884(x44291,x44292),f885(f885(f884(x44291,x44292),a871),f885(f884(x44291,x44292),a871)),x44292),f306(f884(x44291,x44292)))),f257(x44291,x44292)))),f193(f885(f884(x44291,x44292),a871))))),f328(f328(f265(x44291,x44292),x44293),x44294))
% 81.29/80.90 [3985]E(f328(f328(f127(x39851),f328(f328(f174(x39851),x39852),x39853)),f328(f328(f174(x39851),f328(f328(f22(a877),x39852),f328(f194(f878(x39851)),x39853))),x39854)),f328(f328(f174(x39851),x39852),f328(f328(f127(x39851),x39853),x39854)))
% 81.29/80.90 [3986]E(f328(f328(f127(x39861),f328(f328(f137(x39861),x39862),x39863)),f328(f328(f137(x39861),f328(f328(f22(a877),x39862),f328(f194(f878(x39861)),x39863))),x39864)),f328(f328(f137(x39861),x39862),f328(f328(f127(x39861),x39863),x39864)))
% 81.29/80.90 [4038]E(f328(f328(f81(a877),f328(f328(f82(a877),x40381),x40382)),f328(f328(f81(a877),f328(f328(f82(a877),x40383),x40382)),x40384)),f328(f328(f81(a877),f328(f328(f82(a877),f328(f328(f81(a877),x40381),x40383)),x40382)),x40384))
% 81.29/80.90 [4237]P24(f328(f328(f244(f885(x42371,a871)),f328(f328(f22(f885(x42371,a871)),f328(f253(x42372,x42371),x42373)),f328(f253(x42372,x42371),x42374))),f328(f253(x42372,x42371),f328(f328(f22(f885(f884(x42372,x42371),a871)),x42373),x42374))))
% 81.29/80.90 [4238]P24(f328(f328(f244(f885(x42381,a871)),f328(f328(f22(f885(x42381,a871)),f328(f255(x42381,x42382),x42383)),f328(f255(x42381,x42382),x42384))),f328(f255(x42381,x42382),f328(f328(f22(f885(f884(x42381,x42382),a871)),x42383),x42384))))
% 81.29/80.90 [4348]E(f328(f328(f81(a1),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x43481),x43482)),f193(f885(f884(a877,a877),a871)))))),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x43483),x43484)),f193(f885(f884(a877,a877),a871)))))),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),f328(f328(f81(a877),x43481),x43483)),f328(f328(f81(a877),x43482),x43484))),f193(f885(f884(a877,a877),a871))))))
% 81.29/80.90 [4391]E(f328(f328(f82(a1),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x43911),x43912)),f193(f885(f884(a877,a877),a871)))))),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x43913),x43914)),f193(f885(f884(a877,a877),a871)))))),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),f328(f328(f81(a877),f328(f328(f82(a877),x43911),x43913)),f328(f328(f82(a877),x43912),x43914))),f328(f328(f81(a877),f328(f328(f82(a877),x43911),x43914)),f328(f328(f82(a877),x43912),x43913)))),f193(f885(f884(a877,a877),a871))))))
% 81.29/80.90 [4411]E(f328(f249(x44111),f328(f328(f8(f885(x44112,a871),a871,x44111),f89(x44112)),f328(f328(f8(f885(x44112,a871),f885(x44112,a871),x44111),f328(f18(x44112,a871,a871),f328(f328(f8(a871,f885(a871,a871),x44112),a331),f328(f328(f7(x44112,f885(x44112,a871),a871),f330(x44112)),x44113)))),f328(f328(f7(x44111,f885(x44112,f885(x44111,a871)),f885(x44112,a871)),f328(f328(f8(f885(f885(x44111,a871),a871),f885(f885(x44112,f885(x44111,a871)),f885(x44112,a871)),x44111),f8(f885(x44111,a871),a871,x44112)),f330(x44111))),x44114)))),f328(f328(f42(x44112,f885(x44111,a871)),x44113),x44114))
% 81.29/80.90 [4444]E(f328(f328(f285(x44441,x44441,x44441),f328(f328(f306(f884(x44441,x44441)),f328(f328(f257(x44441,x44441),x44442),x44443)),x44444)),f304(x44441,f328(f328(f306(f884(x44441,x44441)),f328(f328(f257(x44441,x44441),x44442),x44443)),x44444))),f328(f328(f116(f885(f884(x44441,x44441),a871)),f328(f328(f285(x44441,x44441,x44441),x44444),f304(x44441,x44444))),f328(f249(f884(x44441,x44441)),f328(f267(x44441,x44441,a871),f328(f328(f7(x44441,f885(x44441,a871),f885(x44441,a871)),f328(f328(f8(f885(a871,a871),f885(f885(x44441,a871),f885(x44441,a871)),x44441),f8(a871,a871,x44441)),f328(f328(f8(a871,f885(a871,a871),x44441),a326),f328(f328(f7(x44441,f885(f884(x44441,x44441),a871),a871),f328(f328(f8(f884(x44441,x44441),f885(f885(f884(x44441,x44441),a871),a871),x44441),f330(f884(x44441,x44441))),f328(f328(f7(x44441,x44441,f884(x44441,x44441)),f257(x44441,x44441)),x44442))),f304(x44441,x44444))))),f328(f328(f7(x44441,f885(f884(x44441,x44441),a871),a871),f328(f328(f8(f884(x44441,x44441),f885(f885(f884(x44441,x44441),a871),a871),x44441),f330(f884(x44441,x44441))),f328(f257(x44441,x44441),x44443))),f304(x44441,x44444)))))))
% 81.29/80.90 [4239]E(f328(f135(x42391,f328(f328(f18(x42391,a871,a871),f328(f328(f8(a871,f885(a871,a871),x42391),a326),x42392)),x42393)),x42394),f328(f135(x42391,x42393),f328(f135(x42391,x42392),x42394)))
% 81.29/80.90 [4342]E(f328(f328(f127(x43421),f328(f328(f328(f102(f878(x43421)),f328(f328(f330(a877),f2(a877)),x43422)),f328(f328(f150(x43421),x43423),f119(x43421))),f119(x43421))),f175(x43421,x43424,f328(f249(a877),f328(f328(f7(a877,f885(a877,a871),a871),f328(f328(f8(a877,f885(f885(a877,a871),a871),a877),f330(a877)),a118)),x43422)))),f175(x43421,f328(f328(f150(x43421),x43423),x43424),x43422))
% 81.29/80.90 [4438]E(f328(f249(f884(x44381,x44382)),f328(f328(f8(f885(a877,a871),a871,f884(x44381,x44382)),f88(a877)),f328(f328(f7(f884(x44381,x44382),f885(a877,a871),f885(a877,a871)),f328(f328(f8(f885(a877,f885(a871,a871)),f885(f885(a877,a871),f885(a877,a871)),f884(x44381,x44382)),f18(a877,a871,a871)),f328(f328(f8(f885(a877,a871),f885(a877,f885(a871,a871)),f884(x44381,x44382)),f328(f8(a871,f885(a871,a871),a877),a326)),f328(f328(f7(f884(x44381,x44382),f885(a877,f884(x44381,x44382)),f885(a877,a871)),f328(f328(f8(f885(f884(x44381,x44382),a871),f885(f885(a877,f884(x44381,x44382)),f885(a877,a871)),f884(x44381,x44382)),f8(f884(x44381,x44382),a871,a877)),a325)),f328(f328(f18(a877,x44382,f884(x44381,x44382)),f328(f328(f8(x44381,f885(x44382,f884(x44381,x44382)),a877),f257(x44381,x44382)),f328(f164(x44381),x44383))),f328(f164(x44382),x44384)))))),f328(f328(f7(a877,a877,a871),f245(a877)),f328(f328(f242(a877),f328(f194(f878(x44381)),x44383)),f328(f194(f878(x44382)),x44384)))))),f328(f171(f884(x44381,x44382)),f328(f328(f181(x44381,x44382),x44383),x44384)))
% 81.29/80.90 [4361]E(f328(f249(f884(x43611,x43612)),f328(f267(x43611,x43612,a871),f328(f328(f7(x43611,f885(x43612,a871),f885(x43612,a871)),f328(f328(f8(f885(a871,a871),f885(f885(x43612,a871),f885(x43612,a871)),x43611),f8(a871,a871,x43612)),f328(f328(f8(a871,f885(a871,a871),x43611),a326),x43613))),x43614))),f328(f328(f265(x43611,x43612),f328(f249(x43611),x43613)),f328(f16(f885(x43612,a871),x43611),f328(f249(x43612),x43614))))
% 81.29/80.90 [4364]E(f328(f249(f884(x43641,x43642)),f328(f267(x43641,x43642,a871),f328(f328(f18(x43641,f885(x43642,a871),f885(x43642,a871)),f328(f328(f8(f885(a871,a871),f885(f885(x43642,a871),f885(x43642,a871)),x43641),f8(a871,a871,x43642)),f328(f328(f8(a871,f885(a871,a871),x43641),a326),x43643))),x43644))),f328(f328(f265(x43641,x43642),f328(f249(x43641),x43643)),f328(f328(f8(f885(x43642,a871),f885(x43642,a871),x43641),f249(x43642)),x43644)))
% 81.29/80.90 [4380]E(f328(f249(x43801),f328(f328(f8(f885(x43802,a871),a871,x43801),f89(x43802)),f328(f328(f8(f885(x43802,a871),f885(x43802,a871),x43801),f328(f18(x43802,a871,a871),f328(f328(f8(a871,f885(a871,a871),x43802),a331),f328(f328(f7(x43802,f885(x43802,a871),a871),f330(x43802)),x43803)))),x43804))),f328(f328(f42(x43802,f885(x43801,a871)),x43803),f328(f328(f8(f885(x43801,a871),f885(x43801,a871),x43802),f249(x43801)),f328(f7(x43801,x43802,a871),x43804))))
% 81.29/80.90 [4424]E(f328(f328(f153(f884(x44241,a877),x44241),f256(x44241,a877)),f328(f135(f884(x44241,a877),f328(f328(f7(f884(x44241,a877),f885(a877,a871),a871),f328(f328(f8(a877,f885(f885(a877,a871),a871),f884(x44241,a877)),f330(a877)),f266(x44241,a877))),x44242)),f328(f328(f181(x44241,a877),x44243),f138(a877,f328(f298(a877,x44244),f328(f328(f81(a877),x44244),f328(f194(f878(x44241)),x44243))))))),f328(f328(f153(f884(x44241,a877),x44241),f256(x44241,a877)),f328(f135(f884(x44241,a877),f328(f328(f7(f884(x44241,a877),f885(a877,a871),a871),f328(f328(f8(a877,f885(f885(a877,a871),a871),f884(x44241,a877)),f330(a877)),f328(f328(f7(f884(x44241,a877),a877,a877),f328(f328(f8(a877,f885(a877,a877),f884(x44241,a877)),f81(a877)),f266(x44241,a877))),x44244))),x44242)),f328(f328(f181(x44241,a877),x44243),f138(a877,f328(f298(a877,f2(a877)),f328(f194(f878(x44241)),x44243)))))))
% 81.29/80.90 [4425]E(f328(a118,f328(f328(f243(a877),f328(f194(f878(x44251)),x44252)),f328(f141(a877,f878(x44253),f328(f7(f878(x44253),a877,a877),f328(f328(f8(a877,f885(a877,a877),f878(x44253)),f243(a877)),f328(f328(f7(f878(x44253),a877,a877),f328(f328(f8(a877,f885(a877,a877),f878(x44253)),f22(a877)),f194(f878(x44253)))),f328(a118,f2(a877))))),f2(a877)),f328(f168(f878(x44253)),f328(f135(f878(x44253),f328(f328(f8(a871,a871,f878(x44253)),a323),f328(f328(f7(f878(x44253),f878(x44253),a871),a325),f119(x44253)))),x44254))))),f328(f328(f243(a877),f328(a118,f328(f194(f878(x44251)),x44252))),f328(f141(a877,f878(x44253),f328(f7(f878(x44253),a877,a877),f328(f328(f8(a877,f885(a877,a877),f878(x44253)),f243(a877)),f194(f878(x44253)))),f2(a877)),f328(f168(f878(x44253)),x44254))))
% 81.29/80.90 [4379]E(f328(f328(f127(x43791),f175(x43791,x43792,x43793)),f175(x43791,x43794,f328(f249(a877),f328(f328(f7(a877,f885(a877,a871),a871),f328(f328(f8(a877,f885(f885(a877,a871),a871),a877),f330(a877)),f328(f328(f7(a877,a877,a877),f81(a877)),f328(f194(f878(x43791)),x43792)))),x43793)))),f175(x43791,f328(f328(f127(x43791),x43792),x43794),x43793))
% 81.29/80.90 [4431]E(f328(f328(f150(f878(x44311)),f328(f328(f150(x44311),x44312),f328(f141(f878(x44311),f878(x44311),f127(x44311),f119(x44311)),f328(f328(f153(f878(x44311),f878(x44311)),f155(f878(x44311),x44311,f119(x44311),f328(f328(f8(f878(x44311),f885(f878(x44311),f878(x44311)),x44311),f16(f878(x44311),f878(x44311))),f328(f328(f7(x44311,f878(x44311),f878(x44311)),f150(x44311)),f119(x44311))))),x44313)))),f179(x44311,f328(f328(f150(f878(x44311)),x44314),f328(f141(f878(f878(x44311)),f878(f878(x44311)),f127(f878(x44311)),f119(f878(x44311))),f328(f328(f153(f878(x44311),f878(f878(x44311))),f155(f878(f878(x44311)),x44311,f119(f878(x44311)),f328(f16(f885(f878(x44311),f878(f878(x44311))),x44311),f328(f328(f7(f878(x44311),f878(f878(x44311)),f878(f878(x44311))),f150(f878(x44311))),f119(f878(x44311)))))),x44313))))),f179(x44311,f328(f328(f150(f878(x44311)),f328(f328(f150(x44311),x44312),x44314)),x44313)))
% 81.29/80.90 [4439]E(f328(f249(f884(x44391,x44391)),f328(f267(x44391,x44391,a871),f328(f328(f7(x44391,f885(f884(x44392,x44392),a871),f885(x44391,a871)),f328(f328(f8(f885(x44391,f885(f885(f884(x44392,x44392),a871),a871)),f885(f885(f884(x44392,x44392),a871),f885(x44391,a871)),x44391),f7(x44391,f885(f884(x44392,x44392),a871),a871)),f328(f328(f8(f885(x44391,f884(x44392,x44392)),f885(x44391,f885(f885(f884(x44392,x44392),a871),a871)),x44391),f328(f8(f884(x44392,x44392),f885(f885(f884(x44392,x44392),a871),a871),x44391),f330(f884(x44392,x44392)))),f328(f328(f7(x44391,f885(x44391,x44392),f885(x44391,f884(x44392,x44392))),f328(f328(f8(f885(x44392,f884(x44392,x44392)),f885(f885(x44391,x44392),f885(x44391,f884(x44392,x44392))),x44391),f8(x44392,f884(x44392,x44392),x44391)),f328(f328(f8(x44392,f885(x44392,f884(x44392,x44392)),x44391),f257(x44392,x44392)),x44393))),x44393)))),x44394))),f328(f328(f284(x44392,x44391),x44394),x44393))
% 81.29/80.90 [4502]~E(f34(x45021,x45022),f29(x45023,x45024,x45025))
% 81.29/80.90 [4503]~E(f34(x45031,x45032),f31(x45033,x45034,x45035))
% 81.29/80.90 [4504]~E(f34(x45041,x45042),f30(x45043,x45044,x45045))
% 81.29/80.90 [4505]~E(f33(x45051,x45052),f29(x45053,x45054,x45055))
% 81.29/80.90 [4506]~E(f33(x45061,x45062),f31(x45063,x45064,x45065))
% 81.29/80.90 [4507]~E(f33(x45071,x45072),f30(x45073,x45074,x45075))
% 81.29/80.90 [4508]~E(f29(x45081,x45082,x45083),f34(x45084,x45085))
% 81.29/80.90 [4509]~E(f29(x45091,x45092,x45093),f33(x45094,x45095))
% 81.29/80.90 [4510]~E(f31(x45101,x45102,x45103),f34(x45104,x45105))
% 81.29/80.90 [4511]~E(f31(x45111,x45112,x45113),f33(x45114,x45115))
% 81.29/80.90 [4512]~E(f30(x45121,x45122,x45123),f34(x45124,x45125))
% 81.29/80.90 [4513]~E(f30(x45131,x45132,x45133),f33(x45134,x45135))
% 81.29/80.90 [3925]E(f328(f184(x39251,x39252,x39253,x39254),x39255),f328(f238(f881(x39252),x39252,f328(x39253,x39255),f236(x39252)),f328(x39254,x39255)))
% 81.29/80.90 [4013]E(f184(x40131,x40132,f184(x40131,x40132,x40133,x40134),x40135),f184(x40131,x40132,x40133,f184(x40131,x40132,x40134,x40135)))
% 81.29/80.90 [4193]E(f328(f328(f116(f885(x41931,a871)),f328(f171(x41931),f328(f328(f174(x41931),f328(f194(f878(x41932)),x41933)),x41934))),f183(x41931,x41932,x41935)),f183(x41931,x41932,f186(x41931,x41932,x41935,x41934,x41933)))
% 81.29/80.90 [3753]E(f328(f328(f267(x37531,x37532,x37533),x37534),x37535),f328(f328(x37534,f328(f256(x37531,x37532),x37535)),f328(f266(x37531,x37532),x37535)))
% 81.29/80.90 [3778]E(f328(f238(x37781,x37782,x37783,x37784),f328(f236(x37782),x37785)),f328(x37784,x37785))
% 81.29/80.90 [3787]E(f328(f328(f328(f66(x37871,x37872,x37873),x37874),x37875),f193(f885(x37872,a871))),x37875)
% 81.29/80.90 [3957]E(f239(x39571,x39572,x39573,x39574,f328(f236(x39572),x39575)),f328(x39574,x39575))
% 81.29/80.90 [4068]E(f328(f74(f881(x40681),f881(x40682),f881(x40683),f328(f207(x40681,x40682),x40684)),f328(f207(x40683,x40681),x40685)),f328(f207(x40683,x40682),f328(f74(x40681,x40682,x40683,x40684),x40685)))
% 81.29/80.90 [4070]E(f328(f74(f878(x40701),f878(x40702),f878(x40703),f328(f153(x40701,x40702),x40704)),f328(f153(x40703,x40701),x40705)),f328(f153(x40703,x40702),f328(f74(x40701,x40702,x40703,x40704),x40705)))
% 81.29/80.90 [4126]E(f328(f238(x41261,f884(x41262,f879(x41262)),x41263,f328(f267(x41262,f879(x41262),x41261),x41264)),f328(f134(x41262),x41265)),f132(x41261,x41262,x41263,x41264,x41265))
% 81.29/80.90 [4150]E(f86(x41501,f67(x41502,x41501,x41503,x41504,x41505)),f328(f328(f65(x41502,x41501,x41503),x41504),x41505))
% 81.29/80.90 [4185]E(f328(f328(f81(a877),f328(f328(f81(a877),f328(x41851,f328(f256(x41852,x41853),x41854))),f328(x41855,f328(f266(x41852,x41853),x41854)))),f328(a118,f2(a877))),f271(x41852,x41853,x41851,x41855,x41854))
% 81.29/80.90 [4375]E(f162(x43751,x43752,f328(f328(f7(x43751,f881(x43752),f881(x43752)),f328(f328(f18(x43751,f881(x43752),f885(f881(x43752),f881(x43752))),f328(f328(f8(a871,f885(f881(x43752),f885(f881(x43752),f881(x43752))),x43751),f102(f881(x43752))),x43753)),f328(f328(f8(x43752,f881(x43752),x43751),f236(x43752)),x43754))),f196(x43752)),x43755),f328(f328(f153(x43751,x43752),x43754),f328(f135(x43751,x43753),x43755)))
% 81.29/80.90 [4553]~E(f328(f328(f328(f73(x45531,f881(x45532)),x45533),x45534),f328(f236(x45532),x45535)),f328(f16(f881(x45532),x45531),f196(x45532)))
% 81.29/80.90 [3689]E(f328(f328(f174(x36891),x36892),f328(f328(f153(x36893,x36891),x36894),x36895)),f328(f328(f153(x36893,x36891),x36894),f328(f328(f174(x36893),x36892),x36895)))
% 81.29/80.90 [3690]E(f328(f328(f137(x36901),x36902),f328(f328(f153(x36903,x36901),x36904),x36905)),f328(f328(f153(x36903,x36901),x36904),f328(f328(f137(x36903),x36902),x36905)))
% 81.29/80.90 [3722]E(f328(f328(f153(x37221,x37222),x37223),f328(f328(f150(x37221),x37224),x37225)),f328(f328(f150(x37222),f328(x37223,x37224)),f328(f328(f153(x37221,x37222),x37223),x37225)))
% 81.29/80.90 [3782]E(f328(f307(x37821,x37822,x37823),f328(f328(f306(x37821),x37824),x37825)),f328(f328(f306(x37822),f328(x37823,x37824)),f328(f307(x37821,x37822,x37823),x37825)))
% 81.29/80.90 [3811]E(f172(x38111,f328(f328(f150(x38111),x38112),x38113),f328(f328(f150(x38111),x38114),x38115)),f328(f328(f150(x38111),x38112),f328(f328(f150(x38111),x38114),f172(x38111,x38113,x38115))))
% 81.29/80.90 [3847]E(f328(f328(f181(x38471,x38472),f328(f328(f174(x38471),x38473),x38474)),f328(f328(f174(x38472),x38473),x38475)),f328(f328(f174(f884(x38471,x38472)),x38473),f328(f328(f181(x38471,x38472),x38474),x38475)))
% 81.29/80.90 [3848]E(f328(f328(f181(x38481,x38482),f328(f328(f137(x38481),x38483),x38484)),f328(f328(f137(x38482),x38483),x38485)),f328(f328(f137(f884(x38481,x38482)),x38483),f328(f328(f181(x38481,x38482),x38484),x38485)))
% 81.29/80.90 [3858]E(f328(f328(f158(x38581,f328(f328(f150(x38581),x38582),x38583)),f328(a118,x38584)),x38585),f328(f328(f150(x38581),x38582),f328(f328(f158(x38581,x38583),x38584),x38585)))
% 81.29/80.90 [3861]E(f328(f238(f881(x38611),x38612,f196(x38611),x38613),f328(f328(f16(f881(x38612),x38614),f196(x38612)),x38615)),f196(x38611))
% 81.29/80.90 [3863]E(f328(f328(f127(x38631),f328(f328(f153(x38632,x38631),x38633),x38634)),f328(f328(f153(x38632,x38631),x38633),x38635)),f328(f328(f153(x38632,x38631),x38633),f328(f328(f127(x38632),x38634),x38635)))
% 81.29/80.90 [3867]E(f328(f328(x38671,x38672),f328(f328(f259(x38673,x38674,x38671),x38672),x38675)),f328(f328(f259(x38673,x38674,x38671),x38672),f328(a118,x38675)))
% 81.29/80.90 [3897]E(f163(x38971,x38972,x38973,f328(f328(f150(x38971),x38974),x38975)),f328(f328(f127(x38972),f328(x38973,x38974)),f163(x38971,x38972,x38973,x38975)))
% 81.29/80.90 [3909]E(f328(f328(f285(x39091,x39092,x39093),f328(f283(x39092,x39091),x39094)),f328(f283(x39093,x39092),x39095)),f328(f283(x39093,x39091),f328(f328(f285(x39093,x39092,x39091),x39095),x39094)))
% 81.29/80.90 [3943]E(f328(f328(f328(f188(f878(x39431),f878(x39431)),x39432),f167(x39431)),f328(f328(f153(x39433,x39431),x39434),x39435)),f328(f328(f153(x39433,x39431),x39434),f328(f328(f328(f188(f878(x39433),f878(x39433)),x39432),f167(x39433)),x39435)))
% 81.29/80.90 [3944]E(f328(f328(f269(x39441,x39442,x39441,x39443),f328(f257(x39442,x39441),x39444)),x39445),f328(x39445,x39444))
% 81.29/80.90 [3971]E(f154(x39711,x39712,f328(f328(f153(x39713,x39711),x39714),x39715)),f154(x39713,f328(f74(x39711,a877,x39713,x39712),x39714),x39715))
% 81.29/80.90 [4036]E(f328(f328(f74(f881(x40361),f881(x40362),x40363,f328(f207(x40361,x40362),x40364)),f328(f16(f881(x40361),x40363),f196(x40361))),x40365),f196(x40362))
% 81.29/80.90 [4037]E(f176(f884(x40371,x40372),f328(f74(x40372,a871,f884(x40371,x40372),x40373),f266(x40371,x40372)),f328(f328(f181(x40371,x40372),x40374),x40375)),f328(f328(f181(x40371,x40372),x40374),f176(x40372,x40373,x40375)))
% 81.29/80.90 [4042]E(f328(f307(x40421,x40422,f328(f328(f8(x40423,x40422,x40421),x40424),x40425)),f252(f885(x40421,a871))),f328(f307(x40423,x40422,x40424),f328(f307(x40421,x40423,x40425),f252(f885(x40421,a871)))))
% 81.29/80.90 [4055]E(f176(f884(x40551,x40552),f328(f74(x40551,a871,f884(x40551,x40552),x40553),f256(x40551,x40552)),f328(f328(f181(x40551,x40552),x40554),x40555)),f328(f328(f181(x40551,x40552),f176(x40551,x40553,x40554)),x40555))
% 81.29/80.90 [4074]E(f328(f328(f116(f885(x40741,a871)),f328(f308(x40741,x40742,x40743),f328(f328(f306(x40742),x40744),f193(f885(x40742,a871))))),f328(f308(x40741,x40742,x40743),x40745)),f328(f308(x40741,x40742,x40743),f328(f328(f306(x40742),x40744),x40745)))
% 81.29/80.90 [4134]E(f328(f328(f127(f884(x41341,x41342)),f328(f328(f153(x41342,f884(x41341,x41342)),f328(f257(x41341,x41342),x41343)),x41344)),f60(x41341,x41342,x41345,x41344)),f60(x41341,x41342,f328(f328(f150(x41341),x41343),x41345),x41344))
% 81.29/80.90 [4135]E(f328(f328(f153(x41351,x41352),x41353),f176(x41351,f328(f74(x41352,a871,x41351,x41354),x41353),x41355)),f176(x41352,x41354,f328(f328(f153(x41351,x41352),x41353),x41355)))
% 81.29/80.90 [4141]E(f328(f141(x41411,x41412,f328(f7(x41412,x41411,x41411),f328(f7(x41411,x41412,x41411),x41413)),x41414),f328(f168(x41412),f328(f168(x41412),x41415))),f328(f141(x41411,x41412,x41413,x41414),x41415))
% 81.29/80.90 [4142]E(f328(f328(f328(f73(x41421,f881(x41422)),f187(x41421,x41422,x41423,x41424)),x41425),f328(x41423,x41425)),f187(x41421,x41422,x41423,f328(f328(f306(x41421),x41425),x41424)))
% 81.29/80.90 [4210]E(f328(f238(f878(x42101),x42101,f162(x42102,x42101,x42103,x42104),f328(f328(f7(x42101,f878(x42101),f878(x42101)),f150(x42101)),f162(x42102,x42101,x42103,x42104))),f328(x42103,x42105)),f162(x42102,x42101,x42103,f328(f328(f150(x42102),x42105),x42104)))
% 81.29/80.90 [4247]P24(f328(f328(f244(f885(x42471,a871)),f328(f307(x42472,x42471,x42473),f328(f328(f107(f885(x42472,a871)),x42474),x42475))),f328(f328(f107(f885(x42471,a871)),f328(f307(x42472,x42471,x42473),x42474)),f328(f307(x42472,x42471,x42473),x42475))))
% 81.29/80.90 [4248]P24(f328(f328(f244(f885(x42481,a871)),f328(f282(x42482,x42481,x42483),f328(f328(f107(f885(x42482,a871)),x42484),x42485))),f328(f328(f107(f885(x42481,a871)),f328(f282(x42482,x42481,x42483),x42484)),f328(f282(x42482,x42481,x42483),x42485))))
% 81.29/80.90 [4349]E(f328(f266(x43491,x43492),f328(f268(x43493,x43491,x43492,x43492,x43494,f35(x43492)),x43495)),f328(f266(x43493,x43492),x43495))
% 81.29/80.90 [4350]E(f328(f256(x43501,x43502),f328(f268(x43501,x43501,x43503,x43502,f35(x43501),x43504),x43505)),f328(f256(x43501,x43503),x43505))
% 81.29/80.91 [4435]E(f328(f141(f885(x44351,f881(x44352)),f884(x44351,x44352),f328(f328(f8(f885(x44351,f885(x44352,f885(x44351,f881(x44352)))),f885(f884(x44351,x44352),f885(x44351,f881(x44352))),f885(x44351,f881(x44352))),f267(x44351,x44352,f885(x44351,f881(x44352)))),f328(f328(f7(f885(x44351,f881(x44352)),f885(x44352,f881(x44352)),f885(x44351,f885(x44352,f885(x44351,f881(x44352))))),f328(f328(f8(f885(x44351,f885(f885(x44352,f881(x44352)),f885(x44352,f885(x44351,f881(x44352))))),f885(f885(x44352,f881(x44352)),f885(x44351,f885(x44352,f885(x44351,f881(x44352))))),f885(x44351,f881(x44352))),f7(x44351,f885(x44352,f881(x44352)),f885(x44352,f885(x44351,f881(x44352))))),f328(f328(f8(f885(x44351,f885(f881(x44352),f885(x44351,f881(x44352)))),f885(x44351,f885(f885(x44352,f881(x44352)),f885(x44352,f885(x44351,f881(x44352))))),f885(x44351,f881(x44352))),f328(f8(f885(f881(x44352),f885(x44351,f881(x44352))),f885(f885(x44352,f881(x44352)),f885(x44352,f885(x44351,f881(x44352)))),x44351),f8(f881(x44352),f885(x44351,f881(x44352)),x44352))),f73(x44351,f881(x44352))))),f236(x44352))),x44353),f328(f328(f181(x44351,x44352),x44354),x44355)),f186(x44351,x44352,x44353,x44354,x44355))
% 81.29/80.91 [4437]P20(x44371,x44372,f328(f328(f306(f876(x44371)),f328(f328(f328(f93(x44371),f328(f328(f7(x44371,f885(a872,a871),f885(a872,a871)),f328(f328(f8(f885(a872,f885(a871,a871)),f885(f885(a872,a871),f885(a872,a871)),x44371),f18(a872,a871,a871)),f328(f328(f8(f885(a872,a871),f885(a872,f885(a871,a871)),x44371),f328(f8(a871,f885(a871,a871),a872),a326)),x44373))),f328(f328(f8(a871,a871,a872),a323),x44374))),f33(x44374,x44375)),x44373)),f193(f885(f876(x44371),a871))))
% 81.29/80.91 [3533]E(f328(f328(f328(f328(f212(x35331),x35332),x35333),x35334),x35335),f198(x35331,x35332))
% 81.29/80.91 [3534]E(f328(f328(f328(f328(f216(x35341),x35342),x35343),x35344),x35345),f208(x35341,x35342))
% 81.29/80.91 [3579]E(f99(x35791,x35792,f328(f328(f328(f93(x35791),x35793),x35794),x35795)),f2(a877))
% 81.29/80.91 [3673]E(f328(f328(f328(f328(f73(x36731,x36732),x36733),x36734),x36735),x36734),x36735)
% 81.29/80.91 [3898]E(f328(f328(f42(x38981,f885(x38982,a871)),f328(f328(f306(x38981),x38983),x38984)),x38985),f328(f328(f107(f885(x38982,a871)),f328(x38985,x38983)),f328(f328(f42(x38981,f885(x38982,a871)),x38984),x38985)))
% 81.29/80.91 [3899]E(f328(f328(f43(x38991,f885(x38992,a871)),f328(f328(f306(x38991),x38993),x38994)),x38995),f328(f328(f116(f885(x38992,a871)),f328(x38995,x38993)),f328(f328(f43(x38991,f885(x38992,a871)),x38994),x38995)))
% 81.29/80.91 [3950]E(f328(f122(x39501,x39502,f328(x39503,x39504)),f328(f328(f7(x39501,a105,f879(x39502)),x39505),x39504)),f328(f205(x39501,x39502,x39503,x39505),x39504))
% 81.29/80.91 [3964]E(f328(f328(f116(f885(x39641,a871)),f328(f307(x39642,x39641,x39643),x39644)),f328(f307(x39642,x39641,x39643),x39645)),f328(f307(x39642,x39641,x39643),f328(f328(f116(f885(x39642,a871)),x39644),x39645)))
% 81.29/80.91 [3965]E(f328(f328(f116(f885(x39651,a871)),f328(f282(x39652,x39651,x39653),x39654)),f328(f282(x39652,x39651,x39653),x39655)),f328(f282(x39652,x39651,x39653),f328(f328(f116(f885(x39652,a871)),x39654),x39655)))
% 81.29/80.91 [3966]E(f328(f328(f22(f885(x39661,a871)),f328(f308(x39661,x39662,x39663),x39664)),f328(f308(x39661,x39662,x39663),x39665)),f328(f308(x39661,x39662,x39663),f328(f328(f22(f885(x39662,a871)),x39664),x39665)))
% 81.29/80.91 [3967]E(f328(f328(f116(f885(x39671,a871)),f328(f308(x39671,x39672,x39673),x39674)),f328(f308(x39671,x39672,x39673),x39675)),f328(f308(x39671,x39672,x39673),f328(f328(f116(f885(x39672,a871)),x39674),x39675)))
% 81.29/80.91 [3968]E(f328(f328(f107(f885(x39681,a871)),f328(f308(x39681,x39682,x39683),x39684)),f328(f308(x39681,x39682,x39683),x39685)),f328(f308(x39681,x39682,x39683),f328(f328(f107(f885(x39682,a871)),x39684),x39685)))
% 81.29/80.91 [3970]E(f187(x39701,x39702,f187(x39701,x39702,x39703,x39704),x39705),f187(x39701,x39702,x39703,f328(f328(f107(f885(x39701,a871)),x39704),x39705)))
% 81.29/80.91 [4032]E(f328(f328(f158(x40321,f328(f328(f127(x40321),x40322),f328(f328(f150(x40321),x40323),x40324))),f328(f194(f878(x40321)),x40322)),x40325),f328(f328(f127(x40321),x40322),f328(f328(f150(x40321),x40325),x40324)))
% 81.29/80.91 [4040]E(f328(f328(f42(x40401,f885(x40402,a871)),x40403),f328(f328(f8(f885(x40402,a871),f885(x40402,a871),x40401),f328(f306(x40402),x40404)),x40405)),f328(f328(f306(x40402),x40404),f328(f328(f42(x40401,f885(x40402,a871)),x40403),x40405)))
% 81.29/80.91 [4108]E(f187(x41081,x41082,f328(f328(f328(f73(x41081,f881(x41082)),x41083),x41084),f328(f236(x41082),x41085)),f328(f80(f885(x41081,a871)),f328(f328(f306(x41081),x41084),f193(f885(x41081,a871))))),f187(x41081,x41082,x41083,f328(f80(f885(x41081,a871)),f328(f328(f306(x41081),x41084),f193(f885(x41081,a871))))))
% 81.29/80.91 [4197]E(f328(f328(f153(x41971,x41972),x41973),f328(f135(x41971,f328(f74(x41972,a871,x41971,x41974),x41973)),x41975)),f328(f135(x41972,x41974),f328(f328(f153(x41971,x41972),x41973),x41975)))
% 81.29/80.91 [4203]E(f328(f194(f878(x42031)),f328(f135(x42031,x42032),f328(f328(f153(x42033,x42031),x42034),x42035))),f328(f194(f878(x42033)),f328(f135(x42033,f328(f74(x42031,a871,x42033,x42032),x42034)),x42035)))
% 81.29/80.91 [4341]E(f328(f328(f116(f885(x43411,a871)),f328(f328(f22(f885(x43411,a871)),f183(x43411,x43412,x43413)),f328(f249(x43411),f328(f328(f7(x43411,f885(x43411,a871),a871),f330(x43411)),f328(f328(f22(f885(x43411,a871)),x43414),f183(x43411,x43412,x43415)))))),f328(f249(x43411),f328(f328(f7(x43411,f885(x43411,a871),a871),f330(x43411)),f328(f328(f107(f885(x43411,a871)),x43414),f183(x43411,x43412,x43415))))),f183(x43411,x43412,f77(x43411,f881(x43412),x43413,x43415,x43414)))
% 81.29/80.91 [4416]E(f328(f155(f878(f884(x44161,x44162)),x44162,f119(f884(x44161,x44162)),f328(f328(f7(x44162,f885(f878(x44162),f878(f884(x44161,x44162))),f885(f878(x44162),f878(f884(x44161,x44162)))),f328(f328(f8(f885(f878(f884(x44161,x44162)),f878(f884(x44161,x44162))),f885(f885(f878(x44162),f878(f884(x44161,x44162))),f885(f878(x44162),f878(f884(x44161,x44162)))),x44162),f8(f878(f884(x44161,x44162)),f878(f884(x44161,x44162)),f878(x44162))),f328(f328(f8(f884(x44161,x44162),f885(f878(f884(x44161,x44162)),f878(f884(x44161,x44162))),x44162),f150(f884(x44161,x44162))),f328(f257(x44161,x44162),x44163)))),f328(f181(x44161,x44162),x44164))),x44165),f328(f328(f181(x44161,x44162),f328(f328(f150(x44161),x44163),x44164)),x44165))
% 81.29/80.91 [3892]E(f328(f328(f158(x38921,f328(f328(f158(x38921,x38922),x38923),x38924)),x38923),x38925),f328(f328(f158(x38921,x38922),x38923),x38925))
% 81.29/80.91 [3945]E(f328(f253(x39451,x39452),f328(f328(f306(f884(x39451,x39452)),f328(f328(f257(x39451,x39452),x39453),x39454)),x39455)),f328(f328(f306(x39452),x39454),f328(f253(x39451,x39452),x39455)))
% 81.29/80.91 [3946]E(f328(f255(x39461,x39462),f328(f328(f306(f884(x39461,x39462)),f328(f328(f257(x39461,x39462),x39463),x39464)),x39465)),f328(f328(f306(x39461),x39463),f328(f255(x39461,x39462),x39465)))
% 81.29/80.91 [3995]E(f125(x39951,x39952,f328(x39953,x39954),f328(f328(f7(x39951,a105,f879(f881(x39952))),x39955),x39954)),f328(f203(x39951,x39952,x39953,x39955),x39954))
% 81.29/80.91 [4025]E(f328(f328(f22(f885(f884(x40251,x40252),a871)),f328(f328(f265(x40251,x40252),x40253),x40254)),f328(f328(f265(x40251,x40252),x40255),x40254)),f328(f328(f265(x40251,x40252),f328(f328(f22(f885(x40251,a871)),x40253),x40255)),x40254))
% 81.29/80.91 [4026]E(f328(f328(f116(f885(f884(x40261,x40262),a871)),f328(f328(f265(x40261,x40262),x40263),x40264)),f328(f328(f265(x40261,x40262),x40265),x40264)),f328(f328(f265(x40261,x40262),f328(f328(f116(f885(x40261,a871)),x40263),x40265)),x40264))
% 81.29/80.91 [4027]E(f328(f328(f107(f885(f884(x40271,x40272),a871)),f328(f328(f265(x40271,x40272),x40273),x40274)),f328(f328(f265(x40271,x40272),x40275),x40274)),f328(f328(f265(x40271,x40272),f328(f328(f107(f885(x40271,a871)),x40273),x40275)),x40274))
% 81.29/80.91 [4086]E(f328(f328(f107(f885(x40861,a871)),f328(f328(f42(x40862,f885(x40861,a871)),x40863),x40864)),f328(f328(f42(x40862,f885(x40861,a871)),x40865),x40864)),f328(f328(f42(x40862,f885(x40861,a871)),f328(f328(f116(f885(x40862,a871)),x40863),x40865)),x40864))
% 81.29/80.91 [4087]E(f328(f328(f116(f885(x40871,a871)),f328(f328(f43(x40872,f885(x40871,a871)),x40873),x40874)),f328(f328(f43(x40872,f885(x40871,a871)),x40875),x40874)),f328(f328(f43(x40872,f885(x40871,a871)),f328(f328(f116(f885(x40872,a871)),x40873),x40875)),x40874))
% 81.29/80.91 [4101]E(f328(f328(f42(x41011,f885(x41012,a871)),x41013),f328(f328(f8(f885(x41012,a871),f885(x41012,a871),x41011),f328(f116(f885(x41012,a871)),x41014)),x41015)),f328(f328(f116(f885(x41012,a871)),x41014),f328(f328(f42(x41011,f885(x41012,a871)),x41013),x41015)))
% 81.29/80.91 [4102]E(f328(f328(f43(x41021,f885(x41022,a871)),x41023),f328(f328(f8(f885(x41022,a871),f885(x41022,a871),x41021),f328(f22(f885(x41022,a871)),x41024)),x41025)),f328(f328(f22(f885(x41022,a871)),x41024),f328(f328(f42(x41021,f885(x41022,a871)),x41023),x41025)))
% 81.29/80.91 [4103]E(f328(f328(f43(x41031,f885(x41032,a871)),x41033),f328(f328(f8(f885(x41032,a871),f885(x41032,a871),x41031),f328(f107(f885(x41032,a871)),x41034)),x41035)),f328(f328(f107(f885(x41032,a871)),x41034),f328(f328(f43(x41031,f885(x41032,a871)),x41033),x41035)))
% 81.29/80.91 [4140]E(f184(x41401,x41402,x41403,f328(f177(x41401,x41402),f328(f168(f884(x41401,x41402)),f328(f328(f181(x41401,x41402),x41404),x41405)))),f186(x41401,x41402,x41403,x41404,x41405))
% 81.29/80.91 [4162]E(f190(f878(x41621),f328(f328(f150(x41621),x41622),x41623),f328(f328(f8(f878(x41621),f878(x41621),a877),f328(f150(x41621),x41624)),f328(f328(f7(a877,x41621,f878(x41621)),f158(x41621,x41623)),x41622)),x41625),f328(f328(f158(x41621,f328(f328(f150(x41621),x41624),x41623)),x41625),x41622))
% 81.29/80.91 [4166]E(f328(f328(f42(x41661,f885(f884(x41662,x41663),a871)),x41664),f328(f328(f8(f885(f884(x41663,x41662),a871),f885(f884(x41662,x41663),a871),x41661),f283(x41663,x41662)),x41665)),f328(f283(x41663,x41662),f328(f328(f42(x41661,f885(f884(x41663,x41662),a871)),x41664),x41665)))
% 81.29/80.91 [4167]E(f328(f328(f43(x41671,f885(f884(x41672,x41673),a871)),x41674),f328(f328(f8(f885(f884(x41673,x41672),a871),f885(f884(x41672,x41673),a871),x41671),f283(x41673,x41672)),x41675)),f328(f283(x41673,x41672),f328(f328(f43(x41671,f885(f884(x41673,x41672),a871)),x41674),x41675)))
% 81.29/80.91 [4221]E(f183(x42211,x42212,f328(f328(f18(x42211,f881(x42213),f881(x42212)),f328(f328(f8(f885(x42213,x42212),f885(f881(x42213),f881(x42212)),x42211),f207(x42213,x42212)),x42214)),x42215)),f183(x42211,x42213,x42215))
% 81.29/80.91 [4272]P24(f328(f328(f244(f885(x42721,a871)),f328(f328(f22(f885(x42721,a871)),f328(f307(x42722,x42721,x42723),x42724)),f328(f307(x42722,x42721,x42723),x42725))),f328(f307(x42722,x42721,x42723),f328(f328(f22(f885(x42722,a871)),x42724),x42725))))
% 81.29/80.91 [4420]E(f328(f155(f878(f884(x44201,x44202)),x44201,f119(f884(x44201,x44202)),f328(f328(f7(x44201,f885(f878(x44201),f878(f884(x44201,x44202))),f885(f878(x44201),f878(f884(x44201,x44202)))),f328(f328(f8(f885(f878(f884(x44201,x44202)),f878(f884(x44201,x44202))),f885(f885(f878(x44201),f878(f884(x44201,x44202))),f885(f878(x44201),f878(f884(x44201,x44202)))),x44201),f8(f878(f884(x44201,x44202)),f878(f884(x44201,x44202)),f878(x44201))),f328(f328(f8(f884(x44201,x44202),f885(f878(f884(x44201,x44202)),f878(f884(x44201,x44202))),x44201),f150(f884(x44201,x44202))),f328(f328(f7(x44201,x44202,f884(x44201,x44202)),f257(x44201,x44202)),x44203)))),f328(f328(f7(f878(x44201),f878(x44202),f878(f884(x44201,x44202))),f181(x44201,x44202)),x44204))),x44205),f328(f328(f181(x44201,x44202),x44205),f328(f328(f150(x44202),x44203),x44204)))
% 81.29/80.91 [4128]E(f328(f328(f116(f885(x41281,a871)),f328(f282(x41282,x41281,x41283),x41284)),f328(f282(x41282,x41281,x41285),x41284)),f328(f282(x41282,x41281,f328(f328(f116(f885(f884(x41282,x41281),a871)),x41283),x41285)),x41284))
% 81.29/80.91 [4169]E(f328(f328(f127(f884(x41691,x41692)),f328(f328(f181(x41691,x41692),x41693),f328(f328(f174(x41692),f328(f194(f878(x41691)),x41693)),x41694))),f328(f328(f181(x41691,x41692),x41695),f328(f328(f137(x41692),f328(f194(f878(x41691)),x41693)),x41694))),f328(f328(f181(x41691,x41692),f328(f328(f127(x41691),x41693),x41695)),x41694))
% 81.29/80.91 [4275]E(f328(f328(f265(x42751,x42752),x42753),f328(f328(f18(x42751,f885(x42752,a871),f885(x42752,a871)),f328(f328(f8(f885(x42752,a871),f885(f885(x42752,a871),f885(x42752,a871)),x42751),f22(f885(x42752,a871))),x42754)),x42755)),f328(f328(f22(f885(f884(x42751,x42752),a871)),f328(f328(f265(x42751,x42752),x42753),x42754)),f328(f328(f265(x42751,x42752),x42753),x42755)))
% 81.29/80.91 [4276]E(f328(f328(f265(x42761,x42762),x42763),f328(f328(f18(x42761,f885(x42762,a871),f885(x42762,a871)),f328(f328(f8(f885(x42762,a871),f885(f885(x42762,a871),f885(x42762,a871)),x42761),f116(f885(x42762,a871))),x42764)),x42765)),f328(f328(f116(f885(f884(x42761,x42762),a871)),f328(f328(f265(x42761,x42762),x42763),x42764)),f328(f328(f265(x42761,x42762),x42763),x42765)))
% 81.29/80.91 [4277]E(f328(f328(f265(x42771,x42772),x42773),f328(f328(f18(x42771,f885(x42772,a871),f885(x42772,a871)),f328(f328(f8(f885(x42772,a871),f885(f885(x42772,a871),f885(x42772,a871)),x42771),f107(f885(x42772,a871))),x42774)),x42775)),f328(f328(f107(f885(f884(x42771,x42772),a871)),f328(f328(f265(x42771,x42772),x42773),x42774)),f328(f328(f265(x42771,x42772),x42773),x42775)))
% 81.29/80.91 [4281]E(f328(f328(f42(x42811,f885(x42812,a871)),x42813),f328(f328(f7(x42811,f885(x42812,a871),f885(x42812,a871)),f328(f328(f8(f885(x42812,a871),f885(f885(x42812,a871),f885(x42812,a871)),x42811),f116(f885(x42812,a871))),x42814)),x42815)),f328(f328(f116(f885(x42812,a871)),f328(f328(f42(x42811,f885(x42812,a871)),x42813),x42814)),x42815))
% 81.29/80.91 [4282]E(f328(f328(f43(x42821,f885(x42822,a871)),x42823),f328(f328(f7(x42821,f885(x42822,a871),f885(x42822,a871)),f328(f328(f8(f885(x42822,a871),f885(f885(x42822,a871),f885(x42822,a871)),x42821),f22(f885(x42822,a871))),x42824)),x42825)),f328(f328(f22(f885(x42822,a871)),f328(f328(f43(x42821,f885(x42822,a871)),x42823),x42824)),x42825))
% 81.29/80.91 [4283]E(f328(f328(f43(x42831,f885(x42832,a871)),x42833),f328(f328(f7(x42831,f885(x42832,a871),f885(x42832,a871)),f328(f328(f8(f885(x42832,a871),f885(f885(x42832,a871),f885(x42832,a871)),x42831),f107(f885(x42832,a871))),x42834)),x42835)),f328(f328(f107(f885(x42832,a871)),f328(f328(f43(x42831,f885(x42832,a871)),x42833),x42834)),x42835))
% 81.29/80.91 [4287]E(f328(f328(f42(x42871,f885(x42872,a871)),x42873),f328(f328(f18(x42871,f885(x42872,a871),f885(x42872,a871)),f328(f328(f8(f885(x42872,a871),f885(f885(x42872,a871),f885(x42872,a871)),x42871),f107(f885(x42872,a871))),x42874)),x42875)),f328(f328(f107(f885(x42872,a871)),f328(f328(f42(x42871,f885(x42872,a871)),x42873),x42874)),f328(f328(f42(x42871,f885(x42872,a871)),x42873),x42875)))
% 81.29/80.91 [4288]E(f328(f328(f43(x42881,f885(x42882,a871)),x42883),f328(f328(f18(x42881,f885(x42882,a871),f885(x42882,a871)),f328(f328(f8(f885(x42882,a871),f885(f885(x42882,a871),f885(x42882,a871)),x42881),f116(f885(x42882,a871))),x42884)),x42885)),f328(f328(f116(f885(x42882,a871)),f328(f328(f43(x42881,f885(x42882,a871)),x42883),x42884)),f328(f328(f43(x42881,f885(x42882,a871)),x42883),x42885)))
% 81.29/80.91 [4302]E(f328(f328(f42(x43021,f885(x43022,a871)),x43023),f328(f328(f18(x43021,f885(x43022,a871),f885(x43022,a871)),f328(f328(f8(f885(x43022,a871),f885(f885(x43022,a871),f885(x43022,a871)),x43021),f107(f885(x43022,a871))),x43024)),x43025)),f328(f328(f107(f885(x43022,a871)),f41(f885(x43022,a871),f328(f307(x43021,f885(x43022,a871),x43024),x43023))),f41(f885(x43022,a871),f328(f307(x43021,f885(x43022,a871),x43025),x43023))))
% 81.29/80.91 [4303]E(f328(f328(f43(x43031,f885(x43032,a871)),x43033),f328(f328(f18(x43031,f885(x43032,a871),f885(x43032,a871)),f328(f328(f8(f885(x43032,a871),f885(f885(x43032,a871),f885(x43032,a871)),x43031),f116(f885(x43032,a871))),x43034)),x43035)),f328(f328(f116(f885(x43032,a871)),f40(f885(x43032,a871),f328(f307(x43031,f885(x43032,a871),x43034),x43033))),f40(f885(x43032,a871),f328(f307(x43031,f885(x43032,a871),x43035),x43033))))
% 81.29/80.91 [4337]E(f328(f328(f137(x43371),f328(f194(f878(x43371)),f176(x43371,x43372,f328(f328(f153(x43373,x43371),x43374),x43375)))),f328(f328(f153(x43373,x43371),x43374),x43375)),f328(f328(f153(x43373,x43371),x43374),f328(f328(f137(x43373),f328(f194(f878(x43373)),f176(x43373,f328(f74(x43371,a871,x43373,x43372),x43374),x43375))),x43375)))
% 81.29/80.91 [4211]E(f328(f328(f127(f884(x42111,x42112)),f328(f328(f181(x42111,x42112),f328(f328(f174(x42111),f328(f194(f878(x42112)),x42113)),x42114)),x42113)),f328(f328(f181(x42111,x42112),f328(f328(f137(x42111),f328(f194(f878(x42112)),x42113)),x42114)),x42115)),f328(f328(f181(x42111,x42112),x42114),f328(f328(f127(x42112),x42113),x42115)))
% 81.29/80.91 [4329]E(f86(x43291,f328(f328(f18(x43291,a871,a871),f328(f328(f8(a871,f885(a871,a871),x43291),a326),f328(f328(f7(x43291,f885(x43291,a871),a871),f330(x43291)),x43292))),f328(f328(f7(x43291,x43293,a871),f328(f328(f8(x43293,f885(x43293,a871),x43291),a325),x43294)),x43295))),f328(f78(x43291,x43293,x43292,x43294),x43295))
% 81.29/80.91 [4381]E(f328(f328(f87(a1,x43811),f328(f109(a1),f328(f328(f81(a1),x43812),a103))),f328(f328(f18(a1,x43811,x43811),f328(f328(f7(a1,x43811,f885(x43811,x43811)),f328(f328(f8(a871,f885(x43811,f885(x43811,x43811)),a1),f102(x43811)),a199)),f190(x43811,x43813,x43814,x43815))),f328(f328(f8(a877,x43811,a1),x43814),f328(f328(f7(a1,a877,a877),f328(f328(f8(a877,f885(a877,a877),a1),f81(a877)),a110)),x43815)))),f190(x43811,x43813,x43814,f328(f328(f81(a877),f328(f109(a877),x43812)),x43815)))
% 81.29/80.91 [4417]E(f328(f177(x44171,x44172),f328(f328(f153(f884(x44171,x44173),f884(x44171,x44172)),f328(f267(x44171,x44173,f884(x44171,x44172)),f328(f328(f7(x44171,f885(x44173,x44172),f885(x44173,f884(x44171,x44172))),f328(f328(f8(f885(x44172,f884(x44171,x44172)),f885(f885(x44173,x44172),f885(x44173,f884(x44171,x44172))),x44171),f8(x44172,f884(x44171,x44172),x44173)),f257(x44171,x44172))),x44174))),x44175)),f328(f74(f881(x44173),f881(x44172),x44171,f328(f207(x44173,x44172),x44174)),f328(f177(x44171,x44173),x44175)))
% 81.29/80.91 [4374]E(f183(x43741,x43742,f328(f328(f18(x43741,f881(x43742),f881(x43742)),f328(f328(f18(x43741,f881(x43742),f885(f881(x43742),f881(x43742))),f328(f328(f8(a871,f885(f881(x43742),f885(f881(x43742),f881(x43742))),x43741),f102(f881(x43742))),x43743)),x43744)),x43745)),f328(f328(f116(f885(x43741,a871)),f328(f328(f107(f885(x43741,a871)),f183(x43741,x43742,x43744)),f328(f249(x43741),x43743))),f328(f328(f107(f885(x43741,a871)),f183(x43741,x43742,x43745)),f328(f249(x43741),f328(f328(f8(a871,a871,x43741),a323),x43743)))))
% 81.29/80.91 [4415]E(f328(f328(f87(a1,x44151),f328(f109(a1),f328(f328(f81(a1),x44152),a103))),f328(f328(f18(a1,x44151,x44151),f328(f328(f7(a1,x44151,f885(x44151,x44151)),f328(f328(f8(a871,f885(x44151,f885(x44151,x44151)),a1),f102(x44151)),a199)),f328(f189(x44151,x44153,x44154),x44155))),f328(f328(f18(a1,x44151,x44151),f328(f328(f8(a877,f885(x44151,x44151),a1),x44154),f328(f328(f7(a1,a877,a877),f328(f328(f8(a877,f885(a877,a877),a1),f81(a877)),a110)),x44155))),f328(f328(f8(a877,x44151,a1),f189(x44151,x44153,x44154)),f328(f328(f7(a1,a877,a877),f328(f328(f8(a877,f885(a877,a877),a1),f81(a877)),a110)),x44155))))),f328(f189(x44151,x44153,x44154),f328(f328(f81(a877),f328(f109(a877),x44152)),x44155)))
% 81.29/80.91 [4449]E(f328(f249(f884(x44491,x44492)),f328(f267(x44491,x44492,a871),f328(f328(f8(f885(x44492,f885(x44493,a871)),f885(x44492,a871),x44491),f328(f8(f885(x44493,a871),a871,x44492),f88(x44493))),f328(f328(f7(x44491,f885(x44492,f885(x44493,a871)),f885(x44492,f885(x44493,a871))),f328(f328(f8(f885(f885(x44493,a871),f885(x44493,a871)),f885(f885(x44492,f885(x44493,a871)),f885(x44492,f885(x44493,a871))),x44491),f8(f885(x44493,a871),f885(x44493,a871),x44492)),f328(f328(f8(f885(x44493,f885(a871,a871)),f885(f885(x44493,a871),f885(x44493,a871)),x44491),f18(x44493,a871,a871)),f328(f328(f8(f885(x44493,a871),f885(x44493,f885(a871,a871)),x44491),f328(f8(a871,f885(a871,a871),x44493),a326)),f328(f328(f7(x44491,f885(f884(x44491,x44493),a871),f885(x44493,a871)),f328(f328(f8(f885(x44493,f885(f885(f884(x44491,x44493),a871),a871)),f885(f885(f884(x44491,x44493),a871),f885(x44493,a871)),x44491),f7(x44493,f885(f884(x44491,x44493),a871),a871)),f328(f328(f8(f885(x44493,f884(x44491,x44493)),f885(x44493,f885(f885(f884(x44491,x44493),a871),a871)),x44491),f328(f8(f884(x44491,x44493),f885(f885(f884(x44491,x44493),a871),a871),x44493),f330(f884(x44491,x44493)))),f257(x44491,x44493)))),x44494))))),f328(f328(f7(x44492,f885(f884(x44493,x44492),a871),f885(x44493,a871)),f328(f328(f8(f885(x44493,f885(f885(f884(x44493,x44492),a871),a871)),f885(f885(f884(x44493,x44492),a871),f885(x44493,a871)),x44492),f7(x44493,f885(f884(x44493,x44492),a871),a871)),f328(f328(f8(f885(x44493,f884(x44493,x44492)),f885(x44493,f885(f885(f884(x44493,x44492),a871),a871)),x44492),f328(f8(f884(x44493,x44492),f885(f885(f884(x44493,x44492),a871),a871),x44493),f330(f884(x44493,x44492)))),f328(f7(x44493,x44492,f884(x44493,x44492)),f257(x44493,x44492))))),x44495))))),f328(f328(f285(x44491,x44493,x44492),x44494),x44495))
% 81.29/80.91 [4534]~E(f31(x45341,x45342,x45343),f29(x45344,x45345,x45346))
% 81.29/80.91 [4537]~E(f30(x45371,x45372,x45373),f29(x45374,x45375,x45376))
% 81.29/80.91 [4538]~E(f30(x45381,x45382,x45383),f31(x45384,x45385,x45386))
% 81.29/80.91 [3980]E(f132(x39801,x39802,x39803,x39804,f129(x39802,x39805,x39806)),f328(f328(x39804,x39805),x39806))
% 81.29/80.91 [4195]E(f186(x41951,x41952,f184(x41951,x41952,x41953,x41954),x41955,x41956),f184(x41951,x41952,x41953,f186(x41951,x41952,x41954,x41955,x41956)))
% 81.29/80.91 [4318]E(f328(f74(f884(x43181,x43182),x43182,f884(x43183,x43184),f266(x43181,x43182)),f268(x43183,x43181,x43184,x43182,x43185,x43186)),f328(f74(x43184,x43182,f884(x43183,x43184),x43186),f266(x43183,x43184)))
% 81.29/80.91 [4319]E(f328(f74(f884(x43191,x43192),x43191,f884(x43193,x43194),f256(x43191,x43192)),f268(x43193,x43191,x43194,x43192,x43195,x43196)),f328(f74(x43193,x43191,f884(x43193,x43194),x43195),f256(x43193,x43194)))
% 81.29/80.91 [3920]E(f328(f328(f74(x39201,x39202,x39203,x39204),x39205),x39206),f328(x39204,f328(x39205,x39206)))
% 81.29/80.91 [3720]E(f328(f328(f267(x37201,x37202,x37203),x37204),f328(f328(f257(x37201,x37202),x37205),x37206)),f328(f328(x37204,x37205),x37206))
% 81.29/80.91 [3779]E(f328(f328(f328(f8(x37791,x37792,x37793),x37794),x37795),x37796),f328(x37794,f328(x37795,x37796)))
% 81.29/80.91 [3780]E(f328(f328(f328(f7(x37801,x37802,x37803),x37804),x37805),x37806),f328(f328(x37804,x37806),x37805))
% 81.29/80.91 [3797]E(f328(f328(f328(f18(x37971,x37972,x37973),x37974),x37975),x37976),f328(f328(x37974,x37976),f328(x37975,x37976)))
% 81.29/80.91 [3819]E(f328(f155(x38191,x38192,x38193,x38194),f328(f328(f150(x38192),x38195),x38196)),f328(f328(x38194,x38195),x38196))
% 81.29/80.91 [3924]E(f328(f328(f150(f884(x39241,x39242)),f328(f328(f257(x39241,x39242),x39243),x39244)),f328(f328(f181(x39241,x39242),x39245),x39246)),f328(f328(f181(x39241,x39242),f328(f328(f150(x39241),x39243),x39245)),f328(f328(f150(x39242),x39244),x39246)))
% 81.29/80.91 [3926]E(f328(f328(f153(x39261,x39262),x39263),f328(f328(f158(x39261,x39264),x39265),x39266)),f328(f328(f158(x39262,f328(f328(f153(x39261,x39262),x39263),x39264)),x39265),f328(x39263,x39266)))
% 81.29/80.91 [3969]E(f328(f141(x39691,x39692,x39693,x39694),f328(f328(f150(x39692),x39695),x39696)),f328(f141(x39691,x39692,x39693,f328(f328(x39693,x39694),x39695)),x39696))
% 81.29/80.91 [3996]E(f270(x39961,x39962,x39963,x39964,f328(f328(f257(x39961,x39962),x39965),x39966)),f328(f328(x39964,x39965),x39966))
% 81.29/80.91 [4079]E(f328(f328(f43(x40791,f885(x40792,a871)),x40793),f328(f74(x40794,f885(x40792,a871),x40791,x40795),x40796)),f328(f328(f43(x40794,f885(x40792,a871)),f328(f307(x40791,x40794,x40796),x40793)),x40795))
% 81.29/80.91 [4131]E(f328(f328(f153(x41311,x41312),x41313),f328(f328(f153(x41314,x41311),x41315),x41316)),f328(f328(f153(x41314,x41312),f328(f74(x41311,x41312,x41314,x41313),x41315)),x41316))
% 81.29/80.91 [4133]E(f328(f328(f207(x41331,x41332),x41333),f328(f328(f207(x41334,x41331),x41335),x41336)),f328(f328(f207(x41334,x41332),f328(f74(x41331,x41332,x41334,x41333),x41335)),x41336))
% 81.29/80.91 [4138]E(f328(f307(x41381,x41382,f328(f74(x41383,x41382,x41381,x41384),x41385)),x41386),f328(f307(x41383,x41382,x41384),f328(f307(x41381,x41383,x41385),x41386)))
% 81.29/80.91 [4139]E(f328(f308(x41391,x41392,f328(f74(x41393,x41392,x41391,x41394),x41395)),x41396),f328(f308(x41391,x41393,x41395),f328(f308(x41393,x41392,x41394),x41396)))
% 81.29/80.91 [4168]E(f184(x41681,x41682,x41683,f328(f328(f328(f73(x41681,f881(x41682)),x41684),x41685),f328(f236(x41682),x41686))),f328(f328(f328(f73(x41681,f881(x41682)),f184(x41681,x41682,x41683,x41684)),x41685),f328(f236(x41682),x41686)))
% 81.29/80.91 [4170]E(f328(f141(x41701,x41702,x41703,f328(f141(x41701,x41702,x41703,x41704),x41705)),x41706),f328(f141(x41701,x41702,x41703,x41704),f328(f328(f127(x41702),x41705),x41706)))
% 81.29/80.91 [4308]E(f328(f268(x43081,x43081,x43082,x43083,f35(x43081),x43084),f328(f328(f257(x43081,x43082),x43085),x43086)),f328(f328(f257(x43081,x43083),x43085),f328(x43084,x43086)))
% 81.29/80.91 [4309]E(f328(f268(x43091,x43092,x43093,x43093,x43094,f35(x43093)),f328(f328(f257(x43091,x43093),x43095),x43096)),f328(f328(f257(x43092,x43093),f328(x43094,x43095)),x43096))
% 81.29/80.91 [4399]E(f328(f328(f153(f884(x43991,x43992),f884(x43991,x43993)),f328(f267(x43991,x43992,f884(x43991,x43993)),f328(f328(f7(x43991,f885(x43992,x43993),f885(x43992,f884(x43991,x43993))),f328(f328(f8(f885(x43993,f884(x43991,x43993)),f885(f885(x43992,x43993),f885(x43992,f884(x43991,x43993))),x43991),f8(x43993,f884(x43991,x43993),x43992)),f257(x43991,x43993))),x43994))),f328(f328(f181(x43991,x43992),x43995),x43996)),f328(f328(f181(x43991,x43993),x43995),f328(f328(f153(x43992,x43993),x43994),x43996)))
% 81.29/80.91 [3784]E(f100(x37841,x37842,x37843,f328(f328(f328(f93(x37841),x37844),x37845),x37846)),f328(f328(f328(x37843,x37844),x37845),x37846))
% 81.29/80.91 [3785]E(f101(x37851,x37852,x37853,f328(f328(f328(f93(x37851),x37854),x37855),x37856)),f328(f328(f328(x37853,x37854),x37855),x37856))
% 81.29/80.91 [3979]E(f328(f328(f74(x39791,x39792,x39793,f328(f16(x39792,x39791),x39794)),x39795),x39796),x39794)
% 81.29/80.91 [4015]E(f328(f307(x40151,x40152,x40153),f328(f307(x40154,x40151,x40155),x40156)),f328(f307(x40154,x40152,f328(f328(f8(x40151,x40152,x40154),x40153),x40155)),x40156))
% 81.29/80.91 [4021]E(f328(f328(f42(x40211,f885(x40212,a871)),f328(f307(x40213,x40211,x40214),x40215)),x40216),f328(f328(f42(x40213,f885(x40212,a871)),x40215),f328(f328(f8(x40211,f885(x40212,a871),x40213),x40216),x40214)))
% 81.29/80.91 [4022]E(f328(f328(f43(x40221,f885(x40222,a871)),f328(f307(x40223,x40221,x40224),x40225)),x40226),f328(f328(f43(x40223,f885(x40222,a871)),x40225),f328(f328(f8(x40221,f885(x40222,a871),x40223),x40226),x40224)))
% 81.29/80.91 [4023]E(f328(f328(f42(x40231,f885(x40232,a871)),x40233),f328(f328(f8(x40234,f885(x40232,a871),x40231),x40235),x40236)),f328(f328(f42(x40234,f885(x40232,a871)),f328(f307(x40231,x40234,x40236),x40233)),x40235))
% 81.29/80.91 [4024]E(f328(f328(f43(x40241,f885(x40242,a871)),x40243),f328(f328(f8(x40244,f885(x40242,a871),x40241),x40245),x40246)),f328(f328(f43(x40244,f885(x40242,a871)),f328(f307(x40241,x40244,x40246),x40243)),x40245))
% 81.29/80.91 [4081]E(f328(f328(f43(x40811,f885(x40812,a871)),x40813),f328(f328(f8(f885(x40814,a871),f885(x40812,a871),x40811),f307(x40814,x40812,x40815)),x40816)),f328(f307(x40814,x40812,x40815),f328(f328(f43(x40811,f885(x40814,a871)),x40813),x40816)))
% 81.29/80.91 [4082]E(f328(f328(f43(x40821,f885(x40822,a871)),x40823),f328(f328(f8(f885(x40824,a871),f885(x40822,a871),x40821),f282(x40824,x40822,x40825)),x40826)),f328(f282(x40824,x40822,x40825),f328(f328(f43(x40821,f885(x40824,a871)),x40823),x40826)))
% 81.29/80.91 [4083]E(f328(f328(f42(x40831,f885(x40832,a871)),x40833),f328(f328(f8(f885(x40834,a871),f885(x40832,a871),x40831),f308(x40832,x40834,x40835)),x40836)),f328(f308(x40832,x40834,x40835),f328(f328(f42(x40831,f885(x40834,a871)),x40833),x40836)))
% 81.29/80.91 [4084]E(f328(f328(f43(x40841,f885(x40842,a871)),x40843),f328(f328(f8(f885(x40844,a871),f885(x40842,a871),x40841),f308(x40842,x40844,x40845)),x40846)),f328(f308(x40842,x40844,x40845),f328(f328(f43(x40841,f885(x40844,a871)),x40843),x40846)))
% 81.29/80.91 [4176]E(f328(f141(x41761,x41762,f328(f7(x41762,x41761,x41761),x41763),x41764),f328(f168(x41762),f328(f328(f150(x41762),x41765),x41766))),f328(f328(x41763,x41765),f328(f141(x41761,x41762,f328(f7(x41762,x41761,x41761),x41763),x41764),f328(f168(x41762),x41766))))
% 81.29/80.91 [4234]E(f328(f328(f18(f884(x42341,x42342),x42342,x42343),f328(f328(f8(x42344,f885(x42342,x42343),f884(x42341,x42342)),x42345),f328(f328(f8(x42341,x42344,f884(x42341,x42342)),x42346),f256(x42341,x42342)))),f266(x42341,x42342)),f328(f267(x42341,x42342,x42343),f328(f328(f8(x42344,f885(x42342,x42343),x42341),x42345),x42346)))
% 81.29/80.91 [4241]E(f328(f141(x42411,x42412,f328(f7(x42412,x42411,x42411),x42413),f328(f141(x42411,x42412,f328(f7(x42412,x42411,x42411),x42413),x42414),f328(f168(x42412),x42415))),f328(f168(x42412),x42416)),f328(f141(x42411,x42412,f328(f7(x42412,x42411,x42411),x42413),x42414),f328(f168(x42412),f328(f328(f127(x42412),x42416),x42415))))
% 81.29/80.91 [4243]E(f328(f328(f153(f884(x42431,x42432),f884(x42433,x42432)),f328(f267(x42431,x42432,f884(x42433,x42432)),f328(f328(f8(x42433,f885(x42432,f884(x42433,x42432)),x42431),f257(x42433,x42432)),x42434))),f328(f328(f181(x42431,x42432),x42435),x42436)),f328(f328(f181(x42433,x42432),f328(f328(f153(x42431,x42433),x42434),x42435)),x42436))
% 81.29/80.91 [4291]P24(f328(f328(f244(f885(x42911,a871)),f328(f282(x42912,x42911,x42913),f328(f328(f42(x42914,f885(x42912,a871)),x42915),x42916))),f328(f328(f42(x42914,f885(x42911,a871)),x42915),f328(f328(f8(f885(x42912,a871),f885(x42911,a871),x42914),f282(x42912,x42911,x42913)),x42916))))
% 81.29/80.91 [4094]E(f328(f328(f181(x40941,x40942),f328(f328(f158(x40941,x40943),x40944),f328(f256(x40941,x40942),x40945))),f328(f328(f158(x40942,x40946),x40944),f328(f266(x40941,x40942),x40945))),f328(f328(f158(f884(x40941,x40942),f328(f328(f181(x40941,x40942),x40943),x40946)),x40944),x40945))
% 81.29/80.91 [4157]E(f328(f328(f116(f885(f884(x41571,x41572),a871)),f328(f328(f285(x41571,x41573,x41572),x41574),x41575)),f328(f328(f285(x41571,x41573,x41572),x41574),x41576)),f328(f328(f285(x41571,x41573,x41572),x41574),f328(f328(f116(f885(f884(x41573,x41572),a871)),x41575),x41576)))
% 81.29/80.91 [4254]E(f328(f328(f306(f884(x42541,x42542)),f328(f328(f257(x42541,x42542),x42543),x42544)),f328(f328(f116(f885(f884(x42541,x42542),a871)),f328(f328(f265(x42541,x42542),x42545),f328(f16(f885(x42542,a871),x42541),f328(f328(f306(x42542),x42544),x42546)))),f328(f328(f265(x42541,x42542),f328(f328(f306(x42541),x42543),x42545)),f328(f16(f885(x42542,a871),x42541),x42546)))),f328(f328(f265(x42541,x42542),f328(f328(f306(x42541),x42543),x42545)),f328(f16(f885(x42542,a871),x42541),f328(f328(f306(x42542),x42544),x42546))))
% 81.29/80.91 [4332]E(f328(f328(f107(f885(x43321,a871)),f328(f308(x43321,x43322,f328(f74(f884(x43322,x43323),x43322,x43321,f256(x43322,x43323)),x43324)),x43325)),f328(f308(x43321,x43323,f328(f74(f884(x43322,x43323),x43323,x43321,f266(x43322,x43323)),x43324)),x43326)),f328(f308(x43321,f884(x43322,x43323),x43324),f328(f328(f265(x43322,x43323),x43325),f328(f16(f885(x43323,a871),x43322),x43326))))
% 81.29/80.91 [4078]E(f328(f328(f328(f73(x40781,x40782),f328(f328(f328(f73(x40781,x40782),x40783),x40784),x40785)),x40784),x40786),f328(f328(f328(f73(x40781,x40782),x40783),x40784),x40786))
% 81.29/80.91 [4182]E(f328(f328(f116(f885(f884(x41821,x41822),a871)),f328(f328(f285(x41821,x41823,x41822),x41824),x41825)),f328(f328(f285(x41821,x41823,x41822),x41826),x41825)),f328(f328(f285(x41821,x41823,x41822),f328(f328(f116(f885(f884(x41821,x41823),a871)),x41824),x41826)),x41825))
% 81.29/80.91 [4316]E(f328(f328(f42(x43161,f885(x43162,a871)),x43163),f328(f328(f7(x43161,f885(x43164,f885(x43162,a871)),f885(x43162,a871)),f328(f328(f8(f885(x43164,a871),f885(f885(x43164,f885(x43162,a871)),f885(x43162,a871)),x43161),f42(x43164,f885(x43162,a871))),x43165)),x43166)),f328(f328(f42(x43164,f885(x43162,a871)),f328(f328(f43(x43161,f885(x43164,a871)),x43163),x43165)),x43166))
% 81.29/80.91 [4317]E(f328(f328(f43(x43171,f885(x43172,a871)),x43173),f328(f328(f7(x43171,f885(x43174,f885(x43172,a871)),f885(x43172,a871)),f328(f328(f8(f885(x43174,a871),f885(f885(x43174,f885(x43172,a871)),f885(x43172,a871)),x43171),f43(x43174,f885(x43172,a871))),x43175)),x43176)),f328(f328(f43(x43174,f885(x43172,a871)),f328(f328(f43(x43171,f885(x43174,a871)),x43173),x43175)),x43176))
% 81.29/80.91 [4369]E(f328(f267(x43691,x43692,f884(x43693,x43694)),f328(f328(f7(x43691,f885(x43692,x43694),f885(x43692,f884(x43693,x43694))),f328(f328(f8(f885(x43694,f884(x43693,x43694)),f885(f885(x43692,x43694),f885(x43692,f884(x43693,x43694))),x43691),f8(x43694,f884(x43693,x43694),x43692)),f328(f328(f8(x43693,f885(x43694,f884(x43693,x43694)),x43691),f257(x43693,x43694)),x43695))),x43696)),f268(x43691,x43693,x43692,x43694,x43695,x43696))
% 81.29/80.91 [4290]E(f328(f328(f328(f73(x42901,f881(x42902)),f187(x42901,x42902,x42903,f328(f328(f22(f885(x42901,a871)),x42904),f328(f328(f306(x42901),x42905),f193(f885(x42901,a871)))))),x42905),x42906),f328(f328(f328(f73(x42901,f881(x42902)),f187(x42901,x42902,x42903,x42904)),x42905),x42906))
% 81.29/80.91 [4394]E(f328(f307(x43941,x43942,f328(f328(f18(x43941,x43942,x43942),f328(f328(f18(x43941,x43942,f885(x43942,x43942)),f328(f328(f8(a871,f885(x43942,f885(x43942,x43942)),x43941),f102(x43942)),x43943)),x43944)),x43945)),x43946),f328(f328(f116(f885(x43942,a871)),f328(f307(x43941,x43942,x43944),f328(f328(f107(f885(x43941,a871)),x43946),f328(f249(x43941),x43943)))),f328(f307(x43941,x43942,x43945),f328(f328(f107(f885(x43941,a871)),x43946),f328(f249(x43941),f328(f328(f8(a871,a871,x43941),a323),x43943))))))
% 81.29/80.91 [4405]E(f328(f307(x44051,f884(x44052,x44053),f328(f328(f18(x44051,x44053,f884(x44052,x44053)),f328(f328(f8(x44052,f885(x44053,f884(x44052,x44053)),x44051),f257(x44052,x44053)),x44054)),x44055)),x44056),f328(f328(f265(x44052,x44053),f328(f307(x44051,x44052,x44054),x44056)),f328(f328(f8(f885(x44051,a871),f885(x44053,a871),x44052),f307(x44051,x44053,x44055)),f328(f328(f7(x44052,f885(x44051,a871),f885(x44051,a871)),f328(f328(f8(f885(x44051,a871),f885(f885(x44051,a871),f885(x44051,a871)),x44052),f107(f885(x44051,a871))),f328(f328(f8(f885(x44052,a871),f885(x44051,a871),x44052),f308(x44051,x44052,x44054)),f328(f328(f7(x44052,f885(x44052,a871),f885(x44052,a871)),f306(x44052)),f193(f885(x44052,a871)))))),x44056))))
% 81.29/80.91 [4351]E(f328(f266(x43511,x43512),f328(f268(x43513,x43511,x43514,x43512,x43515,x43516),x43517)),f328(x43516,f328(f266(x43513,x43514),x43517)))
% 81.29/80.91 [4352]E(f328(f256(x43521,x43522),f328(f268(x43523,x43521,x43524,x43522,x43525,x43526),x43527)),f328(x43525,f328(f256(x43523,x43524),x43527)))
% 81.29/80.91 [4056]E(f328(f328(f181(x40561,x40562),f328(f328(f158(x40561,x40563),x40564),x40565)),f328(f328(f158(x40562,x40566),x40564),x40567)),f328(f328(f158(f884(x40561,x40562),f328(f328(f181(x40561,x40562),x40563),x40566)),x40564),f328(f328(f257(x40561,x40562),x40565),x40567)))
% 81.29/80.91 [4124]E(f328(f328(f328(f269(x41241,x41242,x41243,x41244),x41245),x41246),x41247),f328(f328(f267(x41242,x41243,x41244),x41246),f328(x41245,x41247)))
% 81.29/80.91 [4137]E(f328(f328(f328(f269(x41371,x41372,x41373,x41374),x41375),x41376),x41377),f328(f328(x41376,f328(f256(x41372,x41373),f328(x41375,x41377))),f328(f266(x41372,x41373),f328(x41375,x41377))))
% 81.29/80.91 [4172]E(f186(x41721,x41722,f328(f328(f328(f73(x41721,f881(x41722)),x41723),x41724),f328(f236(x41722),x41725)),x41726,x41727),f186(x41721,x41722,x41723,f328(f328(f150(x41721),x41724),x41726),f328(f328(f150(x41722),x41725),x41727)))
% 81.29/80.91 [4189]E(f328(f74(x41891,x41892,x41893,x41894),f328(f74(x41895,x41891,x41893,x41896),x41897)),f328(f74(x41895,x41892,x41893,f328(f74(x41891,x41892,x41895,x41894),x41896)),x41897))
% 81.29/80.91 [4250]E(f328(f74(f881(x42501),f881(x42502),x42503,f328(f207(x42501,x42502),x42504)),f328(f328(f328(f73(x42503,f881(x42501)),x42505),x42506),f328(f236(x42501),x42507))),f328(f328(f328(f73(x42503,f881(x42502)),f328(f74(f881(x42501),f881(x42502),x42503,f328(f207(x42501,x42502),x42504)),x42505)),x42506),f328(f236(x42502),f328(x42504,x42507))))
% 81.29/80.91 [4376]E(f328(f268(x43761,x43762,x43763,x43763,x43764,f35(x43763)),f328(f268(x43761,x43761,x43765,x43763,f35(x43761),x43766),x43767)),f328(f328(f257(x43762,x43763),f328(x43764,f328(f256(x43761,x43765),x43767))),f328(x43766,f328(f266(x43761,x43765),x43767))))
% 81.29/80.91 [4377]E(f328(f268(x43771,x43771,x43772,x43773,f35(x43771),x43774),f328(f268(x43775,x43771,x43772,x43772,x43776,f35(x43772)),x43777)),f328(f328(f257(x43771,x43773),f328(x43776,f328(f256(x43775,x43772),x43777))),f328(x43774,f328(f266(x43775,x43772),x43777))))
% 81.29/80.91 [4392]E(f328(f268(x43921,x43922,x43923,x43923,x43924,f35(x43923)),f328(f268(x43925,x43921,x43923,x43923,x43926,f35(x43923)),x43927)),f328(f268(x43925,x43922,x43923,x43923,f328(f74(x43921,x43922,x43925,x43924),x43926),f35(x43923)),x43927))
% 81.29/80.91 [4393]E(f328(f268(x43931,x43931,x43932,x43933,f35(x43931),x43934),f328(f268(x43931,x43931,x43935,x43932,f35(x43931),x43936),x43937)),f328(f268(x43931,x43931,x43935,x43933,f35(x43931),f328(f74(x43932,x43933,x43935,x43934),x43936)),x43937))
% 81.29/80.91 [4402]E(f328(f268(x44021,x44022,x44023,x44023,x44024,f35(x44023)),f328(f268(x44021,x44021,x44025,x44023,f35(x44021),x44026),x44027)),f328(f268(x44022,x44022,x44025,x44023,f35(x44022),x44026),f328(f268(x44021,x44022,x44025,x44025,x44024,f35(x44025)),x44027)))
% 81.29/80.91 [4091]E(f328(f328(f285(x40911,x40912,x40913),f328(f328(f285(x40911,x40914,x40912),x40915),x40916)),x40917),f328(f328(f285(x40911,x40914,x40913),x40915),f328(f328(f285(x40914,x40912,x40913),x40916),x40917)))
% 81.29/80.91 [4163]E(f328(f328(f267(x41631,x41632,x41633),f328(f74(x41634,f885(x41632,x41633),x41631,x41635),x41636)),x41637),f328(f328(x41635,f328(x41636,f328(f256(x41631,x41632),x41637))),f328(f266(x41631,x41632),x41637)))
% 81.29/80.91 [4214]E(f328(f74(x42141,x42142,x42143,x42144),f328(f328(f328(f73(x42143,x42141),x42145),x42146),x42147)),f328(f328(f328(f73(x42143,x42142),f328(f74(x42141,x42142,x42143,x42144),x42145)),x42146),f328(x42144,x42147)))
% 81.29/80.91 [4246]E(f328(f141(x42461,x42462,f328(f7(x42462,x42461,x42461),x42463),x42464),f328(f168(x42462),f328(f328(f153(x42465,x42462),x42466),x42467))),f328(f141(x42461,x42465,f328(f7(x42465,x42461,x42461),f328(f74(x42462,f885(x42461,x42461),x42465,x42463),x42466)),x42464),f328(f168(x42465),x42467)))
% 81.29/80.91 [4190]E(f328(f328(f43(x41901,f885(f884(x41902,x41903),a871)),x41904),f328(f328(f8(f885(f884(x41905,x41903),a871),f885(f884(x41902,x41903),a871),x41901),f328(f285(x41902,x41905,x41903),x41906)),x41907)),f328(f328(f285(x41902,x41905,x41903),x41906),f328(f328(f43(x41901,f885(f884(x41905,x41903),a871)),x41904),x41907)))
% 81.29/80.91 [4338]E(f328(f328(f43(x43381,f885(f884(x43382,x43383),a871)),x43384),f328(f328(f7(x43381,f885(f884(x43385,x43383),a871),f885(f884(x43382,x43383),a871)),f328(f328(f8(f885(f884(x43382,x43385),a871),f885(f885(f884(x43385,x43383),a871),f885(f884(x43382,x43383),a871)),x43381),f285(x43382,x43385,x43383)),x43386)),x43387)),f328(f328(f285(x43382,x43385,x43383),f328(f328(f43(x43381,f885(f884(x43382,x43385),a871)),x43384),x43386)),x43387))
% 81.29/80.91 [4339]E(f328(f141(x43391,x43392,f328(f328(f7(x43391,f885(x43392,x43393),f885(x43392,x43391)),f328(f328(f8(f885(x43393,x43391),f885(f885(x43392,x43393),f885(x43392,x43391)),x43391),f8(x43393,x43391,x43392)),x43394)),x43395),x43396),x43397),f328(f141(x43391,x43393,x43394,x43396),f328(f328(f153(x43392,x43393),x43395),x43397)))
% 81.29/80.91 [4403]E(f328(f328(f42(x44031,f885(x44032,a871)),x44033),f328(f328(f8(f885(x44034,f885(x44032,a871)),f885(x44032,a871),x44031),f328(f42(x44034,f885(x44032,a871)),x44035)),f328(f328(f7(x44031,f885(x44034,f885(x44032,a871)),f885(x44034,f885(x44032,a871))),f328(f328(f8(f885(f885(x44032,a871),f885(x44032,a871)),f885(f885(x44034,f885(x44032,a871)),f885(x44034,f885(x44032,a871))),x44031),f8(f885(x44032,a871),f885(x44032,a871),x44034)),f328(f328(f8(f885(x44032,a871),f885(f885(x44032,a871),f885(x44032,a871)),x44031),f116(f885(x44032,a871))),x44036))),x44037))),f328(f328(f116(f885(x44032,a871)),f328(f328(f42(x44031,f885(x44032,a871)),x44033),x44036)),f328(f328(f42(x44034,f885(x44032,a871)),x44035),x44037)))
% 81.29/80.91 [4404]E(f328(f328(f43(x44041,f885(x44042,a871)),x44043),f328(f328(f8(f885(x44044,f885(x44042,a871)),f885(x44042,a871),x44041),f328(f43(x44044,f885(x44042,a871)),x44045)),f328(f328(f7(x44041,f885(x44044,f885(x44042,a871)),f885(x44044,f885(x44042,a871))),f328(f328(f8(f885(f885(x44042,a871),f885(x44042,a871)),f885(f885(x44044,f885(x44042,a871)),f885(x44044,f885(x44042,a871))),x44041),f8(f885(x44042,a871),f885(x44042,a871),x44044)),f328(f328(f8(f885(x44042,a871),f885(f885(x44042,a871),f885(x44042,a871)),x44041),f107(f885(x44042,a871))),x44046))),x44047))),f328(f328(f107(f885(x44042,a871)),f328(f328(f43(x44041,f885(x44042,a871)),x44043),x44046)),f328(f328(f43(x44044,f885(x44042,a871)),x44045),x44047)))
% 81.29/80.91 [4397]E(f205(x43971,x43972,f328(f328(f328(x43973,x43974),x43975),x43976),f328(f328(f7(x43971,f884(a105,a105),f885(a105,f879(x43972))),f328(f328(f7(x43971,a105,f885(f884(a105,a105),f885(a105,f879(x43972)))),f328(f328(f7(x43971,a105,f885(a105,f885(f884(a105,a105),f885(a105,f879(x43972))))),x43977),x43974)),x43975)),x43976)),f328(f328(f328(f217(x43971,x43972,x43973,x43977),x43974),x43975),x43976))
% 81.29/80.91 [4410]E(f206(x44101,x44102,f328(f328(f328(x44103,x44104),x44105),x44106),f328(f328(f7(x44101,f884(a105,a105),f885(a105,f879(x44102))),f328(f328(f7(x44101,a105,f885(f884(a105,a105),f885(a105,f879(x44102)))),f328(f328(f7(x44101,a105,f885(a105,f885(f884(a105,a105),f885(a105,f879(x44102))))),x44107),x44104)),x44105)),x44106)),f219(x44101,x44102,x44103,x44107,x44104,x44105,x44106))
% 81.29/80.91 [4401]E(f203(x44011,x44012,f328(f328(f328(x44013,x44014),x44015),x44016),f328(f328(f7(x44011,f884(a105,a105),f885(a105,f879(f881(x44012)))),f328(f328(f7(x44011,a105,f885(f884(a105,a105),f885(a105,f879(f881(x44012))))),f328(f328(f7(x44011,a105,f885(a105,f885(f884(a105,a105),f885(a105,f879(f881(x44012)))))),x44017),x44014)),x44015)),x44016)),f328(f328(f328(f213(x44011,x44012,x44013,x44017),x44014),x44015),x44016))
% 81.29/80.91 [4412]E(f204(x44121,x44122,f328(f328(f328(x44123,x44124),x44125),x44126),f328(f328(f7(x44121,f884(a105,a105),f885(a105,f879(f881(x44122)))),f328(f328(f7(x44121,a105,f885(f884(a105,a105),f885(a105,f879(f881(x44122))))),f328(f328(f7(x44121,a105,f885(a105,f885(f884(a105,a105),f885(a105,f879(f881(x44122)))))),x44127),x44124)),x44125)),x44126)),f215(x44121,x44122,x44123,x44127,x44124,x44125,x44126))
% 81.29/80.91 [4310]E(f328(f268(x43101,x43102,x43103,x43104,x43105,x43106),f328(f328(f257(x43101,x43103),x43107),x43108)),f328(f328(f257(x43102,x43104),f328(x43105,x43107)),f328(x43106,x43108)))
% 81.29/80.91 [4414]E(f328(f328(f153(f884(x44141,x44142),f884(x44143,x44144)),f328(f267(x44141,x44142,f884(x44143,x44144)),f328(f328(f7(x44141,f885(x44142,x44144),f885(x44142,f884(x44143,x44144))),f328(f328(f8(f885(x44144,f884(x44143,x44144)),f885(f885(x44142,x44144),f885(x44142,f884(x44143,x44144))),x44141),f8(x44144,f884(x44143,x44144),x44142)),f328(f328(f8(x44143,f885(x44144,f884(x44143,x44144)),x44141),f257(x44143,x44144)),x44145))),x44146))),f328(f328(f181(x44141,x44142),x44147),x44148)),f328(f328(f181(x44143,x44144),f328(f328(f153(x44141,x44143),x44145),x44147)),f328(f328(f153(x44142,x44144),x44146),x44148)))
% 81.29/80.91 [4418]E(f328(f328(f153(f884(x44181,x44182),x44183),f328(f267(x44181,x44182,x44183),f328(f328(f8(f885(x44182,f884(x44181,x44184)),f885(x44182,x44183),x44181),f328(f8(f884(x44181,x44184),x44183,x44182),x44185)),f328(f328(f7(x44181,f885(x44182,x44184),f885(x44182,f884(x44181,x44184))),f328(f328(f8(f885(x44184,f884(x44181,x44184)),f885(f885(x44182,x44184),f885(x44182,f884(x44181,x44184))),x44181),f8(x44184,f884(x44181,x44184),x44182)),f257(x44181,x44184))),x44186)))),f328(f328(f181(x44181,x44182),x44187),x44188)),f328(f328(f153(f884(x44181,x44184),x44183),x44185),f328(f328(f181(x44181,x44184),x44187),f328(f328(f153(x44182,x44184),x44186),x44188))))
% 81.29/80.91 [4343]E(f328(f328(f153(f884(x43431,x43432),x43433),f328(f267(x43431,x43432,x43433),f328(f328(f8(f885(x43432,f884(x43434,x43432)),f885(x43432,x43433),x43431),f328(f8(f884(x43434,x43432),x43433,x43432),x43435)),f328(f328(f8(x43434,f885(x43432,f884(x43434,x43432)),x43431),f257(x43434,x43432)),x43436)))),f328(f328(f181(x43431,x43432),x43437),x43438)),f328(f328(f153(f884(x43434,x43432),x43433),x43435),f328(f328(f181(x43434,x43432),f328(f328(f153(x43431,x43434),x43436),x43437)),x43438)))
% 81.29/80.91 [4301]E(f328(f328(f267(x43011,x43012,x43013),f328(f328(f8(f885(x43012,f884(x43014,x43015)),f885(x43012,x43013),x43011),f328(f8(f884(x43014,x43015),x43013,x43012),f328(f267(x43014,x43015,x43013),x43016))),x43017)),x43018),f328(f328(f267(x43014,x43015,x43013),x43016),f328(f328(f267(x43011,x43012,f884(x43014,x43015)),x43017),x43018)))
% 81.29/80.91 [4419]E(f328(f328(f43(f884(x44191,x44192),f885(f884(x44193,x44194),a871)),f328(f328(f265(x44191,x44192),x44195),f328(f16(f885(x44192,a871),x44191),x44196))),f328(f267(x44191,x44192,f885(f884(x44193,x44194),a871)),f328(f328(f7(x44191,f885(x44192,f885(x44193,f885(x44194,a871))),f885(x44192,f885(f884(x44193,x44194),a871))),f328(f328(f8(f885(f885(x44193,f885(x44194,a871)),f885(f884(x44193,x44194),a871)),f885(f885(x44192,f885(x44193,f885(x44194,a871))),f885(x44192,f885(f884(x44193,x44194),a871))),x44191),f8(f885(x44193,f885(x44194,a871)),f885(f884(x44193,x44194),a871),x44192)),f328(f328(f8(f885(x44193,a871),f885(f885(x44193,f885(x44194,a871)),f885(f884(x44193,x44194),a871)),x44191),f265(x44193,x44194)),x44197))),f328(f328(f8(f885(x44194,a871),f885(x44193,f885(x44194,a871)),x44192),f16(f885(x44194,a871),x44193)),x44198)))),f328(f328(f265(x44193,x44194),f328(f328(f43(x44191,f885(x44193,a871)),x44195),x44197)),f328(f16(f885(x44194,a871),x44193),f328(f328(f43(x44192,f885(x44194,a871)),x44196),x44198))))
% 81.29/80.91 [4357]E(f328(f328(f269(x43571,x43572,x43573,x43574),f328(f328(f269(x43571,x43575,x43576,f884(x43572,x43573)),x43577),x43578)),x43579),f328(f328(f269(x43571,x43575,x43576,x43574),x43577),f328(f328(f7(x43575,f885(x43572,f885(x43573,x43574)),f885(x43576,x43574)),f328(f328(f8(f885(x43576,f884(x43572,x43573)),f885(f885(x43572,f885(x43573,x43574)),f885(x43576,x43574)),x43575),f269(x43576,x43572,x43573,x43574)),x43578)),x43579)))
% 81.29/80.91 [4389]E(f328(f74(f884(x43891,x43892),f884(x43893,x43894),f884(x43895,x43896),f268(x43891,x43893,x43892,x43894,x43897,x43898)),f268(x43895,x43891,x43896,x43892,x43899,x438910)),f268(x43895,x43893,x43896,x43894,f328(f74(x43891,x43893,x43895,x43897),x43899),f328(f74(x43892,x43894,x43896,x43898),x438910)))
% 81.29/80.91 [4395]E(f328(f268(x43951,x43952,x43953,x43954,x43955,x43956),f328(f268(x43957,x43951,x43958,x43953,x43959,x439510),x439511)),f328(f268(x43957,x43952,x43958,x43954,f328(f74(x43951,x43952,x43957,x43955),x43959),f328(f74(x43953,x43954,x43958,x43956),x439510)),x439511))
% 81.29/80.91 [4574]~P95(x45741)+E(f92(x45741),a325)
% 81.29/80.91 [4575]~P26(x45751)+P26(f881(x45751))
% 81.29/80.91 [4576]~P60(x45761)+P60(f881(x45761))
% 81.29/80.91 [4579]~P136(x45791)+~E(f79(x45791),f2(x45791))
% 81.29/80.91 [4581]~E(x45811,f2(a105))+E(f328(a20,x45811),f2(a1))
% 81.29/80.91 [4582]~E(x45821,f2(a1))+E(f83(a1,x45821),f2(a1))
% 81.29/80.91 [4589]~P141(x45891)+P31(x45891,f2(x45891))
% 81.29/80.91 [4591]~P106(x45911)+P29(x45911,f119(x45911))
% 81.29/80.91 [4601]P24(x46011)+P24(f328(a323,x46011))
% 81.29/80.91 [4644]~P141(x46441)+~P31(x46441,f79(x46441))
% 81.29/80.91 [4690]~P24(x46901)+~P24(f328(a323,x46901))
% 81.29/80.91 [4713]E(f328(a110,x47131),f2(a877))+~P24(f328(a199,x47131))
% 81.29/80.91 [4777]~P71(x47771)+P12(x47771,x47771,f82(x47771))
% 81.29/80.91 [4778]~P65(x47781)+P11(x47781,x47781,f116(x47781))
% 81.29/80.91 [4779]~P102(x47791)+P11(x47791,x47791,f107(x47791))
% 81.29/80.91 [4780]~P98(x47801)+P11(x47801,x47801,f82(x47801))
% 81.29/80.91 [4781]~P106(x47811)+P11(x47811,x47811,f242(x47811))
% 81.29/80.91 [4782]~P106(x47821)+P11(x47821,x47821,f243(x47821))
% 81.29/80.91 [4586]~E(x45861,f2(a877))+E(f328(f106(a1),x45861),f2(a1))
% 81.29/80.91 [4594]~P96(x45941)+E(f328(f109(x45941),a84),f2(x45941))
% 81.29/80.91 [4597]~E(f530(x45971),f2(a877))+E(f328(f165(a877),x45971),f2(a877))
% 81.29/80.91 [4598]~P107(x45981)+E(f246(x45981,f244(x45981)),f242(x45981))
% 81.29/80.91 [4599]~P107(x45991)+E(f247(x45991,f244(x45991)),f243(x45991))
% 81.29/80.91 [4600]~P91(x46001)+E(f83(x46001,f2(x46001)),f2(x46001))
% 81.29/80.91 [4609]~P141(x46091)+E(f328(f106(x46091),f79(a877)),f79(x46091))
% 81.29/80.91 [4610]~P141(x46101)+E(f328(f106(x46101),f2(a877)),f2(x46101))
% 81.29/80.91 [4611]~P137(x46111)+E(f328(f108(x46111),f79(a1)),f79(x46111))
% 81.29/80.91 [4612]~P137(x46121)+E(f328(f108(x46121),f2(a1)),f2(x46121))
% 81.29/80.91 [4613]E(x46131,f2(a877))+~E(f328(f106(a1),x46131),f2(a1))
% 81.29/80.91 [4638]~P111(x46381)+E(f328(f76(x46381),f79(x46381)),f79(x46381))
% 81.29/80.91 [4639]~P87(x46391)+E(f328(f76(x46391),f2(x46391)),f2(x46391))
% 81.29/80.91 [4640]~P97(x46401)+E(f328(f80(x46401),f193(x46401)),f252(x46401))
% 81.29/80.91 [4641]~P73(x46411)+E(f328(f80(x46411),f2(x46411)),f2(x46411))
% 81.29/80.91 [4642]~P97(x46421)+E(f328(f80(x46421),f252(x46421)),f193(x46421))
% 81.29/80.91 [4643]~P82(x46431)+E(f328(f165(x46431),f119(x46431)),f2(x46431))
% 81.29/80.91 [4664]~P37(x46641)+P40(f328(f171(a1),x46641))
% 81.29/80.91 [4695]~P96(x46951)+E(f328(f80(x46951),f79(x46951)),f328(f109(x46951),a103))
% 81.29/80.91 [4712]~P96(x47121)+P31(x47121,f328(f109(x47121),a84))
% 81.29/80.91 [4729]~P60(x47291)+E(f328(f171(x47291),f56(x47291)),f252(f885(x47291,a871)))
% 81.29/80.91 [4739]P37(x47391)+~P40(f328(f171(a1),x47391))
% 81.29/80.91 [4740]~P60(x47401)+P24(f328(f136(x47401),f56(x47401)))
% 81.29/80.91 [4783]E(f328(f106(a1),f328(a110,x47831)),x47831)+P24(f328(a199,x47831))
% 81.29/80.91 [4800]~P107(x48001)+E(f95(x48001,x48001,f5(x48001)),f96(x48001))
% 81.29/80.91 [4853]~P116(x48531)+E(f259(x48531,f79(x48531),f82(x48531)),f258(x48531))
% 81.29/80.91 [4883]~P96(x48831)+~P31(x48831,f328(f109(x48831),a103))
% 81.29/80.91 [4894]E(f328(a28,x48941),f196(a873))+P24(f328(a25,f328(a26,x48941)))
% 81.29/80.91 [5024]E(f328(f76(a1),x50241),x50241)+P24(f328(f328(f245(a1),x50241),f2(a1)))
% 81.29/80.91 [5045]~E(f328(a110,x50451),f2(a877))+P24(f328(f328(f244(a1),x50451),f2(a1)))
% 81.29/80.91 [5105]~P24(f328(a199,x51051))+P24(f328(f328(f245(a1),x51051),f2(a1)))
% 81.29/80.91 [5145]~P137(x51451)+P24(f328(f328(f330(x51451),f79(x51451)),f115(x51451)))
% 81.29/80.91 [5146]~P141(x51461)+P24(f328(f328(f330(x51461),f79(x51461)),f191(x51461)))
% 81.29/80.91 [5147]~P137(x51471)+P24(f328(f328(f330(x51471),f2(x51471)),f115(x51471)))
% 81.29/80.91 [5148]~P141(x51481)+P24(f328(f328(f330(x51481),f2(x51481)),f191(x51481)))
% 81.29/80.91 [5149]~P110(x51491)+P24(f328(f328(f244(x51491),f2(x51491)),f79(x51491)))
% 81.29/80.91 [5150]~P110(x51501)+P24(f328(f328(f245(x51501),f2(x51501)),f79(x51501)))
% 81.29/80.91 [5153]E(f328(f236(a873),f837(x51531)),f328(a28,x51531))+~P24(f328(a25,f328(a26,x51531)))
% 81.29/80.91 [5154]E(f328(f236(a873),f850(x51541)),f328(a28,x51541))+~P24(f328(a25,f328(a26,x51541)))
% 81.29/80.91 [5209]E(x52091,f2(a877))+~P24(f328(f328(f244(a877),x52091),f2(a877)))
% 81.29/80.91 [5253]E(f328(a110,x52531),f2(a877))+~P24(f328(f328(f244(a1),x52531),f2(a1)))
% 81.29/80.91 [5316]P24(f328(a199,x53161))+~P24(f328(f328(f245(a1),x53161),f2(a1)))
% 81.29/80.91 [5321]~P106(x53211)+P12(x53211,f878(x53211),f147(x53211,x53211,f5(x53211)))
% 81.29/80.91 [5339]P40(x53391)+~P24(f328(f328(f244(a1),f2(a1)),f345(x53391)))
% 81.29/80.91 [5345]E(f328(f76(a1),x53451),f328(f80(a1),x53451))+~P24(f328(f328(f245(a1),x53451),f2(a1)))
% 81.29/80.91 [5519]~P110(x55191)+~P24(f328(f328(f244(x55191),f79(x55191)),f2(x55191)))
% 81.29/80.91 [5520]~P110(x55201)+~P24(f328(f328(f245(x55201),f79(x55201)),f2(x55201)))
% 81.29/80.91 [5530]~E(x55301,f2(a877))+P24(f328(f328(f244(a1),f328(f106(a1),x55301)),f2(a1)))
% 81.29/80.91 [5531]~E(x55311,f2(a1))+P24(f328(f328(f245(a1),f328(f76(a1),x55311)),f79(a1)))
% 81.29/80.91 [5649]~P82(x56491)+E(f141(x56491,x56491,f81(x56491),f2(x56491)),f165(x56491))
% 81.29/80.91 [5820]~P103(x58201)+P21(a877,x58201,f106(x58201),f252(f885(a877,a871)))
% 81.29/80.91 [6018]E(x60181,f2(a877))+~P24(f328(f328(f244(a1),f328(f106(a1),x60181)),f2(a1)))
% 81.29/80.91 [6019]E(x60191,f2(a1))+~P24(f328(f328(f245(a1),f328(f76(a1),x60191)),f79(a1)))
% 81.29/80.91 [6818]~P24(f328(f328(f245(a1),x68181),f2(a1)))+P24(f328(f328(f245(a1),f328(f328(f81(a1),x68181),x68181)),f2(a1)))
% 81.29/80.91 [7364]P24(f328(f328(f245(a1),x73641),f2(a1)))+~P24(f328(f328(f245(a1),f328(f328(f81(a1),x73641),x73641)),f2(a1)))
% 81.29/80.91 [7916]E(x79161,f328(a3,f2(a877)))+P24(f328(f328(f245(a877),f328(f328(f22(a877),f328(a19,x79161)),f328(a118,f2(a877)))),f328(a19,x79161)))
% 81.29/80.91 [8687]~P24(f328(f328(f245(a1),x86871),f2(a1)))+P24(f328(f328(f245(a1),f328(f328(f22(a1),f328(f328(f81(a1),x86871),x86871)),a103)),f2(a1)))
% 81.29/80.91 [8774]~P24(f328(f328(f245(a1),x87741),f2(a1)))+P24(f328(f328(f245(a1),f328(f328(f81(a1),f328(f328(f81(a1),f79(a1)),x87741)),x87741)),f2(a1)))
% 81.29/80.91 [9097]P24(f328(f328(f245(a1),x90971),f2(a1)))+~P24(f328(f328(f245(a1),f328(f328(f22(a1),f328(f328(f81(a1),x90971),x90971)),a103)),f2(a1)))
% 81.29/80.91 [9160]P24(f328(f328(f245(a1),x91601),f2(a1)))+~P24(f328(f328(f245(a1),f328(f328(f81(a1),f328(f328(f81(a1),f79(a1)),x91601)),x91601)),f2(a1)))
% 81.29/80.91 [4683]~E(a84,x46831)+E(f328(f328(f81(a1),x46831),x46831),a84)
% 81.29/80.91 [4684]~E(x46841,a84)+E(f328(f328(f81(a1),x46841),x46841),a84)
% 81.29/80.91 [4698]E(x46981,f2(a1))+E(f328(f328(f39(a1),x46981),x46981),f79(a1))
% 81.29/80.91 [4829]E(x48291,a84)+~E(f328(f328(f81(a1),x48291),x48291),a84)
% 81.29/80.91 [4830]E(a84,x48301)+~E(f328(f328(f81(a1),x48301),x48301),a84)
% 81.29/80.91 [4843]~P27(x48431)+E(f40(x48431,f193(f885(x48431,a871))),f193(x48431))
% 81.29/80.91 [4844]~P27(x48441)+E(f40(x48441,f252(f885(x48441,a871))),f252(x48441))
% 81.29/80.91 [4845]~P27(x48451)+E(f41(x48451,f193(f885(x48451,a871))),f252(x48451))
% 81.29/80.91 [4846]~P27(x48461)+E(f41(x48461,f252(f885(x48461,a871))),f193(x48461))
% 81.29/80.91 [4847]~P106(x48471)+E(f138(x48471,f193(f885(x48471,a871))),f119(x48471))
% 81.29/80.91 [4983]E(x49831,f2(a877))+P24(f328(f328(f245(a877),f2(a877)),x49831))
% 81.29/80.91 [5002]~P28(x50021)+P24(f328(f328(f244(a1),f2(a1)),x50021))
% 81.29/80.91 [5036]~E(f328(f109(a877),x50361),f2(a877))+P24(f328(f328(f244(a1),x50361),a84))
% 81.29/80.91 [5041]P40(x50411)+P24(f328(f328(f330(a1),f345(x50411)),x50411))
% 81.29/80.91 [5042]E(x50421,f328(a3,f2(a877)))+P24(f328(f328(f244(a105),f79(a105)),x50421))
% 81.29/80.91 [5079]P24(f328(a199,x50791))+P24(f328(f328(f244(a1),f2(a1)),x50791))
% 81.29/80.91 [5127]E(f328(f106(a1),f328(a110,x51271)),f2(a1))+P24(f328(f328(f244(a1),f2(a1)),x51271))
% 81.29/80.91 [5195]E(f328(f106(a1),f328(f109(a877),x51951)),f328(f109(a1),x51951))+P24(f328(a199,f328(f109(a1),x51951)))
% 81.29/80.91 [5215]E(f328(f109(a877),x52151),f2(a877))+~P24(f328(a199,f328(f109(a1),x52151)))
% 81.29/80.91 [5216]E(f328(f109(a877),x52161),f2(a877))+~P24(f328(f328(f244(a1),x52161),a84))
% 81.29/80.91 [5250]P28(x52501)+~P24(f328(f328(f244(a1),f2(a1)),x52501))
% 81.29/80.91 [5324]E(f328(a118,f806(x53241)),x53241)+~P24(f328(f328(f245(a877),f2(a877)),x53241))
% 81.29/80.91 [5333]E(f328(a118,f328(f109(a877),x53331)),f79(a877))+~P24(f328(a199,f328(f109(a1),x53331)))
% 81.29/80.91 [5341]E(f328(f106(a1),f861(x53411)),x53411)+~P24(f328(f328(f245(a1),f2(a1)),x53411))
% 81.29/80.91 [5349]~E(x53491,f328(a3,f2(a877)))+~P24(f328(f328(f244(a105),f79(a105)),x53491))
% 81.29/80.91 [5356]E(f328(f106(a1),f328(f109(a877),x53561)),f2(a1))+~P24(f328(a199,f328(f109(a1),x53561)))
% 81.29/80.91 [5382]E(f328(f165(a877),x53821),f2(a877))+P24(f328(f328(f330(a877),f530(x53821)),f328(f171(a877),x53821)))
% 81.29/80.91 [5403]E(f328(f106(a1),f328(a110,x54031)),x54031)+~P24(f328(f328(f244(a1),f2(a1)),x54031))
% 81.29/80.91 [5412]~P24(f328(a199,x54121))+~P24(f328(f328(f244(a1),f2(a1)),x54121))
% 81.29/80.91 [5512]E(f328(f328(f81(a877),f79(a877)),f328(f109(a877),x55121)),f79(a877))+~P24(f328(f328(f245(a1),x55121),a84))
% 81.29/80.91 [5570]E(x55701,f2(a877))+~P24(f328(f328(f245(a877),x55701),f328(a118,f2(a877))))
% 81.29/80.91 [5608]E(f328(f328(f22(a877),f328(f109(a877),x56081)),f79(a877)),f2(a877))+~P24(f328(f328(f244(a1),x56081),a84))
% 81.29/80.91 [5609]E(f328(f328(f81(a877),f328(f109(a877),x56091)),f79(a877)),f79(a877))+~P24(f328(f328(f245(a1),x56091),a84))
% 81.29/80.91 [5619]~P40(x56191)+E(f328(f38(a877),f328(f307(a1,a877,a110),x56191)),f328(f38(a1),x56191))
% 81.29/80.91 [5650]~P106(x56501)+E(f246(x56501,f328(f7(x56501,x56501,a871),f244(x56501))),f243(x56501))
% 81.29/80.91 [5651]~P106(x56511)+E(f247(x56511,f328(f7(x56511,x56511,a871),f244(x56511))),f242(x56511))
% 81.29/80.91 [5661]E(f45(a877,f328(a118,f2(a877)),f328(f109(a877),x56611)),f328(a118,f2(a877)))+~P24(f328(a199,f328(f109(a1),x56611)))
% 81.29/80.91 [5670]~P24(f328(f328(f245(a1),f2(a1)),x56701))+P24(f328(f328(f244(a1),f79(a1)),x56701))
% 81.29/80.91 [5671]P24(f328(f328(f245(a1),f2(a1)),x56711))+~P24(f328(f328(f244(a1),f79(a1)),x56711))
% 81.29/80.91 [5682]E(f328(a118,f328(f328(f22(a877),x56821),f79(a877))),x56821)+~P24(f328(f328(f245(a877),f2(a877)),x56821))
% 81.29/80.91 [5739]P24(f328(f328(f245(a877),f2(a877)),f861(x57391)))+~P24(f328(f328(f245(a1),f2(a1)),x57391))
% 81.29/80.91 [5798]E(f45(a1,f328(f109(a1),a103),x57981),f328(f328(f22(a1),x57981),f79(a1)))+~P24(f328(f328(f245(a1),f2(a1)),x57981))
% 81.29/80.91 [5832]~P24(f328(f328(f245(a1),a84),x58321))+P24(f328(f328(f245(a877),f2(a877)),f328(f109(a877),x58321)))
% 81.29/80.91 [5882]P24(f328(f328(f245(a877),f2(a877)),f328(a110,x58821)))+~P24(f328(f328(f245(a1),f2(a1)),x58821))
% 81.29/80.91 [5934]~P24(f328(f328(f245(a877),f2(a877)),x59341))+P24(f328(f328(f245(a1),f2(a1)),f328(f106(a1),x59341)))
% 81.29/80.91 [5972]~P24(f328(f328(f245(a877),f2(a877)),f328(a110,x59721)))+P24(f328(f328(f245(a1),f2(a1)),x59721))
% 81.29/80.91 [5987]~P40(x59871)+E(f328(f307(a877,a1,f106(a1)),f328(f307(a1,a877,a110),x59871)),x59871)
% 81.29/80.91 [5999]P24(f328(f328(f245(a1),a84),x59991))+~P24(f328(f328(f245(a877),f2(a877)),f328(f109(a877),x59991)))
% 81.29/80.91 [6047]~P60(x60471)+E(f328(f328(f150(f881(x60471)),f196(x60471)),f328(f328(f153(x60471,f881(x60471)),f236(x60471)),f56(x60471))),f56(f881(x60471)))
% 81.29/80.91 [6058]P24(f328(f328(f245(a877),f2(a877)),x60581))+~P24(f328(f328(f245(a1),f2(a1)),f328(f106(a1),x60581)))
% 81.29/80.91 [6173]E(f328(f307(a877,a1,f106(a1)),f328(f250(a877),f328(a110,x61731))),f328(f298(a1,f2(a1)),x61731))+~P24(f328(f328(f244(a1),f2(a1)),x61731))
% 81.29/80.91 [6187]~P110(x61871)+P24(f328(f328(f245(x61871),f2(x61871)),f328(f328(f81(x61871),f79(x61871)),f79(x61871))))
% 81.29/80.91 [6238]P24(f328(f328(f245(a877),f328(a118,f2(a877))),f328(a110,x62381)))+~P24(f328(f328(f245(a1),f79(a1)),x62381))
% 81.29/80.91 [6333]E(x63331,f2(a1))+P24(f328(f49(f2(a1),x63331),f328(f328(f257(a1,a1),f2(a1)),f2(a1))))
% 81.29/80.91 [6501]~P24(f328(f328(f245(a877),f328(a118,f2(a877))),f328(a110,x65011)))+P24(f328(f328(f245(a1),f79(a1)),x65011))
% 81.29/80.91 [6927]~P117(x69271)+P38(x69271,f328(f249(f884(x69271,x69271)),f328(f267(x69271,x69271,a871),f245(x69271))))
% 81.29/80.91 [5557]E(f328(f109(a877),f328(f328(f22(a1),x55571),a103)),f328(a118,f328(f109(a877),x55571)))+P24(f328(a199,f328(f109(a1),x55571)))
% 81.29/80.91 [5573]~P37(x55731)+E(f328(f328(f153(a877,a1),f106(a1)),f328(f328(f153(a1,a877),a110),x55731)),x55731)
% 81.29/80.91 [5688]E(f328(f80(a1),f328(f106(a1),f328(a118,f349(x56881)))),x56881)+~P24(f328(f328(f245(a1),x56881),f2(a1)))
% 81.29/80.91 [5698]E(f328(f328(f81(a877),f79(a877)),f328(f109(a877),x56981)),f328(f109(a877),f328(f328(f22(a1),x56981),a103)))+P24(f328(f328(f245(a1),x56981),a84))
% 81.29/80.91 [5741]E(f328(f328(f39(a1),f328(f109(a1),a103)),x57411),f328(f109(a1),a103))+~P24(f328(f328(f245(a1),f2(a1)),x57411))
% 81.29/80.91 [5828]E(f328(f328(f22(a877),f328(f109(a877),x58281)),f79(a877)),f328(f109(a877),f328(f328(f81(a1),x58281),a103)))+P24(f328(f328(f244(a1),x58281),a84))
% 81.29/80.91 [5829]E(f328(f328(f81(a877),f328(f109(a877),x58291)),f79(a877)),f328(f109(a877),f328(f328(f22(a1),x58291),a103)))+P24(f328(f328(f245(a1),x58291),a84))
% 81.29/80.91 [5870]E(f328(a110,f328(f328(f81(a1),f79(a1)),x58701)),f328(a118,f328(a110,x58701)))+~P24(f328(f328(f244(a1),f2(a1)),x58701))
% 81.29/80.91 [5906]E(f328(a118,f328(f328(f22(a877),x59061),f328(a118,f2(a877)))),x59061)+~P24(f328(f328(f245(a877),f2(a877)),x59061))
% 81.29/80.91 [6118]E(f45(a877,f328(a118,f2(a877)),f328(f109(a877),x61181)),f328(a110,f45(a1,f79(a1),f328(f109(a1),x61181))))+P24(f328(a199,f328(f109(a1),x61181)))
% 81.29/80.91 [6163]~P24(f328(f328(f244(a1),a84),x61631))+P24(f328(f328(f244(a1),a84),f328(f328(f81(a1),x61631),x61631)))
% 81.29/80.91 [6164]~P24(f328(f328(f245(a1),a103),x61641))+P24(f328(f328(f244(a1),a103),f328(f328(f81(a1),x61641),x61641)))
% 81.29/80.91 [6165]~P24(f328(f328(f245(a1),a84),x61651))+P24(f328(f328(f245(a1),a84),f328(f328(f81(a1),x61651),x61651)))
% 81.29/80.91 [6166]~P24(f328(f328(f245(a1),a103),x61661))+P24(f328(f328(f245(a1),a103),f328(f328(f81(a1),x61661),x61661)))
% 81.29/80.91 [6167]~P24(f328(f328(f92(a1),a84),x61671))+P24(f328(f328(f92(a1),a84),f328(f328(f81(a1),x61671),x61671)))
% 81.29/80.91 [6346]~P24(f328(f62(x63461),f252(f885(x63461,a871))))+P24(f328(f62(f881(x63461)),f252(f885(f881(x63461),a871))))
% 81.29/80.91 [6433]~P24(f328(f328(f244(a1),f2(a1)),x64331))+P24(f328(f328(f245(a1),f2(a1)),f328(f328(f81(a1),f79(a1)),x64331)))
% 81.29/80.91 [6440]E(f328(f256(a1,a1),f47(f79(a1),f328(f109(a1),x64401))),f328(f328(f39(a1),f79(a1)),f328(f109(a1),x64401)))+~P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),x64401)))
% 81.29/80.91 [6460]E(f328(f266(a1,a1),f47(f79(a1),f328(f109(a1),x64601))),f45(a1,f79(a1),f328(f109(a1),x64601)))+~P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),x64601)))
% 81.29/80.91 [6472]P24(f328(f62(x64721),f252(f885(x64721,a871))))+~P24(f328(f62(f881(x64721)),f252(f885(f881(x64721),a871))))
% 81.29/80.91 [6502]P24(f328(f328(f244(a1),a84),x65021))+~P24(f328(f328(f244(a1),a84),f328(f328(f81(a1),x65021),x65021)))
% 81.29/80.91 [6503]P24(f328(f328(f245(a1),a84),x65031))+~P24(f328(f328(f245(a1),a84),f328(f328(f81(a1),x65031),x65031)))
% 81.29/80.91 [6504]P24(f328(f328(f245(a1),a103),x65041))+~P24(f328(f328(f244(a1),a103),f328(f328(f81(a1),x65041),x65041)))
% 81.29/80.91 [6505]P24(f328(f328(f245(a1),a103),x65051))+~P24(f328(f328(f245(a1),a103),f328(f328(f81(a1),x65051),x65051)))
% 81.29/80.91 [6506]P24(f328(f328(f92(a1),a84),x65061))+~P24(f328(f328(f92(a1),a84),f328(f328(f81(a1),x65061),x65061)))
% 81.29/80.91 [6822]~P24(f328(f62(x68221),f252(f885(x68221,a871))))+P24(f328(f328(f245(a877),f2(a877)),f328(f38(x68221),f252(f885(x68221,a871)))))
% 81.29/80.91 [7407]P24(f328(f62(a877),x74071))+~P24(f328(f62(a1),f328(f307(a877,a1,f106(a1)),x74071)))
% 81.29/80.91 [5487]~E(a103,x54871)+E(f328(f328(f22(a1),f328(f328(f81(a1),x54871),x54871)),a103),a103)
% 81.29/80.91 [5488]~E(x54881,a103)+E(f328(f328(f22(a1),f328(f328(f81(a1),x54881),x54881)),a103),a103)
% 81.29/80.91 [5992]E(x59921,a103)+~E(f328(f328(f22(a1),f328(f328(f81(a1),x59921),x59921)),a103),a103)
% 81.29/80.91 [5993]E(a103,x59931)+~E(f328(f328(f22(a1),f328(f328(f81(a1),x59931),x59931)),a103),a103)
% 81.29/80.91 [6402]~E(f328(f109(a877),x64021),f2(a877))+P24(f328(a199,f328(f109(a1),f328(f328(f81(a1),x64021),a103))))
% 81.29/80.91 [6749]~P24(f328(a199,f328(f109(a1),x67491)))+P24(f328(a199,f328(f109(a1),f328(f328(f81(a1),x67491),x67491))))
% 81.29/80.91 [6750]~P24(f328(f328(f244(a1),x67501),a84))+P24(f328(f328(f244(a1),f328(f328(f81(a1),x67501),x67501)),a84))
% 81.29/80.91 [6751]~P24(f328(f328(f244(a1),x67511),a103))+P24(f328(f328(f244(a1),f328(f328(f81(a1),x67511),x67511)),a103))
% 81.29/80.91 [6752]~P24(f328(f328(f245(a1),x67521),a84))+P24(f328(f328(f245(a1),f328(f328(f81(a1),x67521),x67521)),a84))
% 81.29/80.91 [6753]~P24(f328(f328(f244(a1),x67531),a103))+P24(f328(f328(f245(a1),f328(f328(f81(a1),x67531),x67531)),a103))
% 81.29/80.91 [6754]~P24(f328(f328(f92(a1),x67541),a84))+P24(f328(f328(f92(a1),f328(f328(f81(a1),x67541),x67541)),a84))
% 81.29/80.91 [7074]E(f328(f109(a877),x70741),f2(a877))+~P24(f328(a199,f328(f109(a1),f328(f328(f81(a1),x70741),a103))))
% 81.29/80.91 [7313]~P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),x73131)))+P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),f328(f328(f81(a1),x73131),x73131))))
% 81.29/80.91 [7314]P24(f328(a199,f328(f109(a1),x73141)))+~P24(f328(a199,f328(f109(a1),f328(f328(f81(a1),x73141),x73141))))
% 81.29/80.91 [7315]P24(f328(f328(f244(a1),x73151),a84))+~P24(f328(f328(f244(a1),f328(f328(f81(a1),x73151),x73151)),a84))
% 81.29/80.91 [7316]P24(f328(f328(f244(a1),x73161),a103))+~P24(f328(f328(f244(a1),f328(f328(f81(a1),x73161),x73161)),a103))
% 81.29/80.91 [7317]P24(f328(f328(f244(a1),x73171),a103))+~P24(f328(f328(f245(a1),f328(f328(f81(a1),x73171),x73171)),a103))
% 81.29/80.91 [7318]P24(f328(f328(f245(a1),x73181),a84))+~P24(f328(f328(f245(a1),f328(f328(f81(a1),x73181),x73181)),a84))
% 81.29/80.91 [7319]P24(f328(f328(f92(a1),x73191),a84))+~P24(f328(f328(f92(a1),f328(f328(f81(a1),x73191),x73191)),a84))
% 81.29/80.91 [7685]E(f328(a112,f712(x76851)),x76851)+~P24(f328(f328(f330(f885(f884(a877,a877),a871)),x76851),a104))
% 81.29/80.91 [6319]~P96(x63191)+E(f328(f109(x63191),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f79(x63191))
% 81.29/80.91 [6801]~P24(f328(a199,f328(f109(a1),x68011)))+E(f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),x68011),x68011)),a103)),f2(a877))
% 81.29/80.91 [7861]~P24(f328(f328(f245(a1),f328(f109(a1),x78611)),f2(a1)))+E(f328(f256(a1,a1),f328(a51,f50(f328(f80(a1),f79(a1)),f328(f80(a1),f328(f109(a1),x78611))))),f328(f328(f39(a1),f79(a1)),f328(f109(a1),x78611)))
% 81.29/80.91 [7874]~P24(f328(f328(f245(a1),f328(f109(a1),x78741)),f2(a1)))+E(f328(f266(a1,a1),f328(a51,f50(f328(f80(a1),f79(a1)),f328(f80(a1),f328(f109(a1),x78741))))),f45(a1,f79(a1),f328(f109(a1),x78741)))
% 81.29/80.91 [7922]~P24(f328(f328(f244(a1),a84),x79221))+P24(f328(f328(f244(a1),a84),f328(f328(f22(a1),f328(f328(f81(a1),x79221),x79221)),a103)))
% 81.29/80.91 [7923]~P24(f328(f328(f244(a1),a103),x79231))+P24(f328(f328(f244(a1),a103),f328(f328(f22(a1),f328(f328(f81(a1),x79231),x79231)),a103)))
% 81.29/80.91 [7924]~P24(f328(f328(f244(a1),a84),x79241))+P24(f328(f328(f245(a1),a84),f328(f328(f22(a1),f328(f328(f81(a1),x79241),x79241)),a103)))
% 81.29/80.91 [7925]~P24(f328(f328(f245(a1),a103),x79251))+P24(f328(f328(f245(a1),a103),f328(f328(f22(a1),f328(f328(f81(a1),x79251),x79251)),a103)))
% 81.29/80.91 [7926]~P24(f328(f328(f92(a1),a103),x79261))+P24(f328(f328(f92(a1),a103),f328(f328(f22(a1),f328(f328(f81(a1),x79261),x79261)),a103)))
% 81.29/80.91 [8235]~P96(x82351)+~P31(x82351,f328(f109(x82351),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))
% 81.29/80.91 [8414]P24(f328(f328(f244(a1),a84),x84141))+~P24(f328(f328(f244(a1),a84),f328(f328(f22(a1),f328(f328(f81(a1),x84141),x84141)),a103)))
% 81.29/80.91 [8415]P24(f328(f328(f244(a1),a84),x84151))+~P24(f328(f328(f245(a1),a84),f328(f328(f22(a1),f328(f328(f81(a1),x84151),x84151)),a103)))
% 81.29/80.91 [8416]P24(f328(f328(f244(a1),a103),x84161))+~P24(f328(f328(f244(a1),a103),f328(f328(f22(a1),f328(f328(f81(a1),x84161),x84161)),a103)))
% 81.29/80.91 [8417]P24(f328(f328(f245(a1),a103),x84171))+~P24(f328(f328(f245(a1),a103),f328(f328(f22(a1),f328(f328(f81(a1),x84171),x84171)),a103)))
% 81.29/80.91 [8418]P24(f328(f328(f92(a1),a103),x84181))+~P24(f328(f328(f92(a1),a103),f328(f328(f22(a1),f328(f328(f81(a1),x84181),x84181)),a103)))
% 81.29/80.91 [8731]E(f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),x87311),x87311)),a103)),f328(f328(f87(a877,a877),f328(f109(a877),x87311)),f328(f328(f8(a877,a877,a877),a118),f328(f328(f18(a877,a877,a877),f81(a877)),f5(a877)))))+P24(f328(a199,f328(f109(a1),x87311)))
% 81.29/80.91 [9575]E(x95751,f193(f885(f884(a877,a877),a871)))+P24(f328(f328(f330(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f328(f328(f257(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),x95751),f193(f885(f884(a877,a877),a871)))),a69))
% 81.29/80.91 [8662]~P24(f328(a199,f328(f109(a1),x86621)))+P24(f328(a199,f328(f109(a1),f328(f328(f22(a1),f328(f328(f81(a1),x86621),x86621)),a103))))
% 81.29/80.91 [8663]~P24(f328(f328(f245(a1),x86631),a84))+P24(f328(f328(f244(a1),f328(f328(f22(a1),f328(f328(f81(a1),x86631),x86631)),a103)),a84))
% 81.29/80.91 [8664]~P24(f328(f328(f244(a1),x86641),a103))+P24(f328(f328(f244(a1),f328(f328(f22(a1),f328(f328(f81(a1),x86641),x86641)),a103)),a103))
% 81.29/80.91 [8665]~P24(f328(f328(f245(a1),x86651),a84))+P24(f328(f328(f245(a1),f328(f328(f22(a1),f328(f328(f81(a1),x86651),x86651)),a103)),a84))
% 81.29/80.91 [8666]~P24(f328(f328(f245(a1),x86661),a103))+P24(f328(f328(f245(a1),f328(f328(f22(a1),f328(f328(f81(a1),x86661),x86661)),a103)),a103))
% 81.29/80.91 [8667]~P24(f328(f328(f92(a1),x86671),a103))+P24(f328(f328(f92(a1),f328(f328(f22(a1),f328(f328(f81(a1),x86671),x86671)),a103)),a103))
% 81.29/80.91 [8767]~P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),x87671)))+P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),f328(f328(f22(a1),f328(f328(f81(a1),x87671),x87671)),a103))))
% 81.29/80.91 [8925]~P96(x89251)+E(f328(f328(f81(x89251),f79(x89251)),f79(x89251)),f328(f109(x89251),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))
% 81.29/80.91 [9081]P24(f328(a199,f328(f109(a1),x90811)))+~P24(f328(a199,f328(f109(a1),f328(f328(f22(a1),f328(f328(f81(a1),x90811),x90811)),a103))))
% 81.29/80.91 [9082]P24(f328(f328(f244(a1),x90821),a103))+~P24(f328(f328(f244(a1),f328(f328(f22(a1),f328(f328(f81(a1),x90821),x90821)),a103)),a103))
% 81.29/80.91 [9083]P24(f328(f328(f245(a1),x90831),a84))+~P24(f328(f328(f244(a1),f328(f328(f22(a1),f328(f328(f81(a1),x90831),x90831)),a103)),a84))
% 81.29/80.91 [9084]P24(f328(f328(f245(a1),x90841),a84))+~P24(f328(f328(f245(a1),f328(f328(f22(a1),f328(f328(f81(a1),x90841),x90841)),a103)),a84))
% 81.29/80.91 [9085]P24(f328(f328(f245(a1),x90851),a103))+~P24(f328(f328(f245(a1),f328(f328(f22(a1),f328(f328(f81(a1),x90851),x90851)),a103)),a103))
% 81.29/80.91 [9086]P24(f328(f328(f92(a1),x90861),a103))+~P24(f328(f328(f92(a1),f328(f328(f22(a1),f328(f328(f81(a1),x90861),x90861)),a103)),a103))
% 81.29/80.91 [9621]~P24(f328(f62(f884(a877,a877)),x96211))+P24(f328(f328(f330(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f328(f328(f257(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),f193(f885(f884(a877,a877),a871))),x96211)),a70))
% 81.29/80.91 [9408]~P141(x94081)+E(f328(f328(f258(x94081),f79(x94081)),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f79(x94081))
% 81.29/80.91 [9409]~P141(x94091)+E(f328(f328(f258(x94091),f2(x94091)),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f2(x94091))
% 81.29/80.91 [9845]~P24(f328(f328(f245(a877),f79(a877)),x98451))+P24(f328(f328(f245(a877),f2(a877)),f328(f328(f39(a877),x98451),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))))
% 81.29/80.91 [9857]~P24(f328(f328(f245(a877),f2(a877)),x98571))+P24(f328(f328(f245(a877),f2(a877)),f328(f328(f39(a877),f328(f328(f81(a877),x98571),f79(a877))),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))))
% 81.29/80.91 [9900]~E(f45(a877,x99001,f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f79(a877))+P24(f328(f328(f245(a877),f2(a877)),f45(a877,x99001,f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))))
% 81.29/80.91 [9921]E(f45(a877,x99211,f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f79(a877))+~P24(f328(f328(f245(a877),f2(a877)),f45(a877,x99211,f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))))
% 81.29/80.91 [4617]~P38(x46171,x46172)+P55(x46171,x46172)
% 81.29/80.91 [4618]~P43(x46181,x46182)+P55(x46181,x46182)
% 81.29/80.91 [4577]~E(x45771,x45772)+E(f275(x45771,x45772),f79(a105))
% 81.29/80.91 [4580]E(f224(x45801,x45802),x45801)+~E(x45802,f2(a877))
% 81.29/80.91 [4585]P39(x45851,x45852)+~E(x45852,f196(x45851))
% 81.29/80.91 [4588]~E(x45882,f119(x45881))+E(f151(x45881,x45882),f119(x45881))
% 81.29/80.91 [4592]~P39(x45922,x45921)+E(x45921,f196(x45922))
% 81.29/80.91 [4608]~E(f151(x46082,x46081),f119(x46082))+E(x46081,f119(x46082))
% 81.29/80.91 [4622]~P25(x46222)+P25(f885(x46221,x46222))
% 81.29/80.91 [4623]~P105(x46232)+P105(f885(x46231,x46232))
% 81.29/80.91 [4624]~P107(x46242)+P107(f885(x46241,x46242))
% 81.29/80.91 [4625]~P108(x46252)+P108(f885(x46251,x46252))
% 81.29/80.91 [4626]~P78(x46262)+P65(f885(x46261,x46262))
% 81.29/80.91 [4627]~P66(x46272)+P66(f885(x46271,x46272))
% 81.29/80.91 [4628]~P78(x46282)+P78(f885(x46281,x46282))
% 81.29/80.91 [4629]~P99(x46292)+P79(f885(x46291,x46292))
% 81.29/80.91 [4630]~P27(x46302)+P27(f885(x46301,x46302))
% 81.29/80.91 [4631]~P78(x46312)+P102(f885(x46311,x46312))
% 81.29/80.91 [4632]~P100(x46322)+P100(f885(x46321,x46322))
% 81.29/80.91 [4633]~P97(x46332)+P97(f885(x46331,x46332))
% 81.29/80.91 [4634]~P90(x46342)+P90(f885(x46341,x46342))
% 81.29/80.91 [4635]~P115(x46352)+P115(f885(x46351,x46352))
% 81.29/80.91 [4636]~P99(x46362)+P101(f885(x46361,x46362))
% 81.29/80.91 [4637]~P99(x46372)+P99(f885(x46371,x46372))
% 81.29/80.91 [4649]E(x46491,x46492)+~E(f328(a26,x46491),f328(a26,x46492))
% 81.29/80.91 [4651]E(x46511,x46512)+~E(f328(a118,x46511),f328(a118,x46512))
% 81.29/80.91 [4652]E(x46521,x46522)+~E(f328(a112,x46521),f328(a112,x46522))
% 81.29/80.91 [4653]E(x46531,x46532)+~E(f328(a3,x46531),f328(a3,x46532))
% 81.29/80.91 [4655]E(x46551,x46552)+~E(f328(a19,x46551),f328(a19,x46552))
% 81.29/80.91 [4756]~P58(x47561)+E(f45(x47561,x47562,x47562),f2(x47561))
% 81.29/80.91 [4790]~P38(x47901,x47902)+P38(f878(x47901),f144(x47901,x47902))
% 81.29/80.91 [4791]~P38(x47911,x47912)+P38(f878(x47911),f145(x47911,x47912))
% 81.29/80.91 [4888]~P38(x48881,x48882)+P38(f885(x48881,a871),f321(x48881,x48882))
% 81.29/80.91 [4889]~P38(x48891,x48892)+P38(f885(x48891,a871),f319(x48891,x48892))
% 81.29/80.91 [5008]~P28(x50081)+P40(f299(a1,x50081,x50082))
% 81.29/80.91 [5108]~P38(x51081,x51082)+P57(x51081,f68(x51081,x51081,x51082))
% 81.29/80.91 [5613]~P80(x56131)+P21(x56131,x56131,f80(x56131),x56132)
% 81.29/80.91 [4603]~E(x46032,f119(x46031))+E(f328(f167(x46031),x46032),f119(x46031))
% 81.29/80.91 [4604]~E(x46042,f119(x46041))+E(f328(f168(x46041),x46042),f119(x46041))
% 81.29/80.91 [4659]E(x46591,f328(a110,x46592))+~E(f328(f106(a1),x46591),x46592)
% 81.29/80.91 [4662]E(x46621,f119(x46622))+~E(f328(f167(x46622),x46621),f119(x46622))
% 81.29/80.91 [4663]E(x46631,f119(x46632))+~E(f328(f168(x46632),x46631),f119(x46632))
% 81.29/80.91 [4680]~P96(x46801)+E(f328(f109(x46801),x46802),f328(f108(x46801),x46802))
% 81.29/80.91 [4687]~E(x46872,f196(x46871))+E(f235(x46871,x46872),f193(f885(x46871,a871)))
% 81.29/80.91 [4689]~P26(x46891)+P24(f328(f62(x46891),x46892))
% 81.29/80.91 [4696]E(x46961,f196(x46962))+E(f328(f236(x46962),f811(x46962,x46961)),x46961)
% 81.29/80.91 [4697]E(x46971,f196(x46972))+E(f328(f236(x46972),f334(x46972,x46971)),x46971)
% 81.29/80.91 [4699]~E(f582(x46992,x46991),f119(x46991))+E(f179(x46991,x46992),f119(f878(x46991)))
% 81.29/80.91 [4708]~E(x47082,f119(x47081))+E(f328(f171(x47081),x47082),f193(f885(x47081,a871)))
% 81.29/80.91 [4709]~E(x47092,f119(x47091))+E(f193(f885(x47091,a871)),f328(f171(x47091),x47092))
% 81.29/80.91 [4711]E(x47111,x47112)+~E(f328(f106(a1),x47111),f328(f106(a1),x47112))
% 81.29/80.91 [4714]E(f222(x47141,x47142),f2(a877))+P24(f328(f62(x47141),x47142))
% 81.29/80.91 [4734]~P111(x47341)+E(f83(x47341,f83(x47341,x47342)),f83(x47341,x47342))
% 81.29/80.91 [4747]~P112(x47471)+E(f328(f328(f258(x47471),x47472),f79(a877)),x47472)
% 81.29/80.91 [4748]~P83(x47481)+E(f328(f328(f258(x47481),x47482),f79(a877)),x47482)
% 81.29/80.91 [4750]E(x47501,x47502)+E(f275(x47501,x47502),f328(f328(f81(a105),x47502),f79(a105)))
% 81.29/80.91 [4753]E(f328(f38(x47531),x47532),f2(a877))+P24(f328(f62(x47531),x47532))
% 81.29/80.91 [4757]~E(f151(x47571,x47572),x47572)+P24(f328(f136(x47571),x47572))
% 81.29/80.91 [4760]~P73(x47601)+E(f328(f328(f22(x47601),x47602),f2(x47601)),x47602)
% 81.29/80.91 [4761]~P79(x47611)+E(f328(f328(f116(x47611),x47612),f193(x47611)),x47612)
% 81.29/80.91 [4762]~P74(x47621)+E(f328(f328(f81(x47621),x47622),f2(x47621)),x47622)
% 81.29/80.91 [4763]~P82(x47631)+E(f328(f328(f81(x47631),x47632),f2(x47631)),x47632)
% 81.29/80.91 [4764]~P112(x47641)+E(f328(f328(f81(x47641),x47642),f2(x47641)),x47642)
% 81.29/80.91 [4765]~P101(x47651)+E(f328(f328(f107(x47651),x47652),f252(x47651)),x47652)
% 81.29/80.91 [4766]~P112(x47661)+E(f328(f328(f82(x47661),x47662),f79(x47661)),x47662)
% 81.29/80.91 [4767]~P75(x47671)+E(f328(f328(f82(x47671),x47672),f79(x47671)),x47672)
% 81.29/80.91 [4768]~P83(x47681)+E(f328(f328(f82(x47681),x47682),f79(x47681)),x47682)
% 81.29/80.91 [4769]~P120(x47691)+E(f328(f328(f286(x47691),x47692),f79(x47691)),x47692)
% 81.29/80.91 [4770]~P58(x47701)+E(f328(f328(f39(x47701),x47702),f79(x47701)),x47702)
% 81.29/80.91 [4771]~P112(x47711)+E(f328(f328(f258(x47711),x47712),f2(a877)),f79(x47711))
% 81.29/80.91 [4772]~P116(x47721)+E(f328(f328(f258(x47721),x47722),f2(a877)),f79(x47721))
% 81.29/80.91 [4773]~E(x47732,f193(f885(x47731,a871)))+E(f328(f38(x47731),x47732),f2(a877))
% 81.29/80.91 [4784]~P58(x47841)+E(f45(x47841,x47842,f2(x47841)),x47842)
% 81.29/80.91 [4792]~P101(x47921)+E(f328(f328(f116(x47921),x47922),f252(x47921)),f252(x47921))
% 81.29/80.91 [4793]~P79(x47931)+E(f328(f328(f107(x47931),x47932),f193(x47931)),f193(x47931))
% 81.29/80.91 [4794]~P112(x47941)+E(f328(f328(f82(x47941),x47942),f2(x47941)),f2(x47941))
% 81.29/80.91 [4795]~P126(x47951)+E(f328(f328(f82(x47951),x47952),f2(x47951)),f2(x47951))
% 81.29/80.91 [4796]~P121(x47961)+E(f328(f328(f286(x47961),x47962),f2(x47961)),f2(x47961))
% 81.29/80.91 [4797]~P58(x47971)+E(f328(f328(f39(x47971),x47972),f2(x47971)),f2(x47971))
% 81.29/80.91 [4798]E(x47981,f196(x47982))+~E(f235(x47982,x47981),f193(f885(x47982,a871)))
% 81.29/80.91 [4801]~P58(x48011)+E(f45(x48011,x48012,f79(x48011)),f2(x48011))
% 81.29/80.91 [4802]~P58(x48021)+E(f45(x48021,f2(x48021),x48022),f2(x48021))
% 81.29/80.91 [4831]E(x48311,f2(a877))+E(f55(x48312,x48311,f119(x48312)),f119(f878(x48312)))
% 81.29/80.91 [4855]P38(x48551,x48552)+~E(f718(x48552,x48551),f193(f885(x48551,a871)))
% 81.29/80.91 [4856]E(x48561,f119(x48562))+~E(f328(f171(x48562),x48561),f193(f885(x48562,a871)))
% 81.29/80.91 [4857]E(x48571,f119(x48572))+~E(f193(f885(x48572,a871)),f328(f171(x48572),x48571))
% 81.29/80.91 [4860]~E(x48601,x48602)+P24(f328(f328(a325,x48601),x48602))
% 81.29/80.91 [4870]P24(x48701)+P24(f328(f328(a331,x48701),x48702))
% 81.29/80.91 [4871]E(x48711,f119(x48712))+E(f328(f328(f164(x48712),x48711),f2(a877)),f328(f140(x48712),x48711))
% 81.29/80.91 [4874]E(f151(x48741,x48742),x48742)+~P24(f328(f136(x48741),x48742))
% 81.29/80.91 [4879]~P24(x48792)+P24(f328(f328(a331,x48791),x48792))
% 81.29/80.91 [4880]~P24(x48802)+P24(f328(f328(a327,x48801),x48802))
% 81.29/80.91 [4881]~P24(x48811)+P24(f328(f328(a327,x48811),x48812))
% 81.29/80.91 [4891]~E(x48912,f193(f885(x48911,a871)))+P24(f328(f62(x48911),x48912))
% 81.29/80.91 [4892]~E(f531(x48922,x48921),f580(x48922,x48921))+P24(f328(f136(x48921),x48922))
% 81.29/80.91 [4900]E(f328(f249(x49001),x49002),f193(f885(x49001,a871)))+P24(f328(x49002,f532(x49002)))
% 81.29/80.91 [4901]E(f193(f885(x49011,a871)),f328(f249(x49011),x49012))+P24(f328(x49012,f533(x49012)))
% 81.29/80.91 [4965]~P111(x49651)+E(f328(f328(f82(x49651),x49652),f83(x49651,x49652)),f328(f76(x49651),x49652))
% 81.29/80.91 [4976]~E(x49761,f2(a1))+E(f46(x49761,x49762),f328(f328(f257(a1,a1),f2(a1)),f2(a1)))
% 81.29/80.91 [5007]~P55(x50071,x50072)+P55(x50071,f328(f283(x50071,x50071),x50072))
% 81.29/80.91 [5025]~E(f328(a28,x50251),f328(f236(a873),x50252))+P24(f328(a25,f328(a26,x50251)))
% 81.29/80.91 [5030]E(x50301,x50302)+~P24(f328(f328(a325,x50301),x50302))
% 81.29/80.91 [5034]~P24(f328(a25,x50342))+P24(f328(a25,f33(x50341,x50342)))
% 81.29/80.91 [5043]P24(x50431)+~P24(f328(f328(a326,x50432),x50431))
% 81.29/80.91 [5044]P24(x50441)+~P24(f328(f328(a326,x50441),x50442))
% 81.29/80.91 [5048]~P115(x50481)+P24(f328(f328(f244(x50481),x50482),f252(x50481)))
% 81.29/80.91 [5052]E(x50521,x50522)+~E(f328(x50521,f406(x50522,x50521)),f328(x50522,f406(x50522,x50521)))
% 81.29/80.91 [5081]E(x50811,f2(a877))+E(f224(x50811,f45(a877,x50812,x50811)),f224(x50812,x50811))
% 81.29/80.91 [5086]~P106(x50861)+P29(x50861,f328(f328(f150(x50861),x50862),f119(x50861)))
% 81.29/80.91 [5088]E(x50881,f2(a1))+P24(f328(f49(x50882,x50881),f46(x50882,x50881)))
% 81.29/80.91 [5106]~E(x51061,x51062)+P24(f328(f328(f245(a877),x51061),f328(a118,x51062)))
% 81.29/80.91 [5116]~E(x51161,f2(a877))+P24(f328(f328(f245(a877),x51161),f328(a118,x51162)))
% 81.29/80.91 [5126]P24(f328(x51261,x51262))+P24(f328(f328(f244(a1),f2(a1)),f347(x51261)))
% 81.29/80.91 [5163]P24(f328(a25,x51631))+~P24(f328(a25,f33(x51632,x51631)))
% 81.29/80.91 [5165]P24(f328(a25,x51651))+~P24(f328(a25,f34(x51652,x51651)))
% 81.29/80.91 [5167]P24(f328(a25,x51671))+~P24(f328(a25,f34(x51671,x51672)))
% 81.29/80.91 [5199]P55(x51991,x51992)+~P55(x51991,f328(f283(x51991,x51991),x51992))
% 81.29/80.91 [5202]~E(f45(a877,x52022,x52021),f2(a877))+E(f328(f328(f82(a877),x52021),f364(x52021,x52022)),x52022)
% 81.29/80.91 [5203]~E(f45(a1,x52032,x52031),f2(a1))+E(f328(f328(f82(a1),x52031),f348(x52031,x52032)),x52032)
% 81.29/80.91 [5229]~P24(f328(x52291,x52292))+P24(f328(f328(f244(a1),f2(a1)),f346(x52291)))
% 81.29/80.91 [5241]E(f328(f328(f22(a877),f328(a110,x52411)),f328(a110,x52412)),f328(a110,x52411))+~P24(f328(a199,x52412))
% 81.29/80.91 [5273]E(f276(x52731,x52732),f79(a105))+~P24(f328(f328(f244(a105),x52731),f79(a105)))
% 81.29/80.91 [5368]E(f328(f328(f164(x53681),x53682),f531(x53682,x53681)),f328(f328(f164(x53681),x53682),f580(x53682,x53681)))+P24(f328(f136(x53681),x53682))
% 81.29/80.91 [5413]~P24(f328(x54131,f91(x54132,x54131)))+P24(f328(x54131,f584(x54132,x54131)))
% 81.29/80.91 [5476]P57(x54761,x54762)+~P24(f328(f316(x54761,x54762),f699(x54762,x54761)))
% 81.29/80.91 [5620]~E(f328(a118,f45(a877,x56201,x56202)),x56202)+E(f45(a877,f328(a118,x56201),x56202),f2(a877))
% 81.29/80.91 [5677]P38(x56771,x56772)+P24(f328(f328(f330(x56771),f765(x56772,x56771)),f766(x56772,x56771)))
% 81.29/80.91 [5684]~P96(x56841)+P24(f328(f328(f330(x56841),f328(f109(x56841),x56842)),f115(x56841)))
% 81.29/80.91 [5685]~P137(x56851)+P24(f328(f328(f330(x56851),f328(f106(x56851),x56852)),f115(x56851)))
% 81.29/80.91 [5686]~P141(x56861)+P24(f328(f328(f330(x56861),f328(f106(x56861),x56862)),f191(x56861)))
% 81.29/80.91 [5687]~P137(x56871)+P24(f328(f328(f330(x56871),f328(f108(x56871),x56872)),f115(x56871)))
% 81.29/80.91 [5831]E(f328(a118,f45(a877,x58311,x58312)),x58312)+E(f45(a877,f328(a118,x58311),x58312),f328(a118,f45(a877,x58311,x58312)))
% 81.29/80.91 [6250]P38(x62501,x62502)+~P24(f328(f328(f330(x62501),f671(x62502,x62501)),f317(x62501,x62502)))
% 81.29/80.91 [6285]~P110(x62851)+~P24(f328(f328(f245(x62851),f328(f106(x62851),x62852)),f2(x62851)))
% 81.29/80.91 [6286]~P87(x62861)+~P24(f328(f328(f245(x62861),f328(f76(x62861),x62862)),f2(x62861)))
% 81.29/80.91 [6375]P24(f328(f328(f245(a1),x63751),f45(a1,x63752,x63751)))+~P24(f328(f328(f245(a1),x63751),f2(a1)))
% 81.29/80.91 [6474]E(f328(f328(f306(a877),f328(a118,x64741)),f299(a877,x64742,x64741)),f299(a877,x64742,f328(a118,x64741)))+~P24(f328(f328(f244(a877),x64742),f328(a118,x64741)))
% 81.29/80.91 [6562]~P106(x65621)+P29(x65621,f149(x65621,x65621,f5(x65621),x65622))
% 81.29/80.91 [6693]E(f328(f167(x66931),x66932),x66932)+~P24(f328(f328(f244(a877),f328(f194(f878(x66931)),x66932)),f79(a877)))
% 81.29/80.91 [6713]~P87(x67131)+P24(f328(f328(f244(x67131),f328(f80(x67131),f328(f76(x67131),x67132))),f2(x67131)))
% 81.29/80.91 [6746]~P38(x67461,x67462)+P38(x67461,f328(f328(f285(x67461,x67461,x67461),x67462),f304(x67461,x67462)))
% 81.29/80.91 [6965]~P24(f328(f328(f245(a1),x69652),f2(a1)))+P24(f328(f328(f244(a1),f45(a1,x69651,x69652)),f2(a1)))
% 81.29/80.91 [7361]~P141(x73611)+E(f195(x73611,f328(f328(f7(x73611,x73611,x73611),f81(x73611)),f79(x73611)),x73612,f2(x73611)),f328(f106(x73611),x73612))
% 81.29/80.91 [7389]~P124(x73891)+~P24(f328(f328(f245(x73891),f328(f328(f82(x73891),x73892),x73892)),f2(x73891)))
% 81.29/80.91 [10013]~P111(x100131)+~P24(f328(f328(f245(x100131),f328(f328(f258(x100131),x100132),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f2(x100131)))
% 81.29/80.91 [4660]~E(x46602,f119(x46601))+E(f328(f194(f878(x46601)),x46602),f2(a877))
% 81.29/80.91 [4700]~E(x47001,f2(a877))+E(f328(f328(f81(a877),x47001),x47002),x47002)
% 81.29/80.91 [4701]~E(x47012,f2(a877))+E(f328(f328(f82(a877),x47011),x47012),f2(a877))
% 81.29/80.91 [4703]~E(x47031,f2(a877))+E(f328(f328(f82(a877),x47031),x47032),f2(a877))
% 81.29/80.91 [4704]~E(x47042,f2(a1))+E(f328(f328(f39(a1),x47041),x47042),f2(a1))
% 81.29/80.91 [4705]~E(x47052,f2(a877))+E(f328(f328(f258(a877),x47051),x47052),f79(a877))
% 81.29/80.91 [4715]E(x47151,f119(x47152))+~E(f328(f194(f878(x47152)),x47151),f2(a877))
% 81.29/80.91 [4717]~P65(x47171)+E(f328(f328(f116(x47171),x47172),x47172),x47172)
% 81.29/80.91 [4718]~P78(x47181)+E(f328(f328(f116(x47181),x47182),x47182),x47182)
% 81.29/80.91 [4719]~P78(x47191)+E(f328(f328(f107(x47191),x47192),x47192),x47192)
% 81.29/80.91 [4721]~P102(x47211)+E(f328(f328(f107(x47211),x47212),x47212),x47212)
% 81.29/80.91 [4723]~P98(x47231)+E(f328(f328(f82(x47231),x47232),x47232),x47232)
% 81.29/80.91 [4725]~P106(x47251)+E(f328(f328(f242(x47251),x47252),x47252),x47252)
% 81.29/80.91 [4727]~P106(x47271)+E(f328(f328(f243(x47271),x47272),x47272),x47272)
% 81.29/80.91 [4746]~P73(x47461)+E(f328(f328(f22(x47461),x47462),x47462),f2(x47461))
% 81.29/80.91 [4758]~P73(x47581)+E(f328(f80(x47581),f328(f80(x47581),x47582)),x47582)
% 81.29/80.91 [4759]~P97(x47591)+E(f328(f80(x47591),f328(f80(x47591),x47592)),x47592)
% 81.29/80.91 [4776]~E(x47762,f2(a877))+E(f328(f328(f258(a877),x47761),x47762),f328(a118,f2(a877)))
% 81.29/80.91 [4810]~P79(x48101)+E(f328(f328(f116(x48101),f193(x48101)),x48102),x48102)
% 81.29/80.91 [4811]~P74(x48111)+E(f328(f328(f81(x48111),f2(x48111)),x48112),x48112)
% 81.29/80.91 [4812]~P82(x48121)+E(f328(f328(f81(x48121),f2(x48121)),x48122),x48122)
% 81.29/80.91 [4813]~P112(x48131)+E(f328(f328(f81(x48131),f2(x48131)),x48132),x48132)
% 81.29/80.91 [4814]~P101(x48141)+E(f328(f328(f107(x48141),f252(x48141)),x48142),x48142)
% 81.29/80.91 [4815]~P112(x48151)+E(f328(f328(f82(x48151),f79(x48151)),x48152),x48152)
% 81.29/80.91 [4816]~P75(x48161)+E(f328(f328(f82(x48161),f79(x48161)),x48162),x48162)
% 81.29/80.91 [4817]~P83(x48171)+E(f328(f328(f82(x48171),f79(x48171)),x48172),x48172)
% 81.29/80.91 [4836]~P101(x48361)+E(f328(f328(f116(x48361),f252(x48361)),x48362),f252(x48361))
% 81.29/80.91 [4837]~P79(x48371)+E(f328(f328(f107(x48371),f193(x48371)),x48372),f193(x48371))
% 81.29/80.91 [4838]~P112(x48381)+E(f328(f328(f82(x48381),f2(x48381)),x48382),f2(x48381))
% 81.29/80.91 [4839]~P126(x48391)+E(f328(f328(f82(x48391),f2(x48391)),x48392),f2(x48391))
% 81.29/80.91 [4840]~P120(x48401)+E(f328(f328(f286(x48401),f2(x48401)),x48402),f2(x48401))
% 81.29/80.91 [4841]~P58(x48411)+E(f328(f328(f39(x48411),f2(x48411)),x48412),f2(x48411))
% 81.29/80.91 [4842]~P83(x48421)+E(f328(f328(f258(x48421),f79(x48421)),x48422),f79(x48421))
% 81.29/80.91 [4850]E(x48501,f119(x48502))+E(f143(x48502,f328(f168(x48502),x48501)),f328(f140(x48502),x48501))
% 81.29/80.91 [4851]E(x48511,f119(x48512))+E(f328(f140(x48512),f328(f168(x48512),x48511)),f143(x48512,x48511))
% 81.29/80.91 [4852]E(x48521,f2(a877))+~E(f328(f328(f81(a877),x48522),x48521),x48522)
% 81.29/80.91 [4858]~P96(x48581)+E(f328(f108(x48581),f328(f109(a1),x48582)),f328(f109(x48581),x48582))
% 81.29/80.91 [4859]~P137(x48591)+E(f328(f108(x48591),f328(f106(a1),x48592)),f328(f106(x48591),x48592))
% 81.29/80.91 [4866]E(x48661,f79(a877))+~E(f328(f328(f82(a877),x48662),x48661),f79(a877))
% 81.29/80.91 [4867]E(x48671,f79(a877))+~E(f328(f328(f82(a877),x48671),x48672),f79(a877))
% 81.29/80.91 [4868]E(x48681,f2(a877))+~E(f328(f328(f81(a877),x48682),x48681),f2(a877))
% 81.29/80.91 [4869]E(x48691,f2(a877))+~E(f328(f328(f81(a877),x48691),x48692),f2(a877))
% 81.29/80.91 [4884]~P111(x48841)+E(f328(f76(x48841),f328(f106(x48841),x48842)),f328(f106(x48841),x48842))
% 81.29/80.91 [4885]~P87(x48851)+E(f328(f76(x48851),f328(f76(x48851),x48852)),f328(f76(x48851),x48852))
% 81.29/80.91 [4886]~P87(x48861)+E(f328(f76(x48861),f328(f80(x48861),x48862)),f328(f76(x48861),x48862))
% 81.29/80.91 [4887]~P74(x48871)+E(f328(f165(x48871),f328(f168(x48871),x48872)),f328(f165(x48871),x48872))
% 81.29/80.91 [4893]~E(x48931,f328(a118,f2(a877)))+E(f328(f328(f258(a877),x48931),x48932),f328(a118,f2(a877)))
% 81.29/80.91 [4903]~P73(x49031)+E(f328(f328(f22(x49031),f2(x49031)),x49032),f328(f80(x49031),x49032))
% 81.29/80.91 [4904]~E(x49042,f2(a877))+E(f138(a877,f328(f298(a877,x49041),x49042)),f119(a877))
% 81.29/80.91 [4913]~P96(x49131)+E(f328(f328(f81(x49131),x49132),f328(f109(x49131),a84)),x49132)
% 81.29/80.91 [4914]E(x49141,f2(a1))+E(f47(f328(f76(a1),x49142),f328(f76(a1),x49141)),f53(x49142,x49141))
% 81.29/80.91 [4928]~E(x49281,x49282)+P24(f328(f328(f244(a877),x49281),x49282))
% 81.29/80.91 [4935]~E(x49351,f2(a105))+E(f328(f328(f81(a877),f328(a19,x49351)),x49352),x49352)
% 81.29/80.91 [4945]~P28(x49451)+P28(f328(f328(f258(a1),x49451),x49452))
% 81.29/80.91 [4946]~P97(x49461)+E(f328(f328(f116(x49461),x49462),f328(f80(x49461),x49462)),f252(x49461))
% 81.29/80.91 [4947]~P73(x49471)+E(f328(f328(f81(x49471),x49472),f328(f80(x49471),x49472)),f2(x49471))
% 81.29/80.91 [4948]~P97(x49481)+E(f328(f328(f107(x49481),x49482),f328(f80(x49481),x49482)),f193(x49481))
% 81.29/80.91 [4973]E(x49731,f2(a877))+~E(f328(f80(a1),f328(f106(a1),x49732)),f328(f106(a1),x49731))
% 81.29/80.91 [4974]E(x49741,f2(a877))+~E(f328(f80(a1),f328(f106(a1),x49741)),f328(f106(a1),x49742))
% 81.29/80.91 [4984]E(f201(x49841,x49842),f2(a1))+P24(f328(f328(f244(a1),x49842),x49841))
% 81.29/80.91 [4985]E(f178(x49851,x49852),f119(a1))+P24(f328(f328(f244(a1),x49851),x49852))
% 81.29/80.91 [4998]E(x49981,f328(a118,f2(a877)))+~E(f328(f328(f82(a877),x49982),x49981),f328(a118,f2(a877)))
% 81.29/80.91 [4999]E(x49991,f328(a118,f2(a877)))+~E(f328(f328(f82(a877),x49991),x49992),f328(a118,f2(a877)))
% 81.29/80.91 [5000]~P105(x50001)+P24(f328(f328(f244(x50001),x50002),x50002))
% 81.29/80.91 [5001]~P95(x50011)+P24(f328(f328(f92(x50011),x50012),x50012))
% 81.29/80.91 [5004]~P96(x50041)+E(f328(f328(f82(x50041),x50042),f328(f109(x50041),a103)),f328(f80(x50041),x50042))
% 81.29/80.91 [5022]~P96(x50221)+E(f328(f80(x50221),f328(f109(x50221),x50222)),f328(f109(x50221),f328(f80(a1),x50222)))
% 81.29/80.91 [5023]~P137(x50231)+E(f328(f80(x50231),f328(f108(x50231),x50232)),f328(f108(x50231),f328(f80(a1),x50232)))
% 81.29/80.91 [5053]~E(x50531,f328(a118,x50532))+P24(f328(f328(f245(a877),f2(a877)),x50531))
% 81.29/80.91 [5070]~P106(x50701)+E(f328(f80(f885(x50701,a871)),f328(f297(x50701),x50702)),f328(f300(x50701),x50702))
% 81.29/80.91 [5071]~P106(x50711)+E(f328(f80(f885(x50711,a871)),f328(f300(x50711),x50712)),f328(f297(x50711),x50712))
% 81.29/80.91 [5072]~P106(x50721)+E(f328(f80(f885(x50721,a871)),f328(f250(x50721),x50722)),f328(f251(x50721),x50722))
% 81.29/80.91 [5073]~P106(x50731)+E(f328(f80(f885(x50731,a871)),f328(f251(x50731),x50732)),f328(f250(x50731),x50732))
% 81.29/80.91 [5080]~E(f328(f106(a1),x50802),x50801)+P24(f328(f328(f244(a1),f2(a1)),x50801))
% 81.29/80.91 [5087]~E(x50872,f2(a1))+E(f53(x50871,x50872),f328(f328(f257(a1,a1),f2(a1)),f328(f76(a1),x50871)))
% 81.29/80.91 [5089]~P25(x50891)+P24(f328(f328(f244(x50891),f193(x50891)),x50892))
% 81.29/80.91 [5121]E(x51211,x51212)+~E(f328(f328(f81(a1),x51211),x51211),f328(f328(f81(a1),x51212),x51212))
% 81.29/80.91 [5125]~P24(f328(x51251,x51252))+P24(f328(x51251,f328(a110,f346(x51251))))
% 81.29/80.91 [5151]~P111(x51511)+E(f328(f328(f82(x51511),f83(x51511,x51512)),f328(f76(x51511),x51512)),x51512)
% 81.29/80.91 [5152]E(x51521,x51522)+~P24(f328(f328(f200(a24),x51521),x51522))
% 81.29/80.91 [5161]~E(x51612,f2(a877))+E(f86(f884(a877,a877),f48(x51611,x51612)),f328(f328(f257(a877,a877),f2(a877)),x51611))
% 81.29/80.91 [5172]~E(x51721,x51722)+~P24(f328(f328(f245(a877),x51721),x51722))
% 81.29/80.91 [5173]~E(x51731,x51732)+~P24(f328(f328(f245(a1),x51731),x51732))
% 81.29/80.91 [5176]~P141(x51761)+E(f328(f328(f81(x51761),f79(x51761)),f328(f106(x51761),x51762)),f328(f106(x51761),f328(a118,x51762)))
% 81.29/80.91 [5180]~E(x51801,f2(a877))+~P24(f328(f328(f245(a877),x51802),x51801))
% 81.29/80.91 [5196]E(f151(x51961,x51962),x51962)+~E(f328(f194(f878(x51961)),f151(x51961,x51962)),f328(f194(f878(x51961)),x51962))
% 81.29/80.91 [5197]E(f328(f38(x51971),f328(f171(x51971),x51972)),f328(f194(f878(x51971)),x51972))+~P24(f328(f136(x51971),x51972))
% 81.29/80.91 [5207]~P24(f328(x52071,f851(x52071)))+P24(f328(x52071,f328(f106(a1),x52072)))
% 81.29/80.91 [5218]E(f276(x52181,x52182),f79(a105))+~P24(f328(f328(f245(a105),x52182),x52181))
% 81.29/80.91 [5219]E(f178(x52191,x52192),f119(a1))+~P24(f328(f328(f245(a1),x52192),x52191))
% 81.29/80.91 [5222]~P108(x52221)+E(f299(x52221,x52222,x52222),f328(f328(f306(x52221),x52222),f193(f885(x52221,a871))))
% 81.29/80.91 [5244]~E(f328(f328(f22(a877),x52441),x52442),f2(a877))+P24(f328(f328(f244(a877),x52441),x52442))
% 81.29/80.91 [5245]~E(f328(f328(f22(a1),x52451),x52452),f2(a1))+P24(f328(f328(f92(a1),x52451),x52452))
% 81.29/80.91 [5270]~E(x52702,f2(a877))+E(f55(x52701,x52702,f119(x52701)),f328(f328(f150(f878(x52701)),f119(x52701)),f119(f878(x52701))))
% 81.29/80.91 [5274]~P105(x52741)+~P24(f328(f328(f245(x52741),x52742),x52742))
% 81.29/80.91 [5277]~E(f45(a1,x52771,x52772),f2(a1))+E(f45(a1,x52771,f328(f80(a1),x52772)),f2(a1))
% 81.29/80.91 [5279]~E(f45(a1,x52791,x52792),f2(a1))+E(f45(a1,f328(f80(a1),x52791),x52792),f2(a1))
% 81.29/80.91 [5287]E(f328(f298(a877,x52871),f328(a118,x52872)),f193(f885(a877,a871)))+P24(f328(f328(f244(a877),x52871),x52872))
% 81.29/80.91 [5307]E(f138(a877,f328(f298(a877,x53071),x53072)),f119(a877))+P24(f328(f328(f245(a877),x53071),x53072))
% 81.29/80.91 [5312]~E(f328(f38(x53121),f328(f171(x53121),x53122)),f328(f194(f878(x53121)),x53122))+P24(f328(f136(x53121),x53122))
% 81.29/80.91 [5317]~P24(f328(f136(x53171),x53172))+P24(f328(f136(x53171),f328(f167(x53171),x53172)))
% 81.29/80.91 [5318]~P24(f328(f136(x53181),x53182))+P24(f328(f136(x53181),f328(f170(x53181),x53182)))
% 81.29/80.91 [5319]~P24(f328(f136(x53191),x53192))+P24(f328(f136(x53191),f328(f168(x53191),x53192)))
% 81.29/80.91 [5326]P24(f328(x53261,x53262))+~P24(f328(x53261,f328(a110,f347(x53261))))
% 81.29/80.91 [5327]P24(f328(f328(f244(a877),x53272),x53271))+P24(f328(f328(f244(a877),x53271),x53272))
% 81.29/80.91 [5328]P24(f328(f328(f244(a1),x53282),x53281))+P24(f328(f328(f244(a1),x53281),x53282))
% 81.29/80.91 [5331]~P87(x53311)+P24(f328(f328(f244(x53311),x53312),f328(f76(x53311),x53312)))
% 81.29/80.91 [5334]P24(f328(x53341,f857(x53341)))+~P24(f328(x53341,f328(f106(a1),x53342)))
% 81.29/80.91 [5360]E(f328(f328(f22(a877),x53601),x53602),f2(a877))+~P24(f328(f328(f244(a877),x53601),x53602))
% 81.29/80.91 [5361]E(f328(f328(f22(a1),x53611),x53612),f2(a1))+~P24(f328(f328(f92(a1),x53611),x53612))
% 81.29/80.91 [5362]E(f328(f328(f39(a877),x53621),x53622),f2(a877))+~P24(f328(f328(f245(a877),x53621),x53622))
% 81.29/80.91 [5380]E(f45(a877,x53801,x53802),x53801)+~P24(f328(f328(f245(a877),x53801),x53802))
% 81.29/80.91 [5389]E(f45(a1,x53891,f328(f80(a1),x53892)),f287(x53891,x53892))+P24(f328(f328(f244(a1),f2(a1)),x53892))
% 81.29/80.91 [5401]E(f328(f328(f22(a1),x54011),x54012),f201(x54011,x54012))+~P24(f328(f328(f244(a1),x54012),x54011))
% 81.29/80.91 [5420]P24(f328(f328(f244(a1),f2(a1)),f851(x54201)))+P24(f328(x54201,f328(f106(a1),x54202)))
% 81.29/80.91 [5432]~P60(x54321)+P24(f328(f328(f330(x54321),x54322),f328(f171(x54321),f56(x54321))))
% 81.29/80.91 [5434]~P110(x54341)+P24(f328(f328(f244(x54341),f2(x54341)),f328(f106(x54341),x54342)))
% 81.29/80.91 [5435]~P87(x54351)+P24(f328(f328(f244(x54351),f2(x54351)),f328(f76(x54351),x54352)))
% 81.29/80.91 [5462]E(f328(f328(f81(a877),x54621),f720(x54622,x54621)),x54622)+~P24(f328(f328(f244(a877),x54621),x54622))
% 81.29/80.91 [5477]E(f299(a1,x54771,x54772),f193(f885(a1,a871)))+~P24(f328(f328(f245(a1),x54772),x54771))
% 81.29/80.91 [5479]~P111(x54791)+E(f328(f328(f82(x54791),f328(f76(x54791),x54792)),f328(f76(x54791),x54792)),f328(f328(f82(x54791),x54792),x54792))
% 81.29/80.91 [5486]E(f138(a877,f328(f298(a877,x54861),f328(a118,x54862))),f119(a877))+P24(f328(f328(f244(a877),x54861),x54862))
% 81.29/80.91 [5490]E(f328(f328(f39(a1),x54901),x54902),f288(x54901,x54902))+~P24(f328(f328(f244(a1),f2(a1)),x54902))
% 81.29/80.91 [5510]P24(f328(f136(x55101),x55102))+~P24(f328(f136(x55101),f328(f167(x55101),x55102)))
% 81.29/80.91 [5511]P24(f328(f136(x55111),x55112))+~P24(f328(f136(x55111),f328(f168(x55111),x55112)))
% 81.29/80.91 [5532]P24(f328(f62(a877),x55321))+P24(f328(f328(f330(a877),f401(x55321,x55322)),x55321))
% 81.29/80.91 [5533]P24(f328(f62(a877),x55331))+P24(f328(f328(f330(a877),f407(x55331,x55332)),x55331))
% 81.29/80.91 [5534]P24(f328(f328(f245(a877),x55342),f328(a118,x55341)))+P24(f328(f328(f245(a877),x55341),x55342))
% 81.29/80.91 [5535]E(f45(a1,x55351,x55352),f287(x55351,x55352))+~P24(f328(f328(f244(a1),f2(a1)),x55352))
% 81.29/80.91 [5538]E(f138(a877,f328(f298(a877,x55381),x55382)),f119(a877))+~P24(f328(f328(f244(a877),x55382),x55381))
% 81.29/80.91 [5539]~P80(x55391)+E(f328(f307(x55391,x55391,f80(x55391)),f328(f297(x55391),x55392)),f328(f251(x55391),f328(f80(x55391),x55392)))
% 81.29/80.91 [5540]~P80(x55401)+E(f328(f307(x55401,x55401,f80(x55401)),f328(f300(x55401),x55402)),f328(f250(x55401),f328(f80(x55401),x55402)))
% 81.29/80.91 [5541]~P80(x55411)+E(f328(f307(x55411,x55411,f80(x55411)),f328(f250(x55411),x55412)),f328(f300(x55411),f328(f80(x55411),x55412)))
% 81.29/80.91 [5542]~P80(x55421)+E(f328(f307(x55421,x55421,f80(x55421)),f328(f251(x55421),x55422)),f328(f297(x55421),f328(f80(x55421),x55422)))
% 81.29/80.91 [5553]E(x55531,f193(f885(x55532,a871)))+P24(f328(f328(f330(x55532),f445(x55531,x55532)),x55531))
% 81.29/80.91 [5554]E(x55541,f193(f885(x55542,a871)))+P24(f328(f328(f330(x55542),f446(x55541,x55542)),x55541))
% 81.29/80.91 [5565]~P24(f328(f328(f245(a877),x55651),x55652))+P24(f328(f328(f244(a877),x55651),x55652))
% 81.29/80.91 [5566]~P24(f328(f328(f245(a1),x55661),x55662))+P24(f328(f328(f244(a1),x55661),x55662))
% 81.29/80.91 [5582]E(f47(x55821,x55822),f328(f328(f257(a1,a1),f2(a1)),x55821))+~P24(f328(f328(f245(a1),x55821),x55822))
% 81.29/80.91 [5583]E(f223(f328(f80(a1),x55831),f328(f80(a1),x55832)),f223(x55831,x55832))+~P24(f328(f328(f245(a1),x55832),f2(a1)))
% 81.29/80.91 [5594]E(x55941,x55942)+~E(f328(a3,f328(a118,f328(a19,x55941))),f328(a3,f328(a118,f328(a19,x55942))))
% 81.29/80.91 [5599]E(f47(x55991,x55992),f328(f328(f257(a1,a1),f2(a1)),x55991))+~P24(f328(f328(f244(a1),x55992),f2(a1)))
% 81.29/80.91 [5626]E(f45(a877,f328(f109(a877),x56261),f328(f109(a877),x56262)),f2(a877))+~P24(f328(a199,f328(f109(a1),x56261)))
% 81.29/80.91 [5641]P24(f328(f328(f244(a1),f2(a1)),f857(x56411)))+~P24(f328(x56411,f328(f106(a1),x56412)))
% 81.29/80.91 [5675]P40(f299(a1,x56751,x56752))+~P24(f328(f328(f244(a1),f2(a1)),x56751))
% 81.29/80.91 [5680]~P24(f328(f62(x56801),x56802))+P24(f328(f62(f885(x56801,a871)),f328(f305(x56801),x56802)))
% 81.29/80.91 [5693]E(f328(f328(f81(a1),x56931),f328(f106(a1),f860(x56932,x56931))),x56932)+~P24(f328(f328(f244(a1),x56931),x56932))
% 81.29/80.91 [5701]P24(f328(f328(f244(a877),x57011),x57012))+P24(f328(f328(f244(a877),f328(a118,x57012)),x57011))
% 81.29/80.91 [5745]E(f328(f328(f39(a877),f328(f109(a877),x57451)),f328(f109(a877),x57452)),f2(a877))+~P24(f328(a199,f328(f109(a1),x57451)))
% 81.29/80.91 [5746]E(f328(f328(f82(a877),f328(f109(a877),x57461)),f328(f109(a877),x57462)),f2(a877))+~P24(f328(f328(f245(a1),x57461),a84))
% 81.29/80.91 [5748]P24(f328(f328(f244(a877),x57481),f328(a118,x57482)))+~P24(f328(f328(f244(a877),x57481),x57482))
% 81.29/80.91 [5750]P24(f328(f328(f245(a877),x57501),f328(a118,x57502)))+~P24(f328(f328(f244(a877),x57501),x57502))
% 81.29/80.91 [5752]P24(f328(f328(f245(a877),x57521),f328(a118,x57522)))+~P24(f328(f328(f245(a877),x57521),x57522))
% 81.29/80.91 [5755]~E(x57551,x57552)+P24(f328(f328(f245(a1),x57551),f328(f328(f81(a1),x57552),f79(a1))))
% 81.29/80.91 [5758]E(f45(a1,x57581,x57582),f2(a1))+E(f328(f328(f22(a1),x57582),f45(a1,x57581,x57582)),f45(a1,f328(f80(a1),x57581),x57582))
% 81.29/80.91 [5767]E(x57671,f119(x57672))+P24(f328(f328(f330(x57672),f143(x57672,x57671)),f328(f171(x57672),x57671)))
% 81.29/80.91 [5779]E(f86(f884(a877,a877),f48(x57791,x57792)),f328(f328(f257(a877,a877),f2(a877)),x57791))+~P24(f328(f328(f245(a877),x57791),x57792))
% 81.29/80.91 [5812]E(f328(f328(f22(a877),f328(f109(a877),x58121)),f328(f109(a877),x58122)),f328(f109(a877),x58121))+~P24(f328(f328(f245(a1),x58122),a84))
% 81.29/80.91 [5813]E(f328(f328(f81(a877),f328(f109(a877),x58131)),f328(f109(a877),x58132)),f328(f109(a877),x58132))+~P24(f328(f328(f245(a1),x58131),a84))
% 81.29/80.91 [5818]E(f328(a118,f328(f328(f81(a877),x58181),f700(x58182,x58181))),x58182)+~P24(f328(f328(f245(a877),x58181),x58182))
% 81.29/80.91 [5841]P24(f328(x58411,x58412))+~P24(f328(x58411,f328(a90,f711(x58412,x58411))))
% 81.29/80.91 [5849]~P24(f328(f328(f245(a877),x58491),f328(a118,x58492)))+P24(f328(f328(f244(a877),x58491),x58492))
% 81.29/80.91 [5895]E(f328(f328(f306(a877),x58951),f328(f298(a877,x58952),x58951)),f328(f298(a877,x58952),f328(a118,x58951)))+~P24(f328(f328(f244(a877),x58952),x58951))
% 81.29/80.91 [5899]E(x58991,f119(x58992))+E(f328(f328(f127(x58992),f120(x58992,x58991)),f328(f328(f150(x58992),f143(x58992,x58991)),f119(x58992))),x58991)
% 81.29/80.91 [5913]P24(f328(f62(x59131),x59132))+~P24(f328(f328(f245(a877),f2(a877)),f328(f38(x59131),x59132)))
% 81.29/80.91 [5915]~E(x59151,f193(f885(x59152,a871)))+~P24(f328(f328(f245(a877),f2(a877)),f328(f38(x59152),x59151)))
% 81.29/80.91 [5927]~P24(f328(f328(f245(a877),x59271),x59272))+P24(f328(f328(f244(a877),f328(a118,x59271)),x59272))
% 81.29/80.91 [5935]~P106(x59351)+E(f149(x59351,x59351,f5(x59351),f151(x59351,x59352)),f138(x59351,f328(f171(x59351),x59352)))
% 81.29/80.91 [5938]E(x59381,f119(x59382))+P24(f328(f328(f330(x59382),f328(f140(x59382),x59381)),f328(f171(x59382),x59381)))
% 81.29/80.91 [5944]~P110(x59441)+P24(f328(f328(f245(x59441),x59442),f328(f328(f81(x59441),x59442),f79(x59441))))
% 81.29/80.91 [5946]~P87(x59461)+P24(f328(f328(f244(x59461),f328(f80(x59461),x59462)),f328(f76(x59461),x59462)))
% 81.29/80.91 [5979]P24(f328(f62(a877),x59791))+~P24(f328(f328(f244(a877),f401(x59791,x59792)),x59792))
% 81.29/80.91 [5980]P24(f328(f62(a877),x59801))+~P24(f328(f328(f245(a877),f407(x59801,x59802)),x59802))
% 81.29/80.91 [5984]~P24(f328(f62(f884(x59841,x59841)),x59842))+P24(f328(f62(x59841),f328(f281(x59841),x59842)))
% 81.29/80.91 [6039]~P24(f328(f328(f245(a877),x60392),f328(a118,x60391)))+~P24(f328(f328(f245(a877),x60391),x60392))
% 81.29/80.91 [6040]~P108(x60401)+E(f328(f328(f107(f885(x60401,a871)),f328(f297(x60401),x60402)),f328(f251(x60401),x60402)),f328(f328(f306(x60401),x60402),f193(f885(x60401,a871))))
% 81.29/80.91 [6053]P24(f328(f62(x60531),x60532))+~P24(f328(f62(f885(x60531,a871)),f328(f305(x60531),x60532)))
% 81.29/80.91 [6077]P24(f328(f328(f244(a877),f328(a118,x60771)),f328(a118,x60772)))+~P24(f328(f328(f244(a877),x60771),x60772))
% 81.29/80.91 [6078]P24(f328(f328(f244(a877),f328(a19,x60781)),f328(a19,x60782)))+~P24(f328(f328(f244(a105),x60781),x60782))
% 81.29/80.91 [6079]P24(f328(f328(f244(a105),f328(a3,x60791)),f328(a3,x60792)))+~P24(f328(f328(f244(a877),x60791),x60792))
% 81.29/80.91 [6081]P24(f328(f328(f245(a877),f328(a118,x60811)),f328(a118,x60812)))+~P24(f328(f328(f245(a877),x60811),x60812))
% 81.29/80.91 [6082]P24(f328(f328(f245(a877),f328(a19,x60821)),f328(a19,x60822)))+~P24(f328(f328(f245(a105),x60821),x60822))
% 81.29/80.91 [6083]P24(f328(f328(f245(a105),f328(a3,x60831)),f328(a3,x60832)))+~P24(f328(f328(f245(a877),x60831),x60832))
% 81.29/80.91 [6086]E(x60861,x60862)+~E(f328(f307(a877,a1,f106(a1)),x60861),f328(f307(a877,a1,f106(a1)),x60862))
% 81.29/80.91 [6102]P24(f328(f328(f244(a877),x61021),x61022))+~P24(f328(f328(f244(a877),f328(a118,x61021)),x61022))
% 81.29/80.91 [6105]P24(f328(f328(f245(a877),x61051),x61052))+~P24(f328(f328(f244(a877),f328(a118,x61051)),x61052))
% 81.29/80.91 [6106]P24(f328(f328(f245(a877),x61061),x61062))+~P24(f328(f328(f245(a877),f328(a118,x61061)),x61062))
% 81.29/80.91 [6121]E(f45(a1,x61211,x61212),f2(a1))+E(f328(f328(f22(a1),f45(a1,x61211,x61212)),x61212),f45(a1,x61211,f328(f80(a1),x61212)))
% 81.29/80.91 [6190]E(f328(f38(f885(x61901,a871)),f328(f305(x61901),x61902)),f328(f328(f258(a877),f328(a118,f328(a118,f2(a877)))),f328(f38(x61901),x61902)))+~P24(f328(f62(x61901),x61902))
% 81.29/80.91 [6193]E(x61931,f119(x61932))+E(f328(f328(f164(x61932),x61931),f328(f328(f22(a877),f328(f194(f878(x61932)),x61931)),f79(a877))),f143(x61932,x61931))
% 81.29/80.91 [6218]E(x62181,f119(x62182))+E(f328(f328(f127(x62182),f328(f170(x62182),x62181)),f328(f328(f150(x62182),f328(f140(x62182),x62181)),f119(x62182))),f328(f167(x62182),x62181))
% 81.29/80.91 [6247]~P24(f328(f62(x62471),f40(f885(x62471,a871),x62472)))+P24(f328(f62(f885(x62471,a871)),x62472))
% 81.29/80.91 [6270]P24(f328(f328(f244(a877),f328(f109(a877),x62701)),f328(f109(a877),x62702)))+~P24(f328(f328(f244(a1),x62701),a84))
% 81.29/80.91 [6287]~P24(f328(f328(f245(a1),x62871),x62872))+P24(f328(f328(f244(a1),x62871),f328(f328(f22(a1),x62872),f79(a1))))
% 81.29/80.91 [6288]~P24(f328(f328(f244(a1),x62881),x62882))+P24(f328(f328(f245(a1),x62881),f328(f328(f81(a1),x62882),f79(a1))))
% 81.29/80.91 [6289]~P24(f328(f328(f245(a1),x62891),x62892))+P24(f328(f328(f245(a1),x62891),f328(f328(f81(a1),x62892),f79(a1))))
% 81.29/80.91 [6291]~P24(f328(f328(f244(a1),x62911),x62912))+P24(f328(f328(f244(a877),f328(f109(a877),x62911)),f328(f109(a877),x62912)))
% 81.29/80.91 [6292]~P24(f328(f328(f244(a1),x62921),x62922))+P24(f328(f328(f244(a1),f328(f109(a1),x62921)),f328(f109(a1),x62922)))
% 81.29/80.91 [6294]~P24(f328(f328(f244(a877),x62941),x62942))+P24(f328(f328(f244(a1),f328(f106(a1),x62941)),f328(f106(a1),x62942)))
% 81.29/80.91 [6295]~P24(f328(f328(f245(a1),x62951),x62952))+P24(f328(f328(f245(a1),f328(f109(a1),x62951)),f328(f109(a1),x62952)))
% 81.29/80.91 [6297]~P24(f328(f328(f245(a877),x62971),x62972))+P24(f328(f328(f245(a1),f328(f106(a1),x62971)),f328(f106(a1),x62972)))
% 81.29/80.91 [6298]~P24(f328(f328(f92(a1),x62981),x62982))+P24(f328(f328(f92(a1),f328(f109(a1),x62981)),f328(f109(a1),x62982)))
% 81.29/80.91 [6316]~P24(f328(f328(f244(a877),x63161),x63162))+~P24(f328(f328(f244(a877),f328(a118,x63162)),x63161))
% 81.29/80.91 [6361]~P24(f328(f328(f244(a877),f328(a118,x63611)),f328(a118,x63612)))+P24(f328(f328(f244(a877),x63611),x63612))
% 81.29/80.91 [6362]~P24(f328(f328(f244(a105),f328(a3,x63621)),f328(a3,x63622)))+P24(f328(f328(f244(a877),x63621),x63622))
% 81.29/80.91 [6363]~P24(f328(f328(f244(a877),f328(a19,x63631)),f328(a19,x63632)))+P24(f328(f328(f244(a105),x63631),x63632))
% 81.29/80.91 [6365]~P24(f328(f328(f245(a877),f328(a118,x63651)),f328(a118,x63652)))+P24(f328(f328(f245(a877),x63651),x63652))
% 81.29/80.91 [6366]~P24(f328(f328(f245(a105),f328(a3,x63661)),f328(a3,x63662)))+P24(f328(f328(f245(a877),x63661),x63662))
% 81.29/80.91 [6367]~P24(f328(f328(f245(a877),f328(a110,x63671)),f328(a110,x63672)))+P24(f328(f328(f245(a1),x63671),x63672))
% 81.29/80.91 [6368]~P24(f328(f328(f245(a877),f328(a19,x63681)),f328(a19,x63682)))+P24(f328(f328(f245(a105),x63681),x63682))
% 81.29/80.91 [6408]~P24(f328(f328(f245(a877),f328(a110,x64082)),f328(a110,x64081)))+P24(f328(f328(f245(a1),f2(a1)),x64081))
% 81.29/80.91 [6439]P24(f328(f328(f244(a1),f2(a1)),f45(a1,x64391,x64392)))+~P24(f328(f328(f245(a1),f2(a1)),x64392))
% 81.29/80.91 [6598]P38(x65981,x65982)+~E(f328(f328(f285(x65981,x65981,x65981),x65982),x65982),f193(f885(f884(x65981,x65981),a871)))
% 81.29/80.91 [6610]~P38(x66101,x66102)+P38(x66101,f328(f328(f285(x66101,x66101,x66101),x66102),x66102))
% 81.29/80.91 [6622]P24(f328(f328(f244(a1),x66221),x66222))+~P24(f328(f328(f245(a1),x66221),f328(f328(f81(a1),x66222),f79(a1))))
% 81.29/80.91 [6623]P24(f328(f328(f245(a1),x66231),x66232))+~P24(f328(f328(f244(a1),x66231),f328(f328(f22(a1),x66232),f79(a1))))
% 81.29/80.91 [6626]P24(f328(f328(f244(a877),x66261),x66262))+~P24(f328(f328(f244(a1),f328(f106(a1),x66261)),f328(f106(a1),x66262)))
% 81.29/80.91 [6627]P24(f328(f328(f244(a1),x66271),x66272))+~P24(f328(f328(f244(a1),f328(f109(a1),x66271)),f328(f109(a1),x66272)))
% 81.29/80.91 [6629]P24(f328(f328(f245(a877),x66291),x66292))+~P24(f328(f328(f245(a1),f328(f106(a1),x66291)),f328(f106(a1),x66292)))
% 81.29/80.91 [6630]P24(f328(f328(f245(a1),x66301),x66302))+~P24(f328(f328(f245(a877),f328(f109(a877),x66301)),f328(f109(a877),x66302)))
% 81.29/80.91 [6631]P24(f328(f328(f245(a1),x66311),x66312))+~P24(f328(f328(f245(a1),f328(f109(a1),x66311)),f328(f109(a1),x66312)))
% 81.29/80.91 [6632]P24(f328(f328(f92(a1),x66321),x66322))+~P24(f328(f328(f92(a1),f328(f109(a1),x66321)),f328(f109(a1),x66322)))
% 81.29/80.91 [6726]~E(f648(x67262,x67261),f119(x67261))+E(f328(f141(f878(x67261),f878(x67261),f127(x67261),f119(x67261)),x67262),f119(x67261))
% 81.29/80.91 [6727]~E(f650(x67272,x67271),f119(x67271))+E(f328(f141(f878(x67271),f878(x67271),f127(x67271),f119(x67271)),x67272),f119(x67271))
% 81.29/80.91 [6734]~P27(x67341)+E(f328(f141(x67341,x67341,f116(x67341),f193(x67341)),x67342),f40(x67341,f328(f171(x67341),x67342)))
% 81.29/80.91 [6735]~P27(x67351)+E(f328(f141(x67351,x67351,f107(x67351),f252(x67351)),x67352),f41(x67351,f328(f171(x67351),x67352)))
% 81.29/80.91 [6747]E(x67471,f2(a105))+E(f328(f328(f81(a877),f328(a19,f328(f328(f22(a105),x67471),f79(a105)))),f328(a118,x67472)),f328(f328(f81(a877),f328(a19,x67471)),x67472))
% 81.29/80.91 [6797]P24(f328(f328(f245(a1),f328(f328(f22(a1),x67971),x67972)),f2(a1)))+~P24(f328(f328(f245(a1),x67971),x67972))
% 81.29/80.91 [6824]~P106(x68241)+E(f328(f328(f116(f885(x68241,a871)),f328(f328(f306(x68241),x68242),f193(f885(x68241,a871)))),f328(f300(x68241),x68242)),f328(f251(x68241),x68242))
% 81.29/80.91 [6896]~P57(x68961,x68962)+P38(x68961,f328(f249(f884(x68961,x68961)),f328(f267(x68961,x68961,a871),x68962)))
% 81.29/80.91 [6897]~P57(x68971,x68972)+P55(x68971,f328(f249(f884(x68971,x68971)),f328(f267(x68971,x68971,a871),x68972)))
% 81.29/80.91 [6898]E(x68981,f193(f885(x68982,a871)))+~P24(f328(f328(f244(f885(x68982,a871)),x68981),f193(f885(x68982,a871))))
% 81.29/80.91 [6981]~P24(f328(f328(f245(a877),f2(a877)),x69812))+P24(f328(f328(f244(a877),f45(a877,x69811,x69812)),x69812))
% 81.29/80.91 [6982]~P24(f328(f328(f244(a1),f2(a1)),x69821))+P24(f328(f328(f244(a1),f45(a1,x69821,x69822)),x69821))
% 81.29/80.91 [6983]~P24(f328(f328(f245(a877),f2(a877)),x69832))+P24(f328(f328(f245(a877),f45(a877,x69831,x69832)),x69832))
% 81.29/80.91 [6985]~P24(f328(f328(f245(a1),f2(a1)),x69852))+P24(f328(f328(f245(a1),f45(a1,x69851,x69852)),x69852))
% 81.29/80.91 [7063]~P108(x70631)+E(f328(f328(f22(f885(x70631,a871)),f328(f328(f306(x70631),x70632),f193(f885(x70631,a871)))),f328(f250(x70631),x70632)),f328(f328(f306(x70631),x70632),f193(f885(x70631,a871))))
% 81.29/80.91 [7136]~P50(x71361,x71362)+P48(x71361,f252(f885(x71361,a871)),f328(f249(f884(x71361,x71361)),f328(f267(x71361,x71361,a871),x71362)))
% 81.29/80.91 [7137]P24(f328(x71371,x71372))+P24(f328(f328(f330(f885(f884(a877,a877),a871)),f711(x71372,x71371)),a104))
% 81.29/80.91 [7182]E(f328(f328(f127(a877),f138(a877,f328(f298(a877,x71821),x71822))),f328(f328(f150(a877),x71822),f119(a877))),f138(a877,f328(f298(a877,x71821),f328(a118,x71822))))+~P24(f328(f328(f244(a877),x71821),x71822))
% 81.29/80.91 [7323]E(x73231,f2(a877))+~E(f328(f141(a877,a877,f81(a877),x73231),x73232),f2(a877))
% 81.29/80.91 [7351]~P24(f328(f328(f245(a1),f328(f328(f22(a1),x73511),x73512)),f2(a1)))+P24(f328(f328(f245(a1),x73511),x73512))
% 81.29/80.91 [7380]P38(x73801,x73802)+~P38(x73801,f328(f328(f285(x73801,x73801,x73801),x73802),x73802))
% 81.29/80.91 [7410]~P24(f328(f328(f244(a877),f328(a118,x74101)),x74102))+P24(f190(a871,a241,f328(f244(a877),x74101),x74102))
% 81.29/80.91 [7565]P21(a877,a877,f328(f328(f7(a877,a877,a877),f22(a877)),x75651),x75652)+P24(f328(f328(f330(a877),f723(x75651,x75652)),x75652))
% 81.29/80.91 [7621]E(f328(f328(f328(f66(a877,x76211,f81(a877)),f328(f16(a877,x76211),f79(a877))),f2(a877)),x76212),f328(f38(x76211),x76212))+~P24(f328(f62(x76211),x76212))
% 81.29/80.91 [7663]P21(a877,a877,f328(f328(f7(a877,a877,a877),f22(a877)),x76631),x76632)+~P24(f328(f328(f244(a877),x76631),f723(x76631,x76632)))
% 81.29/80.91 [7721]P38(x77211,x77212)+P24(f328(f328(f244(f885(x77211,a871)),f718(x77212,x77211)),f328(f282(x77211,x77211,x77212),f718(x77212,x77211))))
% 81.29/80.91 [7726]P57(x77261,x77262)+~P38(x77261,f328(f249(f884(x77261,x77261)),f328(f267(x77261,x77261,a871),x77262)))
% 81.29/80.91 [7795]P24(f328(f328(f244(a877),f328(a118,x77951)),x77952))+~P24(f190(a871,a241,f328(f244(a877),x77951),x77952))
% 81.29/80.91 [7849]P24(f328(f328(f330(f884(a877,a877)),f328(f328(f257(a877,a877),x78491),x78492)),f304(a877,a318)))+~P24(f328(f328(f244(a877),x78491),x78492))
% 81.29/80.91 [7946]P50(x79461,x79462)+~P48(x79461,f252(f885(x79461,a871)),f328(f249(f884(x79461,x79461)),f328(f267(x79461,x79461,a871),x79462)))
% 81.29/80.91 [8006]~P24(f328(f136(x80061),x80062))+P24(f328(f136(f885(x80061,a871)),f328(f328(f153(f878(x80061),f885(x80061,a871)),f171(x80061)),f54(x80061,x80062))))
% 81.29/80.91 [8212]~P38(x82121,f328(f283(x82121,x82121),x82122))+P38(x82121,f328(f283(x82121,x82121),f328(f328(f285(x82121,x82121,x82121),x82122),f304(x82121,x82122))))
% 81.29/80.91 [8333]P24(f328(f62(f884(x83331,x83331)),f328(f328(f285(x83331,x83331,x83331),x83332),f304(x83331,x83332))))+~P24(f328(f62(f884(x83331,x83331)),x83332))
% 81.29/80.91 [8364]E(x83641,f2(a1))+P24(f328(f49(x83642,x83641),f328(f328(f257(a1,a1),f328(f328(f39(a1),x83642),x83641)),f45(a1,x83642,x83641))))
% 81.29/80.91 [8375]~P24(f328(f328(f330(f884(a877,a877)),f328(f328(f257(a877,a877),x83751),x83752)),f304(a877,a318)))+P24(f328(f328(f244(a877),x83751),x83752))
% 81.29/80.91 [8392]~P82(x83921)+E(f328(f141(x83921,x83921,f328(f7(x83921,x83921,x83921),f81(x83921)),f2(x83921)),f328(f168(x83921),x83922)),f328(f141(x83921,x83921,f81(x83921),f2(x83921)),x83922))
% 81.29/80.91 [8570]~P106(x85701)+E(f328(f141(f878(x85701),x85701,f328(f7(x85701,f878(x85701),f878(x85701)),f147(x85701,x85701,f5(x85701))),f119(x85701)),x85702),f149(x85701,x85701,f5(x85701),x85702))
% 81.29/80.91 [8672]~P55(x86721,f328(f249(f884(x86721,x86721)),f328(f267(x86721,x86721,a871),x86722)))+P55(x86721,f328(f249(f884(x86721,x86721)),f328(f267(x86721,x86721,a871),f261(x86721,x86721,x86722))))
% 81.29/80.91 [8686]P24(f328(f328(f330(f884(a877,a877)),f328(f328(f257(a877,a877),x86861),x86862)),f328(f328(f285(a877,a877,a877),a318),f304(a877,a318))))+~P24(f328(f328(f245(a877),x86861),x86862))
% 81.29/80.91 [8729]~P24(f328(f62(f884(x87291,x87291)),f328(f328(f285(x87291,x87291,x87291),x87292),f304(x87291,x87292))))+P24(f328(f62(f884(x87291,x87291)),x87292))
% 81.29/80.91 [8781]~P55(x87811,f328(f249(f884(x87811,x87811)),f328(f267(x87811,x87811,a871),f261(x87811,x87811,x87812))))+P55(x87811,f328(f249(f884(x87811,x87811)),f328(f267(x87811,x87811,a871),x87812)))
% 81.29/80.91 [8982]P55(x89821,x89822)+P24(f328(f328(f330(f884(x89821,x89821)),f328(f328(f257(x89821,x89821),f760(x89822,x89821)),f760(x89822,x89821))),f328(f328(f285(x89821,x89821,x89821),x89822),f304(x89821,x89822))))
% 81.29/80.91 [8983]P55(x89831,x89832)+P24(f328(f328(f330(f884(x89831,x89831)),f328(f328(f257(x89831,x89831),f772(x89832,x89831)),f772(x89832,x89831))),f328(f328(f285(x89831,x89831,x89831),x89832),f304(x89831,x89832))))
% 81.29/80.91 [9100]~P24(f328(f328(f330(f884(a877,a877)),f328(f328(f257(a877,a877),x91001),x91002)),f328(f328(f285(a877,a877,a877),a318),f304(a877,a318))))+P24(f328(f328(f245(a877),x91001),x91002))
% 81.29/80.91 [5066]~P96(x50661)+E(f328(f328(f81(x50661),f328(f109(x50661),a84)),x50662),x50662)
% 81.29/80.91 [5094]~P97(x50941)+E(f328(f328(f116(x50941),f328(f80(x50941),x50942)),x50942),f252(x50941))
% 81.29/80.91 [5095]~P67(x50951)+E(f328(f328(f81(x50951),f328(f80(x50951),x50952)),x50952),f2(x50951))
% 81.29/80.91 [5096]~P73(x50961)+E(f328(f328(f81(x50961),f328(f80(x50961),x50962)),x50962),f2(x50961))
% 81.29/80.91 [5097]~P97(x50971)+E(f328(f328(f107(x50971),f328(f80(x50971),x50972)),x50972),f193(x50971))
% 81.29/80.91 [5129]~P96(x51291)+E(f328(f328(f82(x51291),f328(f109(x51291),a103)),x51292),f328(f80(x51291),x51292))
% 81.29/80.91 [5301]~P114(x53011)+E(f328(f328(f82(x53011),f328(f80(x53011),f79(x53011))),x53012),f328(f80(x53011),x53012))
% 81.29/80.91 [5344]E(f328(f76(a1),x53441),f79(a1))+~E(f328(f76(a1),f328(f328(f82(a1),x53441),x53442)),f79(a1))
% 81.29/80.91 [5437]~P96(x54371)+E(f328(f328(f81(x54371),f79(x54371)),f328(f109(x54371),x54372)),f328(f109(x54371),f328(f328(f22(a1),x54372),a103)))
% 81.29/80.91 [5491]~P78(x54911)+E(f10(x54911,f328(f328(f306(x54911),x54912),f193(f885(x54911,a871)))),x54912)
% 81.29/80.91 [5492]~P27(x54921)+E(f40(x54921,f328(f328(f306(x54921),x54922),f193(f885(x54921,a871)))),x54922)
% 81.29/80.91 [5493]~P78(x54931)+E(f11(x54931,f328(f328(f306(x54931),x54932),f193(f885(x54931,a871)))),x54932)
% 81.29/80.91 [5494]~P27(x54941)+E(f41(x54941,f328(f328(f306(x54941),x54942),f193(f885(x54941,a871)))),x54942)
% 81.29/80.91 [5495]~P106(x54951)+E(f14(x54951,f328(f328(f306(x54951),x54952),f193(f885(x54951,a871)))),x54952)
% 81.29/80.91 [5496]~P106(x54961)+E(f15(x54961,f328(f328(f306(x54961),x54962),f193(f885(x54961,a871)))),x54962)
% 81.29/80.91 [5518]E(f328(f328(f81(a877),x55181),f328(f328(f22(a877),x55182),x55181)),x55182)+P24(f328(f328(f245(a877),x55182),x55181))
% 81.29/80.91 [5548]E(x55481,f119(x55482))+P24(f328(f328(f245(a877),f2(a877)),f328(f194(f878(x55482)),x55481)))
% 81.29/80.91 [5672]~P106(x56721)+E(f12(x56721,f242(x56721),f328(f328(f306(x56721),x56722),f193(f885(x56721,a871)))),x56722)
% 81.29/80.91 [5673]~P106(x56731)+E(f13(x56731,f243(x56731),f328(f328(f306(x56731),x56732),f193(f885(x56731,a871)))),x56732)
% 81.29/80.91 [5735]E(f328(f328(f22(a877),x57351),f328(f328(f22(a877),x57351),x57352)),x57352)+~P24(f328(f328(f244(a877),x57352),x57351))
% 81.29/80.91 [5736]E(f328(f328(f81(a877),x57361),f328(f328(f22(a877),x57362),x57361)),x57362)+~P24(f328(f328(f244(a877),x57361),x57362))
% 81.29/80.91 [5757]E(f45(a877,f328(f328(f22(a877),x57571),x57572),x57572),f45(a877,x57571,x57572))+P24(f328(f328(f245(a877),x57571),x57572))
% 81.29/80.91 [5768]E(f328(f80(a1),f328(f328(f39(a1),x57681),f328(f80(a1),x57682))),f288(x57681,x57682))+P24(f328(f328(f244(a1),f2(a1)),x57682))
% 81.29/80.91 [5770]~E(x57702,f2(a877))+P24(f328(f328(f245(a877),f2(a877)),f328(f328(f258(a877),x57701),x57702)))
% 81.29/80.91 [5821]~P96(x58211)+E(f328(f328(f81(x58211),f328(f80(x58211),f79(x58211))),f328(f109(x58211),x58212)),f328(f109(x58211),f328(f328(f81(a1),x58212),a103)))
% 81.29/80.91 [5822]E(f328(f328(f258(a877),f328(f109(a877),x58221)),x58222),f328(f328(f258(a877),f2(a877)),x58222))+~P24(f328(a199,f328(f109(a1),x58221)))
% 81.29/80.91 [5919]E(f328(f140(a877),f138(a877,f328(f298(a877,x59191),x59192))),x59191)+~P24(f328(f328(f245(a877),x59191),x59192))
% 81.29/80.91 [5939]E(f328(f328(f82(a877),f328(f109(a877),x59391)),f328(f109(a877),x59392)),f328(f109(a877),f328(f328(f82(a1),x59391),x59392)))+P24(f328(f328(f245(a1),x59391),a84))
% 81.29/80.91 [5945]~P124(x59451)+P24(f328(f328(f244(x59451),f2(x59451)),f328(f328(f82(x59451),x59452),x59452)))
% 81.29/80.91 [5957]E(f328(f328(f22(a877),f328(a118,x59571)),x59572),f328(a118,f328(f328(f22(a877),x59571),x59572)))+~P24(f328(f328(f244(a877),x59572),x59571))
% 81.29/80.91 [5960]E(f45(a877,f328(f328(f22(a877),x59601),x59602),x59602),f45(a877,x59601,x59602))+~P24(f328(f328(f244(a877),x59602),x59601))
% 81.29/80.91 [6014]E(f328(f328(f258(a877),f328(a110,x60141)),x60142),f328(a110,f328(f328(f258(a1),x60141),x60142)))+~P24(f328(f328(f244(a1),f2(a1)),x60141))
% 81.29/80.91 [6030]P24(f328(f136(x60301),x60302))+P24(f328(f328(f245(a877),f531(x60302,x60301)),f328(f194(f878(x60301)),x60302)))
% 81.29/80.91 [6031]P24(f328(f136(x60311),x60312))+P24(f328(f328(f245(a877),f580(x60312,x60311)),f328(f194(f878(x60311)),x60312)))
% 81.29/80.91 [6046]~E(x60461,f119(x60462))+~P24(f328(f328(f245(a877),f2(a877)),f328(f194(f878(x60462)),x60461)))
% 81.29/80.91 [6060]E(f143(a877,f138(a877,f328(f298(a877,x60601),x60602))),f328(f328(f22(a877),x60602),f79(a877)))+~P24(f328(f328(f245(a877),x60601),x60602))
% 81.29/80.91 [6063]E(f328(f328(f81(a1),x60631),f328(f106(a1),f328(a118,f862(x60632,x60631)))),x60632)+~P24(f328(f328(f245(a1),x60631),x60632))
% 81.29/80.91 [6070]E(x60701,f2(a877))+E(f328(f328(f82(a877),x60702),f328(f328(f258(a877),x60702),f328(f328(f22(a877),x60701),f79(a877)))),f328(f328(f258(a877),x60702),x60701))
% 81.29/80.91 [6096]E(f328(f328(f82(a877),f328(a110,x60961)),f328(a110,x60962)),f328(a110,f328(f328(f82(a1),x60961),x60962)))+~P24(f328(f328(f244(a1),f2(a1)),x60961))
% 81.29/80.91 [6097]E(f328(f328(f39(a877),f328(a110,x60971)),f328(a110,x60972)),f328(a110,f328(f328(f39(a1),x60971),x60972)))+~P24(f328(f328(f244(a1),f2(a1)),x60971))
% 81.29/80.91 [6111]~P112(x61111)+E(f328(f328(f81(x61111),x61112),x61112),f328(f328(f82(x61111),f328(f328(f81(x61111),f79(x61111)),f79(x61111))),x61112))
% 81.29/80.91 [6128]E(f328(f328(f22(a1),f328(f106(a1),x61281)),f328(f106(a1),x61282)),f328(f106(a1),f328(f328(f22(a877),x61281),x61282)))+~P24(f328(f328(f244(a877),x61282),x61281))
% 81.29/80.91 [6130]E(f328(f328(f257(a1,a1),f328(f109(a1),a103)),f328(f328(f81(a1),x61301),x61302)),f50(x61301,x61302))+~P24(f328(f328(f244(a1),x61302),f2(a1)))
% 81.29/80.91 [6170]E(f179(x61701,x61702),f119(f878(x61701)))+P24(f328(f328(f330(f878(x61701)),f582(x61702,x61701)),f328(f171(f878(x61701)),x61702)))
% 81.29/80.91 [6253]E(f328(f328(f150(a1),x62531),f178(f328(f328(f81(a1),x62531),f79(a1)),x62532)),f178(x62531,x62532))+~P24(f328(f328(f244(a1),x62531),x62532))
% 81.29/80.91 [6290]~P24(f328(f328(f245(a877),x62902),x62901))+P24(f328(f328(f245(a877),f2(a877)),f328(f328(f22(a877),x62901),x62902)))
% 81.29/80.91 [6321]~P24(f328(f328(f245(a877),x63211),f328(a110,x63212)))+P24(f328(f328(f245(a1),f328(f106(a1),x63211)),x63212))
% 81.29/80.91 [6352]~P106(x63521)+E(f328(f328(f116(f885(x63521,a871)),f328(f250(x63521),x63522)),f328(f328(f306(x63521),x63522),f193(f885(x63521,a871)))),f328(f297(x63521),x63522))
% 81.29/80.91 [6353]~P24(f328(f328(f244(a1),f2(a1)),x63531))+P24(f328(f328(f244(a1),f2(a1)),f328(f328(f258(a1),x63531),x63532)))
% 81.29/80.91 [6356]~P24(f328(f328(f245(a877),f2(a877)),x63561))+P24(f328(f328(f245(a877),f2(a877)),f328(f328(f258(a877),x63561),x63562)))
% 81.29/80.91 [6384]~E(f328(x63841,f2(a877)),f2(a877))+E(f328(f328(f6(a877,a877),x63841),f299(a877,f328(a118,f2(a877)),x63842)),f328(f328(f6(a877,a877),x63841),f299(a877,f2(a877),x63842)))
% 81.29/80.91 [6447]~P96(x64471)+E(f328(f328(f82(x64471),f328(f328(f81(x64471),f79(x64471)),f79(x64471))),f328(f109(x64471),x64472)),f328(f109(x64471),f328(f328(f81(a1),x64472),x64472)))
% 81.29/80.91 [6463]E(f328(f328(f306(a1),x64631),f299(a1,f328(f328(f81(a1),x64631),f79(a1)),x64632)),f299(a1,x64631,x64632))+P24(f328(f328(f245(a1),x64632),x64631))
% 81.29/80.91 [6464]P24(f328(f328(f245(a877),x64641),f328(a110,x64642)))+~P24(f328(f328(f245(a1),f328(f106(a1),x64641)),x64642))
% 81.29/80.91 [6565]E(f328(a110,f328(f328(f39(a1),f328(f109(a1),x65651)),f328(f109(a1),x65652))),f328(f328(f39(a877),f328(f109(a877),x65651)),f328(f109(a877),x65652)))+P24(f328(a199,f328(f109(a1),x65651)))
% 81.29/80.91 [6624]P24(f328(f328(f245(a877),x66241),x66242))+~P24(f328(f328(f245(a877),f2(a877)),f328(f328(f22(a877),x66242),x66241)))
% 81.29/80.91 [6669]P24(f328(f328(f245(a877),f2(a877)),x66691))+~P24(f328(f328(f245(a877),f2(a877)),f328(f328(f82(a877),x66692),x66691)))
% 81.29/80.91 [6670]P24(f328(f328(f245(a877),f2(a877)),x66701))+~P24(f328(f328(f245(a877),f2(a877)),f328(f328(f82(a877),x66701),x66702)))
% 81.29/80.91 [6687]~P24(f328(f328(f244(a1),x66871),f2(a1)))+E(f328(f328(f82(a877),f328(a110,f328(f80(a1),x66871))),f328(a110,f328(f80(a1),x66872))),f328(a110,f328(f328(f82(a1),x66871),x66872)))
% 81.29/80.91 [6745]~E(x67452,f193(f885(x67451,a871)))+P24(f328(f328(f244(f885(x67451,a871)),x67452),f328(f80(f885(x67451,a871)),x67452)))
% 81.29/80.91 [6808]~P96(x68081)+E(f328(f328(f81(x68081),f328(f328(f81(x68081),f2(x68081)),f328(f109(x68081),x68082))),f328(f109(x68081),x68082)),f328(f109(x68081),f328(f328(f81(a1),x68082),x68082)))
% 81.29/80.91 [6864]~P24(f328(f328(f245(a1),x68641),x68642))+P24(f328(f328(f244(a1),f328(f328(f81(a1),x68641),f79(a1))),x68642))
% 81.29/80.91 [6928]E(x69281,f2(a877))+~P24(f328(f328(f244(a1),f328(f106(a1),x69282)),f328(f80(a1),f328(f106(a1),x69281))))
% 81.29/80.91 [6929]E(x69291,f2(a877))+~P24(f328(f328(f244(a1),f328(f106(a1),x69291)),f328(f80(a1),f328(f106(a1),x69292))))
% 81.29/80.91 [7034]E(f328(f328(f257(a1,a1),f328(f109(a1),a103)),f328(f328(f81(a1),x70341),x70342)),f50(x70341,x70342))+~P24(f328(f328(f244(a1),f2(a1)),f328(f328(f81(a1),x70341),x70342)))
% 81.29/80.91 [7076]~P22(x70761,x70762)+P38(x70761,f328(f256(f885(f884(x70761,x70761),a871),f885(f884(x70761,x70761),a871)),x70762))
% 81.29/80.91 [7094]~P24(f328(f328(f244(a877),f328(a118,f2(a877))),x70941))+P24(f328(f328(f244(a877),f328(a118,f2(a877))),f328(f328(f258(a877),x70941),x70942)))
% 81.29/80.91 [7264]~P24(f328(f328(f244(a1),x72641),x72642))+P24(f328(f328(f244(a1),f328(f328(f81(a1),x72641),x72641)),f328(f328(f81(a1),x72642),x72642)))
% 81.29/80.91 [7269]~P24(f328(f328(f245(a1),x72691),x72692))+P24(f328(f328(f245(a1),f328(f328(f81(a1),x72691),x72691)),f328(f328(f81(a1),x72692),x72692)))
% 81.29/80.91 [7270]~P24(f328(f328(f92(a1),x72701),x72702))+P24(f328(f328(f92(a1),f328(f328(f81(a1),x72701),x72701)),f328(f328(f81(a1),x72702),x72702)))
% 81.29/80.91 [7325]~P24(f328(f328(f245(a877),f2(a877)),x73251))+P24(f328(f328(f245(a877),f328(f328(f22(a877),x73251),f328(a118,x73252))),x73251))
% 81.29/80.91 [7362]P24(f328(f328(f244(a877),f328(a118,f2(a877))),x73621))+~P24(f328(f328(f244(a877),f328(a118,f2(a877))),f328(f328(f82(a877),x73622),x73621)))
% 81.29/80.91 [7363]P24(f328(f328(f244(a877),f328(a118,f2(a877))),x73631))+~P24(f328(f328(f244(a877),f328(a118,f2(a877))),f328(f328(f82(a877),x73631),x73632)))
% 81.29/80.91 [7367]P24(f328(f328(f244(a877),f328(f328(f164(a877),x73671),x73672)),f328(f165(a877),x73671)))+~P24(f328(f328(f245(a877),x73672),f328(f194(f878(a877)),x73671)))
% 81.29/80.91 [7409]P24(f328(f328(f245(a1),x74091),x74092))+~P24(f328(f328(f244(a1),f328(f328(f81(a1),x74091),f79(a1))),x74092))
% 81.29/80.91 [7454]P24(f328(f62(x74541),f252(f885(x74541,a871))))+~P24(f328(f62(f885(x74542,x74541)),f252(f885(f885(x74542,x74541),a871))))
% 81.29/80.91 [7455]P24(f328(f62(x74551),f252(f885(x74551,a871))))+~P24(f328(f62(f883(x74552,x74551)),f252(f885(f883(x74552,x74551),a871))))
% 81.29/80.91 [7456]P24(f328(f62(x74561),f252(f885(x74561,a871))))+~P24(f328(f62(f883(x74561,x74562)),f252(f885(f883(x74561,x74562),a871))))
% 81.29/80.91 [7495]E(x74951,f193(f885(x74952,a871)))+~P24(f328(f328(f244(f885(x74952,a871)),x74951),f328(f80(f885(x74952,a871)),x74951)))
% 81.29/80.91 [7631]E(f328(f141(f878(x76311),f878(x76311),f127(x76311),f119(x76311)),x76312),f119(x76311))+P24(f328(f328(f330(f878(x76311)),f648(x76312,x76311)),f328(f171(f878(x76311)),x76312)))
% 81.29/80.91 [7632]E(f328(f141(f878(x76321),f878(x76321),f127(x76321),f119(x76321)),x76322),f119(x76321))+P24(f328(f328(f330(f878(x76321)),f650(x76322,x76321)),f328(f171(f878(x76321)),x76322)))
% 81.29/80.91 [7866]P24(f328(f328(f244(a1),x78661),x78662))+~P24(f328(f328(f244(a1),f328(f328(f81(a1),x78661),x78661)),f328(f328(f81(a1),x78662),x78662)))
% 81.29/80.91 [7871]P24(f328(f328(f245(a1),x78711),x78712))+~P24(f328(f328(f245(a1),f328(f328(f81(a1),x78711),x78711)),f328(f328(f81(a1),x78712),x78712)))
% 81.29/80.91 [7872]P24(f328(f328(f92(a1),x78721),x78722))+~P24(f328(f328(f92(a1),f328(f328(f81(a1),x78721),x78721)),f328(f328(f81(a1),x78722),x78722)))
% 81.29/80.91 [7966]~P112(x79661)+E(f328(f328(f82(x79661),f328(f328(f81(x79661),f79(x79661)),f79(x79661))),f328(f328(f6(a877,x79661),f106(x79661)),f299(a877,f79(a877),x79662))),f328(f328(f82(x79661),f328(f106(x79661),x79662)),f328(f328(f81(x79661),f328(f106(x79661),x79662)),f79(x79661))))
% 81.29/80.91 [8022]P24(f328(f328(f330(a877),x80221),x80222))+~P24(f328(f328(f330(a1),f328(f106(a1),x80221)),f328(f307(a877,a1,f106(a1)),x80222)))
% 81.29/80.91 [8183]~P24(f328(f62(x81831),x81832))+E(f328(f307(a877,x81831,f672(x81832,x81831)),f328(f249(a877),f328(f328(f7(a877,a877,a871),f245(a877)),f673(x81832,x81831)))),x81832)
% 81.29/80.91 [8472]P49(x84721,x84722)+P24(f328(f328(f330(f884(x84721,x84721)),f328(f328(f257(x84721,x84721),f522(x84722,x84721)),f522(x84722,x84721))),x84722))
% 81.29/80.91 [8611]~P96(x86111)+E(f328(f328(f22(x86111),f79(x86111)),f328(f109(x86111),x86112)),f328(f109(x86111),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f80(a1),x86112))))
% 81.29/80.91 [8726]~P24(f328(f328(f245(f885(a877,a871)),x87261),x87262))+P24(f328(f328(f245(f885(a1,a871)),f328(f307(a877,a1,f106(a1)),x87261)),f328(f307(a877,a1,f106(a1)),x87262)))
% 81.29/80.91 [8755]~P24(f328(f328(f245(a1),x87551),x87552))+P24(f328(f328(f244(a1),f328(f328(f22(a1),f328(f328(f81(a1),x87551),x87551)),a103)),f328(f328(f81(a1),x87552),x87552)))
% 81.29/80.91 [8757]~P24(f328(f328(f245(a1),x87571),x87572))+P24(f328(f328(f245(a1),f328(f328(f22(a1),f328(f328(f81(a1),x87571),x87571)),a103)),f328(f328(f81(a1),x87572),x87572)))
% 81.29/80.91 [8827]~P24(f328(f328(f330(a877),x88271),f328(f171(a877),x88272)))+P24(f328(f328(f244(a877),x88271),f328(f141(a877,a877,f81(a877),f2(a877)),x88272)))
% 81.29/80.91 [8919]P45(x89191,x89192)+~P24(f328(f328(f330(f884(x89191,x89191)),f328(f328(f257(x89191,x89191),f484(x89192,x89191)),f484(x89192,x89191))),x89192))
% 81.29/80.91 [8998]P20(a872,x89981,f328(f328(f306(f876(a872)),f328(a94,f328(a26,x89982))),f193(f885(f876(a872),a871))))+~P20(a872,f328(f328(f306(f876(a872)),f328(a94,f328(a26,x89982))),x89981),f328(f328(f306(f876(a872)),f328(a94,f328(f240(a873),f328(a28,x89982)))),f193(f885(f876(a872),a871))))
% 81.29/80.91 [9066]~P24(f328(f328(f244(f885(a1,a871)),f328(f307(a877,a1,f106(a1)),x90661)),f328(f307(a877,a1,f106(a1)),x90662)))+P24(f328(f328(f244(f885(a877,a871)),x90661),x90662))
% 81.29/80.91 [9067]~P24(f328(f328(f245(f885(a1,a871)),f328(f307(a877,a1,f106(a1)),x90671)),f328(f307(a877,a1,f106(a1)),x90672)))+P24(f328(f328(f245(f885(a877,a871)),x90671),x90672))
% 81.29/80.91 [9147]P24(f328(f328(f245(a1),x91471),x91472))+~P24(f328(f328(f244(a1),f328(f328(f22(a1),f328(f328(f81(a1),x91471),x91471)),a103)),f328(f328(f81(a1),x91472),x91472)))
% 81.29/80.91 [9149]P24(f328(f328(f245(a1),x91491),x91492))+~P24(f328(f328(f245(a1),f328(f328(f22(a1),f328(f328(f81(a1),x91491),x91491)),a103)),f328(f328(f81(a1),x91492),x91492)))
% 81.29/80.91 [10054]~P24(f328(f62(x100541),x100542))+E(f328(f194(f878(x100541)),f91(f878(x100541),f328(f328(f18(f878(x100541),a871,a871),f328(f328(f8(a871,f885(a871,a871),f878(x100541)),a326),f328(f328(f7(f878(x100541),f885(x100541,a871),a871),f328(f328(f8(f885(x100541,a871),f885(f885(x100541,a871),a871),f878(x100541)),a325),f171(x100541))),x100542))),f136(x100541)))),f222(x100541,x100542))
% 81.29/80.91 [10188]~P20(a872,x101881,f328(f328(f306(f876(a872)),f328(a94,x101882)),f193(f885(f876(a872),a871))))+P20(a872,x101881,f328(f328(f306(f876(a872)),f328(f328(f328(f93(a872),f328(f328(f8(f885(a872,f885(a872,a871)),f885(a872,a871),a872),f328(f8(f885(a872,a871),a871,a872),f89(a872))),f328(f328(f8(f885(a872,a871),f885(a872,f885(a872,a871)),a872),f328(f7(a872,f885(a872,a871),f885(a872,a871)),f328(f328(f8(f885(a872,f885(a871,a871)),f885(f885(a872,a871),f885(a872,a871)),a872),f18(a872,a871,a871)),f328(f328(f8(f885(a872,a871),f885(a872,f885(a871,a871)),a872),f328(f8(a871,f885(a871,a871),a872),a331)),f200(x101882))))),a325))),x101882),a325)),f193(f885(f876(a872),a871))))
% 81.29/80.91 [6059]E(f328(f328(f81(a877),f328(f328(f22(a877),x60591),x60592)),x60592),x60591)+~P24(f328(f328(f244(a877),x60592),x60591))
% 81.29/80.91 [6124]E(f328(f328(f39(a877),f328(f328(f82(a877),x61241),x61242)),x61242),x61241)+~P24(f328(f328(f245(a877),f2(a877)),x61242))
% 81.29/80.91 [6125]E(f328(f328(f39(a877),f328(f328(f82(a877),x61251),x61252)),x61251),x61252)+~P24(f328(f328(f245(a877),f2(a877)),x61251))
% 81.29/80.91 [6129]~P74(x61291)+E(f328(f328(f6(a877,x61291),f328(f164(x61291),x61292)),f328(f298(a877,f2(a877)),f328(f194(f878(x61291)),x61292))),f328(f165(x61291),x61292))
% 81.29/80.91 [6245]E(f45(a877,f328(a118,f328(f328(f82(a877),x62451),x62452)),x62451),f79(a877))+~P24(f328(f328(f245(a877),f79(a877)),x62451))
% 81.29/80.91 [6251]E(f328(a118,f328(f328(f81(a877),f328(f109(a877),x62511)),x62512)),f328(f328(f81(a877),f79(a877)),x62512))+~P24(f328(a199,f328(f109(a1),x62511)))
% 81.29/80.91 [6279]E(f328(a110,f328(f328(f258(a1),f328(f109(a1),x62791)),x62792)),f328(f328(f258(a877),f328(f109(a877),x62791)),x62792))+P24(f328(a199,f328(f109(a1),x62791)))
% 81.29/80.91 [6518]E(f328(f328(f22(a877),x65181),f328(f109(a877),f328(f328(f81(a1),x65182),a103))),f328(f328(f22(a877),f328(a118,x65181)),f328(f109(a877),x65182)))+~P24(f328(f328(f245(a1),a84),x65182))
% 81.29/80.91 [6597]E(x65971,f2(a877))+E(f328(a118,f328(f328(f81(a877),f328(f328(f22(a877),x65971),f79(a877))),x65972)),f328(f328(f81(a877),x65971),x65972))
% 81.29/80.91 [6638]E(x66381,f2(a1))+P24(f328(f328(f245(a1),f2(a1)),f328(f328(f258(a1),f328(f76(a1),x66381)),x66382)))
% 81.29/80.91 [6653]~E(x66532,f2(a877))+P24(f328(f328(f245(a1),f2(a1)),f328(f328(f258(a1),f328(f76(a1),x66531)),x66532)))
% 81.29/80.91 [6691]E(x66911,f2(a877))+E(f328(f328(f81(a877),x66912),f328(f328(f82(a877),f328(f328(f22(a877),x66911),f79(a877))),x66912)),f328(f328(f82(a877),x66911),x66912))
% 81.29/80.91 [6739]~P24(f328(f328(f244(a1),x67391),x67392))+P24(f328(f328(f245(a1),f328(f328(f81(a1),x67391),a103)),x67392))
% 81.29/80.91 [6867]E(f328(f328(f150(a877),x68671),f138(a877,f328(f298(a877,f328(a118,x68671)),x68672))),f138(a877,f328(f298(a877,x68671),x68672)))+~P24(f328(f328(f245(a877),x68671),x68672))
% 81.29/80.91 [7067]E(x70671,x70672)+~E(f328(f328(f22(a1),f328(f328(f81(a1),x70671),x70671)),a103),f328(f328(f22(a1),f328(f328(f81(a1),x70672),x70672)),a103))
% 81.29/80.91 [7070]E(x70701,f119(x70702))+E(f272(x70702,f328(f328(f153(x70702,f884(a105,x70702)),f328(f257(a105,x70702),f79(a105))),x70701)),f279(x70702,x70701))
% 81.29/80.91 [7294]P24(f328(f328(f244(a1),x72941),x72942))+~P24(f328(f328(f245(a1),f328(f328(f81(a1),x72941),a103)),x72942))
% 81.29/80.91 [7772]~P24(f328(f328(f245(a877),x77721),x77722))+P24(f328(f328(f330(f884(a877,a877)),f328(f328(f257(a877,a877),x77721),x77722)),a248))
% 81.29/80.91 [7994]~P24(f328(f328(f245(a105),f2(a105)),x79941))+P24(f328(f328(f245(a105),f328(f256(a105,f884(a105,a105)),f328(f273(x79941),x79942))),x79941))
% 81.29/80.91 [8311]~P87(x83111)+P24(f328(f328(f244(x83111),f328(f76(x83111),f328(f165(x83111),x83112))),f328(f165(x83111),f328(f328(f153(x83111,x83111),f76(x83111)),x83112))))
% 81.29/80.91 [8335]P24(f328(f328(f245(a877),x83351),x83352))+~P24(f328(f328(f330(f884(a877,a877)),f328(f328(f257(a877,a877),x83351),x83352)),a248))
% 81.29/80.91 [8495]E(f328(f328(f257(x84951,x84951),f781(x84952,x84951)),f781(x84952,x84951)),x84952)+~P24(f328(f328(f330(f884(x84951,x84951)),x84952),f304(x84951,f193(f885(f884(x84951,x84951),a871)))))
% 81.29/80.91 [8536]E(f328(f298(a877,x85361),f328(f328(f81(a877),x85361),f328(f38(a877),x85362))),x85362)+~P24(f328(f328(f244(f885(a877,a871)),x85362),f328(f298(a877,x85361),f328(f328(f81(a877),x85361),f328(f38(a877),x85362)))))
% 81.29/80.91 [8866]E(f328(f328(f39(a1),f328(f109(a1),f328(f328(f22(a1),f328(f328(f81(a1),x88661),x88661)),a103))),f328(f109(a1),f328(f328(f81(a1),x88662),x88662))),f328(f328(f39(a1),f328(f109(a1),x88661)),f328(f109(a1),x88662)))+~P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),x88662)))
% 81.29/80.91 [8993]E(f176(f878(x89931),f328(f328(f8(a871,a871,f878(x89931)),a323),f328(f328(f7(f878(x89931),f878(x89931),a871),a325),f119(x89931))),x89932),f179(x89931,f179(x89931,x89932)))+~P29(a877,f328(f168(a877),f328(f328(f153(f878(x89931),a877),f194(f878(x89931))),x89932)))
% 81.29/80.91 [8996]E(f328(f328(f39(a1),f328(f109(a1),f328(f328(f22(a1),f328(f328(f81(a1),x89961),x89961)),a103))),f328(f109(a1),f328(f328(f81(a1),x89962),x89962))),f328(f328(f39(a1),f328(f328(f81(a1),f328(f109(a1),x89961)),f79(a1))),f328(f109(a1),x89962)))+P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),x89962)))
% 81.29/80.91 [9824]P24(f328(a199,x98242))+E(f328(f328(f87(a1,a877),f328(f328(f22(a1),x98241),x98242)),f328(f328(f18(a1,a877,a877),f328(f328(f7(a1,a877,f885(a877,a877)),f328(f328(f8(a871,f885(a877,f885(a877,a877)),a1),f102(a877)),a199)),f2(a877))),a110)),f328(f328(f22(a877),f328(a110,x98241)),f328(a110,x98242)))
% 81.29/80.91 [9832]E(f328(f328(f87(a1,a877),f328(f109(a1),f328(f328(f81(a1),x98321),f328(f80(a1),x98322)))),f328(f328(f18(a1,a877,a877),f328(f328(f7(a1,a877,f885(a877,a877)),f328(f328(f8(a871,f885(a877,f885(a877,a877)),a1),f102(a877)),a199)),f2(a877))),a110)),f328(f328(f22(a877),f328(f109(a877),x98321)),f328(f109(a877),x98322)))+P24(f328(f328(f245(a1),x98322),a84))
% 81.29/80.91 [9834]~P22(x98341,x98342)+P24(f328(f328(f244(f885(f884(x98341,x98341),a871)),f328(f328(f285(x98341,x98341,x98341),f328(f256(f885(f884(x98341,x98341),a871),f885(f884(x98341,x98341),a871)),x98342)),f328(f266(f885(f884(x98341,x98341),a871),f885(f884(x98341,x98341),a871)),x98342))),f328(f256(f885(f884(x98341,x98341),a871),f885(f884(x98341,x98341),a871)),x98342)))
% 81.29/80.91 [9901]~E(f328(f38(a877),f328(f249(a877),f328(f328(f18(a877,a871,a871),f328(f328(f8(a871,f885(a871,a871),a877),a326),f328(f328(f7(a877,f885(a877,a871),a871),f330(a877)),x99011))),f328(f328(f7(a877,a877,a871),f245(a877)),f328(a118,x99012))))),f2(a877))+~P24(f328(f328(f330(a877),f2(a877)),x99011))
% 81.29/80.91 [9959]E(f45(a1,f328(f109(a1),f328(f328(f22(a1),f328(f328(f81(a1),x99591),x99591)),a103)),f328(f109(a1),f328(f328(f81(a1),x99592),x99592))),f328(f328(f81(a1),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f45(a1,f328(f109(a1),x99591),f328(f109(a1),x99592)))),f79(a1)))+~P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),x99592)))
% 81.29/80.91 [9968]E(f45(a1,f328(f109(a1),f328(f328(f22(a1),f328(f328(f81(a1),x99681),x99681)),a103)),f328(f109(a1),f328(f328(f81(a1),x99682),x99682))),f328(f328(f22(a1),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f45(a1,f328(f328(f81(a1),f328(f109(a1),x99681)),f79(a1)),f328(f109(a1),x99682)))),f79(a1)))+P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),x99682)))
% 81.29/80.91 [10022]~P27(x100221)+E(f40(x100221,f328(f249(x100221),f328(f328(f8(f885(x100221,a871),a871,x100221),f89(x100221)),f328(f328(f8(f885(x100221,a871),f885(x100221,a871),x100221),f328(f18(x100221,a871,a871),f328(f328(f8(a871,f885(a871,a871),x100221),a331),f328(f328(f7(x100221,f885(x100221,a871),a871),f330(x100221)),x100222)))),f244(x100221))))),f41(x100221,x100222))
% 81.29/80.91 [10047]~P38(x100471,x100472)+P57(x100471,f328(f328(f7(x100471,f885(f884(x100471,x100471),a871),f885(x100471,a871)),f328(f328(f8(f885(x100471,f885(f885(f884(x100471,x100471),a871),a871)),f885(f885(f884(x100471,x100471),a871),f885(x100471,a871)),x100471),f7(x100471,f885(f884(x100471,x100471),a871),a871)),f328(f328(f8(f885(x100471,f884(x100471,x100471)),f885(x100471,f885(f885(f884(x100471,x100471),a871),a871)),x100471),f328(f8(f884(x100471,x100471),f885(f885(f884(x100471,x100471),a871),a871),x100471),f330(f884(x100471,x100471)))),f257(x100471,x100471)))),x100472))
% 81.29/80.91 [10048]~P6(x100481,f252(f885(x100481,a871)),x100482)+P5(x100481,f328(f328(f7(x100481,f885(f884(x100481,x100481),a871),f885(x100481,a871)),f328(f328(f8(f885(x100481,f885(f885(f884(x100481,x100481),a871),a871)),f885(f885(f884(x100481,x100481),a871),f885(x100481,a871)),x100481),f7(x100481,f885(f884(x100481,x100481),a871),a871)),f328(f328(f8(f885(x100481,f884(x100481,x100481)),f885(x100481,f885(f885(f884(x100481,x100481),a871),a871)),x100481),f328(f8(f884(x100481,x100481),f885(f885(f884(x100481,x100481),a871),a871),x100481),f330(f884(x100481,x100481)))),f257(x100481,x100481)))),x100482))
% 81.29/80.91 [10085]P38(x100851,x100852)+~P57(x100851,f328(f328(f7(x100851,f885(f884(x100851,x100851),a871),f885(x100851,a871)),f328(f328(f8(f885(x100851,f885(f885(f884(x100851,x100851),a871),a871)),f885(f885(f884(x100851,x100851),a871),f885(x100851,a871)),x100851),f7(x100851,f885(f884(x100851,x100851),a871),a871)),f328(f328(f8(f885(x100851,f884(x100851,x100851)),f885(x100851,f885(f885(f884(x100851,x100851),a871),a871)),x100851),f328(f8(f884(x100851,x100851),f885(f885(f884(x100851,x100851),a871),a871),x100851),f330(f884(x100851,x100851)))),f257(x100851,x100851)))),x100852))
% 81.29/80.91 [10086]P6(x100861,f252(f885(x100861,a871)),x100862)+~P5(x100861,f328(f328(f7(x100861,f885(f884(x100861,x100861),a871),f885(x100861,a871)),f328(f328(f8(f885(x100861,f885(f885(f884(x100861,x100861),a871),a871)),f885(f885(f884(x100861,x100861),a871),f885(x100861,a871)),x100861),f7(x100861,f885(f884(x100861,x100861),a871),a871)),f328(f328(f8(f885(x100861,f884(x100861,x100861)),f885(x100861,f885(f885(f884(x100861,x100861),a871),a871)),x100861),f328(f8(f884(x100861,x100861),f885(f885(f884(x100861,x100861),a871),a871),x100861),f330(f884(x100861,x100861)))),f257(x100861,x100861)))),x100862))
% 81.29/80.91 [7245]E(f328(f328(f81(a877),f328(f109(a877),f328(f328(f22(a1),x72451),a103))),x72452),f328(a118,f328(f328(f81(a877),f328(f109(a877),x72451)),x72452)))+P24(f328(a199,f328(f109(a1),x72451)))
% 81.29/80.91 [7689]~P96(x76891)+E(f328(f328(f81(x76891),f328(f328(f81(x76891),f79(x76891)),f328(f109(x76891),x76892))),f328(f109(x76891),x76892)),f328(f109(x76891),f328(f328(f22(a1),f328(f328(f81(a1),x76892),x76892)),a103)))
% 81.29/80.91 [8337]~P24(f328(f328(f244(a1),x83371),x83372))+P24(f328(f328(f244(a1),f328(f328(f81(a1),x83371),x83371)),f328(f328(f22(a1),f328(f328(f81(a1),x83372),x83372)),a103)))
% 81.29/80.91 [8339]~P24(f328(f328(f244(a1),x83391),x83392))+P24(f328(f328(f245(a1),f328(f328(f81(a1),x83391),x83391)),f328(f328(f22(a1),f328(f328(f81(a1),x83392),x83392)),a103)))
% 81.29/80.91 [8759]P24(f328(f328(f244(a1),x87591),x87592))+~P24(f328(f328(f244(a1),f328(f328(f81(a1),x87591),x87591)),f328(f328(f22(a1),f328(f328(f81(a1),x87592),x87592)),a103)))
% 81.29/80.91 [8761]P24(f328(f328(f244(a1),x87611),x87612))+~P24(f328(f328(f245(a1),f328(f328(f81(a1),x87611),x87611)),f328(f328(f22(a1),f328(f328(f81(a1),x87612),x87612)),a103)))
% 81.29/80.91 [9054]~P24(f328(f328(f244(a1),x90541),x90542))+P24(f328(f328(f244(a1),f328(f328(f22(a1),f328(f328(f81(a1),x90541),x90541)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),x90542),x90542)),a103)))
% 81.29/80.91 [9056]~P24(f328(f328(f245(a1),x90561),x90562))+P24(f328(f328(f245(a1),f328(f328(f22(a1),f328(f328(f81(a1),x90561),x90561)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),x90562),x90562)),a103)))
% 81.29/80.91 [9057]~P24(f328(f328(f92(a1),x90571),x90572))+P24(f328(f328(f92(a1),f328(f328(f22(a1),f328(f328(f81(a1),x90571),x90571)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),x90572),x90572)),a103)))
% 81.29/80.91 [9321]P24(f328(f328(f244(a1),x93211),x93212))+~P24(f328(f328(f244(a1),f328(f328(f22(a1),f328(f328(f81(a1),x93211),x93211)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),x93212),x93212)),a103)))
% 81.29/80.91 [9323]P24(f328(f328(f245(a1),x93231),x93232))+~P24(f328(f328(f245(a1),f328(f328(f22(a1),f328(f328(f81(a1),x93231),x93231)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),x93232),x93232)),a103)))
% 81.29/80.91 [9324]P24(f328(f328(f92(a1),x93241),x93242))+~P24(f328(f328(f92(a1),f328(f328(f22(a1),f328(f328(f81(a1),x93241),x93241)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),x93242),x93242)),a103)))
% 81.29/80.91 [9356]~P24(f328(f62(x93561),x93562))+P24(f328(f62(f885(x93561,a871)),f328(f249(f885(x93561,a871)),f328(f328(f7(f885(x93561,a871),f885(x93561,a871),a871),f244(f885(x93561,a871))),x93562))))
% 81.29/80.91 [9403]~E(f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),x94031),f193(f885(f884(a877,a877),a871)))),f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),x94032),f193(f885(f884(a877,a877),a871)))))+P24(f328(f328(f330(f884(f884(a877,a877),f884(a877,a877))),f328(f328(f257(f884(a877,a877),f884(a877,a877)),x94031),x94032)),a114))
% 81.29/80.91 [9487]E(f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),x94871),f193(f885(f884(a877,a877),a871)))),f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),x94872),f193(f885(f884(a877,a877),a871)))))+~P24(f328(f328(f330(f884(f884(a877,a877),f884(a877,a877))),f328(f328(f257(f884(a877,a877),f884(a877,a877)),x94871),x94872)),a114))
% 81.29/80.91 [9523]P24(f328(f328(f244(a1),f2(a1)),f799(x95231,x95232)))+E(f328(f249(a1),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f244(a1),f2(a1)))),x95231)),f328(f249(a1),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f244(a1),f2(a1)))),x95232)))
% 81.29/80.91 [10032]~P27(x100321)+E(f41(x100321,f328(f249(x100321),f328(f328(f8(f885(x100321,a871),a871,x100321),f89(x100321)),f328(f328(f8(f885(x100321,a871),f885(x100321,a871),x100321),f328(f18(x100321,a871,a871),f328(f328(f8(a871,f885(a871,a871),x100321),a331),f328(f328(f7(x100321,f885(x100321,a871),a871),f330(x100321)),x100322)))),f328(f7(x100321,x100321,a871),f244(x100321)))))),f40(x100321,x100322))
% 81.29/80.91 [10053]P24(f328(f328(f330(a877),f2(a877)),x100531))+E(f328(f38(a877),f328(f249(a877),f328(f328(f18(a877,a871,a871),f328(f328(f8(a871,f885(a871,a871),a877),a326),f328(f328(f7(a877,f885(a877,a871),a871),f328(f328(f8(a877,f885(f885(a877,a871),a871),a877),f330(a877)),a118)),x100531))),f328(f328(f7(a877,a877,a871),f245(a877)),x100532)))),f328(f38(a877),f328(f249(a877),f328(f328(f18(a877,a871,a871),f328(f328(f8(a871,f885(a871,a871),a877),a326),f328(f328(f7(a877,f885(a877,a871),a871),f330(a877)),x100531))),f328(f328(f7(a877,a877,a871),f245(a877)),f328(a118,x100532))))))
% 81.29/80.91 [7559]~P96(x75591)+E(f328(f328(f82(x75591),x75592),f328(f109(x75591),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),x75592)
% 81.29/80.91 [7819]~P96(x78191)+E(f328(f328(f81(x78191),f328(f109(x78191),x78192)),f79(x78191)),f328(f109(x78191),f328(f328(f81(a1),x78192),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))
% 81.29/80.91 [7964]P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),x79642)))+E(f328(f328(f258(a1),x79641),f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),x79642),x79642)),a103))),f79(a1))
% 81.29/80.91 [9381]~P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),x93812)))+E(f328(f328(f258(a1),x93811),f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),x93812),x93812)),a103))),f328(f328(f87(a1,a1),f328(f328(f258(a1),x93811),f328(f109(a877),x93812))),f328(f328(f18(a1,a1,a1),f328(f328(f8(a1,f885(a1,a1),a1),f82(a1)),f328(f82(a1),x93811))),f5(a1))))
% 81.29/80.91 [9741]~P24(f328(f328(f244(a877),f810(x97412,x97411)),f328(x97411,f810(x97412,x97411))))+P24(f328(f62(a877),f328(f249(a877),f328(f328(f7(a877,a877,a871),f328(f328(f8(a877,f885(a877,a871),a877),f244(a877)),x97411)),x97412))))
% 81.29/80.91 [9891]~P24(f328(f328(f244(a877),f328(f109(a877),x98911)),f328(a118,x98912)))+P24(f328(f328(f87(a1,a871),f328(f109(a1),f328(f328(f81(a1),x98911),a103))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a331),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f7(a1,a877,a871),f328(f328(f8(a877,f885(a877,a871),a1),f244(a877)),a110)),x98912))))
% 81.29/80.91 [9892]~P24(f328(f328(f245(a877),f328(f109(a877),x98921)),f328(a118,x98922)))+P24(f328(f328(f87(a1,a871),f328(f109(a1),f328(f328(f81(a1),x98921),a103))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a331),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f7(a1,a877,a871),f328(f328(f8(a877,f885(a877,a871),a1),f245(a877)),a110)),x98922))))
% 81.29/80.91 [9943]P24(f328(f328(f244(a877),f328(f109(a877),x99431)),f328(a118,x99432)))+~P24(f328(f328(f87(a1,a871),f328(f109(a1),f328(f328(f81(a1),x99431),a103))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a331),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f7(a1,a877,a871),f328(f328(f8(a877,f885(a877,a871),a1),f244(a877)),a110)),x99432))))
% 81.29/80.91 [9944]P24(f328(f328(f245(a877),f328(f109(a877),x99441)),f328(a118,x99442)))+~P24(f328(f328(f87(a1,a871),f328(f109(a1),f328(f328(f81(a1),x99441),a103))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a331),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f7(a1,a877,a871),f328(f328(f8(a877,f885(a877,a871),a1),f245(a877)),a110)),x99442))))
% 81.29/80.91 [9974]~P24(f328(f328(f244(a877),f328(a118,x99742)),f328(f109(a877),x99741)))+P24(f328(f328(f87(a1,a871),f328(f109(a1),f328(f328(f81(a1),x99741),a103))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a331),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f8(a877,a871,a1),f328(f244(a877),x99742)),a110)))))
% 81.29/80.91 [9975]~P24(f328(f328(f245(a877),f328(a118,x99752)),f328(f109(a877),x99751)))+P24(f328(f328(f87(a1,a871),f328(f109(a1),f328(f328(f81(a1),x99751),a103))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a331),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f8(a877,a871,a1),f328(f245(a877),x99752)),a110)))))
% 81.29/80.91 [10020]P24(f328(f328(f244(a877),f328(a118,x100201)),f328(f109(a877),x100202)))+~P24(f328(f328(f87(a1,a871),f328(f109(a1),f328(f328(f81(a1),x100202),a103))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a331),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f8(a877,a871,a1),f328(f244(a877),x100201)),a110)))))
% 81.29/80.91 [10021]P24(f328(f328(f245(a877),f328(a118,x100211)),f328(f109(a877),x100212)))+~P24(f328(f328(f87(a1,a871),f328(f109(a1),f328(f328(f81(a1),x100212),a103))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a331),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f8(a877,a871,a1),f328(f245(a877),x100211)),a110)))))
% 81.29/80.91 [10093]~P24(f328(f328(f330(a877),f2(a877)),x100931))+E(f328(a118,f328(f38(a877),f328(f249(a877),f328(f328(f18(a877,a871,a871),f328(f328(f8(a871,f885(a871,a871),a877),a326),f328(f328(f7(a877,f885(a877,a871),a871),f328(f328(f8(a877,f885(f885(a877,a871),a871),a877),f330(a877)),a118)),x100931))),f328(f328(f7(a877,a877,a871),f245(a877)),x100932))))),f328(f38(a877),f328(f249(a877),f328(f328(f18(a877,a871,a871),f328(f328(f8(a871,f885(a871,a871),a877),a326),f328(f328(f7(a877,f885(a877,a871),a871),f330(a877)),x100931))),f328(f328(f7(a877,a877,a871),f245(a877)),f328(a118,x100932))))))
% 81.29/80.91 [8520]~P96(x85201)+E(f328(f328(f82(x85201),f328(f109(x85201),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),x85202),x85202)
% 81.29/80.91 [8579]~P96(x85791)+E(f328(f328(f81(x85791),f79(x85791)),f328(f109(x85791),x85792)),f328(f109(x85791),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),x85792)))
% 81.29/80.91 [8637]~P96(x86371)+E(f328(f328(f22(x86371),f328(f109(x86371),x86372)),f79(x86371)),f328(f109(x86371),f328(f328(f81(a1),x86372),f328(f80(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))
% 81.29/80.91 [8777]~P24(f328(f328(f245(a877),f328(f109(a877),a84)),x87772))+E(f328(f328(f22(a877),x87771),f328(f328(f22(a877),x87772),f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f328(f328(f22(a877),f328(a118,x87771)),x87772))
% 81.29/80.91 [9419]~P112(x94191)+E(f328(f328(f82(x94191),x94192),x94192),f328(f328(f258(x94191),x94192),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))
% 81.29/80.91 [9420]~P83(x94201)+E(f328(f328(f258(x94201),x94202),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f328(f328(f82(x94201),x94202),x94202))
% 81.29/80.91 [9422]~P96(x94221)+E(f328(f328(f82(x94221),x94222),f328(f109(x94221),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f328(f328(f81(x94221),x94222),x94222))
% 81.29/80.91 [9660]~P111(x96601)+E(f328(f328(f258(x96601),f328(f76(x96601),x96602)),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f328(f328(f258(x96601),x96602),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))
% 81.29/80.91 [9661]~P137(x96611)+E(f328(f328(f258(x96611),f328(f80(x96611),x96612)),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f328(f328(f258(x96611),x96612),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))
% 81.29/80.91 [9657]~P96(x96571)+E(f328(f328(f82(x96571),f328(f109(x96571),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x96572),f328(f328(f81(x96571),x96572),x96572))
% 81.29/80.91 [9781]~P111(x97811)+E(f328(f76(x97811),f328(f328(f258(x97811),x97812),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x97811),x97812),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))
% 81.29/80.91 [9842]~P111(x98421)+P24(f328(f328(f244(x98421),f2(x98421)),f328(f328(f258(x98421),x98422),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))))
% 81.29/80.91 [10011]~E(f328(a118,x100112),f328(f109(a877),x100111))+P24(f328(f328(f87(a1,a871),f328(f109(a1),f328(f328(f81(a1),x100111),a103))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a331),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f7(a1,a877,a871),f328(f328(f8(a877,f885(a877,a871),a1),a325),a110)),x100112)))))
% 81.29/80.91 [10012]~E(f328(f109(a877),x100121),f328(a118,x100122))+P24(f328(f328(f87(a1,a871),f328(f109(a1),f328(f328(f81(a1),x100121),a103))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a331),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f7(a1,a877,a871),f328(f328(f8(a877,f885(a877,a871),a1),a325),a110)),x100122)))))
% 81.29/80.91 [10056]E(f328(a118,x100561),f328(f109(a877),x100562))+~P24(f328(f328(f87(a1,a871),f328(f109(a1),f328(f328(f81(a1),x100562),a103))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a331),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f7(a1,a877,a871),f328(f328(f8(a877,f885(a877,a871),a1),a325),a110)),x100561)))))
% 81.29/80.91 [10057]E(f328(f109(a877),x100571),f328(a118,x100572))+~P24(f328(f328(f87(a1,a871),f328(f109(a1),f328(f328(f81(a1),x100571),a103))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a331),f328(f328(f8(a871,a871,a1),a323),a199))),f328(f328(f7(a1,a877,a871),f328(f328(f8(a877,f885(a877,a871),a1),a325),a110)),x100572)))))
% 81.29/80.91 [9839]~P96(x98391)+E(f328(f328(f258(x98391),f328(f109(x98391),a103)),f328(f328(f82(a877),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x98392)),f79(x98391))
% 81.29/80.91 [9840]~P137(x98401)+E(f328(f328(f258(x98401),f328(f80(x98401),f79(x98401))),f328(f328(f82(a877),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x98402)),f79(x98401))
% 81.29/80.91 [9844]~P83(x98441)+E(f328(f328(f258(x98441),x98442),f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),a103))),f328(f328(f82(x98441),f328(f328(f82(x98441),x98442),x98442)),x98442))
% 81.29/80.91 [10035]~P24(f328(f328(f244(a1),f2(a1)),x100352))+E(f45(a1,f328(f328(f81(a1),f79(a1)),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x100351)),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x100352)),f328(f328(f81(a1),f79(a1)),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f45(a1,x100351,x100352))))
% 81.29/80.91 [10059]~P24(f328(f328(f244(a1),f2(a1)),x100592))+E(f328(f328(f39(a1),f328(f328(f81(a1),f79(a1)),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x100591))),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x100592)),f328(f328(f39(a1),x100591),x100592))
% 81.29/80.91 [10061]~P24(f328(f328(f244(a1),x100612),f2(a1)))+E(f328(f328(f39(a1),f328(f328(f81(a1),f79(a1)),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x100611))),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x100612)),f328(f328(f39(a1),f328(f328(f81(a1),x100611),f79(a1))),x100612))
% 81.29/80.91 [10062]~P24(f328(f328(f244(a1),x100622),f2(a1)))+E(f45(a1,f328(f328(f81(a1),f79(a1)),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x100621)),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x100622)),f328(f328(f22(a1),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f45(a1,f328(f328(f81(a1),x100621),f79(a1)),x100622))),f79(a1)))
% 81.29/80.91 [9934]~P96(x99341)+E(f328(f328(f258(x99341),f328(f109(x99341),a103)),f328(a118,f328(f328(f82(a877),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x99342))),f328(f109(x99341),a103))
% 81.29/80.91 [9936]~P137(x99361)+E(f328(f328(f258(x99361),f328(f80(x99361),f79(x99361))),f328(a118,f328(f328(f82(a877),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x99362))),f328(f80(x99361),f79(x99361)))
% 81.29/80.91 [5102]~P20(x51021,x51022,x51023)+P23(x51021,x51022,x51023)
% 81.29/80.91 [8037]~E(x80372,x80373)+P35(x80371,x80371,a325,x80372,x80373)
% 81.29/80.91 [8592]E(x85921,x85922)+~P35(x85923,x85923,a325,x85921,x85922)
% 81.29/80.91 [5107]~P38(x51071,x51073)+P38(x51071,f322(x51071,x51072,x51073))
% 81.29/80.91 [5282]P30(x52821,x52822,x52823)+~P30(x52821,f328(a118,x52822),x52823)
% 81.29/80.91 [5369]~P6(x53691,x53692,x53693)+P6(f878(x53691),f160(x53691,x53692),f157(x53691,x53693))
% 81.29/80.91 [5370]~P48(x53701,x53702,x53703)+P48(f878(x53701),f160(x53701,x53702),f157(x53701,x53703))
% 81.29/80.91 [5482]P52(x54821,x54822,x54823)+~E(f737(x54823,x54822,x54821),f738(x54823,x54822,x54821))
% 81.29/80.91 [5483]P53(x54831,x54832,x54833)+~E(f763(x54833,x54832,x54831),f764(x54833,x54832,x54831))
% 81.29/80.91 [6422]P23(x64221,x64222,x64223)+~P30(x64221,f601(x64223,x64222,x64221),f610(x64223,x64222,x64221))
% 81.29/80.91 [4657]~E(x46571,f196(x46572))+~E(x46571,f328(f236(x46572),x46573))
% 81.29/80.91 [4706]~E(f328(f168(x47062),x47061),x47063)+E(x47061,f328(f168(x47062),x47063))
% 81.29/80.91 [4707]~E(x47072,f328(f168(x47071),x47073))+E(f328(f168(x47071),x47072),x47073)
% 81.29/80.91 [4754]E(x47541,x47542)+~E(f328(f236(x47543),x47541),f328(f236(x47543),x47542))
% 81.29/80.91 [4755]E(x47551,x47552)+~E(f328(f168(x47553),x47551),f328(f168(x47553),x47552))
% 81.29/80.91 [4961]~P5(x49613,x49611)+P24(f328(f328(x49611,x49612),x49612))
% 81.29/80.91 [4962]~P50(x49623,x49621)+P24(f328(f328(x49621,x49622),x49622))
% 81.29/80.91 [4964]~P57(x49641,x49642)+P24(f328(f316(x49641,x49642),x49643))
% 81.29/80.91 [5026]~P38(x50261,x50262)+P38(f878(x50261),f328(f142(x50261,x50262),x50263))
% 81.29/80.91 [5031]~P24(f328(x50312,x50313))+~E(f328(f249(x50311),x50312),f193(f885(x50311,a871)))
% 81.29/80.91 [5032]~P24(f328(x50322,x50323))+~E(f193(f885(x50321,a871)),f328(f249(x50321),x50322))
% 81.29/80.91 [5063]~P24(f328(x50631,x50633))+P24(f328(x50631,f91(x50632,x50631)))
% 81.29/80.91 [5188]~E(x51882,x51883)+P24(f328(f328(f330(x51881),x51882),f328(a325,x51883)))
% 81.29/80.91 [5200]P24(f328(x52001,x52002))+~P24(f328(x52001,f583(x52001,x52003)))
% 81.29/80.91 [5246]E(f328(f168(x52461),x52462),f328(f328(f150(x52461),x52463),f119(x52461)))+~E(x52462,f328(f328(f150(x52461),x52463),f119(x52461)))
% 81.29/80.91 [5247]~E(x52473,f328(f328(f150(x52471),x52472),f119(x52471)))+E(f328(f328(f150(x52471),x52472),f119(x52471)),f328(f168(x52471),x52473))
% 81.29/80.91 [5275]~E(x52753,f328(f16(f881(x52752),x52751),f196(x52752)))+E(f183(x52751,x52752,x52753),f193(f885(x52751,a871)))
% 81.29/80.91 [5296]~P34(x52961,x52962,x52963)+P34(x52961,x52962,f328(f168(x52961),x52963))
% 81.29/80.91 [5297]~P32(x52971,x52972,x52973)+P32(x52971,x52972,f328(f168(x52971),x52973))
% 81.29/80.91 [5300]E(f328(f38(x53001),f812(x53002,x53003,x53001)),x53002)+~E(f328(f38(x53001),x53003),f328(a118,x53002))
% 81.29/80.91 [5306]~P38(x53061,x53063)+P24(f328(f328(f330(x53061),x53062),f317(x53061,x53063)))
% 81.29/80.91 [5309]~E(f328(f168(x53092),x53091),f328(f328(f150(x53092),x53093),f119(x53092)))+E(x53091,f328(f328(f150(x53092),x53093),f119(x53092)))
% 81.29/80.91 [5310]~E(f328(f328(f150(x53102),x53103),f119(x53102)),f328(f168(x53102),x53101))+E(x53101,f328(f328(f150(x53102),x53103),f119(x53102)))
% 81.29/80.91 [5325]E(x53251,f328(f16(f881(x53252),x53253),f196(x53252)))+~E(f183(x53253,x53252,x53251),f193(f885(x53253,a871)))
% 81.29/80.91 [5332]E(f86(f884(a877,a877),f48(x53321,x53322)),x53323)+~P24(f328(f48(x53321,x53322),x53323))
% 81.29/80.91 [5340]~E(x53403,f328(f236(x53401),x53402))+P24(f328(f328(f330(x53401),x53402),f235(x53401,x53403)))
% 81.29/80.91 [5373]P34(x53731,x53732,x53733)+~P34(x53731,x53732,f328(f168(x53731),x53733))
% 81.29/80.91 [5374]P32(x53741,x53742,x53743)+~P32(x53741,x53742,f328(f168(x53741),x53743))
% 81.29/80.91 [5436]~E(x54362,f119(x54361))+P24(f328(f328(f330(f878(x54361)),x54362),f160(x54361,x54363)))
% 81.29/80.91 [5443]~P48(x54431,x54432,x54433)+P48(x54431,x54432,f328(f283(x54431,x54431),x54433))
% 81.29/80.91 [5444]~P53(x54441,x54442,x54443)+P53(x54441,x54442,f328(f283(x54441,x54441),x54443))
% 81.29/80.91 [5463]~P58(x54631)+E(f45(x54631,f45(x54631,x54632,x54633),x54633),f45(x54631,x54632,x54633))
% 81.29/80.91 [5559]E(x55591,x55592)+~P24(f328(f328(f330(x55593),x55591),f328(a325,x55592)))
% 81.29/80.91 [5604]~P141(x56041)+E(f195(x56041,x56042,f2(a877),x56043),x56043)
% 81.29/80.91 [5624]P48(x56241,x56242,x56243)+~P48(x56241,x56242,f328(f283(x56241,x56241),x56243))
% 81.29/80.91 [5625]P53(x56251,x56252,x56253)+~P53(x56251,x56252,f328(f283(x56251,x56251),x56253))
% 81.29/80.91 [5629]~P106(x56292)+E(f149(x56291,x56292,x56293,f119(x56291)),f119(x56291))
% 81.29/80.91 [5642]E(f169(x56421,x56422,f151(x56421,x56423)),f151(x56421,f169(x56421,x56422,x56423)))+~P24(f328(f136(x56421),x56423))
% 81.29/80.91 [5648]E(x56481,f328(f236(x56482),x56483))+~P24(f328(f328(f330(x56482),x56483),f235(x56482,x56481)))
% 81.29/80.91 [5733]~P24(f328(a25,x57333))+P24(f328(a25,f30(x57331,x57332,x57333)))
% 81.29/80.91 [5744]E(f328(f135(x57441,x57442),x57443),f119(x57441))+P24(f328(x57442,f598(x57443,x57442,x57441)))
% 81.29/80.91 [5887]~P24(f328(f136(x58871),x58873))+P24(f328(f136(x58871),f169(x58871,x58872,x58873)))
% 81.29/80.91 [5888]~P24(f328(f136(x58881),x58882))+P24(f328(f136(x58881),f175(x58881,x58882,x58883)))
% 81.29/80.91 [5889]~P24(f328(f136(x58891),x58893))+P24(f328(f136(x58891),f176(x58891,x58892,x58893)))
% 81.29/80.91 [5890]~P24(f328(f136(x58901),x58903))+P24(f328(f136(x58901),f139(x58901,x58902,x58903)))
% 81.29/80.91 [5891]~P145(x58911,x58913,x58912)+P24(f328(x58911,f45(a1,x58912,x58913)))
% 81.29/80.91 [5910]~P34(x59103,x59101,x59102)+P24(f328(x59101,f757(x59102,x59101,x59103)))
% 81.29/80.91 [5911]~P36(x59113,x59111,x59112)+P24(f328(x59111,f807(x59112,x59111,x59113)))
% 81.29/80.91 [5933]E(f328(f135(x59331,x59332),x59333),f176(x59331,x59332,x59333))+P24(f328(x59332,f662(x59333,x59332,x59331)))
% 81.29/80.91 [5975]~P24(f328(f136(x59751),x59753))+P24(f328(f136(f878(x59751)),f55(x59751,x59752,x59753)))
% 81.29/80.91 [5997]P24(f328(a25,f29(x59971,x59972,x59973)))+~P24(f328(a25,f328(a26,x59972)))
% 81.29/80.91 [6009]~P108(x60091)+E(f328(f328(f107(f885(x60091,a871)),f328(f297(x60091),x60092)),f302(x60091,x60092,x60093)),f193(f885(x60091,a871)))
% 81.29/80.91 [6010]~P108(x60101)+E(f328(f328(f107(f885(x60101,a871)),f328(f297(x60101),x60102)),f301(x60101,x60102,x60103)),f193(f885(x60101,a871)))
% 81.29/80.91 [6011]~P108(x60111)+E(f328(f328(f107(f885(x60111,a871)),f328(f250(x60111),x60112)),f299(x60111,x60112,x60113)),f193(f885(x60111,a871)))
% 81.29/80.91 [6158]P24(f328(a25,x61581))+~P24(f328(a25,f30(x61582,x61583,x61581)))
% 81.29/80.91 [6160]P24(f328(a25,x61601))+~P24(f328(a25,f31(x61602,x61603,x61601)))
% 81.29/80.91 [6162]P24(f328(a25,x61621))+~P24(f328(a25,f31(x61622,x61621,x61623)))
% 81.29/80.91 [6241]E(f328(f135(x62411,x62412),x62413),x62413)+~P24(f328(x62412,f599(x62413,x62412,x62411)))
% 81.29/80.91 [6243]E(f328(f328(f306(x62431),f828(x62432,x62433,x62431)),f812(x62432,x62433,x62431)),x62433)+~E(f328(f38(x62431),x62433),f328(a118,x62432))
% 81.29/80.91 [6259]P145(x62591,x62592,x62593)+~P24(f328(x62591,f45(a1,x62593,x62592)))
% 81.29/80.91 [6306]P32(x63061,x63062,x63063)+~P24(f328(x63062,f793(x63063,x63062,x63061)))
% 81.29/80.91 [6307]P32(x63071,x63072,x63073)+~P24(f328(x63072,f804(x63072,x63073,x63071)))
% 81.29/80.91 [6308]P32(x63081,x63082,x63083)+~P24(f328(x63082,f805(x63083,x63082,x63081)))
% 81.29/80.91 [6310]E(f176(x63101,x63102,x63103),x63103)+~P24(f328(x63102,f647(x63103,x63102,x63101)))
% 81.29/80.91 [6348]~P24(f328(a25,f29(x63482,x63481,x63483)))+P24(f328(a25,f328(a26,x63481)))
% 81.29/80.91 [6391]~P24(f328(x63912,f602(x63913,x63912,x63911)))+P24(f328(f262(x63911,x63912),x63913))
% 81.29/80.91 [6392]~P24(f328(x63922,f664(x63923,x63922,x63921)))+P24(f328(f159(x63921,x63922),x63923))
% 81.29/80.91 [6639]~P24(f328(f316(x66391,x66392),f477(x66393,x66392,x66391)))+P24(f328(f316(x66391,x66392),x66393))
% 81.29/80.91 [6640]~P24(f328(f316(x66401,x66402),f487(x66403,x66402,x66401)))+P24(f328(f316(x66401,x66402),x66403))
% 81.29/80.91 [7246]~P58(x72461)+E(f328(f328(f81(x72461),f328(f328(f82(x72461),x72462),f328(f328(f39(x72461),x72463),x72462))),f45(x72461,x72463,x72462)),x72463)
% 81.29/80.91 [7713]E(f328(f328(f257(x77131,x77131),f535(x77132,x77133,x77131)),f535(x77132,x77133,x77131)),x77133)+~P24(f328(f328(f330(f884(x77131,x77131)),x77133),f254(x77131,x77132)))
% 81.29/80.91 [7827]~P24(f328(f328(f330(x78271),f559(x78273,x78272,x78271)),f317(x78271,x78273)))+P24(f328(f328(f330(x78271),x78272),f317(x78271,x78273)))
% 81.29/80.91 [7828]~P24(f328(f328(f330(x78281),f741(x78283,x78282,x78281)),f317(x78281,x78283)))+P24(f328(f328(f330(x78281),x78282),f317(x78281,x78283)))
% 81.29/80.91 [7829]~P24(f328(f328(f330(x78291),f750(x78293,x78292,x78291)),f317(x78291,x78293)))+P24(f328(f328(f330(x78291),x78292),f317(x78291,x78293)))
% 81.29/80.91 [8018]~P58(x80181)+E(f328(f328(f81(x80181),f328(f328(f82(x80181),f328(f328(f39(x80181),x80182),x80183)),x80183)),f45(x80181,x80182,x80183)),x80182)
% 81.29/80.91 [8063]~E(f328(f38(x80631),x80632),f328(a118,x80633))+~P24(f328(f328(f330(x80631),f828(x80633,x80632,x80631)),f812(x80633,x80632,x80631)))
% 81.29/80.91 [8688]P24(f328(f328(f244(f885(f884(x86881,x86881),a871)),f304(x86881,x86882)),f304(x86881,x86883)))+~P24(f328(f328(f244(f885(f884(x86881,x86881),a871)),x86882),f304(x86881,x86883)))
% 81.29/80.91 [8962]E(x89621,f119(x89622))+~P24(f328(f328(f330(f884(f878(x89622),f878(x89622))),f328(f328(f257(f878(x89622),f878(x89622)),x89621),f119(x89622))),f157(x89622,x89623)))
% 81.29/80.91 [8987]E(x89871,f119(x89872))+~P24(f328(f328(f330(f884(f878(x89872),f878(x89872))),f328(f328(f257(f878(x89872),f878(x89872)),f119(x89872)),x89871)),f157(x89872,x89873)))
% 81.29/80.91 [9111]E(f328(f328(f150(x91111),f627(x91112,x91113,x91111)),f628(x91112,x91113,x91111)),x91113)+~P24(f328(f328(f330(f884(f878(x91111),f878(x91111))),f328(f328(f257(f878(x91111),f878(x91111)),f119(x91111)),x91113)),f146(x91111,x91112)))
% 81.29/80.91 [9349]~P124(x93491)+~P24(f328(f328(f245(x93491),f328(f328(f81(x93491),f328(f328(f82(x93491),x93492),x93492)),f328(f328(f82(x93491),x93493),x93493))),f2(x93491)))
% 81.29/80.91 [9398]P24(f328(f62(x93981),x93982))+~P24(f328(f328(f330(f884(f885(x93981,a871),f885(x93981,a871))),f328(f328(f257(f885(x93981,a871),f885(x93981,a871)),x93983),x93982)),f303(x93981)))
% 81.29/80.91 [9682]~P46(x96821,x96822,x96823)+P24(f328(f328(f244(a1),f328(f328(f74(f884(a1,a1),a1,x96821,f256(a1,a1)),f220(x96821)),f231(x96821,x96822,f228(x96821,x96823)))),f2(a1)))
% 81.29/80.91 [9683]~P47(x96831,x96832,x96833)+P24(f328(f328(f245(a1),f328(f328(f74(f884(a1,a1),a1,x96831,f256(a1,a1)),f220(x96831)),f231(x96831,x96832,f228(x96831,x96833)))),f2(a1)))
% 81.29/80.91 [9809]P47(x98091,x98092,x98093)+~P24(f328(f328(f245(a1),f328(f328(f74(f884(a1,a1),a1,x98091,f256(a1,a1)),f220(x98091)),f231(x98091,x98092,f228(x98091,x98093)))),f2(a1)))
% 81.29/80.91 [9810]P46(x98101,x98102,x98103)+~P24(f328(f328(f244(a1),f328(f328(f74(f884(a1,a1),a1,x98101,f256(a1,a1)),f220(x98101)),f231(x98101,x98102,f228(x98101,x98103)))),f2(a1)))
% 81.29/80.91 [10138]~P111(x101381)+~P24(f328(f328(f245(x101381),f328(f328(f81(x101381),f328(f328(f258(x101381),x101382),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x101381),x101383),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))),f2(x101381)))
% 81.29/80.91 [4737]~E(x47373,f119(x47371))+E(f328(f328(f127(x47371),x47372),x47373),x47372)
% 81.29/80.91 [4738]~E(x47382,f119(x47381))+E(f328(f328(f127(x47381),x47382),x47383),x47383)
% 81.29/80.91 [4745]~E(x47452,f2(a877))+E(f328(f328(f174(x47451),x47452),x47453),f119(x47451))
% 81.29/80.91 [4749]~E(x47493,f119(x47491))+E(f328(f328(f174(x47491),x47492),x47493),f119(x47491))
% 81.29/80.91 [4789]~E(x47891,x47893)+E(x47891,f328(f328(f127(x47892),f119(x47892)),x47893))
% 81.29/80.91 [4877]~P25(x48772)+E(f328(f193(f885(x48771,x48772)),x48773),f193(x48772))
% 81.29/80.91 [4878]~P115(x48782)+E(f328(f252(f885(x48781,x48782)),x48783),f252(x48782))
% 81.29/80.91 [4898]E(x48981,f119(x48982))+~E(f328(f328(f127(x48982),x48983),x48981),x48983)
% 81.29/80.91 [4899]E(x48991,f119(x48992))+~E(f328(f328(f127(x48992),x48991),x48993),x48993)
% 81.29/80.91 [4907]E(x49071,f119(x49072))+~E(f328(f328(f127(x49072),x49073),x49071),f119(x49072))
% 81.29/80.91 [4908]E(x49081,f119(x49082))+~E(f328(f328(f127(x49082),x49081),x49083),f119(x49082))
% 81.29/80.91 [4931]~E(x49312,f2(a877))+E(f328(f328(f82(a877),x49311),x49312),f328(f328(f82(a877),x49313),x49312))
% 81.29/80.91 [4933]~E(x49331,f2(a877))+E(f328(f328(f82(a877),x49331),x49332),f328(f328(f82(a877),x49331),x49333))
% 81.29/80.91 [4987]~P65(x49871)+E(f328(f328(f116(x49871),x49872),x49873),f328(f328(f116(x49871),x49873),x49872))
% 81.29/80.91 [4988]~P78(x49881)+E(f328(f328(f116(x49881),x49882),x49883),f328(f328(f116(x49881),x49883),x49882))
% 81.29/80.91 [4989]~P112(x49891)+E(f328(f328(f81(x49891),x49892),x49893),f328(f328(f81(x49891),x49893),x49892))
% 81.29/80.91 [4990]~P78(x49901)+E(f328(f328(f107(x49901),x49902),x49903),f328(f328(f107(x49901),x49903),x49902))
% 81.29/80.91 [4992]~P102(x49921)+E(f328(f328(f107(x49921),x49922),x49923),f328(f328(f107(x49921),x49923),x49922))
% 81.29/80.91 [4993]~P112(x49931)+E(f328(f328(f82(x49931),x49932),x49933),f328(f328(f82(x49931),x49933),x49932))
% 81.29/80.91 [4995]~P106(x49951)+E(f328(f328(f242(x49951),x49952),x49953),f328(f328(f242(x49951),x49953),x49952))
% 81.29/80.91 [4997]~P106(x49971)+E(f328(f328(f243(x49971),x49972),x49973),f328(f328(f243(x49971),x49973),x49972))
% 81.29/80.91 [5058]E(f45(a877,x50581,x50582),f2(a877))+~E(x50581,f328(f328(f82(a877),x50582),x50583))
% 81.29/80.91 [5059]E(f45(a1,x50591,x50592),f2(a1))+~E(x50591,f328(f328(f82(a1),x50592),x50593))
% 81.29/80.91 [5119]E(x51191,x51192)+~E(f328(f328(f81(a877),x51193),x51191),f328(f328(f81(a877),x51193),x51192))
% 81.29/80.91 [5120]E(x51201,x51202)+~E(f328(f328(f81(a877),x51201),x51203),f328(f328(f81(a877),x51202),x51203))
% 81.29/80.91 [5130]~P67(x51301)+E(f328(f328(f81(x51301),x51302),f328(f80(x51301),x51303)),f328(f328(f22(x51301),x51302),x51303))
% 81.29/80.91 [5131]~P73(x51311)+E(f328(f328(f81(x51311),x51312),f328(f80(x51311),x51313)),f328(f328(f22(x51311),x51312),x51313))
% 81.29/80.91 [5132]~P114(x51321)+E(f328(f328(f81(x51321),x51322),f328(f80(x51321),x51323)),f328(f328(f22(x51321),x51322),x51323))
% 81.29/80.91 [5133]~P97(x51331)+E(f328(f328(f107(x51331),x51332),f328(f80(x51331),x51333)),f328(f328(f22(x51331),x51332),x51333))
% 81.29/80.91 [5134]~P73(x51341)+E(f328(f328(f22(x51341),x51342),f328(f80(x51341),x51343)),f328(f328(f81(x51341),x51342),x51343))
% 81.29/80.91 [5181]~P24(f328(x51813,x51812))+P24(f328(f328(f330(x51811),x51812),x51813))
% 81.29/80.91 [5183]~P74(x51832)+E(f328(f328(f6(x51831,x51832),x51833),f193(f885(x51831,a871))),f2(x51832))
% 81.29/80.91 [5185]~P75(x51852)+E(f328(f328(f9(x51851,x51852),x51853),f193(f885(x51851,a871))),f79(x51852))
% 81.29/80.91 [5234]~E(x52342,f328(f328(f81(a877),x52341),x52343))+P24(f328(f328(f244(a877),x52341),x52342))
% 81.29/80.91 [5237]~E(x52372,f193(f885(x52371,a871)))+E(f328(f328(f61(x52371),x52372),x52373),f193(f885(f885(x52371,a871),a871)))
% 81.29/80.91 [5238]~E(x52382,f193(f885(x52381,a871)))+E(f193(f885(f885(x52381,a871),a871)),f328(f328(f61(x52381),x52382),x52383))
% 81.29/80.91 [5314]~E(f328(f253(x53142,x53143),x53141),f193(f885(x53143,a871)))+E(x53141,f193(f885(f884(x53142,x53143),a871)))
% 81.29/80.91 [5315]~E(f328(f255(x53152,x53153),x53151),f193(f885(x53152,a871)))+E(x53151,f193(f885(f884(x53152,x53153),a871)))
% 81.29/80.91 [5346]E(f328(f253(x53461,x53462),x53463),f193(f885(x53462,a871)))+~E(x53463,f193(f885(f884(x53461,x53462),a871)))
% 81.29/80.91 [5347]E(f328(f255(x53471,x53472),x53473),f193(f885(x53471,a871)))+~E(x53473,f193(f885(f884(x53471,x53472),a871)))
% 81.29/80.91 [5351]E(f278(x53511,x53512,x53513),f328(f328(f22(a105),x53512),x53513))+P24(f328(f328(f245(a105),x53512),x53513))
% 81.29/80.91 [5367]P24(f328(x53671,x53672))+~P24(f328(f328(f330(x53673),x53672),x53671))
% 81.29/80.91 [5406]E(x54061,x54062)+~E(f328(f80(f885(x54063,a871)),x54061),f328(f80(f885(x54063,a871)),x54062))
% 81.29/80.91 [5411]E(f310(x54111,x54112,x54113),f196(f878(a324)))+~P24(f328(f328(f245(a1),x54112),x54113))
% 81.29/80.91 [5416]~E(x54161,f193(f885(x54162,a871)))+~P24(f328(f328(f330(x54162),x54163),x54161))
% 81.29/80.91 [5445]~E(x54452,f328(f328(f81(a1),x54451),f328(f106(a1),x54453)))+P24(f328(f328(f244(a1),x54451),x54452))
% 81.29/80.91 [5461]E(f328(f328(f306(x54611),x54612),x54613),x54613)+~P24(f328(f328(f330(x54611),x54612),x54613))
% 81.29/80.91 [5472]E(x54721,f193(f885(x54722,a871)))+~E(f328(f328(f61(x54722),x54721),x54723),f193(f885(f885(x54722,a871),a871)))
% 81.29/80.91 [5473]E(x54731,f193(f885(x54732,a871)))+~E(f193(f885(f885(x54732,a871),a871)),f328(f328(f61(x54732),x54731),x54733))
% 81.29/80.91 [5480]~P109(x54801)+E(f328(f328(f82(x54801),f328(f80(x54801),x54802)),f328(f80(x54801),x54803)),f328(f328(f82(x54801),x54802),x54803))
% 81.29/80.91 [5481]~P61(x54811)+E(f328(f328(f286(x54811),f328(f80(x54811),x54812)),f328(f80(x54811),x54813)),f328(f328(f286(x54811),x54812),x54813))
% 81.29/80.91 [5514]~P24(f328(x55143,x55142))+P24(f328(f328(f330(x55141),x55142),f328(f249(x55141),x55143)))
% 81.29/80.91 [5552]E(f169(x55521,x55522,x55523),x55523)+P24(f328(f328(f330(x55521),x55522),f328(f171(x55521),x55523)))
% 81.29/80.91 [5633]~P24(f328(f136(x56331),x56333))+P24(f328(f136(x56331),f328(f135(x56331,x56332),x56333)))
% 81.29/80.91 [5678]~P58(x56781)+E(f328(f328(f39(x56781),f45(x56781,x56782,x56783)),x56783),f2(x56781))
% 81.29/80.91 [5697]E(f175(x56971,f328(f328(f150(x56971),x56972),f119(x56971)),x56973),f119(x56971))+P24(f328(f328(f330(a877),f2(a877)),x56973))
% 81.29/80.91 [5754]E(f328(f328(f150(x57541),x57542),x57543),f139(x57541,x57542,x57543))+P24(f328(f328(f330(x57541),x57542),f328(f171(x57541),x57543)))
% 81.29/80.91 [5763]E(x57631,x57632)+~E(f328(f328(f82(a877),f328(a118,x57633)),x57631),f328(f328(f82(a877),f328(a118,x57633)),x57632))
% 81.29/80.91 [5764]~E(x57642,f328(f328(f81(a1),x57641),f328(f106(a1),f328(a118,x57643))))+P24(f328(f328(f245(a1),x57641),x57642))
% 81.29/80.91 [5869]~E(x58693,f119(x58691))+E(f328(f328(f328(f188(f878(x58691),f878(x58691)),x58692),f167(x58691)),x58693),f119(x58691))
% 81.29/80.91 [5873]P24(f328(x58731,x58732))+~P24(f328(f328(f330(x58733),x58732),f328(f249(x58733),x58731)))
% 81.29/80.91 [5905]E(x59051,x59052)+~E(f328(f328(f306(x59053),x59051),f193(f885(x59053,a871))),f328(f328(f306(x59053),x59052),f193(f885(x59053,a871))))
% 81.29/80.91 [5916]~P108(x59161)+E(f328(f328(f107(f885(x59161,a871)),f328(f250(x59161),x59162)),f328(f298(x59161,x59162),x59163)),f193(f885(x59161,a871)))
% 81.29/80.91 [5959]E(f139(x59591,x59592,x59593),x59593)+~P24(f328(f328(f330(x59591),x59592),f328(f171(x59591),x59593)))
% 81.29/80.91 [5983]~P80(x59831)+E(f328(f307(x59831,x59831,f80(x59831)),f328(f298(x59831,x59832),x59833)),f301(x59831,f328(f80(x59831),x59833),f328(f80(x59831),x59832)))
% 81.29/80.91 [5991]E(f328(f194(f878(x59911)),f169(x59911,x59912,x59913)),f328(f194(f878(x59911)),x59913))+P24(f328(f328(f330(x59911),x59912),f328(f171(x59911),x59913)))
% 81.29/80.91 [6045]~P108(x60451)+E(f328(f328(f107(f885(x60451,a871)),f328(f298(x60451,x60452),x60453)),f328(f251(x60451),x60453)),f193(f885(x60451,a871)))
% 81.29/80.91 [6068]~P80(x60681)+E(f328(f307(x60681,x60681,f80(x60681)),f302(x60681,x60682,x60683)),f302(x60681,f328(f80(x60681),x60683),f328(f80(x60681),x60682)))
% 81.29/80.91 [6069]~P80(x60691)+E(f328(f307(x60691,x60691,f80(x60691)),f299(x60691,x60692,x60693)),f299(x60691,f328(f80(x60691),x60693),f328(f80(x60691),x60692)))
% 81.29/80.91 [6126]E(f175(x61261,f328(f328(f150(x61261),x61262),f119(x61261)),x61263),f328(f328(f150(x61261),x61262),f119(x61261)))+~P24(f328(f328(f330(a877),f2(a877)),x61263))
% 81.29/80.91 [6133]~P80(x61331)+E(f328(f307(x61331,x61331,f80(x61331)),f301(x61331,x61332,x61333)),f328(f298(x61331,f328(f80(x61331),x61333)),f328(f80(x61331),x61332)))
% 81.29/80.91 [6153]~P59(x61531)+E(f45(x61531,f328(f80(x61531),f45(x61531,x61532,x61533)),x61533),f45(x61531,f328(f80(x61531),x61532),x61533))
% 81.29/80.91 [6256]~P24(f328(f62(f884(x62562,x62561)),x62563))+P24(f328(f62(x62561),f328(f253(x62562,x62561),x62563)))
% 81.29/80.91 [6257]~P24(f328(f62(f884(x62571,x62572)),x62573))+P24(f328(f62(x62571),f328(f255(x62571,x62572),x62573)))
% 81.29/80.91 [6263]~P108(x62631)+E(f328(f328(f107(f885(x62631,a871)),f302(x62631,x62632,x62633)),f328(f251(x62631),x62633)),f193(f885(x62631,a871)))
% 81.29/80.91 [6264]~P108(x62641)+E(f328(f328(f107(f885(x62641,a871)),f301(x62641,x62642,x62643)),f328(f300(x62641),x62643)),f193(f885(x62641,a871)))
% 81.29/80.91 [6265]~P108(x62651)+E(f328(f328(f107(f885(x62651,a871)),f299(x62651,x62652,x62653)),f328(f300(x62651),x62653)),f193(f885(x62651,a871)))
% 81.29/80.91 [6331]E(f328(f328(f164(x63311),x63312),f581(x63312,x63313,x63311)),x63313)+~P24(f328(f328(f330(x63311),x63313),f328(f171(x63311),x63312)))
% 81.29/80.91 [6473]E(x64731,f119(x64732))+~E(f328(f328(f328(f188(f878(x64732),f878(x64732)),x64733),f167(x64732)),x64731),f119(x64732))
% 81.29/80.91 [6576]~P24(f328(f62(f884(x65762,x65761)),x65763))+P24(f328(f62(f884(x65761,x65762)),f328(f283(x65762,x65761),x65763)))
% 81.29/80.91 [6728]P53(x67281,x67282,x67283)+P24(f328(f328(f330(x67281),f764(x67283,x67282,x67281)),x67282))
% 81.29/80.91 [6729]P53(x67291,x67292,x67293)+P24(f328(f328(f330(x67291),f763(x67293,x67292,x67291)),x67292))
% 81.29/80.91 [6741]P24(f328(f316(x67411,x67412),x67413))+P24(f328(f328(x67412,f477(x67413,x67412,x67411)),x67413))
% 81.29/80.91 [6742]P24(f328(f316(x67421,x67422),x67423))+P24(f328(f328(x67422,f487(x67423,x67422,x67421)),x67423))
% 81.29/80.91 [6773]E(f328(f194(f878(x67731)),f169(x67731,x67732,x67733)),f328(f328(f22(a877),f328(f194(f878(x67731)),x67733)),f79(a877)))+~P24(f328(f328(f330(x67731),x67732),f328(f171(x67731),x67733)))
% 81.29/80.91 [6813]P24(f328(f262(x68131,x68132),x68133))+P24(f328(f328(f330(x68131),f602(x68133,x68132,x68131)),x68133))
% 81.29/80.91 [6823]~P24(f328(f62(f884(x68232,x68231)),f328(f283(x68231,x68232),x68233)))+P24(f328(f62(f884(x68231,x68232)),x68233))
% 81.29/80.91 [6879]~P24(f328(f328(f330(x68791),x68792),f328(f171(x68791),f120(x68791,x68793))))+P24(f328(f328(f330(x68791),x68792),f328(f171(x68791),x68793)))
% 81.29/80.91 [6884]P23(x68841,x68842,x68843)+P24(f328(f328(f330(f876(x68841)),f610(x68843,x68842,x68841)),x68843))
% 81.29/80.91 [6911]E(f328(f135(x69111,x69112),x69113),x69113)+P24(f328(f328(f330(x69111),f599(x69113,x69112,x69111)),f328(f171(x69111),x69113)))
% 81.29/80.91 [6926]E(f328(f135(x69261,x69262),x69263),f119(x69261))+P24(f328(f328(f330(x69261),f598(x69263,x69262,x69261)),f328(f171(x69261),x69263)))
% 81.29/80.91 [6949]P32(x69491,x69492,x69493)+P24(f328(f328(f330(x69491),f793(x69493,x69492,x69491)),f328(f171(x69491),x69493)))
% 81.29/80.91 [6950]P32(x69501,x69502,x69503)+P24(f328(f328(f330(x69501),f805(x69503,x69502,x69501)),f328(f171(x69501),x69503)))
% 81.29/80.91 [6951]P32(x69511,x69512,x69513)+P24(f328(f328(f330(x69511),f804(x69512,x69513,x69511)),f328(f171(x69511),x69513)))
% 81.29/80.91 [6954]E(f176(x69541,x69542,x69543),x69543)+P24(f328(f328(f330(x69541),f647(x69543,x69542,x69541)),f328(f171(x69541),x69543)))
% 81.29/80.91 [7035]P24(f328(f159(x70351,x70352),x70353))+P24(f328(f328(f330(x70351),f664(x70353,x70352,x70351)),f328(f171(x70351),x70353)))
% 81.29/80.91 [7044]~P34(x70441,x70443,x70442)+P24(f328(f328(f330(x70441),f757(x70442,x70443,x70441)),f328(f171(x70441),x70442)))
% 81.29/80.91 [7045]~P36(x70451,x70453,x70452)+P24(f328(f328(f330(x70451),f807(x70452,x70453,x70451)),f328(f171(x70451),x70452)))
% 81.29/80.91 [7080]P24(f328(f328(f330(x70801),x70802),f382(x70803,x70802,x70801)))+~P24(f328(f328(f330(x70801),x70802),f40(f885(x70801,a871),x70803)))
% 81.29/80.91 [7081]~P74(x70811)+E(f328(f328(f81(x70811),f328(f328(f6(a877,x70811),x70812),f328(f250(a877),x70813))),f328(x70812,x70813)),f328(f328(f6(a877,x70811),x70812),f328(f250(a877),f328(a118,x70813))))
% 81.29/80.91 [7170]~P34(x71702,x71701,x71703)+P24(f328(x71701,f328(f328(f164(x71702),x71703),f754(x71703,x71701,x71702))))
% 81.29/80.91 [7183]~P24(f328(f328(f330(x71831),x71832),f383(x71832,x71833,x71831)))+P24(f328(f328(f330(x71831),x71832),f41(f885(x71831,a871),x71833)))
% 81.29/80.91 [7213]~P74(x72131)+E(f328(f328(f81(x72131),f328(f328(f6(a877,x72131),x72132),f328(f297(a877),x72133))),f328(x72132,f328(a118,x72133))),f328(f328(f6(a877,x72131),x72132),f328(f297(a877),f328(a118,x72133))))
% 81.29/80.91 [7348]P24(f328(f328(f330(f878(x73481)),x73482),f160(x73481,x73483)))+P24(f328(f328(f330(x73481),f626(x73483,x73482,x73481)),f328(f171(x73481),x73482)))
% 81.29/80.91 [7365]~P24(f328(f328(f330(f878(x73651)),x73652),f160(x73651,f317(x73651,x73653))))+P24(f328(f328(f330(f878(x73651)),x73652),f317(f878(x73651),f156(x73651,x73653))))
% 81.29/80.91 [7391]~P24(f328(f328(f330(f878(x73911)),x73912),f317(f878(x73911),f156(x73911,x73913))))+P24(f328(f328(f330(f878(x73911)),x73912),f160(x73911,f317(x73911,x73913))))
% 81.29/80.91 [7427]E(f328(f328(f328(f188(f878(x74271),f878(x74271)),x74272),f167(x74271)),x74273),x74273)+~P24(f328(f328(f244(a877),f328(f194(f878(x74271)),x74273)),f79(a877)))
% 81.29/80.91 [7463]E(f328(f328(f127(x74631),f758(x74632,x74633,x74631)),f328(f328(f150(x74631),x74633),f759(x74632,x74633,x74631))),x74632)+~P24(f328(f328(f330(x74631),x74633),f328(f171(x74631),x74632)))
% 81.29/80.91 [7464]E(f328(f328(f127(x74641),f769(x74642,x74643,x74641)),f328(f328(f150(x74641),x74643),f789(x74642,x74643,x74641))),x74642)+~P24(f328(f328(f330(x74641),x74643),f328(f171(x74641),x74642)))
% 81.29/80.91 [7465]E(f328(f328(f127(x74651),f790(x74652,x74653,x74651)),f328(f328(f150(x74651),x74653),f792(x74652,x74653,x74651))),x74652)+~P24(f328(f328(f330(x74651),x74653),f328(f171(x74651),x74652)))
% 81.29/80.91 [7486]~P21(x74861,x74862,x74863,f252(f885(x74861,a871)))+P21(f878(x74861),f878(x74862),f328(f153(x74861,x74862),x74863),f252(f885(f878(x74861),a871)))
% 81.29/80.91 [7634]E(x76341,f328(f328(f81(a877),f328(f328(f82(a877),f328(f256(a877,a877),x76342)),x76343)),f328(f266(a877,a877),x76342)))+~P24(f328(f48(x76341,x76343),x76342))
% 81.29/80.91 [7642]P21(x76421,x76422,x76423,f252(f885(x76421,a871)))+~P21(f878(x76421),f878(x76422),f328(f153(x76421,x76422),x76423),f252(f885(f878(x76421),a871)))
% 81.29/80.91 [7680]~P24(f328(f328(f200(x76801),x76802),x76803))+P24(f328(f328(f328(f328(a202,x76801),x76802),f603(x76803,x76802,x76801)),x76803))
% 81.29/80.91 [7684]P24(f328(f328(f330(f885(x76841,a871)),f383(x76842,x76843,x76841)),x76843))+P24(f328(f328(f330(x76841),x76842),f41(f885(x76841,a871),x76843)))
% 81.29/80.91 [7776]P24(f328(f328(f330(f878(x77761)),x77762),f160(x77761,x77763)))+~P24(f328(f328(f330(x77761),f626(x77763,x77762,x77761)),x77763))
% 81.29/80.91 [7876]P32(x78761,x78762,x78763)+~P24(f328(x78762,f328(f328(f164(x78761),x78763),f794(x78763,x78762,x78761))))
% 81.29/80.91 [7901]E(x79011,x79012)+~E(f328(f328(f7(x79013,f885(x79013,a871),a871),f330(x79013)),x79011),f328(f328(f7(x79013,f885(x79013,a871),a871),f330(x79013)),x79012))
% 81.29/80.91 [7907]~P24(f328(f328(f330(f884(x79071,x79071)),x79073),f254(x79071,x79072)))+P24(f328(f328(f330(x79071),f535(x79072,x79073,x79071)),x79072))
% 81.29/80.91 [7909]~P24(f328(f328(f330(x79091),x79093),f40(f885(x79091,a871),x79092)))+P24(f328(f328(f330(f885(x79091,a871)),f382(x79092,x79093,x79091)),x79092))
% 81.29/80.91 [8091]~P24(f328(f328(f330(x80911),x80912),f328(f171(x80911),f769(x80913,x80912,x80911))))+~P24(f328(f328(f330(x80911),x80912),f328(f171(x80911),x80913)))
% 81.29/80.91 [8092]~P24(f328(f328(f330(x80921),x80922),f328(f171(x80921),f792(x80923,x80922,x80921))))+~P24(f328(f328(f330(x80921),x80922),f328(f171(x80921),x80923)))
% 81.29/80.91 [8182]E(f328(f238(f881(f878(a324)),f878(a324),f310(x81821,x81822,f328(f328(f81(a1),x81823),f79(a1))),f236(f878(a324))),f328(x81821,x81823)),f310(x81821,x81822,x81823))+P24(f328(f328(f245(a1),x81822),x81823))
% 81.29/80.91 [8284]E(x82841,f119(x82842))+P24(f328(f328(f330(x82842),f328(f256(x82842,f884(a105,a105)),f328(f279(x82842,x82841),x82843))),f328(f171(x82842),x82841)))
% 81.29/80.91 [8380]~P68(x83801)+E(f328(f141(x83801,x83801,f328(f7(x83801,x83801,x83801),f81(x83801)),x83802),f328(f168(x83801),x83803)),f328(f141(x83801,x83801,f81(x83801),x83802),x83803))
% 81.29/80.91 [8872]~P106(x88721)+E(f328(f171(x88721),f148(x88721,x88721,f5(x88721),x88722,x88723)),f328(f328(f306(x88721),x88722),f328(f171(x88721),x88723)))
% 81.29/80.91 [8883]P24(f328(f328(f245(a877),f2(a877)),f773(x88831,x88832,x88833)))+~P24(f328(f328(f330(f884(x88833,x88833)),x88832),f328(f328(f285(x88833,x88833,x88833),x88831),f304(x88833,x88831))))
% 81.29/80.91 [9171]~P55(x91711,x91712)+~P24(f328(f328(f330(f884(x91711,x91711)),f328(f328(f257(x91711,x91711),x91713),x91713)),f328(f328(f285(x91711,x91711,x91711),x91712),f304(x91711,x91712))))
% 81.29/80.91 [9304]~E(f328(f328(f107(f885(f884(x93041,x93041),a871)),f328(f283(x93041,x93041),x93042)),f304(x93041,x93042)),f193(f885(f884(x93041,x93041),a871)))+~P24(f328(f328(f330(f884(x93041,x93041)),f328(f328(f257(x93041,x93041),x93043),x93043)),f328(f328(f285(x93041,x93041,x93041),x93042),f304(x93041,x93042))))
% 81.29/80.91 [9482]~P24(f328(f62(x94821),x94822))+P24(f328(f328(f244(a877),f328(f38(x94821),f328(f328(f22(f885(x94821,a871)),x94822),f328(f328(f306(x94821),x94823),f193(f885(x94821,a871)))))),f328(f38(x94821),x94822)))
% 81.29/80.91 [5047]~E(x50473,f119(x50471))+E(f143(x50471,f328(f328(f150(x50471),x50472),x50473)),x50472)
% 81.29/80.91 [5055]~E(x50553,f119(x50551))+E(f120(x50551,f328(f328(f150(x50551),x50552),x50553)),f119(x50551))
% 81.29/80.91 [5083]E(x50831,f119(x50832))+E(f143(x50832,f328(f328(f150(x50832),x50833),x50831)),f143(x50832,x50831))
% 81.29/80.91 [5085]E(x50851,f119(x50852))+E(f143(x50852,f328(f328(f127(x50852),x50853),x50851)),f143(x50852,x50851))
% 81.29/80.91 [5091]~E(x50913,f119(x50911))+E(f143(x50911,f328(f328(f127(x50911),x50912),x50913)),f143(x50911,x50912))
% 81.29/80.91 [5092]~E(x50923,f119(x50921))+E(f120(x50921,f328(f328(f127(x50921),x50922),x50923)),f120(x50921,x50922))
% 81.29/80.91 [5124]E(x51241,f119(x51242))+E(f328(f140(x51242),f328(f328(f127(x51242),x51241),x51243)),f328(f140(x51242),x51241))
% 81.29/80.91 [5155]~E(x51552,f119(x51551))+E(f328(f140(x51551),f328(f328(f127(x51551),x51552),x51553)),f328(f140(x51551),x51553))
% 81.29/80.91 [5210]~P78(x52101)+E(f328(f328(f116(x52101),x52102),f328(f328(f107(x52101),x52102),x52103)),x52102)
% 81.29/80.91 [5211]~P78(x52111)+E(f328(f328(f107(x52111),x52112),f328(f328(f116(x52111),x52112),x52113)),x52112)
% 81.29/80.91 [5212]~P106(x52121)+E(f328(f328(f242(x52121),x52122),f328(f328(f243(x52121),x52122),x52123)),x52122)
% 81.29/80.91 [5213]~P106(x52131)+E(f328(f328(f243(x52131),x52132),f328(f328(f242(x52131),x52132),x52133)),x52132)
% 81.29/80.91 [5232]~P58(x52321)+E(f45(x52321,f328(f328(f82(x52321),x52322),x52323),x52323),f2(x52321))
% 81.29/80.91 [5233]~P58(x52331)+E(f45(x52331,f328(f328(f82(x52331),x52332),x52333),x52332),f2(x52331))
% 81.29/80.91 [5308]~P67(x53081)+E(f328(f80(x53081),f328(f328(f22(x53081),x53082),x53083)),f328(f328(f22(x53081),x53083),x53082))
% 81.29/80.91 [5371]E(x53711,f119(x53712))+E(f120(x53712,f328(f328(f150(x53712),x53713),x53711)),f328(f328(f150(x53712),x53713),f120(x53712,x53711)))
% 81.29/80.91 [5372]E(x53721,f119(x53722))+E(f120(x53722,f328(f328(f127(x53722),x53723),x53721)),f328(f328(f127(x53722),x53723),f120(x53722,x53721)))
% 81.29/80.91 [5375]~P27(x53751)+E(f40(x53751,f328(f328(f306(x53751),x53752),x53753)),f328(f328(f116(x53751),x53752),f40(x53751,x53753)))
% 81.29/80.91 [5376]~P27(x53761)+E(f41(x53761,f328(f328(f306(x53761),x53762),x53763)),f328(f328(f107(x53761),x53762),f41(x53761,x53763)))
% 81.29/80.91 [5422]~P65(x54221)+E(f328(f328(f116(x54221),x54222),f328(f328(f116(x54221),x54222),x54223)),f328(f328(f116(x54221),x54222),x54223))
% 81.29/80.91 [5423]~P78(x54231)+E(f328(f328(f116(x54231),x54232),f328(f328(f116(x54231),x54232),x54233)),f328(f328(f116(x54231),x54232),x54233))
% 81.29/80.91 [5424]~P78(x54241)+E(f328(f328(f107(x54241),x54242),f328(f328(f107(x54241),x54242),x54243)),f328(f328(f107(x54241),x54242),x54243))
% 81.29/80.91 [5426]~P102(x54261)+E(f328(f328(f107(x54261),x54262),f328(f328(f107(x54261),x54262),x54263)),f328(f328(f107(x54261),x54262),x54263))
% 81.29/80.91 [5427]~P98(x54271)+E(f328(f328(f82(x54271),x54272),f328(f328(f82(x54271),x54272),x54273)),f328(f328(f82(x54271),x54272),x54273))
% 81.29/80.91 [5429]~P106(x54291)+E(f328(f328(f242(x54291),x54292),f328(f328(f242(x54291),x54292),x54293)),f328(f328(f242(x54291),x54292),x54293))
% 81.29/80.91 [5431]~P106(x54311)+E(f328(f328(f243(x54311),x54312),f328(f328(f243(x54311),x54312),x54313)),f328(f328(f243(x54311),x54312),x54313))
% 81.29/80.91 [5439]~P58(x54391)+E(f45(x54391,f328(f328(f81(x54391),x54392),x54393),x54393),f45(x54391,x54392,x54393))
% 81.29/80.91 [5440]~P58(x54401)+E(f45(x54401,f328(f328(f81(x54401),x54402),x54403),x54402),f45(x54401,x54403,x54402))
% 81.29/80.91 [5446]~P109(x54461)+E(f328(f328(f82(x54461),x54462),f328(f80(x54461),x54463)),f328(f80(x54461),f328(f328(f82(x54461),x54462),x54463)))
% 81.29/80.91 [5447]~P61(x54471)+E(f328(f328(f286(x54471),x54472),f328(f80(x54471),x54473)),f328(f80(x54471),f328(f328(f286(x54471),x54472),x54473)))
% 81.29/80.91 [5448]~P82(x54481)+E(f328(f328(f81(x54481),x54482),f328(f165(x54481),x54483)),f328(f165(x54481),f328(f328(f150(x54481),x54482),x54483)))
% 81.29/80.91 [5478]~P109(x54781)+E(f328(f328(f82(x54781),f328(f80(x54781),x54782)),x54783),f328(f328(f82(x54781),x54782),f328(f80(x54781),x54783)))
% 81.29/80.91 [5485]~P6(x54851,x54852,x54853)+E(f40(f885(x54851,a871),f328(f328(f61(x54851),x54852),x54853)),x54852)
% 81.29/80.91 [5544]~P116(x55441)+E(f328(f328(f82(x55441),x55442),f328(f328(f258(x55441),x55442),x55443)),f328(f328(f258(x55441),x55442),f328(a118,x55443)))
% 81.29/80.91 [5545]~P112(x55451)+E(f328(f328(f82(x55451),x55452),f328(f328(f258(x55451),x55452),x55453)),f328(f328(f258(x55451),x55452),f328(a118,x55453)))
% 81.29/80.91 [5555]~P73(x55551)+E(f328(f328(f81(x55551),f328(f80(x55551),x55552)),f328(f328(f81(x55551),x55552),x55553)),x55553)
% 81.29/80.91 [5578]~P141(x55781)+E(f328(f328(f258(x55781),f328(f106(x55781),x55782)),x55783),f328(f106(x55781),f328(f328(f258(a877),x55782),x55783)))
% 81.29/80.91 [5579]~P137(x55791)+E(f328(f328(f258(x55791),f328(f108(x55791),x55792)),x55793),f328(f108(x55791),f328(f328(f258(a1),x55792),x55793)))
% 81.29/80.91 [5584]~P87(x55841)+E(f328(f76(x55841),f328(f328(f22(x55841),x55842),x55843)),f328(f76(x55841),f328(f328(f22(x55841),x55843),x55842)))
% 81.29/80.91 [5586]~P111(x55861)+E(f328(f328(f82(x55861),f83(x55861,x55862)),f83(x55861,x55863)),f83(x55861,f328(f328(f82(x55861),x55862),x55863)))
% 81.29/80.91 [5590]E(x55901,f119(x55902))+E(f328(f328(f127(x55902),f328(f170(x55902),x55901)),x55903),f328(f170(x55902),f328(f328(f127(x55902),x55901),x55903)))
% 81.29/80.91 [5595]~E(x55952,f328(a118,f328(f328(f81(a877),x55951),x55953)))+P24(f328(f328(f245(a877),x55951),x55952))
% 81.29/80.91 [5596]~P111(x55961)+E(f328(f328(f258(x55961),f328(f76(x55961),x55962)),x55963),f328(f76(x55961),f328(f328(f258(x55961),x55962),x55963)))
% 81.29/80.91 [5597]~P109(x55971)+E(f328(f328(f82(x55971),f328(f80(x55971),x55972)),x55973),f328(f80(x55971),f328(f328(f82(x55971),x55972),x55973)))
% 81.29/80.91 [5598]~P120(x55981)+E(f328(f328(f286(x55981),f328(f80(x55981),x55982)),x55983),f328(f80(x55981),f328(f328(f286(x55981),x55982),x55983)))
% 81.29/80.91 [5696]E(f739(x56961,x56962,x56963),f767(x56961,x56962,x56963))+E(f328(f328(f107(f885(x56963,a871)),x56962),x56961),f193(f885(x56963,a871)))
% 81.29/80.91 [5710]~P74(x57102)+E(f328(f328(f6(x57101,x57102),f328(f16(x57102,x57101),f2(x57102))),x57103),f2(x57102))
% 81.29/80.91 [5711]~P75(x57112)+E(f328(f328(f9(x57111,x57112),f328(f16(x57112,x57111),f79(x57112))),x57113),f79(x57112))
% 81.29/80.91 [5713]~P96(x57131)+E(f328(f328(f22(x57131),f328(f109(x57131),x57132)),f328(f109(x57131),x57133)),f328(f109(x57131),f328(f328(f22(a1),x57132),x57133)))
% 81.29/80.91 [5716]~P141(x57161)+E(f328(f328(f81(x57161),f328(f106(x57161),x57162)),f328(f106(x57161),x57163)),f328(f106(x57161),f328(f328(f81(a877),x57162),x57163)))
% 81.29/80.91 [5717]~P141(x57171)+E(f328(f328(f82(x57171),f328(f106(x57171),x57172)),f328(f106(x57171),x57173)),f328(f106(x57171),f328(f328(f82(a877),x57172),x57173)))
% 81.29/80.91 [5718]~P137(x57181)+E(f328(f328(f22(x57181),f328(f108(x57181),x57182)),f328(f108(x57181),x57183)),f328(f108(x57181),f328(f328(f22(a1),x57182),x57183)))
% 81.29/80.91 [5719]~P137(x57191)+E(f328(f328(f81(x57191),f328(f108(x57191),x57192)),f328(f108(x57191),x57193)),f328(f108(x57191),f328(f328(f81(a1),x57192),x57193)))
% 81.29/80.91 [5720]~P137(x57201)+E(f328(f328(f82(x57201),f328(f108(x57201),x57202)),f328(f108(x57201),x57203)),f328(f108(x57201),f328(f328(f82(a1),x57202),x57203)))
% 81.29/80.91 [5721]~P96(x57211)+E(f328(f328(f81(x57211),f328(f109(x57211),x57212)),f328(f109(x57211),x57213)),f328(f109(x57211),f328(f328(f81(a1),x57212),x57213)))
% 81.29/80.91 [5722]~P96(x57221)+E(f328(f328(f82(x57221),f328(f109(x57221),x57222)),f328(f109(x57221),x57223)),f328(f109(x57221),f328(f328(f82(a1),x57222),x57223)))
% 81.29/80.91 [5771]~E(x57713,x57712)+P24(f328(f328(f244(f885(x57711,a871)),x57712),x57713))
% 81.29/80.91 [5777]~E(x57772,x57773)+P24(f328(f328(f244(f885(x57771,a871)),x57772),x57773))
% 81.29/80.91 [5782]~P111(x57821)+E(f328(f328(f82(x57821),f328(f76(x57821),x57822)),f328(f76(x57821),x57823)),f328(f76(x57821),f328(f328(f82(x57821),x57822),x57823)))
% 81.29/80.91 [5783]~P63(x57831)+E(f328(f328(f286(x57831),f328(f76(x57831),x57832)),f328(f76(x57831),x57833)),f328(f76(x57831),f328(f328(f286(x57831),x57832),x57833)))
% 81.29/80.91 [5784]~P97(x57841)+E(f328(f328(f107(x57841),f328(f80(x57841),x57842)),f328(f80(x57841),x57843)),f328(f80(x57841),f328(f328(f116(x57841),x57842),x57843)))
% 81.29/80.91 [5785]~P73(x57851)+E(f328(f328(f81(x57851),f328(f80(x57851),x57852)),f328(f80(x57851),x57853)),f328(f80(x57851),f328(f328(f81(x57851),x57853),x57852)))
% 81.29/80.91 [5786]~P67(x57861)+E(f328(f328(f81(x57861),f328(f80(x57861),x57862)),f328(f80(x57861),x57863)),f328(f80(x57861),f328(f328(f81(x57861),x57862),x57863)))
% 81.29/80.91 [5787]~P97(x57871)+E(f328(f328(f116(x57871),f328(f80(x57871),x57872)),f328(f80(x57871),x57873)),f328(f80(x57871),f328(f328(f107(x57871),x57872),x57873)))
% 81.29/80.91 [5788]~P76(x57881)+E(f328(f328(f243(x57881),f328(f80(x57881),x57882)),f328(f80(x57881),x57883)),f328(f80(x57881),f328(f328(f242(x57881),x57882),x57883)))
% 81.29/80.91 [5789]~P76(x57891)+E(f328(f328(f242(x57891),f328(f80(x57891),x57892)),f328(f80(x57891),x57893)),f328(f80(x57891),f328(f328(f243(x57891),x57892),x57893)))
% 81.29/80.91 [5790]~P82(x57901)+E(f328(f328(f81(x57901),f328(f165(x57901),x57902)),f328(f165(x57901),x57903)),f328(f165(x57901),f328(f328(f127(x57901),x57902),x57903)))
% 81.29/80.91 [5791]E(x57911,f193(f885(x57912,a871)))+~E(f328(f328(f116(f885(x57912,a871)),x57913),x57911),f193(f885(x57912,a871)))
% 81.29/80.91 [5792]E(x57921,f193(f885(x57922,a871)))+~E(f328(f328(f116(f885(x57922,a871)),x57921),x57923),f193(f885(x57922,a871)))
% 81.29/80.91 [5793]~P146(x57931,x57933,x57932)+P24(f328(x57931,f328(f328(f39(a1),x57932),x57933)))
% 81.29/80.91 [5843]~P24(f328(f62(x58431),x58433))+P24(f328(f62(x58431),f328(f328(f306(x58431),x58432),x58433)))
% 81.29/80.91 [5844]~P24(f328(f136(x58441),x58443))+P24(f328(f136(x58441),f328(f328(f174(x58441),x58442),x58443)))
% 81.29/80.91 [5845]~P24(f328(f136(x58451),x58453))+P24(f328(f136(x58451),f328(f328(f137(x58451),x58452),x58453)))
% 81.29/80.91 [5874]~P65(x58741)+P24(f328(f328(f244(x58741),x58742),f328(f328(f116(x58741),x58743),x58742)))
% 81.29/80.91 [5875]~P78(x58751)+P24(f328(f328(f244(x58751),x58752),f328(f328(f116(x58751),x58753),x58752)))
% 81.29/80.91 [5876]~P65(x58761)+P24(f328(f328(f244(x58761),x58762),f328(f328(f116(x58761),x58762),x58763)))
% 81.29/80.91 [5877]~P78(x58771)+P24(f328(f328(f244(x58771),x58772),f328(f328(f116(x58771),x58772),x58773)))
% 81.29/80.91 [5878]~P106(x58781)+P24(f328(f328(f244(x58781),x58782),f328(f328(f243(x58781),x58783),x58782)))
% 81.29/80.91 [5879]~P106(x58791)+P24(f328(f328(f244(x58791),x58792),f328(f328(f243(x58791),x58792),x58793)))
% 81.29/80.91 [5893]~E(x58931,f2(a877))+E(f328(f328(f39(a877),f328(f328(f82(a877),x58931),x58932)),f328(f328(f82(a877),x58931),x58933)),f2(a877))
% 81.29/80.91 [5962]P24(f328(x59621,x59622))+P24(f328(f328(f200(f33(x59621,x59623)),x59622),x59622))
% 81.29/80.91 [5977]~P96(x59771)+E(f328(f328(f22(x59771),f328(f109(x59771),x59772)),f328(f109(x59771),x59773)),f328(f109(x59771),f328(f328(f81(a1),x59772),f328(f80(a1),x59773))))
% 81.29/80.91 [6032]E(x60321,f2(a877))+E(f328(f328(f39(a877),f328(f328(f82(a877),x60321),x60322)),f328(f328(f82(a877),x60321),x60323)),f328(f328(f39(a877),x60322),x60323))
% 81.29/80.91 [6066]E(f151(x60661,f328(f328(f150(x60661),x60662),x60663)),f328(f328(f150(x60661),x60662),f151(x60661,x60663)))+P24(f328(f328(f330(x60661),x60662),f328(f171(x60661),x60663)))
% 81.29/80.91 [6100]P146(x61001,x61002,x61003)+~P24(f328(x61001,f328(f328(f39(a1),x61003),x61002)))
% 81.29/80.91 [6175]E(x61751,f119(x61752))+E(f328(f328(f150(x61752),f328(f140(x61752),x61751)),f328(f328(f174(x61752),x61753),f328(f170(x61752),x61751))),f328(f328(f174(x61752),f328(a118,x61753)),x61751))
% 81.29/80.91 [6181]E(f328(f328(f22(f885(x61811,a871)),x61812),x61813),x61812)+~E(f328(f328(f107(f885(x61811,a871)),x61812),x61813),f193(f885(x61811,a871)))
% 81.29/80.91 [6194]E(f151(x61941,f328(f328(f150(x61941),x61942),x61943)),f151(x61941,x61943))+~P24(f328(f328(f330(x61941),x61942),f328(f171(x61941),x61943)))
% 81.29/80.91 [6226]~P24(f328(f328(f244(a877),x62261),x62263))+P24(f328(f328(f244(a877),x62261),f328(f328(f81(a877),x62262),x62263)))
% 81.29/80.91 [6228]~P24(f328(f328(f244(a877),x62281),x62282))+P24(f328(f328(f244(a877),x62281),f328(f328(f81(a877),x62282),x62283)))
% 81.29/80.91 [6230]~P24(f328(f328(f245(a877),x62301),x62303))+P24(f328(f328(f245(a877),x62301),f328(f328(f81(a877),x62302),x62303)))
% 81.29/80.91 [6232]~P24(f328(f328(f245(a877),x62321),x62322))+P24(f328(f328(f245(a877),x62321),f328(f328(f81(a877),x62322),x62323)))
% 81.29/80.91 [6271]P24(f328(f62(x62711),x62712))+~P24(f328(f62(x62711),f328(f328(f306(x62711),x62713),x62712)))
% 81.29/80.91 [6272]P24(f328(f136(x62721),x62722))+~P24(f328(f136(x62721),f328(f328(f150(x62721),x62723),x62722)))
% 81.29/80.91 [6273]P24(f328(f136(x62731),x62732))+~P24(f328(f136(x62731),f328(f328(f127(x62731),x62733),x62732)))
% 81.29/80.91 [6274]P24(f328(f136(x62741),x62742))+~P24(f328(f136(x62741),f328(f328(f127(x62741),x62742),x62743)))
% 81.29/80.91 [6320]~P112(x63201)+E(f328(f328(f81(x63201),x63202),f328(f328(f82(x63201),x63203),x63202)),f328(f328(f82(x63201),f328(f328(f81(x63201),x63203),f79(x63201))),x63202))
% 81.29/80.91 [6369]~E(x63691,x63692)+~P24(f328(f328(f245(f885(x63693,a871)),x63691),x63692))
% 81.29/80.91 [6413]P24(f328(f328(f330(x64131),x64132),x64133))+P24(f328(f328(f330(x64131),x64132),f328(f80(f885(x64131,a871)),x64133)))
% 81.29/80.91 [6419]E(f143(x64191,f328(f328(f137(x64191),x64192),x64193)),f143(x64191,x64193))+~P24(f328(f328(f245(a877),x64192),f328(f194(f878(x64191)),x64193)))
% 81.29/80.91 [6420]E(f328(f328(f174(x64201),x64202),f120(x64201,x64203)),f328(f328(f174(x64201),x64202),x64203))+~P24(f328(f328(f245(a877),x64202),f328(f194(f878(x64201)),x64203)))
% 81.29/80.91 [6475]E(f328(f328(f328(f188(f878(x64751),f878(x64751)),x64752),f167(x64751)),x64753),x64753)+~E(f45(a877,x64752,f328(f194(f878(x64751)),x64753)),f2(a877))
% 81.29/80.91 [6482]~P6(x64821,x64823,x64822)+E(f328(f328(f285(x64821,x64821,x64821),f328(f283(x64821,x64821),x64822)),x64822),x64822)
% 81.29/80.91 [6525]~E(f328(f328(f116(f885(x65251,a871)),x65252),x65253),x65253)+P24(f328(f328(f244(f885(x65251,a871)),x65252),x65253))
% 81.29/80.91 [6530]~P52(x65301,x65301,x65303)+P52(x65301,x65301,f328(f328(f188(f884(x65301,x65301),a871),x65302),x65303))
% 81.29/80.91 [6532]~P24(f328(f328(f330(x65321),x65323),f328(f171(x65321),x65322)))+P24(f328(f328(f245(a877),f2(a877)),f328(f194(f878(x65321)),x65322)))
% 81.29/80.91 [6558]~P87(x65581)+E(f328(f76(x65581),f328(f328(f81(x65581),f328(f76(x65581),x65582)),f328(f76(x65581),x65583))),f328(f328(f81(x65581),f328(f76(x65581),x65582)),f328(f76(x65581),x65583)))
% 81.29/80.91 [6569]E(f328(f328(f39(a877),f328(f328(f82(a877),x65691),x65692)),f328(f328(f82(a877),x65691),x65693)),f328(f328(f39(a877),x65692),x65693))+~P24(f328(f328(f245(a877),f2(a877)),x65691))
% 81.29/80.91 [6617]E(x66171,x66172)+~P24(f328(f328(f328(f328(a202,a24),x66171),x66173),x66172))
% 81.29/80.91 [6707]~P24(f328(f62(x67071),x67073))+E(f328(f328(f65(x67071,f885(x67071,a871),f306(x67071)),x67072),x67073),f328(f328(f116(f885(x67071,a871)),x67073),x67072))
% 81.29/80.91 [6766]E(f328(f328(f116(f885(x67661,a871)),x67662),x67663),x67662)+~P24(f328(f328(f244(f885(x67661,a871)),x67663),x67662))
% 81.29/80.91 [6768]E(f328(f328(f116(f885(x67681,a871)),x67682),x67683),x67683)+~P24(f328(f328(f244(f885(x67681,a871)),x67682),x67683))
% 81.29/80.91 [6769]E(f328(f328(f107(f885(x67691,a871)),x67692),x67693),x67693)+~P24(f328(f328(f244(f885(x67691,a871)),x67693),x67692))
% 81.29/80.91 [6770]E(f328(f328(f107(f885(x67701,a871)),x67702),x67703),x67702)+~P24(f328(f328(f244(f885(x67701,a871)),x67702),x67703))
% 81.29/80.91 [6821]~P24(f328(f136(x68211),x68212))+E(f328(f328(f22(f885(x68211,a871)),f328(f171(x68211),x68212)),f328(f328(f306(x68211),x68213),f193(f885(x68211,a871)))),f328(f171(x68211),f169(x68211,x68213,x68212)))
% 81.29/80.91 [6874]P38(x68741,x68742)+~P38(x68741,f328(f328(f188(f884(x68741,x68741),a871),x68743),x68742))
% 81.29/80.91 [6937]P24(f328(f49(x69371,x69372),f328(a51,x69373)))+~P24(f328(f49(f328(f80(a1),x69371),f328(f80(a1),x69372)),x69373))
% 81.29/80.91 [6942]E(f328(f328(f22(f885(x69421,a871)),f328(f328(f306(x69421),x69422),x69423)),f328(f328(f306(x69421),x69422),f193(f885(x69421,a871)))),x69423)+P24(f328(f328(f330(x69421),x69422),x69423))
% 81.29/80.91 [6963]E(f328(f328(f107(f885(x69631,a871)),f328(f171(x69631),x69632)),f328(f171(x69631),x69633)),f193(f885(x69631,a871)))+~P24(f328(f136(x69631),f328(f328(f127(x69631),x69632),x69633)))
% 81.29/80.91 [6979]~P24(f328(f328(f330(x69791),x69792),f328(f171(x69791),x69793)))+~P24(f328(f136(x69791),f328(f328(f150(x69791),x69792),x69793)))
% 81.29/80.91 [7051]P32(x70511,x70512,x70513)+P24(f328(f328(f245(a877),f794(x70513,x70512,x70511)),f328(f194(f878(x70511)),x70513)))
% 81.29/80.91 [7061]E(f328(f328(f107(f885(x70611,a871)),x70612),x70613),f193(f885(x70611,a871)))+P24(f328(f328(f330(x70611),f739(x70613,x70612,x70611)),x70612))
% 81.29/80.91 [7062]E(f328(f328(f107(f885(x70621,a871)),x70622),x70623),f193(f885(x70621,a871)))+P24(f328(f328(f330(x70621),f767(x70623,x70622,x70621)),x70623))
% 81.29/80.91 [7066]E(f120(x70661,f328(f328(f174(x70661),x70662),x70663)),f328(f328(f174(x70661),f328(f328(f22(a877),x70662),f79(a877))),x70663))+~P24(f328(f328(f244(a877),x70662),f328(f194(f878(x70661)),x70663)))
% 81.29/80.91 [7125]~P34(x71253,x71252,x71251)+P24(f328(f328(f245(a877),f754(x71251,x71252,x71253)),f328(f194(f878(x71253)),x71251)))
% 81.29/80.91 [7143]P24(f328(f328(f245(a877),f2(a877)),x71431))+P24(f328(f328(f244(a877),f328(f328(f82(a877),x71432),x71431)),f328(f328(f82(a877),x71433),x71431)))
% 81.29/80.91 [7144]P24(f328(f328(f245(a877),f2(a877)),x71441))+P24(f328(f328(f244(a877),f328(f328(f82(a877),x71441),x71442)),f328(f328(f82(a877),x71441),x71443)))
% 81.29/80.91 [7147]~P24(f328(f328(f330(x71471),x71472),x71473))+~P24(f328(f328(f330(x71471),x71472),f328(f80(f885(x71471,a871)),x71473)))
% 81.29/80.91 [7154]~P24(f328(f328(f245(f885(x71541,a871)),x71542),x71543))+P24(f328(f328(f244(f885(x71541,a871)),x71542),x71543))
% 81.29/80.91 [7253]~P24(f328(f328(f244(a877),x72533),x72532))+P24(f328(f328(f244(a877),f328(f328(f22(a877),x72531),x72532)),f328(f328(f22(a877),x72531),x72533)))
% 81.29/80.91 [7254]~P24(f328(f328(f244(a877),x72541),x72543))+P24(f328(f328(f244(a877),f328(f328(f22(a877),x72541),x72542)),f328(f328(f22(a877),x72543),x72542)))
% 81.29/80.91 [7255]~P24(f328(f328(f244(a877),x72552),x72553))+P24(f328(f328(f244(a877),f328(f328(f81(a877),x72551),x72552)),f328(f328(f81(a877),x72551),x72553)))
% 81.29/80.91 [7256]~P24(f328(f328(f244(a877),x72561),x72563))+P24(f328(f328(f244(a877),f328(f328(f81(a877),x72561),x72562)),f328(f328(f81(a877),x72563),x72562)))
% 81.29/80.91 [7258]~P24(f328(f328(f244(a877),x72582),x72583))+P24(f328(f328(f244(a877),f328(f328(f82(a877),x72581),x72582)),f328(f328(f82(a877),x72581),x72583)))
% 81.29/80.91 [7260]~P24(f328(f328(f244(a877),x72601),x72603))+P24(f328(f328(f244(a877),f328(f328(f82(a877),x72601),x72602)),f328(f328(f82(a877),x72603),x72602)))
% 81.29/80.91 [7261]~P24(f328(f328(f244(a877),x72611),x72613))+P24(f328(f328(f244(a877),f328(f328(f39(a877),x72611),x72612)),f328(f328(f39(a877),x72613),x72612)))
% 81.29/80.91 [7262]~P24(f328(f328(f244(a1),x72622),x72623))+P24(f328(f328(f244(a1),f328(f328(f81(a1),x72621),x72622)),f328(f328(f81(a1),x72621),x72623)))
% 81.29/80.91 [7265]~P24(f328(f328(f245(a877),x72652),x72653))+P24(f328(f328(f245(a877),f328(f328(f81(a877),x72651),x72652)),f328(f328(f81(a877),x72651),x72653)))
% 81.29/80.91 [7266]~P24(f328(f328(f245(a877),x72661),x72663))+P24(f328(f328(f245(a877),f328(f328(f81(a877),x72661),x72662)),f328(f328(f81(a877),x72663),x72662)))
% 81.29/80.91 [7267]~P24(f328(f328(f245(a1),x72671),x72673))+P24(f328(f328(f245(a1),f328(f328(f81(a1),x72671),x72672)),f328(f328(f81(a1),x72673),x72672)))
% 81.29/80.91 [7347]E(x73471,x73472)+~P24(f328(f328(f330(x73473),x73471),f328(f328(f306(x73473),x73472),f193(f885(x73473,a871)))))
% 81.29/80.91 [7349]~E(f328(f328(f107(f885(x73491,a871)),x73492),x73493),f193(f885(x73491,a871)))+P24(f328(f328(f244(f885(x73491,a871)),x73492),f328(f80(f885(x73491,a871)),x73493)))
% 81.29/80.91 [7357]P24(f328(f328(f330(f885(x73571,a871)),x73572),f328(f305(x73571),x73573)))+~P24(f328(f328(f244(f885(x73571,a871)),x73572),x73573))
% 81.29/80.91 [7411]E(f328(f328(f150(x74111),f328(f328(f164(x74111),x74112),x74113)),f328(f328(f137(x74111),f328(a118,x74113)),x74112)),f328(f328(f137(x74111),x74113),x74112))+~P24(f328(f328(f245(a877),x74113),f328(f194(f878(x74111)),x74112)))
% 81.29/80.91 [7438]P24(f328(f328(f330(f884(x74381,x74381)),x74382),f304(x74381,x74383)))+~P24(f328(f328(f330(f884(x74381,x74381)),x74382),x74383))
% 81.29/80.91 [7449]~P24(f328(f328(f330(f885(x74491,a871)),x74492),f328(f305(x74491),x74493)))+P24(f328(f328(f244(f885(x74491,a871)),x74492),x74493))
% 81.29/80.91 [7492]P24(f328(f328(f244(f885(x74921,a871)),x74922),f40(f885(x74921,a871),x74923)))+~P24(f328(f328(f330(f885(x74921,a871)),x74922),x74923))
% 81.29/80.91 [7517]~P137(x75171)+E(f328(f328(f82(x75171),f328(f328(f258(x75171),f328(f80(x75171),f79(x75171))),x75172)),f328(f328(f258(x75171),x75173),x75172)),f328(f328(f258(x75171),f328(f80(x75171),x75173)),x75172))
% 81.29/80.91 [7538]E(f328(f328(f164(x75381),x75382),f328(f328(f22(a877),f328(f194(f878(x75381)),x75382)),f328(a118,x75383))),f328(f328(f164(x75381),f328(f168(x75381),x75382)),x75383))+~P24(f328(f328(f245(a877),x75383),f328(f194(f878(x75381)),x75382)))
% 81.29/80.91 [7555]~E(f328(f328(f107(f885(x75551,a871)),f770(x75553,x75552,x75551)),x75553),f193(f885(x75551,a871)))+E(f328(f328(f107(f885(x75551,a871)),f40(f885(x75551,a871),x75552)),x75553),f193(f885(x75551,a871)))
% 81.29/80.91 [7616]~P24(f328(f328(f330(x76163),x76162),f328(f171(x76163),x76161)))+P24(f328(f328(f245(a877),f581(x76161,x76162,x76163)),f328(f194(f878(x76163)),x76161)))
% 81.29/80.91 [7624]P24(f328(f328(f330(x76241),f328(f328(f164(x76241),x76242),x76243)),f328(f171(x76241),x76242)))+~P24(f328(f328(f245(a877),x76243),f328(f194(f878(x76241)),x76242)))
% 81.29/80.91 [7724]~P24(f328(x77242,f653(x77243,x77242,x77241)))+E(f328(f328(f137(x77241),f328(f194(f878(x77241)),f176(x77241,x77242,x77243))),x77243),f119(x77241))
% 81.29/80.91 [7734]P24(f328(f328(f244(f885(f878(x77341),a871)),f160(x77341,x77342)),f160(x77341,x77343)))+~P24(f328(f328(f244(f885(x77341,a871)),x77342),x77343))
% 81.29/80.91 [7735]P24(f328(f328(f244(f885(f878(x77351),a871)),f159(x77351,x77352)),f159(x77351,x77353)))+~P24(f328(f328(f244(f885(x77351,a871)),x77352),x77353))
% 81.29/80.91 [7763]E(f328(f328(f107(f885(x77631,a871)),f40(f885(x77631,a871),x77632)),x77633),f193(f885(x77631,a871)))+P24(f328(f328(f330(f885(x77631,a871)),f770(x77633,x77632,x77631)),x77632))
% 81.29/80.91 [7766]~P24(f328(f328(f330(f885(x77661,a871)),x77663),x77662))+P24(f328(f328(f244(f885(x77661,a871)),f41(f885(x77661,a871),x77662)),x77663))
% 81.29/80.91 [7768]E(f328(f328(f107(f885(x77681,a871)),x77682),x77683),f193(f885(x77681,a871)))+~P24(f328(f328(f244(f885(x77681,a871)),x77682),f328(f80(f885(x77681,a871)),x77683)))
% 81.29/80.91 [7815]E(f328(f328(f22(a877),f328(f328(f81(a877),f328(f165(a877),x78151)),x78152)),f328(f328(f164(a877),x78151),x78153)),f328(f165(a877),f328(f328(f158(a877,x78151),x78153),x78152)))+~P24(f328(f328(f245(a877),x78153),f328(f194(f878(a877)),x78151)))
% 81.29/80.91 [7864]P24(f328(f328(f244(a877),x78641),x78642))+~P24(f328(f328(f244(a877),f328(f328(f81(a877),x78643),x78641)),f328(f328(f81(a877),x78643),x78642)))
% 81.29/80.91 [7867]P24(f328(f328(f245(a877),x78671),x78672))+~P24(f328(f328(f245(a877),f328(f328(f81(a877),x78673),x78671)),f328(f328(f81(a877),x78673),x78672)))
% 81.29/80.91 [7868]P24(f328(f328(f245(a877),x78681),x78682))+~P24(f328(f328(f245(a877),f328(f328(f82(a877),x78683),x78681)),f328(f328(f82(a877),x78683),x78682)))
% 81.29/80.91 [7869]P24(f328(f328(f245(a877),x78691),x78692))+~P24(f328(f328(f245(a877),f328(f328(f82(a877),x78691),x78693)),f328(f328(f82(a877),x78692),x78693)))
% 81.29/80.91 [7899]P24(f328(f328(f245(a877),f2(a877)),x78991))+~P24(f328(f328(f245(a877),f328(f328(f82(a877),x78992),x78991)),f328(f328(f82(a877),x78993),x78991)))
% 81.29/80.91 [7900]P24(f328(f328(f245(a877),f2(a877)),x79001))+~P24(f328(f328(f245(a877),f328(f328(f82(a877),x79001),x79002)),f328(f328(f82(a877),x79001),x79003)))
% 81.29/80.91 [7973]E(f260(x79731,x79732,x79733),x79732)+~P24(f328(f328(f244(f885(x79731,a871)),x79733),f328(f328(f306(x79731),x79732),f193(f885(x79731,a871)))))
% 81.29/80.91 [8031]~P24(f328(f136(x80311),x80313))+E(f328(f135(x80311,f328(f328(f8(a871,a871,x80311),a323),f328(a325,x80312))),x80313),f169(x80311,x80312,x80313))
% 81.29/80.91 [8054]E(f328(f328(f137(x80541),f328(f194(f878(x80541)),f176(x80541,x80542,x80543))),x80543),f119(x80541))+P24(f328(f328(f330(x80541),f653(x80543,x80542,x80541)),f328(f171(x80541),x80543)))
% 81.29/80.91 [8058]E(f328(f328(f127(x80581),f328(f328(f174(x80581),x80582),x80583)),f328(f328(f150(x80581),f328(f328(f164(x80581),x80583),x80582)),f119(x80581))),f328(f328(f174(x80581),f328(a118,x80582)),x80583))+~P24(f328(f328(f245(a877),x80582),f328(f194(f878(x80581)),x80583)))
% 81.29/80.91 [8120]E(f328(f135(x81201,f328(f328(f8(a871,a871,x81201),a323),f328(a325,x81202))),x81203),x81203)+P24(f328(f328(f330(x81201),x81202),f328(f171(x81201),x81203)))
% 81.29/80.91 [8128]P24(f328(f328(f244(f885(f885(x81281,a871),a871)),f262(x81281,x81282)),f262(x81281,x81283)))+~P24(f328(f328(f244(f885(x81281,a871)),x81282),x81283))
% 81.29/80.91 [8173]~P24(f328(f136(x81731),x81733))+P24(f328(f136(x81731),f328(f328(f328(f188(f878(x81731),f878(x81731)),x81732),f167(x81731)),x81733)))
% 81.29/80.91 [8179]~P24(f328(f328(f245(a877),x81792),x81793))+P24(f328(f328(f245(a877),f328(f328(f82(a877),f328(a118,x81791)),x81792)),f328(f328(f82(a877),f328(a118,x81791)),x81793)))
% 81.29/80.91 [8201]P24(f328(f328(f244(f885(f885(x82011,a871),a871)),f328(f305(x82011),x82012)),f328(f305(x82011),x82013)))+~P24(f328(f328(f244(f885(x82011,a871)),x82012),x82013))
% 81.29/80.91 [8363]~P24(f328(f328(f244(f885(x83631,a871)),x83633),x83632))+P24(f328(f328(f244(f885(x83631,a871)),f328(f80(f885(x83631,a871)),x83632)),f328(f80(f885(x83631,a871)),x83633)))
% 81.29/80.91 [8395]E(f328(f307(a877,a877,f328(f328(f7(a877,a877,a877),f22(a877)),x83951)),f328(f298(a877,x83952),x83953)),f328(f298(a877,f328(f328(f22(a877),x83952),x83951)),f328(f328(f22(a877),x83953),x83951)))+~P24(f328(f328(f245(a877),x83951),x83953))
% 81.29/80.91 [8423]~P82(x84231)+E(f328(f328(f81(x84231),x84232),f328(f141(x84231,x84231,f81(x84231),f2(x84231)),x84233)),f328(f141(x84231,x84231,f81(x84231),x84232),x84233))
% 81.29/80.91 [8507]~P87(x85071)+P24(f328(f328(f244(x85071),f328(f76(x85071),f328(f328(f22(x85071),x85072),x85073))),f328(f328(f81(x85071),f328(f76(x85071),x85072)),f328(f76(x85071),x85073))))
% 81.29/80.91 [8508]~P87(x85081)+P24(f328(f328(f244(x85081),f328(f76(x85081),f328(f328(f81(x85081),x85082),x85083))),f328(f328(f81(x85081),f328(f76(x85081),x85082)),f328(f76(x85081),x85083))))
% 81.29/80.91 [8518]E(f328(f328(f81(a1),f328(f328(f82(a1),x85181),f45(a1,f328(f328(f39(a1),x85182),x85181),x85183))),f45(a1,x85182,x85181)),f45(a1,x85182,f328(f328(f82(a1),x85181),x85183)))+~P24(f328(f328(f245(a1),f2(a1)),x85183))
% 81.29/80.91 [8524]E(f328(f328(f127(x85241),f328(f328(f174(x85241),x85242),x85243)),f328(f328(f150(x85241),f328(f140(x85241),f328(f328(f137(x85241),x85242),x85243))),f119(x85241))),f328(f328(f174(x85241),f328(a118,x85242)),x85243))+~P24(f328(f328(f245(a877),x85242),f328(f194(f878(x85241)),x85243)))
% 81.29/80.91 [8543]E(f328(f274(x85431,f328(f328(f153(x85431,f884(a105,x85431)),f328(f257(a105,x85431),f79(a105))),x85432)),f328(a3,x85433)),f328(f328(f164(x85431),x85432),x85433))+~P24(f328(f328(f245(a877),x85433),f328(f194(f878(x85431)),x85432)))
% 81.29/80.91 [8608]P24(f328(f328(f330(f884(x86081,x86081)),x86082),f328(f328(f285(x86081,x86081,x86081),x86083),f304(x86081,x86083))))+~P24(f328(f328(f330(f884(x86081,x86081)),x86082),x86083))
% 81.29/80.91 [8627]P24(f328(f328(f244(a877),x86271),x86272))+~P24(f328(f328(f244(a877),f328(f328(f82(a877),f328(a118,x86273)),x86271)),f328(f328(f82(a877),f328(a118,x86273)),x86272)))
% 81.29/80.91 [8642]P24(f328(f328(f244(f885(x86421,a871)),x86422),x86423))+~P24(f328(f328(f244(f885(x86421,a871)),f328(f80(f885(x86421,a871)),x86423)),f328(f80(f885(x86421,a871)),x86422)))
% 81.29/80.91 [8661]P24(f328(f136(x86611),x86612))+~P24(f328(f136(x86611),f328(f328(f328(f188(f878(x86611),f878(x86611)),x86613),f167(x86611)),x86612)))
% 81.29/80.91 [8721]E(f328(f307(f884(x87211,x87212),x87212,f266(x87211,x87212)),f328(f171(f884(x87211,x87212)),x87213)),f185(x87211,x87212,f328(f177(x87211,x87212),x87213)))+~P24(f328(f136(x87211),f328(f328(f153(f884(x87211,x87212),x87211),f256(x87211,x87212)),x87213)))
% 81.29/80.91 [8730]E(f328(f282(x87301,x87301,f304(x87301,x87302)),x87303),x87303)+~P24(f328(f328(f244(f885(x87301,a871)),f328(f282(x87301,x87301,x87302),x87303)),x87303))
% 81.29/80.91 [8773]~P106(x87731)+P29(x87731,f328(f135(x87731,f328(f328(f7(x87731,x87731,a871),a325),f328(x87732,x87733))),x87733))
% 81.29/80.91 [8779]~P24(f328(f328(f244(a877),x87791),x87792))+P24(f328(f328(f244(a877),x87791),f328(f141(a877,a877,f81(a877),x87792),x87793)))
% 81.29/80.91 [8856]~P24(f328(f328(f330(f884(x88561,x88561)),x88562),f304(x88561,x88563)))+P24(f328(f328(f330(f884(x88561,x88561)),x88562),f328(f328(f188(f884(x88561,x88561),a871),f771(x88563,x88562,x88561)),x88563)))
% 81.29/80.91 [8948]~P82(x89481)+E(f328(f328(f81(x89481),x89482),f328(f141(x89481,x89481,f328(f7(x89481,x89481,x89481),f81(x89481)),f2(x89481)),f328(f168(x89481),x89483))),f328(f141(x89481,x89481,f81(x89481),x89482),x89483))
% 81.29/80.91 [9217]P52(x92171,x92172,x92173)+P24(f328(f328(f330(f884(x92171,x92172)),f328(f328(f257(x92171,x92172),f761(x92173,x92172,x92171)),f738(x92173,x92172,x92171))),x92173))
% 81.29/80.91 [9218]P52(x92181,x92182,x92183)+P24(f328(f328(f330(f884(x92181,x92182)),f328(f328(f257(x92181,x92182),f761(x92183,x92182,x92181)),f737(x92183,x92182,x92181))),x92183))
% 81.29/80.91 [9289]~P24(f328(f328(f330(f884(x92891,x92891)),x92892),f328(f328(f285(x92891,x92891,x92891),x92893),f304(x92891,x92893))))+P24(f328(f328(f330(f884(x92891,x92891)),x92892),f328(f328(f188(f884(x92891,x92891),a871),f773(x92893,x92892,x92891)),x92893)))
% 81.29/80.91 [9290]~P24(f328(x92901,f328(f328(f164(x92902),x92903),f328(f194(f878(x92902)),f176(x92902,x92901,x92903)))))+~P24(f328(f328(f245(a877),f328(f194(f878(x92902)),f176(x92902,x92901,x92903))),f328(f194(f878(x92902)),x92903)))
% 81.29/80.91 [9379]~P24(f328(f328(f244(f885(x93791,a871)),x93792),x93793))+P24(f328(f328(f244(f885(x93791,a871)),f328(f328(f7(x93791,f885(x93791,a871),a871),f330(x93791)),x93792)),f328(f328(f7(x93791,f885(x93791,a871),a871),f330(x93791)),x93793)))
% 81.29/80.91 [9431]~P24(f328(f328(f330(f884(f885(x94311,a871),f885(x94311,a871))),f328(f328(f257(f885(x94311,a871),f885(x94311,a871)),x94312),x94313)),f303(x94311)))+P24(f328(f328(f245(f885(x94311,a871)),x94312),x94313))
% 81.29/80.91 [9456]P53(x94561,x94562,x94563)+~P24(f328(f328(f330(f884(x94561,x94561)),f328(f328(f257(x94561,x94561),f764(x94563,x94562,x94561)),f763(x94563,x94562,x94561))),x94563))
% 81.29/80.91 [9457]P53(x94571,x94572,x94573)+~P24(f328(f328(f330(f884(x94571,x94571)),f328(f328(f257(x94571,x94571),f763(x94573,x94572,x94571)),f764(x94573,x94572,x94571))),x94573))
% 81.29/80.91 [9493]~P24(f328(f328(f330(f884(f878(x94931),f878(x94931))),f328(f328(f257(f878(x94931),f878(x94931)),x94932),x94932)),f146(x94931,x94933)))+P24(f328(f328(f330(f884(x94931,x94931)),f328(f328(f257(x94931,x94931),f632(x94932,x94933,x94931)),f632(x94932,x94933,x94931))),x94933))
% 81.29/80.91 [9544]P24(f328(f328(f244(f885(x95441,a871)),x95442),x95443))+~P24(f328(f328(f244(f885(x95441,a871)),f328(f328(f7(x95441,f885(x95441,a871),a871),f330(x95441)),x95442)),f328(f328(f7(x95441,f885(x95441,a871),a871),f330(x95441)),x95443)))
% 81.29/80.91 [9625]E(f328(f328(f22(a877),f328(f328(f6(a877,a877),x96251),f328(f250(a877),x96252))),f328(f328(f6(a877,a877),x96253),f328(f250(a877),x96252))),f328(f328(f6(a877,a877),f328(f328(f18(a877,a877,a877),f328(f328(f8(a877,f885(a877,a877),a877),f22(a877)),x96251)),x96253)),f328(f250(a877),x96252)))+~P24(f328(f328(f244(a877),f328(x96253,f499(x96252,x96251,x96253))),f328(x96251,f499(x96252,x96251,x96253))))
% 81.29/80.91 [9928]E(f328(f249(f884(x99281,x99282)),f328(f267(x99281,x99282,a871),f328(f328(f7(x99281,f885(x99282,f881(x99282)),f885(x99282,a871)),f328(f328(f8(f885(f881(x99282),a871),f885(f885(x99282,f881(x99282)),f885(x99282,a871)),x99281),f8(f881(x99282),a871,x99282)),f328(f328(f8(f881(x99282),f885(f881(x99282),a871),x99281),a325),f328(f177(x99281,x99282),x99283)))),f236(x99282)))),f328(f171(f884(x99281,x99282)),x99283))+~P24(f328(f136(x99281),f328(f328(f153(f884(x99281,x99282),x99281),f256(x99281,x99282)),x99283)))
% 81.29/80.91 [5630]~P73(x56301)+E(f328(f328(f22(x56301),f328(f328(f81(x56301),x56302),x56303)),x56303),x56302)
% 81.29/80.91 [5631]~P73(x56311)+E(f328(f328(f81(x56311),f328(f328(f22(x56311),x56312),x56313)),x56313),x56312)
% 81.29/80.91 [5851]~P73(x58511)+E(f328(f328(f81(x58511),x58512),f328(f328(f81(x58511),f328(f80(x58511),x58512)),x58513)),x58513)
% 81.29/80.91 [5936]~P83(x59361)+E(f328(f328(f82(x59361),f328(f328(f258(x59361),x59362),x59363)),x59362),f328(f328(f258(x59361),x59362),f328(a118,x59363)))
% 81.29/80.91 [5937]~P112(x59371)+E(f328(f328(f82(x59371),f328(f328(f258(x59371),x59372),x59373)),x59372),f328(f328(f258(x59371),x59372),f328(a118,x59373)))
% 81.29/80.91 [6150]~P111(x61501)+E(f328(f76(x61501),f328(f328(f258(x61501),f328(f80(x61501),x61502)),x61503)),f328(f76(x61501),f328(f328(f258(x61501),x61502),x61503)))
% 81.29/80.91 [6208]~P83(x62081)+E(f328(f328(f82(x62081),f328(f328(f258(x62081),x62082),x62083)),x62082),f328(f328(f82(x62081),x62082),f328(f328(f258(x62081),x62082),x62083)))
% 81.29/80.91 [6262]E(f328(f328(f22(a105),f328(f328(f81(a105),x62621),x62622)),x62623),f278(x62621,x62622,x62623))+~P24(f328(f328(f245(a105),x62622),x62623))
% 81.29/80.91 [6283]~E(f328(f328(f137(x62831),x62833),x62832),f119(x62831))+P24(f328(f328(f244(a877),f328(f194(f878(x62831)),x62832)),x62833))
% 81.29/80.91 [6418]E(f328(f328(f82(a877),f328(f109(a877),x64181)),f328(f328(f82(a877),f328(f109(a877),x64182)),x64183)),f2(a877))+~P24(f328(f328(f245(a1),x64181),a84))
% 81.29/80.91 [6434]~P61(x64341)+E(f328(f328(f258(x64341),f328(f328(f286(x64341),f79(x64341)),x64342)),x64343),f328(f328(f286(x64341),f79(x64341)),f328(f328(f258(x64341),x64342),x64343)))
% 81.29/80.91 [6512]E(f328(f328(f22(a877),f328(f328(f81(a877),x65121),x65122)),x65123),f328(f328(f22(a877),x65121),f328(f328(f22(a877),x65123),x65122)))+~P24(f328(f328(f244(a877),x65122),x65123))
% 81.29/80.91 [6514]E(f328(f328(f22(a877),f328(f328(f81(a877),x65141),x65142)),x65143),f328(f328(f81(a877),x65141),f328(f328(f22(a877),x65142),x65143)))+~P24(f328(f328(f244(a877),x65143),x65142))
% 81.29/80.91 [6549]~P78(x65491)+P24(f328(f328(f244(x65491),f328(f328(f107(x65491),x65492),x65493)),x65493))
% 81.29/80.91 [6550]~P102(x65501)+P24(f328(f328(f244(x65501),f328(f328(f107(x65501),x65502),x65503)),x65503))
% 81.29/80.91 [6551]~P78(x65511)+P24(f328(f328(f244(x65511),f328(f328(f107(x65511),x65512),x65513)),x65512))
% 81.29/80.91 [6552]~P102(x65521)+P24(f328(f328(f244(x65521),f328(f328(f107(x65521),x65522),x65523)),x65522))
% 81.29/80.91 [6553]~P106(x65531)+P24(f328(f328(f244(x65531),f328(f328(f242(x65531),x65532),x65533)),x65533))
% 81.29/80.91 [6554]~P106(x65541)+P24(f328(f328(f244(x65541),f328(f328(f242(x65541),x65542),x65543)),x65542))
% 81.29/80.91 [6568]E(f328(f328(f39(a1),f328(f328(f39(a1),x65681),x65682)),x65683),f328(f328(f39(a1),x65681),f328(f328(f82(a1),x65682),x65683)))+~P24(f328(f328(f245(a1),f2(a1)),x65683))
% 81.29/80.91 [6620]~P112(x66201)+E(f328(f328(f81(x66201),f328(f328(f82(x66201),x66202),x66203)),x66203),f328(f328(f82(x66201),f328(f328(f81(x66201),x66202),f79(x66201))),x66203))
% 81.29/80.91 [6621]~P96(x66211)+E(f328(f328(f82(x66211),f328(f80(x66211),f328(f109(x66211),x66212))),x66213),f328(f328(f82(x66211),f328(f109(x66211),f328(f80(a1),x66212))),x66213))
% 81.29/80.91 [6694]~P82(x66941)+E(f328(f165(x66941),f328(f328(f153(x66942,x66941),f328(f16(x66941,x66942),f2(x66941))),x66943)),f2(x66941))
% 81.29/80.91 [6710]E(f328(f328(f81(a877),f328(f109(a877),x67101)),f328(f328(f81(a877),f328(f109(a877),x67102)),x67103)),f328(f328(f81(a877),f328(f109(a877),x67102)),x67103))+~P24(f328(a199,f328(f109(a1),x67101)))
% 81.29/80.91 [6724]~P27(x67241)+E(f40(x67241,f328(f328(f306(x67241),x67242),f328(f328(f306(x67241),x67243),f193(f885(x67241,a871))))),f328(f328(f116(x67241),x67242),x67243))
% 81.29/80.91 [6725]~P27(x67251)+E(f41(x67251,f328(f328(f306(x67251),x67252),f328(f328(f306(x67251),x67253),f193(f885(x67251,a871))))),f328(f328(f107(x67251),x67252),x67253))
% 81.29/80.91 [6748]E(f328(f328(f174(x67481),x67482),x67483),x67483)+~P24(f328(f328(f244(a877),f328(f194(f878(x67481)),x67483)),x67482))
% 81.29/80.91 [6761]E(f328(f328(f137(x67611),x67612),x67613),f119(x67611))+~P24(f328(f328(f244(a877),f328(f194(f878(x67611)),x67613)),x67612))
% 81.29/80.91 [6772]E(f328(f328(f81(a877),f328(f328(f22(a877),x67721),x67722)),x67723),f328(f328(f22(a877),f328(f328(f81(a877),x67721),x67723)),x67722))+~P24(f328(f328(f244(a877),x67722),x67721))
% 81.29/80.91 [6786]~P24(f328(f328(f245(a877),x67861),x67863))+P24(f328(f328(f245(a877),f328(f328(f22(a877),x67861),x67862)),x67863))
% 81.29/80.91 [6814]~P106(x68141)+E(f169(x68141,x68142,f328(f328(f147(x68141,x68141,f5(x68141)),x68142),x68143)),x68143)
% 81.29/80.91 [6899]E(f328(f328(f22(a877),f328(f328(f81(a877),x68991),x68992)),f328(a118,x68993)),f328(f328(f22(a877),x68991),f328(a118,f328(f328(f22(a877),x68993),x68992))))+~P24(f328(f328(f244(a877),x68992),x68993))
% 81.29/80.91 [6900]~P111(x69001)+P24(f328(f328(f244(x69001),f2(x69001)),f328(f328(f258(x69001),f328(f76(x69001),x69002)),x69003)))
% 81.29/80.91 [6947]P20(x69471,x69472,x69473)+~P24(f328(f328(f244(f885(f876(x69471),a871)),x69473),x69472))
% 81.29/80.91 [6990]~P24(f328(f62(x69901),x69902))+P24(f328(f62(x69901),f328(f328(f22(f885(x69901,a871)),x69902),x69903)))
% 81.29/80.91 [6991]~P24(f328(f62(x69911),x69913))+P24(f328(f62(x69911),f328(f328(f107(f885(x69911,a871)),x69912),x69913)))
% 81.29/80.91 [6992]~P24(f328(f62(x69921),x69922))+P24(f328(f62(x69921),f328(f328(f107(f885(x69921,a871)),x69922),x69923)))
% 81.29/80.91 [7133]~P38(x71331,x71333)+P38(x71331,f328(f328(f107(f885(f884(x71331,x71331),a871)),x71332),x71333))
% 81.29/80.91 [7134]~P38(x71341,x71342)+P38(x71341,f328(f328(f107(f885(f884(x71341,x71341),a871)),x71342),x71343))
% 81.29/80.91 [7249]~P78(x72491)+E(f10(x72491,f328(f171(x72491),f328(f328(f150(x72491),x72492),x72493))),f328(f141(x72491,x72491,f116(x72491),x72492),x72493))
% 81.29/80.91 [7250]~P78(x72501)+E(f11(x72501,f328(f171(x72501),f328(f328(f150(x72501),x72502),x72503))),f328(f141(x72501,x72501,f107(x72501),x72502),x72503))
% 81.29/80.91 [7251]~P106(x72511)+E(f14(x72511,f328(f171(x72511),f328(f328(f150(x72511),x72512),x72513))),f328(f141(x72511,x72511,f242(x72511),x72512),x72513))
% 81.29/80.91 [7252]~P106(x72521)+E(f15(x72521,f328(f171(x72521),f328(f328(f150(x72521),x72522),x72523))),f328(f141(x72521,x72521,f243(x72521),x72522),x72523))
% 81.29/80.91 [7312]~P24(f328(f62(x73121),x73122))+P24(f328(f328(f244(a877),f328(f38(x73121),x73122)),f328(f38(x73121),f328(f328(f306(x73121),x73123),x73122))))
% 81.29/80.91 [7320]E(f328(f328(f116(f885(a877,a871)),f328(f298(a877,x73201),x73202)),f328(f298(a877,x73202),f328(f328(f81(a877),x73202),x73203))),f328(f298(a877,x73201),f328(f328(f81(a877),x73202),x73203)))+~P24(f328(f328(f244(a877),x73201),x73202))
% 81.29/80.91 [7330]P24(f328(f328(f244(a877),x73301),x73302))+~P24(f328(f328(f244(a877),f328(f328(f81(a877),x73303),x73301)),x73302))
% 81.29/80.91 [7331]P24(f328(f328(f244(a877),x73311),x73312))+~P24(f328(f328(f244(a877),f328(f328(f81(a877),x73311),x73313)),x73312))
% 81.29/80.91 [7332]P24(f328(f328(f245(a877),x73321),x73322))+~P24(f328(f328(f245(a877),f328(f328(f81(a877),x73321),x73323)),x73322))
% 81.29/80.91 [7374]~P106(x73741)+E(f12(x73741,f242(x73741),f328(f171(x73741),f328(f328(f150(x73741),x73742),x73743))),f328(f141(x73741,x73741,f242(x73741),x73742),x73743))
% 81.29/80.91 [7375]~P106(x73751)+E(f13(x73751,f243(x73751),f328(f171(x73751),f328(f328(f150(x73751),x73752),x73753))),f328(f141(x73751,x73751,f243(x73751),x73752),x73753))
% 81.29/80.91 [7379]~E(x73792,f193(f885(f884(x73791,x73791),a871)))+P24(f328(f328(f244(f885(f884(x73791,x73791),a871)),x73792),x73793))
% 81.29/80.91 [7487]E(f328(f328(f116(f885(x74871,a871)),x74872),f328(f328(f22(f885(x74871,a871)),x74873),x74872)),x74873)+~P24(f328(f328(f244(f885(x74871,a871)),x74872),x74873))
% 81.29/80.91 [7488]~P24(f328(f328(f244(a877),x74881),f328(f328(f81(a877),x74883),x74882)))+P24(f328(f328(f244(a877),f328(f328(f22(a877),x74881),x74882)),x74883))
% 81.29/80.91 [7489]~P24(f328(f328(f245(a877),x74891),f328(f328(f22(a877),x74893),x74892)))+P24(f328(f328(f245(a877),f328(f328(f81(a877),x74891),x74892)),x74893))
% 81.29/80.91 [7545]E(x75451,f119(x75452))+E(f328(f140(x75452),f328(f328(f328(f188(f878(x75452),f878(x75452)),x75453),f167(x75452)),x75451)),f328(f328(f164(x75452),x75451),f45(a877,x75453,f328(f194(f878(x75452)),x75451))))
% 81.29/80.91 [7554]E(f328(f328(f306(x75541),x75542),f328(f328(f22(f885(x75541,a871)),x75543),f328(f328(f306(x75541),x75542),f193(f885(x75541,a871))))),x75543)+~P24(f328(f328(f330(x75541),x75542),x75543))
% 81.29/80.91 [7715]P24(f328(f328(f244(a877),x77151),f328(f328(f81(a877),x77152),x77153)))+~P24(f328(f328(f244(a877),f328(f328(f22(a877),x77151),x77153)),x77152))
% 81.29/80.91 [7716]P24(f328(f328(f245(a877),x77161),f328(f328(f22(a877),x77162),x77163)))+~P24(f328(f328(f245(a877),f328(f328(f81(a877),x77161),x77163)),x77162))
% 81.29/80.91 [7738]P24(f328(f62(x77381),x77382))+~P24(f328(f62(x77381),f328(f328(f116(f885(x77381,a871)),x77383),x77382)))
% 81.29/80.91 [7739]P24(f328(f62(x77391),x77392))+~P24(f328(f62(x77391),f328(f328(f116(f885(x77391,a871)),x77392),x77393)))
% 81.29/80.91 [7814]~P45(x78141,x78143)+P24(f328(f328(f330(f884(x78141,x78141)),f328(f328(f257(x78141,x78141),x78142),x78142)),x78143))
% 81.29/80.91 [7947]E(f328(f328(f164(a877),f138(a877,f328(f298(a877,x79471),x79472))),x79473),f328(f328(f81(a877),x79471),x79473))+~P24(f328(f328(f245(a877),f328(f328(f81(a877),x79471),x79473)),x79472))
% 81.29/80.91 [8015]~P24(f328(f328(f200(f328(a26,x80151)),x80152),x80153))+P24(f328(f328(f200(f328(f240(a873),f328(a28,x80151))),x80152),x80153))
% 81.29/80.91 [8020]E(f328(f328(f174(a877),x80201),f138(a877,f328(f298(a877,x80202),x80203))),f138(a877,f328(f298(a877,x80202),f328(f328(f81(a877),x80202),x80201))))+~P24(f328(f328(f244(a877),f328(f328(f81(a877),x80202),x80201)),x80203))
% 81.29/80.91 [8073]~P96(x80731)+E(f328(f328(f258(x80731),x80732),f328(f109(a877),f328(f328(f81(a1),x80733),x80733))),f328(f328(f87(x80731,x80731),f328(f328(f258(x80731),x80732),f328(f109(a877),x80733))),f328(f328(f18(x80731,x80731,x80731),f82(x80731)),f5(x80731))))
% 81.29/80.91 [8283]P24(f328(f328(f200(f328(a26,x82831)),x82832),x82833))+~P24(f328(f328(f200(f328(f240(a873),f328(a28,x82831))),x82832),x82833))
% 81.29/80.91 [8343]E(f328(f328(f127(x83431),f328(f328(f174(x83431),x83432),x83433)),f328(f328(f150(x83431),f328(f328(f164(x83431),x83433),x83432)),f328(f328(f137(x83431),f328(a118,x83432)),x83433))),x83433)+~P24(f328(f328(f245(a877),x83432),f328(f194(f878(x83431)),x83433)))
% 81.29/80.91 [8350]P24(f328(f328(f244(f885(x83501,a871)),f316(x83501,x83502)),f316(x83501,x83503)))+~P24(f328(f328(f244(f885(x83501,f885(x83501,a871))),x83503),x83502))
% 81.29/80.91 [8352]~P53(x83521,x83522,x83523)+P53(x83521,x83522,f328(f328(f22(f885(f884(x83521,x83521),a871)),x83523),f304(x83521,f193(f885(f884(x83521,x83521),a871)))))
% 81.29/80.91 [8369]P24(f328(f328(f244(f885(x83691,a871)),f317(x83691,x83692)),f317(x83691,x83693)))+~P24(f328(f328(f244(f885(f884(x83691,x83691),a871)),x83693),x83692))
% 81.29/80.91 [8376]~P124(x83761)+P24(f328(f328(f244(x83761),f2(x83761)),f328(f328(f81(x83761),f328(f328(f82(x83761),x83762),x83762)),f328(f328(f82(x83761),x83763),x83763))))
% 81.29/80.91 [8411]P24(f328(f328(f244(f885(x84111,a871)),f328(f281(x84111),x84112)),f328(f281(x84111),x84113)))+~P24(f328(f328(f244(f885(f884(x84111,x84111),a871)),x84112),x84113))
% 81.29/80.91 [8444]~P49(x84441,x84442)+~P24(f328(f328(f330(f884(x84441,x84441)),f328(f328(f257(x84441,x84441),x84443),x84443)),x84442))
% 81.29/80.91 [8446]~P38(x84461,x84462)+~P24(f328(f328(f330(f884(x84461,x84461)),f328(f328(f257(x84461,x84461),x84463),x84463)),x84462))
% 81.29/80.91 [8509]P24(f328(f328(f244(f885(x85091,a871)),f40(f885(x85091,a871),x85092)),f40(f885(x85091,a871),x85093)))+~P24(f328(f328(f244(f885(f885(x85091,a871),a871)),x85092),x85093))
% 81.29/80.91 [8510]P24(f328(f328(f244(f885(x85101,a871)),f41(f885(x85101,a871),x85102)),f41(f885(x85101,a871),x85103)))+~P24(f328(f328(f244(f885(f885(x85101,a871),a871)),x85103),x85102))
% 81.29/80.91 [8562]~P6(x85621,x85623,x85622)+P24(f328(f328(f244(f885(f884(x85621,x85621),a871)),x85622),f328(f328(f265(x85621,x85621),x85623),f328(f16(f885(x85621,a871),x85621),x85623))))
% 81.29/80.91 [8563]~P48(x85631,x85633,x85632)+P24(f328(f328(f244(f885(f884(x85631,x85631),a871)),x85632),f328(f328(f265(x85631,x85631),x85633),f328(f16(f885(x85631,a871),x85631),x85633))))
% 81.29/80.91 [8609]~P87(x86091)+P24(f328(f328(f244(x86091),f328(f328(f22(x86091),f328(f76(x86091),x86092)),f328(f76(x86091),x86093))),f328(f76(x86091),f328(f328(f22(x86091),x86093),x86092))))
% 81.29/80.91 [8610]~P87(x86101)+P24(f328(f328(f244(x86101),f328(f328(f22(x86101),f328(f76(x86101),x86102)),f328(f76(x86101),x86103))),f328(f76(x86101),f328(f328(f22(x86101),x86102),x86103))))
% 81.29/80.91 [8640]P24(f328(f328(f244(f885(f884(x86401,x86401),a871)),f304(x86401,x86402)),f304(x86401,x86403)))+~P24(f328(f328(f244(f885(f884(x86401,x86401),a871)),x86402),x86403))
% 81.29/80.91 [8797]P53(x87971,x87972,x87973)+~P53(x87971,x87972,f328(f328(f22(f885(f884(x87971,x87971),a871)),x87973),f304(x87971,f193(f885(f884(x87971,x87971),a871)))))
% 81.29/80.91 [8815]P24(f328(f328(f244(f885(f884(f878(x88151),f878(x88151)),a871)),f157(x88151,x88152)),f157(x88151,x88153)))+~P24(f328(f328(f244(f885(f884(x88151,x88151),a871)),x88152),x88153))
% 81.29/80.91 [8816]P24(f328(f328(f244(f885(f884(f878(x88161),f878(x88161)),a871)),f156(x88161,x88162)),f156(x88161,x88163)))+~P24(f328(f328(f244(f885(f884(x88161,x88161),a871)),x88162),x88163))
% 81.29/80.91 [8835]~P48(x88351,x88353,x88352)+P24(f328(f328(f244(f885(f884(x88351,x88351),a871)),x88352),f328(f328(f285(x88351,x88351,x88351),f328(f283(x88351,x88351),x88352)),x88352)))
% 81.29/80.91 [8884]~P24(f328(f136(x88841),x88842))+E(f328(f135(x88841,f328(f328(f7(x88841,f885(x88841,a871),a871),f330(x88841)),f328(f171(x88841),f175(x88841,x88842,x88843)))),x88842),f175(x88841,x88842,x88843))
% 81.29/80.91 [8946]E(x89461,x89462)+~P24(f328(f328(f330(f884(x89463,x89463)),f328(f328(f257(x89463,x89463),x89461),x89462)),f304(x89463,f193(f885(f884(x89463,x89463),a871)))))
% 81.29/80.91 [9032]P24(f328(f328(f330(x90321),x90322),f317(x90321,x90323)))+P24(f328(f328(f330(f884(x90321,x90321)),f328(f328(f257(x90321,x90321),f559(x90323,x90322,x90321)),x90322)),x90323))
% 81.29/80.91 [9033]P24(f328(f328(f330(x90331),x90332),f317(x90331,x90333)))+P24(f328(f328(f330(f884(x90331,x90331)),f328(f328(f257(x90331,x90331),f741(x90333,x90332,x90331)),x90332)),x90333))
% 81.29/80.91 [9034]P24(f328(f328(f330(x90341),x90342),f317(x90341,x90343)))+P24(f328(f328(f330(f884(x90341,x90341)),f328(f328(f257(x90341,x90341),f750(x90343,x90342,x90341)),x90342)),x90343))
% 81.29/80.91 [9120]~P24(f328(f328(f330(f878(x91201)),x91203),f160(x91201,x91202)))+P24(f328(f159(x91201,f328(f328(f7(x91201,f885(x91201,a871),a871),f330(x91201)),x91202)),x91203))
% 81.29/80.91 [9141]P24(f328(x91413,x91412))+E(f328(f249(x91411),f328(f328(f18(x91411,a871,a871),f328(f328(f8(a871,f885(a871,a871),x91411),a326),f328(a325,x91412))),x91413)),f193(f885(x91411,a871)))
% 81.29/80.91 [9162]~P87(x91621)+P24(f328(f328(f244(x91621),f328(f76(x91621),f328(f328(f22(x91621),f328(f76(x91621),x91622)),f328(f76(x91621),x91623)))),f328(f76(x91621),f328(f328(f22(x91621),x91622),x91623))))
% 81.29/80.91 [9176]~P24(f328(x91763,x91762))+E(f328(f249(x91761),f328(f328(f18(x91761,a871,a871),f328(f328(f8(a871,f885(a871,a871),x91761),a326),f328(a325,x91762))),x91763)),f328(f328(f306(x91761),x91762),f193(f885(x91761,a871))))
% 81.29/80.91 [9183]~P24(f328(f328(f330(f885(x91831,a871)),x91833),f328(f305(x91831),x91832)))+P24(f328(f262(x91831,f328(f328(f7(x91831,f885(x91831,a871),a871),f330(x91831)),x91832)),x91833))
% 81.29/80.91 [9216]P38(x92161,x92162)+P24(f328(f328(f330(f884(x92161,x92161)),f328(f328(f257(x92161,x92161),f328(f685(x92162,x92161),f328(a118,x92163))),f328(f685(x92162,x92161),x92163))),x92162))
% 81.29/80.91 [9358]P24(f328(f328(f330(f878(x93581)),x93582),f160(x93581,x93583)))+~P24(f328(f159(x93581,f328(f328(f7(x93581,f885(x93581,a871),a871),f330(x93581)),x93583)),x93582))
% 81.29/80.91 [9371]P24(f328(f328(f330(f885(x93711,a871)),x93712),f328(f305(x93711),x93713)))+~P24(f328(f262(x93711,f328(f328(f7(x93711,f885(x93711,a871),a871),f330(x93711)),x93713)),x93712))
% 81.29/80.91 [9427]P24(f328(f328(f330(x94271),f328(f274(x94271,x94272),x94273)),f328(f171(x94271),f328(f328(f153(f884(a105,x94271),x94271),f266(a105,x94271)),x94272))))+~P24(f328(f328(f245(a105),x94273),f328(f165(a105),f328(f328(f153(f884(a105,x94271),a105),f256(a105,x94271)),x94272))))
% 81.29/80.91 [9475]P24(f328(f328(f244(f885(f884(f878(x94751),f878(x94751)),a871)),f157(x94751,x94752)),f328(f328(f265(f878(x94751),f878(x94751)),f160(x94751,x94753)),f328(f16(f885(f878(x94751),a871),f878(x94751)),f160(x94751,x94753)))))+~P24(f328(f328(f244(f885(f884(x94751,x94751),a871)),x94752),f328(f328(f265(x94751,x94751),x94753),f328(f16(f885(x94751,a871),x94751),x94753))))
% 81.29/80.91 [9496]P24(f328(f328(f330(x94961),f328(f256(x94961,f884(a105,a105)),f328(f272(x94961,x94962),x94963))),f328(f171(x94961),f328(f328(f153(f884(a105,x94961),x94961),f266(a105,x94961)),x94962))))+~P24(f328(f328(f245(a105),f2(a105)),f328(f165(a105),f328(f328(f153(f884(a105,x94961),a105),f256(a105,x94961)),x94962))))
% 81.29/80.91 [9513]~P24(f328(f328(f244(f885(f884(x95131,x95131),a871)),x95132),f328(f328(f265(x95131,x95131),x95133),f328(f16(f885(x95131,a871),x95131),x95133))))+P24(f328(f328(f244(f885(f884(x95131,x95131),a871)),f328(f328(f285(x95131,x95131,x95131),x95132),f304(x95131,x95132))),f328(f328(f265(x95131,x95131),x95133),f328(f16(f885(x95131,a871),x95131),x95133))))
% 81.29/80.91 [9812]~P38(x98121,x98122)+~P24(f328(f328(f330(f884(x98121,x98121)),f328(f328(f257(x98121,x98121),f328(x98123,f328(a118,f686(x98122,x98121,x98123)))),f328(x98123,f686(x98122,x98121,x98123)))),x98122))
% 81.29/80.91 [9813]~P38(x98131,x98132)+~P24(f328(f328(f330(f884(x98131,x98131)),f328(f328(f257(x98131,x98131),f328(x98133,f328(a118,f755(x98133,x98132,x98131)))),f328(x98133,f755(x98133,x98132,x98131)))),x98132))
% 81.29/80.91 [10070]P24(f328(f328(f244(f885(f884(f885(x100701,a871),f885(x100701,a871)),a871)),f328(f328(f285(f885(x100701,a871),f885(x100701,a871),f885(x100701,a871)),f321(x100701,x100702)),f328(f328(f116(f885(f884(f885(x100701,a871),f885(x100701,a871)),a871)),f321(x100701,x100703)),f328(f328(f306(f884(f885(x100701,a871),f885(x100701,a871))),f328(f328(f257(f885(x100701,a871),f885(x100701,a871)),f193(f885(x100701,a871))),f193(f885(x100701,a871)))),f193(f885(f884(f885(x100701,a871),f885(x100701,a871)),a871)))))),f321(x100701,x100702)))+~P24(f328(f328(f244(f885(f884(x100701,x100701),a871)),f328(f328(f285(x100701,x100701,x100701),x100702),x100703)),x100702))
% 81.29/80.91 [10071]P24(f328(f328(f244(f885(f884(f885(x100711,a871),f885(x100711,a871)),a871)),f328(f328(f285(f885(x100711,a871),f885(x100711,a871),f885(x100711,a871)),f319(x100711,x100712)),f328(f328(f116(f885(f884(f885(x100711,a871),f885(x100711,a871)),a871)),f319(x100711,x100713)),f328(f328(f306(f884(f885(x100711,a871),f885(x100711,a871))),f328(f328(f257(f885(x100711,a871),f885(x100711,a871)),f193(f885(x100711,a871))),f193(f885(x100711,a871)))),f193(f885(f884(f885(x100711,a871),f885(x100711,a871)),a871)))))),f319(x100711,x100712)))+~P24(f328(f328(f244(f885(f884(x100711,x100711),a871)),f328(f328(f285(x100711,x100711,x100711),x100712),x100713)),x100712))
% 81.29/80.91 [7248]~P24(f328(f328(f244(a877),x72482),x72481))+E(f328(f328(f22(a877),f328(a118,f328(f328(f22(a877),x72481),x72482))),x72483),f328(f328(f22(a877),f328(a118,x72481)),f328(f328(f81(a877),x72482),x72483)))
% 81.29/80.91 [7287]~P58(x72871)+E(f328(f328(f81(x72871),f45(x72871,x72872,x72873)),f328(f328(f82(x72871),f328(f328(f39(x72871),x72872),x72873)),x72873)),x72872)
% 81.29/80.91 [7493]E(f328(f328(f82(a877),f328(f109(a877),x74931)),f328(f328(f82(a877),f328(f109(a877),x74932)),x74933)),f328(f328(f82(a877),f328(f109(a877),f328(f328(f82(a1),x74931),x74932))),x74933))+P24(f328(f328(f245(a1),x74931),a84))
% 81.29/80.91 [7956]~P24(f328(f328(f244(a877),x79563),x79562))+P24(f328(f328(f244(a877),x79561),f328(f328(f22(a877),f328(f328(f81(a877),x79562),x79561)),x79563)))
% 81.29/80.91 [8163]~P24(f328(f328(f244(a877),x81631),x81632))+E(f328(f328(f127(a877),f138(a877,f328(f298(a877,x81631),x81632))),f138(a877,f328(f298(a877,x81632),f328(f328(f81(a877),x81632),x81633)))),f138(a877,f328(f298(a877,x81631),f328(f328(f81(a877),x81632),x81633))))
% 81.29/80.91 [8420]~P24(f328(f62(x84201),x84202))+E(f328(a118,f328(f38(x84201),f328(f328(f22(f885(x84201,a871)),x84202),f328(f328(f306(x84201),x84203),f193(f885(x84201,a871)))))),f328(f38(x84201),f328(f328(f306(x84201),x84203),x84202)))
% 81.29/80.91 [8469]~P24(f328(f62(x84691),x84692))+E(f328(f328(f81(a877),f79(a877)),f328(f38(x84691),f328(f328(f22(f885(x84691,a871)),x84692),f328(f328(f306(x84691),x84693),f193(f885(x84691,a871)))))),f328(f38(x84691),f328(f328(f306(x84691),x84693),x84692)))
% 81.29/80.91 [8649]E(f328(f328(f22(a877),f328(f38(x86491),x86492)),f328(f38(x86491),f328(f328(f107(f885(x86491,a871)),x86492),x86493))),f328(f38(x86491),f328(f328(f22(f885(x86491,a871)),x86492),x86493)))+~P24(f328(f62(x86491),f328(f328(f107(f885(x86491,a871)),x86492),x86493)))
% 81.29/80.91 [8880]~P28(f328(x88802,f482(x88802,x88803,x88801)))+E(f328(f106(a1),f328(f328(f6(x88801,a877),f328(f328(f8(a1,a877,x88801),a110),x88802)),x88803)),f328(f328(f6(x88801,a1),x88802),x88803))
% 81.29/80.91 [8881]~P28(f328(x88812,f481(x88812,x88813,x88811)))+E(f328(f106(a1),f328(f328(f9(x88811,a877),f328(f328(f8(a1,a877,x88811),a110),x88812)),x88813)),f328(f328(f9(x88811,a1),x88812),x88813))
% 81.29/80.91 [8928]~P24(f328(f62(x89281),x89283))+P24(f328(f328(f244(a877),f328(f328(f22(a877),f328(f38(x89281),x89282)),f328(f38(x89281),x89283))),f328(f38(x89281),f328(f328(f22(f885(x89281,a871)),x89282),x89283))))
% 81.29/80.91 [8954]P24(f328(f328(f330(x89541),f482(x89542,x89543,x89541)),x89543))+E(f328(f106(a1),f328(f328(f6(x89541,a877),f328(f328(f8(a1,a877,x89541),a110),x89542)),x89543)),f328(f328(f6(x89541,a1),x89542),x89543))
% 81.29/80.91 [8955]P24(f328(f328(f330(x89551),f481(x89552,x89553,x89551)),x89553))+E(f328(f106(a1),f328(f328(f9(x89551,a877),f328(f328(f8(a1,a877,x89551),a110),x89552)),x89553)),f328(f328(f9(x89551,a1),x89552),x89553))
% 81.29/80.91 [9024]E(f86(x90241,f328(f328(f7(x90241,f885(x90241,a871),a871),f330(x90241)),f328(f328(f22(f885(x90241,a871)),x90242),f328(f328(f306(x90241),x90243),f193(f885(x90241,a871)))))),f260(x90241,x90243,x90242))+P24(f328(f328(f244(f885(x90241,a871)),x90242),f328(f328(f306(x90241),x90243),f193(f885(x90241,a871)))))
% 81.29/80.91 [9372]E(f328(f328(f153(f878(x93721),x93721),f328(f328(f7(f878(x93721),a877,x93721),f164(x93721)),x93722)),f328(f135(f878(x93721),f328(f328(f8(a877,a871,f878(x93721)),f328(f245(a877),x93722)),f194(f878(x93721)))),x93723)),f328(f328(f164(f878(x93721)),f179(x93721,x93723)),x93722))+~P24(f328(f328(f245(a877),x93722),f328(f194(f878(f878(x93721))),f179(x93721,x93723))))
% 81.29/80.91 [9444]E(f328(f135(x94441,x94442),x94443),f176(x94441,x94442,x94443))+P24(f328(f328(f330(x94441),f662(x94443,x94442,x94441)),f328(f171(x94441),f328(f328(f137(x94441),f328(f194(f878(x94441)),f176(x94441,x94442,x94443))),x94443))))
% 81.29/80.91 [9584]E(f328(f328(f137(x95841),f328(f194(f878(x95841)),f176(x95841,x95842,x95843))),x95843),f119(x95841))+~P24(f328(x95842,f328(f140(x95841),f328(f328(f137(x95841),f328(f194(f878(x95841)),f176(x95841,x95842,x95843))),x95843))))
% 81.29/80.91 [9675]~P24(f328(f328(f330(f884(x96751,x96751)),x96752),f304(x96751,x96753)))+P24(f328(f328(f330(f884(x96751,x96751)),x96752),f328(f328(f43(a877,f885(f884(x96751,x96751),a871)),f252(f885(a877,a871))),f328(f328(f7(a877,f885(f884(x96751,x96751),a871),f885(f884(x96751,x96751),a871)),f188(f884(x96751,x96751),a871)),x96753))))
% 81.29/80.91 [9731]~P24(f328(f328(f244(f885(x97311,a871)),f328(f328(f43(a877,f885(x97311,a871)),f328(f298(a877,f2(a877)),f527(x97313,x97312,x97311))),x97312)),x97313))+P24(f328(f328(f244(f885(x97311,a871)),f328(f328(f43(a877,f885(x97311,a871)),f252(f885(a877,a871))),x97312)),x97313))
% 81.29/80.91 [9789]~P24(f328(f328(f245(a1),f2(a1)),x97893))+P24(f328(f328(f245(a1),x97891),f328(f328(f81(a1),x97892),f328(f328(f82(a1),f328(f328(f81(a1),f328(f76(a1),f328(f328(f22(a1),x97892),x97891))),f79(a1))),x97893))))
% 81.29/80.91 [9799]~P38(x97991,f328(f328(f116(f885(f884(x97991,x97991),a871)),x97992),x97993))+P38(x97991,f328(f328(f116(f885(f884(x97991,x97991),a871)),f328(f328(f116(f885(f884(x97991,x97991),a871)),f328(f328(f285(x97991,x97991,x97991),x97992),x97992)),f328(f328(f285(x97991,x97991,x97991),x97993),x97992))),x97993))
% 81.29/80.91 [9882]P38(x98821,f328(f328(f116(f885(f884(x98821,x98821),a871)),x98822),x98823))+~P38(x98821,f328(f328(f116(f885(f884(x98821,x98821),a871)),f328(f328(f116(f885(f884(x98821,x98821),a871)),f328(f328(f285(x98821,x98821,x98821),x98822),x98822)),f328(f328(f285(x98821,x98821,x98821),x98823),x98822))),x98823))
% 81.29/80.91 [9448]~P137(x94481)+E(f328(f108(x94481),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x94482),x94483)),f193(f885(f884(a877,a877),a871)))))),f328(f328(f22(x94481),f328(f106(x94481),x94482)),f328(f106(x94481),x94483)))
% 81.29/80.91 [9531]P24(f328(x95313,x95312))+E(f328(f249(x95311),f328(f328(f18(x95311,a871,a871),f328(f328(f8(a871,f885(a871,a871),x95311),a326),f328(f328(f7(x95311,x95311,a871),a325),x95312))),x95313)),f193(f885(x95311,a871)))
% 81.29/80.91 [9533]~P24(f328(x95333,x95332))+E(f328(f249(x95331),f328(f328(f18(x95331,a871,a871),f328(f328(f8(a871,f885(a871,a871),x95331),a326),f328(f328(f7(x95331,x95331,a871),a325),x95332))),x95333)),f328(f328(f306(x95331),x95332),f193(f885(x95331,a871))))
% 81.29/80.91 [9767]E(x97671,x97672)+P24(f328(f328(f261(x97673,x97673,f328(f328(f8(f885(x97673,a871),f885(x97673,a871),x97673),f328(f8(a871,a871,x97673),a323)),a325)),x97671),x97672))
% 81.29/80.91 [9859]~E(x98591,x98592)+~P24(f328(f328(f261(x98593,x98593,f328(f328(f8(f885(x98593,a871),f885(x98593,a871),x98593),f328(f8(a871,a871,x98593),a323)),a325)),x98591),x98592))
% 81.29/80.91 [9874]~P24(f328(f62(x98741),x98743))+E(f328(f328(f65(x98741,f885(x98741,a871),f328(f328(f8(f885(x98741,a871),f885(f885(x98741,a871),f885(x98741,a871)),x98741),f328(f7(f885(x98741,a871),f885(x98741,a871),f885(x98741,a871)),f22(f885(x98741,a871)))),f328(f328(f7(x98741,f885(x98741,a871),f885(x98741,a871)),f306(x98741)),f193(f885(x98741,a871))))),x98742),x98743),f328(f328(f22(f885(x98741,a871)),x98742),x98743))
% 81.29/80.91 [9908]~P24(f328(f328(f245(a1),f2(a1)),x99083))+P24(f328(f328(f245(a1),f328(f328(f22(a1),x99081),f328(f328(f82(a1),f328(f328(f81(a1),f328(f76(a1),f328(f328(f22(a1),x99081),x99082))),f79(a1))),x99083))),x99082))
% 81.29/80.91 [10134]~P24(f328(f328(f330(x101341),x101343),f317(x101341,x101342)))+P24(f328(f316(x101341,f328(f328(f7(x101341,f885(f884(x101341,x101341),a871),f885(x101341,a871)),f328(f328(f8(f885(x101341,f885(f885(f884(x101341,x101341),a871),a871)),f885(f885(f884(x101341,x101341),a871),f885(x101341,a871)),x101341),f7(x101341,f885(f884(x101341,x101341),a871),a871)),f328(f328(f8(f885(x101341,f884(x101341,x101341)),f885(x101341,f885(f885(f884(x101341,x101341),a871),a871)),x101341),f328(f8(f884(x101341,x101341),f885(f885(f884(x101341,x101341),a871),a871),x101341),f330(f884(x101341,x101341)))),f257(x101341,x101341)))),x101342)),x101343))
% 81.29/80.91 [10146]P24(f328(f328(f330(x101461),x101462),f317(x101461,x101463)))+~P24(f328(f316(x101461,f328(f328(f7(x101461,f885(f884(x101461,x101461),a871),f885(x101461,a871)),f328(f328(f8(f885(x101461,f885(f885(f884(x101461,x101461),a871),a871)),f885(f885(f884(x101461,x101461),a871),f885(x101461,a871)),x101461),f7(x101461,f885(f884(x101461,x101461),a871),a871)),f328(f328(f8(f885(x101461,f884(x101461,x101461)),f885(x101461,f885(f885(f884(x101461,x101461),a871),a871)),x101461),f328(f8(f884(x101461,x101461),f885(f885(f884(x101461,x101461),a871),a871),x101461),f330(f884(x101461,x101461)))),f257(x101461,x101461)))),x101463)),x101462))
% 81.29/80.91 [9729]~P24(f328(f62(x97291),f328(f249(x97291),x97293)))+P24(f328(f62(x97291),f328(f249(x97291),f328(f328(f18(x97291,a871,a871),f328(f328(f8(a871,f885(a871,a871),x97291),a326),x97292)),x97293))))
% 81.29/80.91 [9730]~P24(f328(f62(x97301),f328(f249(x97301),x97302)))+P24(f328(f62(x97301),f328(f249(x97301),f328(f328(f18(x97301,a871,a871),f328(f328(f8(a871,f885(a871,a871),x97301),a326),x97302)),x97303))))
% 81.29/80.91 [9830]P24(f328(f62(x98301),f328(f249(x98301),x98302)))+~P24(f328(f62(x98301),f328(f249(x98301),f328(f328(f18(x98301,a871,a871),f328(f328(f8(a871,f885(a871,a871),x98301),a327),x98303)),x98302))))
% 81.29/80.91 [9831]P24(f328(f62(x98311),f328(f249(x98311),x98312)))+~P24(f328(f62(x98311),f328(f249(x98311),f328(f328(f18(x98311,a871,a871),f328(f328(f8(a871,f885(a871,a871),x98311),a327),x98312)),x98313))))
% 81.29/80.91 [10120]~P24(f328(f62(x101201),x101202))+P24(f328(f62(f878(x101201)),f328(f249(f878(x101201)),f328(f328(f18(f878(x101201),a871,a871),f328(f328(f8(a871,f885(a871,a871),f878(x101201)),a326),f328(f328(f7(f878(x101201),f885(x101201,a871),a871),f328(f328(f8(f885(x101201,a871),f885(f885(x101201,a871),a871),f878(x101201)),f244(f885(x101201,a871))),f171(x101201))),x101202))),f328(f328(f7(f878(x101201),a877,a871),f328(f328(f8(a877,f885(a877,a871),f878(x101201)),a325),f194(f878(x101201)))),x101203)))))
% 81.29/80.91 [10121]~P24(f328(f62(x101211),x101212))+P24(f328(f62(f878(x101211)),f328(f249(f878(x101211)),f328(f328(f18(f878(x101211),a871,a871),f328(f328(f8(a871,f885(a871,a871),f878(x101211)),a326),f328(f328(f7(f878(x101211),f885(x101211,a871),a871),f328(f328(f8(f885(x101211,a871),f885(f885(x101211,a871),a871),f878(x101211)),f244(f885(x101211,a871))),f171(x101211))),x101212))),f328(f328(f7(f878(x101211),a877,a871),f328(f328(f8(a877,f885(a877,a871),f878(x101211)),f244(a877)),f194(f878(x101211)))),x101213)))))
% 81.29/80.91 [9846]~P112(x98461)+E(f328(f328(f258(x98461),x98462),f328(f328(f82(a877),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x98463)),f328(f328(f82(x98461),f328(f328(f258(x98461),x98462),x98463)),f328(f328(f258(x98461),x98462),x98463)))
% 81.29/80.91 [9887]~P83(x98871)+E(f328(f328(f258(x98871),f328(f328(f258(x98871),x98872),x98873)),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f328(f328(f258(x98871),x98872),f328(f328(f82(a877),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x98873)))
% 81.29/80.91 [9935]~P137(x99351)+E(f328(f328(f258(x99351),f328(f80(x99351),x99352)),f328(f328(f82(a877),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x99353)),f328(f328(f258(x99351),x99352),f328(f328(f82(a877),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x99353)))
% 81.29/80.91 [10077]~P111(x100771)+P24(f328(f328(f244(x100771),f2(x100771)),f328(f328(f81(x100771),f328(f328(f258(x100771),x100772),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x100771),x100773),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))))
% 81.29/80.91 [9945]~P112(x99451)+E(f328(f328(f258(x99451),x99452),f328(a118,f328(f328(f82(a877),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x99453))),f328(f328(f82(x99451),x99452),f328(f328(f82(x99451),f328(f328(f258(x99451),x99452),x99453)),f328(f328(f258(x99451),x99452),x99453))))
% 81.29/80.91 [9996]~P83(x99961)+E(f328(f328(f82(x99961),x99962),f328(f328(f258(x99961),f328(f328(f258(x99961),x99962),x99963)),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x99961),x99962),f328(a118,f328(f328(f82(a877),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x99963))))
% 81.29/80.91 [10034]~P111(x100341)+P24(f328(f328(f244(x100341),f2(x100341)),f328(f328(f258(x100341),x100342),f328(f328(f82(a877),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x100343))))
% 81.29/80.91 [10100]~P96(x101001)+E(f328(f328(f22(x101001),f328(f328(f81(x101001),f328(f328(f258(x101001),x101002),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x101001),x101003),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))),f328(f328(f82(x101001),f328(f328(f82(x101001),f328(f109(x101001),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x101002)),x101003)),f328(f328(f258(x101001),f328(f328(f22(x101001),x101002),x101003)),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))
% 81.29/80.91 [10101]~P96(x101011)+E(f328(f328(f81(x101011),f328(f328(f81(x101011),f328(f328(f258(x101011),x101012),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x101011),x101013),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))),f328(f328(f82(x101011),f328(f328(f82(x101011),f328(f109(x101011),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x101012)),x101013)),f328(f328(f258(x101011),f328(f328(f81(x101011),x101012),x101013)),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))
% 81.29/80.91 [10197]~P30(x101971,x101972,x101973)+P24(f101(x101971,a871,f328(f328(f8(f885(a873,f885(f885(x101971,f885(a872,a871)),f885(x101971,a871))),f885(a873,f885(f885(x101971,f885(a872,a871)),a871)),f885(x101971,f885(a872,a871))),f328(f8(f885(f885(x101971,f885(a872,a871)),f885(x101971,a871)),f885(f885(x101971,f885(a872,a871)),a871),a873),f328(f8(f885(x101971,a871),a871,f885(x101971,f885(a872,a871))),f89(x101971)))),f328(f328(f8(f885(a873,f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871)))),f885(a873,f885(f885(x101971,f885(a872,a871)),f885(x101971,a871))),f885(x101971,f885(a872,a871))),f328(f8(f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871))),f885(f885(x101971,f885(a872,a871)),f885(x101971,a871)),a873),f328(f8(f885(x101971,f885(a872,a871)),f885(x101971,a871),f885(x101971,f885(a872,a871))),f328(f8(f885(a872,a871),a871,x101971),f89(a872))))),f328(f328(f7(f885(x101971,f885(a872,a871)),f885(a873,f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871)))),f885(a873,f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871))))),f328(f328(f8(f885(f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871))),f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871)))),f885(f885(a873,f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871)))),f885(a873,f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871))))),f885(x101971,f885(a872,a871))),f8(f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871))),f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871))),a873)),f328(f328(f8(f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871))),f885(f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871))),f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871)))),f885(x101971,f885(a872,a871))),f8(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871)))),f328(f328(f8(f885(x101971,f885(f885(a872,a871),f885(a872,a871))),f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871))),f885(x101971,f885(a872,a871))),f18(x101971,f885(a872,a871),f885(a872,a871))),f328(f328(f8(f885(x101971,f885(a872,f885(a871,a871))),f885(x101971,f885(f885(a872,a871),f885(a872,a871))),f885(x101971,f885(a872,a871))),f328(f8(f885(a872,f885(a871,a871)),f885(f885(a872,a871),f885(a872,a871)),x101971),f18(a872,a871,a871))),f328(f8(f885(a872,a871),f885(a872,f885(a871,a871)),x101971),f328(f8(a871,f885(a871,a871),a872),a331))))))),f328(f328(f8(f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,f885(a872,a871)))),f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871))),a873),f328(f8(f885(x101971,f885(a872,f885(a872,a871))),f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,a871))),f328(f8(f885(a872,f885(a872,a871)),f885(a872,a871),x101971),f328(f8(f885(a872,a871),a871,a872),f89(a872))))),f328(f328(f8(f885(f885(a872,a871),f885(a872,f885(a872,a871))),f885(f885(x101971,f885(a872,a871)),f885(x101971,f885(a872,f885(a872,a871)))),a873),f8(f885(a872,a871),f885(a872,f885(a872,a871)),x101971)),f328(f328(f8(f885(a872,f885(f885(a872,a871),f885(a872,a871))),f885(f885(a872,a871),f885(a872,f885(a872,a871))),a873),f7(a872,f885(a872,a871),f885(a872,a871))),f328(f328(f8(f885(a872,f885(a872,f885(a871,a871))),f885(a872,f885(f885(a872,a871),f885(a872,a871))),a873),f328(f8(f885(a872,f885(a871,a871)),f885(f885(a872,a871),f885(a872,a871)),a872),f18(a872,a871,a871))),f328(f328(f8(f885(a872,f885(a872,a871)),f885(a872,f885(a872,f885(a871,a871))),a873),f328(f8(f885(a872,a871),f885(a872,f885(a871,a871)),a872),f328(f8(a871,f885(a871,a871),a872),a331))),f328(f328(f7(a873,a877,f885(a872,f885(a872,a871))),f328(f328(f8(f885(a872,f885(a877,f885(a872,a871))),f885(a877,f885(a872,f885(a872,a871))),a873),f7(a872,a877,f885(a872,a871))),a202)),x101972))))))))),x101973))
% 81.29/80.91 [10199]P30(x101991,x101992,x101993)+~P24(f101(x101991,a871,f328(f328(f8(f885(a873,f885(f885(x101991,f885(a872,a871)),f885(x101991,a871))),f885(a873,f885(f885(x101991,f885(a872,a871)),a871)),f885(x101991,f885(a872,a871))),f328(f8(f885(f885(x101991,f885(a872,a871)),f885(x101991,a871)),f885(f885(x101991,f885(a872,a871)),a871),a873),f328(f8(f885(x101991,a871),a871,f885(x101991,f885(a872,a871))),f89(x101991)))),f328(f328(f8(f885(a873,f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871)))),f885(a873,f885(f885(x101991,f885(a872,a871)),f885(x101991,a871))),f885(x101991,f885(a872,a871))),f328(f8(f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871))),f885(f885(x101991,f885(a872,a871)),f885(x101991,a871)),a873),f328(f8(f885(x101991,f885(a872,a871)),f885(x101991,a871),f885(x101991,f885(a872,a871))),f328(f8(f885(a872,a871),a871,x101991),f89(a872))))),f328(f328(f7(f885(x101991,f885(a872,a871)),f885(a873,f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871)))),f885(a873,f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871))))),f328(f328(f8(f885(f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871))),f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871)))),f885(f885(a873,f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871)))),f885(a873,f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871))))),f885(x101991,f885(a872,a871))),f8(f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871))),f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871))),a873)),f328(f328(f8(f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871))),f885(f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871))),f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871)))),f885(x101991,f885(a872,a871))),f8(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871)))),f328(f328(f8(f885(x101991,f885(f885(a872,a871),f885(a872,a871))),f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871))),f885(x101991,f885(a872,a871))),f18(x101991,f885(a872,a871),f885(a872,a871))),f328(f328(f8(f885(x101991,f885(a872,f885(a871,a871))),f885(x101991,f885(f885(a872,a871),f885(a872,a871))),f885(x101991,f885(a872,a871))),f328(f8(f885(a872,f885(a871,a871)),f885(f885(a872,a871),f885(a872,a871)),x101991),f18(a872,a871,a871))),f328(f8(f885(a872,a871),f885(a872,f885(a871,a871)),x101991),f328(f8(a871,f885(a871,a871),a872),a331))))))),f328(f328(f8(f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,f885(a872,a871)))),f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871))),a873),f328(f8(f885(x101991,f885(a872,f885(a872,a871))),f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,a871))),f328(f8(f885(a872,f885(a872,a871)),f885(a872,a871),x101991),f328(f8(f885(a872,a871),a871,a872),f89(a872))))),f328(f328(f8(f885(f885(a872,a871),f885(a872,f885(a872,a871))),f885(f885(x101991,f885(a872,a871)),f885(x101991,f885(a872,f885(a872,a871)))),a873),f8(f885(a872,a871),f885(a872,f885(a872,a871)),x101991)),f328(f328(f8(f885(a872,f885(f885(a872,a871),f885(a872,a871))),f885(f885(a872,a871),f885(a872,f885(a872,a871))),a873),f7(a872,f885(a872,a871),f885(a872,a871))),f328(f328(f8(f885(a872,f885(a872,f885(a871,a871))),f885(a872,f885(f885(a872,a871),f885(a872,a871))),a873),f328(f8(f885(a872,f885(a871,a871)),f885(f885(a872,a871),f885(a872,a871)),a872),f18(a872,a871,a871))),f328(f328(f8(f885(a872,f885(a872,a871)),f885(a872,f885(a872,f885(a871,a871))),a873),f328(f8(f885(a872,a871),f885(a872,f885(a871,a871)),a872),f328(f8(a871,f885(a871,a871),a872),a331))),f328(f328(f7(a873,a877,f885(a872,f885(a872,a871))),f328(f328(f8(f885(a872,f885(a877,f885(a872,a871))),f885(a877,f885(a872,f885(a872,a871))),a873),f7(a872,a877,f885(a872,a871))),a202)),x101992))))))))),x101993))
% 81.29/80.91 [4676]E(x46761,x46762)+~E(f34(x46763,x46761),f34(x46764,x46762))
% 81.29/80.91 [4677]E(x46771,x46772)+~E(f34(x46771,x46773),f34(x46772,x46774))
% 81.29/80.91 [4678]E(x46781,x46782)+~E(f33(x46783,x46781),f33(x46784,x46782))
% 81.29/80.91 [4679]E(x46791,x46792)+~E(f33(x46791,x46793),f33(x46792,x46794))
% 81.29/80.91 [7757]P21(x77571,x77572,x77573,x77574)+~E(f541(x77574,x77573,x77572,x77571),f548(x77574,x77573,x77572,x77571))
% 81.29/80.91 [8052]P35(x80521,x80522,x80523,x80524,f119(x80522))+~E(x80524,f119(x80521))
% 81.29/80.91 [8053]P35(x80531,x80532,x80533,f119(x80531),x80534)+~E(x80534,f119(x80532))
% 81.29/80.91 [8268]~P21(x82681,f881(x82682),x82684,f183(x82681,x82682,x82684))+P21(x82681,f881(x82682),f184(x82681,x82682,x82683,x82684),f183(x82681,x82682,x82684))
% 81.29/80.91 [8483]~P21(x84831,f881(x84832),f184(x84831,x84832,x84834,x84833),f183(x84831,x84832,x84833))+P21(x84831,f881(x84832),x84833,f183(x84831,x84832,x84833))
% 81.29/80.91 [8599]~P35(x85992,x85993,x85994,x85991,f119(x85993))+E(x85991,f119(x85992))
% 81.29/80.91 [8600]~P35(x86003,x86002,x86004,f119(x86003),x86001)+E(x86001,f119(x86002))
% 81.29/80.91 [5051]~P13(x50513,x50511,x50514)+E(f328(f328(x50511,x50512),x50512),x50512)
% 81.29/80.91 [5343]~E(x53434,f193(f885(x53431,a871)))+E(f328(f307(x53431,x53432,x53433),x53434),f193(f885(x53432,a871)))
% 81.29/80.91 [5611]~E(f328(f307(x56112,x56113,x56114),x56111),f193(f885(x56113,a871)))+E(x56111,f193(f885(x56112,a871)))
% 81.29/80.91 [5894]~P106(x58942)+E(f328(f328(f147(x58941,x58942,x58943),x58944),f119(x58941)),f328(f328(f150(x58941),x58944),f119(x58941)))
% 81.29/80.91 [5932]E(f328(x59321,x59322),f196(x59323))+P24(f328(f328(f330(x59324),x59322),f183(x59324,x59323,x59321)))
% 81.29/80.91 [6255]~E(x62551,f193(f885(x62552,a871)))+~P24(f328(f63(x62552,x62553,x62551),x62554))
% 81.29/80.91 [6277]~P56(x62771,x62773,x62774,x62772)+P24(f328(f62(x62771),x62772))
% 81.29/80.91 [6278]~P56(x62781,x62783,x62782,x62784)+P24(f328(f62(x62781),x62782))
% 81.29/80.91 [6284]~P56(x62842,x62843,x62844,x62841)+~E(x62841,f193(f885(x62842,a871)))
% 81.29/80.91 [6315]~P108(x63151)+E(f328(f328(f107(f885(x63151,a871)),f328(f298(x63151,x63152),x63153)),f299(x63151,x63153,x63154)),f193(f885(x63151,a871)))
% 81.29/80.91 [6342]~P24(f328(f328(x63423,x63424),x63422))+P24(f328(f328(f330(x63421),x63422),f289(x63421,x63423,x63424)))
% 81.29/80.91 [6343]~P24(f328(f328(x63433,x63434),x63432))+P24(f328(f328(f330(x63431),x63432),f290(x63431,x63433,x63434)))
% 81.29/80.91 [6344]~P24(f328(f328(x63443,x63442),x63444))+P24(f328(f328(f330(x63441),x63442),f291(x63441,x63443,x63444)))
% 81.29/80.91 [6345]~P24(f328(f328(x63453,x63452),x63454))+P24(f328(f328(f330(x63451),x63452),f294(x63451,x63453,x63454)))
% 81.29/80.91 [6486]~P108(x64861)+E(f328(f328(f107(f885(x64861,a871)),f302(x64861,x64862,x64863)),f299(x64861,x64863,x64864)),f193(f885(x64861,a871)))
% 81.29/80.91 [6487]~P108(x64871)+E(f328(f328(f107(f885(x64871,a871)),f301(x64871,x64872,x64873)),f302(x64871,x64873,x64874)),f193(f885(x64871,a871)))
% 81.29/80.91 [6488]~P108(x64881)+E(f328(f328(f107(f885(x64881,a871)),f301(x64881,x64882,x64883)),f301(x64881,x64883,x64884)),f193(f885(x64881,a871)))
% 81.29/80.91 [6489]~P108(x64891)+E(f328(f328(f107(f885(x64891,a871)),f299(x64891,x64892,x64893)),f302(x64891,x64893,x64894)),f193(f885(x64891,a871)))
% 81.29/80.91 [6490]~P108(x64901)+E(f328(f328(f107(f885(x64901,a871)),f299(x64901,x64902,x64903)),f301(x64901,x64903,x64904)),f193(f885(x64901,a871)))
% 81.29/80.91 [6528]P24(f328(f328(x65281,x65282),f682(x65282,x65281)))+~P24(f328(f263(x65283,x65284,x65281),x65282))
% 81.29/80.91 [6577]~E(f328(x65771,x65772),f196(x65773))+~P24(f328(f328(f330(x65774),x65772),f183(x65774,x65773,x65771)))
% 81.29/80.91 [6606]~P106(x66062)+E(f328(f171(x66061),f149(x66061,x66062,x66063,x66064)),f328(f171(x66061),x66064))
% 81.29/80.91 [6658]~P141(x66581)+E(f195(x66581,x66582,f328(a118,x66583),x66584),f195(x66581,x66582,x66583,f328(x66582,x66584)))
% 81.29/80.91 [6719]~P24(f328(f328(f330(x67194),x67193),f289(x67194,x67191,x67192)))+P24(f328(f328(x67191,x67192),x67193))
% 81.29/80.91 [6720]~P24(f328(f328(f330(x67204),x67203),f290(x67204,x67201,x67202)))+P24(f328(f328(x67201,x67202),x67203))
% 81.29/80.91 [6721]~P24(f328(f328(f330(x67214),x67212),f291(x67214,x67211,x67213)))+P24(f328(f328(x67211,x67212),x67213))
% 81.29/80.91 [6722]~P24(f328(f328(f330(x67224),x67222),f294(x67224,x67221,x67223)))+P24(f328(f328(x67221,x67222),x67223))
% 81.29/80.91 [6799]E(f328(f38(f883(x67991,x67992)),f315(x67991,x67992,x67993,x67994)),f2(a877))+P24(f328(f62(x67992),x67994))
% 81.29/80.91 [6800]E(f328(f38(f883(x68001,x68002)),f315(x68001,x68002,x68003,x68004)),f2(a877))+P24(f328(f62(x68001),x68003))
% 81.29/80.91 [6999]~P11(x69994,x69991,x69992)+E(f328(f74(x69991,x69991,x69991,f328(x69992,x69993)),f328(x69992,x69993)),f328(x69992,x69993))
% 81.29/80.91 [7794]~P24(f328(x77941,x77944))+P24(f328(x77941,f97(x77942,a877,x77943,x77941)))
% 81.29/80.91 [7877]~E(x78772,x78773)+P24(f328(f328(f330(f884(x78771,x78771)),f328(f328(f257(x78771,x78771),x78772),x78773)),f304(x78771,x78774)))
% 81.29/80.91 [7906]~P21(x79061,x79062,x79063,f252(f885(x79061,a871)))+E(f328(f78(x79061,x79062,f252(f885(x79061,a871)),x79063),f328(x79063,x79064)),x79064)
% 81.29/80.91 [7998]~P24(f328(f328(f330(f878(x79981)),f328(f328(f150(x79981),x79984),x79982)),f160(x79981,x79983)))+P24(f328(f328(f330(f878(x79981)),x79982),f160(x79981,x79983)))
% 81.29/80.91 [7999]~P24(f328(f328(f330(f878(x79991)),f328(f328(f127(x79991),x79994),x79992)),f160(x79991,x79993)))+P24(f328(f328(f330(f878(x79991)),x79992),f160(x79991,x79993)))
% 81.29/80.91 [8000]~P24(f328(f328(f330(f878(x80001)),f328(f328(f127(x80001),x80002),x80004)),f160(x80001,x80003)))+P24(f328(f328(f330(f878(x80001)),x80002),f160(x80001,x80003)))
% 81.29/80.91 [8016]~P106(x80161)+P29(x80161,f328(f328(f153(x80162,x80161),x80163),f149(x80162,x80161,x80163,x80164)))
% 81.29/80.91 [8114]P21(x81144,x81143,x81141,x81142)+E(f328(x81141,f541(x81142,x81141,x81143,x81144)),f328(x81141,f548(x81142,x81141,x81143,x81144)))
% 81.29/80.91 [8127]E(f184(x81271,x81272,x81273,x81274),f184(x81271,x81272,x81274,x81273))+~E(f328(f328(f107(f885(x81271,a871)),f183(x81271,x81272,x81273)),f183(x81271,x81272,x81274)),f193(f885(x81271,a871)))
% 81.29/80.91 [8231]~P21(x82312,x82311,x82314,x82313)+P21(x82311,x82312,f78(x82312,x82311,x82313,x82314),f328(f307(x82312,x82311,x82314),x82313))
% 81.29/80.91 [8367]P38(f884(x83672,x83674),f280(x83672,x83674,x83671,x83673))+P24(f328(x83671,f690(x83672,x83673,x83674,x83671)))
% 81.29/80.91 [8490]E(x84901,x84902)+~P24(f328(f328(f330(f884(x84903,x84903)),f328(f328(f257(x84903,x84903),x84901),x84902)),f254(x84903,x84904)))
% 81.29/80.91 [8554]~P24(f328(f62(f883(x85543,x85541)),f315(x85543,x85541,x85544,x85542)))+P24(f328(f62(x85541),x85542))
% 81.29/80.91 [8555]~P24(f328(f62(f883(x85551,x85553)),f315(x85551,x85553,x85552,x85554)))+P24(f328(f62(x85551),x85552))
% 81.29/80.91 [8733]P38(f884(x87331,x87332),f280(x87331,x87332,x87333,x87334))+~P38(x87332,f328(x87334,f690(x87331,x87334,x87332,x87333)))
% 81.29/80.91 [9294]E(f328(f328(f158(x92941,x92942),f614(x92943,x92944,x92942,x92941)),f615(x92943,x92944,x92942,x92941)),x92944)+~P24(f328(f328(f330(f884(f878(x92941),f878(x92941))),f328(f328(f257(f878(x92941),f878(x92941)),x92942),x92944)),f156(x92941,x92943)))
% 81.29/80.91 [9295]~P24(f328(x92953,x92954))+P24(f328(f328(f244(a877),f328(x92951,f97(x92952,a877,x92951,x92953))),f328(x92951,x92954)))
% 81.29/80.91 [9301]~P24(f328(f328(f330(f884(f878(x93011),f878(x93011))),f328(f328(f257(f878(x93011),f878(x93011)),x93012),x93013)),f144(x93011,x93014)))+P24(f328(f328(f330(f884(f878(x93011),f878(x93011))),f328(f328(f257(f878(x93011),f878(x93011)),x93012),x93013)),f146(x93011,x93014)))
% 81.29/80.91 [9406]P24(f328(f62(x94061),x94062))+~P24(f328(f328(f330(f884(f885(x94061,a871),f885(x94061,a871))),f328(f328(f257(f885(x94061,a871),f885(x94061,a871)),x94063),x94062)),f319(x94061,x94064)))
% 81.29/80.91 [9407]P24(f328(f62(x94071),x94072))+~P24(f328(f328(f330(f884(f885(x94071,a871),f885(x94071,a871))),f328(f328(f257(f885(x94071,a871),f885(x94071,a871)),x94072),x94073)),f319(x94071,x94074)))
% 81.29/80.91 [9410]~E(x94101,f193(f885(x94102,a871)))+~P24(f328(f328(f330(f884(f885(x94102,a871),f885(x94102,a871))),f328(f328(f257(f885(x94102,a871),f885(x94102,a871)),x94103),x94101)),f319(x94102,x94104)))
% 81.29/80.91 [10046]P9(x100461,x100462,x100463,x100464)+~P24(f328(f328(f267(x100461,x100461,a871),f328(f328(f7(x100461,f885(x100461,x100462),f885(x100461,a871)),f328(f328(f8(f885(x100462,a871),f885(f885(x100461,x100462),f885(x100461,a871)),x100461),f8(x100462,a871,x100461)),f328(f328(f8(x100462,f885(x100462,a871),x100461),a325),x100464))),x100464)),f606(x100464,x100463,x100462,x100461)))
% 81.29/80.91 [4952]~E(x49524,f119(x49521))+E(f328(f328(f153(x49521,x49522),x49523),x49524),f119(x49522))
% 81.29/80.91 [4953]~E(x49534,f196(x49531))+E(f328(f328(f207(x49531,x49532),x49533),x49534),f196(x49532))
% 81.29/80.91 [4954]~E(x49542,f119(x49541))+E(f328(f328(f158(x49541,x49542),x49543),x49544),f119(x49541))
% 81.29/80.91 [5190]E(x51901,f196(x51902))+~E(f328(f328(f207(x51902,x51903),x51904),x51901),f196(x51903))
% 81.29/80.91 [5191]E(x51911,f119(x51912))+~E(f328(f328(f153(x51912,x51913),x51914),x51911),f119(x51913))
% 81.29/80.91 [5192]E(x51921,f119(x51922))+~E(f328(f328(f158(x51922,x51921),x51923),x51924),f119(x51922))
% 81.29/80.91 [5224]E(x52241,x52242)+~E(f328(f328(f127(x52243),x52244),x52241),f328(f328(f127(x52243),x52244),x52242))
% 81.29/80.91 [5225]E(x52251,x52252)+~E(f328(f328(f127(x52253),x52251),x52254),f328(f328(f127(x52253),x52252),x52254))
% 81.29/80.91 [5381]P24(f328(x53813,x53812))+E(f169(x53811,x53812,f328(f135(x53811,x53813),x53814)),f328(f135(x53811,x53813),x53814))
% 81.29/80.91 [5384]~P24(f328(x53842,x53843))+P34(x53841,x53842,f328(f328(f150(x53841),x53843),x53844))
% 81.29/80.91 [5393]E(x53931,x53932)+~E(f138(a877,f328(f298(a877,x53931),x53933)),f328(f328(f150(a877),x53932),x53934))
% 81.29/80.91 [5441]~P22(x54412,x54413)+P22(x54411,f328(f328(f75(x54412,x54411),x54413),x54414))
% 81.29/80.91 [5442]~P38(x54422,x54423)+P38(x54421,f328(f328(f284(x54422,x54421),x54423),x54424))
% 81.29/80.91 [5567]~P34(x55671,x55672,x55674)+P34(x55671,x55672,f328(f328(f150(x55671),x55673),x55674))
% 81.29/80.91 [5568]~P34(x55681,x55682,x55684)+P34(x55681,x55682,f328(f328(f127(x55681),x55683),x55684))
% 81.29/80.91 [5569]~P34(x55691,x55692,x55693)+P34(x55691,x55692,f328(f328(f127(x55691),x55693),x55694))
% 81.29/80.91 [5654]~E(x56541,f119(x56542))+~E(f328(f328(f127(x56542),x56543),f328(f328(f150(x56542),x56544),f119(x56542))),x56541)
% 81.29/80.91 [5679]~P32(x56793,x56791,f328(f328(f150(x56793),x56792),x56794))+P24(f328(x56791,x56792))
% 81.29/80.91 [5689]E(f143(x56891,x56892),x56893)+~E(f328(f328(f127(x56891),x56894),f328(f328(f150(x56891),x56893),f119(x56891))),x56892)
% 81.29/80.91 [5690]E(f120(x56901,x56902),x56903)+~E(f328(f328(f127(x56901),x56903),f328(f328(f150(x56901),x56904),f119(x56901))),x56902)
% 81.29/80.91 [5799]~E(f138(a877,f328(f298(a877,x57991),x57992)),f328(f328(f150(a877),x57993),x57994))+P24(f328(f328(f245(a877),x57991),x57992))
% 81.29/80.91 [5807]P32(x58071,x58072,x58073)+~P32(x58071,x58072,f328(f328(f150(x58071),x58074),x58073))
% 81.29/80.91 [5808]P32(x58081,x58082,x58083)+~P32(x58081,x58082,f328(f328(f127(x58081),x58084),x58083))
% 81.29/80.91 [5809]P32(x58091,x58092,x58093)+~P32(x58091,x58092,f328(f328(f127(x58091),x58093),x58094))
% 81.29/80.91 [6000]E(x60001,f328(f328(f127(x60002),f328(f168(x60002),x60003)),f328(f328(f150(x60002),x60004),f119(x60002))))+~E(f328(f168(x60002),x60001),f328(f328(f150(x60002),x60004),x60003))
% 81.29/80.91 [6177]~P108(x61771)+E(f328(f328(f107(f885(x61771,a871)),f328(f298(x61771,x61772),x61773)),f328(f298(x61771,x61773),x61774)),f193(f885(x61771,a871)))
% 81.29/80.91 [6213]~P74(x62131)+E(f328(f165(x62131),f328(f328(f153(a1,x62131),x62132),f178(x62133,x62134))),f328(f328(f6(a1,x62131),x62132),f328(f171(a1),f178(x62133,x62134))))
% 81.29/80.91 [6214]~P74(x62141)+E(f328(f328(f6(a1,x62141),x62142),f328(f171(a1),f178(x62143,x62144))),f328(f165(x62141),f328(f328(f153(a1,x62141),x62142),f178(x62143,x62144))))
% 81.29/80.91 [6357]~E(x63572,f328(f328(f127(x63571),f328(f168(x63571),x63574)),f328(f328(f150(x63571),x63573),f119(x63571))))+E(f328(f168(x63571),x63572),f328(f328(f150(x63571),x63573),x63574))
% 81.29/80.91 [6373]~P15(x63732,x63733,x63734,x63731)+E(f328(x63731,f193(f885(x63732,a871))),f35(x63733))
% 81.29/80.91 [6399]~P108(x63991)+E(f328(f328(f107(f885(x63991,a871)),f302(x63991,x63992,x63993)),f328(f298(x63991,x63993),x63994)),f193(f885(x63991,a871)))
% 81.29/80.91 [6607]E(x66071,f193(f885(x66072,a871)))+~E(f315(x66073,x66072,x66074,x66071),f193(f885(f883(x66073,x66072),a871)))
% 81.29/80.91 [6608]E(x66081,f193(f885(x66082,a871)))+~E(f315(x66082,x66083,x66081,x66084),f193(f885(f883(x66082,x66083),a871)))
% 81.29/80.91 [6678]~P106(x66782)+E(f328(f194(f878(x66781)),f149(x66781,x66782,x66783,x66784)),f328(f194(f878(x66781)),x66784))
% 81.29/80.91 [6690]~P24(f328(f264(x66903,x66904,x66901),x66902))+P24(f328(f328(x66901,f683(x66902,x66901)),x66902))
% 81.29/80.91 [6730]~P24(f328(f62(x67302),x67304))+P24(f328(f62(x67301),f328(f307(x67302,x67301,x67303),x67304)))
% 81.29/80.91 [6959]~P21(x69592,x69591,x69593,x69594)+E(f328(f38(x69591),f328(f307(x69592,x69591,x69593),x69594)),f328(f38(x69592),x69594))
% 81.29/80.91 [6978]E(f328(f307(x69781,x69782,x69783),f328(f308(x69781,x69782,x69783),x69784)),x69784)+~E(f328(f307(x69781,x69782,x69783),f252(f885(x69781,a871))),f252(f885(x69782,a871)))
% 81.29/80.91 [7388]~P21(x73881,x73882,x73883,f252(f885(x73881,a871)))+E(f328(f308(x73881,x73882,x73883),f328(f307(x73881,x73882,x73883),x73884)),x73884)
% 81.29/80.91 [7718]P24(f328(x77181,x77182))+~P24(f328(f328(f330(x77183),x77182),f328(f171(x77183),f176(x77183,x77181,x77184))))
% 81.29/80.91 [7824]~P24(f328(f328(f330(f878(x78241)),f328(f328(f150(x78241),x78242),x78244)),f160(x78241,x78243)))+P24(f328(f328(f330(x78241),x78242),x78243))
% 81.29/80.91 [7952]~P24(f328(f328(f330(x79521),x79522),f328(f171(x79521),f169(x79521,x79524,x79523))))+P24(f328(f328(f330(x79521),x79522),f328(f171(x79521),x79523)))
% 81.29/80.91 [7954]~P24(f328(f328(f330(x79541),x79542),f328(f171(x79541),f175(x79541,x79543,x79544))))+P24(f328(f328(f330(x79541),x79542),f328(f171(x79541),x79543)))
% 81.29/80.91 [7955]~P24(f328(f328(f330(x79551),x79552),f328(f171(x79551),f176(x79551,x79554,x79553))))+P24(f328(f328(f330(x79551),x79552),f328(f171(x79551),x79553)))
% 81.29/80.91 [7965]E(f328(f194(f878(x79651)),x79652),x79653)+~P24(f328(f328(f330(f878(x79651)),x79652),f328(f171(f878(x79651)),f55(x79651,x79653,x79654))))
% 81.29/80.91 [8064]P24(f328(x80643,x80642))+E(f328(f135(x80641,f328(f328(f8(a871,a871,x80641),a323),f328(a325,x80642))),f328(f135(x80641,x80643),x80644)),f328(f135(x80641,x80643),x80644))
% 81.29/80.91 [8180]E(f328(f328(f164(x81801),f176(x81801,x81802,x81803)),x81804),f328(f328(f164(x81801),x81803),x81804))+~P24(f328(f328(f245(a877),x81804),f328(f194(f878(x81801)),f176(x81801,x81802,x81803))))
% 81.29/80.91 [8266]~P74(x82661)+E(f328(f328(f6(a877,x82661),f328(f328(f8(a877,x82661,a877),x82662),a118)),f328(f298(a877,x82663),x82664)),f328(f328(f6(a877,x82661),x82662),f328(f298(a877,f328(a118,x82663)),f328(a118,x82664))))
% 81.29/80.91 [8275]~P74(x82751)+E(f328(f328(f6(a877,x82751),f328(f328(f8(a877,x82751,a877),x82752),a118)),f299(a877,x82753,x82754)),f328(f328(f6(a877,x82751),x82752),f299(a877,f328(a118,x82753),f328(a118,x82754))))
% 81.29/80.91 [8404]~P21(x84041,x84043,x84044,f252(f885(x84041,a871)))+P21(x84041,f885(x84042,x84043),f328(f328(f8(x84043,f885(x84042,x84043),x84041),f16(x84043,x84042)),x84044),f252(f885(x84041,a871)))
% 81.29/80.91 [8498]~P21(x84982,x84981,x84984,x84983)+E(f328(f307(x84981,x84982,f78(x84982,x84981,x84983,x84984)),f328(f307(x84982,x84981,x84984),x84983)),x84983)
% 81.29/80.91 [8556]~P24(f328(f328(f330(f884(x85561,x85561)),f328(f328(f257(x85561,x85561),x85562),x85564)),f254(x85561,x85563)))+P24(f328(f328(f330(x85561),x85562),x85563))
% 81.29/80.91 [8645]E(f328(f328(f328(f73(x86451,f881(x86452)),f328(f16(f881(x86452),x86451),f196(x86452))),x86453),f328(f236(x86452),f480(x86453,x86454,x86452,x86451))),x86454)+~E(f183(x86451,x86452,x86454),f328(f328(f306(x86451),x86453),f193(f885(x86451,a871))))
% 81.29/80.91 [8769]~E(f328(f328(f6(x87691,a877),x87694),x87693),f328(a118,x87692))+P24(f328(f328(f330(x87691),f842(x87692,x87693,x87694,x87691)),x87693))
% 81.29/80.91 [8789]~E(f328(f328(f6(x87894,a877),x87891),x87893),f328(a118,x87892))+P24(f328(f328(f245(a877),f2(a877)),f328(x87891,f842(x87892,x87893,x87891,x87894))))
% 81.29/80.91 [8800]~P24(f328(f62(x88002),x88004))+P24(f328(f328(f244(a877),f328(f38(x88001),f328(f307(x88002,x88001,x88003),x88004))),f328(f38(x88002),x88004)))
% 81.29/80.91 [8801]E(f328(f328(f257(x88011,x88012),f797(x88013,x88014,x88012,x88011)),f798(x88013,x88014,x88012,x88011)),x88014)+~P24(f328(f328(f330(f884(x88011,x88012)),x88014),f328(f283(x88012,x88011),x88013)))
% 81.29/80.91 [8809]P21(x88091,x88092,x88093,x88094)+P24(f328(f328(f330(x88091),f541(x88094,x88093,x88092,x88091)),x88094))
% 81.29/80.91 [8810]P21(x88101,x88102,x88103,x88104)+P24(f328(f328(f330(x88101),f548(x88104,x88103,x88102,x88101)),x88104))
% 81.29/80.91 [8871]P9(x88711,x88712,x88713,x88714)+P24(f328(f328(f330(f884(x88711,x88711)),f606(x88714,x88713,x88712,x88711)),x88713))
% 81.29/80.91 [8932]P24(f328(x89321,x89322))+~P24(f328(x89321,f328(f328(f257(x89323,x89324),f485(x89324,x89323,x89321)),f486(x89324,x89323,x89321))))
% 81.29/80.91 [8951]E(f328(f194(f878(x89511)),x89512),f328(f194(f878(x89511)),x89513))+~P24(f328(f328(f330(f884(f878(x89511),f878(x89511))),f328(f328(f257(f878(x89511),f878(x89511)),x89512),x89513)),f157(x89511,x89514)))
% 81.29/80.91 [8952]E(f328(f194(f878(x89521)),x89522),f328(f194(f878(x89521)),x89523))+~P24(f328(f328(f330(f884(f878(x89521),f878(x89521))),f328(f328(f257(f878(x89521),f878(x89521)),x89522),x89523)),f144(x89521,x89524)))
% 81.29/80.91 [8953]E(f328(f194(f878(x89531)),x89532),f328(f194(f878(x89531)),x89533))+~P24(f328(f328(f330(f884(f878(x89531),f878(x89531))),f328(f328(f257(f878(x89531),f878(x89531)),x89532),x89533)),f156(x89531,x89534)))
% 81.29/80.91 [9028]P24(f328(f328(f244(a877),f154(x90281,x90282,x90283)),f154(x90281,x90284,x90283)))+P24(f328(f328(f330(x90281),f635(x90284,x90282,x90283,x90281)),f328(f171(x90281),x90283)))
% 81.29/80.91 [9031]E(f328(f194(f878(x90311)),x90312),f328(f194(f878(x90311)),x90313))+~P24(f328(f328(f330(f884(f878(x90311),f878(x90311))),f328(f328(f257(f878(x90311),f878(x90311)),x90312),x90313)),f304(f878(x90311),f156(x90311,x90314))))
% 81.29/80.91 [9266]~P21(x92661,x92662,x92663,x92664)+~P24(f328(f328(f245(a877),f328(f38(x92662),f328(f307(x92661,x92662,x92663),x92664))),f328(f38(x92661),x92664)))
% 81.29/80.91 [9312]~P24(f328(f328(f330(f884(f878(x93121),f878(x93121))),f328(f328(f257(f878(x93121),f878(x93121)),x93122),x93123)),f156(x93121,x93124)))+P24(f328(f328(f330(f884(f878(x93121),f878(x93121))),f328(f328(f257(f878(x93121),f878(x93121)),x93122),x93123)),f157(x93121,f304(x93121,x93124))))
% 81.29/80.91 [9316]~P24(f328(f328(f330(f884(f878(x93161),f878(x93161))),f328(f328(f257(f878(x93161),f878(x93161)),x93162),x93163)),f157(x93161,x93164)))+P24(f328(f328(f330(f884(f878(x93161),f878(x93161))),f328(f328(f257(f878(x93161),f878(x93161)),x93162),x93163)),f304(f878(x93161),f156(x93161,x93164))))
% 81.29/80.91 [9333]P24(f328(f328(f330(f884(x93331,x93331)),f328(f328(f257(x93331,x93331),x93332),x93333)),f304(x93331,x93334)))+~P24(f328(f328(f330(f884(x93331,x93331)),f328(f328(f257(x93331,x93331),x93332),x93333)),f328(f328(f285(x93331,x93331,x93331),x93334),f304(x93331,x93334))))
% 81.29/80.91 [9514]E(f328(f328(f127(x95141),f617(x95142,x95143,x95144,x95141)),f328(f328(f150(x95141),f618(x95142,x95143,x95144,x95141)),f620(x95142,x95143,x95144,x95141))),x95144)+~P24(f328(f328(f330(f884(f878(x95141),f878(x95141))),f328(f328(f257(f878(x95141),f878(x95141)),x95144),x95143)),f156(x95141,x95142)))
% 81.29/80.91 [9515]E(f328(f328(f127(x95151),f617(x95152,x95153,x95154,x95151)),f328(f328(f150(x95151),f619(x95152,x95153,x95154,x95151)),f620(x95152,x95153,x95154,x95151))),x95153)+~P24(f328(f328(f330(f884(f878(x95151),f878(x95151))),f328(f328(f257(f878(x95151),f878(x95151)),x95154),x95153)),f156(x95151,x95152)))
% 81.29/80.91 [9591]P24(f328(f328(f330(f884(x95911,x95911)),f328(f328(f257(x95911,x95911),x95912),f783(x95913,x95914,x95912,x95911))),f304(x95911,x95913)))+~P24(f328(f328(f330(f884(x95911,x95911)),f328(f328(f257(x95911,x95911),x95912),x95914)),f328(f328(f285(x95911,x95911,x95911),x95913),f304(x95911,x95913))))
% 81.29/80.91 [9658]P24(f328(f328(f244(a877),f154(x96581,x96582,x96583)),f154(x96581,x96584,x96583)))+~P24(f328(f328(f245(a877),f328(x96582,f635(x96584,x96582,x96583,x96581))),f328(x96584,f635(x96584,x96582,x96583,x96581))))
% 81.29/80.91 [9725]P24(f328(f328(f330(f884(x97251,x97251)),f328(f328(f257(x97251,x97251),f782(x97252,x97253,x97254,x97251)),x97253)),f304(x97251,x97252)))+~P24(f328(f328(f330(f884(x97251,x97251)),f328(f328(f257(x97251,x97251),x97254),x97253)),f328(f328(f285(x97251,x97251,x97251),x97252),f304(x97251,x97252))))
% 81.29/80.91 [5206]~E(x52062,x52063)+E(f169(x52061,x52062,f328(f328(f150(x52061),x52063),x52064)),x52064)
% 81.29/80.91 [5335]P24(f328(x53352,x53353))+E(f176(x53351,x53352,f328(f328(f150(x53351),x53353),x53354)),f119(x53351))
% 81.29/80.91 [5405]~P90(x54052)+E(f328(f328(f80(f885(x54051,x54052)),x54053),x54054),f328(f80(x54052),f328(x54053,x54054)))
% 81.29/80.91 [5417]~E(x54172,f2(a877))+E(f328(f328(f137(x54171),x54172),f328(f328(f150(x54171),x54173),x54174)),f328(f328(f150(x54171),x54173),x54174))
% 81.29/80.91 [5418]P24(f328(x54182,x54183))+E(f328(f135(x54181,x54182),f328(f328(f150(x54181),x54183),x54184)),f328(f135(x54181,x54182),x54184))
% 81.29/80.91 [5550]~E(x55502,x55504)+P24(f328(f328(f328(f306(x55501),x55502),x55503),x55504))
% 81.29/80.91 [5558]E(x55581,f119(x55582))+E(f143(x55583,f328(f328(f153(x55582,x55583),x55584),x55581)),f328(x55584,f143(x55582,x55581)))
% 81.29/80.91 [5572]~E(x55721,f64(x55722,x55724))+E(f328(x55721,f328(f328(f306(x55722),x55723),f193(f885(x55722,a871)))),x55723)
% 81.29/80.91 [5606]E(x56061,f119(x56062))+E(f328(f140(x56063),f328(f328(f153(x56062,x56063),x56064),x56061)),f328(x56064,f328(f140(x56062),x56061)))
% 81.29/80.91 [5708]~P24(f328(x57083,x57084))+P24(f328(f328(f328(f306(x57081),x57082),x57083),x57084))
% 81.29/80.91 [5824]~P14(x58242,x58244,x58241)+E(f328(x58241,f328(f328(f306(x58242),x58243),f193(f885(x58242,a871)))),x58243)
% 81.29/80.91 [5848]~E(x58482,x58483)+P24(f328(f328(f330(x58481),x58482),f328(f328(f306(x58481),x58483),x58484)))
% 81.29/80.91 [5853]~P65(x58531)+E(f328(f328(f116(x58531),x58532),f328(f328(f116(x58531),x58533),x58534)),f328(f328(f116(x58531),x58533),f328(f328(f116(x58531),x58532),x58534)))
% 81.29/80.91 [5854]~P78(x58541)+E(f328(f328(f116(x58541),x58542),f328(f328(f116(x58541),x58543),x58544)),f328(f328(f116(x58541),x58543),f328(f328(f116(x58541),x58542),x58544)))
% 81.29/80.91 [5855]~P112(x58551)+E(f328(f328(f81(x58551),x58552),f328(f328(f81(x58551),x58553),x58554)),f328(f328(f81(x58551),x58553),f328(f328(f81(x58551),x58552),x58554)))
% 81.29/80.91 [5856]~P78(x58561)+E(f328(f328(f107(x58561),x58562),f328(f328(f107(x58561),x58563),x58564)),f328(f328(f107(x58561),x58563),f328(f328(f107(x58561),x58562),x58564)))
% 81.29/80.91 [5858]~P102(x58581)+E(f328(f328(f107(x58581),x58582),f328(f328(f107(x58581),x58583),x58584)),f328(f328(f107(x58581),x58583),f328(f328(f107(x58581),x58582),x58584)))
% 81.29/80.91 [5859]~P112(x58591)+E(f328(f328(f82(x58591),x58592),f328(f328(f82(x58591),x58593),x58594)),f328(f328(f82(x58591),x58593),f328(f328(f82(x58591),x58592),x58594)))
% 81.29/80.91 [5861]~P106(x58611)+E(f328(f328(f242(x58611),x58612),f328(f328(f242(x58611),x58613),x58614)),f328(f328(f242(x58611),x58613),f328(f328(f242(x58611),x58612),x58614)))
% 81.29/80.91 [5863]~P106(x58631)+E(f328(f328(f243(x58631),x58632),f328(f328(f243(x58631),x58633),x58634)),f328(f328(f243(x58631),x58633),f328(f328(f243(x58631),x58632),x58634)))
% 81.29/80.91 [5868]E(x58681,x58682)+E(f169(x58683,x58681,f328(f328(f150(x58683),x58682),x58684)),f328(f328(f150(x58683),x58682),f169(x58683,x58681,x58684)))
% 81.29/80.91 [5881]~P24(f328(x58812,x58813))+E(f328(f135(x58811,x58812),f328(f328(f150(x58811),x58813),x58814)),f328(f328(f150(x58811),x58813),f328(f135(x58811,x58812),x58814)))
% 81.29/80.91 [6020]~P24(f328(x60202,x60203))+E(f176(x60201,x60202,f328(f328(f150(x60201),x60203),x60204)),f328(f328(f150(x60201),x60203),f176(x60201,x60202,x60204)))
% 81.29/80.91 [6071]P20(x60711,x60712,x60713)+~P20(x60711,x60712,f328(f328(f306(f876(x60711)),x60714),x60713))
% 81.29/80.91 [6084]E(x60841,f193(f885(x60842,a871)))+E(f328(f328(f42(x60842,f885(x60843,a871)),x60841),f328(f16(f885(x60843,a871),x60842),x60844)),x60844)
% 81.29/80.91 [6085]E(x60851,f193(f885(x60852,a871)))+E(f328(f328(f43(x60852,f885(x60853,a871)),x60851),f328(f16(f885(x60853,a871),x60852),x60854)),x60854)
% 81.29/80.91 [6094]~E(x60944,f193(f885(x60942,a871)))+E(f328(f328(f265(x60941,x60942),x60943),f328(f16(f885(x60942,a871),x60941),x60944)),f193(f885(f884(x60941,x60942),a871)))
% 81.29/80.91 [6095]~E(x60953,f193(f885(x60951,a871)))+E(f328(f328(f265(x60951,x60952),x60953),f328(f16(f885(x60952,a871),x60951),x60954)),f193(f885(f884(x60951,x60952),a871)))
% 81.29/80.91 [6141]E(x61411,f2(a877))+E(f328(f328(f137(x61412),x61411),f328(f328(f150(x61412),x61413),x61414)),f328(f328(f137(x61412),f328(f328(f22(a877),x61411),f79(a877))),x61414))
% 81.29/80.91 [6171]E(x61711,f193(f885(x61712,a871)))+E(f328(f307(x61712,x61713,f328(f16(x61713,x61712),x61714)),x61711),f328(f328(f306(x61713),x61714),f193(f885(x61713,a871))))
% 81.29/80.91 [6174]E(f328(f308(x61741,x61742,f328(f16(x61742,x61741),x61743)),x61744),f193(f885(x61741,a871)))+P24(f328(f328(f330(x61742),x61743),x61744))
% 81.29/80.91 [6239]~E(x62393,f193(f885(x62391,a871)))+E(f328(f328(f42(x62391,f885(x62392,a871)),x62393),f328(f16(f885(x62392,a871),x62391),x62394)),f252(f885(x62392,a871)))
% 81.29/80.91 [6240]~E(x62403,f193(f885(x62401,a871)))+E(f328(f328(f43(x62401,f885(x62402,a871)),x62403),f328(f16(f885(x62402,a871),x62401),x62404)),f193(f885(x62402,a871)))
% 81.29/80.91 [6242]~P58(x62421)+E(f45(x62421,f328(f328(f82(x62421),x62422),x62423),f328(f328(f82(x62421),x62422),x62424)),f328(f328(f82(x62421),x62422),f45(x62421,x62423,x62424)))
% 81.29/80.91 [6409]E(f328(f308(x64091,x64092,f328(f16(x64092,x64091),x64093)),x64094),f252(f885(x64091,a871)))+~P24(f328(f328(f330(x64092),x64093),x64094))
% 81.29/80.91 [6432]~P24(f328(f328(f330(x64321),x64322),x64324))+P24(f328(f328(f330(x64321),x64322),f328(f328(f306(x64321),x64323),x64324)))
% 81.29/80.91 [6437]P24(f328(x64371,x64372))+~P24(f328(f159(x64373,x64371),f328(f328(f150(x64373),x64372),x64374)))
% 81.29/80.91 [6446]~E(x64463,f328(f328(f22(a877),f328(f194(f878(x64461)),x64462)),f79(a877)))+E(f120(x64461,f328(f328(f158(x64461,x64462),x64463),x64464)),f120(x64461,x64462))
% 81.29/80.91 [6465]~P106(x64651)+E(f328(f328(f107(f885(x64651,a871)),f328(f297(x64651),x64652)),f299(x64651,x64653,x64654)),f299(x64651,x64653,f328(f328(f242(x64651),x64652),x64654)))
% 81.29/80.91 [6466]~P106(x64661)+E(f328(f328(f107(f885(x64661,a871)),f328(f251(x64661),x64662)),f299(x64661,x64663,x64664)),f299(x64661,f328(f328(f243(x64661),x64662),x64663),x64664))
% 81.29/80.91 [6481]E(f328(f328(f107(f885(x64811,a871)),x64812),f328(f328(f306(x64811),x64813),x64814)),f328(f328(f107(f885(x64811,a871)),x64812),x64814))+P24(f328(f328(f330(x64811),x64813),x64812))
% 81.29/80.91 [6493]E(f169(x64931,x64932,f328(f328(f127(x64931),x64933),x64934)),f328(f328(f127(x64931),x64933),f169(x64931,x64932,x64934)))+P24(f328(f328(f330(x64931),x64932),f328(f171(x64931),x64933)))
% 81.29/80.91 [6497]~P83(x64971)+E(f328(f328(f82(x64971),f328(f328(f258(x64971),x64972),x64973)),f328(f328(f258(x64971),x64972),x64974)),f328(f328(f258(x64971),x64972),f328(f328(f81(a877),x64973),x64974)))
% 81.29/80.91 [6498]~P112(x64981)+E(f328(f328(f82(x64981),f328(f328(f258(x64981),x64982),x64983)),f328(f328(f258(x64981),x64982),x64984)),f328(f328(f258(x64981),x64982),f328(f328(f81(a877),x64983),x64984)))
% 81.29/80.91 [6535]~P100(x65351)+E(f328(f328(f107(x65351),f328(f328(f116(x65351),x65352),x65353)),f328(f328(f116(x65351),x65352),x65354)),f328(f328(f116(x65351),x65352),f328(f328(f107(x65351),x65353),x65354)))
% 81.29/80.91 [6536]~P100(x65361)+E(f328(f328(f116(x65361),f328(f328(f107(x65361),x65362),x65363)),f328(f328(f107(x65361),x65362),x65364)),f328(f328(f107(x65361),x65362),f328(f328(f116(x65361),x65363),x65364)))
% 81.29/80.91 [6537]~P112(x65371)+E(f328(f328(f81(x65371),f328(f328(f82(x65371),x65372),x65373)),f328(f328(f82(x65371),x65372),x65374)),f328(f328(f82(x65371),x65372),f328(f328(f81(x65371),x65373),x65374)))
% 81.29/80.91 [6538]~P106(x65381)+E(f328(f328(f243(x65381),f328(f328(f242(x65381),x65382),x65383)),f328(f328(f242(x65381),x65382),x65384)),f328(f328(f242(x65381),x65382),f328(f328(f243(x65381),x65383),x65384)))
% 81.29/80.91 [6539]~P106(x65391)+E(f328(f328(f242(x65391),f328(f328(f243(x65391),x65392),x65393)),f328(f328(f243(x65391),x65392),x65394)),f328(f328(f243(x65391),x65392),f328(f328(f242(x65391),x65393),x65394)))
% 81.29/80.91 [6571]~P58(x65711)+E(f45(x65711,f328(f328(f82(x65711),x65712),x65713),f328(f328(f82(x65711),x65714),x65713)),f328(f328(f82(x65711),f45(x65711,x65712,x65714)),x65713))
% 81.29/80.91 [6574]~E(f328(f194(f878(x65741)),x65743),f328(f194(f878(x65742)),x65744))+E(f328(f328(f153(f884(x65741,x65742),x65742),f266(x65741,x65742)),f328(f328(f181(x65741,x65742),x65743),x65744)),x65744)
% 81.29/80.91 [6575]~E(f328(f194(f878(x65751)),x65753),f328(f194(f878(x65752)),x65754))+E(f328(f328(f153(f884(x65751,x65752),x65751),f256(x65751,x65752)),f328(f328(f181(x65751,x65752),x65753),x65754)),x65753)
% 81.29/80.91 [6581]P24(f328(f159(x65811,x65812),x65813))+~P24(f328(f159(x65811,x65812),f328(f328(f150(x65811),x65814),x65813)))
% 81.29/80.91 [6582]P24(f328(f159(x65821,x65822),x65823))+~P24(f328(f159(x65821,x65822),f328(f328(f127(x65821),x65824),x65823)))
% 81.29/80.91 [6583]P24(f328(f159(x65831,x65832),x65833))+~P24(f328(f159(x65831,x65832),f328(f328(f127(x65831),x65833),x65834)))
% 81.29/80.91 [6588]~P59(x65881)+E(f45(x65881,f328(f328(f22(x65881),x65882),f45(x65881,x65883,x65884)),x65884),f45(x65881,f328(f328(f22(x65881),x65882),x65883),x65884))
% 81.29/80.91 [6590]~P58(x65901)+E(f45(x65901,f328(f328(f82(x65901),x65902),f45(x65901,x65903,x65904)),x65904),f45(x65901,f328(f328(f82(x65901),x65902),x65903),x65904))
% 81.29/80.91 [6591]~P58(x65911)+E(f45(x65911,f328(f328(f81(x65911),x65912),f45(x65911,x65913,x65914)),x65914),f45(x65911,f328(f328(f81(x65911),x65912),x65913),x65914))
% 81.29/80.91 [6672]~P106(x66721)+E(f328(f328(f107(f885(x66721,a871)),f299(x66721,x66722,x66723)),f328(f297(x66721),x66724)),f299(x66721,x66722,f328(f328(f242(x66721),x66723),x66724)))
% 81.29/80.91 [6673]~P106(x66731)+E(f328(f328(f107(f885(x66731,a871)),f299(x66731,x66732,x66733)),f328(f251(x66731),x66734)),f299(x66731,f328(f328(f243(x66731),x66732),x66734),x66733))
% 81.29/80.91 [6676]~E(f328(f194(f878(x66761)),x66763),f328(f194(f878(x66762)),x66764))+E(f328(f328(f181(x66761,x66762),f328(f168(x66761),x66763)),f328(f168(x66762),x66764)),f328(f168(f884(x66761,x66762)),f328(f328(f181(x66761,x66762),x66763),x66764)))
% 81.29/80.91 [6686]E(x66861,f328(f328(f22(a877),f328(f194(f878(x66862)),x66863)),f79(a877)))+E(f120(x66862,f328(f328(f158(x66862,x66863),x66861),x66864)),f328(f328(f158(x66862,f120(x66862,x66863)),x66861),x66864))
% 81.29/80.91 [6701]~P24(f328(f136(x67012),x67014))+P24(f328(f136(f884(x67011,x67012)),f328(f328(f181(x67011,x67012),x67013),x67014)))
% 81.29/80.91 [6702]~P24(f328(f136(x67021),x67023))+P24(f328(f136(f884(x67021,x67022)),f328(f328(f181(x67021,x67022),x67023),x67024)))
% 81.29/80.91 [6962]E(f328(f328(f39(a877),x69621),x69622),x69623)+~P24(f328(f48(x69621,x69622),f328(f328(f257(a877,a877),x69623),x69624)))
% 81.29/80.91 [6986]E(f45(a877,x69861,x69862),x69863)+~P24(f328(f48(x69861,x69862),f328(f328(f257(a877,a877),x69864),x69863)))
% 81.29/80.91 [6989]P24(f328(f136(x69891),x69892))+~P24(f328(f136(x69893),f328(f328(f153(x69891,x69893),x69894),x69892)))
% 81.29/80.91 [6997]~P20(x69971,x69972,f328(f328(f306(f876(x69971)),x69973),x69974))+P20(x69971,x69972,f328(f328(f306(f876(x69971)),x69973),f193(f885(f876(x69971),a871))))
% 81.29/80.91 [7003]P24(f328(f328(f200(x70031),x70032),x70033))+~P24(f328(f328(f328(f328(a202,x70031),x70032),x70034),x70033))
% 81.29/80.91 [7075]E(f169(x70751,x70752,f328(f328(f127(x70751),x70753),x70754)),f328(f328(f127(x70751),f169(x70751,x70752,x70753)),x70754))+~P24(f328(f328(f330(x70751),x70752),f328(f171(x70751),x70753)))
% 81.29/80.91 [7165]~P59(x71651)+E(f45(x71651,f328(f328(f22(x71651),f45(x71651,x71652,x71653)),x71654),x71653),f45(x71651,f328(f328(f22(x71651),x71652),x71654),x71653))
% 81.29/80.91 [7168]~P58(x71681)+E(f45(x71681,f328(f328(f81(x71681),f45(x71681,x71682,x71683)),x71684),x71683),f45(x71681,f328(f328(f81(x71681),x71682),x71684),x71683))
% 81.29/80.91 [7169]~P58(x71691)+E(f45(x71691,f328(f328(f82(x71691),f45(x71691,x71692,x71693)),x71694),x71693),f45(x71691,f328(f328(f82(x71691),x71692),x71694),x71693))
% 81.29/80.91 [7359]~E(x73591,f328(f328(f150(x73592),x73593),x73594))+~P24(f328(f328(f244(a877),f328(f194(f878(x73592)),x73591)),f328(f194(f878(x73592)),x73594)))
% 81.29/80.91 [7435]~E(f328(f177(x74351,x74352),x74353),f328(f177(x74351,x74352),x74354))+E(f328(f307(f884(x74351,x74352),x74351,f256(x74351,x74352)),f328(f171(f884(x74351,x74352)),x74353)),f328(f307(f884(x74351,x74352),x74351,f256(x74351,x74352)),f328(f171(f884(x74351,x74352)),x74354)))
% 81.29/80.91 [7566]P21(x75661,x75662,x75663,f328(f171(x75661),x75664))+~P24(f328(f136(x75662),f328(f328(f153(x75661,x75662),x75663),x75664)))
% 81.29/80.91 [7640]~P24(f328(f328(f244(f885(x76401,a871)),x76402),x76404))+P24(f328(f328(f244(f885(x76401,a871)),x76402),f328(f328(f306(x76401),x76403),x76404)))
% 81.29/80.91 [7673]~P59(x76731)+E(f45(x76731,f328(f328(f22(x76731),f45(x76731,x76732,x76733)),f45(x76731,x76734,x76733)),x76733),f45(x76731,f328(f328(f22(x76731),x76732),x76734),x76733))
% 81.29/80.91 [7674]~P58(x76741)+E(f45(x76741,f328(f328(f81(x76741),f45(x76741,x76742,x76743)),f45(x76741,x76744,x76743)),x76743),f45(x76741,f328(f328(f81(x76741),x76742),x76744),x76743))
% 81.29/80.91 [7675]~P58(x76751)+E(f45(x76751,f328(f328(f82(x76751),f45(x76751,x76752,x76753)),f45(x76751,x76754,x76753)),x76753),f45(x76751,f328(f328(f82(x76751),x76752),x76754),x76753))
% 81.29/80.91 [7773]P24(f328(f328(f328(f328(a202,x77731),x77732),f328(a118,x77733)),x77734))+~P24(f328(f328(f328(f328(a202,x77731),x77732),x77733),x77734))
% 81.29/80.91 [7780]~E(f328(x77804,f512(x77804,x77803,x77801,x77802)),f193(f885(x77802,a871)))+E(f328(f328(f43(x77801,f885(x77802,a871)),x77803),x77804),f193(f885(x77802,a871)))
% 81.29/80.91 [7781]~E(f328(x77814,f488(x77814,x77813,x77811,x77812)),f252(f885(x77812,a871)))+E(f328(f328(f42(x77811,f885(x77812,a871)),x77813),x77814),f252(f885(x77812,a871)))
% 81.29/80.91 [7782]~E(f328(x77824,f506(x77824,x77823,x77822,x77821)),f252(f885(x77822,a871)))+E(f328(f328(f42(x77821,f885(x77822,a871)),x77823),x77824),f252(f885(x77822,a871)))
% 81.29/80.91 [7783]~E(f328(x77834,f516(x77834,x77833,x77832,x77831)),f193(f885(x77832,a871)))+E(f328(f328(f43(x77831,f885(x77832,a871)),x77833),x77834),f193(f885(x77832,a871)))
% 81.29/80.91 [8181]P24(f328(x81811,x81812))+~P24(f328(f328(f330(x81813),x81812),f328(f328(f107(f885(x81813,a871)),x81814),f328(f249(x81813),x81811))))
% 81.29/80.91 [8220]~P24(f328(f328(f244(f885(x82201,a871)),x82203),x82204))+P24(f328(f328(f244(f885(x82201,a871)),f328(f328(f306(x82201),x82202),x82203)),f328(f328(f306(x82201),x82202),x82204)))
% 81.29/80.91 [8387]P24(f328(f328(f200(x83871),x83872),f489(x83873,x83872,x83874,x83871)))+~P24(f328(f328(f200(f34(x83871,x83874)),x83872),x83873))
% 81.29/80.91 [8396]P24(f328(x83962,x83963))+E(f328(f328(f137(x83961),f328(f194(f878(x83961)),f176(x83961,x83962,f328(f328(f150(x83961),x83963),x83964)))),f328(f328(f150(x83961),x83963),x83964)),f328(f328(f150(x83961),x83963),x83964))
% 81.29/80.91 [8512]~P24(f328(f328(f245(a877),f328(x85124,x85122)),f328(x85124,x85123)))+P24(f328(f328(f330(f884(x85121,x85121)),f328(f328(f257(x85121,x85121),x85122),x85123)),f328(f328(f284(a877,x85121),a248),x85124)))
% 81.29/80.91 [8602]~P24(f328(x86022,f733(x86024,x86022,x86023,x86021)))+E(f176(x86021,x86022,f328(f328(f127(x86021),x86023),x86024)),f328(f328(f127(x86021),x86023),f176(x86021,x86022,x86024)))
% 81.29/80.91 [8673]P21(f878(x86731),f878(x86732),f328(f153(x86731,x86732),x86733),x86734)+~P21(x86731,x86732,x86733,f40(f885(x86731,a871),f328(f307(f878(x86731),f885(x86731,a871),f171(x86731)),x86734)))
% 81.29/80.91 [8740]~P24(f328(x87402,x87403))+E(f328(f328(f137(x87401),f328(f194(f878(x87401)),f176(x87401,x87402,f328(f328(f150(x87401),x87403),x87404)))),f328(f328(f150(x87401),x87403),x87404)),f328(f328(f137(x87401),f328(f194(f878(x87401)),f176(x87401,x87402,x87404))),x87404))
% 81.29/80.91 [8780]~E(x87802,x87803)+E(f328(f135(x87801,f328(f328(f8(a871,a871,x87801),a323),f328(a325,x87802))),f328(f328(f150(x87801),x87803),x87804)),f328(f135(x87801,f328(f328(f8(a871,a871,x87801),a323),f328(a325,x87802))),x87804))
% 81.29/80.91 [8790]E(f328(f328(f43(x87901,f885(x87902,a871)),x87903),x87904),f193(f885(x87902,a871)))+P24(f328(f328(f330(x87901),f512(x87904,x87903,x87901,x87902)),x87903))
% 81.29/80.91 [8791]E(f328(f328(f42(x87911,f885(x87912,a871)),x87913),x87914),f252(f885(x87912,a871)))+P24(f328(f328(f330(x87911),f488(x87914,x87913,x87911,x87912)),x87913))
% 81.29/80.91 [8792]E(f328(f328(f42(x87921,f885(x87922,a871)),x87923),x87924),f252(f885(x87922,a871)))+P24(f328(f328(f330(x87921),f506(x87924,x87923,x87922,x87921)),x87923))
% 81.29/80.91 [8793]E(f328(f328(f43(x87931,f885(x87932,a871)),x87933),x87934),f193(f885(x87932,a871)))+P24(f328(f328(f330(x87931),f516(x87934,x87933,x87932,x87931)),x87933))
% 81.29/80.91 [8829]P24(f328(f328(f245(a877),f328(x88291,x88292)),f328(x88291,x88293)))+~P24(f328(f328(f330(f884(x88294,x88294)),f328(f328(f257(x88294,x88294),x88292),x88293)),f328(f328(f284(a877,x88294),a248),x88291)))
% 81.29/80.91 [8850]E(f176(x88501,x88502,f328(f328(f127(x88501),x88503),x88504)),f328(f328(f127(x88501),x88503),f176(x88501,x88502,x88504)))+P24(f328(f328(f330(x88501),f733(x88504,x88502,x88503,x88501)),f328(f171(x88501),x88503)))
% 81.29/80.91 [8887]P24(f328(f328(f200(x88871),f489(x88872,x88873,x88871,x88874)),x88872))+~P24(f328(f328(f200(f34(x88874,x88871)),x88873),x88872))
% 81.29/80.91 [9017]P24(f328(f328(f330(x90171),f536(x90172,x90173,x90174,x90171)),x90173))+~P24(f328(f328(f330(f885(x90171,a871)),x90174),f328(f328(f61(x90171),x90173),x90172)))
% 81.29/80.91 [9020]E(x90201,x90202)+~P24(f328(f328(f330(f884(x90203,x90203)),f328(f328(f257(x90203,x90203),x90201),x90202)),f328(f328(f188(f884(x90203,x90203),a871),f2(a877)),x90204)))
% 81.29/80.91 [9099]E(f328(f282(x90991,x90991,x90992),f328(f328(f306(x90991),f536(x90992,x90993,x90994,x90991)),f193(f885(x90991,a871)))),x90994)+~P24(f328(f328(f330(f885(x90991,a871)),x90994),f328(f328(f61(x90991),x90993),x90992)))
% 81.29/80.91 [9104]~P24(f328(f328(f330(f884(x91041,x91041)),f328(f328(f257(x91041,x91041),x91043),x91042)),f304(x91041,x91044)))+P24(f328(f328(f330(f884(x91041,x91041)),f328(f328(f257(x91041,x91041),x91042),x91043)),f304(x91041,f328(f283(x91041,x91041),x91044))))
% 81.29/80.91 [9116]~P58(x91161)+E(f328(f328(f81(x91161),f328(f328(f81(x91161),f328(f328(f82(x91161),x91162),f328(f328(f39(x91161),x91163),x91162))),f45(x91161,x91163,x91162))),x91164),f328(f328(f81(x91161),x91163),x91164))
% 81.29/80.91 [9126]~P24(f328(f328(f330(x91261),x91263),x91264))+P24(f328(f328(f330(f885(x91261,a871)),f328(f282(x91261,x91261,x91262),f328(f328(f306(x91261),x91263),f193(f885(x91261,a871))))),f328(f328(f61(x91261),x91264),x91262)))
% 81.29/80.91 [9137]P24(f328(f328(f330(f884(x91371,x91371)),f328(f328(f257(x91371,x91371),x91372),x91373)),f304(x91371,x91374)))+~P24(f328(f328(f330(f884(x91371,x91371)),f328(f328(f257(x91371,x91371),x91373),x91372)),f304(x91371,f328(f283(x91371,x91371),x91374))))
% 81.29/80.91 [9229]E(f328(f328(f158(x92291,f328(f168(x92291),x92292)),f328(f328(f22(a877),f328(f328(f22(a877),f328(f194(f878(x92291)),x92292)),x92293)),f79(a877))),x92294),f328(f168(x92291),f328(f328(f158(x92291,x92292),x92293),x92294)))+~P24(f328(f328(f245(a877),x92293),f328(f194(f878(x92291)),x92292)))
% 81.29/80.91 [9232]~P24(f328(x92322,f727(x92324,x92322,x92323,x92321)))+E(f328(f328(f137(x92321),f328(f194(f878(x92321)),f176(x92321,x92322,f328(f328(f127(x92321),x92323),x92324)))),f328(f328(f127(x92321),x92323),x92324)),f328(f328(f137(x92321),f328(f194(f878(x92321)),f176(x92321,x92322,x92324))),x92324))
% 81.29/80.91 [9272]~P21(x92722,x92721,x92723,f252(f885(x92722,a871)))+P24(f328(f328(f244(f885(x92721,a871)),f328(f307(x92722,x92721,x92723),f328(f80(f885(x92722,a871)),x92724))),f328(f80(f885(x92721,a871)),f328(f307(x92722,x92721,x92723),x92724))))
% 81.29/80.91 [9285]~P27(x92851)+E(f328(f141(x92851,x92852,f328(f7(x92852,x92851,x92851),f328(f328(f8(x92851,f885(x92851,x92851),x92852),f107(x92851)),x92853)),f252(x92851)),x92854),f328(f328(f42(x92852,x92851),f328(f171(x92852),x92854)),x92853))
% 81.29/80.91 [9286]~P27(x92861)+E(f328(f141(x92861,x92862,f328(f7(x92862,x92861,x92861),f328(f328(f8(x92861,f885(x92861,x92861),x92862),f116(x92861)),x92863)),f193(x92861)),x92864),f328(f328(f43(x92862,x92861),f328(f171(x92862),x92864)),x92863))
% 81.29/80.91 [9298]E(f328(f328(f137(x92981),f328(f194(f878(x92981)),f176(x92981,x92982,f328(f328(f127(x92981),x92983),x92984)))),f328(f328(f127(x92981),x92983),x92984)),f328(f328(f137(x92981),f328(f194(f878(x92981)),f176(x92981,x92982,x92984))),x92984))+P24(f328(f328(f330(x92981),f727(x92984,x92982,x92983,x92981)),f328(f171(x92981),x92983)))
% 81.29/80.91 [9366]~P24(f328(f328(f330(f884(f878(x93664),f878(x93664))),f328(f328(f257(f878(x93664),f878(x93664)),x93663),x93662)),f156(x93664,x93661)))+P24(f328(f328(f245(a877),f614(x93661,x93662,x93663,x93664)),f328(f194(f878(x93664)),x93663)))
% 81.29/80.91 [9367]~P58(x93671)+E(f328(f328(f81(x93671),f328(f328(f81(x93671),f328(f328(f82(x93671),f328(f328(f39(x93671),x93672),x93673)),x93673)),f45(x93671,x93672,x93673))),x93674),f328(f328(f81(x93671),x93672),x93674))
% 81.29/80.91 [9394]~P24(f328(f328(f330(f884(f878(x93941),f878(x93941))),f328(f328(f257(f878(x93941),f878(x93941)),x93942),x93943)),f328(f283(f878(x93941),f878(x93941)),f156(x93941,x93944))))+P24(f328(f328(f330(f884(f878(x93941),f878(x93941))),f328(f328(f257(f878(x93941),f878(x93941)),x93942),x93943)),f156(x93941,f328(f283(x93941,x93941),x93944))))
% 81.29/80.91 [9395]P24(f328(f328(f330(f884(f878(x93951),f878(x93951))),f328(f328(f257(f878(x93951),f878(x93951)),x93952),x93953)),f328(f283(f878(x93951),f878(x93951)),f156(x93951,x93954))))+~P24(f328(f328(f330(f884(f878(x93951),f878(x93951))),f328(f328(f257(f878(x93951),f878(x93951)),x93952),x93953)),f156(x93951,f328(f283(x93951,x93951),x93954))))
% 81.29/80.91 [9429]~P24(f328(f328(f330(x94291),x94293),f328(f255(x94291,x94292),x94294)))+P24(f328(f328(f330(f884(x94291,x94292)),f328(f328(f257(x94291,x94292),x94293),f695(x94294,x94292,x94293,x94291))),x94294))
% 81.29/80.91 [9430]~P24(f328(f328(f330(x94301),x94303),f328(f255(x94301,x94302),x94304)))+P24(f328(f328(f330(f884(x94301,x94302)),f328(f328(f257(x94301,x94302),x94303),f707(x94304,x94302,x94303,x94301))),x94304))
% 81.29/80.91 [9539]~P24(f328(f62(f881(x95391)),f328(f307(x95392,f881(x95391),x95393),f252(f885(x95392,a871)))))+P24(f328(f62(f881(x95391)),f328(f307(x95392,f881(x95391),f184(x95392,x95391,x95393,f328(f177(x95392,x95391),x95394))),f252(f885(x95392,a871)))))
% 81.29/80.91 [9586]~P24(f328(f328(f330(f884(x95861,x95861)),f328(f328(f257(x95861,x95861),x95862),x95864)),f328(f328(f285(x95861,x95861,x95861),x95863),f304(x95861,x95863))))+P24(f328(f328(f330(f884(x95861,x95861)),f328(f328(f257(x95861,x95861),x95862),f782(x95863,x95864,x95862,x95861))),x95863))
% 81.29/80.91 [9752]~P24(f328(f328(f330(f884(x97522,x97521)),x97524),f328(f283(x97521,x97522),x97523)))+P24(f328(f328(f330(f884(x97521,x97522)),f328(f328(f257(x97521,x97522),f798(x97523,x97524,x97521,x97522)),f797(x97523,x97524,x97521,x97522))),x97523))
% 81.29/80.91 [9780]~P24(f328(f328(f330(f884(f878(x97801),f878(x97801))),f328(f328(f257(f878(x97801),f878(x97801)),x97804),x97803)),f156(x97801,x97802)))+P24(f328(f328(f330(f884(x97801,x97801)),f328(f328(f257(x97801,x97801),f618(x97802,x97803,x97804,x97801)),f619(x97802,x97803,x97804,x97801))),x97802))
% 81.29/80.91 [9876]~P24(f328(f328(f330(f884(f878(x98761),f878(x98761))),f328(f328(f257(f878(x98761),f878(x98761)),x98762),x98764)),f156(x98761,x98763)))+P24(f328(f328(f330(f884(x98761,x98761)),f328(f328(f257(x98761,x98761),f328(f328(f164(x98761),x98762),f614(x98763,x98764,x98762,x98761))),f615(x98763,x98764,x98762,x98761))),x98763))
% 81.29/80.91 [9898]~P24(f328(f62(x98982),x98984))+E(f328(f328(f328(f66(f885(x98981,a871),x98982,f116(f885(x98981,a871))),f328(f328(f7(x98982,f885(x98981,a871),f885(x98981,a871)),f328(f328(f8(x98981,f885(f885(x98981,a871),f885(x98981,a871)),x98982),f306(x98981)),x98983)),f193(f885(x98981,a871)))),f193(f885(x98981,a871))),x98984),f328(f307(x98982,x98981,x98983),x98984))
% 81.29/80.91 [9997]~P21(x99971,x99972,x99973,f252(f885(x99971,a871)))+P24(f328(f328(f244(f885(x99971,a871)),f328(f308(x99971,x99972,x99973),f328(f328(f306(x99972),x99974),f193(f885(x99972,a871))))),f328(f328(f306(x99971),f86(x99971,f328(f328(f7(x99971,x99972,a871),f328(f328(f8(x99972,f885(x99972,a871),x99971),a325),x99973)),x99974))),f193(f885(x99971,a871)))))
% 81.29/80.91 [5615]~E(f328(f328(f127(x56151),x56152),x56154),x56153)+E(f328(f328(f174(x56151),f328(f194(f878(x56151)),x56152)),x56153),x56152)
% 81.29/80.91 [5616]~E(f328(f328(f127(x56162),x56163),x56161),x56164)+E(x56161,f328(f328(f137(x56162),f328(f194(f878(x56162)),x56163)),x56164))
% 81.29/80.91 [5627]~E(x56274,f2(a877))+E(f328(f328(f164(x56271),f328(f328(f150(x56271),x56272),x56273)),x56274),x56272)
% 81.29/80.91 [6154]~P112(x61541)+E(f328(f328(f258(x61541),f328(f328(f258(x61541),x61542),x61543)),x61544),f328(f328(f258(x61541),x61542),f328(f328(f82(a877),x61543),x61544)))
% 81.29/80.91 [6155]~P83(x61551)+E(f328(f328(f258(x61551),f328(f328(f258(x61551),x61552),x61553)),x61554),f328(f328(f258(x61551),x61552),f328(f328(f82(a877),x61553),x61554)))
% 81.29/80.91 [6172]E(x61721,f2(a877))+E(f328(f328(f164(x61722),f328(f328(f150(x61722),x61723),x61724)),x61721),f328(f328(f164(x61722),x61724),f328(f328(f22(a877),x61721),f79(a877))))
% 81.29/80.91 [6197]~P120(x61971)+E(f328(f328(f286(x61971),f328(f328(f82(x61971),x61972),x61973)),x61974),f328(f328(f82(x61971),x61972),f328(f328(f286(x61971),x61973),x61974)))
% 81.29/80.92 [6199]~P65(x61991)+E(f328(f328(f116(x61991),f328(f328(f116(x61991),x61992),x61993)),x61994),f328(f328(f116(x61991),x61992),f328(f328(f116(x61991),x61993),x61994)))
% 81.29/80.92 [6200]~P78(x62001)+E(f328(f328(f116(x62001),f328(f328(f116(x62001),x62002),x62003)),x62004),f328(f328(f116(x62001),x62002),f328(f328(f116(x62001),x62003),x62004)))
% 81.29/80.92 [6201]~P68(x62011)+E(f328(f328(f81(x62011),f328(f328(f81(x62011),x62012),x62013)),x62014),f328(f328(f81(x62011),x62012),f328(f328(f81(x62011),x62013),x62014)))
% 81.29/80.92 [6202]~P112(x62021)+E(f328(f328(f81(x62021),f328(f328(f81(x62021),x62022),x62023)),x62024),f328(f328(f81(x62021),x62022),f328(f328(f81(x62021),x62023),x62024)))
% 81.29/80.92 [6203]~P78(x62031)+E(f328(f328(f107(x62031),f328(f328(f107(x62031),x62032),x62033)),x62034),f328(f328(f107(x62031),x62032),f328(f328(f107(x62031),x62033),x62034)))
% 81.29/80.92 [6205]~P102(x62051)+E(f328(f328(f107(x62051),f328(f328(f107(x62051),x62052),x62053)),x62054),f328(f328(f107(x62051),x62052),f328(f328(f107(x62051),x62053),x62054)))
% 81.29/80.92 [6206]~P112(x62061)+E(f328(f328(f82(x62061),f328(f328(f82(x62061),x62062),x62063)),x62064),f328(f328(f82(x62061),x62062),f328(f328(f82(x62061),x62063),x62064)))
% 81.29/80.92 [6207]~P71(x62071)+E(f328(f328(f82(x62071),f328(f328(f82(x62071),x62072),x62073)),x62074),f328(f328(f82(x62071),x62072),f328(f328(f82(x62071),x62073),x62074)))
% 81.29/80.92 [6210]~P106(x62101)+E(f328(f328(f242(x62101),f328(f328(f242(x62101),x62102),x62103)),x62104),f328(f328(f242(x62101),x62102),f328(f328(f242(x62101),x62103),x62104)))
% 81.29/80.92 [6212]~P106(x62121)+E(f328(f328(f243(x62121),f328(f328(f243(x62121),x62122),x62123)),x62124),f328(f328(f243(x62121),x62122),f328(f328(f243(x62121),x62123),x62124)))
% 81.29/80.92 [6223]~P58(x62231)+E(f45(x62231,f328(f328(f81(x62231),x62232),f328(f328(f82(x62231),x62233),x62234)),x62234),f45(x62231,x62232,x62234))
% 81.29/80.92 [6224]~P58(x62241)+E(f45(x62241,f328(f328(f81(x62241),x62242),f328(f328(f82(x62241),x62243),x62244)),x62243),f45(x62241,x62242,x62243))
% 81.29/80.92 [6358]E(f328(f328(f164(x63581),f328(f328(f174(x63581),x63582),x63583)),x63584),f328(f328(f164(x63581),x63583),x63584))+~P24(f328(f328(f245(a877),x63584),x63582))
% 81.29/80.92 [6533]~P112(x65331)+E(f328(f328(f81(x65331),f328(f328(f81(x65331),x65332),x65333)),x65334),f328(f328(f81(x65331),f328(f328(f81(x65331),x65332),x65334)),x65333))
% 81.29/80.92 [6534]~P112(x65341)+E(f328(f328(f82(x65341),f328(f328(f82(x65341),x65342),x65343)),x65344),f328(f328(f82(x65341),f328(f328(f82(x65341),x65342),x65344)),x65343))
% 81.29/80.92 [6594]~P141(x65942)+E(f328(f328(f6(x65941,x65942),f328(f16(x65942,x65941),x65943)),x65944),f328(f328(f82(x65942),f328(f106(x65942),f328(f38(x65941),x65944))),x65943))
% 81.29/80.92 [6764]E(f328(f328(f107(f885(x67641,a871)),f328(f328(f306(x67641),x67642),x67643)),x67644),f328(f328(f107(f885(x67641,a871)),x67643),x67644))+P24(f328(f328(f330(x67641),x67642),x67644))
% 81.29/80.92 [6833]~P80(x68331)+E(f328(f328(f242(x68331),f328(f328(f22(x68331),x68332),x68333)),f328(f328(f22(x68331),x68334),x68333)),f328(f328(f22(x68331),f328(f328(f242(x68331),x68332),x68334)),x68333))
% 81.29/80.92 [6834]~P80(x68341)+E(f328(f328(f243(x68341),f328(f328(f22(x68341),x68342),x68343)),f328(f328(f22(x68341),x68344),x68343)),f328(f328(f22(x68341),f328(f328(f243(x68341),x68342),x68344)),x68343))
% 81.29/80.92 [6835]~P100(x68351)+E(f328(f328(f107(x68351),f328(f328(f116(x68351),x68352),x68353)),f328(f328(f116(x68351),x68354),x68353)),f328(f328(f116(x68351),f328(f328(f107(x68351),x68352),x68354)),x68353))
% 81.29/80.92 [6836]~P85(x68361)+E(f328(f328(f242(x68361),f328(f328(f81(x68361),x68362),x68363)),f328(f328(f81(x68361),x68364),x68363)),f328(f328(f81(x68361),f328(f328(f242(x68361),x68362),x68364)),x68363))
% 81.29/80.92 [6837]~P85(x68371)+E(f328(f328(f243(x68371),f328(f328(f81(x68371),x68372),x68373)),f328(f328(f81(x68371),x68374),x68373)),f328(f328(f81(x68371),f328(f328(f243(x68371),x68372),x68374)),x68373))
% 81.29/80.92 [6838]~P100(x68381)+E(f328(f328(f116(x68381),f328(f328(f107(x68381),x68382),x68383)),f328(f328(f107(x68381),x68384),x68383)),f328(f328(f107(x68381),f328(f328(f116(x68381),x68382),x68384)),x68383))
% 81.29/80.92 [6840]~P113(x68401)+E(f328(f328(f81(x68401),f328(f328(f82(x68401),x68402),x68403)),f328(f328(f82(x68401),x68404),x68403)),f328(f328(f82(x68401),f328(f328(f81(x68401),x68402),x68404)),x68403))
% 81.29/80.92 [6841]~P120(x68411)+E(f328(f328(f22(x68411),f328(f328(f286(x68411),x68412),x68413)),f328(f328(f286(x68411),x68414),x68413)),f328(f328(f286(x68411),f328(f328(f22(x68411),x68412),x68414)),x68413))
% 81.29/80.92 [6842]~P120(x68421)+E(f328(f328(f81(x68421),f328(f328(f286(x68421),x68422),x68423)),f328(f328(f286(x68421),x68424),x68423)),f328(f328(f286(x68421),f328(f328(f81(x68421),x68422),x68424)),x68423))
% 81.29/80.92 [6843]~P112(x68431)+E(f328(f328(f82(x68431),f328(f328(f258(x68431),x68432),x68433)),f328(f328(f258(x68431),x68434),x68433)),f328(f328(f258(x68431),f328(f328(f82(x68431),x68432),x68434)),x68433))
% 81.29/80.92 [6844]~P75(x68441)+E(f328(f328(f82(x68441),f328(f328(f258(x68441),x68442),x68443)),f328(f328(f258(x68441),x68444),x68443)),f328(f328(f258(x68441),f328(f328(f82(x68441),x68442),x68444)),x68443))
% 81.29/80.92 [6845]~P61(x68451)+E(f328(f328(f286(x68451),f328(f328(f258(x68451),x68452),x68453)),f328(f328(f258(x68451),x68454),x68453)),f328(f328(f258(x68451),f328(f328(f286(x68451),x68452),x68454)),x68453))
% 81.29/80.92 [6846]~P106(x68461)+E(f328(f328(f243(x68461),f328(f328(f242(x68461),x68462),x68463)),f328(f328(f242(x68461),x68464),x68463)),f328(f328(f242(x68461),f328(f328(f243(x68461),x68462),x68464)),x68463))
% 81.29/80.92 [6847]~P106(x68471)+E(f328(f328(f242(x68471),f328(f328(f243(x68471),x68472),x68473)),f328(f328(f243(x68471),x68474),x68473)),f328(f328(f243(x68471),f328(f328(f242(x68471),x68472),x68474)),x68473))
% 81.29/80.92 [6848]~P112(x68481)+E(f328(f328(f81(x68481),f328(f328(f82(x68481),x68482),x68483)),f328(f328(f82(x68481),x68484),x68483)),f328(f328(f82(x68481),f328(f328(f81(x68481),x68482),x68484)),x68483))
% 81.29/80.92 [6880]E(f328(f328(f158(x68801,x68802),x68803),x68804),x68802)+~P24(f328(f328(f244(a877),f328(f194(f878(x68801)),x68802)),x68803))
% 81.29/80.92 [6902]~P24(f328(x69023,x69024))+P24(f328(f328(f328(f116(f885(x69021,a871)),x69022),x69023),x69024))
% 81.29/80.92 [6904]~P24(f328(x69042,x69044))+P24(f328(f328(f328(f116(f885(x69041,a871)),x69042),x69043),x69044))
% 81.29/80.92 [6925]E(f328(f328(f164(x69251),f328(f328(f127(x69251),x69252),x69253)),x69254),f328(f328(f164(x69251),x69252),x69254))+~P24(f328(f328(f245(a877),x69254),f328(f194(f878(x69251)),x69252)))
% 81.29/80.92 [6935]E(f328(f328(f22(f885(x69351,a871)),f328(f328(f306(x69351),x69352),x69353)),x69354),f328(f328(f22(f885(x69351,a871)),x69353),x69354))+~P24(f328(f328(f330(x69351),x69352),x69354))
% 81.29/80.92 [6976]~E(f138(a877,f328(f298(a877,x69761),x69762)),f328(f328(f150(a877),x69764),x69763))+E(f138(a877,f328(f298(a877,f328(f328(f81(a877),x69761),f79(a877))),x69762)),x69763)
% 81.29/80.92 [7049]E(x70491,f2(a877))+E(f328(f328(f150(x70492),x70493),f328(f328(f174(x70492),f328(f328(f22(a877),x70491),f79(a877))),x70494)),f328(f328(f174(x70492),x70491),f328(f328(f150(x70492),x70493),x70494)))
% 81.29/80.92 [7149]E(f328(f328(f164(x71491),x71492),f328(f328(f22(a877),x71493),f328(f194(f878(x71491)),x71494))),f328(f328(f164(x71491),f328(f328(f127(x71491),x71494),x71492)),x71493))+P24(f328(f328(f245(a877),x71493),f328(f194(f878(x71491)),x71494)))
% 81.29/80.92 [7179]E(f328(f328(f107(f885(x71791,a871)),x71792),f328(f328(f306(x71791),x71793),x71794)),f328(f328(f306(x71791),x71793),f328(f328(f107(f885(x71791,a871)),x71792),x71794)))+~P24(f328(f328(f330(x71791),x71793),x71792))
% 81.29/80.92 [7214]E(f328(f328(f164(x72141),f328(f328(f158(x72141,x72142),x72143),x72144)),x72143),x72144)+~P24(f328(f328(f245(a877),x72143),f328(f194(f878(x72141)),x72142)))
% 81.29/80.92 [7235]E(x72351,f193(f885(x72352,a871)))+E(f328(f307(f884(x72353,x72352),x72353,f256(x72353,x72352)),f328(f328(f265(x72353,x72352),x72354),f328(f16(f885(x72352,a871),x72353),x72351))),x72354)
% 81.29/80.92 [7236]E(x72361,f193(f885(x72362,a871)))+E(f328(f307(f884(x72362,x72363),x72363,f266(x72362,x72363)),f328(f328(f265(x72362,x72363),x72361),f328(f16(f885(x72363,a871),x72362),x72364))),x72364)
% 81.29/80.92 [7303]E(f328(f328(f22(f885(x73031,a871)),f328(f328(f306(x73031),x73032),x73033)),x73034),f328(f328(f306(x73031),x73032),f328(f328(f22(f885(x73031,a871)),x73033),x73034)))+P24(f328(f328(f330(x73031),x73032),x73034))
% 81.29/80.92 [7335]P24(f328(x73351,x73352))+P24(f328(f328(f328(f328(a202,f33(x73351,x73353)),x73352),x73354),x73352))
% 81.29/80.92 [7342]~E(x73424,f193(f885(x73422,a871)))+E(f328(f307(f884(x73421,x73422),x73421,f256(x73421,x73422)),f328(f328(f265(x73421,x73422),x73423),f328(f16(f885(x73422,a871),x73421),x73424))),f193(f885(x73421,a871)))
% 81.29/80.92 [7343]~E(x73433,f193(f885(x73431,a871)))+E(f328(f307(f884(x73431,x73432),x73432,f266(x73431,x73432)),f328(f328(f265(x73431,x73432),x73433),f328(f16(f885(x73432,a871),x73431),x73434))),f193(f885(x73432,a871)))
% 81.29/80.92 [7400]~P24(f328(f328(f330(x74001),x74002),x74004))+P24(f328(f328(f330(x74001),x74002),f328(f328(f116(f885(x74001,a871)),x74003),x74004)))
% 81.29/80.92 [7403]~P24(f328(f328(f330(x74031),x74032),x74033))+P24(f328(f328(f330(x74031),x74032),f328(f328(f116(f885(x74031,a871)),x74033),x74034)))
% 81.29/80.92 [7422]E(f328(f328(f107(f885(x74221,a871)),f328(f328(f306(x74221),x74222),x74223)),x74224),f328(f328(f306(x74221),x74222),f328(f328(f107(f885(x74221,a871)),x74223),x74224)))+~P24(f328(f328(f330(x74221),x74222),x74224))
% 81.29/80.92 [7696]P24(f328(x76961,x76962))+~P24(f328(f328(f328(f107(f885(x76963,a871)),x76964),x76961),x76962))
% 81.29/80.92 [7697]P24(f328(x76971,x76972))+~P24(f328(f328(f328(f107(f885(x76973,a871)),x76971),x76974),x76972))
% 81.29/80.92 [7700]E(f328(f328(f6(x77001,a877),x77002),f328(f328(f22(f885(x77001,a871)),x77003),f328(f328(f306(x77001),x77004),f193(f885(x77001,a871))))),f328(f328(f6(x77001,a877),x77002),x77003))+P24(f328(f328(f330(x77001),x77004),x77003))
% 81.29/80.92 [7706]~P74(x77061)+E(f328(f165(x77061),f328(f328(f153(a877,x77061),x77062),f138(a877,f328(f298(a877,x77063),x77064)))),f328(f328(f6(a877,x77061),x77062),f328(f171(a877),f138(a877,f328(f298(a877,x77063),x77064)))))
% 81.29/80.92 [7707]~P74(x77071)+E(f328(f328(f6(a877,x77071),x77072),f328(f171(a877),f138(a877,f328(f298(a877,x77073),x77074)))),f328(f165(x77071),f328(f328(f153(a877,x77071),x77072),f138(a877,f328(f298(a877,x77073),x77074)))))
% 81.29/80.92 [7817]~E(x78173,x78174)+P24(f328(f63(x78171,x78172,f328(f328(f306(x78171),x78173),f193(f885(x78171,a871)))),x78174))
% 81.29/80.92 [7914]P24(f328(f328(f330(x79141),x79142),f328(f171(x79141),x79143)))+~P24(f328(f328(f330(x79141),x79142),f328(f171(x79141),f328(f328(f174(x79141),x79144),x79143))))
% 81.29/80.92 [7915]P24(f328(f328(f330(x79151),x79152),f328(f171(x79151),x79153)))+~P24(f328(f328(f330(x79151),x79152),f328(f171(x79151),f328(f328(f137(x79151),x79154),x79153))))
% 81.29/80.92 [7988]P24(f328(f328(f330(x79881),x79882),x79883))+~P24(f328(f328(f330(x79881),x79882),f328(f328(f22(f885(x79881,a871)),x79883),x79884)))
% 81.29/80.92 [7990]P24(f328(f328(f330(x79901),x79902),x79903))+~P24(f328(f328(f330(x79901),x79902),f328(f328(f107(f885(x79901,a871)),x79904),x79903)))
% 81.29/80.92 [7993]P24(f328(f328(f330(x79931),x79932),x79933))+~P24(f328(f328(f330(x79931),x79932),f328(f328(f107(f885(x79931,a871)),x79933),x79934)))
% 81.29/80.92 [8011]E(f328(f328(f127(x80111),f328(f328(f174(x80111),x80112),x80113)),f328(f328(f150(x80111),x80114),f328(f328(f137(x80111),f328(a118,x80112)),x80113))),f328(f328(f158(x80111,x80113),x80112),x80114))+~P24(f328(f328(f245(a877),x80112),f328(f194(f878(x80111)),x80113)))
% 81.29/80.92 [8036]P24(f328(f328(f330(x80361),x80362),x80363))+~P24(f328(f328(f244(f885(x80361,a871)),f328(f328(f306(x80361),x80362),x80364)),x80363))
% 81.29/80.92 [8069]~P24(f328(f328(f330(x80691),x80692),x80693))+~P24(f328(f328(f330(x80691),x80692),f328(f328(f22(f885(x80691,a871)),x80694),x80693)))
% 81.29/80.92 [8102]~P24(f328(f328(f245(a877),x81024),f328(f194(f878(x81021)),x81023)))+P24(f328(f328(f330(x81021),x81022),f328(f171(x81021),f328(f328(f158(x81021,x81023),x81024),x81022))))
% 81.29/80.92 [8158]E(f328(f328(f164(x81581),f328(f328(f137(x81581),x81582),x81583)),x81584),f328(f328(f164(x81581),x81583),f328(f328(f81(a877),x81582),x81584)))+~P24(f328(f328(f244(a877),f328(f328(f81(a877),x81582),x81584)),f328(f194(f878(x81581)),x81583)))
% 81.29/80.92 [8168]~P141(x81682)+E(f328(f328(f6(x81681,x81682),f328(f328(f8(a877,x81682,x81681),f106(x81682)),x81683)),x81684),f328(f106(x81682),f328(f328(f6(x81681,a877),x81683),x81684)))
% 81.29/80.92 [8169]~P137(x81692)+E(f328(f328(f6(x81691,x81692),f328(f328(f8(a1,x81692,x81691),f108(x81692)),x81693)),x81694),f328(f108(x81692),f328(f328(f6(x81691,a1),x81693),x81694)))
% 81.29/80.92 [8222]~P64(x82222)+E(f328(f328(f9(x82221,x82222),f328(f328(f8(x82222,x82222,x82221),f76(x82222)),x82223)),x82224),f328(f76(x82222),f328(f328(f9(x82221,x82222),x82223),x82224)))
% 81.29/80.92 [8223]~P67(x82232)+E(f328(f328(f6(x82231,x82232),f328(f328(f8(x82232,x82232,x82231),f80(x82232)),x82233)),x82234),f328(f80(x82232),f328(f328(f6(x82231,x82232),x82233),x82234)))
% 81.29/80.92 [8225]E(f328(f328(f6(x82251,a877),x82252),f328(f328(f22(f885(x82251,a871)),x82253),f328(f328(f306(x82251),x82254),f193(f885(x82251,a871))))),f328(f328(f22(a877),f328(f328(f6(x82251,a877),x82252),x82253)),f328(x82252,x82254)))+~P24(f328(f328(f330(x82251),x82254),x82253))
% 81.29/80.92 [8245]P24(f328(f328(f244(f885(x82451,a871)),x82452),x82453))+~P24(f328(f328(f244(f885(x82451,a871)),f328(f328(f306(x82451),x82454),x82452)),x82453))
% 81.29/80.92 [8453]E(f328(a118,f656(x84531,x84532,x84533,x84534)),x84532)+~P24(f328(f328(f328(f328(a202,f328(a26,x84534)),x84533),x84532),x84531))
% 81.29/80.92 [8455]E(f328(f328(f177(x84551,x84552),x84553),x84554),f196(x84552))+P24(f328(f328(f330(x84551),x84554),f328(f307(f884(x84551,x84552),x84551,f256(x84551,x84552)),f328(f171(f884(x84551,x84552)),x84553))))
% 81.29/80.92 [8456]P38(x84561,x84562)+~P38(x84561,f328(f328(f306(f884(x84561,x84561)),f328(f328(f257(x84561,x84561),x84563),x84564)),x84562))
% 81.29/80.92 [8457]P55(x84571,x84572)+~P55(x84571,f328(f328(f306(f884(x84571,x84571)),f328(f328(f257(x84571,x84571),x84573),x84574)),x84572))
% 81.29/80.92 [8466]~P106(x84661)+E(f328(f328(f147(x84661,x84661,f5(x84661)),x84662),f328(f328(f147(x84661,x84661,f5(x84661)),x84663),x84664)),f328(f328(f147(x84661,x84661,f5(x84661)),x84663),f328(f328(f147(x84661,x84661,f5(x84661)),x84662),x84664)))
% 81.29/80.92 [8476]E(x84761,x84762)+~P24(f328(f63(x84763,x84764,f328(f328(f306(x84763),x84761),f193(f885(x84763,a871)))),x84762))
% 81.29/80.92 [8486]E(f328(f328(f127(x84861),f328(f328(f174(x84861),x84862),x84863)),f328(f328(f174(x84861),x84864),f328(f328(f137(x84861),x84862),x84863))),f328(f328(f174(x84861),f328(f328(f81(a877),x84862),x84864)),x84863))+~P24(f328(f328(f244(a877),f328(f328(f81(a877),x84862),x84864)),f328(f194(f878(x84861)),x84863)))
% 81.29/80.92 [8526]P24(f328(f62(x85261),x85262))+~E(x85262,f328(f307(a877,x85261,x85263),f328(f249(a877),f328(f328(f7(a877,a877,a871),f245(a877)),x85264))))
% 81.29/80.92 [8546]~P92(x85461)+E(f328(f141(x85461,x85461,f81(x85461),f328(f328(f81(x85461),x85462),x85463)),x85464),f328(f328(f81(x85461),x85462),f328(f141(x85461,x85461,f81(x85461),x85463),x85464)))
% 81.29/80.92 [8580]P24(f328(f328(f244(f885(x85801,a871)),f328(f255(x85801,x85802),x85803)),f328(f255(x85801,x85802),x85804)))+~P24(f328(f328(f244(f885(f884(x85801,x85802),a871)),x85803),x85804))
% 81.29/80.92 [8593]~P24(f328(f328(f244(a877),x85932),x85934))+P24(f328(f328(f244(f885(x85931,a871)),f328(f171(x85931),f328(f328(f174(x85931),x85932),x85933))),f328(f171(x85931),f328(f328(f174(x85931),x85934),x85933))))
% 81.29/80.92 [8594]~P24(f328(f328(f244(a877),x85944),x85942))+P24(f328(f328(f244(f885(x85941,a871)),f328(f171(x85941),f328(f328(f137(x85941),x85942),x85943))),f328(f171(x85941),f328(f328(f137(x85941),x85944),x85943))))
% 81.29/80.92 [8647]~P24(f328(f62(x86471),f328(f328(f22(f885(x86471,a871)),x86472),x86474)))+P24(f328(f62(x86471),f328(f328(f22(f885(x86471,a871)),x86472),f328(f328(f306(x86471),x86473),x86474))))
% 81.29/80.92 [8684]P24(f328(f328(f330(f884(x86841,x86841)),x86842),f304(x86841,x86843)))+~P24(f328(f328(f330(f884(x86841,x86841)),x86842),f328(f328(f188(f884(x86841,x86841),a871),x86844),x86843)))
% 81.29/80.92 [8762]~P24(f328(f62(x87621),f328(f328(f22(f885(x87621,a871)),x87622),f328(f328(f306(x87621),x87624),x87623))))+P24(f328(f62(x87621),f328(f328(f22(f885(x87621,a871)),x87622),x87623)))
% 81.29/80.92 [8909]~E(f328(f328(f177(x89091,x89092),x89093),x89094),f196(x89092))+~P24(f328(f328(f330(x89091),x89094),f328(f307(f884(x89091,x89092),x89091,f256(x89091,x89092)),f328(f171(f884(x89091,x89092)),x89093))))
% 81.29/80.92 [8975]~P78(x89751)+P24(f328(f328(f244(x89751),f328(f328(f116(x89751),x89752),f328(f328(f107(x89751),x89753),x89754))),f328(f328(f107(x89751),f328(f328(f116(x89751),x89752),x89753)),f328(f328(f116(x89751),x89752),x89754))))
% 81.29/80.92 [8976]~P106(x89761)+P24(f328(f328(f244(x89761),f328(f328(f243(x89761),x89762),f328(f328(f242(x89761),x89763),x89764))),f328(f328(f242(x89761),f328(f328(f243(x89761),x89762),x89763)),f328(f328(f243(x89761),x89762),x89764))))
% 81.29/80.92 [9122]E(x91221,x91222)+~P24(f328(f328(f330(f884(x91223,x91223)),f328(f328(f257(x91223,x91223),x91221),x91222)),f328(f171(f884(x91223,x91223)),f328(f328(f181(x91223,x91223),x91224),x91224))))
% 81.29/80.92 [9155]~P24(f328(f328(f330(f884(x91551,x91551)),f328(f328(f257(x91551,x91551),x91553),x91552)),f304(x91551,x91554)))+~P38(x91551,f328(f328(f306(f884(x91551,x91551)),f328(f328(f257(x91551,x91551),x91552),x91553)),x91554))
% 81.29/80.92 [9156]~P24(f328(f328(f330(f884(x91561,x91561)),f328(f328(f257(x91561,x91561),x91563),x91562)),f304(x91561,x91564)))+~P55(x91561,f328(f328(f306(f884(x91561,x91561)),f328(f328(f257(x91561,x91561),x91562),x91563)),x91564))
% 81.29/80.92 [9161]E(x91611,x91612)+E(f328(f135(x91613,f328(f328(f8(a871,a871,x91613),a323),f328(a325,x91611))),f328(f328(f150(x91613),x91612),x91614)),f328(f328(f150(x91613),x91612),f328(f135(x91613,f328(f328(f8(a871,a871,x91613),a323),f328(a325,x91611))),x91614)))
% 81.29/80.92 [9205]~P78(x92051)+P24(f328(f328(f244(x92051),f328(f328(f116(x92051),f328(f328(f107(x92051),x92052),x92053)),f328(f328(f107(x92051),x92052),x92054))),f328(f328(f107(x92051),x92052),f328(f328(f116(x92051),x92053),x92054))))
% 81.29/80.92 [9206]~P106(x92061)+P24(f328(f328(f244(x92061),f328(f328(f243(x92061),f328(f328(f242(x92061),x92062),x92063)),f328(f328(f242(x92061),x92062),x92064))),f328(f328(f242(x92061),x92062),f328(f328(f243(x92061),x92063),x92064))))
% 81.29/80.92 [9281]~E(f328(f307(x92812,x92811,x92813),f252(f885(x92812,a871))),f252(f885(x92811,a871)))+P24(f328(f328(f244(f885(x92811,a871)),f328(f80(f885(x92811,a871)),f328(f307(x92812,x92811,x92813),x92814))),f328(f307(x92812,x92811,x92813),f328(f80(f885(x92812,a871)),x92814))))
% 81.29/80.92 [9359]P24(f328(f328(f328(f328(a202,f328(f240(a873),f328(a28,x93591))),x93592),f656(x93593,x93594,x93592,x93591)),x93593))+~P24(f328(f328(f328(f328(a202,f328(a26,x93591)),x93592),x93594),x93593))
% 81.29/80.92 [9600]P24(f328(f328(f330(f884(x96001,x96001)),f328(f328(f257(x96001,x96001),x96002),x96003)),f328(f283(x96001,x96001),f328(f328(f285(x96001,x96001,x96001),x96004),f304(x96001,x96004)))))+~P24(f328(f328(f330(f884(x96001,x96001)),f328(f328(f257(x96001,x96001),x96002),x96003)),f328(f328(f285(x96001,x96001,x96001),f328(f283(x96001,x96001),x96004)),f304(x96001,f328(f283(x96001,x96001),x96004)))))
% 81.29/80.92 [9601]~P24(f328(f328(f330(f884(x96011,x96011)),f328(f328(f257(x96011,x96011),x96012),x96013)),f328(f283(x96011,x96011),f328(f328(f285(x96011,x96011,x96011),x96014),f304(x96011,x96014)))))+P24(f328(f328(f330(f884(x96011,x96011)),f328(f328(f257(x96011,x96011),x96012),x96013)),f328(f328(f285(x96011,x96011,x96011),f328(f283(x96011,x96011),x96014)),f304(x96011,f328(f283(x96011,x96011),x96014)))))
% 81.29/80.92 [9622]~P24(f328(f328(f330(x96222),x96224),f328(f253(x96221,x96222),x96223)))+P24(f328(f328(f330(f884(x96221,x96222)),f328(f328(f257(x96221,x96222),f694(x96223,x96221,x96224,x96222)),x96224)),x96223))
% 81.29/80.92 [9623]~P24(f328(f328(f330(x96232),x96234),f328(f253(x96231,x96232),x96233)))+P24(f328(f328(f330(f884(x96231,x96232)),f328(f328(f257(x96231,x96232),f696(x96233,x96231,x96234,x96232)),x96234)),x96233))
% 81.29/80.92 [9646]~P24(f328(f328(f330(x96461),x96464),f328(f328(f116(f885(x96461,a871)),x96462),x96463)))+P24(f328(f328(f328(f116(f885(x96461,a871)),f328(f328(f7(x96461,f885(x96461,a871),a871),f330(x96461)),x96462)),f328(f328(f7(x96461,f885(x96461,a871),a871),f330(x96461)),x96463)),x96464))
% 81.29/80.92 [9647]~P24(f328(f328(f330(x96471),x96474),f328(f328(f107(f885(x96471,a871)),x96472),x96473)))+P24(f328(f328(f328(f107(f885(x96471,a871)),f328(f328(f7(x96471,f885(x96471,a871),a871),f330(x96471)),x96472)),f328(f328(f7(x96471,f885(x96471,a871),a871),f330(x96471)),x96473)),x96474))
% 81.29/80.92 [9723]~P24(f328(f328(f330(f884(x97231,x97231)),f328(f328(f257(x97231,x97231),x97234),x97233)),f328(f328(f285(x97231,x97231,x97231),x97232),f304(x97231,x97232))))+P24(f328(f328(f330(f884(x97231,x97231)),f328(f328(f257(x97231,x97231),f783(x97232,x97233,x97234,x97231)),x97233)),x97232))
% 81.29/80.92 [9768]P24(f328(f328(f330(x97681),x97682),f328(f328(f116(f885(x97681,a871)),x97683),x97684)))+~P24(f328(f328(f328(f116(f885(x97681,a871)),f328(f328(f7(x97681,f885(x97681,a871),a871),f330(x97681)),x97683)),f328(f328(f7(x97681,f885(x97681,a871),a871),f330(x97681)),x97684)),x97682))
% 81.29/80.92 [9769]P24(f328(f328(f330(x97691),x97692),f328(f328(f107(f885(x97691,a871)),x97693),x97694)))+~P24(f328(f328(f328(f107(f885(x97691,a871)),f328(f328(f7(x97691,f885(x97691,a871),a871),f330(x97691)),x97693)),f328(f328(f7(x97691,f885(x97691,a871),a871),f330(x97691)),x97694)),x97692))
% 81.29/80.92 [10051]P33(x100511,f328(f328(f7(x100511,f885(f884(x100511,x100511),a871),f885(x100511,a871)),f328(f328(f8(f885(x100511,f885(f885(f884(x100511,x100511),a871),a871)),f885(f885(f884(x100511,x100511),a871),f885(x100511,a871)),x100511),f7(x100511,f885(f884(x100511,x100511),a871),a871)),f328(f328(f8(f885(x100511,f884(x100511,x100511)),f885(x100511,f885(f885(f884(x100511,x100511),a871),a871)),x100511),f328(f8(f884(x100511,x100511),f885(f885(f884(x100511,x100511),a871),a871),x100511),f330(f884(x100511,x100511)))),f257(x100511,x100511)))),x100512),x100513,x100514)+~P24(f328(f328(f330(f884(f878(x100511),f878(x100511))),f328(f328(f257(f878(x100511),f878(x100511)),x100513),x100514)),f157(x100511,x100512)))
% 81.29/80.92 [10055]P56(x100551,f328(f328(f7(x100551,f885(f884(x100551,x100551),a871),f885(x100551,a871)),f328(f328(f8(f885(x100551,f885(f885(f884(x100551,x100551),a871),a871)),f885(f885(f884(x100551,x100551),a871),f885(x100551,a871)),x100551),f7(x100551,f885(f884(x100551,x100551),a871),a871)),f328(f328(f8(f885(x100551,f884(x100551,x100551)),f885(x100551,f885(f885(f884(x100551,x100551),a871),a871)),x100551),f328(f8(f884(x100551,x100551),f885(f885(f884(x100551,x100551),a871),a871),x100551),f330(f884(x100551,x100551)))),f257(x100551,x100551)))),x100552),x100553,x100554)+~P24(f328(f328(f330(f884(f885(x100551,a871),f885(x100551,a871))),f328(f328(f257(f885(x100551,a871),f885(x100551,a871)),x100553),x100554)),f319(x100551,x100552)))
% 81.29/80.92 [10084]E(x100841,x100842)+~E(f328(f328(f7(x100843,f885(f884(x100843,x100844),a871),f885(x100844,a871)),f328(f328(f8(f885(x100844,f885(f885(f884(x100843,x100844),a871),a871)),f885(f885(f884(x100843,x100844),a871),f885(x100844,a871)),x100843),f7(x100844,f885(f884(x100843,x100844),a871),a871)),f328(f328(f8(f885(x100844,f884(x100843,x100844)),f885(x100844,f885(f885(f884(x100843,x100844),a871),a871)),x100843),f328(f8(f884(x100843,x100844),f885(f885(f884(x100843,x100844),a871),a871),x100844),f330(f884(x100843,x100844)))),f257(x100843,x100844)))),x100841),f328(f328(f7(x100843,f885(f884(x100843,x100844),a871),f885(x100844,a871)),f328(f328(f8(f885(x100844,f885(f885(f884(x100843,x100844),a871),a871)),f885(f885(f884(x100843,x100844),a871),f885(x100844,a871)),x100843),f7(x100844,f885(f884(x100843,x100844),a871),a871)),f328(f328(f8(f885(x100844,f884(x100843,x100844)),f885(x100844,f885(f885(f884(x100843,x100844),a871),a871)),x100843),f328(f8(f884(x100843,x100844),f885(f885(f884(x100843,x100844),a871),a871),x100844),f330(f884(x100843,x100844)))),f257(x100843,x100844)))),x100842))
% 81.29/80.92 [10088]~P33(x100881,f328(f328(f7(x100881,f885(f884(x100881,x100881),a871),f885(x100881,a871)),f328(f328(f8(f885(x100881,f885(f885(f884(x100881,x100881),a871),a871)),f885(f885(f884(x100881,x100881),a871),f885(x100881,a871)),x100881),f7(x100881,f885(f884(x100881,x100881),a871),a871)),f328(f328(f8(f885(x100881,f884(x100881,x100881)),f885(x100881,f885(f885(f884(x100881,x100881),a871),a871)),x100881),f328(f8(f884(x100881,x100881),f885(f885(f884(x100881,x100881),a871),a871),x100881),f330(f884(x100881,x100881)))),f257(x100881,x100881)))),x100884),x100882,x100883)+P24(f328(f328(f330(f884(f878(x100881),f878(x100881))),f328(f328(f257(f878(x100881),f878(x100881)),x100882),x100883)),f157(x100881,x100884)))
% 81.29/80.92 [10089]~P56(x100891,f328(f328(f7(x100891,f885(f884(x100891,x100891),a871),f885(x100891,a871)),f328(f328(f8(f885(x100891,f885(f885(f884(x100891,x100891),a871),a871)),f885(f885(f884(x100891,x100891),a871),f885(x100891,a871)),x100891),f7(x100891,f885(f884(x100891,x100891),a871),a871)),f328(f328(f8(f885(x100891,f884(x100891,x100891)),f885(x100891,f885(f885(f884(x100891,x100891),a871),a871)),x100891),f328(f8(f884(x100891,x100891),f885(f885(f884(x100891,x100891),a871),a871),x100891),f330(f884(x100891,x100891)))),f257(x100891,x100891)))),x100894),x100892,x100893)+P24(f328(f328(f330(f884(f885(x100891,a871),f885(x100891,a871))),f328(f328(f257(f885(x100891,a871),f885(x100891,a871)),x100892),x100893)),f319(x100891,x100894)))
% 81.29/80.92 [7474]~P96(x74741)+E(f328(f328(f81(x74741),f328(f109(x74741),x74742)),f328(f328(f22(x74741),f328(f109(x74741),x74743)),x74744)),f328(f328(f22(x74741),f328(f109(x74741),f328(f328(f81(a1),x74742),x74743))),x74744))
% 81.29/80.92 [7475]~P96(x74751)+E(f328(f328(f81(x74751),f328(f109(x74751),x74752)),f328(f328(f81(x74751),f328(f109(x74751),x74753)),x74754)),f328(f328(f81(x74751),f328(f109(x74751),f328(f328(f81(a1),x74752),x74753))),x74754))
% 81.29/80.92 [7476]~P96(x74761)+E(f328(f328(f82(x74761),f328(f109(x74761),x74762)),f328(f328(f82(x74761),f328(f109(x74761),x74763)),x74764)),f328(f328(f82(x74761),f328(f109(x74761),f328(f328(f82(a1),x74762),x74763))),x74764))
% 81.29/80.92 [7518]~P141(x75181)+E(f328(f165(x75181),f328(f328(f153(x75182,x75181),f328(f16(x75181,x75182),x75183)),x75184)),f328(f328(f82(x75181),f328(f106(x75181),f328(f194(f878(x75182)),x75184))),x75183))
% 81.29/80.92 [7751]E(f328(f274(x77511,f328(f328(f150(f884(a105,x77511)),x77512),x77513)),x77514),f328(f266(a105,x77511),x77512))+~P24(f328(f328(f245(a105),x77514),f328(f256(a105,x77511),x77512)))
% 81.29/80.92 [7796]~P96(x77961)+E(f328(f328(f81(x77961),f328(f109(x77961),x77962)),f328(f328(f22(x77961),x77963),f328(f109(x77961),x77964))),f328(f328(f81(x77961),f328(f109(x77961),f328(f328(f81(a1),x77962),f328(f80(a1),x77964)))),x77963))
% 81.29/80.92 [7927]E(f328(f274(x79271,x79272),f328(f328(f22(a105),x79273),f328(f256(a105,x79271),x79274))),f328(f274(x79271,f328(f328(f150(f884(a105,x79271)),x79274),x79272)),x79273))+P24(f328(f328(f245(a105),x79273),f328(f256(a105,x79271),x79274)))
% 81.29/80.92 [8371]~P24(f328(f328(f330(x83711),x83712),f328(f171(x83711),f120(x83711,x83714))))+P24(f328(f328(f330(x83711),x83712),f328(f171(x83711),f120(x83711,f328(f328(f127(x83711),x83713),x83714)))))
% 81.29/80.92 [8372]~P24(f328(f328(f330(x83721),x83722),f328(f171(x83721),f120(x83721,x83723))))+P24(f328(f328(f330(x83721),x83722),f328(f171(x83721),f120(x83721,f328(f328(f127(x83721),x83723),x83724)))))
% 81.29/80.92 [8391]E(f328(f328(f116(f885(x83911,a871)),f328(f328(f107(f885(x83911,a871)),x83912),x83913)),x83914),f328(f328(f107(f885(x83911,a871)),x83912),f328(f328(f116(f885(x83911,a871)),x83913),x83914)))+~P24(f328(f328(f244(f885(x83911,a871)),x83914),x83912))
% 81.29/80.92 [8697]~E(f328(f328(f116(f885(x86971,a871)),f328(f328(f107(f885(x86971,a871)),x86973),x86974)),x86972),f328(f328(f107(f885(x86971,a871)),x86973),f328(f328(f116(f885(x86971,a871)),x86974),x86972)))+P24(f328(f328(f244(f885(x86971,a871)),x86972),x86973))
% 81.29/80.92 [8981]~P24(f328(f328(f244(f885(x89811,a871)),x89812),f328(f328(f116(f885(x89811,a871)),x89813),x89814)))+P24(f328(f328(f244(f885(x89811,a871)),f328(f328(f22(f885(x89811,a871)),x89812),x89813)),x89814))
% 81.29/80.92 [9041]~P24(f328(f328(f328(f328(a202,f328(a26,x90411)),x90412),f328(a118,x90413)),x90414))+P24(f328(f328(f328(f328(a202,f328(f240(a873),f328(a28,x90411))),x90412),x90413),x90414))
% 81.29/80.92 [9101]P24(f328(f328(f244(f885(x91011,a871)),x91012),f328(f328(f116(f885(x91011,a871)),x91013),x91014)))+~P24(f328(f328(f244(f885(x91011,a871)),f328(f328(f22(f885(x91011,a871)),x91012),x91013)),x91014))
% 81.29/80.92 [9154]P24(f328(f328(f328(f328(a202,f328(a26,x91541)),x91542),f328(a118,x91543)),x91544))+~P24(f328(f328(f328(f328(a202,f328(f240(a873),f328(a28,x91541))),x91542),x91543),x91544))
% 81.29/80.92 [9186]~P87(x91861)+E(f328(f76(x91861),f328(f328(f6(x91862,x91861),f328(f328(f8(x91861,x91861,x91862),f76(x91861)),x91863)),x91864)),f328(f328(f6(x91862,x91861),f328(f328(f8(x91861,x91861,x91862),f76(x91861)),x91863)),x91864))
% 81.29/80.92 [9357]~P87(x93571)+P24(f328(f328(f244(x93571),f2(x93571)),f328(f328(f6(x93572,x93571),f328(f328(f8(x93571,x93571,x93572),f76(x93571)),x93573)),x93574)))
% 81.29/80.92 [9362]~P67(x93621)+E(f328(f165(x93621),f328(f328(f153(x93622,x93621),f328(f74(x93621,x93621,x93622,f80(x93621)),x93623)),x93624)),f328(f80(x93621),f328(f165(x93621),f328(f328(f153(x93622,x93621),x93623),x93624))))
% 81.29/80.92 [9495]~P87(x94951)+P24(f328(f328(f244(x94951),f328(f76(x94951),f328(f328(f6(x94952,x94951),x94953),x94954))),f328(f328(f6(x94952,x94951),f328(f328(f8(x94951,x94951,x94952),f76(x94951)),x94953)),x94954)))
% 81.29/80.92 [9525]~E(f328(f328(f81(a877),x95251),x95254),f328(f328(f81(a877),x95253),x95252))+P24(f328(f328(f330(f884(f884(a877,a877),f884(a877,a877))),f328(f328(f257(f884(a877,a877),f884(a877,a877)),f328(f328(f257(a877,a877),x95251),x95252)),f328(f328(f257(a877,a877),x95253),x95254))),a114))
% 81.29/80.92 [9526]~P24(f328(f328(f245(a877),x95261),x95263))+P24(f328(f328(f330(f884(f884(a877,a877),f884(a877,a877))),f328(f328(f257(f884(a877,a877),f884(a877,a877)),f328(f328(f257(a877,a877),x95261),x95262)),f328(f328(f257(a877,a877),x95263),x95264))),a36))
% 81.29/80.92 [9527]~P24(f328(f328(f245(a877),x95271),x95273))+P24(f328(f328(f330(f884(f884(a877,a877),f884(a877,a877))),f328(f328(f257(f884(a877,a877),f884(a877,a877)),f328(f328(f257(a877,a877),x95271),x95272)),f328(f328(f257(a877,a877),x95273),x95274))),a71))
% 81.29/80.92 [9671]E(f328(f328(f81(a877),x96711),x96712),f328(f328(f81(a877),x96713),x96714))+~P24(f328(f328(f330(f884(f884(a877,a877),f884(a877,a877))),f328(f328(f257(f884(a877,a877),f884(a877,a877)),f328(f328(f257(a877,a877),x96711),x96714)),f328(f328(f257(a877,a877),x96713),x96712))),a114))
% 81.29/80.92 [9697]E(f328(f328(f164(x96971),f328(f328(f137(x96971),f328(f194(f878(x96971)),f176(x96971,x96972,x96973))),x96973)),x96974),f328(f328(f164(x96971),x96973),f328(f328(f81(a877),x96974),f328(f194(f878(x96971)),f176(x96971,x96972,x96973)))))+~P24(f328(f328(f245(a877),x96974),f328(f194(f878(x96971)),f328(f328(f137(x96971),f328(f194(f878(x96971)),f176(x96971,x96972,x96973))),x96973))))
% 81.29/80.92 [9714]~P24(f328(f328(f330(x97142),x97144),f328(f328(f42(x97141,f885(x97142,a871)),f252(f885(x97141,a871))),x97143)))+P24(f328(f328(f328(f42(x97141,f885(x97142,a871)),f252(f885(x97141,a871))),f328(f328(f8(f885(x97142,a871),f885(x97142,a871),x97141),f328(f7(x97142,f885(x97142,a871),a871),f330(x97142))),x97143)),x97144))
% 81.29/80.92 [9715]~P24(f328(f328(f330(x97152),x97154),f328(f328(f43(x97151,f885(x97152,a871)),f252(f885(x97151,a871))),x97153)))+P24(f328(f328(f328(f43(x97151,f885(x97152,a871)),f252(f885(x97151,a871))),f328(f328(f8(f885(x97152,a871),f885(x97152,a871),x97151),f328(f7(x97152,f885(x97152,a871),a871),f330(x97152))),x97153)),x97154))
% 81.29/80.92 [9795]~P24(f328(f49(x97951,x97952),f328(f328(f257(a1,a1),x97954),x97953)))+P24(f328(f49(f328(f80(a1),x97951),x97952),f328(f328(f257(a1,a1),f328(f328(f328(f102(a1),f328(f328(a325,x97953),f2(a1))),f328(f80(a1),x97954)),f328(f328(f22(a1),f328(f80(a1),x97954)),f79(a1)))),f328(f328(f328(f102(a1),f328(f328(a325,x97953),f2(a1))),f2(a1)),f328(f328(f22(a1),x97952),x97953)))))
% 81.29/80.92 [9804]P24(f328(f328(f330(x98041),x98042),f328(f328(f42(x98043,f885(x98041,a871)),f252(f885(x98043,a871))),x98044)))+~P24(f328(f328(f328(f42(x98043,f885(x98041,a871)),f252(f885(x98043,a871))),f328(f328(f8(f885(x98041,a871),f885(x98041,a871),x98043),f328(f7(x98041,f885(x98041,a871),a871),f330(x98041))),x98044)),x98042))
% 81.29/80.92 [9805]P24(f328(f328(f330(x98051),x98052),f328(f328(f43(x98053,f885(x98051,a871)),f252(f885(x98053,a871))),x98054)))+~P24(f328(f328(f328(f43(x98053,f885(x98051,a871)),f252(f885(x98053,a871))),f328(f328(f8(f885(x98051,a871),f885(x98051,a871),x98053),f328(f7(x98051,f885(x98051,a871),a871),f330(x98051))),x98054)),x98052))
% 81.29/80.92 [9816]E(f328(f328(f43(a877,f885(x98161,a871)),f252(f885(a877,a871))),x98162),f328(f328(f43(a877,f885(x98161,a871)),f252(f885(a877,a871))),x98163))+~E(f328(f328(f43(a877,f885(x98161,a871)),f328(f298(a877,f2(a877)),f528(x98162,x98164,x98163,x98161))),x98163),f328(f328(f43(a877,f885(x98161,a871)),f328(f298(a877,f2(a877)),f328(f328(f81(a877),f528(x98162,x98164,x98163,x98161)),x98164))),x98162))
% 81.29/80.92 [10144]~P24(f328(f328(f244(f885(f884(x101441,x101442),a871)),x101443),x101444))+P24(f328(f328(f244(f885(x101441,f885(x101442,a871))),f328(f328(f7(x101441,f885(f884(x101441,x101442),a871),f885(x101442,a871)),f328(f328(f8(f885(x101442,f885(f885(f884(x101441,x101442),a871),a871)),f885(f885(f884(x101441,x101442),a871),f885(x101442,a871)),x101441),f7(x101442,f885(f884(x101441,x101442),a871),a871)),f328(f328(f8(f885(x101442,f884(x101441,x101442)),f885(x101442,f885(f885(f884(x101441,x101442),a871),a871)),x101441),f328(f8(f884(x101441,x101442),f885(f885(f884(x101441,x101442),a871),a871),x101442),f330(f884(x101441,x101442)))),f257(x101441,x101442)))),x101443)),f328(f328(f7(x101441,f885(f884(x101441,x101442),a871),f885(x101442,a871)),f328(f328(f8(f885(x101442,f885(f885(f884(x101441,x101442),a871),a871)),f885(f885(f884(x101441,x101442),a871),f885(x101442,a871)),x101441),f7(x101442,f885(f884(x101441,x101442),a871),a871)),f328(f328(f8(f885(x101442,f884(x101441,x101442)),f885(x101442,f885(f885(f884(x101441,x101442),a871),a871)),x101441),f328(f8(f884(x101441,x101442),f885(f885(f884(x101441,x101442),a871),a871),x101442),f330(f884(x101441,x101442)))),f257(x101441,x101442)))),x101444)))
% 81.29/80.92 [10160]P24(f328(f328(f244(f885(f884(x101601,x101602),a871)),x101603),x101604))+~P24(f328(f328(f244(f885(x101601,f885(x101602,a871))),f328(f328(f7(x101601,f885(f884(x101601,x101602),a871),f885(x101602,a871)),f328(f328(f8(f885(x101602,f885(f885(f884(x101601,x101602),a871),a871)),f885(f885(f884(x101601,x101602),a871),f885(x101602,a871)),x101601),f7(x101602,f885(f884(x101601,x101602),a871),a871)),f328(f328(f8(f885(x101602,f884(x101601,x101602)),f885(x101602,f885(f885(f884(x101601,x101602),a871),a871)),x101601),f328(f8(f884(x101601,x101602),f885(f885(f884(x101601,x101602),a871),a871),x101602),f330(f884(x101601,x101602)))),f257(x101601,x101602)))),x101603)),f328(f328(f7(x101601,f885(f884(x101601,x101602),a871),f885(x101602,a871)),f328(f328(f8(f885(x101602,f885(f885(f884(x101601,x101602),a871),a871)),f885(f885(f884(x101601,x101602),a871),f885(x101602,a871)),x101601),f7(x101602,f885(f884(x101601,x101602),a871),a871)),f328(f328(f8(f885(x101602,f884(x101601,x101602)),f885(x101602,f885(f885(f884(x101601,x101602),a871),a871)),x101601),f328(f8(f884(x101601,x101602),f885(f885(f884(x101601,x101602),a871),a871),x101602),f330(f884(x101601,x101602)))),f257(x101601,x101602)))),x101604)))
% 81.29/80.92 [9235]~P24(f328(f328(f330(f884(x92351,x92351)),x92352),f304(x92351,x92354)))+P24(f328(f328(f330(f884(x92351,x92351)),x92352),f304(x92351,f328(f328(f116(f885(f884(x92351,x92351),a871)),x92353),x92354))))
% 81.29/80.92 [9236]~P24(f328(f328(f330(f884(x92361,x92361)),x92362),f304(x92361,x92363)))+P24(f328(f328(f330(f884(x92361,x92361)),x92362),f304(x92361,f328(f328(f116(f885(f884(x92361,x92361),a871)),x92363),x92364))))
% 81.29/80.92 [9592]~E(f328(f171(x95921),x95924),f183(x95921,x95922,x95923))+E(f328(f177(x95921,x95922),f328(f328(f153(x95921,f884(x95921,x95922)),f328(f328(f18(x95921,x95922,f884(x95921,x95922)),f257(x95921,x95922)),f328(f328(f8(f881(x95922),x95922,x95921),f240(x95922)),x95923))),x95924)),x95923)
% 81.29/80.92 [9914]~P24(f328(f328(f244(a877),f328(f328(f81(a877),x99141),x99144)),f328(f328(f81(a877),x99143),x99142)))+P24(f328(f328(f244(a1),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x99141),x99142)),f193(f885(f884(a877,a877),a871)))))),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x99143),x99144)),f193(f885(f884(a877,a877),a871)))))))
% 81.29/80.92 [9915]~P24(f328(f328(f245(a877),f328(f328(f81(a877),x99151),x99154)),f328(f328(f81(a877),x99153),x99152)))+P24(f328(f328(f245(a1),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x99151),x99152)),f193(f885(f884(a877,a877),a871)))))),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x99153),x99154)),f193(f885(f884(a877,a877),a871)))))))
% 81.29/80.92 [9994]P24(f328(f328(f244(a877),f328(f328(f81(a877),x99941),x99942)),f328(f328(f81(a877),x99943),x99944)))+~P24(f328(f328(f244(a1),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x99941),x99944)),f193(f885(f884(a877,a877),a871)))))),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x99943),x99942)),f193(f885(f884(a877,a877),a871)))))))
% 81.29/80.92 [9995]P24(f328(f328(f245(a877),f328(f328(f81(a877),x99951),x99952)),f328(f328(f81(a877),x99953),x99954)))+~P24(f328(f328(f245(a1),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x99951),x99954)),f193(f885(f884(a877,a877),a871)))))),f328(a90,f328(f282(f884(a877,a877),f884(a877,a877),a114),f328(f328(f306(f884(a877,a877)),f328(f328(f257(a877,a877),x99953),x99952)),f193(f885(f884(a877,a877),a871)))))))
% 81.29/80.92 [10036]P24(f328(f328(f244(f885(x100361,a871)),f328(f328(f43(a877,f885(x100361,a871)),f252(f885(a877,a871))),x100362)),f328(f328(f43(a877,f885(x100361,a871)),f252(f885(a877,a871))),x100363)))+~P24(f328(f328(f244(f885(x100361,a871)),f328(f328(f43(a877,f885(x100361,a871)),f328(f298(a877,f2(a877)),f520(x100363,x100364,x100362,x100361))),x100362)),f328(f328(f43(a877,f885(x100361,a871)),f328(f298(a877,f2(a877)),f328(f328(f81(a877),f520(x100363,x100364,x100362,x100361)),x100364))),x100363)))
% 81.29/80.92 [10135]~P24(f328(f328(f330(x101352),x101354),f328(f253(x101351,x101352),x101353)))+P24(f328(f264(x101351,x101352,f328(f328(f7(x101351,f885(f884(x101351,x101352),a871),f885(x101352,a871)),f328(f328(f8(f885(x101352,f885(f885(f884(x101351,x101352),a871),a871)),f885(f885(f884(x101351,x101352),a871),f885(x101352,a871)),x101351),f7(x101352,f885(f884(x101351,x101352),a871),a871)),f328(f328(f8(f885(x101352,f884(x101351,x101352)),f885(x101352,f885(f885(f884(x101351,x101352),a871),a871)),x101351),f328(f8(f884(x101351,x101352),f885(f885(f884(x101351,x101352),a871),a871),x101352),f330(f884(x101351,x101352)))),f257(x101351,x101352)))),x101353)),x101354))
% 81.29/80.92 [10136]~P24(f328(f328(f330(x101361),x101364),f328(f255(x101361,x101362),x101363)))+P24(f328(f263(x101361,x101362,f328(f328(f7(x101361,f885(f884(x101361,x101362),a871),f885(x101362,a871)),f328(f328(f8(f885(x101362,f885(f885(f884(x101361,x101362),a871),a871)),f885(f885(f884(x101361,x101362),a871),f885(x101362,a871)),x101361),f7(x101362,f885(f884(x101361,x101362),a871),a871)),f328(f328(f8(f885(x101362,f884(x101361,x101362)),f885(x101362,f885(f885(f884(x101361,x101362),a871),a871)),x101361),f328(f8(f884(x101361,x101362),f885(f885(f884(x101361,x101362),a871),a871),x101362),f330(f884(x101361,x101362)))),f257(x101361,x101362)))),x101363)),x101364))
% 81.29/80.92 [10147]P24(f328(f328(f330(x101471),x101472),f328(f253(x101473,x101471),x101474)))+~P24(f328(f264(x101473,x101471,f328(f328(f7(x101473,f885(f884(x101473,x101471),a871),f885(x101471,a871)),f328(f328(f8(f885(x101471,f885(f885(f884(x101473,x101471),a871),a871)),f885(f885(f884(x101473,x101471),a871),f885(x101471,a871)),x101473),f7(x101471,f885(f884(x101473,x101471),a871),a871)),f328(f328(f8(f885(x101471,f884(x101473,x101471)),f885(x101471,f885(f885(f884(x101473,x101471),a871),a871)),x101473),f328(f8(f884(x101473,x101471),f885(f885(f884(x101473,x101471),a871),a871),x101471),f330(f884(x101473,x101471)))),f257(x101473,x101471)))),x101474)),x101472))
% 81.29/80.92 [10148]P24(f328(f328(f330(x101481),x101482),f328(f255(x101481,x101483),x101484)))+~P24(f328(f263(x101481,x101483,f328(f328(f7(x101481,f885(f884(x101481,x101483),a871),f885(x101483,a871)),f328(f328(f8(f885(x101483,f885(f885(f884(x101481,x101483),a871),a871)),f885(f885(f884(x101481,x101483),a871),f885(x101483,a871)),x101481),f7(x101483,f885(f884(x101481,x101483),a871),a871)),f328(f328(f8(f885(x101483,f884(x101481,x101483)),f885(x101483,f885(f885(f884(x101481,x101483),a871),a871)),x101481),f328(f8(f884(x101481,x101483),f885(f885(f884(x101481,x101483),a871),a871),x101483),f330(f884(x101481,x101483)))),f257(x101481,x101483)))),x101484)),x101482))
% 81.29/80.92 [9826]P24(f328(f159(x98261,x98262),x98263))+~P24(f328(f159(x98261,f328(f328(f18(x98261,a871,a871),f328(f328(f8(a871,f885(a871,a871),x98261),a326),x98264)),x98262)),x98263))
% 81.29/80.92 [9827]P24(f328(f159(x98271,x98272),x98273))+~P24(f328(f159(x98271,f328(f328(f18(x98271,a871,a871),f328(f328(f8(a871,f885(a871,a871),x98271),a326),x98272)),x98274)),x98273))
% 81.29/80.92 [9916]~P112(x99161)+E(f328(f328(f82(x99161),f328(f328(f81(x99161),f79(x99161)),f79(x99161))),f328(f328(f6(a877,x99161),f328(f328(f8(x99161,x99161,a877),f328(f81(x99161),x99162)),f328(f328(f7(a877,x99161,x99161),f328(f328(f8(x99161,f885(x99161,x99161),a877),f82(x99161)),f106(x99161))),x99163))),f328(f250(a877),x99164))),f328(f328(f82(x99161),f328(f106(x99161),x99164)),f328(f328(f81(x99161),x99162),f328(f328(f81(x99161),x99162),f328(f328(f82(x99161),f328(f106(x99161),f328(f328(f22(a877),x99164),f79(a877)))),x99163)))))
% 81.29/80.92 [10058]P24(f328(x100581,f689(x100582,x100583,x100584,x100581)))+P38(x100582,f328(f249(f884(x100582,x100582)),f328(f267(x100582,x100582,a871),f328(f328(f8(f885(x100582,a871),f885(x100582,a871),x100582),f328(f18(x100582,a871,a871),f328(f328(f8(a871,f885(a871,a871),x100582),a326),x100581))),f328(f328(f7(x100582,f885(x100582,x100582),f885(x100582,a871)),f328(f328(f8(f885(x100582,a871),f885(f885(x100582,x100582),f885(x100582,a871)),x100582),f8(x100582,a871,x100582)),a325)),x100583)))))
% 81.29/80.92 [10072]~P24(f328(f328(f245(a877),f328(x100724,f328(x100723,f689(x100721,x100723,x100724,x100722)))),f328(x100724,f689(x100721,x100723,x100724,x100722))))+P38(x100721,f328(f249(f884(x100721,x100721)),f328(f267(x100721,x100721,a871),f328(f328(f8(f885(x100721,a871),f885(x100721,a871),x100721),f328(f18(x100721,a871,a871),f328(f328(f8(a871,f885(a871,a871),x100721),a326),x100722))),f328(f328(f7(x100721,f885(x100721,x100721),f885(x100721,a871)),f328(f328(f8(f885(x100721,a871),f885(f885(x100721,x100721),f885(x100721,a871)),x100721),f8(x100721,a871,x100721)),a325)),x100723)))))
% 81.29/80.92 [10172]~P24(f328(f328(f330(f884(x101721,x101721)),f328(f328(f257(x101721,x101721),x101723),x101724)),f328(f328(f116(f885(f884(x101721,x101721),a871)),x101722),f304(x101721,f193(f885(f884(x101721,x101721),a871))))))+P24(f328(f328(f328(f328(f116(f885(x101721,f885(x101721,a871))),f328(f328(f7(x101721,f885(f884(x101721,x101721),a871),f885(x101721,a871)),f328(f328(f8(f885(x101721,f885(f885(f884(x101721,x101721),a871),a871)),f885(f885(f884(x101721,x101721),a871),f885(x101721,a871)),x101721),f7(x101721,f885(f884(x101721,x101721),a871),a871)),f328(f328(f8(f885(x101721,f884(x101721,x101721)),f885(x101721,f885(f885(f884(x101721,x101721),a871),a871)),x101721),f328(f8(f884(x101721,x101721),f885(f885(f884(x101721,x101721),a871),a871),x101721),f330(f884(x101721,x101721)))),f257(x101721,x101721)))),x101722)),a325),x101723),x101724))
% 81.29/80.92 [10181]P24(f328(f328(f330(f884(x101811,x101811)),f328(f328(f257(x101811,x101811),x101812),x101813)),f328(f328(f116(f885(f884(x101811,x101811),a871)),x101814),f304(x101811,f193(f885(f884(x101811,x101811),a871))))))+~P24(f328(f328(f328(f328(f116(f885(x101811,f885(x101811,a871))),f328(f328(f7(x101811,f885(f884(x101811,x101811),a871),f885(x101811,a871)),f328(f328(f8(f885(x101811,f885(f885(f884(x101811,x101811),a871),a871)),f885(f885(f884(x101811,x101811),a871),f885(x101811,a871)),x101811),f7(x101811,f885(f884(x101811,x101811),a871),a871)),f328(f328(f8(f885(x101811,f884(x101811,x101811)),f885(x101811,f885(f885(f884(x101811,x101811),a871),a871)),x101811),f328(f8(f884(x101811,x101811),f885(f885(f884(x101811,x101811),a871),a871),x101811),f330(f884(x101811,x101811)))),f257(x101811,x101811)))),x101814)),a325),x101812),x101813))
% 81.29/80.92 [10044]~P107(x100443)+E(f91(x100441,f328(f328(f18(x100441,a871,a871),f328(f328(f8(a871,f885(a871,a871),x100441),a326),x100442)),f328(f328(f8(f885(x100441,a871),a871,x100441),f89(x100441)),f328(f328(f8(f885(x100441,a871),f885(x100441,a871),x100441),f328(f18(x100441,a871,a871),f328(f328(f8(a871,f885(a871,a871),x100441),a331),x100442))),f328(f328(f8(x100443,f885(x100441,a871),x100441),f328(f7(x100441,x100443,a871),f328(f328(f8(x100443,f885(x100443,a871),x100441),f244(x100443)),x100444))),x100444))))),f328(f95(x100441,x100443,x100444),x100442))
% 81.29/80.92 [10087]~P107(x100873)+E(f91(x100871,f328(f328(f18(x100871,a871,a871),f328(f328(f8(a871,f885(a871,a871),x100871),a326),x100872)),f328(f328(f8(f885(x100871,a871),a871,x100871),f89(x100871)),f328(f328(f8(f885(x100871,a871),f885(x100871,a871),x100871),f328(f18(x100871,a871,a871),f328(f328(f8(a871,f885(a871,a871),x100871),a331),x100872))),f328(f328(f7(x100871,f885(x100871,x100873),f885(x100871,a871)),f328(f328(f8(f885(x100873,a871),f885(f885(x100871,x100873),f885(x100871,a871)),x100871),f8(x100873,a871,x100871)),f328(f328(f8(x100873,f885(x100873,a871),x100871),f244(x100873)),x100874))),x100874))))),f97(x100871,x100873,x100874,x100872))
% 81.29/80.92 [10133]E(f328(f328(f150(f878(x101331)),f328(f328(f150(x101331),x101332),f328(f141(f878(x101331),f878(x101331),f127(x101331),f119(x101331)),f328(f328(f153(f878(x101331),f878(x101331)),f155(f878(x101331),x101331,f119(x101331),f328(f328(f8(f878(x101331),f885(f878(x101331),f878(x101331)),x101331),f16(f878(x101331),f878(x101331))),f328(f328(f7(x101331,f878(x101331),f878(x101331)),f150(x101331)),f119(x101331))))),x101333)))),f179(x101331,f328(f328(f150(f878(x101331)),x101334),f328(f141(f878(f878(x101331)),f878(f878(x101331)),f127(f878(x101331)),f119(f878(x101331))),f328(f328(f153(f878(x101331),f878(f878(x101331))),f155(f878(f878(x101331)),x101331,f119(f878(x101331)),f328(f16(f885(f878(x101331),f878(f878(x101331))),x101331),f328(f328(f7(f878(x101331),f878(f878(x101331)),f878(f878(x101331))),f150(f878(x101331))),f119(f878(x101331)))))),x101333))))),f179(x101331,f328(f328(f150(f878(x101331)),f328(f328(f150(x101331),x101332),x101334)),x101333)))+~P24(f328(f316(f878(f878(x101331)),f180(x101331)),f328(f328(f150(f878(x101331)),f328(f328(f150(x101331),x101332),x101334)),x101333)))
% 81.29/80.92 [10171]~P24(f328(f62(x101712),f328(f249(x101712),x101714)))+P24(f328(f62(x101711),f328(f249(x101711),f328(f328(f8(f885(x101712,a871),a871,x101711),f88(x101712)),f328(f328(f7(x101711,f885(x101712,a871),f885(x101712,a871)),f328(f328(f8(f885(x101712,f885(a871,a871)),f885(f885(x101712,a871),f885(x101712,a871)),x101711),f18(x101712,a871,a871)),f328(f328(f8(f885(x101712,a871),f885(x101712,f885(a871,a871)),x101711),f328(f8(a871,f885(a871,a871),x101712),a326)),f328(f328(f7(x101711,f885(x101712,x101711),f885(x101712,a871)),f328(f328(f8(f885(x101711,a871),f885(f885(x101712,x101711),f885(x101712,a871)),x101711),f8(x101711,a871,x101712)),a325)),x101713)))),x101714)))))
% 81.29/80.92 [5263]E(x52631,x52632)+~E(f129(x52633,x52634,x52631),f129(x52633,x52635,x52632))
% 81.29/80.92 [5264]E(x52641,x52642)+~E(f129(x52643,x52641,x52644),f129(x52643,x52642,x52645))
% 81.29/80.92 [5640]E(f328(f328(f306(x56401),x56402),f183(x56401,x56403,x56404)),f183(x56401,x56403,x56404))+~E(f328(x56404,x56402),f328(f236(x56403),x56405))
% 81.29/80.92 [6050]P24(f328(f264(x60501,x60502,x60503),x60504))+~P24(f328(f328(x60503,x60505),x60504))
% 81.29/80.92 [6052]P24(f328(f263(x60521,x60522,x60523),x60524))+~P24(f328(f328(x60523,x60524),x60525))
% 81.29/80.92 [6055]~E(f328(x60554,x60552),f328(f236(x60553),x60555))+P24(f328(f328(f330(x60551),x60552),f183(x60551,x60553,x60554)))
% 81.29/80.92 [6056]~E(f328(x60564,x60565),f328(f236(x60561),x60562))+P24(f328(f328(f330(x60561),x60562),f185(x60563,x60561,x60564)))
% 81.29/80.92 [6523]~E(x65235,f2(a105))+E(f328(f204(x65231,x65232,x65233,x65234),x65235),f130(x65232))
% 81.29/80.92 [6524]~E(x65245,f2(a105))+E(f328(f206(x65241,x65242,x65243,x65244),x65245),f121(x65242))
% 81.29/80.92 [6660]~E(x66603,f2(a105))+E(f328(f277(x66601,x66602,x66603,x66604),x66605),f328(f257(x66601,x66602),x66605))
% 81.29/80.92 [6733]~E(f328(x67334,x67335),f196(x67332))+E(f328(f238(f881(x67331),x67332,f196(x67331),x67333),f328(x67334,x67335)),f196(x67331))
% 81.29/80.92 [7354]E(f328(x73541,x73542),f196(x73543))+~E(f328(f184(x73544,x73543,x73545,x73541),x73542),f196(x73543))
% 81.29/80.92 [7355]E(f328(x73551,x73552),f196(x73553))+~E(f328(f184(x73554,x73553,x73551,x73555),x73552),f196(x73553))
% 81.29/80.92 [7392]E(f328(f184(x73921,x73922,x73923,x73924),x73925),f328(x73923,x73925))+P24(f328(f328(f330(x73921),x73925),f183(x73921,x73922,x73924)))
% 81.29/80.92 [7393]E(f328(f184(x73931,x73932,x73933,x73934),x73935),f328(x73934,x73935))+P24(f328(f328(f330(x73931),x73935),f183(x73931,x73932,x73933)))
% 81.29/80.92 [7711]~P16(x77114,x77111,x77112,x77115)+E(f328(f74(x77111,x77111,x77111,f328(x77112,x77113)),f328(x77112,x77113)),f328(x77112,x77113))
% 81.29/80.92 [7755]E(f328(f184(x77551,x77552,x77553,x77554),x77555),f328(x77554,x77555))+~P24(f328(f328(f330(x77551),x77555),f183(x77551,x77552,x77554)))
% 81.29/80.92 [8103]~P12(x81035,x81031,x81032)+E(f328(f74(x81031,x81031,x81031,f328(x81032,x81033)),f328(x81032,x81034)),f328(f74(x81031,x81031,x81031,f328(x81032,x81034)),f328(x81032,x81033)))
% 81.29/80.92 [8433]P24(f328(f328(f330(f884(x84331,x84331)),f328(f328(f257(x84331,x84331),x84332),x84333)),f322(x84331,x84334,x84335)))+~P24(f328(f328(f245(a877),f328(x84334,x84332)),f328(x84334,x84333)))
% 81.29/80.92 [8532]~P24(f328(f328(f330(x85324),x85323),f295(x85324,x85321,x85322,x85325)))+P24(f328(f328(x85321,x85322),x85323))
% 81.29/80.92 [8533]~P24(f328(f328(f330(x85334),x85333),f292(x85334,x85331,x85332,x85335)))+P24(f328(f328(x85331,x85332),x85333))
% 81.29/80.92 [8534]~P24(f328(f328(f330(x85344),x85342),f295(x85344,x85341,x85345,x85343)))+P24(f328(f328(x85341,x85342),x85343))
% 81.29/80.92 [8535]~P24(f328(f328(f330(x85354),x85352),f292(x85354,x85351,x85355,x85353)))+P24(f328(f328(x85351,x85352),x85353))
% 81.29/80.92 [8674]~P54(x86742,x86741,x86745,x86743,x86744)+E(f328(f307(x86741,x86742,x86743),x86744),f252(f885(x86742,a871)))
% 81.29/80.92 [9112]~P35(x91121,x91122,x91123,x91124,x91125)+P35(x91121,x91122,x91123,f328(f168(x91121),x91124),f328(f168(x91122),x91125))
% 81.29/80.92 [9114]~P35(x91141,x91142,x91143,f328(f168(x91141),x91144),x91145)+P35(x91141,x91142,x91143,x91144,f328(f168(x91142),x91145))
% 81.29/80.92 [9115]~P35(x91151,x91152,x91153,x91154,f328(f168(x91152),x91155))+P35(x91151,x91152,x91153,f328(f168(x91151),x91154),x91155)
% 81.29/80.92 [9121]P35(x91211,x91212,x91213,x91214,x91215)+~P35(x91211,x91212,x91213,f328(f168(x91211),x91214),f328(f168(x91212),x91215))
% 81.29/80.92 [9516]P24(f328(f328(f330(f884(f878(x95161),f878(x95161))),f328(f328(f257(f878(x95161),f878(x95161)),f328(f328(f150(x95161),x95162),x95163)),f328(f328(f150(x95161),x95162),x95164))),f156(x95161,x95165)))+~P24(f328(f328(f330(f884(f878(x95161),f878(x95161))),f328(f328(f257(f878(x95161),f878(x95161)),x95163),x95164)),f156(x95161,x95165)))
% 81.29/80.92 [9517]P24(f328(f328(f330(f884(f878(x95171),f878(x95171))),f328(f328(f257(f878(x95171),f878(x95171)),f328(f328(f127(x95171),x95172),x95173)),f328(f328(f127(x95171),x95172),x95174))),f146(x95171,x95175)))+~P24(f328(f328(f330(f884(f878(x95171),f878(x95171))),f328(f328(f257(f878(x95171),f878(x95171)),x95173),x95174)),f146(x95171,x95175)))
% 81.29/80.92 [9704]E(f328(f328(f150(x97041),f594(x97042,x97043,x97044,x97045,x97041)),f597(x97042,x97043,x97044,x97045,x97041)),x97045)+~P24(f328(f328(f330(f884(f878(x97041),f878(x97041))),f328(f328(f257(f878(x97041),f878(x97041)),x97045),f328(f328(f150(x97041),x97044),x97043))),f157(x97041,x97042)))
% 81.29/80.92 [9726]E(f328(f328(f150(x97261),f595(x97262,x97263,x97264,x97265,x97261)),f596(x97262,x97263,x97264,x97265,x97261)),x97263)+~P24(f328(f328(f330(f884(f878(x97261),f878(x97261))),f328(f328(f257(f878(x97261),f878(x97261)),f328(f328(f150(x97261),x97265),x97264)),x97263)),f157(x97261,x97262)))
% 81.29/80.92 [9888]~P24(f328(f328(f330(f884(f878(x98881),f878(x98881))),f328(f328(f257(f878(x98881),f878(x98881)),f328(f328(f150(x98881),x98885),x98882)),x98884)),f157(x98881,x98883)))+P24(f328(f328(f330(f884(f878(x98881),f878(x98881))),f328(f328(f257(f878(x98881),f878(x98881)),x98882),f596(x98883,x98884,x98882,x98885,x98881))),f157(x98881,x98883)))
% 81.29/80.92 [9960]~P24(f328(f328(f330(f884(f878(x99601),f878(x99601))),f328(f328(f257(f878(x99601),f878(x99601)),x99605),f328(f328(f150(x99601),x99604),x99603))),f157(x99601,x99602)))+P24(f328(f328(f330(f884(f878(x99601),f878(x99601))),f328(f328(f257(f878(x99601),f878(x99601)),f597(x99602,x99603,x99604,x99605,x99601)),x99603)),f157(x99601,x99602)))
% 81.29/80.92 [10127]P24(f328(f328(f330(f884(x101271,x101271)),f328(f328(f257(x101271,x101271),f328(x101272,f328(f328(f81(a877),x101273),x101274))),f328(x101272,x101273))),f304(x101271,x101275)))+~P24(f328(f328(f330(f884(x101271,x101271)),f328(f328(f257(x101271,x101271),f328(x101272,f328(a118,f762(x101274,x101273,x101275,x101272,x101271)))),f328(x101272,f762(x101274,x101273,x101275,x101272,x101271)))),f304(x101271,x101275)))
% 81.29/80.92 [5226]E(x52261,x52262)+~E(f328(f328(f150(x52263),x52264),x52261),f328(f328(f150(x52263),x52265),x52262))
% 81.29/80.92 [5227]E(x52271,x52272)+~E(f328(f328(f150(x52273),x52271),x52274),f328(f328(f150(x52273),x52272),x52275))
% 81.29/80.92 [5280]P24(f328(x52801,x52802))+~E(f328(f135(x52803,x52801),x52804),f328(f328(f150(x52803),x52802),x52805))
% 81.29/80.92 [5281]P24(f328(x52811,x52812))+~E(f328(f328(f150(x52813),x52812),x52814),f328(f135(x52813,x52811),x52815))
% 81.29/80.92 [5438]~E(f328(f328(f137(x54381),x54383),x54382),f328(f328(f150(x54381),x54384),x54385))+E(f328(f328(f164(x54381),x54382),x54383),x54384)
% 81.29/80.92 [5571]~P11(x55714,x55715,x55711)+E(f328(f328(x55711,x55712),f328(f328(x55711,x55712),x55713)),f328(f328(x55711,x55712),x55713))
% 81.29/80.92 [6108]~E(x61084,f2(a105))+E(f328(f328(f123(x61081,x61082,x61083),x61084),x61085),f328(f328(f257(f878(x61082),x61081),f119(x61082)),x61085))
% 81.29/80.92 [6180]~P106(x61802)+~E(f328(f328(f147(x61801,x61802,x61803),x61804),x61805),f119(x61801))
% 81.29/80.92 [6560]E(x65601,x65602)+~E(f328(f328(f127(x65603),x65604),f328(f328(f150(x65603),x65601),f119(x65603))),f328(f328(f127(x65603),x65605),f328(f328(f150(x65603),x65602),f119(x65603))))
% 81.29/80.92 [6561]E(x65611,x65612)+~E(f328(f328(f127(x65613),x65611),f328(f328(f150(x65613),x65614),f119(x65613))),f328(f328(f127(x65613),x65612),f328(f328(f150(x65613),x65615),f119(x65613))))
% 81.29/80.92 [6816]E(f328(f187(x68161,x68162,x68163,x68164),x68165),f196(x68162))+P24(f328(f328(f330(x68161),x68165),x68164))
% 81.29/80.92 [6878]E(f328(f328(f306(x68781),f328(x68782,x68783)),f328(f307(x68784,x68781,x68782),x68785)),f328(f307(x68784,x68781,x68782),x68785))+~P24(f328(f328(f330(x68784),x68783),x68785))
% 81.29/80.92 [6885]~P24(f328(x68854,f328(x68853,x68855)))+P24(f328(f328(f308(x68851,x68852,x68853),x68854),x68855))
% 81.29/80.92 [6980]~E(f328(f307(x69801,x69802,x69803),x69804),x69805)+E(f328(f307(f885(x69801,a871),f885(x69802,a871),f307(x69801,x69802,x69803)),f328(f305(x69801),x69804)),f328(f305(x69802),x69805))
% 81.29/80.92 [7012]E(f328(f187(x70121,x70122,x70123,x70124),x70125),f328(x70123,x70125))+~P24(f328(f328(f330(x70121),x70125),x70124))
% 81.29/80.92 [7311]P21(x73111,x73112,x73113,x73114)+~P21(x73111,x73112,x73113,f328(f328(f306(x73111),x73115),x73114))
% 81.29/80.92 [7381]P24(f328(x73811,x73812))+~P24(f328(f328(f98(x73813,x73814,x73811),x73815),x73812))
% 81.29/80.92 [7426]~P24(f328(f328(f330(x74264),x74263),x74265))+P24(f328(f328(f330(x74261),f328(x74262,x74263)),f328(f307(x74264,x74261,x74262),x74265)))
% 81.29/80.92 [7450]~P106(x74502)+E(f149(x74501,x74502,x74503,f328(f135(x74501,x74504),x74505)),f328(f135(x74501,x74504),f149(x74501,x74502,x74503,x74505)))
% 81.29/80.92 [7483]P24(f328(x74831,f328(x74832,x74833)))+~P24(f328(f328(f308(x74834,x74835,x74832),x74831),x74833))
% 81.29/80.92 [7484]P24(f328(f328(x74841,x74842),x74843))+~P24(f328(f328(f98(x74844,x74841,x74845),x74842),x74843))
% 81.29/80.92 [7547]~P24(f328(f328(f330(x75473),f328(x75474,x75472)),x75475))+P24(f328(f328(f330(x75471),x75472),f328(f308(x75471,x75473,x75474),x75475)))
% 81.29/80.92 [7941]~P24(f328(f328(f330(x79415),x79413),f328(f308(x79415,x79411,x79412),x79414)))+P24(f328(f328(f330(x79411),f328(x79412,x79413)),x79414))
% 81.29/80.92 [8170]~E(x81703,f328(f328(f328(f73(x81701,f881(x81702)),f328(f16(f881(x81702),x81701),f196(x81702))),x81704),f328(f236(x81702),x81705)))+E(f183(x81701,x81702,x81703),f328(f328(f306(x81701),x81704),f193(f885(x81701,a871))))
% 81.29/80.92 [8250]~P12(x82502,x82501,x82503)+E(f328(f141(x82501,x82502,f328(f7(x82502,x82501,x82501),x82503),x82504),f151(x82502,x82505)),f328(f328(f65(x82502,x82501,x82503),x82504),f328(f171(x82502),x82505)))
% 81.29/80.92 [8269]E(f328(x82691,f392(x82692,x82691,x82693,x82694)),x82694)+~P24(f328(f328(f330(x82695),x82694),f328(f307(x82693,x82695,x82691),x82692)))
% 81.29/80.92 [8578]~E(x85782,f328(f328(f150(x85781),x85784),x85785))+P24(f328(f328(f330(f884(f878(x85781),f878(x85781))),f328(f328(f257(f878(x85781),f878(x85781)),f119(x85781)),x85782)),f146(x85781,x85783)))
% 81.29/80.92 [8631]~P35(x86311,x86313,x86315,x86312,x86314)+E(f328(f194(f878(x86311)),x86312),f328(f194(f878(x86313)),x86314))
% 81.29/80.92 [8641]P24(f328(f328(f244(f885(x86411,a871)),f328(f328(f42(x86412,f885(x86411,a871)),x86413),x86414)),f328(x86414,x86415)))+~P24(f328(f328(f330(x86412),x86415),x86413))
% 81.29/80.92 [8690]~P54(x86901,x86902,x86903,x86905,x86904)+E(f328(f307(x86901,x86902,x86903),f252(f885(x86901,a871))),x86904)
% 81.29/80.92 [8895]E(f328(f328(f328(f73(x88951,f881(x88952)),f187(x88951,x88952,x88953,x88954)),x88955),f196(x88952)),f187(x88951,x88952,x88953,x88954))+P24(f328(f328(f330(x88951),x88955),x88954))
% 81.29/80.92 [8900]E(f328(f135(x89001,x89002),f742(x89003,x89004,x89005,x89002,x89001)),x89003)+~E(f328(f135(x89001,x89002),x89005),f328(f328(f150(x89001),x89004),x89003))
% 81.29/80.92 [8901]E(f328(f135(x89011,x89012),f744(x89013,x89012,x89014,x89015,x89011)),x89014)+~E(f328(f328(f150(x89011),x89015),x89014),f328(f135(x89011,x89012),x89013))
% 81.29/80.92 [8902]E(f328(x89021,f569(x89022,x89023,x89021,x89024,x89025)),x89022)+~E(f328(f328(f207(x89025,x89024),x89021),x89023),f328(f236(x89024),x89022))
% 81.29/80.92 [8906]E(f328(f236(x89061),f569(x89062,x89063,x89064,x89065,x89061)),x89063)+~E(f328(f328(f207(x89061,x89065),x89064),x89063),f328(f236(x89065),x89062))
% 81.29/80.92 [9004]E(f328(f194(f878(x90041)),x90042),x90043)+~P24(f328(f328(f330(f884(f878(x90041),f878(x90041))),f328(f328(f257(f878(x90041),f878(x90041)),x90044),x90042)),f328(f142(x90041,x90045),x90043)))
% 81.29/80.92 [9005]E(f328(f194(f878(x90051)),x90052),x90053)+~P24(f328(f328(f330(f884(f878(x90051),f878(x90051))),f328(f328(f257(f878(x90051),f878(x90051)),x90052),x90054)),f328(f142(x90051,x90055),x90053)))
% 81.29/80.92 [9072]P24(f328(f328(f330(x90721),f392(x90722,x90723,x90721,x90724)),x90722))+~P24(f328(f328(f330(x90725),x90724),f328(f307(x90721,x90725,x90723),x90722)))
% 81.29/80.92 [9233]E(f328(f307(x92331,x92332,x92333),f389(x92334,x92333,x92331,x92335,x92332)),x92335)+~P24(f328(f328(f244(f885(x92332,a871)),x92335),f328(f307(x92331,x92332,x92333),x92334)))
% 81.29/80.92 [9486]E(f328(x94861,f852(x94862,x94861,x94863,x94864,x94865)),f328(f236(x94865),x94864))+~P24(f328(f328(f330(x94865),x94864),f185(x94863,x94865,f187(x94863,x94865,x94861,x94862))))
% 81.29/80.92 [9532]P24(f328(f328(f330(f884(f878(x95321),f878(x95321))),f328(f328(f257(f878(x95321),f878(x95321)),f328(f328(f150(x95321),x95322),x95323)),f328(f328(f150(x95321),x95322),x95324))),f304(f878(x95321),f156(x95321,x95325))))+~P24(f328(f328(f330(f884(f878(x95321),f878(x95321))),f328(f328(f257(f878(x95321),f878(x95321)),x95323),x95324)),f304(f878(x95321),f156(x95321,x95325))))
% 81.29/80.92 [9563]~E(f328(x95633,f561(x95635,x95634,x95633,x95632,x95631)),f328(x95635,f561(x95635,x95634,x95633,x95632,x95631)))+E(f328(f328(f153(x95631,x95632),x95633),x95634),f328(f328(f153(x95631,x95632),x95635),x95634))
% 81.29/80.92 [9639]~E(f328(f135(x96391,x96395),x96394),f328(f328(f150(x96391),x96393),x96392))+E(f328(f328(f127(x96391),f743(x96392,x96393,x96394,x96395,x96391)),f328(f328(f150(x96391),x96393),f742(x96392,x96393,x96394,x96395,x96391))),x96394)
% 81.29/80.92 [9640]~E(f328(f328(f150(x96401),x96405),x96404),f328(f135(x96401,x96403),x96402))+E(f328(f328(f127(x96401),f745(x96402,x96403,x96404,x96405,x96401)),f328(f328(f150(x96401),x96405),f744(x96402,x96403,x96404,x96405,x96401))),x96402)
% 81.29/80.92 [9642]E(f328(f328(f153(x96421,x96422),x96423),x96424),f328(f328(f153(x96421,x96422),x96425),x96424))+P24(f328(f328(f330(x96421),f561(x96423,x96424,x96425,x96422,x96421)),f328(f171(x96421),x96424)))
% 81.29/80.92 [9672]~P24(f328(f328(f330(x96725),x96724),f328(f282(x96721,x96725,x96723),x96722)))+P24(f328(f328(f330(x96721),f526(x96722,x96723,x96721,x96724,x96725)),x96722))
% 81.29/80.92 [9673]~P24(f328(f328(f330(x96735),x96734),f328(f282(x96731,x96735,x96733),x96732)))+P24(f328(f328(f330(x96731),f542(x96732,x96733,x96731,x96734,x96735)),x96732))
% 81.29/80.92 [9698]~P24(f328(f328(f244(f885(x96985,a871)),x96984),f328(f307(x96981,x96985,x96983),x96982)))+P24(f328(f328(f244(f885(x96981,a871)),f389(x96982,x96983,x96981,x96984,x96985)),x96982))
% 81.29/80.92 [9749]~P24(f328(f328(f330(x97495),x97494),f185(x97491,x97495,f187(x97491,x97495,x97493,x97492))))+P24(f328(f328(f330(x97491),f852(x97492,x97493,x97491,x97494,x97495)),x97492))
% 81.29/80.92 [10150]E(x101501,f2(a105))+E(f328(f238(f884(f878(x101502),x101503),f884(x101502,x101503),f328(f328(f257(f878(x101502),x101503),f119(x101502)),x101504),f328(f267(x101502,x101503,f884(f878(x101502),x101503)),f328(f328(f7(x101502,f885(x101503,f884(f878(x101502),x101503)),f885(x101503,f884(f878(x101502),x101503))),f328(f328(f8(f885(f884(f878(x101502),x101503),f884(f878(x101502),x101503)),f885(f885(x101503,f884(f878(x101502),x101503)),f885(x101503,f884(f878(x101502),x101503))),x101502),f8(f884(f878(x101502),x101503),f884(f878(x101502),x101503),x101503)),f328(f328(f8(f885(f878(x101502),f885(x101503,f884(f878(x101502),x101503))),f885(f884(f878(x101502),x101503),f884(f878(x101502),x101503)),x101502),f267(f878(x101502),x101503,f884(f878(x101502),x101503))),f328(f328(f8(f885(f878(x101502),f878(x101502)),f885(f878(x101502),f885(x101503,f884(f878(x101502),x101503))),x101502),f328(f8(f878(x101502),f885(x101503,f884(f878(x101502),x101503)),f878(x101502)),f257(f878(x101502),x101503))),f150(x101502))))),f328(f123(x101503,x101502,x101505),f328(f328(f22(a105),x101501),f79(a105)))))),f328(x101505,x101504)),f328(f328(f123(x101503,x101502,x101505),x101501),x101504))
% 81.29/80.92 [5451]~E(f328(x54513,x54514),x54515)+E(f328(f328(f328(f73(x54511,x54512),x54513),x54514),x54515),x54513)
% 81.29/80.92 [5892]E(f328(x58921,x58922),x58923)+~E(f328(f328(f328(f73(x58924,x58925),x58921),x58922),x58923),x58921)
% 81.29/80.92 [5988]E(x59881,x59882)+~E(f328(f266(x59883,x59884),f328(f328(f257(x59883,x59884),x59885),x59881)),x59882)
% 81.29/80.92 [5989]E(x59891,x59892)+~E(f328(f256(x59893,x59894),f328(f328(f257(x59893,x59894),x59891),x59895)),x59892)
% 81.29/80.92 [6254]~E(x62543,f328(f328(f127(x62541),x62544),f328(f328(f150(x62541),x62542),x62545)))+P24(f328(f328(f330(x62541),x62542),f328(f171(x62541),x62543)))
% 81.29/80.92 [6647]E(f328(f307(x66471,x66472,f328(f16(x66472,x66471),x66473)),x66474),f328(f328(f306(x66472),x66473),f193(f885(x66472,a871))))+~P24(f328(f328(f330(x66471),x66475),x66474))
% 81.29/80.92 [6718]E(f328(f328(f116(f885(x67181,a871)),f328(f171(x67181),x67182)),f328(f171(x67181),x67183)),f328(f171(x67181),x67184))+~E(f166(x67181,x67185,x67184),f328(f328(f257(f878(x67181),f878(x67181)),x67182),x67183))
% 81.29/80.92 [6820]~P106(x68202)+E(f328(f194(f878(x68201)),f328(f328(f147(x68201,x68202,x68203),x68204),x68205)),f328(a118,f328(f194(f878(x68201)),x68205)))
% 81.29/80.92 [6832]~P106(x68322)+E(f328(f171(x68321),f328(f328(f147(x68321,x68322,x68323),x68324),x68325)),f328(f328(f306(x68321),x68324),f328(f171(x68321),x68325)))
% 81.29/80.92 [7103]~P112(x71031)+E(f328(f328(f81(x71031),f328(f328(f81(x71031),x71032),x71033)),f328(f328(f81(x71031),x71034),x71035)),f328(f328(f81(x71031),f328(f328(f81(x71031),x71032),x71034)),f328(f328(f81(x71031),x71033),x71035)))
% 81.29/80.92 [7104]~P112(x71041)+E(f328(f328(f82(x71041),f328(f328(f82(x71041),x71042),x71043)),f328(f328(f82(x71041),x71044),x71045)),f328(f328(f82(x71041),f328(f328(f82(x71041),x71042),x71044)),f328(f328(f82(x71041),x71043),x71045)))
% 81.29/80.92 [7105]~P61(x71051)+E(f328(f328(f286(x71051),f328(f328(f82(x71051),x71052),x71053)),f328(f328(f82(x71051),x71054),x71055)),f328(f328(f82(x71051),f328(f328(f286(x71051),x71052),x71054)),f328(f328(f286(x71051),x71053),x71055)))
% 81.29/80.92 [7119]~P106(x71191)+E(f302(x71191,f328(f328(f243(x71191),x71192),x71193),f328(f328(f242(x71191),x71194),x71195)),f328(f328(f107(f885(x71191,a871)),f302(x71191,x71192,x71194)),f302(x71191,x71193,x71195)))
% 81.29/80.92 [7120]~P106(x71201)+E(f301(x71201,f328(f328(f243(x71201),x71202),x71203),f328(f328(f242(x71201),x71204),x71205)),f328(f328(f107(f885(x71201,a871)),f301(x71201,x71202,x71204)),f301(x71201,x71203,x71205)))
% 81.29/80.92 [7121]~P106(x71211)+E(f299(x71211,f328(f328(f243(x71211),x71212),x71213),f328(f328(f242(x71211),x71214),x71215)),f328(f328(f107(f885(x71211,a871)),f299(x71211,x71212,x71214)),f299(x71211,x71213,x71215)))
% 81.29/80.92 [7122]~P106(x71221)+E(f328(f328(f107(f885(x71221,a871)),f328(f298(x71221,x71222),x71223)),f328(f298(x71221,x71224),x71225)),f328(f298(x71221,f328(f328(f243(x71221),x71222),x71224)),f328(f328(f242(x71221),x71223),x71225)))
% 81.29/80.92 [7237]~P24(f328(x72371,f478(x72373,x72372,x72371)))+P24(f328(x72371,f328(f328(f257(x72372,x72373),x72374),x72375)))
% 81.29/80.92 [7324]~E(f328(x73243,x73244),f196(x73242))+E(f185(x73241,x73242,f328(f328(f328(f73(x73241,f881(x73242)),x73243),x73244),f328(f236(x73242),x73245))),f328(f328(f306(x73242),x73245),f185(x73241,x73242,x73243)))
% 81.29/80.92 [7345]~E(x73452,f328(x73454,x73455))+P24(f328(f328(f330(x73451),x73452),f328(f307(x73453,x73451,x73454),f252(f885(x73453,a871)))))
% 81.29/80.92 [7404]~E(f328(x74043,x74044),f196(x74042))+E(f328(f328(f22(f885(x74041,a871)),f183(x74041,x74042,x74043)),f328(f328(f306(x74041),x74044),x74045)),f328(f328(f22(f885(x74041,a871)),f183(x74041,x74042,x74043)),x74045))
% 81.29/80.92 [7423]~P12(x74233,x74232,x74234)+P12(x74231,x74232,f328(f328(f8(x74233,f885(x74232,x74232),x74231),x74234),x74235))
% 81.29/80.92 [7424]~P11(x74243,x74242,x74244)+P11(x74241,x74242,f328(f328(f8(x74243,f885(x74242,x74242),x74241),x74244),x74245))
% 81.29/80.92 [7563]~P21(x75631,x75632,x75633,x75634)+P21(x75631,x75632,x75633,f328(f328(f22(f885(x75631,a871)),x75634),x75635))
% 81.29/80.92 [7720]~P24(f328(f328(x77203,x77204),x77205))+P24(f328(f328(f267(x77201,x77202,a871),x77203),f328(f328(f257(x77201,x77202),x77204),x77205)))
% 81.29/80.92 [7830]~P24(f328(x78302,x78304))+~E(f328(f328(f137(x78301),f328(f194(f878(x78301)),f176(x78301,x78302,x78303))),x78303),f328(f328(f150(x78301),x78304),x78305))
% 81.29/80.92 [7850]P21(x78501,x78502,x78503,x78504)+~P21(x78501,x78502,x78503,f328(f328(f116(f885(x78501,a871)),x78505),x78504))
% 81.29/80.92 [7851]P21(x78511,x78512,x78513,x78514)+~P21(x78511,x78512,x78513,f328(f328(f116(f885(x78511,a871)),x78514),x78515))
% 81.29/80.92 [7898]~P106(x78982)+E(f328(f328(f147(x78981,x78982,x78983),x78984),f149(x78981,x78982,x78983,x78985)),f149(x78981,x78982,x78983,f328(f328(f150(x78981),x78984),x78985)))
% 81.29/80.92 [8062]~P30(x80621,f328(a118,x80622),f328(f328(f328(f93(x80621),x80623),f328(a26,x80624)),x80625))+P30(x80621,x80622,f328(f328(f328(f93(x80621),x80623),f328(f240(a873),f328(a28,x80624))),x80625))
% 81.29/80.92 [8197]P30(x81971,f328(a118,x81972),f328(f328(f328(f93(x81971),x81973),f328(a26,x81974)),x81975))+~P30(x81971,x81972,f328(f328(f328(f93(x81971),x81973),f328(f240(a873),f328(a28,x81974))),x81975))
% 81.29/80.92 [8226]~P11(x82262,x82261,x82263)+E(f328(f141(x82261,x82262,f328(f7(x82262,x82261,x82261),x82263),x82264),x82265),f328(f328(f65(x82262,x82261,x82263),x82264),f328(f171(x82262),x82265)))
% 81.29/80.92 [8255]~E(f328(f328(f137(x82551),f328(f194(f878(x82551)),f176(x82551,x82552,x82553))),x82553),f328(f328(f150(x82551),x82554),x82555))+E(f328(f328(f127(x82551),f176(x82551,x82552,x82553)),f328(f328(f150(x82551),x82554),x82555)),x82553)
% 81.29/80.92 [8279]P24(f328(f328(x82791,x82792),x82793))+~P24(f328(f328(f267(x82794,x82795,a871),x82791),f328(f328(f257(x82794,x82795),x82792),x82793)))
% 81.29/80.92 [8342]~E(f328(f328(f177(x83421,x83422),x83425),x83423),f328(f236(x83422),x83424))+P24(f328(f328(f330(f884(x83421,x83422)),f328(f328(f257(x83421,x83422),x83423),x83424)),f328(f171(f884(x83421,x83422)),x83425)))
% 81.29/80.92 [8745]P24(f328(f328(f244(f885(x87451,a871)),f328(f307(x87452,x87451,x87453),x87454)),f328(f307(x87452,x87451,x87453),x87455)))+~P24(f328(f328(f244(f885(x87452,a871)),x87454),x87455))
% 81.29/80.92 [8746]P24(f328(f328(f244(f885(x87461,a871)),f328(f308(x87461,x87462,x87463),x87464)),f328(f308(x87461,x87462,x87463),x87465)))+~P24(f328(f328(f244(f885(x87462,a871)),x87464),x87465))
% 81.29/80.92 [8822]E(x88221,f2(a105))+E(f328(f328(f269(x88222,x88223,x88222,f884(x88223,x88222)),f328(x88224,x88225)),f277(x88223,x88222,f328(f328(f22(a105),x88221),f79(a105)),x88224)),f328(f277(x88223,x88222,x88221,x88224),x88225))
% 81.29/80.92 [9142]P30(x91421,x91422,f328(f328(f328(f93(x91421),x91423),x91424),x91425))+P24(f328(f328(x91423,f622(x91425,x91424,x91423,x91422)),f636(x91425,x91424,x91423,x91422)))
% 81.29/80.92 [9343]E(f328(f236(x93431),f575(x93432,x93433,x93434,x93431,x93435)),f328(f328(f177(x93435,x93431),x93432),x93434))+~P24(f328(f328(f330(f884(x93435,x93431)),f328(f328(f257(x93435,x93431),x93434),x93433)),f328(f171(f884(x93435,x93431)),x93432)))
% 81.29/80.92 [9387]P30(x93871,x93872,f328(f328(f328(f93(x93871),x93873),x93874),x93875))+~P24(f328(f328(x93875,f622(x93875,x93874,x93873,x93872)),f645(x93875,x93874,x93873,x93872)))
% 81.29/80.92 [9446]P30(x94461,x94462,f328(f328(f328(f93(x94461),x94463),x94464),x94465))+P24(f328(f328(f328(f328(a202,x94464),f636(x94465,x94464,x94463,x94462)),x94462),f645(x94465,x94464,x94463,x94462)))
% 81.29/80.92 [9449]~P20(x94491,x94492,f328(f328(f306(f876(x94491)),f328(f328(f328(f93(x94491),x94493),f328(f240(a873),f328(a28,x94494))),x94495)),f193(f885(f876(x94491),a871))))+P20(x94491,x94492,f328(f328(f306(f876(x94491)),f328(f328(f328(f93(x94491),x94493),f328(a26,x94494)),x94495)),f193(f885(f876(x94491),a871))))
% 81.29/80.92 [9477]~P24(f328(f62(x94773),f328(f307(x94772,x94773,x94775),f252(f885(x94772,a871)))))+P24(f328(f62(x94771),f328(f307(x94772,x94771,f328(f328(f8(x94773,x94771,x94772),x94774),x94775)),f252(f885(x94772,a871)))))
% 81.29/80.92 [9499]P24(f328(f328(f244(f885(f885(x94991,a871),a871)),f328(f307(f885(x94992,a871),f885(x94991,a871),f307(x94992,x94991,x94993)),f328(f305(x94992),x94994))),f328(f305(x94991),x94995)))+~P24(f328(f328(f244(f885(x94991,a871)),f328(f307(x94992,x94991,x94993),x94994)),x94995))
% 81.29/80.92 [9512]~P24(f328(f62(f881(x95121)),f328(f307(x95122,f881(x95121),x95123),f252(f885(x95122,a871)))))+P24(f328(f62(f881(x95121)),f328(f307(x95122,f881(x95121),f328(f328(f328(f73(x95122,f881(x95121)),x95123),x95124),f328(f236(x95121),x95125))),f252(f885(x95122,a871)))))
% 81.29/80.92 [9572]E(x95721,x95722)+~P24(f328(f67(x95723,x95724,x95725,x95721,f193(f885(x95723,a871))),x95722))
% 81.29/80.92 [9587]E(f328(f328(f257(x95871,x95872),f708(x95873,x95874,x95875,x95872,x95871)),f709(x95873,x95874,x95875,x95872,x95871)),x95875)+~P24(f328(f328(f330(f884(x95871,x95872)),x95875),f328(f328(f265(x95871,x95872),x95874),x95873)))
% 81.29/80.92 [9677]P24(f328(f328(f330(x96771),f708(x96772,x96773,x96774,x96775,x96771)),x96773))+~P24(f328(f328(f330(f884(x96771,x96775)),x96774),f328(f328(f265(x96771,x96775),x96773),x96772)))
% 81.29/80.92 [9785]P20(x97855,x97854,f328(f328(f306(f876(x97855)),f328(f328(f328(f93(x97855),x97851),x97853),x97852)),f193(f885(f876(x97855),a871))))+P24(f328(f328(x97851,f556(x97852,x97853,x97854,x97855,x97851)),f558(x97852,x97853,x97854,x97855,x97851)))
% 81.29/80.92 [9835]P24(f328(f328(f330(x98351),f709(x98352,x98353,x98354,x98351,x98355)),f328(x98352,f708(x98352,x98353,x98354,x98351,x98355))))+~P24(f328(f328(f330(f884(x98355,x98351)),x98354),f328(f328(f265(x98355,x98351),x98353),x98352)))
% 81.29/80.92 [9863]P24(f328(f328(f330(f884(x98631,x98631)),f328(f328(f257(x98631,x98631),x98632),f786(x98633,x98634,x98635,x98632,x98631))),x98633))+~P24(f328(f328(f330(f884(x98631,x98631)),f328(f328(f257(x98631,x98631),x98632),x98635)),f328(f328(f188(f884(x98631,x98631),a871),f328(a118,x98634)),x98633)))
% 81.29/80.92 [9864]P24(f328(f328(f330(f884(x98641,x98641)),f328(f328(f257(x98641,x98641),x98642),f787(x98643,x98644,x98645,x98642,x98641))),x98643))+~P24(f328(f328(f330(f884(x98641,x98641)),f328(f328(f257(x98641,x98641),x98642),x98645)),f328(f328(f188(f884(x98641,x98641),a871),f328(a118,x98644)),x98643)))
% 81.29/80.92 [9883]~P24(f328(f328(f330(f884(f878(x98831),f878(x98831))),f328(f328(f257(f878(x98831),f878(x98831)),f328(f328(f150(x98831),x98832),x98835)),x98834)),f157(x98831,x98833)))+P24(f328(f328(f330(f884(x98831,x98831)),f328(f328(f257(x98831,x98831),x98832),f595(x98833,x98834,x98835,x98832,x98831))),x98833))
% 81.29/80.92 [9885]~P20(x98851,x98852,f328(f328(f306(f876(x98851)),f328(f328(f328(f93(x98851),f98(x98851,x98853,x98854)),x98855),x98853)),f193(f885(f876(x98851),a871))))+P20(x98851,x98852,f328(f328(f306(f876(x98851)),f328(f328(f328(f93(x98851),x98853),f33(x98854,x98855)),f98(x98851,x98853,f328(f74(a871,a871,a872,a323),x98854)))),f193(f885(f876(x98851),a871))))
% 81.29/80.92 [9886]~P23(x98861,x98862,f328(f328(f306(f876(x98861)),f328(f328(f328(f93(x98861),f98(x98861,x98863,x98864)),x98865),x98863)),f193(f885(f876(x98861),a871))))+P23(x98861,x98862,f328(f328(f306(f876(x98861)),f328(f328(f328(f93(x98861),x98863),f33(x98864,x98865)),f98(x98861,x98863,f328(f74(a871,a871,a872,a323),x98864)))),f193(f885(f876(x98861),a871))))
% 81.29/80.92 [10151]P20(x101511,x101512,f328(f328(f306(f876(x101511)),f328(f328(f328(f93(x101511),x101513),x101514),x101515)),f193(f885(f876(x101511),a871))))+~P20(x101511,x101512,f328(f328(f306(f876(x101511)),f328(f328(f328(f93(x101511),f328(f16(f885(a872,a871),x101511),f328(f328(f7(a872,a872,a871),a325),f558(x101515,x101514,x101512,x101511,x101513)))),x101514),f328(f16(f885(a872,a871),x101511),f328(x101515,f556(x101515,x101514,x101512,x101511,x101513))))),f193(f885(f876(x101511),a871))))
% 81.29/80.92 [6328]P24(f328(x63282,x63284))+E(f176(x63281,x63282,f328(f328(f127(x63281),x63283),f328(f328(f150(x63281),x63284),x63285))),f176(x63281,x63282,x63283))
% 81.29/80.92 [6378]~P66(x63782)+E(f328(f328(f328(f22(f885(x63781,x63782)),x63783),x63784),x63785),f328(f328(f22(x63782),f328(x63783,x63785)),f328(x63784,x63785)))
% 81.29/80.92 [6380]~P78(x63802)+E(f328(f328(f328(f116(f885(x63801,x63802)),x63803),x63804),x63805),f328(f328(f116(x63802),f328(x63803,x63805)),f328(x63804,x63805)))
% 81.29/80.92 [6382]~P78(x63822)+E(f328(f328(f328(f107(f885(x63821,x63822)),x63823),x63824),x63825),f328(f328(f107(x63822),f328(x63823,x63825)),f328(x63824,x63825)))
% 81.29/80.92 [6400]E(x64001,x64002)+E(f328(f328(f164(x64003),f328(f328(f158(x64003,x64004),x64001),x64005)),x64002),f328(f328(f164(x64003),x64004),x64002))
% 81.29/80.92 [6666]~E(x66664,f193(f885(x66663,a871)))+E(f328(f328(f22(f885(x66661,a871)),x66662),f328(f328(f43(x66663,f885(x66661,a871)),x66664),x66665)),x66662)
% 81.29/80.92 [6667]~E(x66674,f193(f885(x66673,a871)))+E(f328(f328(f116(f885(x66671,a871)),x66672),f328(f328(f43(x66673,f885(x66671,a871)),x66674),x66675)),x66672)
% 81.29/80.92 [6668]~E(x66684,f193(f885(x66683,a871)))+E(f328(f328(f107(f885(x66681,a871)),x66682),f328(f328(f42(x66683,f885(x66681,a871)),x66684),x66685)),x66682)
% 81.29/80.92 [6682]~E(x66824,f193(f885(x66823,a871)))+E(f328(f328(f306(x66821),x66822),f328(f328(f43(x66823,f885(x66821,a871)),x66824),x66825)),f328(f328(f306(x66821),x66822),f193(f885(x66821,a871))))
% 81.29/80.92 [7472]E(f328(f328(f164(x74721),f328(f328(f153(x74722,x74721),x74723),x74724)),x74725),f328(x74723,f328(f328(f164(x74722),x74724),x74725)))+~P24(f328(f328(f245(a877),x74725),f328(f194(f878(x74722)),x74724)))
% 81.29/80.92 [7535]E(f328(f328(f116(f885(x75351,a871)),f328(x75352,x75353)),f328(f328(f43(x75354,f885(x75351,a871)),x75355),x75352)),f328(f328(f43(x75354,f885(x75351,a871)),x75355),x75352))+~P24(f328(f328(f330(x75354),x75353),x75355))
% 81.29/80.92 [7536]E(f328(f328(f107(f885(x75361,a871)),f328(x75362,x75363)),f328(f328(f42(x75364,f885(x75361,a871)),x75365),x75362)),f328(f328(f42(x75364,f885(x75361,a871)),x75365),x75362))+~P24(f328(f328(f330(x75364),x75363),x75365))
% 81.29/80.92 [8142]~E(x81423,f193(f885(x81421,a871)))+E(f328(f328(f43(x81421,f885(x81422,a871)),x81423),f328(f328(f8(f885(x81422,a871),f885(x81422,a871),x81421),f328(f306(x81422),x81424)),x81425)),f193(f885(x81422,a871)))
% 81.29/80.92 [8148]~P24(f328(f328(f330(x81484),x81483),x81485))+P24(f328(f328(f244(f885(x81481,a871)),f328(x81482,x81483)),f328(f328(f43(x81484,f885(x81481,a871)),x81485),x81482)))
% 81.29/80.92 [8278]~E(f328(x82784,x82782),x82785)+P24(f328(f328(f330(x82781),x82782),f328(f308(x82781,x82783,x82784),f328(f328(f306(x82783),x82785),f193(f885(x82783,a871))))))
% 81.29/80.92 [8324]~P52(x83241,x83242,f328(f283(x83242,x83241),x83243))+E(f328(f328(f107(f885(x83241,a871)),f328(f282(x83242,x83241,x83243),x83244)),f328(f282(x83242,x83241,x83243),x83245)),f328(f282(x83242,x83241,x83243),f328(f328(f107(f885(x83242,a871)),x83244),x83245)))
% 81.29/80.92 [8400]E(x84001,f2(a105))+E(f328(f122(x84002,x84003,f328(x84004,f328(f328(f22(a105),x84001),f79(a105)))),f328(f328(f7(x84002,a105,f879(x84003)),x84005),x84001)),f328(f206(x84002,x84003,x84004,x84005),x84001))
% 81.29/80.92 [8443]E(x84431,f193(f885(x84432,a871)))+E(f328(f328(f43(x84432,f885(x84433,a871)),x84431),f328(f328(f8(f885(x84433,a871),f885(x84433,a871),x84432),f328(f306(x84433),x84434)),x84435)),f328(f328(f306(x84433),x84434),f328(f328(f43(x84432,f885(x84433,a871)),x84431),x84435)))
% 81.29/80.92 [8499]~P21(x84992,x84991,x84993,f252(f885(x84992,a871)))+E(f328(f328(f22(f885(x84991,a871)),f328(f307(x84992,x84991,x84993),x84994)),f328(f307(x84992,x84991,x84993),x84995)),f328(f307(x84992,x84991,x84993),f328(f328(f22(f885(x84992,a871)),x84994),x84995)))
% 81.29/80.92 [8500]~P21(x85002,x85001,x85003,f252(f885(x85002,a871)))+E(f328(f328(f107(f885(x85001,a871)),f328(f307(x85002,x85001,x85003),x85004)),f328(f307(x85002,x85001,x85003),x85005)),f328(f307(x85002,x85001,x85003),f328(f328(f107(f885(x85002,a871)),x85004),x85005)))
% 81.29/80.92 [8564]~P24(f328(f328(f68(x85641,x85642,x85645),x85643),x85644))+P24(f328(f328(f330(f884(x85641,x85642)),f328(f328(f257(x85641,x85642),x85643),x85644)),x85645))
% 81.29/80.92 [8596]P24(f328(f328(f330(x85961),x85962),f328(f253(x85963,x85961),x85964)))+~P24(f328(f328(f330(f884(x85963,x85961)),f328(f328(f257(x85963,x85961),x85965),x85962)),x85964))
% 81.29/80.92 [8598]P24(f328(f328(f330(x85981),x85982),f328(f255(x85981,x85983),x85984)))+~P24(f328(f328(f330(f884(x85981,x85983)),f328(f328(f257(x85981,x85983),x85982),x85985)),x85984))
% 81.29/80.92 [8732]P24(f328(f328(f68(x87321,x87322,x87323),x87324),x87325))+~P24(f328(f328(f330(f884(x87321,x87322)),f328(f328(f257(x87321,x87322),x87324),x87325)),x87323))
% 81.29/80.92 [8768]E(f328(x87681,x87682),x87683)+~P24(f328(f328(f330(x87684),x87682),f328(f308(x87684,x87685,x87681),f328(f328(f306(x87685),x87683),f193(f885(x87685,a871))))))
% 81.29/80.92 [9001]P24(f328(f328(f330(f884(x90011,x90012)),f328(f328(f257(x90011,x90012),x90013),x90014)),f328(f283(x90012,x90011),x90015)))+~P24(f328(f328(f330(f884(x90012,x90011)),f328(f328(f257(x90012,x90011),x90014),x90013)),x90015))
% 81.29/80.92 [9019]~P24(f328(f328(x90191,x90195),x90194))+P24(f328(f328(x90191,f328(f266(x90192,x90193),f328(f328(f257(x90192,x90193),x90194),x90195))),f328(f256(x90192,x90193),f328(f328(f257(x90192,x90193),x90194),x90195))))
% 81.29/80.92 [9049]~P24(f328(f328(f330(f884(x90492,x90491)),f328(f328(f257(x90492,x90491),x90494),x90493)),f328(f283(x90491,x90492),x90495)))+P24(f328(f328(f330(f884(x90491,x90492)),f328(f328(f257(x90491,x90492),x90493),x90494)),x90495))
% 81.29/80.92 [9079]~P24(f328(f328(f330(f884(x90793,x90791)),f328(f328(f257(x90793,x90791),x90795),x90792)),x90794))+P24(f328(f328(f330(x90791),x90792),f328(f282(x90793,x90791,x90794),f328(f328(f306(x90793),x90795),f193(f885(x90793,a871))))))
% 81.29/80.92 [9124]P24(f328(f328(f330(f884(x91241,x91242)),f328(f328(f257(x91241,x91242),x91243),x91244)),x91245))+~P24(f328(f328(f330(x91242),x91244),f328(f282(x91241,x91242,x91245),f328(f328(f306(x91241),x91243),f193(f885(x91241,a871))))))
% 81.29/80.92 [9145]E(f328(f328(f328(f73(x91451,f881(x91452)),f187(x91451,x91452,x91453,x91454)),x91455),f196(x91452)),f187(x91451,x91452,x91453,f328(f328(f22(f885(x91451,a871)),x91454),f328(f328(f306(x91451),x91455),f193(f885(x91451,a871))))))+~P24(f328(f328(f330(x91451),x91455),x91454))
% 81.29/80.92 [9213]~P74(x92131)+E(f328(f328(f6(a877,x92131),x92132),f299(a877,f328(f328(f81(a877),x92133),x92134),f328(f328(f81(a877),x92135),x92134))),f328(f328(f6(a877,x92131),f328(f328(f8(a877,x92131,a877),x92132),f328(f328(f7(a877,a877,a877),f81(a877)),x92134))),f299(a877,x92133,x92135)))
% 81.29/80.92 [9237]~P74(x92371)+E(f328(f328(f6(a877,x92371),x92372),f328(f298(a877,f328(f328(f81(a877),x92373),x92374)),f328(f328(f81(a877),x92375),x92374))),f328(f328(f6(a877,x92371),f328(f328(f8(a877,x92371,a877),x92372),f328(f328(f7(a877,a877,a877),f81(a877)),x92374))),f328(f298(a877,x92373),x92375)))
% 81.29/80.92 [9291]~P21(x92911,x92912,x92913,f252(f885(x92911,a871)))+E(f328(f328(f153(x92911,x92912),x92913),f328(f135(x92911,f328(f328(f8(a871,a871,x92911),a323),f328(a325,x92914))),x92915)),f328(f135(x92912,f328(f328(f8(a871,a871,x92912),a323),f328(a325,f328(x92913,x92914)))),f328(f328(f153(x92911,x92912),x92913),x92915)))
% 81.29/80.92 [9309]~P21(x93091,x93092,x93093,f328(f328(f306(x93091),x93094),f328(f171(x93091),x93095)))+E(f328(f328(f153(x93091,x93092),x93093),f328(f135(x93091,f328(f328(f8(a871,a871,x93091),a323),f328(a325,x93094))),x93095)),f328(f135(x93092,f328(f328(f8(a871,a871,x93092),a323),f328(a325,f328(x93093,x93094)))),f328(f328(f153(x93091,x93092),x93093),x93095)))
% 81.29/80.92 [9464]P24(f328(f328(f330(f884(f878(x94641),f878(x94641))),f328(f328(f257(f878(x94641),f878(x94641)),f328(f328(f150(x94641),x94642),x94643)),f328(f328(f150(x94641),x94644),x94643))),f156(x94641,x94645)))+~P24(f328(f328(f330(f884(x94641,x94641)),f328(f328(f257(x94641,x94641),x94642),x94644)),x94645))
% 81.29/80.92 [9500]P24(f328(f328(f328(f328(a202,x95001),x95002),x95003),f616(x95004,x95003,x95002,x95005,x95001)))+~P24(f328(f328(f328(f328(a202,f34(x95001,x95005)),x95002),x95003),x95004))
% 81.29/80.92 [9570]P20(x95701,x95702,f328(f328(f306(f876(x95701)),f328(f328(f328(f93(x95701),x95703),f328(a26,x95704)),x95705)),f193(f885(f876(x95701),a871))))+~P20(x95701,f328(f328(f306(f876(x95701)),f328(f328(f328(f93(x95701),x95703),f328(a26,x95704)),x95705)),x95702),f328(f328(f306(f876(x95701)),f328(f328(f328(f93(x95701),x95703),f328(f240(a873),f328(a28,x95704))),x95705)),f193(f885(f876(x95701),a871))))
% 81.29/80.92 [9582]E(f328(f328(f306(x95821),f848(x95822,x95823,x95824,x95825,x95821)),f853(x95822,x95823,x95824,x95825,x95821)),f328(f328(f306(x95821),x95824),x95823))+~P24(f328(f63(x95821,x95825,f328(f328(f306(x95821),x95824),x95823)),x95822))
% 81.29/80.92 [9583]E(f328(f328(f306(x95831),f854(x95832,x95833,x95834,x95835,x95831)),f855(x95832,x95833,x95834,x95835,x95831)),f328(f328(f306(x95831),x95834),x95833))+~P24(f328(f63(x95831,x95835,f328(f328(f306(x95831),x95834),x95833)),x95832))
% 81.29/80.92 [9663]P24(f328(f328(f330(x96631),f509(x96632,x96633,x96634,x96635,x96631)),x96634))+P24(f328(f328(f328(f42(x96631,f885(x96635,a871)),x96634),x96633),x96632))
% 81.29/80.92 [9668]P24(f328(f328(f330(x96681),f508(x96682,x96683,x96681,x96684,x96685)),x96683))+P24(f328(f328(f330(x96685),x96684),f328(f328(f42(x96681,f885(x96685,a871)),x96683),x96682)))
% 81.29/80.92 [9676]P24(f328(f328(f330(x96761),f503(x96762,x96763,x96761,x96764,x96765)),x96763))+P24(f328(f328(f244(f885(x96765,a871)),x96764),f328(f328(f42(x96761,f885(x96765,a871)),x96763),x96762)))
% 81.29/80.92 [9678]P24(f328(f328(x96781,f519(x96782,x96781,x96783,x96784,x96785)),x96782))+~P24(f328(f328(f328(f43(x96785,f885(x96784,a871)),x96783),x96781),x96782))
% 81.29/80.92 [9681]P24(f328(f328(f330(x96811),f519(x96812,x96813,x96814,x96815,x96811)),x96814))+~P24(f328(f328(f328(f43(x96811,f885(x96815,a871)),x96814),x96813),x96812))
% 81.29/80.92 [9691]P24(f328(f328(f330(x96911),f514(x96912,x96913,x96911,x96914,x96915)),x96913))+~P24(f328(f328(f330(x96915),x96914),f328(f328(f43(x96911,f885(x96915,a871)),x96913),x96912)))
% 81.29/80.92 [9696]P24(f328(f328(f330(x96961),x96962),f328(x96963,f514(x96963,x96964,x96965,x96962,x96961))))+~P24(f328(f328(f330(x96961),x96962),f328(f328(f43(x96965,f885(x96961,a871)),x96964),x96963)))
% 81.29/80.92 [9790]~P24(f328(f328(x97904,f509(x97905,x97904,x97903,x97902,x97901)),x97905))+P24(f328(f328(f328(f42(x97901,f885(x97902,a871)),x97903),x97904),x97905))
% 81.29/80.92 [9793]~P24(f328(f328(f330(x97931),x97932),f328(x97935,f508(x97935,x97934,x97933,x97932,x97931))))+P24(f328(f328(f330(x97931),x97932),f328(f328(f42(x97933,f885(x97931,a871)),x97934),x97935)))
% 81.29/80.92 [9796]~P24(f328(f328(f244(f885(x97961,a871)),x97962),f328(x97965,f503(x97965,x97964,x97963,x97962,x97961))))+P24(f328(f328(f244(f885(x97961,a871)),x97962),f328(f328(f42(x97963,f885(x97961,a871)),x97964),x97965)))
% 81.29/80.92 [9841]P24(f328(f328(f328(f328(a202,x98411),f616(x98412,x98413,x98414,x98411,x98415)),x98413),x98412))+~P24(f328(f328(f328(f328(a202,f34(x98415,x98411)),x98414),x98413),x98412))
% 81.29/80.92 [9868]~P24(f328(f328(f330(x98681),f848(x98685,x98684,x98683,x98682,x98681)),f853(x98685,x98684,x98683,x98682,x98681)))+~P24(f328(f63(x98681,x98682,f328(f328(f306(x98681),x98683),x98684)),x98685))
% 81.29/80.92 [9869]~P24(f328(f328(f330(x98691),f854(x98695,x98694,x98693,x98692,x98691)),f855(x98695,x98694,x98693,x98692,x98691)))+~P24(f328(f63(x98691,x98692,f328(f328(f306(x98691),x98693),x98694)),x98695))
% 81.29/80.92 [9870]~P24(f328(f328(f330(f884(x98701,x98701)),f328(f328(f257(x98701,x98701),x98702),x98705)),f328(f328(f188(f884(x98701,x98701),a871),f328(a118,x98704)),x98703)))+P24(f328(f328(f330(f884(x98701,x98701)),f328(f328(f257(x98701,x98701),x98702),f788(x98703,x98704,x98705,x98702,x98701))),f328(f328(f188(f884(x98701,x98701),a871),x98704),x98703)))
% 81.29/80.92 [9877]P24(f328(f67(x98771,x98771,x98772,f848(x98773,x98774,x98775,x98772,x98771),f853(x98773,x98774,x98775,x98772,x98771)),x98773))+~P24(f328(f63(x98771,x98772,f328(f328(f306(x98771),x98775),x98774)),x98773))
% 81.29/80.92 [9878]P24(f328(f67(x98781,x98781,x98782,f854(x98783,x98784,x98785,x98782,x98781),f855(x98783,x98784,x98785,x98782,x98781)),x98783))+~P24(f328(f63(x98781,x98782,f328(f328(f306(x98781),x98785),x98784)),x98783))
% 81.29/80.92 [9890]~P106(x98901)+P29(x98901,f328(f328(f153(x98902,x98901),x98903),f328(f135(x98902,f328(f328(f7(x98902,x98901,a871),f328(f328(f8(x98901,f885(x98901,a871),x98902),a325),x98903)),f328(x98904,x98905))),x98905)))
% 81.29/80.92 [9932]~P24(f328(f328(f330(x99322),x99325),f328(f282(x99321,x99322,x99324),x99323)))+P24(f328(f328(f330(f884(x99321,x99322)),f328(f328(f257(x99321,x99322),f526(x99323,x99324,x99321,x99325,x99322)),x99325)),x99324))
% 81.29/80.92 [9933]~P24(f328(f328(f330(x99332),x99335),f328(f282(x99331,x99332,x99334),x99333)))+P24(f328(f328(f330(f884(x99331,x99332)),f328(f328(f257(x99331,x99332),f542(x99333,x99334,x99331,x99335,x99332)),x99335)),x99334))
% 81.29/80.92 [9953]~P24(f328(f328(f330(f884(x99531,x99531)),f328(f328(f257(x99531,x99531),x99535),x99534)),f328(f328(f188(f884(x99531,x99531),a871),f328(a118,x99533)),x99532)))+P24(f328(f328(f330(f884(x99531,x99531)),f328(f328(f257(x99531,x99531),f788(x99532,x99533,x99534,x99535,x99531)),x99534)),x99532))
% 81.29/80.92 [9956]~P24(f328(f328(f330(f884(x99561,x99561)),f328(f328(f257(x99561,x99561),x99565),x99564)),f328(f328(f188(f884(x99561,x99561),a871),f328(a118,x99563)),x99562)))+P24(f328(f328(f330(f884(x99561,x99561)),f328(f328(f257(x99561,x99561),f786(x99562,x99563,x99564,x99565,x99561)),x99564)),f328(f328(f188(f884(x99561,x99561),a871),x99563),x99562)))
% 81.29/80.92 [9957]~P24(f328(f328(f330(f884(x99571,x99571)),f328(f328(f257(x99571,x99571),x99575),x99574)),f328(f328(f188(f884(x99571,x99571),a871),f328(a118,x99573)),x99572)))+P24(f328(f328(f330(f884(x99571,x99571)),f328(f328(f257(x99571,x99571),f787(x99572,x99573,x99574,x99575,x99571)),x99574)),f328(f328(f188(f884(x99571,x99571),a871),x99573),x99572)))
% 81.29/80.92 [9958]~P24(f328(f328(f330(f884(f878(x99581),f878(x99581))),f328(f328(f257(f878(x99581),f878(x99581)),x99585),f328(f328(f150(x99581),x99584),x99583))),f157(x99581,x99582)))+P24(f328(f328(f330(f884(x99581,x99581)),f328(f328(f257(x99581,x99581),f594(x99582,x99583,x99584,x99585,x99581)),x99584)),x99582))
% 81.29/80.92 [7065]E(x70651,f196(x70652))+E(f183(x70653,x70652,f328(f328(f328(f73(x70653,f881(x70652)),x70654),x70655),x70651)),f328(f328(f306(x70653),x70655),f183(x70653,x70652,x70654)))
% 81.29/80.92 [7556]~E(x75563,f193(f885(x75562,a871)))+E(f328(f328(f116(f885(x75561,a871)),f328(f328(f43(x75562,f885(x75561,a871)),x75563),x75564)),x75565),x75565)
% 81.29/80.92 [7557]~E(x75573,f193(f885(x75572,a871)))+E(f328(f328(f107(f885(x75571,a871)),f328(f328(f42(x75572,f885(x75571,a871)),x75573),x75574)),x75575),x75575)
% 81.29/80.92 [7913]~E(x79135,f196(x79132))+E(f183(x79131,x79132,f328(f328(f328(f73(x79131,f881(x79132)),x79133),x79134),x79135)),f328(f328(f22(f885(x79131,a871)),f183(x79131,x79132,x79133)),f328(f328(f306(x79131),x79134),f193(f885(x79131,a871)))))
% 81.29/80.92 [7982]~E(x79823,f193(f885(x79822,a871)))+E(f328(f328(f22(f885(x79821,a871)),f328(f328(f42(x79822,f885(x79821,a871)),x79823),x79824)),x79825),f328(f328(f22(f885(x79821,a871)),f252(f885(x79821,a871))),x79825))
% 81.29/80.92 [8113]E(f328(f328(f158(x81131,f328(f328(f127(x81131),x81132),x81133)),x81134),x81135),f328(f328(f127(x81131),f328(f328(f158(x81131,x81132),x81134),x81135)),x81133))+~P24(f328(f328(f245(a877),x81134),f328(f194(f878(x81131)),x81132)))
% 81.29/80.92 [8230]P24(f328(f328(f330(x82301),x82305),f328(f171(x82301),x82303)))+E(f328(f328(f177(x82301,x82302),f328(f328(f181(x82301,x82302),x82303),f328(f328(f153(x82301,x82302),x82304),x82303))),x82305),f196(x82302))
% 81.29/80.92 [8351]~P24(f328(f328(f330(x83511),x83515),f328(f171(x83511),x83513)))+E(f328(f328(f177(x83511,x83512),f328(f328(f181(x83511,x83512),x83513),f328(f328(f153(x83511,x83512),x83514),x83513))),x83515),f328(f236(x83512),f328(x83514,x83515)))
% 81.29/80.92 [8390]E(f328(f328(f164(x83901),f328(f328(f153(a877,x83901),x83902),f138(a877,f328(f298(a877,x83903),x83904)))),x83905),f328(x83902,f328(f328(f81(a877),x83903),x83905)))+~P24(f328(f328(f245(a877),x83905),f328(f328(f22(a877),x83904),x83903)))
% 81.29/80.92 [8405]E(x84051,f2(a105))+E(f125(x84052,x84053,f328(x84054,f328(f328(f22(a105),x84051),f79(a105))),f328(f328(f7(x84052,a105,f879(f881(x84053))),x84055),x84051)),f328(f204(x84052,x84053,x84054,x84055),x84051))
% 81.29/80.92 [8430]~E(x84303,f193(f885(x84301,a871)))+E(f328(f328(f42(x84301,f885(x84302,a871)),x84303),f328(f328(f8(f885(x84302,a871),f885(x84302,a871),x84301),f328(f22(f885(x84302,a871)),x84304)),x84305)),f252(f885(x84302,a871)))
% 81.29/80.92 [8431]~E(x84313,f193(f885(x84311,a871)))+E(f328(f328(f42(x84311,f885(x84312,a871)),x84313),f328(f328(f8(f885(x84312,a871),f885(x84312,a871),x84311),f328(f107(f885(x84312,a871)),x84314)),x84315)),f252(f885(x84312,a871)))
% 81.29/80.92 [8432]~E(x84323,f193(f885(x84321,a871)))+E(f328(f328(f43(x84321,f885(x84322,a871)),x84323),f328(f328(f8(f885(x84322,a871),f885(x84322,a871),x84321),f328(f116(f885(x84322,a871)),x84324)),x84325)),f193(f885(x84322,a871)))
% 81.29/80.92 [8437]~P142(x84372)+E(f328(f328(f6(x84371,x84372),f328(f328(f8(x84372,x84372,x84371),f328(f82(x84372),x84373)),x84374)),x84375),f328(f328(f82(x84372),x84373),f328(f328(f6(x84371,x84372),x84374),x84375)))
% 81.29/80.92 [8717]E(x87171,f193(f885(x87172,a871)))+E(f328(f328(f42(x87172,f885(x87173,a871)),x87171),f328(f328(f8(f885(x87173,a871),f885(x87173,a871),x87172),f328(f22(f885(x87173,a871)),x87174)),x87175)),f328(f328(f22(f885(x87173,a871)),x87174),f328(f328(f43(x87172,f885(x87173,a871)),x87171),x87175)))
% 81.29/80.92 [8718]E(x87181,f193(f885(x87182,a871)))+E(f328(f328(f42(x87182,f885(x87183,a871)),x87181),f328(f328(f8(f885(x87183,a871),f885(x87183,a871),x87182),f328(f107(f885(x87183,a871)),x87184)),x87185)),f328(f328(f107(f885(x87183,a871)),x87184),f328(f328(f42(x87182,f885(x87183,a871)),x87181),x87185)))
% 81.29/80.92 [8719]E(x87191,f193(f885(x87192,a871)))+E(f328(f328(f43(x87192,f885(x87193,a871)),x87191),f328(f328(f8(f885(x87193,a871),f885(x87193,a871),x87192),f328(f116(f885(x87193,a871)),x87194)),x87195)),f328(f328(f116(f885(x87193,a871)),x87194),f328(f328(f43(x87192,f885(x87193,a871)),x87191),x87195)))
% 81.29/80.92 [8914]~P24(f328(f328(f245(a877),f328(x89144,x89142)),f328(x89144,x89143)))+P24(f328(f328(f330(f884(x89141,x89141)),f328(f328(f257(x89141,x89141),x89142),x89143)),f152(x89141,f328(f328(f150(f885(x89141,a877)),x89144),x89145))))
% 81.29/80.92 [9180]~P21(x91802,x91801,x91803,f328(f328(f116(f885(x91802,a871)),x91804),x91805))+E(f328(f328(f107(f885(x91801,a871)),f328(f307(x91802,x91801,x91803),f328(f328(f22(f885(x91802,a871)),x91804),x91805))),f328(f307(x91802,x91801,x91803),f328(f328(f22(f885(x91802,a871)),x91805),x91804))),f193(f885(x91801,a871)))
% 81.29/80.92 [9460]~P24(f328(f328(f244(f885(x94603,a871)),f328(f282(x94601,x94603,x94604),x94602)),x94605))+P24(f328(f328(f244(f885(x94601,a871)),x94602),f328(f80(f885(x94601,a871)),f328(f282(x94603,x94601,f328(f283(x94601,x94603),x94604)),f328(f80(f885(x94603,a871)),x94605)))))
% 81.29/80.92 [9485]~P21(x94851,x94852,x94853,f328(f328(f306(x94851),x94854),x94855))+~P24(f328(f328(f330(x94852),f328(x94853,x94854)),f328(f307(x94851,x94852,x94853),f328(f328(f22(f885(x94851,a871)),x94855),f328(f328(f306(x94851),x94854),f193(f885(x94851,a871)))))))
% 81.29/80.92 [9536]P24(f328(f328(f244(f885(x95361,a871)),f328(f282(x95362,x95361,x95363),x95364)),x95365))+~P24(f328(f328(f244(f885(x95362,a871)),x95364),f328(f80(f885(x95362,a871)),f328(f282(x95361,x95362,f328(f283(x95362,x95361),x95363)),f328(f80(f885(x95361,a871)),x95365)))))
% 81.29/80.92 [9610]~P87(x96101)+P24(f328(f328(f244(x96101),f328(f76(x96101),f328(f328(f22(x96101),f328(f328(f81(x96101),x96102),x96103)),f328(f328(f81(x96101),x96104),x96105)))),f328(f328(f81(x96101),f328(f76(x96101),f328(f328(f22(x96101),x96102),x96104))),f328(f76(x96101),f328(f328(f22(x96101),x96103),x96105)))))
% 81.29/80.92 [9711]P24(f328(f328(f330(x97111),f515(x97112,x97113,x97114,x97111,x97115)),x97114))+P24(f328(f328(f244(f885(x97115,a871)),f328(f328(f43(x97111,f885(x97115,a871)),x97114),x97113)),x97112))
% 81.29/80.92 [9910]~P24(f328(f328(f244(f885(x99101,a871)),f328(x99104,f515(x99105,x99104,x99103,x99102,x99101))),x99105))+P24(f328(f328(f244(f885(x99101,a871)),f328(f328(f43(x99102,f885(x99101,a871)),x99103),x99104)),x99105))
% 81.29/80.92 [8545]E(f328(f328(f127(x85451),x85452),f328(f328(f158(x85451,x85453),f328(f328(f22(a877),x85454),f328(f194(f878(x85451)),x85452))),x85455)),f328(f328(f158(x85451,f328(f328(f127(x85451),x85452),x85453)),x85454),x85455))+P24(f328(f328(f245(a877),x85454),f328(f194(f878(x85451)),x85452)))
% 81.29/80.92 [8572]~P140(x85721)+E(f328(f328(f81(x85721),f328(f328(f82(x85721),x85722),x85723)),f328(f328(f81(x85721),f328(f328(f82(x85721),x85724),x85723)),x85725)),f328(f328(f81(x85721),f328(f328(f82(x85721),f328(f328(f81(x85721),x85722),x85724)),x85723)),x85725))
% 81.29/80.92 [9134]~P142(x91341)+E(f328(f165(x91341),f328(f328(f153(x91342,x91341),f328(f328(f8(x91341,x91341,x91342),f328(f82(x91341),x91343)),x91344)),x91345)),f328(f328(f82(x91341),x91343),f328(f165(x91341),f328(f328(f153(x91342,x91341),x91344),x91345))))
% 81.29/80.92 [9308]E(f328(f194(f878(x93081)),f328(f328(f174(x93081),f328(f328(f242(a877),f328(f194(f878(x93081)),x93082)),f328(f194(f878(x93083)),x93084))),x93082)),f328(f194(f878(x93083)),f328(f328(f174(x93083),f328(f328(f242(a877),f328(f194(f878(x93081)),x93082)),f328(f194(f878(x93083)),x93084))),x93084)))+P24(f328(x93085,f328(f328(f181(x93081,x93083),x93082),x93084)))
% 81.29/80.92 [9547]~P142(x95472)+E(f328(f328(f6(x95471,x95472),f328(f328(f7(x95471,x95472,x95472),f328(f328(f8(x95472,f885(x95472,x95472),x95471),f82(x95472)),x95473)),x95474)),x95475),f328(f328(f82(x95472),f328(f328(f6(x95471,x95472),x95473),x95475)),x95474))
% 81.29/80.92 [9548]~P62(x95482)+E(f328(f328(f6(x95481,x95482),f328(f328(f7(x95481,x95482,x95482),f328(f328(f8(x95482,f885(x95482,x95482),x95481),f286(x95482)),x95483)),x95484)),x95485),f328(f328(f286(x95482),f328(f328(f6(x95481,x95482),x95483),x95485)),x95484))
% 81.29/80.92 [9555]~P67(x95552)+E(f328(f328(f6(x95551,x95552),f328(f328(f18(x95551,x95552,x95552),f328(f328(f8(x95552,f885(x95552,x95552),x95551),f22(x95552)),x95553)),x95554)),x95555),f328(f328(f22(x95552),f328(f328(f6(x95551,x95552),x95553),x95555)),f328(f328(f6(x95551,x95552),x95554),x95555)))
% 81.29/80.92 [9556]~P74(x95562)+E(f328(f328(f6(x95561,x95562),f328(f328(f18(x95561,x95562,x95562),f328(f328(f8(x95562,f885(x95562,x95562),x95561),f81(x95562)),x95563)),x95564)),x95565),f328(f328(f81(x95562),f328(f328(f6(x95561,x95562),x95563),x95565)),f328(f328(f6(x95561,x95562),x95564),x95565)))
% 81.29/80.92 [9557]~P75(x95572)+E(f328(f328(f9(x95571,x95572),f328(f328(f18(x95571,x95572,x95572),f328(f328(f8(x95572,f885(x95572,x95572),x95571),f82(x95572)),x95573)),x95574)),x95575),f328(f328(f82(x95572),f328(f328(f9(x95571,x95572),x95573),x95575)),f328(f328(f9(x95571,x95572),x95574),x95575)))
% 81.29/80.92 [9595]~E(x95953,f193(f885(x95951,a871)))+E(f328(f328(f42(x95951,f885(x95952,a871)),x95953),f328(f328(f7(x95951,f885(x95952,a871),f885(x95952,a871)),f328(f328(f8(f885(x95952,a871),f885(f885(x95952,a871),f885(x95952,a871)),x95951),f22(f885(x95952,a871))),x95954)),x95955)),f252(f885(x95952,a871)))
% 81.29/80.92 [9596]~E(x95963,f193(f885(x95961,a871)))+E(f328(f328(f42(x95961,f885(x95962,a871)),x95963),f328(f328(f7(x95961,f885(x95962,a871),f885(x95962,a871)),f328(f328(f8(f885(x95962,a871),f885(f885(x95962,a871),f885(x95962,a871)),x95961),f107(f885(x95962,a871))),x95964)),x95965)),f252(f885(x95962,a871)))
% 81.29/80.92 [9597]~E(x95973,f193(f885(x95971,a871)))+E(f328(f328(f43(x95971,f885(x95972,a871)),x95973),f328(f328(f7(x95971,f885(x95972,a871),f885(x95972,a871)),f328(f328(f8(f885(x95972,a871),f885(f885(x95972,a871),f885(x95972,a871)),x95971),f116(f885(x95972,a871))),x95974)),x95975)),f193(f885(x95972,a871)))
% 81.29/80.92 [9618]E(x96181,f193(f885(x96182,a871)))+E(f328(f328(f42(x96182,f885(x96183,a871)),x96181),f328(f328(f7(x96182,f885(x96183,a871),f885(x96183,a871)),f328(f328(f8(f885(x96183,a871),f885(f885(x96183,a871),f885(x96183,a871)),x96182),f22(f885(x96183,a871))),x96184)),x96185)),f328(f328(f22(f885(x96183,a871)),f328(f328(f42(x96182,f885(x96183,a871)),x96181),x96184)),x96185))
% 81.29/80.92 [9619]E(x96191,f193(f885(x96192,a871)))+E(f328(f328(f42(x96192,f885(x96193,a871)),x96191),f328(f328(f7(x96192,f885(x96193,a871),f885(x96193,a871)),f328(f328(f8(f885(x96193,a871),f885(f885(x96193,a871),f885(x96193,a871)),x96192),f107(f885(x96193,a871))),x96194)),x96195)),f328(f328(f107(f885(x96193,a871)),f328(f328(f42(x96192,f885(x96193,a871)),x96191),x96194)),x96195))
% 81.29/80.92 [9620]E(x96201,f193(f885(x96202,a871)))+E(f328(f328(f43(x96202,f885(x96203,a871)),x96201),f328(f328(f7(x96202,f885(x96203,a871),f885(x96203,a871)),f328(f328(f8(f885(x96203,a871),f885(f885(x96203,a871),f885(x96203,a871)),x96202),f116(f885(x96203,a871))),x96204)),x96205)),f328(f328(f116(f885(x96203,a871)),f328(f328(f43(x96202,f885(x96203,a871)),x96201),x96204)),x96205))
% 81.29/80.92 [9187]~P24(f328(f328(f244(a877),x91871),x91874))+E(f328(f328(f22(a877),f328(f328(f81(a877),f328(f328(f82(a877),x91871),x91872)),x91873)),f328(f328(f81(a877),f328(f328(f82(a877),x91874),x91872)),x91875)),f328(f328(f22(a877),x91873),f328(f328(f81(a877),f328(f328(f82(a877),f328(f328(f22(a877),x91874),x91871)),x91872)),x91875)))
% 81.29/80.92 [9771]~P142(x97711)+E(f328(f165(x97711),f328(f328(f153(x97712,x97711),f328(f328(f7(x97712,x97711,x97711),f328(f328(f8(x97711,f885(x97711,x97711),x97712),f82(x97711)),x97713)),x97714)),x97715)),f328(f328(f82(x97711),f328(f165(x97711),f328(f328(f153(x97712,x97711),x97713),x97715))),x97714))
% 81.29/80.92 [9777]~P67(x97771)+E(f328(f165(x97771),f328(f328(f153(x97772,x97771),f328(f328(f18(x97772,x97771,x97771),f328(f328(f8(x97771,f885(x97771,x97771),x97772),f22(x97771)),x97773)),x97774)),x97775)),f328(f328(f22(x97771),f328(f165(x97771),f328(f328(f153(x97772,x97771),x97773),x97775))),f328(f165(x97771),f328(f328(f153(x97772,x97771),x97774),x97775))))
% 81.29/80.92 [9778]~P74(x97781)+E(f328(f165(x97781),f328(f328(f153(x97782,x97781),f328(f328(f18(x97782,x97781,x97781),f328(f328(f8(x97781,f885(x97781,x97781),x97782),f81(x97781)),x97783)),x97784)),x97785)),f328(f328(f81(x97781),f328(f165(x97781),f328(f328(f153(x97782,x97781),x97783),x97785))),f328(f165(x97781),f328(f328(f153(x97782,x97781),x97784),x97785))))
% 81.29/80.92 [9923]P24(f328(x99231,f328(f328(f181(x99232,x99233),x99234),x99235)))+~P24(f328(x99231,f328(f328(f181(x99232,x99233),f328(f328(f174(x99232),f328(f328(f242(a877),f328(f194(f878(x99232)),x99234)),f328(f194(f878(x99233)),x99235))),x99234)),f328(f328(f174(x99233),f328(f328(f242(a877),f328(f194(f878(x99232)),x99234)),f328(f194(f878(x99233)),x99235))),x99235))))
% 81.29/80.92 [9428]~P24(f328(f328(f244(a877),x94284),x94281))+E(f328(f328(f22(a877),f328(f328(f81(a877),f328(f328(f82(a877),x94281),x94282)),x94283)),f328(f328(f81(a877),f328(f328(f82(a877),x94284),x94282)),x94285)),f328(f328(f22(a877),f328(f328(f81(a877),f328(f328(f82(a877),f328(f328(f22(a877),x94281),x94284)),x94282)),x94283)),x94285))
% 81.29/80.92 [10175]P20(x101751,x101752,f328(f307(a874,f876(x101751),f328(f328(f18(a874,f885(x101751,f885(a872,a871)),f876(x101751)),f328(f328(f18(a874,a873,f885(f885(x101751,f885(a872,a871)),f876(x101751))),f328(f328(f8(f885(x101751,f885(a872,a871)),f885(a873,f885(f885(x101751,f885(a872,a871)),f876(x101751))),a874),f93(x101751)),x101753)),a26)),x101754)),x101755))+~P20(x101751,f328(f328(f116(f885(f876(x101751),a871)),x101752),f328(f307(a874,f876(x101751),f328(f328(f18(a874,f885(x101751,f885(a872,a871)),f876(x101751)),f328(f328(f18(a874,a873,f885(f885(x101751,f885(a872,a871)),f876(x101751))),f328(f328(f8(f885(x101751,f885(a872,a871)),f885(a873,f885(f885(x101751,f885(a872,a871)),f876(x101751))),a874),f93(x101751)),x101753)),a26)),x101754)),x101755)),f328(f307(a874,f876(x101751),f328(f328(f18(a874,f885(x101751,f885(a872,a871)),f876(x101751)),f328(f328(f18(a874,a873,f885(f885(x101751,f885(a872,a871)),f876(x101751))),f328(f328(f8(f885(x101751,f885(a872,a871)),f885(a873,f885(f885(x101751,f885(a872,a871)),f876(x101751))),a874),f93(x101751)),x101753)),f328(f328(f8(f881(a873),a873,a874),f240(a873)),a28))),x101754)),x101755))
% 81.29/80.92 [10176]P23(x101761,x101762,f328(f307(a874,f876(x101761),f328(f328(f18(a874,f885(x101761,f885(a872,a871)),f876(x101761)),f328(f328(f18(a874,a873,f885(f885(x101761,f885(a872,a871)),f876(x101761))),f328(f328(f8(f885(x101761,f885(a872,a871)),f885(a873,f885(f885(x101761,f885(a872,a871)),f876(x101761))),a874),f93(x101761)),x101763)),a26)),x101764)),x101765))+~P23(x101761,f328(f328(f116(f885(f876(x101761),a871)),x101762),f328(f307(a874,f876(x101761),f328(f328(f18(a874,f885(x101761,f885(a872,a871)),f876(x101761)),f328(f328(f18(a874,a873,f885(f885(x101761,f885(a872,a871)),f876(x101761))),f328(f328(f8(f885(x101761,f885(a872,a871)),f885(a873,f885(f885(x101761,f885(a872,a871)),f876(x101761))),a874),f93(x101761)),x101763)),a26)),x101764)),x101765)),f328(f307(a874,f876(x101761),f328(f328(f18(a874,f885(x101761,f885(a872,a871)),f876(x101761)),f328(f328(f18(a874,a873,f885(f885(x101761,f885(a872,a871)),f876(x101761))),f328(f328(f8(f885(x101761,f885(a872,a871)),f885(a873,f885(f885(x101761,f885(a872,a871)),f876(x101761))),a874),f93(x101761)),x101763)),f328(f328(f8(f881(a873),a873,a874),f240(a873)),a28))),x101764)),x101765))
% 81.29/80.92 [5254]E(x52541,x52542)+~E(f29(x52543,x52544,x52541),f29(x52545,x52546,x52542))
% 81.29/80.92 [5255]E(x52551,x52552)+~E(f29(x52553,x52551,x52554),f29(x52555,x52552,x52556))
% 81.29/80.92 [5256]E(x52561,x52562)+~E(f29(x52561,x52563,x52564),f29(x52562,x52565,x52566))
% 81.29/80.92 [5257]E(x52571,x52572)+~E(f31(x52573,x52574,x52571),f31(x52575,x52576,x52572))
% 81.29/80.92 [5258]E(x52581,x52582)+~E(f31(x52583,x52581,x52584),f31(x52585,x52582,x52586))
% 81.29/80.92 [5259]E(x52591,x52592)+~E(f31(x52591,x52593,x52594),f31(x52592,x52595,x52596))
% 81.29/80.92 [5260]E(x52601,x52602)+~E(f30(x52603,x52604,x52601),f30(x52605,x52606,x52602))
% 81.29/80.92 [5261]E(x52611,x52612)+~E(f30(x52613,x52611,x52614),f30(x52615,x52612,x52616))
% 81.29/80.92 [5262]E(x52621,x52622)+~E(f30(x52621,x52623,x52624),f30(x52622,x52625,x52626))
% 81.29/80.92 [6709]E(f328(f184(x67091,x67092,x67093,x67094),x67095),f328(f236(x67092),x67096))+~E(f328(x67094,x67095),f328(f236(x67092),x67096))
% 81.29/80.92 [6852]E(f328(f238(f881(x68521),x68522,f196(x68521),x68523),f328(x68524,x68525)),f328(x68523,x68526))+~E(f328(x68524,x68525),f328(f236(x68522),x68526))
% 81.29/80.92 [8374]~P15(x83745,x83741,x83742,x83746)+E(f328(f74(x83741,x83741,x83741,f328(x83742,x83743)),f328(x83742,x83744)),f328(f74(x83741,x83741,x83741,f328(x83742,x83744)),f328(x83742,x83743)))
% 81.29/80.92 [8613]~P54(x86134,x86135,x86132,x86131,x86136)+E(f328(x86131,f328(x86132,x86133)),x86133)
% 81.29/80.92 [8766]P21(x87661,x87662,x87663,x87664)+~P21(x87661,x87665,f328(f74(x87662,x87665,x87661,x87666),x87663),x87664)
% 81.29/80.92 [8849]~P21(x88494,x88492,f328(f74(x88491,x88492,x88494,x88493),x88495),x88496)+P21(x88491,x88492,x88493,f328(f307(x88494,x88491,x88495),x88496))
% 81.29/80.92 [9558]P24(f328(f62(x95581),x95582))+~P24(f328(f67(x95581,x95583,x95584,x95585,x95582),x95586))
% 81.29/80.92 [9566]~P24(f328(f328(f330(x95664),x95663),f296(x95664,x95665,x95661,x95662,x95666)))+P24(f328(f328(x95661,x95662),x95663))
% 81.29/80.92 [9567]~P24(f328(f328(f330(x95674),x95673),f293(x95674,x95671,x95675,x95672,x95676)))+P24(f328(f328(x95671,x95672),x95673))
% 81.29/80.92 [9568]~P24(f328(f328(f330(x95684),x95682),f296(x95684,x95681,x95685,x95686,x95683)))+P24(f328(f328(x95681,x95682),x95683))
% 81.29/80.92 [9569]~P24(f328(f328(f330(x95694),x95692),f293(x95694,x95695,x95691,x95696,x95693)))+P24(f328(f328(x95691,x95692),x95693))
% 81.29/80.92 [5760]E(x57601,x57602)+~E(f328(f328(f257(x57603,x57604),x57605),x57601),f328(f328(f257(x57603,x57604),x57606),x57602))
% 81.29/80.92 [5762]E(x57621,x57622)+~E(f328(f328(f257(x57623,x57624),x57621),x57625),f328(f328(f257(x57623,x57624),x57622),x57626))
% 81.29/80.92 [5886]~P12(x58865,x58866,x58861)+E(f328(f328(x58861,x58862),f328(f328(x58861,x58863),x58864)),f328(f328(x58861,x58863),f328(f328(x58861,x58862),x58864)))
% 81.29/80.92 [7305]~P33(x73054,x73051,f328(f328(f150(x73054),x73052),x73055),f328(f328(f150(x73054),x73053),x73056))+P24(f328(f328(x73051,x73052),x73053))
% 81.29/80.92 [7670]P33(x76701,x76702,x76703,x76704)+~P33(x76701,x76702,f328(f328(f150(x76701),x76705),x76703),f328(f328(f150(x76701),x76706),x76704))
% 81.29/80.92 [8708]~P54(x87085,x87081,x87082,x87086,x87084)+P24(f328(f328(f330(x87081),f328(x87082,x87083)),x87084))
% 81.29/80.92 [8877]E(f328(f77(x88771,x88772,x88773,x88774,x88775),x88776),f328(x88773,x88776))+P24(f328(f328(f330(x88771),x88776),x88775))
% 81.29/80.92 [8898]~E(x88983,f328(f328(f150(x88981),x88985),x88986))+P24(f328(f328(f330(f884(f878(x88981),f878(x88981))),f328(f328(f257(f878(x88981),f878(x88981)),x88982),f328(f328(f127(x88981),x88982),x88983))),f146(x88981,x88984)))
% 81.29/80.92 [8905]E(f328(f77(x89051,x89052,x89053,x89054,x89055),x89056),f328(x89054,x89056))+~P24(f328(f328(f330(x89051),x89056),x89055))
% 81.29/80.92 [8910]E(f328(f186(x89101,x89102,x89103,x89104,x89105),x89106),f328(x89103,x89106))+P24(f328(f328(f330(x89101),x89106),f328(f171(x89101),x89104)))
% 81.29/80.92 [9138]~P35(x91381,x91382,x91383,x91385,x91386)+P35(x91381,x91382,x91383,f328(f328(f174(x91381),x91384),x91385),f328(f328(f174(x91382),x91384),x91386))
% 81.29/80.92 [9139]~P35(x91391,x91392,x91393,x91395,x91396)+P35(x91391,x91392,x91393,f328(f328(f137(x91391),x91394),x91395),f328(f328(f137(x91392),x91394),x91396))
% 81.29/80.92 [9630]~P19(x96304,x96302,x96305,x96303,x96306,x96301)+E(f328(x96301,f193(f885(x96302,a871))),x96303)
% 81.29/80.92 [9871]~E(f328(x98714,f328(f256(x98711,x98713),x98715)),f328(x98716,f328(f256(x98711,x98713),x98715)))+E(f328(f268(x98711,x98712,x98713,x98713,x98714,f35(x98713)),x98715),f328(f268(x98711,x98712,x98713,x98713,x98716,f35(x98713)),x98715))
% 81.29/80.92 [9872]~E(f328(x98724,f328(f266(x98721,x98722),x98725)),f328(x98726,f328(f266(x98721,x98722),x98725)))+E(f328(f268(x98721,x98721,x98722,x98723,f35(x98721),x98724),x98725),f328(f268(x98721,x98721,x98722,x98723,f35(x98721),x98726),x98725))
% 81.29/80.92 [9919]~E(f328(f268(x99192,x99196,x99193,x99193,x99191,f35(x99193)),x99194),f328(f268(x99192,x99196,x99193,x99193,x99195,f35(x99193)),x99194))+E(f328(x99191,f328(f256(x99192,x99193),x99194)),f328(x99195,f328(f256(x99192,x99193),x99194)))
% 81.29/80.92 [9920]~E(f328(f268(x99202,x99202,x99203,x99206,f35(x99202),x99201),x99204),f328(f268(x99202,x99202,x99203,x99206,f35(x99202),x99205),x99204))+E(f328(x99201,f328(f266(x99202,x99203),x99204)),f328(x99205,f328(f266(x99202,x99203),x99204)))
% 81.29/80.92 [8805]P24(f328(f328(f330(x88051),x88052),x88053))+~P24(f328(f328(f330(f884(x88051,x88054)),f328(f328(f257(x88051,x88054),x88052),x88055)),f328(f328(f265(x88051,x88054),x88053),x88056)))
% 81.29/80.92 [8819]P24(f328(f328(f330(x88191),x88192),f328(x88193,x88194)))+~P24(f328(f328(f330(f884(x88195,x88191)),f328(f328(f257(x88195,x88191),x88194),x88192)),f328(f328(f265(x88195,x88191),x88196),x88193)))
% 81.29/80.92 [8907]~E(f328(f194(f878(x89071)),x89074),f328(f194(f878(x89072)),x89075))+E(f186(x89071,x89072,x89073,x89074,f328(f328(f127(x89072),x89075),x89076)),f186(x89071,x89072,x89073,x89074,x89075))
% 81.29/80.92 [8908]~E(f328(f194(f878(x89081)),x89084),f328(f194(f878(x89082)),x89086))+E(f186(x89081,x89082,x89083,f328(f328(f127(x89081),x89084),x89085),x89086),f186(x89081,x89082,x89083,x89084,x89086))
% 81.29/80.92 [9159]P24(f328(f328(f330(x91591),x91594),f183(x91591,x91592,x91596)))+E(f184(x91591,x91592,f328(f328(f328(f73(x91591,f881(x91592)),x91593),x91594),f328(f236(x91592),x91595)),x91596),f328(f328(f328(f73(x91591,f881(x91592)),f184(x91591,x91592,x91593,x91596)),x91594),f328(f236(x91592),x91595)))
% 81.29/80.92 [9259]P24(f328(f328(f330(f884(x92591,x92591)),f328(f328(f257(x92591,x92591),f328(x92592,x92593)),f328(x92592,x92594))),x92595))+~P24(f328(f328(f330(f884(x92596,x92596)),f328(f328(f257(x92596,x92596),x92593),x92594)),f328(f328(f284(x92591,x92596),x92595),x92592)))
% 81.29/80.92 [9279]~P24(f328(f328(f330(f884(x92794,x92794)),f328(f328(f257(x92794,x92794),f328(x92796,x92792)),f328(x92796,x92793))),x92795))+P24(f328(f328(f330(f884(x92791,x92791)),f328(f328(f257(x92791,x92791),x92792),x92793)),f328(f328(f284(x92794,x92791),x92795),x92796)))
% 81.29/80.92 [9922]E(f328(f328(f257(x99221,x99222),f801(x99223,x99224,x99225,x99226,x99222,x99221)),f802(x99223,x99224,x99225,x99226,x99222,x99221)),x99226)+~P24(f328(f328(f330(f884(x99221,x99222)),x99226),f328(f328(f285(x99221,x99225,x99222),x99224),x99223)))
% 81.29/80.92 [10125]~P24(f328(f328(f330(f884(x101251,x101256)),x101255),f328(f328(f285(x101251,x101252,x101256),x101254),x101253)))+P24(f328(f328(f330(f884(x101251,x101252)),f328(f328(f257(x101251,x101252),f801(x101253,x101254,x101252,x101255,x101256,x101251)),f803(x101253,x101254,x101252,x101255,x101256,x101251))),x101254))
% 81.29/80.92 [10126]~P24(f328(f328(f330(f884(x101266,x101262)),x101265),f328(f328(f285(x101266,x101261,x101262),x101264),x101263)))+P24(f328(f328(f330(f884(x101261,x101262)),f328(f328(f257(x101261,x101262),f803(x101263,x101264,x101261,x101265,x101262,x101266)),f802(x101263,x101264,x101261,x101265,x101262,x101266))),x101263))
% 81.29/80.92 [6169]~E(x61696,x61694)+E(f328(f328(f328(f328(f73(x61691,x61692),x61693),x61694),x61695),x61696),x61695)
% 81.29/80.92 [6217]E(x62171,x62172)+E(f328(f328(f328(f328(f73(x62173,x62174),x62175),x62172),x62176),x62171),f328(x62175,x62171))
% 81.29/80.92 [7740]~P27(x77402)+E(f328(f328(f42(x77401,x77402),x77403),f328(f328(f7(x77401,x77404,x77402),x77405),x77406)),f328(f328(f328(f42(x77401,f885(x77404,x77402)),x77403),x77405),x77406))
% 81.29/80.92 [7741]~P27(x77412)+E(f328(f328(f43(x77411,x77412),x77413),f328(f328(f7(x77411,x77414,x77412),x77415),x77416)),f328(f328(f328(f43(x77411,f885(x77414,x77412)),x77413),x77415),x77416))
% 81.29/80.92 [8528]E(f328(f328(f43(x85281,f885(x85282,a871)),x85283),f328(f328(f8(f885(x85282,a871),f885(x85282,a871),x85281),f328(f306(x85282),x85284)),x85285)),f328(f328(f306(x85282),x85284),f328(f328(f43(x85281,f885(x85282,a871)),x85283),x85285)))+~P24(f328(f328(f330(x85281),x85286),x85283))
% 81.29/80.92 [8960]~P27(x89602)+E(f328(f328(f42(x89601,x89602),x89603),f328(f328(f8(f885(x89604,x89602),x89602,x89601),f328(f42(x89604,x89602),x89605)),f328(f7(x89604,x89601,x89602),x89606))),f328(f328(f42(x89604,x89602),x89605),f328(f328(f8(f885(x89601,x89602),x89602,x89604),f328(f42(x89601,x89602),x89603)),x89606)))
% 81.29/80.92 [8961]~P27(x89612)+E(f328(f328(f43(x89611,x89612),x89613),f328(f328(f8(f885(x89614,x89612),x89612,x89611),f328(f43(x89614,x89612),x89615)),f328(f7(x89614,x89611,x89612),x89616))),f328(f328(f43(x89614,x89612),x89615),f328(f328(f8(f885(x89611,x89612),x89612,x89614),f328(f43(x89611,x89612),x89613)),x89616)))
% 81.29/80.92 [9168]P24(f328(f328(f330(x91681),x91682),f328(f171(x91681),x91683)))+~P24(f328(f328(f330(f884(x91684,x91681)),f328(f328(f257(x91684,x91681),x91685),x91682)),f328(f171(f884(x91684,x91681)),f328(f328(f181(x91684,x91681),x91686),x91683))))
% 81.29/80.92 [9169]P24(f328(f328(f330(x91691),x91692),f328(f171(x91691),x91693)))+~P24(f328(f328(f330(f884(x91691,x91694)),f328(f328(f257(x91691,x91694),x91692),x91695)),f328(f171(f884(x91691,x91694)),f328(f328(f181(x91691,x91694),x91693),x91696))))
% 81.29/80.92 [9273]P24(f328(f328(f244(f885(x92731,a871)),f328(f282(x92732,x92731,x92733),x92734)),x92735))+~P24(f328(f328(f244(f885(f884(x92732,x92731),a871)),x92733),f328(f328(f265(x92732,x92731),x92736),f328(f16(f885(x92731,a871),x92732),x92735))))
% 81.29/80.92 [9463]P24(f328(f328(f330(f884(f878(x94631),f878(x94631))),f328(f328(f257(f878(x94631),f878(x94631)),f328(f328(f150(x94631),x94632),x94633)),f328(f328(f150(x94631),x94634),x94635))),f146(x94631,x94636)))+~P24(f328(f328(f330(f884(x94631,x94631)),f328(f328(f257(x94631,x94631),x94632),x94634)),x94636))
% 81.29/80.92 [9918]E(f328(f328(f257(x99181,x99182),f729(x99183,x99184,x99185,x99182,x99181,x99186)),f730(x99183,x99184,x99185,x99182,x99181,x99186)),x99186)+P24(f328(f328(f330(x99185),x99184),f328(f328(f267(x99181,x99182,f885(x99185,a871)),x99183),x99186)))
% 81.29/80.92 [9924]E(f328(f328(f257(x99241,x99242),f731(x99243,x99244,x99242,x99241,x99245,x99246)),f732(x99243,x99244,x99242,x99241,x99245,x99246)),x99243)+~P24(f328(f328(f330(x99246),x99245),f328(f328(f267(x99241,x99242,f885(x99246,a871)),x99244),x99243)))
% 81.29/80.92 [10083]P24(f328(f328(f330(x100831),x100832),f328(f328(x100833,f731(x100834,x100833,x100835,x100836,x100832,x100831)),f732(x100834,x100833,x100835,x100836,x100832,x100831))))+~P24(f328(f328(f330(x100831),x100832),f328(f328(f267(x100836,x100835,f885(x100831,a871)),x100833),x100834)))
% 81.29/80.92 [10103]~P24(f328(f328(f330(x101031),x101032),f328(f328(x101035,f729(x101035,x101032,x101031,x101034,x101033,x101036)),f730(x101035,x101032,x101031,x101034,x101033,x101036))))+P24(f328(f328(f330(x101031),x101032),f328(f328(f267(x101033,x101034,f885(x101031,a871)),x101035),x101036)))
% 81.29/80.92 [7859]P24(f328(f328(f330(x78591),x78594),x78596))+E(f187(x78591,x78592,f328(f328(f328(f73(x78591,f881(x78592)),x78593),x78594),x78595),x78596),f187(x78591,x78592,x78593,x78596))
% 81.29/80.92 [7936]P24(f328(f328(f330(x79361),x79364),x79366))+E(f328(f307(x79361,x79362,f328(f328(f328(f73(x79361,x79362),x79363),x79364),x79365)),x79366),f328(f307(x79361,x79362,x79363),x79366))
% 81.29/80.92 [7963]P24(f328(f328(f330(x79631),x79634),f328(f171(x79631),x79636)))+E(f328(f328(f153(x79631,x79632),f328(f328(f328(f73(x79631,x79632),x79633),x79634),x79635)),x79636),f328(f328(f153(x79631,x79632),x79633),x79636))
% 81.29/80.92 [8422]E(x84221,x84222)+E(f328(f328(f158(x84223,f328(f328(f158(x84223,x84224),x84221),x84225)),x84222),x84226),f328(f328(f158(x84223,f328(f328(f158(x84223,x84224),x84222),x84226)),x84221),x84225))
% 81.29/80.92 [8966]~P24(f328(f328(f330(x89663),x89666),x89665))+E(f328(f328(f306(x89661),x89662),f328(f307(x89663,x89661,x89664),f328(f328(f22(f885(x89663,a871)),x89665),f328(f328(f306(x89663),x89666),f193(f885(x89663,a871)))))),f328(f307(x89663,x89661,f328(f328(f328(f73(x89663,x89661),x89664),x89666),x89662)),x89665))
% 81.29/80.92 [9733]E(f186(x97331,x97332,x97333,f328(f328(f127(x97331),x97334),f328(f328(f150(x97331),x97335),f119(x97331))),x97336),f328(f328(f328(f73(x97331,f881(x97332)),f186(x97331,x97332,x97333,x97334,x97336)),x97335),f328(f236(x97332),f328(f328(f164(x97332),x97336),f328(f194(f878(x97331)),x97334)))))+~P24(f328(f328(f245(a877),f328(f194(f878(x97331)),x97334)),f328(f194(f878(x97332)),x97336)))
% 81.29/80.92 [8747]~E(x87473,x87476)+E(f328(f328(f177(x87471,x87472),f328(f328(f150(f884(x87471,x87472)),f328(f328(f257(x87471,x87472),x87473),x87474)),x87475)),x87476),f328(f236(x87472),x87474))
% 81.29/80.92 [8775]E(x87751,x87752)+E(f328(f328(f177(x87753,x87754),f328(f328(f150(f884(x87753,x87754)),f328(f328(f257(x87753,x87754),x87751),x87755)),x87756)),x87752),f328(f328(f177(x87753,x87754),x87756),x87752))
% 81.29/80.92 [9043]~P24(f328(f328(x90434,x90435),x90436))+P24(f328(f328(f328(f328(f116(f885(x90431,f885(x90432,a871))),x90433),x90434),x90435),x90436))
% 81.29/80.92 [9045]~P24(f328(f328(x90453,x90455),x90456))+P24(f328(f328(f328(f328(f116(f885(x90451,f885(x90452,a871))),x90453),x90454),x90455),x90456))
% 81.29/80.92 [9330]P24(f328(f328(x93301,x93302),x93303))+~P24(f328(f328(f328(f328(f107(f885(x93304,f885(x93305,a871))),x93306),x93301),x93302),x93303))
% 81.29/80.92 [9331]P24(f328(f328(x93311,x93312),x93313))+~P24(f328(f328(f328(f328(f107(f885(x93314,f885(x93315,a871))),x93311),x93316),x93312),x93313))
% 81.29/80.92 [9755]~P74(x97552)+E(f328(f328(f6(x97551,x97552),f328(f328(f7(x97551,f885(x97553,a871),x97552),f328(f328(f8(f885(x97553,x97552),f885(f885(x97553,a871),x97552),x97551),f6(x97553,x97552)),x97554)),x97555)),x97556),f328(f328(f6(f884(x97551,x97553),x97552),f328(f267(x97551,x97553,x97552),x97554)),f328(f328(f265(x97551,x97553),x97556),f328(f16(f885(x97553,a871),x97551),x97555))))
% 81.29/80.92 [9756]~P75(x97562)+E(f328(f328(f9(x97561,x97562),f328(f328(f7(x97561,f885(x97563,a871),x97562),f328(f328(f8(f885(x97563,x97562),f885(f885(x97563,a871),x97562),x97561),f9(x97563,x97562)),x97564)),x97565)),x97566),f328(f328(f9(f884(x97561,x97563),x97562),f328(f267(x97561,x97563,x97562),x97564)),f328(f328(f265(x97561,x97563),x97566),f328(f16(f885(x97563,a871),x97561),x97565))))
% 81.29/80.92 [9899]~P74(x98992)+E(f328(f328(f6(x98991,x98992),f328(f328(f7(x98991,f885(x98993,a871),x98992),f328(f328(f8(f885(x98993,x98992),f885(f885(x98993,a871),x98992),x98991),f6(x98993,x98992)),f328(f7(x98993,x98991,x98992),x98994))),x98995)),x98996),f328(f328(f6(x98993,x98992),f328(f328(f7(x98993,f885(x98991,a871),x98992),f328(f328(f8(f885(x98991,x98992),f885(f885(x98991,a871),x98992),x98993),f6(x98991,x98992)),x98994)),x98996)),x98995))
% 81.29/80.92 [9599]~P24(f328(f328(f330(x95991),x95995),x95994))+E(f328(f328(f328(f73(x95991,f881(x95992)),f187(x95991,x95992,x95993,f328(f328(f22(f885(x95991,a871)),x95994),f328(f328(f306(x95991),x95995),f193(f885(x95991,a871)))))),x95995),x95996),f187(x95991,x95992,f328(f328(f328(f73(x95991,f881(x95992)),x95993),x95995),x95996),x95994))
% 81.29/80.92 [10179]~P24(f328(f328(f330(f884(x101791,x101792)),f328(f328(f257(x101791,x101792),x101795),x101796)),f328(f328(f116(f885(f884(x101791,x101792),a871)),x101793),x101794)))+P24(f328(f328(f328(f328(f116(f885(x101791,f885(x101792,a871))),f328(f328(f7(x101791,f885(f884(x101791,x101792),a871),f885(x101792,a871)),f328(f328(f8(f885(x101792,f885(f885(f884(x101791,x101792),a871),a871)),f885(f885(f884(x101791,x101792),a871),f885(x101792,a871)),x101791),f7(x101792,f885(f884(x101791,x101792),a871),a871)),f328(f328(f8(f885(x101792,f884(x101791,x101792)),f885(x101792,f885(f885(f884(x101791,x101792),a871),a871)),x101791),f328(f8(f884(x101791,x101792),f885(f885(f884(x101791,x101792),a871),a871),x101792),f330(f884(x101791,x101792)))),f257(x101791,x101792)))),x101793)),f328(f328(f7(x101791,f885(f884(x101791,x101792),a871),f885(x101792,a871)),f328(f328(f8(f885(x101792,f885(f885(f884(x101791,x101792),a871),a871)),f885(f885(f884(x101791,x101792),a871),f885(x101792,a871)),x101791),f7(x101792,f885(f884(x101791,x101792),a871),a871)),f328(f328(f8(f885(x101792,f884(x101791,x101792)),f885(x101792,f885(f885(f884(x101791,x101792),a871),a871)),x101791),f328(f8(f884(x101791,x101792),f885(f885(f884(x101791,x101792),a871),a871),x101792),f330(f884(x101791,x101792)))),f257(x101791,x101792)))),x101794)),x101795),x101796))
% 81.29/80.92 [10180]~P24(f328(f328(f330(f884(x101801,x101802)),f328(f328(f257(x101801,x101802),x101805),x101806)),f328(f328(f107(f885(f884(x101801,x101802),a871)),x101803),x101804)))+P24(f328(f328(f328(f328(f107(f885(x101801,f885(x101802,a871))),f328(f328(f7(x101801,f885(f884(x101801,x101802),a871),f885(x101802,a871)),f328(f328(f8(f885(x101802,f885(f885(f884(x101801,x101802),a871),a871)),f885(f885(f884(x101801,x101802),a871),f885(x101802,a871)),x101801),f7(x101802,f885(f884(x101801,x101802),a871),a871)),f328(f328(f8(f885(x101802,f884(x101801,x101802)),f885(x101802,f885(f885(f884(x101801,x101802),a871),a871)),x101801),f328(f8(f884(x101801,x101802),f885(f885(f884(x101801,x101802),a871),a871),x101802),f330(f884(x101801,x101802)))),f257(x101801,x101802)))),x101803)),f328(f328(f7(x101801,f885(f884(x101801,x101802),a871),f885(x101802,a871)),f328(f328(f8(f885(x101802,f885(f885(f884(x101801,x101802),a871),a871)),f885(f885(f884(x101801,x101802),a871),f885(x101802,a871)),x101801),f7(x101802,f885(f884(x101801,x101802),a871),a871)),f328(f328(f8(f885(x101802,f884(x101801,x101802)),f885(x101802,f885(f885(f884(x101801,x101802),a871),a871)),x101801),f328(f8(f884(x101801,x101802),f885(f885(f884(x101801,x101802),a871),a871),x101802),f330(f884(x101801,x101802)))),f257(x101801,x101802)))),x101804)),x101805),x101806))
% 81.29/80.92 [10185]P24(f328(f328(f330(f884(x101851,x101852)),f328(f328(f257(x101851,x101852),x101853),x101854)),f328(f328(f116(f885(f884(x101851,x101852),a871)),x101855),x101856)))+~P24(f328(f328(f328(f328(f116(f885(x101851,f885(x101852,a871))),f328(f328(f7(x101851,f885(f884(x101851,x101852),a871),f885(x101852,a871)),f328(f328(f8(f885(x101852,f885(f885(f884(x101851,x101852),a871),a871)),f885(f885(f884(x101851,x101852),a871),f885(x101852,a871)),x101851),f7(x101852,f885(f884(x101851,x101852),a871),a871)),f328(f328(f8(f885(x101852,f884(x101851,x101852)),f885(x101852,f885(f885(f884(x101851,x101852),a871),a871)),x101851),f328(f8(f884(x101851,x101852),f885(f885(f884(x101851,x101852),a871),a871),x101852),f330(f884(x101851,x101852)))),f257(x101851,x101852)))),x101855)),f328(f328(f7(x101851,f885(f884(x101851,x101852),a871),f885(x101852,a871)),f328(f328(f8(f885(x101852,f885(f885(f884(x101851,x101852),a871),a871)),f885(f885(f884(x101851,x101852),a871),f885(x101852,a871)),x101851),f7(x101852,f885(f884(x101851,x101852),a871),a871)),f328(f328(f8(f885(x101852,f884(x101851,x101852)),f885(x101852,f885(f885(f884(x101851,x101852),a871),a871)),x101851),f328(f8(f884(x101851,x101852),f885(f885(f884(x101851,x101852),a871),a871),x101852),f330(f884(x101851,x101852)))),f257(x101851,x101852)))),x101856)),x101853),x101854))
% 81.29/80.92 [10186]P24(f328(f328(f330(f884(x101861,x101862)),f328(f328(f257(x101861,x101862),x101863),x101864)),f328(f328(f107(f885(f884(x101861,x101862),a871)),x101865),x101866)))+~P24(f328(f328(f328(f328(f107(f885(x101861,f885(x101862,a871))),f328(f328(f7(x101861,f885(f884(x101861,x101862),a871),f885(x101862,a871)),f328(f328(f8(f885(x101862,f885(f885(f884(x101861,x101862),a871),a871)),f885(f885(f884(x101861,x101862),a871),f885(x101862,a871)),x101861),f7(x101862,f885(f884(x101861,x101862),a871),a871)),f328(f328(f8(f885(x101862,f884(x101861,x101862)),f885(x101862,f885(f885(f884(x101861,x101862),a871),a871)),x101861),f328(f8(f884(x101861,x101862),f885(f885(f884(x101861,x101862),a871),a871),x101862),f330(f884(x101861,x101862)))),f257(x101861,x101862)))),x101865)),f328(f328(f7(x101861,f885(f884(x101861,x101862),a871),f885(x101862,a871)),f328(f328(f8(f885(x101862,f885(f885(f884(x101861,x101862),a871),a871)),f885(f885(f884(x101861,x101862),a871),f885(x101862,a871)),x101861),f7(x101862,f885(f884(x101861,x101862),a871),a871)),f328(f328(f8(f885(x101862,f884(x101861,x101862)),f885(x101862,f885(f885(f884(x101861,x101862),a871),a871)),x101861),f328(f8(f884(x101861,x101862),f885(f885(f884(x101861,x101862),a871),a871),x101862),f330(f884(x101861,x101862)))),f257(x101861,x101862)))),x101866)),x101863),x101864))
% 81.29/80.92 [10173]~P24(f328(f328(f330(f884(x101732,x101733)),f328(f328(f257(x101732,x101733),x101735),x101736)),f328(f328(f42(x101731,f885(f884(x101732,x101733),a871)),f252(f885(x101731,a871))),x101734)))+P24(f328(f328(f328(f328(f42(x101731,f885(x101732,f885(x101733,a871))),f252(f885(x101731,a871))),f328(f328(f8(f885(f884(x101732,x101733),a871),f885(x101732,f885(x101733,a871)),x101731),f328(f7(x101732,f885(f884(x101732,x101733),a871),f885(x101733,a871)),f328(f328(f8(f885(x101733,f885(f885(f884(x101732,x101733),a871),a871)),f885(f885(f884(x101732,x101733),a871),f885(x101733,a871)),x101732),f7(x101733,f885(f884(x101732,x101733),a871),a871)),f328(f328(f8(f885(x101733,f884(x101732,x101733)),f885(x101733,f885(f885(f884(x101732,x101733),a871),a871)),x101732),f328(f8(f884(x101732,x101733),f885(f885(f884(x101732,x101733),a871),a871),x101733),f330(f884(x101732,x101733)))),f257(x101732,x101733))))),x101734)),x101735),x101736))
% 81.29/80.92 [10174]~P24(f328(f328(f330(f884(x101742,x101743)),f328(f328(f257(x101742,x101743),x101745),x101746)),f328(f328(f43(x101741,f885(f884(x101742,x101743),a871)),f252(f885(x101741,a871))),x101744)))+P24(f328(f328(f328(f328(f43(x101741,f885(x101742,f885(x101743,a871))),f252(f885(x101741,a871))),f328(f328(f8(f885(f884(x101742,x101743),a871),f885(x101742,f885(x101743,a871)),x101741),f328(f7(x101742,f885(f884(x101742,x101743),a871),f885(x101743,a871)),f328(f328(f8(f885(x101743,f885(f885(f884(x101742,x101743),a871),a871)),f885(f885(f884(x101742,x101743),a871),f885(x101743,a871)),x101742),f7(x101743,f885(f884(x101742,x101743),a871),a871)),f328(f328(f8(f885(x101743,f884(x101742,x101743)),f885(x101743,f885(f885(f884(x101742,x101743),a871),a871)),x101742),f328(f8(f884(x101742,x101743),f885(f885(f884(x101742,x101743),a871),a871),x101743),f330(f884(x101742,x101743)))),f257(x101742,x101743))))),x101744)),x101745),x101746))
% 81.29/80.92 [10182]P24(f328(f328(f330(f884(x101821,x101822)),f328(f328(f257(x101821,x101822),x101823),x101824)),f328(f328(f42(x101825,f885(f884(x101821,x101822),a871)),f252(f885(x101825,a871))),x101826)))+~P24(f328(f328(f328(f328(f42(x101825,f885(x101821,f885(x101822,a871))),f252(f885(x101825,a871))),f328(f328(f8(f885(f884(x101821,x101822),a871),f885(x101821,f885(x101822,a871)),x101825),f328(f7(x101821,f885(f884(x101821,x101822),a871),f885(x101822,a871)),f328(f328(f8(f885(x101822,f885(f885(f884(x101821,x101822),a871),a871)),f885(f885(f884(x101821,x101822),a871),f885(x101822,a871)),x101821),f7(x101822,f885(f884(x101821,x101822),a871),a871)),f328(f328(f8(f885(x101822,f884(x101821,x101822)),f885(x101822,f885(f885(f884(x101821,x101822),a871),a871)),x101821),f328(f8(f884(x101821,x101822),f885(f885(f884(x101821,x101822),a871),a871),x101822),f330(f884(x101821,x101822)))),f257(x101821,x101822))))),x101826)),x101823),x101824))
% 81.29/80.92 [10183]P24(f328(f328(f330(f884(x101831,x101832)),f328(f328(f257(x101831,x101832),x101833),x101834)),f328(f328(f43(x101835,f885(f884(x101831,x101832),a871)),f252(f885(x101835,a871))),x101836)))+~P24(f328(f328(f328(f328(f43(x101835,f885(x101831,f885(x101832,a871))),f252(f885(x101835,a871))),f328(f328(f8(f885(f884(x101831,x101832),a871),f885(x101831,f885(x101832,a871)),x101835),f328(f7(x101831,f885(f884(x101831,x101832),a871),f885(x101832,a871)),f328(f328(f8(f885(x101832,f885(f885(f884(x101831,x101832),a871),a871)),f885(f885(f884(x101831,x101832),a871),f885(x101832,a871)),x101831),f7(x101832,f885(f884(x101831,x101832),a871),a871)),f328(f328(f8(f885(x101832,f884(x101831,x101832)),f885(x101832,f885(f885(f884(x101831,x101832),a871),a871)),x101831),f328(f8(f884(x101831,x101832),f885(f885(f884(x101831,x101832),a871),a871),x101832),f330(f884(x101831,x101832)))),f257(x101831,x101832))))),x101836)),x101833),x101834))
% 81.29/80.92 [7419]E(f328(x74191,f328(x74192,x74193)),f328(x74194,x74193))+~E(f328(f74(x74195,x74196,x74197,x74191),x74192),x74194)
% 81.29/80.92 [9629]~P18(x96293,x96294,x96291,x96295,x96296,x96297)+E(f328(f328(x96291,x96292),x96292),x96292)
% 81.29/80.92 [9981]~P51(x99815,x99816,x99817,x99811,x99814,x99812,x99813)+P24(f328(f328(x99811,x99812),f687(x99813,x99812,x99814,x99811)))
% 81.29/80.92 [10000]~E(f328(f238(f881(x100007),x100001,f196(x100007),x100005),f328(x100004,x100003)),f328(f236(x100007),x100002))+E(f328(f236(x100001),f369(x100002,x100003,x100004,x100005,x100006,x100007,x100001)),f328(x100004,x100003))
% 81.29/80.92 [10001]~E(f328(f238(f881(x100016),x100017,f196(x100016),x100011),f328(x100014,x100013)),f328(f236(x100016),x100012))+E(f328(x100011,f369(x100012,x100013,x100014,x100011,x100015,x100016,x100017)),f328(f236(x100016),x100012))
% 81.29/80.92 [5990]~E(f328(f328(f153(x59901,x59905),x59906),x59902),f328(f328(f153(x59903,x59905),x59907),x59904))+E(f328(f194(f878(x59901)),x59902),f328(f194(f878(x59903)),x59904))
% 81.29/80.92 [7494]E(x74941,x74942)+~E(f328(f328(f328(f73(x74943,f881(x74944)),x74945),x74946),f328(f236(x74944),x74941)),f328(f328(f328(f73(x74943,f881(x74944)),x74947),x74946),f328(f236(x74944),x74942)))
% 81.29/80.92 [8462]E(f328(x84621,f328(x84622,x84623)),f328(x84624,x84623))+~E(f328(f74(x84625,x84626,x84627,x84621),x84622),f328(f74(x84626,x84626,x84627,f35(x84626)),x84624))
% 81.29/80.92 [8794]~P35(x87944,x87945,x87941,f328(f328(f150(x87944),x87942),x87946),f328(f328(f150(x87945),x87943),x87947))+P24(f328(f328(x87941,x87942),x87943))
% 81.29/80.92 [9175]P35(x91751,x91752,x91753,x91754,x91755)+~P35(x91751,x91752,x91753,f328(f328(f150(x91751),x91756),x91754),f328(f328(f150(x91752),x91757),x91755))
% 81.29/80.92 [9986]~P51(x99865,x99866,x99867,x99864,x99861,x99863,x99862)+P24(f328(f328(x99861,f687(x99862,x99863,x99861,x99864)),x99862))
% 81.29/80.92 [6035]E(x60351,x60352)+~E(f328(f328(f328(f93(x60353),x60354),x60355),x60351),f328(f328(f328(f93(x60353),x60356),x60357),x60352))
% 81.29/80.92 [6036]E(x60361,x60362)+~E(f328(f328(f328(f93(x60363),x60364),x60361),x60365),f328(f328(f328(f93(x60363),x60366),x60362),x60367))
% 81.29/80.92 [6037]E(x60371,x60372)+~E(f328(f328(f328(f93(x60373),x60371),x60374),x60375),f328(f328(f328(f93(x60373),x60372),x60376),x60377))
% 81.29/80.92 [8912]~P16(x89126,x89121,x89123,x89127)+E(f328(f74(x89121,x89121,x89122,f328(x89123,x89124)),f328(f74(x89121,x89121,x89122,f328(x89123,x89124)),x89125)),f328(f74(x89121,x89121,x89122,f328(x89123,x89124)),x89125))
% 81.29/80.92 [9282]~P35(x92823,x92822,x92824,f328(f328(f153(x92821,x92823),x92825),x92826),x92827)+P35(x92821,x92822,f328(f328(f8(x92823,f885(x92822,a871),x92821),x92824),x92825),x92826,x92827)
% 81.29/80.92 [9305]P35(x93051,x93052,x93053,f328(f328(f153(x93054,x93051),x93055),x93056),x93057)+~P35(x93054,x93052,f328(f328(f8(x93051,f885(x93052,a871),x93054),x93053),x93055),x93056,x93057)
% 81.29/80.92 [9713]E(f186(x97131,x97132,f328(f328(f328(f73(x97131,f881(x97132)),x97133),x97134),f328(f236(x97132),x97135)),x97136,x97137),f328(f328(f328(f73(x97131,f881(x97132)),f186(x97131,x97132,x97133,x97136,x97137)),x97134),f328(f236(x97132),x97135)))+P24(f328(f328(f330(x97131),x97134),f328(f171(x97131),x97136)))
% 81.29/80.92 [8911]~P24(f328(f328(f330(x89111),x89112),f328(f328(x89115,x89116),x89117)))+P24(f328(f328(f330(x89111),x89112),f328(f328(f267(x89113,x89114,f885(x89111,a871)),x89115),f328(f328(f257(x89113,x89114),x89116),x89117))))
% 81.29/80.92 [9201]P24(f328(f328(f328(x92011,x92012),x92013),x92014))+~P24(f328(f328(f328(f267(x92015,x92016,f885(x92017,a871)),x92011),f328(f328(f257(x92015,x92016),x92012),x92013)),x92014))
% 81.29/80.92 [9344]P24(f328(f328(f330(x93441),f328(f328(x93442,x93443),x93444)),f328(f307(f884(x93445,x93446),x93441,f328(f267(x93445,x93446,x93441),x93442)),x93447)))+~P24(f328(f328(f330(f884(x93445,x93446)),f328(f328(f257(x93445,x93446),x93443),x93444)),x93447))
% 81.29/80.92 [9674]P24(f328(f328(f330(f884(f878(x96741),f878(x96741))),f328(f328(f257(f878(x96741),f878(x96741)),f328(f328(f127(x96741),x96742),f328(f328(f150(x96741),x96743),x96744))),f328(f328(f127(x96741),x96742),f328(f328(f150(x96741),x96745),x96746)))),f146(x96741,x96747)))+~P24(f328(f328(f330(f884(x96741,x96741)),f328(f328(f257(x96741,x96741),x96743),x96745)),x96747))
% 81.29/80.92 [9735]~P35(x97351,x97353,x97354,x97356,f328(f328(f153(x97352,x97353),x97355),x97357))+P35(x97351,x97352,f328(f328(f7(x97351,f885(x97352,x97353),f885(x97352,a871)),f328(f328(f8(f885(x97353,a871),f885(f885(x97352,x97353),f885(x97352,a871)),x97351),f8(x97353,a871,x97352)),x97354)),x97355),x97356,x97357)
% 81.29/80.92 [9817]P35(x98171,x98172,x98173,x98174,f328(f328(f153(x98175,x98172),x98176),x98177))+~P35(x98171,x98175,f328(f328(f7(x98171,f885(x98175,x98172),f885(x98175,a871)),f328(f328(f8(f885(x98172,a871),f885(f885(x98175,x98172),f885(x98175,a871)),x98171),f8(x98172,a871,x98175)),x98173)),x98176),x98174,x98177)
% 81.29/80.92 [10102]P51(x101021,x101022,x101023,f328(f328(f7(x101021,f885(f884(x101021,x101022),a871),f885(x101022,a871)),f328(f328(f8(f885(x101022,f885(f885(f884(x101021,x101022),a871),a871)),f885(f885(f884(x101021,x101022),a871),f885(x101022,a871)),x101021),f7(x101022,f885(f884(x101021,x101022),a871),a871)),f328(f328(f8(f885(x101022,f884(x101021,x101022)),f885(x101022,f885(f885(f884(x101021,x101022),a871),a871)),x101021),f328(f8(f884(x101021,x101022),f885(f885(f884(x101021,x101022),a871),a871),x101022),f330(f884(x101021,x101022)))),f257(x101021,x101022)))),x101024),f328(f328(f7(x101022,f885(f884(x101022,x101023),a871),f885(x101023,a871)),f328(f328(f8(f885(x101023,f885(f885(f884(x101022,x101023),a871),a871)),f885(f885(f884(x101022,x101023),a871),f885(x101023,a871)),x101022),f7(x101023,f885(f884(x101022,x101023),a871),a871)),f328(f328(f8(f885(x101023,f884(x101022,x101023)),f885(x101023,f885(f885(f884(x101022,x101023),a871),a871)),x101022),f328(f8(f884(x101022,x101023),f885(f885(f884(x101022,x101023),a871),a871),x101023),f330(f884(x101022,x101023)))),f257(x101022,x101023)))),x101025),x101026,x101027)+~P24(f328(f328(f330(f884(x101021,x101023)),f328(f328(f257(x101021,x101023),x101026),x101027)),f328(f328(f285(x101021,x101022,x101023),x101024),x101025)))
% 81.29/80.92 [10132]~P51(x101321,x101325,x101322,f328(f328(f7(x101321,f885(f884(x101321,x101325),a871),f885(x101325,a871)),f328(f328(f8(f885(x101325,f885(f885(f884(x101321,x101325),a871),a871)),f885(f885(f884(x101321,x101325),a871),f885(x101325,a871)),x101321),f7(x101325,f885(f884(x101321,x101325),a871),a871)),f328(f328(f8(f885(x101325,f884(x101321,x101325)),f885(x101325,f885(f885(f884(x101321,x101325),a871),a871)),x101321),f328(f8(f884(x101321,x101325),f885(f885(f884(x101321,x101325),a871),a871),x101325),f330(f884(x101321,x101325)))),f257(x101321,x101325)))),x101326),f328(f328(f7(x101325,f885(f884(x101325,x101322),a871),f885(x101322,a871)),f328(f328(f8(f885(x101322,f885(f885(f884(x101325,x101322),a871),a871)),f885(f885(f884(x101325,x101322),a871),f885(x101322,a871)),x101325),f7(x101322,f885(f884(x101325,x101322),a871),a871)),f328(f328(f8(f885(x101322,f884(x101325,x101322)),f885(x101322,f885(f885(f884(x101325,x101322),a871),a871)),x101325),f328(f8(f884(x101325,x101322),f885(f885(f884(x101325,x101322),a871),a871),x101322),f330(f884(x101325,x101322)))),f257(x101325,x101322)))),x101327),x101323,x101324)+P24(f328(f328(f330(f884(x101321,x101322)),f328(f328(f257(x101321,x101322),x101323),x101324)),f328(f328(f285(x101321,x101325,x101322),x101326),x101327)))
% 81.29/80.92 [9193]E(x91931,x91932)+E(f328(f328(f328(f73(x91933,x91934),f328(f328(f328(f73(x91933,x91934),x91935),x91931),x91936)),x91932),x91937),f328(f328(f328(f73(x91933,x91934),f328(f328(f328(f73(x91933,x91934),x91935),x91932),x91937)),x91931),x91936))
% 81.29/80.92 [9437]E(f186(x94371,x94372,f328(f328(f328(f73(x94371,f881(x94372)),x94373),x94374),f328(f236(x94372),x94375)),x94376,x94377),f186(x94371,x94372,x94373,x94376,x94377))+~P24(f328(f328(f330(x94371),x94374),f328(f171(x94371),f328(f328(f174(x94371),f328(f194(f878(x94372)),x94377)),x94376))))
% 81.29/80.92 [9746]E(f186(x97461,x97462,f328(f328(f328(f73(x97461,f881(x97462)),x97463),x97464),f328(f236(x97462),x97465)),x97466,x97467),f328(f328(f328(f73(x97461,f881(x97462)),f186(x97461,x97462,x97463,x97466,x97467)),x97464),f328(f236(x97462),x97465)))+P24(f328(f328(f330(x97461),x97464),f328(f171(x97461),f328(f328(f174(x97461),f328(f194(f878(x97462)),x97467)),x97466))))
% 81.29/80.92 [10114]P24(f328(f328(f330(x101141),f511(x101142,x101143,x101144,x101145,x101146,x101147,x101141)),x101145))+P24(f328(f328(f328(f328(f42(x101141,f885(x101147,f885(x101146,a871))),x101145),x101144),x101143),x101142))
% 81.29/80.92 [10115]P24(f328(f328(f330(x101151),f521(x101152,x101153,x101154,x101155,x101156,x101157,x101151)),x101155))+~P24(f328(f328(f328(f328(f43(x101151,f885(x101157,f885(x101156,a871))),x101155),x101154),x101153),x101152))
% 81.29/80.92 [10141]P24(f328(f328(f328(x101411,f521(x101412,x101413,x101411,x101414,x101415,x101416,x101417)),x101413),x101412))+~P24(f328(f328(f328(f328(f43(x101417,f885(x101416,f885(x101415,a871))),x101414),x101411),x101413),x101412))
% 81.29/80.92 [10158]~P24(f328(f328(f328(x101585,f511(x101587,x101586,x101585,x101584,x101583,x101582,x101581)),x101586),x101587))+P24(f328(f328(f328(f328(f42(x101581,f885(x101582,f885(x101583,a871))),x101584),x101585),x101586),x101587))
% 81.29/80.92 [10124]~P142(x101242)+E(f328(f328(f6(x101241,x101242),f328(f328(f7(x101241,f885(x101243,a871),x101242),f328(f328(f8(f885(x101243,x101242),f885(f885(x101243,a871),x101242),x101241),f6(x101243,x101242)),f328(f328(f7(x101241,f885(x101243,x101242),f885(x101243,x101242)),f328(f328(f8(f885(x101242,x101242),f885(f885(x101243,x101242),f885(x101243,x101242)),x101241),f8(x101242,x101242,x101243)),f328(f328(f8(x101242,f885(x101242,x101242),x101241),f82(x101242)),x101244))),x101245))),x101246)),x101247),f328(f328(f82(x101242),f328(f328(f6(x101241,x101242),x101244),x101247)),f328(f328(f6(x101243,x101242),x101245),x101246)))
% 81.29/80.92 [9234]~P15(x92347,x92341,x92343,x92348)+E(f328(f74(x92341,x92341,x92342,f328(x92343,x92344)),f328(f74(x92341,x92341,x92342,f328(x92343,x92345)),x92346)),f328(f74(x92341,x92341,x92342,f328(x92343,x92345)),f328(f74(x92341,x92341,x92342,f328(x92343,x92344)),x92346)))
% 81.29/80.92 [10177]E(f328(f328(f257(x101771,x101772),f328(x101773,f623(x101774,x101775,x101773,x101776,x101777,x101778,x101772,x101771))),f328(x101775,f624(x101774,x101775,x101773,x101776,x101777,x101778,x101772,x101771))),x101778)+~P24(f328(f328(f330(f884(x101771,x101772)),x101778),f328(f307(f884(x101777,x101776),f884(x101771,x101772),f268(x101777,x101771,x101776,x101772,x101773,x101775)),x101774)))
% 81.29/80.92 [10192]~P24(f328(f328(f330(f884(x101928,x101927)),x101926),f328(f307(f884(x101921,x101922),f884(x101928,x101927),f268(x101921,x101928,x101922,x101927,x101925,x101924)),x101923)))+P24(f328(f328(f330(f884(x101921,x101922)),f328(f328(f257(x101921,x101922),f623(x101923,x101924,x101925,x101922,x101921,x101926,x101927,x101928)),f624(x101923,x101924,x101925,x101922,x101921,x101926,x101927,x101928))),x101923))
% 81.29/80.92 [9664]P24(f328(f328(f330(f884(f884(x96641,x96642),f884(x96641,x96642))),f328(f328(f257(f884(x96641,x96642),f884(x96641,x96642)),f328(f328(f257(x96641,x96642),x96643),x96644)),f328(f328(f257(x96641,x96642),x96645),x96646))),f320(x96641,x96642,x96647,x96648)))+~P24(f328(f328(f330(f884(x96641,x96641)),f328(f328(f257(x96641,x96641),x96643),x96645)),x96647))
% 81.29/80.92 [10167]E(f328(f141(x101671,x101672,f328(f7(x101672,x101671,x101671),x101673),f328(x101674,x101675)),x101676),f328(x101674,f328(f141(x101677,x101672,f328(f7(x101672,x101677,x101677),x101678),x101675),x101676)))+P24(f328(f328(f330(x101672),f710(x101675,x101678,x101674,x101673,x101677,x101671,x101676,x101672)),f328(f171(x101672),x101676)))
% 81.29/80.92 [10184]~E(f328(f74(x101841,x101841,x101847,f328(x101843,f710(x101845,x101848,x101844,x101843,x101847,x101841,x101846,x101842))),x101844),f328(f74(x101847,x101841,x101847,x101844),f328(x101848,f710(x101845,x101848,x101844,x101843,x101847,x101841,x101846,x101842))))+E(f328(f141(x101841,x101842,f328(f7(x101842,x101841,x101841),x101843),f328(x101844,x101845)),x101846),f328(x101844,f328(f141(x101847,x101842,f328(f7(x101842,x101847,x101847),x101848),x101845),x101846)))
% 81.29/80.92 [8468]E(f328(x84681,f328(x84682,x84683)),f328(x84684,f328(x84685,x84683)))+~E(f328(f74(x84686,x84687,x84688,x84681),x84682),f328(f74(x84689,x84687,x84688,x84684),x84685))
% 81.29/80.92 [10052]P24(f328(f328(f330(f884(x100521,x100522)),f328(f328(f257(x100521,x100522),f328(x100523,x100524)),f328(x100525,x100526))),f328(f307(f884(x100527,x100528),f884(x100521,x100522),f268(x100527,x100521,x100528,x100522,x100523,x100525)),x100529)))+~P24(f328(f328(f330(f884(x100527,x100528)),f328(f328(f257(x100527,x100528),x100524),x100526)),x100529))
% 81.29/80.92 [8741]~E(f328(x87414,f328(x87415,x87416)),f328(x87419,f328(x874110,x874111)))+E(f328(f328(f74(x87411,x87412,x87413,x87414),x87415),x87416),f328(f328(f74(x87417,x87412,x87418,x87419),x874110),x874111))
% 81.29/80.92 [4583]~P106(x45831)+~P102(x45831)+E(f107(x45831),f242(x45831))
% 81.29/80.92 [4584]~P106(x45841)+~P65(x45841)+E(f116(x45841),f243(x45841))
% 81.29/80.92 [4828]~P111(x48281)+~P96(x48281)+E(f328(f76(x48281),f328(f109(x48281),a103)),f79(x48281))
% 81.29/80.92 [5104]E(x51041,f2(a1))+E(f83(a1,x51041),f328(f80(a1),f79(a1)))+P24(f328(f328(f245(a1),f2(a1)),x51041))
% 81.29/80.92 [5320]E(x53201,f2(a1))+E(f83(a1,x53201),f79(a1))+~P24(f328(f328(f245(a1),f2(a1)),x53201))
% 81.29/80.92 [7309]~P40(x73091)+P24(f328(f62(a1),x73091))+~P24(f328(f62(a877),f328(f307(a1,a877,a110),x73091)))
% 81.29/80.92 [8569]~P2(a5000)+~P24(f328(f328(f330(f884(a874,a873)),x85691),f328(f171(f884(a874,a873)),a27)))+P24(f328(f328(f267(a874,a873,a871),f328(f16(f885(a873,a871),a874),a25)),x85691))
% 81.29/80.92 [9628]E(x96281,f193(f885(f884(a877,a877),a871)))+~P24(f328(f62(f884(a877,a877)),x96281))+P24(f328(f328(f330(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f328(f328(f257(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),f193(f885(f884(a877,a877),a871))),x96281)),a37))
% 81.29/80.92 [9794]E(x97941,f2(a877))+E(x97941,f328(a118,f2(a877)))+~P24(f328(f328(f245(a877),x97941),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))
% 81.29/80.92 [10080]E(x100801,f2(a105))+E(f328(f328(f81(a1),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f328(a20,f328(f328(f39(a105),x100801),f328(f109(a105),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))))),f79(a1)),f328(a20,x100801))+E(f45(a105,x100801,f328(f109(a105),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f2(a105))
% 81.29/80.92 [9929]E(x99291,f2(a105))+~E(f45(a105,x99291,f328(f109(a105),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f2(a105))+E(f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f328(a20,f328(f328(f39(a105),x99291),f328(f109(a105),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))),f328(a20,x99291))
% 81.29/80.92 [4658]~P55(x46581,x46582)+P43(x46581,x46582)+~P44(a871)
% 81.29/80.92 [4595]~P141(x45951)+P31(x45951,x45952)+~E(x45952,f2(x45951))
% 81.29/80.92 [4596]~P106(x45961)+P29(x45961,x45962)+~E(x45962,f119(x45961))
% 81.29/80.92 [4605]~P111(x46051)+~E(x46052,f2(x46051))+E(f83(x46051,x46052),f2(x46051))
% 81.29/80.92 [4606]~P91(x46061)+~E(x46062,f2(x46061))+E(f83(x46061,x46062),f2(x46061))
% 81.29/80.92 [4614]~P141(x46142)+~P31(x46142,x46141)+E(x46141,f2(x46142))
% 81.29/80.92 [4648]~P111(x46482)+~E(f83(x46482,x46481),f2(x46482))+E(x46481,f2(x46482))
% 81.29/80.92 [4665]~P26(x46652)+~P26(x46651)+P26(f885(x46651,x46652))
% 81.29/80.92 [4666]~P26(x46662)+~P26(x46661)+P26(f883(x46661,x46662))
% 81.29/80.92 [4667]~P26(x46672)+~P26(x46671)+P26(f884(x46671,x46672))
% 81.29/80.92 [4668]~P28(x46682)+~P28(x46681)+P28(f201(x46681,x46682))
% 81.29/80.92 [4669]~P144(x46692)+~P144(x46691)+P144(f884(x46691,x46692))
% 81.29/80.92 [4670]~P60(x46702)+~P60(x46701)+P60(f885(x46701,x46702))
% 81.29/80.92 [4671]~P60(x46712)+~P60(x46711)+P60(f883(x46711,x46712))
% 81.29/80.92 [4672]~P60(x46722)+~P60(x46721)+P60(f884(x46721,x46722))
% 81.29/80.92 [4673]~P60(x46731)+~P95(x46732)+P95(f885(x46731,x46732))
% 81.29/80.92 [4799]~P106(x47991)+~P29(x47991,x47992)+P29(x47991,f151(x47991,x47992))
% 81.29/80.92 [5037]~P28(x50372)+~P28(x50371)+P28(f45(a1,x50371,x50372))
% 81.29/80.92 [4616]~P76(x46161)+~E(x46162,f2(x46161))+E(f328(f80(x46161),x46162),x46162)
% 81.29/80.92 [4620]~P137(x46201)+~E(x46202,f2(a1))+E(f328(f108(x46201),x46202),f2(x46201))
% 81.29/80.92 [4621]~P93(x46211)+~E(x46212,f2(a1))+E(f328(f108(x46211),x46212),f2(x46211))
% 81.29/80.92 [4645]~P73(x46451)+~E(f2(x46451),x46452)+E(f328(f80(x46451),x46452),f2(x46451))
% 81.29/80.92 [4646]~P87(x46461)+~E(x46462,f2(x46461))+E(f328(f76(x46461),x46462),f2(x46461))
% 81.29/80.92 [4647]~P73(x46471)+~E(x46472,f2(x46471))+E(f328(f80(x46471),x46472),f2(x46471))
% 81.29/80.92 [4675]~P76(x46752)+E(x46751,f2(x46752))+~E(f328(f80(x46752),x46751),x46751)
% 81.29/80.92 [4681]E(x46811,f328(a110,x46812))+~E(x46811,f2(a877))+~E(x46812,f328(f106(a1),x46811))
% 81.29/80.92 [4682]E(f328(a110,x46821),x46822)+~E(x46822,f2(a877))+~E(x46821,f328(f106(a1),x46822))
% 81.29/80.92 [4686]~P93(x46862)+E(x46861,f2(a1))+~E(f328(f108(x46862),x46861),f2(x46862))
% 81.29/80.92 [4691]~P87(x46912)+E(x46911,f2(x46912))+~E(f328(f76(x46912),x46911),f2(x46912))
% 81.29/80.92 [4692]~P73(x46922)+E(x46921,f2(x46922))+~E(f328(f80(x46922),x46921),f2(x46922))
% 81.29/80.92 [4693]~P73(x46931)+E(f2(x46931),x46932)+~E(f328(f80(x46931),x46932),f2(x46931))
% 81.29/80.92 [4833]~P2(a5000)+~E(f328(a28,x48332),f328(f236(a873),x48331))+P24(f328(a25,x48331))
% 81.29/80.92 [4875]~P106(x48751)+~P29(x48751,x48752)+P29(x48751,f328(f170(x48751),x48752))
% 81.29/80.92 [4902]~P24(x49022)+~P24(x49021)+P24(f328(f328(a326,x49021),x49022))
% 81.29/80.92 [4934]~E(f79(a877),f2(a877))+E(f328(f38(x49341),x49342),f2(a877))+~P24(f328(f62(x49341),x49342))
% 81.29/80.92 [4967]~P116(x49671)+~P142(x49671)+E(f328(f328(f258(x49671),f2(x49671)),f328(a118,x49672)),f2(x49671))
% 81.29/80.92 [5005]~P106(x50051)+P29(x50051,f138(x50051,x50052))+~P24(f328(f62(x50051),x50052))
% 81.29/80.92 [5006]~P106(x50061)+P29(x50061,f719(x50062,x50061))+~P24(f328(f62(x50061),x50062))
% 81.29/80.92 [5027]~P106(x50271)+E(f328(f171(x50271),f138(x50271,x50272)),x50272)+~P24(f328(f62(x50271),x50272))
% 81.29/80.92 [5028]~P106(x50281)+E(f328(f171(x50281),f719(x50282,x50281)),x50282)+~P24(f328(f62(x50281),x50282))
% 81.29/80.92 [5057]P24(x50571)+P24(x50572)+~P24(f328(f328(a327,x50572),x50571))
% 81.29/80.92 [5069]E(x50691,f193(f885(x50692,a871)))+~E(f328(f38(x50692),x50691),f2(a877))+~P24(f328(f62(x50692),x50691))
% 81.29/80.92 [5074]P24(x50741)+~P24(x50742)+~P24(f328(f328(a331,x50742),x50741))
% 81.29/80.92 [5122]~P72(x51221)+E(f328(f76(x51221),x51222),x51222)+P24(f328(f328(f245(x51221),x51222),f2(x51221)))
% 81.29/80.92 [5193]~P60(x51932)+~P24(f328(f58(x51932),x51931))+P24(f328(x51931,f638(x51931,x51932)))
% 81.29/80.92 [5194]~P60(x51942)+~P24(f328(f58(x51942),x51941))+P24(f328(x51941,f659(x51941,x51942)))
% 81.29/80.92 [5221]~P24(f328(a25,x52212))+~P24(f328(a25,x52211))+P24(f328(a25,f34(x52211,x52212)))
% 81.29/80.92 [5230]E(x52301,f119(x52302))+P24(f328(f136(x52302),f120(x52302,x52301)))+~P24(f328(f136(x52302),x52301))
% 81.29/80.92 [5235]~P106(x52351)+~P24(f328(f62(x52351),x52352))+P24(f328(f136(x52351),f138(x52351,x52352)))
% 81.29/80.92 [5236]~P106(x52361)+~P24(f328(f62(x52361),x52362))+P24(f328(f136(x52361),f719(x52362,x52361)))
% 81.29/80.92 [5242]~P137(x52421)+E(f328(f106(x52421),f328(a110,x52422)),f328(f108(x52421),x52422))+P24(f328(f328(f245(a1),x52422),f2(a1)))
% 81.29/80.92 [5272]P5(x52722,x52721)+E(f328(x52721,f534(x52721)),f328(x52721,f538(x52721)))+P24(f328(f328(x52721,f534(x52721)),f538(x52721)))
% 81.29/80.92 [5286]E(f328(f106(a1),f366(x52861,x52862)),x52861)+P24(f328(x52862,f328(a110,x52861)))+~P24(f328(x52862,f2(a877)))
% 81.29/80.92 [5298]~P60(x52981)+~P24(f328(x52982,f660(x52982,x52981)))+P24(f328(f59(x52981),x52982))
% 81.29/80.92 [5299]~P60(x52991)+~P24(f328(x52992,f661(x52992,x52991)))+P24(f328(f59(x52991),x52992))
% 81.29/80.92 [5313]~P60(x53132)+~P36(x53132,x53131,f56(x53132))+P24(f328(x53131,f735(x53131,x53132)))
% 81.29/80.92 [5329]~P111(x53291)+~E(f83(x53291,x53292),f328(f80(x53291),f79(x53291)))+P24(f328(f328(f245(x53291),x53292),f2(x53291)))
% 81.29/80.92 [5330]E(x53301,f193(f885(x53302,a871)))+P24(f328(f62(x53302),f370(x53301,x53302)))+~P24(f328(f62(x53302),x53301))
% 81.29/80.92 [5407]~E(x54072,f2(a1))+E(f223(x54071,x54072),f328(f328(f257(a1,a1),f2(a1)),f79(a1)))+P24(f328(f328(f245(a1),x54072),f2(a1)))
% 81.29/80.92 [5408]~E(x54081,f2(a1))+E(f223(x54081,x54082),f328(f328(f257(a1,a1),f2(a1)),f79(a1)))+P24(f328(f328(f245(a1),x54082),f2(a1)))
% 81.29/80.92 [5460]E(f328(f106(a1),f366(x54601,x54602)),x54601)+P24(f328(x54602,f328(a110,x54601)))+P24(f328(f328(f245(a1),x54601),f2(a1)))
% 81.29/80.92 [5484]E(f328(f328(f306(x54842),f390(x54841,x54842)),f370(x54841,x54842)),x54841)+E(x54841,f193(f885(x54842,a871)))+~P24(f328(f62(x54842),x54841))
% 81.29/80.92 [5524]~P111(x55241)+E(f83(x55241,x55242),f328(f80(x55241),f79(x55241)))+~P24(f328(f328(f245(x55241),x55242),f2(x55241)))
% 81.29/80.92 [5525]~P87(x55251)+E(f328(f76(x55251),x55252),f328(f80(x55251),x55252))+~P24(f328(f328(f244(x55251),x55252),f2(x55251)))
% 81.29/80.92 [5526]~P87(x55261)+E(f328(f76(x55261),x55262),f328(f80(x55261),x55262))+~P24(f328(f328(f245(x55261),x55262),f2(x55261)))
% 81.29/80.92 [5527]~P72(x55271)+E(f328(f76(x55271),x55272),f328(f80(x55271),x55272))+~P24(f328(f328(f245(x55271),x55272),f2(x55271)))
% 81.29/80.92 [5621]~P24(f328(x56211,f366(x56212,x56211)))+P24(f328(x56211,f328(a110,x56212)))+~P24(f328(x56211,f2(a877)))
% 81.29/80.92 [5628]E(x56281,f2(a877))+E(f328(a118,f813(x56282,x56281)),x56281)+~P24(f328(f328(f245(a877),x56281),f328(a118,x56282)))
% 81.29/80.92 [5632]P5(x56321,x56322)+~E(f328(x56322,f534(x56322)),f328(x56322,f538(x56322)))+~P24(f328(f328(x56322,f534(x56322)),f538(x56322)))
% 81.29/80.92 [5652]~P106(x56521)+P29(x56521,x56522)+P24(f328(f328(f244(a877),f639(x56522,x56521)),f640(x56522,x56521)))
% 81.29/80.92 [5653]~P106(x56531)+P29(x56531,x56532)+P24(f328(f328(f244(a877),f646(x56532,x56531)),f655(x56532,x56531)))
% 81.29/80.92 [5740]~P87(x57401)+~E(x57402,f2(x57401))+P24(f328(f328(f244(x57401),f328(f76(x57401),x57402)),f2(x57401)))
% 81.29/80.92 [5819]~P60(x58192)+~P60(x58191)+E(f60(x58191,x58192,f56(x58191),f56(x58192)),f56(f884(x58191,x58192)))
% 81.29/80.92 [5823]~P24(f328(x58231,f366(x58232,x58231)))+P24(f328(x58231,f328(a110,x58232)))+P24(f328(f328(f245(a1),x58232),f2(a1)))
% 81.29/80.92 [5846]~P24(f328(x58461,f328(a110,x58462)))+P24(f328(x58461,f2(a877)))+~P24(f328(f328(f245(a1),x58462),f2(a1)))
% 81.29/80.92 [6189]~P111(x61891)+~P24(f328(f328(f245(x61891),x61892),f2(x61891)))+P24(f328(f328(f245(x61891),f83(x61891,x61892)),f2(x61891)))
% 81.29/80.92 [6303]~P111(x63031)+P24(f328(f328(f244(x63031),f328(f108(x63031),x63032)),f2(x63031)))+~P24(f328(f328(f244(a1),x63032),f2(a1)))
% 81.29/80.92 [6304]~P111(x63041)+P24(f328(f328(f245(x63041),f328(f108(x63041),x63042)),f2(x63041)))+~P24(f328(f328(f245(a1),x63042),f2(a1)))
% 81.29/80.92 [6311]~P87(x63112)+E(x63111,f2(x63112))+~P24(f328(f328(f244(x63112),f328(f76(x63112),x63111)),f2(x63112)))
% 81.29/80.92 [6389]~P137(x63891)+~P24(f328(f328(f330(x63891),x63892),f115(x63891)))+P24(f328(f328(f330(x63891),f328(f80(x63891),x63892)),f115(x63891)))
% 81.29/80.92 [6421]~P111(x64211)+~P24(f328(f328(f245(x64211),f83(x64211,x64212)),f2(x64211)))+P24(f328(f328(f245(x64211),x64212),f2(x64211)))
% 81.29/80.92 [6592]~P111(x65922)+~P24(f328(f328(f244(x65922),f328(f108(x65922),x65921)),f2(x65922)))+P24(f328(f328(f244(a1),x65921),f2(a1)))
% 81.29/80.92 [6593]~P111(x65932)+~P24(f328(f328(f245(x65932),f328(f108(x65932),x65931)),f2(x65932)))+P24(f328(f328(f245(a1),x65931),f2(a1)))
% 81.29/80.92 [7096]~P76(x70961)+~P24(f328(f328(f244(x70961),x70962),f2(x70961)))+P24(f328(f328(f244(x70961),f328(f328(f81(x70961),x70962),x70962)),f2(x70961)))
% 81.29/80.92 [7097]~P111(x70971)+~P24(f328(f328(f245(x70971),x70972),f2(x70971)))+P24(f328(f328(f245(x70971),f328(f328(f81(x70971),x70972),x70972)),f2(x70971)))
% 81.29/80.92 [7098]~P76(x70981)+~P24(f328(f328(f245(x70981),x70982),f2(x70981)))+P24(f328(f328(f245(x70981),f328(f328(f81(x70981),x70982),x70982)),f2(x70981)))
% 81.29/80.92 [7664]~P76(x76641)+~P24(f328(f328(f244(x76641),f328(f328(f81(x76641),x76642),x76642)),f2(x76641)))+P24(f328(f328(f244(x76641),x76642),f2(x76641)))
% 81.29/80.92 [7665]~P111(x76651)+~P24(f328(f328(f245(x76651),f328(f328(f81(x76651),x76652),x76652)),f2(x76651)))+P24(f328(f328(f245(x76651),x76652),f2(x76651)))
% 81.29/80.92 [7666]~P76(x76661)+~P24(f328(f328(f245(x76661),f328(f328(f81(x76661),x76662),x76662)),f2(x76661)))+P24(f328(f328(f245(x76661),x76662),f2(x76661)))
% 81.29/80.92 [4731]~E(x47312,f2(a877))+~E(x47311,f2(a877))+E(f328(f328(f81(a877),x47311),x47312),f2(a877))
% 81.29/80.92 [4732]~E(x47322,f79(a877))+~E(x47321,f79(a877))+E(f328(f328(f82(a877),x47321),x47322),f79(a877))
% 81.29/80.92 [4733]~E(x47332,f79(a1))+~E(x47331,f79(a1))+E(f328(f328(f82(a1),x47331),x47332),f79(a1))
% 81.29/80.92 [4785]~P120(x47852)+E(x47851,f2(x47852))+E(f328(f328(f286(x47852),x47851),x47851),f79(x47852))
% 81.29/80.92 [4786]~P58(x47862)+E(x47861,f2(x47862))+E(f328(f328(f39(x47862),x47861),x47861),f79(x47862))
% 81.29/80.92 [4787]~P121(x47872)+E(x47871,f2(x47872))+E(f328(f328(f286(x47872),x47871),x47871),f79(x47872))
% 81.29/80.92 [4804]~P76(x48041)+~E(x48042,f2(x48041))+E(f328(f328(f81(x48041),x48042),x48042),f2(x48041))
% 81.29/80.92 [4807]~P139(x48071)+~E(x48072,f79(x48071))+E(f328(f328(f82(x48071),x48072),x48072),f79(x48071))
% 81.29/80.92 [4808]~P121(x48081)+~E(x48082,f2(x48081))+E(f328(f328(f286(x48081),x48082),x48082),f2(x48081))
% 81.29/80.92 [4854]~E(x48542,f2(a877))+~E(x48541,f2(a877))+E(f328(f80(a1),f328(f106(a1),x48541)),f328(f106(a1),x48542))
% 81.29/80.92 [4872]E(x48721,f79(a877))+E(x48722,f2(a877))+~E(f328(f328(f82(a877),x48722),x48721),x48722)
% 81.29/80.92 [4882]E(x48821,f2(a877))+E(x48822,f2(a877))+~E(f328(f328(f82(a877),x48822),x48821),f2(a877))
% 81.29/80.92 [4911]~E(x49112,f2(a877))+~E(x49111,f328(a118,f2(a877)))+E(f328(f328(f81(a877),x49111),x49112),f328(a118,f2(a877)))
% 81.29/80.92 [4912]~E(x49121,f2(a877))+~E(x49122,f328(a118,f2(a877)))+E(f328(f328(f81(a877),x49121),x49122),f328(a118,f2(a877)))
% 81.29/80.92 [4917]E(x49171,f79(a1))+E(x49172,f328(f109(a1),a103))+~E(f328(f328(f82(a1),x49171),x49172),f79(a1))
% 81.29/80.92 [4918]E(x49181,f79(a1))+E(x49182,f328(f109(a1),a103))+~E(f328(f328(f82(a1),x49182),x49181),f79(a1))
% 81.29/80.92 [4919]E(x49191,f79(a1))+E(x49191,f328(f109(a1),a103))+~E(f328(f328(f82(a1),x49192),x49191),f79(a1))
% 81.29/80.92 [4921]E(x49211,f79(a1))+E(x49211,f328(f109(a1),a103))+~E(f328(f328(f82(a1),x49211),x49212),f79(a1))
% 81.29/80.92 [4938]~P76(x49382)+E(x49381,f2(x49382))+~E(f328(f328(f81(x49382),x49381),x49381),f2(x49382))
% 81.29/80.92 [4944]~E(x49441,f328(f109(a1),a103))+~E(x49442,f328(f109(a1),a103))+E(f328(f328(f82(a1),x49441),x49442),f79(a1))
% 81.29/80.92 [4956]E(x49561,f2(a877))+E(x49562,f2(a877))+~E(f328(f328(f81(a877),x49562),x49561),f328(a118,f2(a877)))
% 81.29/80.92 [4966]~P96(x49661)+~P61(x49661)+E(f328(f328(f286(x49661),x49662),f328(f109(x49661),a84)),f2(x49661))
% 81.29/80.92 [4972]~P139(x49721)+~E(x49722,f328(f80(x49721),f79(x49721)))+E(f328(f328(f82(x49721),x49722),x49722),f79(x49721))
% 81.29/80.92 [4977]~P28(x49772)+~P28(x49771)+P28(f328(f328(f81(a1),x49771),x49772))
% 81.29/80.92 [4978]~P28(x49782)+~P28(x49781)+P28(f328(f328(f82(a1),x49781),x49782))
% 81.29/80.92 [4979]~P28(x49792)+~P28(x49791)+P28(f328(f328(f39(a1),x49791),x49792))
% 81.29/80.92 [4981]~E(x49812,f2(a1))+E(x49811,f2(a1))+E(f46(x49811,x49812),f328(f328(f257(a1,a1),f2(a1)),x49811))
% 81.29/80.92 [5003]~E(x50032,f328(a118,f2(a877)))+~E(x50031,f328(a118,f2(a877)))+E(f328(f328(f82(a877),x50031),x50032),f328(a118,f2(a877)))
% 81.29/80.92 [5018]E(x50181,f2(a877))+E(x50182,f328(a118,f2(a877)))+~E(f328(f328(f258(a877),x50182),x50181),f328(a118,f2(a877)))
% 81.29/80.92 [5019]E(x50191,f2(a877))+E(x50191,f328(a118,f2(a877)))+~E(f328(f328(f81(a877),x50192),x50191),f328(a118,f2(a877)))
% 81.29/80.92 [5020]E(x50201,f2(a877))+E(x50201,f328(a118,f2(a877)))+~E(f328(f328(f81(a877),x50201),x50202),f328(a118,f2(a877)))
% 81.29/80.92 [5029]~P96(x50291)+~P61(x50291)+E(f328(f328(f286(x50291),x50292),f328(f109(x50291),a103)),f328(f80(x50291),x50292))
% 81.29/80.92 [5049]E(x50491,f328(a110,x50492))+~E(x50491,f2(a877))+P24(f328(f328(f244(a1),f2(a1)),x50492))
% 81.29/80.92 [5050]E(f328(a110,x50501),x50502)+~E(x50502,f2(a877))+P24(f328(f328(f244(a1),f2(a1)),x50501))
% 81.29/80.92 [5065]E(x50651,f328(a118,f2(a877)))+E(x50652,f328(a118,f2(a877)))+~E(f328(f328(f81(a877),x50651),x50652),f328(a118,f2(a877)))
% 81.29/80.92 [5075]~E(x50751,f328(a110,x50752))+E(x50751,f2(a877))+P24(f328(f328(f244(a1),f2(a1)),x50752))
% 81.29/80.92 [5076]~E(f328(a110,x50762),x50761)+E(x50761,f2(a877))+P24(f328(f328(f244(a1),f2(a1)),x50762))
% 81.29/80.92 [5098]~P78(x50981)+E(f328(f64(x50981,f116(x50981)),x50982),f10(x50981,x50982))+~P24(f328(f62(x50981),x50982))
% 81.29/80.92 [5099]~P78(x50991)+E(f328(f64(x50991,f107(x50991)),x50992),f11(x50991,x50992))+~P24(f328(f62(x50991),x50992))
% 81.29/80.92 [5100]~P106(x51001)+E(f328(f64(x51001,f242(x51001)),x51002),f14(x51001,x51002))+~P24(f328(f62(x51001),x51002))
% 81.29/80.92 [5101]~P106(x51011)+E(f328(f64(x51011,f243(x51011)),x51012),f15(x51011,x51012))+~P24(f328(f62(x51011),x51012))
% 81.29/80.92 [5103]~P60(x51031)+~P24(f328(x51032,f196(x51031)))+P24(f328(f58(f881(x51031)),x51032))
% 81.29/80.92 [5186]~P60(x51862)+P24(f328(x51861,f196(x51862)))+~P24(f328(f59(f881(x51862)),x51861))
% 81.29/80.92 [5187]E(x51871,x51872)+~E(f328(f328(f22(a877),x51872),x51871),f2(a877))+~E(f328(f328(f22(a877),x51871),x51872),f2(a877))
% 81.29/80.92 [5201]P28(x52011)+~P40(x52012)+~P24(f328(f328(f330(a1),x52011),x52012))
% 81.29/80.92 [5231]~P111(x52311)+~E(f83(x52311,x52312),f79(x52311))+P24(f328(f328(f245(x52311),f2(x52311)),x52312))
% 81.29/80.92 [5243]~P96(x52431)+E(f328(f106(x52431),f328(f109(a877),x52432)),f328(f109(x52431),x52432))+P24(f328(a199,f328(f109(a1),x52432)))
% 81.29/80.92 [5249]~P43(x52491,x52492)+P44(a871)+P24(f328(f62(f884(x52491,x52491)),x52492))
% 81.29/80.92 [5322]~P106(x53221)+E(f328(f64(x53221,f242(x53221)),x53222),f12(x53221,f242(x53221),x53222))+~P24(f328(f62(x53221),x53222))
% 81.29/80.92 [5323]~P106(x53231)+E(f328(f64(x53231,f243(x53231)),x53232),f13(x53231,f243(x53231),x53232))+~P24(f328(f62(x53231),x53232))
% 81.29/80.92 [5337]E(x53371,x53372)+P24(f328(f328(f245(a877),x53372),x53371))+P24(f328(f328(f245(a877),x53371),x53372))
% 81.29/80.92 [5338]E(x53381,x53382)+P24(f328(f328(f245(a1),x53382),x53381))+P24(f328(f328(f245(a1),x53381),x53382))
% 81.29/80.92 [5394]~P96(x53941)+E(f328(f106(x53941),f328(f109(a877),x53942)),f2(x53941))+~P24(f328(a199,f328(f109(a1),x53942)))
% 81.29/80.92 [5397]~E(x53972,f328(a110,x53971))+E(x53971,f328(f106(a1),x53972))+~P24(f328(f328(f244(a1),f2(a1)),x53971))
% 81.29/80.92 [5398]~E(f328(a110,x53981),x53982)+E(x53981,f328(f106(a1),x53982))+~P24(f328(f328(f244(a1),f2(a1)),x53981))
% 81.29/80.92 [5399]~E(x53991,f328(a110,x53992))+E(f328(f106(a1),x53991),x53992)+~P24(f328(f328(f244(a1),f2(a1)),x53992))
% 81.29/80.92 [5409]E(x54091,f328(a110,x54092))+~E(x54092,f328(f106(a1),x54091))+~P24(f328(f328(f244(a1),f2(a1)),x54092))
% 81.29/80.92 [5410]E(f328(a110,x54101),x54102)+~E(x54101,f328(f106(a1),x54102))+~P24(f328(f328(f244(a1),f2(a1)),x54101))
% 81.29/80.92 [5449]~P87(x54492)+E(x54491,f2(x54492))+P24(f328(f328(f245(x54492),f2(x54492)),f328(f76(x54492),x54491)))
% 81.29/80.92 [5517]~P111(x55171)+E(f83(x55171,x55172),f79(x55171))+~P24(f328(f328(f245(x55171),f2(x55171)),x55172))
% 81.29/80.92 [5521]~P96(x55211)+E(f328(f106(x55211),f328(f109(a877),x55212)),f2(x55211))+P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),x55212)))
% 81.29/80.92 [5528]~P87(x55281)+E(f328(f76(x55281),x55282),x55282)+~P24(f328(f328(f244(x55281),f2(x55281)),x55282))
% 81.29/80.92 [5529]~P87(x55291)+E(f328(f76(x55291),x55292),x55292)+~P24(f328(f328(f245(x55291),f2(x55291)),x55292))
% 81.29/80.92 [5536]E(x55361,f2(a877))+~E(f138(a877,f328(f298(a877,x55362),x55361)),f119(a877))+P24(f328(f328(f244(a877),x55361),x55362))
% 81.29/80.92 [5546]~P74(x55461)+E(f328(f328(f6(x55461,x55461),f5(x55461)),f328(f171(x55461),x55462)),f328(f165(x55461),x55462))+~P24(f328(f136(x55461),x55462))
% 81.29/80.92 [5549]~P137(x55491)+E(f328(f106(x55491),f328(a110,x55492)),f328(f108(x55491),x55492))+~P24(f328(f328(f244(a1),f2(a1)),x55492))
% 81.29/80.92 [5576]E(x55761,x55762)+P24(f328(f328(f245(a877),x55761),x55762))+~P24(f328(f328(f244(a877),x55761),x55762))
% 81.29/80.92 [5577]E(x55771,x55772)+P24(f328(f328(f245(a1),x55771),x55772))+~P24(f328(f328(f244(a1),x55771),x55772))
% 81.29/80.92 [5580]E(x55801,f79(a1))+~E(f328(f328(f82(a1),x55802),x55801),f79(a1))+~P24(f328(f328(f245(a1),f2(a1)),x55802))
% 81.29/80.92 [5581]E(x55811,f79(a1))+~E(f328(f328(f82(a1),x55811),x55812),f79(a1))+~P24(f328(f328(f245(a1),f2(a1)),x55811))
% 81.29/80.92 [5618]~P40(x56182)+P24(f328(f328(f244(a1),f2(a1)),x56181))+~P24(f328(f328(f330(a1),x56181),x56182))
% 81.29/80.92 [5637]~P55(x56371,x56372)+P38(x56371,x56372)+~P24(f328(f62(f884(x56371,x56371)),x56372))
% 81.29/80.92 [5639]~P55(x56391,x56392)+P43(x56391,x56392)+~P24(f328(f62(f884(x56391,x56391)),x56392))
% 81.29/80.92 [5683]E(x56831,f193(f885(x56832,a871)))+~P24(f328(f62(x56832),x56831))+P24(f328(f328(f245(a877),f2(a877)),f328(f38(x56832),x56831)))
% 81.29/80.92 [5709]~P24(f328(x57091,x57092))+P24(f328(x57091,f2(a877)))+P24(f328(f328(f245(a877),f838(x57092,x57091)),x57092))
% 81.29/80.92 [5734]E(x57341,f2(a877))+~E(f328(f165(a877),x57342),f2(a877))+~P24(f328(f328(f330(a877),x57341),f328(f171(a877),x57342)))
% 81.29/80.92 [5800]E(x58001,x58002)+~P24(f328(f328(f244(a877),x58002),x58001))+~P24(f328(f328(f244(a877),x58001),x58002))
% 81.29/80.92 [5801]E(x58011,x58012)+~P24(f328(f328(f244(a1),x58012),x58011))+~P24(f328(f328(f244(a1),x58011),x58012))
% 81.29/80.92 [5802]E(f328(f38(x58021),x58022),f2(a877))+~P24(f328(f62(x58021),x58022))+P24(f328(f328(f330(x58021),f841(x58022,x58021)),x58022))
% 81.29/80.92 [5811]E(f50(x58111,x58112),f46(x58111,x58112))+P24(f328(f328(f244(a1),f2(a1)),x58111))+~P24(f328(f328(f245(a1),f2(a1)),x58112))
% 81.29/80.92 [5835]~P24(f328(x58351,f358(x58351)))+P24(f328(x58351,f328(a110,x58352)))+~P24(f328(f328(f244(a1),f2(a1)),x58352))
% 81.29/80.92 [5837]P24(f328(f328(f244(a877),x58371),f402(x58372)))+~P24(f328(f62(a877),x58372))+~P24(f328(f328(f330(a877),x58371),x58372))
% 81.29/80.92 [5838]P24(f328(f328(f245(a877),x58381),f408(x58382)))+~P24(f328(f62(a877),x58382))+~P24(f328(f328(f330(a877),x58381),x58382))
% 81.29/80.92 [5867]E(x58671,x58672)+~P24(f328(f328(f245(a877),x58671),f328(a118,x58672)))+P24(f328(f328(f245(a877),x58671),x58672))
% 81.29/80.92 [5901]E(x59011,f328(a118,x59012))+~P24(f328(f328(f244(a877),x59011),f328(a118,x59012)))+P24(f328(f328(f244(a877),x59011),x59012))
% 81.29/80.92 [5914]P24(f328(x59141,f365(x59141)))+~P24(f328(x59141,f328(a110,x59142)))+~P24(f328(f328(f244(a1),f2(a1)),x59142))
% 81.29/80.92 [5928]~P24(f328(x59281,x59282))+~P24(f328(f328(f244(a1),f2(a1)),x59282))+P24(f328(x59281,f328(f106(a1),f858(x59281))))
% 81.29/80.92 [5943]~P87(x59432)+~E(x59431,f2(x59432))+~P24(f328(f328(f245(x59432),f2(x59432)),f328(f76(x59432),x59431)))
% 81.29/80.92 [5970]~P55(x59701,x59702)+P38(x59701,f328(f283(x59701,x59701),x59702))+~P24(f328(f62(f884(x59701,x59701)),x59702))
% 81.29/80.92 [5978]~P96(x59781)+E(f328(f106(x59781),f328(f109(a877),x59782)),f328(f109(x59781),x59782))+~P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),x59782)))
% 81.29/80.92 [5982]E(f328(a118,x59821),x59822)+~P24(f328(f328(f245(a877),x59821),x59822))+P24(f328(f328(f245(a877),f328(a118,x59821)),x59822))
% 81.29/80.92 [5995]E(f328(f328(f39(a1),x59951),x59952),f2(a1))+~P24(f328(f328(f244(a1),x59951),f2(a1)))+~P24(f328(f328(f245(a1),x59952),x59951))
% 81.29/80.92 [6008]E(f45(a1,x60081,x60082),x60081)+~P24(f328(f328(f244(a1),x60081),f2(a1)))+~P24(f328(f328(f245(a1),x60082),x60081))
% 81.29/80.92 [6021]E(f47(x60211,x60212),f46(x60211,x60212))+~P24(f328(f328(f244(a1),f2(a1)),x60211))+~P24(f328(f328(f244(a1),f2(a1)),x60212))
% 81.29/80.92 [6029]E(f328(f328(f39(a1),x60291),x60292),f2(a1))+~P24(f328(f328(f244(a1),f2(a1)),x60291))+~P24(f328(f328(f245(a1),x60291),x60292))
% 81.29/80.92 [6041]E(f45(a877,f328(f109(a877),x60411),f328(f109(a877),x60412)),f328(f109(a877),x60411))+P24(f328(a199,f328(f109(a1),x60411)))+~P24(f328(a199,f328(f109(a1),x60412)))
% 81.29/80.92 [6043]E(f45(a1,x60431,x60432),x60431)+~P24(f328(f328(f244(a1),f2(a1)),x60431))+~P24(f328(f328(f245(a1),x60431),x60432))
% 81.29/80.92 [6044]E(x60441,x60442)+~P24(f328(f328(f245(a877),x60441),f328(a118,x60442)))+~P24(f328(f328(f244(a877),x60442),x60441))
% 81.29/80.92 [6061]~P76(x60611)+~P24(f328(f328(f244(x60611),x60612),f2(x60611)))+P24(f328(f328(f244(x60611),x60612),f328(f80(x60611),x60612)))
% 81.29/80.92 [6062]~P111(x60621)+~P24(f328(f328(f245(x60621),x60622),f2(x60621)))+P24(f328(f328(f245(x60621),x60622),f328(f80(x60621),x60622)))
% 81.29/80.92 [6072]~P27(x60721)+E(f328(f328(f65(x60721,x60721,f116(x60721)),f193(x60721)),x60722),f40(x60721,x60722))+~P24(f328(f62(x60721),x60722))
% 81.29/80.92 [6073]~P27(x60731)+E(f328(f328(f65(x60731,x60731,f107(x60731)),f252(x60731)),x60732),f41(x60731,x60732))+~P24(f328(f62(x60731),x60732))
% 81.29/80.92 [6087]~P111(x60871)+~P24(f328(f328(f244(a1),f2(a1)),x60872))+P24(f328(f328(f244(x60871),f2(x60871)),f328(f108(x60871),x60872)))
% 81.29/80.92 [6088]~P110(x60881)+~P24(f328(f328(f245(a877),f2(a877)),x60882))+P24(f328(f328(f245(x60881),f2(x60881)),f328(f106(x60881),x60882)))
% 81.29/80.92 [6089]~P111(x60891)+~P24(f328(f328(f245(a1),f2(a1)),x60892))+P24(f328(f328(f245(x60891),f2(x60891)),f328(f108(x60891),x60892)))
% 81.29/80.92 [6092]~P28(x60922)+~P28(x60921)+E(f328(f307(a877,a1,f106(a1)),f299(a877,f328(a110,x60921),f328(a110,x60922))),f299(a1,x60921,x60922))
% 81.29/80.92 [6098]P24(f328(x60981,x60982))+~P24(f328(f328(f244(a1),f2(a1)),x60982))+~P24(f328(x60981,f328(f106(a1),f859(x60981))))
% 81.29/80.92 [6123]E(f328(f328(f81(a877),f328(f109(a877),x61231)),f328(f109(a877),x61232)),f328(f109(a877),x61231))+P24(f328(f328(f245(a1),x61231),a84))+~P24(f328(f328(f245(a1),x61232),a84))
% 81.29/80.92 [6127]~P111(x61271)+P24(f328(f328(f245(x61271),f2(x61271)),f83(x61271,x61272)))+~P24(f328(f328(f245(x61271),f2(x61271)),x61272))
% 81.29/80.92 [6138]~P80(x61381)+~P24(f328(f328(f244(x61381),x61382),f2(x61381)))+P24(f328(f328(f244(x61381),f2(x61381)),f328(f80(x61381),x61382)))
% 81.29/80.92 [6139]~P80(x61391)+~P24(f328(f328(f245(x61391),x61392),f2(x61391)))+P24(f328(f328(f245(x61391),f2(x61391)),f328(f80(x61391),x61392)))
% 81.29/80.92 [6142]E(x61421,f252(f885(x61422,a871)))+~E(f328(f38(x61422),x61421),f328(f38(x61422),f252(f885(x61422,a871))))+~P24(f328(f62(x61422),f252(f885(x61422,a871))))
% 81.29/80.92 [6182]~P76(x61821)+P24(f328(f328(f244(x61821),x61822),f2(x61821)))+~P24(f328(f328(f244(x61821),x61822),f328(f80(x61821),x61822)))
% 81.29/80.92 [6183]~P111(x61831)+P24(f328(f328(f245(x61831),x61832),f2(x61831)))+~P24(f328(f328(f245(x61831),x61832),f328(f80(x61831),x61832)))
% 81.29/80.92 [6191]~P96(x61911)+P24(f328(f328(f330(x61911),f328(f109(x61911),x61912)),f191(x61911)))+~P24(f328(f328(f244(a1),a84),x61912))
% 81.29/80.92 [6222]E(x62221,f2(a877))+~P24(f328(f328(f245(a877),x62221),f328(a118,x62222)))+P24(f328(f328(f245(a877),f813(x62222,x62221)),x62222))
% 81.29/80.92 [6244]~P111(x62441)+~P24(f328(f328(f245(x62441),f2(x62441)),f83(x62441,x62442)))+P24(f328(f328(f245(x62441),f2(x62441)),x62442))
% 81.29/80.92 [6246]~E(f328(f109(a877),x62462),f328(f109(a877),x62461))+P24(f328(f328(f244(a1),f328(f109(a1),x62461)),f2(a1)))+~P24(f328(a199,f328(f109(a1),x62462)))
% 81.29/80.92 [6276]E(f328(f256(a1,a1),f50(x62761,x62762)),f328(f328(f39(a1),x62761),x62762))+~P24(f328(f328(f245(a1),x62761),f2(a1)))+~P24(f328(f328(f245(a1),f2(a1)),x62762))
% 81.29/80.92 [6309]E(f328(f266(a1,a1),f50(x63091,x63092)),f45(a1,x63091,x63092))+~P24(f328(f328(f245(a1),x63091),f2(a1)))+~P24(f328(f328(f245(a1),f2(a1)),x63092))
% 81.29/80.92 [6312]~P111(x63122)+~P24(f328(f328(f244(x63122),f2(x63122)),f328(f108(x63122),x63121)))+P24(f328(f328(f244(a1),f2(a1)),x63121))
% 81.29/80.92 [6313]~P110(x63132)+~P24(f328(f328(f245(x63132),f2(x63132)),f328(f106(x63132),x63131)))+P24(f328(f328(f245(a877),f2(a877)),x63131))
% 81.29/80.92 [6314]~P111(x63142)+~P24(f328(f328(f245(x63142),f2(x63142)),f328(f108(x63142),x63141)))+P24(f328(f328(f245(a1),f2(a1)),x63141))
% 81.29/80.92 [6317]E(f328(f256(a1,a1),f47(x63171,x63172)),f328(f328(f39(a1),x63171),x63172))+~P24(f328(f328(f244(a1),f2(a1)),x63172))+~P24(f328(f328(f245(a1),f2(a1)),x63171))
% 81.29/80.92 [6332]E(f328(f266(a1,a1),f47(x63321,x63322)),f45(a1,x63321,x63322))+~P24(f328(f328(f244(a1),f2(a1)),x63322))+~P24(f328(f328(f245(a1),f2(a1)),x63321))
% 81.29/80.92 [6349]~P80(x63491)+P24(f328(f328(f244(x63491),x63492),f2(x63491)))+~P24(f328(f328(f244(x63491),f2(x63491)),f328(f80(x63491),x63492)))
% 81.29/80.92 [6350]~P80(x63501)+P24(f328(f328(f245(x63501),x63502),f2(x63501)))+~P24(f328(f328(f245(x63501),f2(x63501)),f328(f80(x63501),x63502)))
% 81.29/80.92 [6376]P24(f328(f49(x63761,x63762),f50(x63761,x63762)))+~P24(f328(f328(f245(a1),x63761),f2(a1)))+~P24(f328(f328(f245(a1),f2(a1)),x63762))
% 81.29/80.92 [6401]P24(f328(f49(x64011,x64012),f47(x64011,x64012)))+~P24(f328(f328(f244(a1),f2(a1)),x64011))+~P24(f328(f328(f245(a1),f2(a1)),x64012))
% 81.29/80.92 [6444]~P80(x64441)+P24(f328(f328(f244(x64441),f328(f80(x64441),x64442)),f2(x64441)))+~P24(f328(f328(f244(x64441),f2(x64441)),x64442))
% 81.29/80.92 [6445]~P80(x64451)+P24(f328(f328(f245(x64451),f328(f80(x64451),x64452)),f2(x64451)))+~P24(f328(f328(f245(x64451),f2(x64451)),x64452))
% 81.29/80.92 [6462]E(f328(f328(f22(a877),f328(a110,x64621)),f328(a110,x64622)),f328(a110,f201(x64621,x64622)))+~P24(f328(f328(f244(a1),f2(a1)),x64622))+~P24(f328(f328(f244(a1),f2(a1)),x64621))
% 81.29/80.92 [6479]P24(f328(f328(f244(a1),f2(a1)),f201(x64791,x64792)))+~P24(f328(f328(f244(a1),f2(a1)),x64792))+~P24(f328(f328(f244(a1),f2(a1)),x64791))
% 81.29/80.92 [6517]~P24(f328(x65171,x65172))+P24(f328(x65171,f2(a877)))+P24(f328(x65171,f328(f328(f81(a877),f838(x65172,x65171)),f79(a877))))
% 81.29/80.92 [6599]E(f328(f109(a877),x65991),f328(f109(a877),x65992))+~P24(f328(f328(f244(a1),f328(f109(a1),x65992)),f2(a1)))+~P24(f328(a199,f328(f109(a1),x65991)))
% 81.29/80.92 [6609]~E(x66091,f2(a877))+~E(f611(x66092,x66091),f2(a877))+E(f328(f141(a877,a877,f81(a877),x66091),x66092),f2(a877))
% 81.29/80.92 [6635]~P24(f328(f62(x66351),f697(x66352,x66351)))+~P24(f328(f62(f885(x66351,a871)),x66352))+P24(f328(f62(x66351),f40(f885(x66351,a871),x66352)))
% 81.29/80.92 [6641]E(x66411,x66412)+P24(f328(f328(f245(a1),x66411),x66412))+~P24(f328(f328(f245(a1),x66411),f328(f328(f81(a1),x66412),f79(a1))))
% 81.29/80.92 [6642]P24(f328(f328(f244(a877),f328(a110,x66421)),f328(a110,x66422)))+~P24(f328(f328(f244(a1),f2(a1)),x66422))+~P24(f328(f328(f244(a1),x66421),x66422))
% 81.29/80.92 [6643]P24(f328(f328(f244(a877),f328(a110,x66431)),f328(a110,x66432)))+~P24(f328(f328(f245(a1),f2(a1)),x66431))+~P24(f328(f328(f244(a1),x66431),x66432))
% 81.29/80.92 [6645]P24(f328(f328(f245(a877),f328(a110,x66451)),f328(a110,x66452)))+~P24(f328(f328(f244(a1),f2(a1)),x66451))+~P24(f328(f328(f245(a1),x66451),x66452))
% 81.29/80.92 [6646]P24(f328(f328(f245(a877),f328(a110,x66461)),f328(a110,x66462)))+~P24(f328(f328(f245(a1),f2(a1)),x66462))+~P24(f328(f328(f245(a1),x66461),x66462))
% 81.29/80.92 [6657]E(f45(a877,f328(a110,x66571),f328(a110,x66572)),f328(a110,f45(a1,x66571,x66572)))+~P24(f328(f328(f244(a1),f2(a1)),x66572))+~P24(f328(f328(f244(a1),f2(a1)),x66571))
% 81.29/80.92 [6680]~P80(x66801)+~P24(f328(f328(f244(x66801),f328(f80(x66801),x66802)),f2(x66801)))+P24(f328(f328(f244(x66801),f2(x66801)),x66802))
% 81.29/80.92 [6681]~P80(x66811)+~P24(f328(f328(f245(x66811),f328(f80(x66811),x66812)),f2(x66811)))+P24(f328(f328(f245(x66811),f2(x66811)),x66812))
% 81.29/80.92 [6696]~P24(f328(f328(f245(a1),a84),x66962))+~P24(f328(f328(f245(a1),x66961),x66962))+P24(f328(f328(f245(a877),f328(f109(a877),x66961)),f328(f109(a877),x66962)))
% 81.29/80.92 [6787]~P24(f328(f328(f244(a1),f2(a1)),x67871))+P24(f328(f328(f245(a877),f328(a110,x67871)),x67872))+~P24(f328(f328(f245(a1),x67871),f328(f106(a1),x67872)))
% 81.29/80.92 [6804]E(x68041,f2(a1))+E(f45(a1,x68042,x68041),f2(a1))+E(f328(f328(f22(a1),f328(f80(a1),f328(f328(f39(a1),x68042),x68041))),f79(a1)),f328(f328(f39(a1),x68042),f328(f80(a1),x68041)))
% 81.29/80.92 [6819]~P24(f328(f328(f244(a1),f2(a1)),x68191))+~P24(f328(f328(f245(a877),f328(a110,x68191)),x68192))+P24(f328(f328(f245(a1),x68191),f328(f106(a1),x68192)))
% 81.29/80.92 [6854]~P24(f328(f328(f244(a877),f328(a110,x68541)),f328(a110,x68542)))+~P24(f328(f328(f244(a1),f2(a1)),x68542))+P24(f328(f328(f244(a1),x68541),x68542))
% 81.29/80.92 [6855]~P24(f328(f328(f244(a877),f328(a110,x68551)),f328(a110,x68552)))+~P24(f328(f328(f245(a1),f2(a1)),x68551))+P24(f328(f328(f244(a1),x68551),x68552))
% 81.29/80.92 [6883]P24(f328(f328(f244(a1),x68831),x68832))+~P24(f328(f328(f244(a877),f328(f109(a877),x68831)),f328(f109(a877),x68832)))+P24(f328(f328(f244(a1),x68831),a84))
% 81.29/80.92 [6907]P24(f328(f328(f244(a1),f2(a1)),f45(a1,x69071,x69072)))+~P24(f328(f328(f244(a1),f2(a1)),x69072))+~P24(f328(f328(f244(a1),f2(a1)),x69071))
% 81.29/80.92 [7007]P24(f328(f328(f245(a1),a84),x70071))+~P24(f328(f328(f245(a1),x70072),x70071))+~P24(f328(f328(f245(a877),f328(f109(a877),x70072)),f328(f109(a877),x70071)))
% 81.29/80.92 [7058]E(f328(f328(f257(a1,a1),f328(f328(f39(a1),x70581),x70582)),f45(a1,x70581,x70582)),f50(x70581,x70582))+~P24(f328(f328(f245(a1),x70581),f2(a1)))+~P24(f328(f328(f245(a1),f2(a1)),x70582))
% 81.29/80.92 [7079]E(f328(f328(f257(a1,a1),f328(f328(f39(a1),x70791),x70792)),f45(a1,x70791,x70792)),f47(x70791,x70792))+~P24(f328(f328(f244(a1),f2(a1)),x70792))+~P24(f328(f328(f244(a1),f2(a1)),x70791))
% 81.29/80.92 [7130]~P98(x71302)+E(x71301,f119(x71302))+E(f328(f141(x71302,x71302,f82(x71302),f328(f140(x71302),x71301)),f328(f170(x71302),x71301)),f328(f64(x71302,f82(x71302)),f328(f171(x71302),x71301)))
% 81.29/80.92 [7242]~E(x72421,f2(a877))+E(f328(f141(a877,a877,f81(a877),x72421),x72422),f2(a877))+P24(f328(f328(f330(a877),f611(x72422,x72421)),f328(f171(a877),x72422)))
% 81.29/80.92 [7289]~P24(f328(f328(f244(a1),x72891),f2(a1)))+P24(f328(f328(f244(a1),f328(f328(f39(a1),x72891),x72892)),f2(a1)))+~P24(f328(f328(f245(a1),f2(a1)),x72892))
% 81.29/80.92 [7290]~P24(f328(f328(f245(a1),x72902),f2(a1)))+P24(f328(f328(f244(a1),f328(f328(f39(a1),x72901),x72902)),f2(a1)))+~P24(f328(f328(f244(a1),f2(a1)),x72901))
% 81.29/80.92 [7291]~P24(f328(f328(f245(a1),x72912),f2(a1)))+P24(f328(f328(f245(a1),f328(f328(f39(a1),x72911),x72912)),f2(a1)))+~P24(f328(f328(f245(a1),f2(a1)),x72911))
% 81.29/80.92 [7293]~P24(f328(f328(f245(a1),x72931),f2(a1)))+P24(f328(f328(f245(a1),f328(f328(f39(a1),x72931),x72932)),f2(a1)))+~P24(f328(f328(f245(a1),f2(a1)),x72932))
% 81.29/80.92 [7299]P24(f328(f328(f330(f885(x72991,a871)),f697(x72992,x72991)),x72992))+~P24(f328(f62(f885(x72991,a871)),x72992))+P24(f328(f62(x72991),f40(f885(x72991,a871),x72992)))
% 81.29/80.92 [7397]P21(x73971,x73971,x73972,f252(f885(x73971,a871)))+~E(f328(f307(x73971,x73971,x73972),f252(f885(x73971,a871))),f252(f885(x73971,a871)))+~P24(f328(f62(x73971),f252(f885(x73971,a871))))
% 81.29/80.92 [7522]~P21(x75221,x75221,x75222,f252(f885(x75221,a871)))+E(f328(f307(x75221,x75221,x75222),f252(f885(x75221,a871))),f252(f885(x75221,a871)))+~P24(f328(f62(x75221),f252(f885(x75221,a871))))
% 81.29/80.92 [7658]E(f328(f328(f39(a1),x76581),x76582),f328(f109(a1),a103))+~P24(f328(f328(f244(a1),f328(f328(f81(a1),x76581),x76582)),f2(a1)))+~P24(f328(f328(f245(a1),f2(a1)),x76581))
% 81.29/80.92 [7717]~P24(f328(f328(f245(a1),x77172),f2(a1)))+~P24(f328(f328(f245(a1),f328(f328(f39(a1),x77171),x77172)),f2(a1)))+P24(f328(f328(f245(a1),f2(a1)),x77171))
% 81.29/80.92 [7722]E(f328(f328(f81(a1),x77221),x77222),f45(a1,x77221,x77222))+~P24(f328(f328(f244(a1),f328(f328(f81(a1),x77221),x77222)),f2(a1)))+~P24(f328(f328(f245(a1),f2(a1)),x77221))
% 81.29/80.92 [7725]P24(f328(f328(f245(a1),x77251),f2(a1)))+~P24(f328(f328(f245(a1),f328(f328(f39(a1),x77251),x77252)),f2(a1)))+~P24(f328(f328(f245(a1),f2(a1)),x77252))
% 81.29/80.92 [8116]~P60(x81161)+~P24(f328(f59(f881(x81161)),x81162))+P24(f328(f59(x81161),f328(f328(f8(f881(x81161),a871,x81161),x81162),f236(x81161))))
% 81.29/80.92 [8427]~P106(x84271)+P29(x84271,x84272)+~P24(f328(f328(f244(x84271),f328(f328(f164(x84271),x84272),f639(x84272,x84271))),f328(f328(f164(x84271),x84272),f640(x84272,x84271))))
% 81.29/80.92 [8428]~P106(x84281)+P29(x84281,x84282)+~P24(f328(f328(f244(x84281),f328(f328(f164(x84281),x84282),f646(x84282,x84281))),f328(f328(f164(x84281),x84282),f655(x84282,x84281))))
% 81.29/80.92 [8583]~P60(x85831)+P24(f328(f58(f881(x85831)),x85832))+~P24(f328(f58(x85831),f328(f328(f8(f881(x85831),a871,x85831),x85832),f236(x85831))))
% 81.29/80.92 [9743]~P60(x97431)+~P60(x97432)+E(f328(f328(f153(f878(x97431),f885(x97432,x97431)),f328(f328(f8(f885(x97432,f881(x97431)),f885(x97432,x97431),f878(x97431)),f74(f881(x97431),x97431,x97432,f240(x97431))),f328(f328(f8(f878(f884(x97432,x97431)),f885(x97432,f881(x97431)),f878(x97431)),f177(x97432,x97431)),f328(f181(x97432,x97431),f56(x97432))))),f55(x97431,f328(f194(f878(x97432)),f56(x97432)),f56(x97431))),f56(f885(x97432,x97431)))
% 81.29/80.92 [5676]E(x56761,f2(a1))+~E(f45(a1,x56762,x56761),f2(a1))+E(f328(f328(f39(a1),x56762),f328(f80(a1),x56761)),f328(f80(a1),f328(f328(f39(a1),x56762),x56761)))
% 81.29/80.92 [5694]~P40(x56942)+~P40(x56941)+P40(f328(f328(f116(f885(a1,a871)),x56941),x56942))
% 81.29/80.92 [5695]~P40(x56952)+~P40(x56951)+P40(f328(f328(f107(f885(a1,a871)),x56951),x56952))
% 81.29/80.92 [5712]~P96(x57121)+~P61(x57121)+E(f328(f80(x57121),f328(f328(f286(x57121),f79(x57121)),x57122)),f328(f328(f286(x57121),f328(f109(x57121),a103)),x57122))
% 81.29/80.92 [5827]E(x58271,f2(a1))+~E(f45(a1,x58272,x58271),f2(a1))+E(f328(f328(f39(a1),f328(f80(a1),x58272)),x58271),f328(f80(a1),f328(f328(f39(a1),x58272),x58271)))
% 81.29/80.92 [5964]~P106(x59641)+P29(x59641,x59642)+P24(f328(f328(f245(a877),f640(x59642,x59641)),f328(f194(f878(x59641)),x59642)))
% 81.29/80.92 [5965]~P106(x59651)+P29(x59651,x59652)+P24(f328(f328(f245(a877),f655(x59652,x59651)),f328(f194(f878(x59651)),x59652)))
% 81.29/80.92 [6119]~P96(x61191)+~E(f328(f109(x61191),x61192),f2(x61191))+P31(x61191,f328(f109(x61191),f328(f328(f81(a1),x61192),f328(f80(a1),a84))))
% 81.29/80.92 [6120]~P96(x61201)+~E(f328(f109(x61201),x61202),f2(x61201))+P31(x61201,f328(f109(x61201),f328(f328(f81(a1),a84),f328(f80(a1),x61202))))
% 81.29/80.92 [6122]E(f328(a51,f47(f328(f80(a1),x61221),f328(f80(a1),x61222))),f46(x61221,x61222))+P24(f328(f328(f244(a1),f2(a1)),x61221))+P24(f328(f328(f245(a1),f2(a1)),x61222))
% 81.29/80.92 [6252]~E(x62522,f2(a877))+~E(x62521,f2(a877))+P24(f328(f328(f244(a1),f328(f106(a1),x62521)),f328(f80(a1),f328(f106(a1),x62522))))
% 81.29/80.92 [6280]E(f328(f328(f81(a877),f328(f109(a877),x62801)),f328(f109(a877),x62802)),f328(f109(a877),f328(f328(f81(a1),x62801),x62802)))+P24(f328(f328(f245(a1),x62801),a84))+P24(f328(f328(f245(a1),x62802),a84))
% 81.29/80.92 [6410]~P76(x64101)+~P24(f328(f328(f244(x64101),f2(x64101)),x64102))+P24(f328(f328(f244(x64101),f328(f80(x64101),x64102)),x64102))
% 81.29/80.92 [6411]~P76(x64111)+~P24(f328(f328(f245(x64111),f2(x64111)),x64112))+P24(f328(f328(f245(x64111),f328(f80(x64111),x64112)),x64112))
% 81.29/80.92 [6585]E(f328(f328(f22(a877),f328(a110,x65851)),f328(a110,x65852)),f328(a110,f328(f328(f22(a1),x65851),x65852)))+~P24(f328(f328(f244(a1),f2(a1)),x65852))+~P24(f328(f328(f244(a1),x65852),x65851))
% 81.29/80.92 [6618]E(f328(a110,f45(a1,f328(f109(a1),x66181),f328(f109(a1),x66182))),f45(a877,f328(f109(a877),x66181),f328(f109(a877),x66182)))+P24(f328(a199,f328(f109(a1),x66181)))+P24(f328(a199,f328(f109(a1),x66182)))
% 81.29/80.92 [6636]~P76(x66361)+P24(f328(f328(f244(x66361),f2(x66361)),x66362))+~P24(f328(f328(f244(x66361),f328(f80(x66361),x66362)),x66362))
% 81.29/80.92 [6637]~P76(x66371)+P24(f328(f328(f245(x66371),f2(x66371)),x66372))+~P24(f328(f328(f245(x66371),f328(f80(x66371),x66372)),x66372))
% 81.29/80.92 [6649]~P76(x66491)+~P24(f328(f328(f244(x66491),f2(x66491)),x66492))+P24(f328(f328(f244(x66491),f2(x66491)),f328(f328(f81(x66491),x66492),x66492)))
% 81.29/80.92 [6651]~P76(x66511)+~P24(f328(f328(f245(x66511),f2(x66511)),x66512))+P24(f328(f328(f245(x66511),f2(x66511)),f328(f328(f81(x66511),x66512),x66512)))
% 81.29/80.92 [6663]E(f328(f328(f81(a877),f328(a110,x66631)),f328(a110,x66632)),f328(a110,f328(f328(f81(a1),x66631),x66632)))+~P24(f328(f328(f244(a1),f2(a1)),x66632))+~P24(f328(f328(f244(a1),f2(a1)),x66631))
% 81.29/80.92 [6675]E(x66751,f2(a877))+P24(f328(f328(f245(a877),f2(a877)),x66752))+~P24(f328(f328(f245(a877),f2(a877)),f328(f328(f258(a877),x66752),x66751)))
% 81.29/80.92 [6705]~P96(x67051)+E(f328(f109(x67051),x67052),f2(x67051))+~P31(x67051,f328(f109(x67051),f328(f328(f81(a1),a84),f328(f80(a1),x67052))))
% 81.29/80.92 [6706]~P96(x67061)+E(f328(f109(x67061),x67062),f2(x67061))+~P31(x67061,f328(f109(x67061),f328(f328(f81(a1),x67062),f328(f80(a1),a84))))
% 81.29/80.92 [6765]~P24(f328(f62(x67651),x67652))+~P24(f328(f62(x67651),f252(f885(x67651,a871))))+P24(f328(f62(x67651),f328(f80(f885(x67651,a871)),x67652)))
% 81.29/80.92 [6788]~P24(f328(f328(f245(a1),f2(a1)),x67882))+~P24(f328(f328(f244(a1),x67882),x67881))+P24(f328(f328(f245(a1),f2(a1)),f328(f328(f39(a1),x67881),x67882)))
% 81.29/80.92 [6789]~P24(f328(f328(f244(a1),x67891),f2(a1)))+~P24(f328(f328(f245(a1),x67892),f2(a1)))+P24(f328(f328(f244(a1),f2(a1)),f328(f328(f39(a1),x67891),x67892)))
% 81.29/80.92 [6827]~P24(f328(f328(f244(a1),f2(a1)),x68272))+~P24(f328(f328(f244(a1),f2(a1)),x68271))+P24(f328(f328(f244(a1),f2(a1)),f328(f328(f81(a1),x68271),x68272)))
% 81.29/80.92 [6828]~P24(f328(f328(f244(a1),f2(a1)),x68282))+~P24(f328(f328(f244(a1),f2(a1)),x68281))+P24(f328(f328(f244(a1),f2(a1)),f328(f328(f82(a1),x68281),x68282)))
% 81.29/80.92 [6829]~P24(f328(f328(f244(a1),f2(a1)),x68292))+~P24(f328(f328(f244(a1),f2(a1)),x68291))+P24(f328(f328(f244(a1),f2(a1)),f328(f328(f39(a1),x68291),x68292)))
% 81.29/80.92 [6830]~P24(f328(f328(f244(a1),f2(a1)),x68301))+~P24(f328(f328(f245(a1),f2(a1)),x68302))+P24(f328(f328(f244(a1),f2(a1)),f328(f328(f39(a1),x68301),x68302)))
% 81.29/80.92 [6831]~P24(f328(f328(f245(a877),f2(a877)),x68312))+~P24(f328(f328(f245(a877),f2(a877)),x68311))+P24(f328(f328(f245(a877),f2(a877)),f328(f328(f82(a877),x68311),x68312)))
% 81.29/80.92 [6893]E(x68931,f2(a1))+E(f45(a1,x68932,x68931),f2(a1))+E(f328(f328(f22(a1),f328(f80(a1),f328(f328(f39(a1),x68932),x68931))),f79(a1)),f328(f328(f39(a1),f328(f80(a1),x68932)),x68931))
% 81.29/80.92 [6948]P24(f328(f328(f245(a877),f2(a877)),x69481))+P24(f328(f328(f245(a877),f2(a877)),x69482))+~P24(f328(f328(f245(a877),f2(a877)),f328(f328(f81(a877),x69482),x69481)))
% 81.29/80.92 [6952]~P76(x69521)+P24(f328(f328(f244(x69521),f2(x69521)),x69522))+~P24(f328(f328(f244(x69521),f2(x69521)),f328(f328(f81(x69521),x69522),x69522)))
% 81.29/80.92 [6953]~P76(x69531)+P24(f328(f328(f245(x69531),f2(x69531)),x69532))+~P24(f328(f328(f245(x69531),f2(x69531)),f328(f328(f81(x69531),x69532),x69532)))
% 81.29/80.92 [7008]~P24(f328(f62(x70081),x70082))+P24(f328(f62(x70081),f252(f885(x70081,a871))))+~P24(f328(f62(x70081),f328(f80(f885(x70081,a871)),x70082)))
% 81.29/80.92 [7071]P24(f328(f328(f244(a1),x70711),f2(a1)))+~P24(f328(f328(f245(a1),x70712),f2(a1)))+~P24(f328(f328(f244(a1),f2(a1)),f328(f328(f39(a1),x70711),x70712)))
% 81.29/80.92 [7077]~P24(f328(f328(f245(a1),f2(a1)),x70771))+P24(f328(f328(f244(a1),x70771),x70772))+~P24(f328(f328(f245(a1),f2(a1)),f328(f328(f39(a1),x70772),x70771)))
% 81.29/80.92 [7078]~P24(f328(f328(f244(a1),f2(a1)),x70782))+P24(f328(f328(f244(a1),x70781),x70782))+~P24(f328(f328(f245(a1),f2(a1)),f328(f328(f39(a1),x70782),x70781)))
% 81.29/80.92 [7107]P24(f328(f328(f244(a1),f2(a1)),x71071))+~P24(f328(f328(f245(a1),f2(a1)),x71072))+~P24(f328(f328(f244(a1),f2(a1)),f328(f328(f39(a1),x71071),x71072)))
% 81.29/80.92 [7108]P24(f328(f328(f245(a1),f2(a1)),x71081))+~P24(f328(f328(f244(a1),f2(a1)),x71082))+~P24(f328(f328(f245(a1),f2(a1)),f328(f328(f39(a1),x71082),x71081)))
% 81.29/80.92 [7552]~P24(f328(f62(x75522),f252(f885(x75522,a871))))+~P24(f328(f62(x75521),f252(f885(x75521,a871))))+P24(f328(f62(f883(x75521,x75522)),f252(f885(f883(x75521,x75522),a871))))
% 81.29/80.92 [7553]~P24(f328(f62(x75532),f252(f885(x75532,a871))))+~P24(f328(f62(x75531),f252(f885(x75531,a871))))+P24(f328(f62(f884(x75531,x75532)),f252(f885(f884(x75531,x75532),a871))))
% 81.29/80.92 [7622]~P24(f328(f328(f245(a877),f328(a118,f2(a877))),x76221))+~P24(f328(f328(f245(a877),f328(a118,f2(a877))),x76222))+P24(f328(f328(f245(a877),x76221),f328(f328(f82(a877),x76222),x76221)))
% 81.29/80.92 [7623]~P24(f328(f328(f245(a877),f328(a118,f2(a877))),x76231))+~P24(f328(f328(f245(a877),f328(a118,f2(a877))),x76232))+P24(f328(f328(f245(a877),x76231),f328(f328(f82(a877),x76231),x76232)))
% 81.29/80.92 [7657]E(f328(f38(x76571),f252(f885(x76571,a871))),f328(a118,f2(a877)))+P24(f328(f62(x76572),f252(f885(x76572,a871))))+~P24(f328(f62(f885(x76572,x76571)),f252(f885(f885(x76572,x76571),a871))))
% 81.29/80.92 [7784]~P24(f328(f328(f244(a877),f328(a118,f2(a877))),x77841))+~P24(f328(f328(f244(a877),f328(a118,f2(a877))),x77842))+P24(f328(f328(f244(a877),f328(a118,f2(a877))),f328(f328(f82(a877),x77841),x77842)))
% 81.29/80.92 [7785]~P24(f328(f328(f245(a877),f328(a118,f2(a877))),x77852))+~P24(f328(f328(f245(a877),f328(a118,f2(a877))),x77851))+P24(f328(f328(f245(a877),f328(a118,f2(a877))),f328(f328(f82(a877),x77851),x77852)))
% 81.29/80.92 [8479]E(x84791,f119(x84792))+~P24(f328(f136(x84792),x84791))+E(f176(x84792,f328(f328(f8(a871,a871,x84792),a323),f328(f328(f7(x84792,x84792,a871),a325),f143(x84792,x84791))),x84791),f120(x84792,x84791))
% 81.29/80.92 [8574]~P40(x85742)+~P40(x85741)+E(f328(f307(a877,a1,f106(a1)),f328(f328(f116(f885(a877,a871)),f328(f307(a1,a877,a110),x85741)),f328(f307(a1,a877,a110),x85742))),f328(f328(f116(f885(a1,a871)),x85741),x85742))
% 81.29/80.92 [8575]~P40(x85752)+~P40(x85751)+E(f328(f307(a877,a1,f106(a1)),f328(f328(f107(f885(a877,a871)),f328(f307(a1,a877,a110),x85751)),f328(f307(a1,a877,a110),x85752))),f328(f328(f107(f885(a1,a871)),x85751),x85752))
% 81.29/80.92 [9228]~P96(x92281)+~E(f328(f109(x92281),x92282),f79(x92281))+P31(x92281,f328(f109(x92281),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f80(a1),x92282))))
% 81.29/80.92 [9461]~P96(x94611)+E(f328(f109(x94611),x94612),f79(x94611))+~P31(x94611,f328(f109(x94611),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f80(a1),x94612))))
% 81.29/80.92 [10189]E(x101891,f2(a1))+E(x101892,f2(a1))+E(f328(f268(a1,a1,a1,a1,f35(a1),f328(f82(a1),f83(a1,x101892))),f328(f328(f328(f102(f884(a1,a1)),f328(f328(a325,f83(a1,x101891)),f83(a1,x101892))),f53(x101891,x101892)),f328(f328(f267(a1,a1,f884(a1,a1)),f328(f328(f18(a1,f885(a1,f884(a1,a1)),f885(a1,f884(a1,a1))),f328(f328(f8(f885(a1,f885(f884(a1,a1),f884(a1,a1))),f885(f885(a1,f884(a1,a1)),f885(a1,f884(a1,a1))),a1),f18(a1,f884(a1,a1),f884(a1,a1))),f328(f328(f8(f884(a1,a1),f885(a1,f885(f884(a1,a1),f884(a1,a1))),a1),f328(f7(a1,f884(a1,a1),f885(f884(a1,a1),f884(a1,a1))),f328(f328(f8(a871,f885(f884(a1,a1),f885(f884(a1,a1),f884(a1,a1))),a1),f102(f884(a1,a1))),f328(f328(f7(a1,a1,a871),a325),f2(a1))))),f328(f328(f7(a1,a1,f884(a1,a1)),f328(f328(f8(a1,f885(a1,f884(a1,a1)),a1),f257(a1,a1)),f80(a1))),f2(a1))))),f328(f328(f7(a1,f885(a1,a1),f885(a1,f884(a1,a1))),f328(f328(f8(f885(a1,f884(a1,a1)),f885(f885(a1,a1),f885(a1,f884(a1,a1))),a1),f8(a1,f884(a1,a1),a1)),f328(f328(f8(a1,f885(a1,f884(a1,a1)),a1),f257(a1,a1)),f328(f328(f7(a1,a1,a1),f328(f328(f8(a1,f885(a1,a1),a1),f22(a1)),f80(a1))),f79(a1))))),f328(f22(a1),f328(f76(a1),x101892))))),f53(x101891,x101892)))),f46(x101891,x101892))
% 81.29/80.92 [10190]E(x101901,f2(a1))+E(x101902,f2(a1))+E(f328(f268(a1,a1,a1,a1,f35(a1),f328(f82(a1),f83(a1,x101902))),f328(f328(f328(f102(f884(a1,a1)),f328(f328(a327,f328(f328(a326,f328(f328(f245(a1),f2(a1)),x101902)),f328(f328(f244(a1),f2(a1)),x101901))),f328(f328(a326,f328(f328(f245(a1),x101902),f2(a1))),f328(f328(f245(a1),x101901),f2(a1))))),f53(x101901,x101902)),f328(f328(f267(a1,a1,f884(a1,a1)),f328(f328(f18(a1,f885(a1,f884(a1,a1)),f885(a1,f884(a1,a1))),f328(f328(f8(f885(a1,f885(f884(a1,a1),f884(a1,a1))),f885(f885(a1,f884(a1,a1)),f885(a1,f884(a1,a1))),a1),f18(a1,f884(a1,a1),f884(a1,a1))),f328(f328(f8(f884(a1,a1),f885(a1,f885(f884(a1,a1),f884(a1,a1))),a1),f328(f7(a1,f884(a1,a1),f885(f884(a1,a1),f884(a1,a1))),f328(f328(f8(a871,f885(f884(a1,a1),f885(f884(a1,a1),f884(a1,a1))),a1),f102(f884(a1,a1))),f328(f328(f7(a1,a1,a871),a325),f2(a1))))),f328(f328(f7(a1,a1,f884(a1,a1)),f328(f328(f8(a1,f885(a1,f884(a1,a1)),a1),f257(a1,a1)),f80(a1))),f2(a1))))),f328(f328(f7(a1,f885(a1,a1),f885(a1,f884(a1,a1))),f328(f328(f8(f885(a1,f884(a1,a1)),f885(f885(a1,a1),f885(a1,f884(a1,a1))),a1),f8(a1,f884(a1,a1),a1)),f328(f328(f8(a1,f885(a1,f884(a1,a1)),a1),f257(a1,a1)),f328(f328(f7(a1,a1,a1),f328(f328(f8(a1,f885(a1,a1),a1),f22(a1)),f80(a1))),f79(a1))))),f328(f22(a1),f328(f76(a1),x101902))))),f53(x101901,x101902)))),f46(x101901,x101902))
% 81.29/80.92 [10191]~P1(a5000)+P20(a872,x101911,f328(f328(f306(f876(a872)),f328(a94,x101912)),f193(f885(f876(a872),a871))))+~P20(a872,x101911,f328(f328(f306(f876(a872)),f328(f328(f328(f93(a872),f328(f328(f8(f885(a872,f885(a872,a871)),f885(a872,a871),a872),f328(f8(f885(a872,a871),a871,a872),f89(a872))),f328(f328(f8(f885(a872,a871),f885(a872,f885(a872,a871)),a872),f328(f7(a872,f885(a872,a871),f885(a872,a871)),f328(f328(f8(f885(a872,f885(a871,a871)),f885(f885(a872,a871),f885(a872,a871)),a872),f18(a872,a871,a871)),f328(f328(f8(f885(a872,a871),f885(a872,f885(a871,a871)),a872),f328(f8(a871,f885(a871,a871),a872),a331)),f200(x101912))))),a325))),x101912),a325)),f193(f885(f876(a872),a871))))
% 81.29/80.92 [5702]~P111(x57021)+~P96(x57021)+E(f328(f76(x57021),f328(f328(f258(x57021),f328(f109(x57021),a103)),x57022)),f79(x57021))
% 81.29/80.92 [6192]~P137(x61921)+~P24(f328(f328(f245(a1),x61922),f2(a1)))+E(f328(f80(x61921),f328(f106(x61921),f328(a110,f328(f80(a1),x61922)))),f328(f108(x61921),x61922))
% 81.29/80.92 [6394]P24(f328(f328(f244(a105),x63941),f79(a105)))+E(f328(f328(f81(a105),f79(a105)),f276(x63941,f328(f328(f39(a105),x63942),x63941))),f276(x63941,x63942))+P24(f328(f328(f245(a105),x63942),x63941))
% 81.29/80.92 [6993]~P93(x69931)+~P24(f328(f328(f330(x69931),x69932),f115(x69931)))+~E(f328(f328(f81(x69931),f328(f328(f81(x69931),f79(x69931)),x69932)),x69932),f2(x69931))
% 81.29/80.92 [7109]~P24(f328(f328(f244(a1),x71092),f2(a1)))+~P24(f328(f328(f245(a1),x71091),f2(a1)))+E(f328(f256(a1,a1),f328(a51,f47(f328(f80(a1),x71091),f328(f80(a1),x71092)))),f328(f328(f39(a1),x71091),x71092))
% 81.29/80.92 [7126]~P24(f328(f328(f244(a1),x71262),f2(a1)))+~P24(f328(f328(f245(a1),x71261),f2(a1)))+E(f328(f266(a1,a1),f328(a51,f47(f328(f80(a1),x71261),f328(f80(a1),x71262)))),f45(a1,x71261,x71262))
% 81.29/80.92 [7132]~P24(f328(f328(f245(a1),x71322),f2(a1)))+E(f328(f256(a1,a1),f328(a51,f50(f328(f80(a1),x71321),f328(f80(a1),x71322)))),f328(f328(f39(a1),x71321),x71322))+~P24(f328(f328(f245(a1),f2(a1)),x71321))
% 81.29/80.92 [7150]~P24(f328(f328(f245(a1),x71502),f2(a1)))+E(f328(f266(a1,a1),f328(a51,f50(f328(f80(a1),x71501),f328(f80(a1),x71502)))),f45(a1,x71501,x71502))+~P24(f328(f328(f245(a1),f2(a1)),x71501))
% 81.29/80.92 [7203]E(f328(f328(f39(a1),f328(f328(f258(a1),x72031),x72032)),x72031),f328(f328(f258(a1),x72031),f328(f328(f22(a877),x72032),f328(a118,f2(a877)))))+~P24(f328(f328(f245(a877),f2(a877)),x72032))+~P24(f328(f328(f245(a1),f2(a1)),x72031))
% 81.29/80.92 [7296]~P24(f328(f328(f245(a877),f2(a877)),x72961))+~P24(f328(f328(f245(a877),f2(a877)),x72962))+P24(f328(f328(f245(a877),f328(f328(f22(a877),x72961),x72962)),x72961))
% 81.29/80.92 [7297]~P24(f328(f328(f245(a877),f2(a877)),x72971))+~P24(f328(f328(f245(a877),f79(a877)),x72972))+P24(f328(f328(f245(a877),f328(f328(f39(a877),x72971),x72972)),x72971))
% 81.29/80.92 [7298]~P24(f328(f328(f245(a1),f2(a1)),x72981))+~P24(f328(f328(f245(a1),f79(a1)),x72982))+P24(f328(f328(f245(a1),f328(f328(f39(a1),x72981),x72982)),x72981))
% 81.29/80.92 [7447]E(x74471,f2(a877))+~E(x74472,f2(a1))+~P24(f328(f328(f245(a1),f2(a1)),f328(f328(f258(a1),f328(f76(a1),x74472)),x74471)))
% 81.29/80.92 [7862]~E(x78622,f119(f878(x78621)))+E(f328(f194(f878(f878(x78621))),f179(x78621,x78622)),f2(a877))+~P29(a877,f328(f168(a877),f328(f328(f153(f878(x78621),a877),f194(f878(x78621))),x78622)))
% 81.29/80.92 [8115]P24(f328(x81151,x81152))+~P24(f328(x81151,f328(a112,f713(x81151,x81152))))+~P24(f328(f328(f330(f885(f884(a877,a877),a871)),x81152),a104))
% 81.29/80.92 [8134]E(x81341,f119(f878(x81342)))+E(f328(f194(f878(x81342)),f328(f328(f164(f878(x81342)),x81341),f2(a877))),f328(f194(f878(f878(x81342))),f179(x81342,x81341)))+~P29(a877,f328(f168(a877),f328(f328(f153(f878(x81342),a877),f194(f878(x81342))),x81341)))
% 81.29/80.92 [8837]~P24(f328(f62(x88371),f328(f249(x88371),x88372)))+~P24(f328(f62(x88371),f252(f885(x88371,a871))))+P24(f328(f62(x88371),f328(f249(x88371),f328(f328(f8(a871,a871,x88371),a323),x88372))))
% 81.29/80.92 [8899]E(f328(f328(f257(a877,a877),f328(a118,f328(f328(f39(a877),f328(f328(f22(a877),x88991),x88992)),x88992))),f45(a877,f328(f328(f22(a877),x88991),x88992),x88992)),f86(f884(a877,a877),f48(x88991,x88992)))+~P24(f328(f328(f245(a877),f2(a877)),x88992))+~P24(f328(f328(f244(a877),x88992),x88991))
% 81.29/80.92 [9191]~P24(f328(f62(x91911),f328(f249(x91911),x91912)))+P24(f328(f62(x91911),f252(f885(x91911,a871))))+~P24(f328(f62(x91911),f328(f249(x91911),f328(f328(f8(a871,a871,x91911),a323),x91912))))
% 81.29/80.92 [9912]P22(x99121,x99122)+~P38(x99121,f328(f256(f885(f884(x99121,x99121),a871),f885(f884(x99121,x99121),a871)),x99122))+~P24(f328(f328(f244(f885(f884(x99121,x99121),a871)),f328(f328(f285(x99121,x99121,x99121),f328(f256(f885(f884(x99121,x99121),a871),f885(f884(x99121,x99121),a871)),x99122)),f328(f266(f885(f884(x99121,x99121),a871),f885(f884(x99121,x99121),a871)),x99122))),f328(f256(f885(f884(x99121,x99121),a871),f885(f884(x99121,x99121),a871)),x99122)))
% 81.29/80.92 [7229]~P24(f328(f328(f245(a877),f2(a877)),x72292))+P24(f328(f328(f245(a877),x72291),x72292))+E(f328(a118,f328(f328(f39(a877),f328(f328(f22(a877),x72291),x72292)),x72292)),f328(f328(f39(a877),x72291),x72292))
% 81.29/80.92 [7366]~P24(f328(f328(f245(a877),f2(a877)),x73662))+~P24(f328(f328(f244(a877),x73662),x73661))+E(f328(a118,f328(f328(f39(a877),f328(f328(f22(a877),x73661),x73662)),x73662)),f328(f328(f39(a877),x73661),x73662))
% 81.29/80.92 [8344]~P96(x83441)+~P93(x83441)+~P31(x83441,f328(f109(x83441),f328(f328(f22(a1),f328(f328(f81(a1),x83442),x83442)),a103)))
% 81.29/80.92 [9098]E(x90981,f2(a877))+E(f328(f328(f267(a877,a877,f884(a877,a877)),f328(f328(f8(a877,f885(a877,f884(a877,a877)),a877),f257(a877,a877)),a118)),f86(f884(a877,a877),f48(f328(f328(f22(a877),x90982),x90981),x90981))),f86(f884(a877,a877),f48(x90982,x90981)))+P24(f328(f328(f245(a877),x90982),x90981))
% 81.29/80.92 [9524]P24(f328(x95242,f799(x95242,x95241)))+P24(f328(x95241,f799(x95242,x95241)))+E(f328(f249(a1),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f244(a1),f2(a1)))),x95241)),f328(f249(a1),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f244(a1),f2(a1)))),x95242)))
% 81.29/80.92 [9528]~P24(f328(x95282,f799(x95282,x95281)))+~P24(f328(x95281,f799(x95282,x95281)))+E(f328(f249(a1),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f244(a1),f2(a1)))),x95281)),f328(f249(a1),f328(f328(f18(a1,a871,a871),f328(f328(f8(a871,f885(a871,a871),a1),a326),f328(f244(a1),f2(a1)))),x95282)))
% 81.29/80.92 [7580]~P96(x75801)+~P62(x75801)+E(f328(f328(f286(x75801),x75802),f328(f109(x75801),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))),x75802)
% 81.29/80.92 [9833]~P24(f328(f62(a874),x98332))+P20(a872,x98331,f328(f307(a874,f876(a872),f328(f328(f8(a873,f876(a872),a874),a94),a26)),x98332))+~P20(a872,f328(f328(f116(f885(f876(a872),a871)),x98331),f328(f307(a874,f876(a872),f328(f328(f8(a873,f876(a872),a874),a94),a26)),x98332)),f328(f307(a874,f876(a872),f328(f328(f8(a873,f876(a872),a874),a94),f328(f328(f8(f881(a873),a873,a874),f240(a873)),a28))),x98332))
% 81.29/80.92 [9227]~P96(x92271)+~E(f328(f109(x92271),x92272),f79(x92271))+P31(x92271,f328(f109(x92271),f328(f328(f81(a1),x92272),f328(f80(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))
% 81.29/80.92 [9404]~P139(x94041)+~E(x94042,f79(x94041))+E(f328(f328(f258(x94041),x94042),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f79(x94041))
% 81.29/80.92 [9405]~P139(x94051)+~E(x94052,f2(x94051))+E(f328(f328(f258(x94051),x94052),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f2(x94051))
% 81.29/80.92 [9418]~P139(x94181)+~E(x94182,f328(f80(x94181),f79(x94181)))+E(f328(f328(f258(x94181),x94182),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f79(x94181))
% 81.29/80.92 [9462]~P96(x94621)+E(f328(f109(x94621),x94622),f79(x94621))+~P31(x94621,f328(f109(x94621),f328(f328(f81(a1),x94622),f328(f80(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))
% 81.29/80.92 [9843]~P111(x98432)+E(x98431,f2(x98432))+P24(f328(f328(f245(x98432),f2(x98432)),f328(f328(f258(x98432),x98431),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))))
% 81.29/80.92 [9911]~P111(x99112)+~E(x99111,f2(x99112))+~P24(f328(f328(f245(x99112),f2(x99112)),f328(f328(f258(x99112),x99111),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))))
% 81.29/80.92 [9937]P24(f328(f328(f244(a1),x99371),f2(a1)))+P24(f328(f328(f245(a1),x99372),x99371))+E(f328(f44(x99371),f47(x99372,f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x99371))),f47(x99372,x99371))
% 81.29/80.92 [9938]~P24(f328(f328(f245(a1),f2(a1)),x99381))+P24(f328(f328(f245(a1),x99382),x99381))+E(f328(f44(x99381),f47(x99382,f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x99381))),f47(x99382,x99381))
% 81.29/80.92 [9939]P24(f328(f328(f244(a1),x99391),f2(a1)))+P24(f328(f328(f244(a1),f2(a1)),f328(f328(f81(a1),x99392),x99391)))+E(f328(f44(x99391),f50(x99392,f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x99391))),f50(x99392,x99391))
% 81.29/80.92 [9940]~P24(f328(f328(f245(a1),f2(a1)),x99401))+P24(f328(f328(f244(a1),f2(a1)),f328(f328(f81(a1),x99402),x99401)))+E(f328(f44(x99401),f50(x99402,f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x99401))),f50(x99402,x99401))
% 81.29/80.92 [9941]~P141(x99411)+~P24(f328(f328(f244(a1),f2(a1)),x99412))+E(f328(f106(x99411),f328(a110,f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x99412))),f328(f328(f81(x99411),f328(f106(x99411),f328(a110,x99412))),f328(f106(x99411),f328(a110,x99412))))
% 81.29/80.92 [5038]~P145(x50381,x50383,x50382)+~E(x50383,f2(a1))+P24(f328(x50381,x50382))
% 81.29/80.92 [5159]~P106(x51591)+~P29(x51591,x51593)+P29(x51591,f169(x51591,x51592,x51593))
% 81.29/80.92 [5160]~P106(x51601)+~P29(x51601,x51603)+P29(x51601,f176(x51601,x51602,x51603))
% 81.29/80.92 [4742]~P73(x47422)+~E(x47423,f328(f80(x47422),x47421))+E(x47421,f328(f80(x47422),x47423))
% 81.29/80.92 [4744]~P73(x47441)+~E(f328(f80(x47441),x47443),x47442)+E(f328(f80(x47441),x47442),x47443)
% 81.29/80.92 [4818]~P103(x48183)+E(x48181,x48182)+~E(f328(f106(x48183),x48181),f328(f106(x48183),x48182))
% 81.29/80.92 [4819]~P73(x48193)+E(x48191,x48192)+~E(f328(f80(x48193),x48191),f328(f80(x48193),x48192))
% 81.29/80.92 [4820]~P97(x48203)+E(x48201,x48202)+~E(f328(f80(x48203),x48201),f328(f80(x48203),x48202))
% 81.29/80.92 [4821]~P93(x48213)+E(x48211,x48212)+~E(f328(f108(x48213),x48211),f328(f108(x48213),x48212))
% 81.29/80.92 [4822]~P106(x48223)+E(x48221,x48222)+~E(f328(f297(x48223),x48221),f328(f297(x48223),x48222))
% 81.29/80.92 [4823]~P106(x48233)+E(x48231,x48232)+~E(f328(f300(x48233),x48231),f328(f300(x48233),x48232))
% 81.29/80.92 [4824]~P106(x48243)+E(x48241,x48242)+~E(f328(f250(x48243),x48241),f328(f250(x48243),x48242))
% 81.29/80.92 [4825]~P106(x48253)+E(x48251,x48252)+~E(f328(f251(x48253),x48251),f328(f251(x48253),x48252))
% 81.29/80.92 [4925]~P60(x49251)+~P24(f328(x49252,x49253))+P24(f328(f58(x49251),x49252))
% 81.29/80.92 [4958]~P60(x49583)+P24(f328(x49581,x49582))+~P24(f328(f59(x49583),x49581))
% 81.29/80.92 [5056]~P146(x50561,x50562,x50563)+~E(x50562,f2(a1))+P24(f328(x50561,f2(a1)))
% 81.29/80.92 [5093]~E(x50931,f2(a877))+E(f812(x50931,x50932,x50933),f193(f885(x50933,a871)))+~E(f328(f38(x50933),x50932),f328(a118,x50931))
% 81.29/80.92 [5248]~E(x52482,f2(a877))+E(f328(f256(a877,a877),x52481),f2(a877))+~P24(f328(f48(x52483,x52482),x52481))
% 81.29/80.92 [5295]P24(f328(x52951,x52952))+~E(x52953,f328(f106(a1),x52952))+~P24(f328(x52951,f328(a110,x52953)))
% 81.29/80.92 [5766]~E(x57663,f2(a877))+~P24(f328(x57661,x57662))+P24(f328(x57661,f45(a877,x57662,x57663)))
% 81.29/80.92 [5897]~P24(f328(a25,x58973))+~P24(f328(a25,x58972))+P24(f328(a25,f31(x58971,x58972,x58973)))
% 81.29/80.92 [5929]~P60(x59293)+~P7(x59293,x59291,x59292)+P24(f328(x59291,f657(x59292,x59291,x59293)))
% 81.29/80.92 [6176]~E(x61763,f2(a877))+P24(f328(x61761,x61762))+~P24(f328(x61761,f45(a877,x61762,x61763)))
% 81.29/80.92 [6323]~P60(x63231)+P8(x63231,x63232,x63233)+~P24(f328(x63232,f658(x63233,x63232,x63231)))
% 81.29/80.92 [6661]E(x66611,f193(f885(x66612,a871)))+~P24(f328(f62(x66612),x66611))+P24(f328(f63(x66612,x66613,x66611),f372(x66613,x66611,x66612)))
% 81.29/80.92 [6853]E(x68531,f2(a877))+~P24(f328(x68532,f374(x68531,x68533,x68532)))+P24(f328(x68532,f45(a877,x68533,x68531)))
% 81.29/80.92 [6958]~P27(x69581)+~P24(f328(f328(f244(x69581),x69582),f377(x69583,x69582,x69581)))+P24(f328(f328(f244(x69581),x69582),f41(x69581,x69583)))
% 81.29/80.92 [6960]~P24(f328(x69601,x69602))+~P24(f328(x69601,f374(x69603,x69602,x69601)))+P24(f328(x69601,f45(a877,x69602,x69603)))
% 81.29/80.92 [7064]E(x70641,f119(x70642))+E(f328(f328(f150(x70642),f625(x70643,x70641,x70642)),f633(x70643,x70641,x70642)),x70641)+~P24(f328(f328(f330(f878(x70642)),x70641),f160(x70642,x70643)))
% 81.29/80.92 [7095]~P137(x70951)+~P24(f328(f328(f330(x70951),x70952),f115(x70951)))+P24(f328(f328(f330(x70951),f328(f328(f258(x70951),x70952),x70953)),f115(x70951)))
% 81.29/80.92 [7416]P38(x74161,x74162)+~P24(f328(f328(f330(x74161),x74163),f766(x74162,x74161)))+P24(f328(f328(f330(x74161),f796(x74162,x74161,x74163)),f766(x74162,x74161)))
% 81.29/80.92 [7683]E(x76831,f119(x76832))+~P24(f328(f328(f330(f878(x76832)),x76831),f160(x76832,x76833)))+P24(f328(f328(f330(f878(x76832)),f633(x76833,x76831,x76832)),f160(x76832,x76833)))
% 81.29/80.92 [7736]E(x77361,f2(a877))+E(f328(f328(f81(a877),f328(f328(f82(a877),x77361),f375(x77361,x77362,x77363))),f374(x77361,x77362,x77363)),x77362)+P24(f328(x77363,f45(a877,x77362,x77361)))
% 81.29/80.92 [7779]~P24(f328(x77793,x77792))+E(f328(f328(f81(a877),f328(f328(f82(a877),x77791),f375(x77791,x77792,x77793))),f374(x77791,x77792,x77793)),x77792)+P24(f328(x77793,f45(a877,x77792,x77791)))
% 81.29/80.92 [7918]P24(f328(f328(f245(a1),x79181),f359(x79182,x79183,x79181)))+P24(f328(f328(x79183,f328(f328(f39(a1),x79182),x79181)),f45(a1,x79182,x79181)))+~P24(f328(f328(f245(a1),x79181),f2(a1)))
% 81.29/80.92 [8196]P24(f328(f328(x81962,f328(f328(f39(a1),x81961),x81963)),f45(a1,x81961,x81963)))+~P24(f328(f328(f245(a1),x81963),f2(a1)))+P24(f328(f328(f244(a1),f359(x81961,x81962,x81963)),f2(a1)))
% 81.29/80.92 [8377]E(f328(f328(f81(a1),f328(f328(f82(a1),x83771),f360(x83772,x83773,x83771))),f359(x83772,x83773,x83771)),x83772)+P24(f328(f328(x83773,f328(f328(f39(a1),x83772),x83771)),f45(a1,x83772,x83771)))+~P24(f328(f328(f245(a1),x83771),f2(a1)))
% 81.29/80.92 [8620]~P24(f328(f328(x86201,f360(x86202,x86201,x86203)),f359(x86202,x86201,x86203)))+P24(f328(f328(x86201,f328(f328(f39(a1),x86202),x86203)),f45(a1,x86202,x86203)))+~P24(f328(f328(f245(a1),x86203),f2(a1)))
% 81.29/80.92 [8847]~P106(x88471)+~P29(x88471,x88473)+P29(x88471,f148(x88471,x88471,f5(x88471),x88472,x88473))
% 81.29/80.92 [9354]~P123(x93542)+E(x93541,f2(x93542))+~P24(f328(f328(f244(x93542),f328(f328(f81(x93542),f328(f328(f82(x93542),x93543),x93543)),f328(f328(f82(x93542),x93541),x93541))),f2(x93542)))
% 81.29/80.92 [9355]~P123(x93552)+E(x93551,f2(x93552))+~P24(f328(f328(f244(x93552),f328(f328(f81(x93552),f328(f328(f82(x93552),x93551),x93551)),f328(f328(f82(x93552),x93553),x93553))),f2(x93552)))
% 81.29/80.92 [10130]~P111(x101301)+~P24(f328(f328(f245(x101301),x101302),f2(x101301)))+P24(f328(f328(f245(x101301),f328(f328(f258(x101301),x101302),f328(a118,f328(f328(f82(a877),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x101303)))),f2(x101301)))
% 81.29/80.92 [10139]~P111(x101392)+E(x101391,f2(x101392))+~P24(f328(f328(f244(x101392),f328(f328(f81(x101392),f328(f328(f258(x101392),x101393),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x101392),x101391),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))),f2(x101392)))
% 81.29/80.92 [10140]~P111(x101402)+E(x101401,f2(x101402))+~P24(f328(f328(f244(x101402),f328(f328(f81(x101402),f328(f328(f258(x101402),x101401),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x101402),x101403),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))),f2(x101402)))
% 81.29/80.92 [4774]~E(x47742,x47743)+~P67(x47741)+E(f328(f328(f22(x47741),x47742),x47743),f2(x47741))
% 81.29/80.92 [4775]~E(x47752,x47753)+~P73(x47751)+E(f328(f328(f22(x47751),x47752),x47753),f2(x47751))
% 81.29/80.92 [4788]~P143(x47881)+~E(x47883,f2(x47881))+E(f328(f328(f81(x47881),x47882),x47883),x47882)
% 81.29/80.92 [4805]~P138(x48051)+~E(x48053,f2(x48051))+E(f328(f328(f82(x48051),x48052),x48053),f2(x48051))
% 81.29/80.92 [4806]~P138(x48061)+~E(x48062,f2(x48061))+E(f328(f328(f82(x48061),x48062),x48063),f2(x48061))
% 81.29/80.92 [4827]~E(x48273,f119(x48271))+~E(x48272,f119(x48271))+E(f328(f328(f127(x48271),x48272),x48273),f119(x48271))
% 81.29/80.92 [4915]~P143(x49152)+E(x49151,f2(x49152))+~E(f328(f328(f81(x49152),x49153),x49151),x49153)
% 81.29/80.92 [4916]~P73(x49161)+~E(x49162,f328(f80(x49161),x49163))+E(f328(f328(f81(x49161),x49162),x49163),f2(x49161))
% 81.29/80.92 [4923]E(x49231,f119(x49232))+E(x49233,f2(a877))+~E(f328(f328(f174(x49232),x49233),x49231),f119(x49232))
% 81.29/80.92 [4929]~P67(x49293)+E(x49291,x49292)+~E(f328(f328(f22(x49293),x49291),x49292),f2(x49293))
% 81.29/80.92 [4930]~P73(x49303)+E(x49301,x49302)+~E(f328(f328(f22(x49303),x49301),x49302),f2(x49303))
% 81.29/80.92 [4939]~P139(x49392)+E(x49391,f2(x49392))+~E(f328(f328(f258(x49392),x49391),x49393),f2(x49392))
% 81.29/80.92 [4940]~P79(x49402)+E(x49401,f193(x49402))+~E(f328(f328(f116(x49402),x49403),x49401),f193(x49402))
% 81.29/80.92 [4941]~P79(x49412)+E(x49411,f193(x49412))+~E(f328(f328(f116(x49412),x49411),x49413),f193(x49412))
% 81.29/80.92 [4942]~P101(x49422)+E(x49421,f252(x49422))+~E(f328(f328(f107(x49422),x49423),x49421),f252(x49422))
% 81.29/80.92 [4943]~P101(x49432)+E(x49431,f252(x49432))+~E(f328(f328(f107(x49432),x49431),x49433),f252(x49432))
% 81.29/80.92 [5009]~P73(x50092)+E(x50091,f328(f80(x50092),x50093))+~E(f328(f328(f81(x50092),x50091),x50093),f2(x50092))
% 81.29/80.92 [5010]~P73(x50101)+E(f328(f80(x50101),x50102),x50103)+~E(f328(f328(f81(x50101),x50102),x50103),f2(x50101))
% 81.29/80.92 [5012]~E(x50122,x50123)+~P105(x50121)+P24(f328(f328(f244(x50121),x50122),x50123))
% 81.29/80.92 [5014]~E(x50142,x50143)+~P108(x50141)+P24(f328(f328(f244(x50141),x50142),x50143))
% 81.29/80.92 [5015]~E(x50152,x50153)+~P95(x50151)+P24(f328(f328(f92(x50151),x50152),x50153))
% 81.29/80.92 [5109]~P119(x51091)+~E(x51092,f328(f80(x51091),x51093))+E(f328(f328(f82(x51091),x51092),x51092),f328(f328(f82(x51091),x51093),x51093))
% 81.29/80.92 [5117]~P106(x51171)+~P29(x51171,x51173)+P29(x51171,f328(f328(f174(x51171),x51172),x51173))
% 81.29/80.92 [5118]~P106(x51181)+~P29(x51181,x51183)+P29(x51181,f328(f328(f137(x51181),x51182),x51183))
% 81.29/80.92 [5157]E(x51571,x51572)+E(x51573,f2(a877))+~E(f328(f328(f82(a877),x51573),x51571),f328(f328(f82(a877),x51573),x51572))
% 81.29/80.92 [5158]E(x51581,x51582)+E(x51583,f2(a877))+~E(f328(f328(f82(a877),x51581),x51583),f328(f328(f82(a877),x51582),x51583))
% 81.29/80.92 [5239]~E(x52392,x52393)+~P108(x52391)+E(f299(x52391,x52392,x52393),f328(f328(f306(x52391),x52392),f193(f885(x52391,a871))))
% 81.29/80.92 [5283]E(x52831,x52832)+~P95(x52833)+~P24(f328(f328(f92(x52833),x52831),x52832))
% 81.29/80.92 [5293]~E(x52931,x52932)+~P106(x52933)+~P24(f328(f328(f245(x52933),x52931),x52932))
% 81.29/80.92 [5294]~E(x52941,x52942)+~P108(x52943)+~P24(f328(f328(f245(x52943),x52941),x52942))
% 81.29/80.92 [5304]~P108(x53041)+E(f328(f298(x53041,x53042),x53043),f193(f885(x53041,a871)))+P24(f328(f328(f245(x53041),x53042),x53043))
% 81.29/80.92 [5352]~P108(x53521)+E(f301(x53521,x53522,x53523),f193(f885(x53521,a871)))+P24(f328(f328(f245(x53521),x53522),x53523))
% 81.29/80.92 [5353]~P108(x53531)+E(f299(x53531,x53532,x53533),f193(f885(x53531,a871)))+P24(f328(f328(f244(x53531),x53532),x53533))
% 81.29/80.92 [5354]~P108(x53541)+E(f193(f885(x53541,a871)),f301(x53541,x53542,x53543))+P24(f328(f328(f245(x53541),x53542),x53543))
% 81.29/80.92 [5355]~P108(x53551)+E(f193(f885(x53551,a871)),f299(x53551,x53552,x53553))+P24(f328(f328(f244(x53551),x53552),x53553))
% 81.29/80.92 [5363]~P65(x53631)+~E(f328(f328(f116(x53631),x53632),x53633),x53633)+P24(f328(f328(f244(x53631),x53632),x53633))
% 81.29/80.92 [5364]~P102(x53641)+~E(f328(f328(f107(x53641),x53642),x53643),x53642)+P24(f328(f328(f244(x53641),x53642),x53643))
% 81.29/80.92 [5365]~P106(x53651)+~E(f328(f328(f242(x53651),x53652),x53653),x53652)+P24(f328(f328(f244(x53651),x53652),x53653))
% 81.29/80.92 [5366]~P106(x53661)+~E(f328(f328(f243(x53661),x53662),x53663),x53663)+P24(f328(f328(f244(x53661),x53662),x53663))
% 81.29/80.92 [5386]~P106(x53861)+P29(x53861,x53862)+~P29(x53861,f328(f328(f150(x53861),x53863),x53862))
% 81.29/80.92 [5387]~P106(x53871)+P29(x53871,x53872)+~P29(x53871,f328(f328(f127(x53871),x53873),x53872))
% 81.29/80.92 [5388]~P106(x53881)+P29(x53881,x53882)+~P29(x53881,f328(f328(f127(x53881),x53882),x53883))
% 81.29/80.92 [5453]~P106(x54531)+P24(f328(f328(f244(x54531),x54533),x54532))+P24(f328(f328(f244(x54531),x54532),x54533))
% 81.29/80.92 [5458]~P106(x54581)+P24(f328(f328(f245(x54581),x54583),x54582))+P24(f328(f328(f244(x54581),x54582),x54583))
% 81.29/80.92 [5497]~P65(x54971)+E(f328(f328(f116(x54971),x54972),x54973),x54972)+~P24(f328(f328(f244(x54971),x54973),x54972))
% 81.29/80.92 [5499]~P65(x54991)+E(f328(f328(f116(x54991),x54992),x54993),x54993)+~P24(f328(f328(f244(x54991),x54992),x54993))
% 81.29/80.92 [5500]~P102(x55001)+E(f328(f328(f107(x55001),x55002),x55003),x55003)+~P24(f328(f328(f244(x55001),x55003),x55002))
% 81.29/80.92 [5502]~P102(x55021)+E(f328(f328(f107(x55021),x55022),x55023),x55022)+~P24(f328(f328(f244(x55021),x55022),x55023))
% 81.29/80.92 [5503]~P106(x55031)+E(f328(f328(f242(x55031),x55032),x55033),x55033)+~P24(f328(f328(f244(x55031),x55033),x55032))
% 81.29/80.92 [5505]~P106(x55051)+E(f328(f328(f242(x55051),x55052),x55053),x55052)+~P24(f328(f328(f244(x55051),x55052),x55053))
% 81.29/80.92 [5506]~P106(x55061)+E(f328(f328(f243(x55061),x55062),x55063),x55062)+~P24(f328(f328(f244(x55061),x55063),x55062))
% 81.29/80.92 [5508]~P106(x55081)+E(f328(f328(f243(x55081),x55082),x55083),x55083)+~P24(f328(f328(f244(x55081),x55082),x55083))
% 81.29/80.92 [5515]~P120(x55152)+E(x55151,f2(x55152))+E(f328(f328(f286(x55152),f328(f80(x55152),x55153)),f328(f80(x55152),x55151)),f328(f328(f286(x55152),x55153),x55151))
% 81.29/80.92 [5560]~P108(x55601)+E(f328(f298(x55601,x55602),x55603),f193(f885(x55601,a871)))+~P24(f328(f328(f244(x55601),x55603),x55602))
% 81.29/80.92 [5591]~P108(x55911)+E(f302(x55911,x55912,x55913),f193(f885(x55911,a871)))+~P24(f328(f328(f244(x55911),x55913),x55912))
% 81.29/80.92 [5592]~P108(x55921)+E(f301(x55921,x55922,x55923),f193(f885(x55921,a871)))+~P24(f328(f328(f244(x55921),x55923),x55922))
% 81.29/80.92 [5593]~P108(x55931)+E(f299(x55931,x55932,x55933),f193(f885(x55931,a871)))+~P24(f328(f328(f245(x55931),x55933),x55932))
% 81.29/80.92 [5644]~E(f328(f328(f22(a877),x56441),x56443),x56442)+E(x56441,f328(f328(f81(a877),x56442),x56443))+~P24(f328(f328(f244(a877),x56443),x56441))
% 81.29/80.92 [5645]~E(x56451,f328(f328(f81(a877),x56453),x56452))+E(f328(f328(f22(a877),x56451),x56452),x56453)+~P24(f328(f328(f244(a877),x56452),x56451))
% 81.29/80.92 [5691]~P24(f328(x56911,x56913))+P24(f328(x56911,f409(x56911,x56912)))+~P24(f328(f328(f244(a877),x56913),x56912))
% 81.29/80.92 [5692]~P24(f328(x56921,x56923))+P24(f328(x56921,f447(x56921,x56922)))+~P24(f328(f328(f245(a877),x56923),x56922))
% 81.29/80.92 [5700]~P108(x57001)+~E(f328(f298(x57001,x57002),x57003),f193(f885(x57001,a871)))+~P24(f328(f328(f245(x57001),x57002),x57003))
% 81.29/80.92 [5704]~P105(x57041)+~P24(f328(f328(f245(x57041),x57042),x57043))+P24(f328(f328(f244(x57041),x57042),x57043))
% 81.29/80.92 [5706]~P108(x57061)+~P24(f328(f328(f245(x57061),x57062),x57063))+P24(f328(f328(f244(x57061),x57062),x57063))
% 81.29/80.92 [5814]~P108(x58141)+~E(f301(x58141,x58142,x58143),f193(f885(x58141,a871)))+~P24(f328(f328(f245(x58141),x58142),x58143))
% 81.29/80.92 [5815]~P108(x58151)+~E(f299(x58151,x58152,x58153),f193(f885(x58151,a871)))+~P24(f328(f328(f244(x58151),x58152),x58153))
% 81.29/80.92 [5816]~P108(x58161)+~E(f193(f885(x58161,a871)),f301(x58161,x58162,x58163))+~P24(f328(f328(f245(x58161),x58162),x58163))
% 81.29/80.92 [5817]~P108(x58171)+~E(f193(f885(x58171,a871)),f299(x58171,x58172,x58173))+~P24(f328(f328(f244(x58171),x58172),x58173))
% 81.29/80.92 [5825]P24(f328(x58251,x58252))+~P24(f328(x58251,f428(x58251,x58253)))+~P24(f328(f328(f244(a877),x58252),x58253))
% 81.29/80.92 [5826]P24(f328(x58261,x58262))+~P24(f328(x58261,f456(x58261,x58263)))+~P24(f328(f328(f245(a877),x58262),x58263))
% 81.29/80.92 [5834]~E(x58341,f328(a118,x58343))+P24(f328(f328(f245(a877),x58341),f328(a118,x58342)))+~P24(f328(f328(f245(a877),x58343),x58342))
% 81.29/80.92 [5850]E(x58501,x58502)+~E(f328(f328(f82(a877),x58503),x58501),f328(f328(f82(a877),x58503),x58502))+~P24(f328(f328(f245(a877),f2(a877)),x58503))
% 81.29/80.92 [5908]E(f328(x59081,f821(x59081,x59082,x59083)),f79(a877))+~E(f328(f328(f6(x59083,a877),x59081),x59082),f79(a877))+~P24(f328(f62(x59083),x59082))
% 81.29/80.92 [5920]~P27(x59201)+P24(f328(f328(f244(x59201),x59202),f40(x59201,x59203)))+~P24(f328(f328(f330(x59201),x59202),x59203))
% 81.29/80.92 [5947]~P105(x59471)+~P24(f328(f328(f245(x59471),x59473),x59472))+~P24(f328(f328(f244(x59471),x59472),x59473))
% 81.29/80.92 [5951]~P105(x59511)+~P24(f328(f328(f245(x59511),x59513),x59512))+~P24(f328(f328(f245(x59511),x59512),x59513))
% 81.29/80.92 [5954]~P106(x59541)+~P24(f328(f328(f245(x59541),x59543),x59542))+~P24(f328(f328(f244(x59541),x59542),x59543))
% 81.29/80.92 [5955]~P106(x59551)+~P24(f328(f328(f245(x59551),x59553),x59552))+~P24(f328(f328(f245(x59551),x59552),x59553))
% 81.29/80.92 [5956]~P108(x59561)+~P24(f328(f328(f245(x59561),x59563),x59562))+~P24(f328(f328(f245(x59561),x59562),x59563))
% 81.29/80.92 [5985]~E(f328(x59852,f822(x59852,x59853,x59851)),f2(a877))+E(f328(f328(f6(x59851,a877),x59852),x59853),f2(a877))+~P24(f328(f62(x59851),x59853))
% 81.29/80.92 [5986]~E(f328(x59862,f335(x59862,x59863,x59861)),f79(a877))+E(f328(f328(f9(x59861,a877),x59862),x59863),f79(a877))+~P24(f328(f62(x59861),x59863))
% 81.29/80.92 [6001]~P107(x60011)+~P24(f328(f328(f245(x60011),x60013),x60012))+P24(f328(f328(f330(x60011),x60012),f328(f300(x60011),x60013)))
% 81.29/80.92 [6002]~P107(x60021)+~P24(f328(f328(f244(x60021),x60023),x60022))+P24(f328(f328(f330(x60021),x60022),f328(f251(x60021),x60023)))
% 81.29/80.92 [6003]~P107(x60031)+~P24(f328(f328(f244(x60031),x60032),x60033))+P24(f328(f328(f330(x60031),x60032),f328(f297(x60031),x60033)))
% 81.29/80.92 [6004]~P107(x60041)+~P24(f328(f328(f245(x60041),x60042),x60043))+P24(f328(f328(f330(x60041),x60042),f328(f250(x60041),x60043)))
% 81.29/80.92 [6016]E(f328(x60161,f824(x60161,x60162,x60163)),f328(a118,f2(a877)))+~E(f328(f328(f6(x60163,a877),x60161),x60162),f328(a118,f2(a877)))+~P24(f328(f62(x60163),x60162))
% 81.29/80.92 [6099]~P27(x60991)+~P24(f328(f328(f330(x60991),x60993),x60992))+P24(f328(f328(f244(x60991),f41(x60991,x60992)),x60993))
% 81.29/80.92 [6116]~P24(f328(f328(f244(a877),x61161),x61163))+P24(f328(f328(f244(a877),x61161),x61162))+~P24(f328(f328(f244(a877),x61163),x61162))
% 81.29/80.92 [6117]~P24(f328(f328(f244(a1),x61171),x61173))+P24(f328(f328(f244(a1),x61171),x61172))+~P24(f328(f328(f244(a1),x61173),x61172))
% 81.29/80.92 [6134]~P107(x61341)+~P24(f328(f328(f330(x61341),x61343),f328(f251(x61341),x61342)))+P24(f328(f328(f244(x61341),x61342),x61343))
% 81.29/80.92 [6135]~P107(x61351)+~P24(f328(f328(f330(x61351),x61352),f328(f297(x61351),x61353)))+P24(f328(f328(f244(x61351),x61352),x61353))
% 81.29/80.92 [6136]~P107(x61361)+~P24(f328(f328(f330(x61361),x61363),f328(f300(x61361),x61362)))+P24(f328(f328(f245(x61361),x61362),x61363))
% 81.29/80.92 [6137]~P107(x61371)+~P24(f328(f328(f330(x61371),x61372),f328(f250(x61371),x61373)))+P24(f328(f328(f245(x61371),x61372),x61373))
% 81.29/80.92 [6258]P24(f328(x62581,x62582))+~P24(f328(x62581,f600(x62581)))+~P24(f328(f328(f330(x62583),x62582),f252(f885(x62583,a871))))
% 81.29/80.92 [6359]~P63(x63591)+P24(f328(f328(f245(x63591),f2(x63591)),f356(x63593,x63592,x63591)))+P24(f328(f328(f244(x63591),x63592),x63593))
% 81.29/80.92 [6360]~P64(x63601)+P24(f328(f328(f245(x63601),f2(x63601)),f460(x63603,x63602,x63601)))+P24(f328(f328(f244(x63601),x63602),x63603))
% 81.29/80.92 [6427]~P80(x64271)+~P24(f328(f328(f244(x64271),x64273),f328(f80(x64271),x64272)))+P24(f328(f328(f244(x64271),x64272),f328(f80(x64271),x64273)))
% 81.29/80.92 [6429]~P80(x64291)+~P24(f328(f328(f245(x64291),x64293),f328(f80(x64291),x64292)))+P24(f328(f328(f245(x64291),x64292),f328(f80(x64291),x64293)))
% 81.29/80.92 [6441]~P24(f328(f328(f245(a877),x64411),x64413))+~P24(f328(f328(f245(a877),x64413),x64412))+P24(f328(f328(f245(a877),f328(a118,x64411)),x64412))
% 81.29/80.92 [6467]~P110(x64671)+P24(f328(f328(f244(x64671),f328(f106(x64671),x64672)),f328(f106(x64671),x64673)))+~P24(f328(f328(f244(a877),x64672),x64673))
% 81.29/80.92 [6468]~P111(x64681)+P24(f328(f328(f244(x64681),f328(f108(x64681),x64682)),f328(f108(x64681),x64683)))+~P24(f328(f328(f244(a1),x64682),x64683))
% 81.29/80.92 [6470]~P111(x64701)+P24(f328(f328(f245(x64701),f328(f108(x64701),x64702)),f328(f108(x64701),x64703)))+~P24(f328(f328(f245(a1),x64702),x64703))
% 81.29/80.92 [6471]~P110(x64711)+P24(f328(f328(f245(x64711),f328(f106(x64711),x64712)),f328(f106(x64711),x64713)))+~P24(f328(f328(f245(a877),x64712),x64713))
% 81.29/80.92 [6477]~P106(x64771)+E(f328(f328(f116(f885(x64771,a871)),f328(f250(x64771),x64772)),f328(f298(x64771,x64772),x64773)),f328(f250(x64771),x64773))+~P24(f328(f328(f244(x64771),x64772),x64773))
% 81.29/80.92 [6508]~P80(x65081)+~P24(f328(f328(f244(x65081),x65083),x65082))+P24(f328(f328(f244(x65081),f328(f80(x65081),x65082)),f328(f80(x65081),x65083)))
% 81.29/80.92 [6510]~P97(x65101)+~P24(f328(f328(f244(x65101),x65103),x65102))+P24(f328(f328(f244(x65101),f328(f80(x65101),x65102)),f328(f80(x65101),x65103)))
% 81.29/80.92 [6511]~P80(x65111)+~P24(f328(f328(f245(x65111),x65113),x65112))+P24(f328(f328(f245(x65111),f328(f80(x65111),x65112)),f328(f80(x65111),x65113)))
% 81.29/80.92 [6543]~P106(x65431)+E(f328(f328(f116(f885(x65431,a871)),f328(f297(x65431),x65432)),f302(x65431,x65432,x65433)),f328(f250(x65431),x65433))+~P24(f328(f328(f245(x65431),x65432),x65433))
% 81.29/80.92 [6544]~P106(x65441)+E(f328(f328(f116(f885(x65441,a871)),f328(f297(x65441),x65442)),f301(x65441,x65442,x65443)),f328(f297(x65441),x65443))+~P24(f328(f328(f244(x65441),x65442),x65443))
% 81.29/80.92 [6545]~P106(x65451)+E(f328(f328(f116(f885(x65451,a871)),f328(f250(x65451),x65452)),f299(x65451,x65452,x65453)),f328(f297(x65451),x65453))+~P24(f328(f328(f244(x65451),x65452),x65453))
% 81.29/80.92 [6580]~P106(x65801)+E(f328(f328(f116(f885(x65801,a871)),f328(f298(x65801,x65802),x65803)),f328(f251(x65801),x65803)),f328(f251(x65801),x65802))+~P24(f328(f328(f244(x65801),x65802),x65803))
% 81.29/80.92 [6736]~P106(x67361)+E(f328(f328(f116(f885(x67361,a871)),f302(x67361,x67362,x67363)),f328(f251(x67361),x67363)),f328(f300(x67361),x67362))+~P24(f328(f328(f245(x67361),x67362),x67363))
% 81.29/80.92 [6737]~P106(x67371)+E(f328(f328(f116(f885(x67371,a871)),f301(x67371,x67372,x67373)),f328(f300(x67371),x67373)),f328(f300(x67371),x67372))+~P24(f328(f328(f244(x67371),x67372),x67373))
% 81.29/80.92 [6738]~P106(x67381)+E(f328(f328(f116(f885(x67381,a871)),f299(x67381,x67382,x67383)),f328(f300(x67381),x67383)),f328(f251(x67381),x67382))+~P24(f328(f328(f244(x67381),x67382),x67383))
% 81.29/80.92 [6756]P24(f328(x67561,x67562))+~P24(f328(f328(f244(a877),x67562),x67563))+P24(f328(f328(f330(a877),f428(x67561,x67563)),f299(a877,f2(a877),x67563)))
% 81.29/80.92 [6790]E(x67901,x67902)+~E(f328(f328(f164(x67903),x67901),f568(x67903,x67902,x67901)),f328(f328(f164(x67903),x67902),f568(x67903,x67902,x67901)))+~E(f328(f194(f878(x67903)),x67901),f328(f194(f878(x67903)),x67902))
% 81.29/80.92 [6795]~E(x67953,f328(f328(f39(a877),x67951),x67952))+~P24(f328(f328(f245(a877),f2(a877)),x67952))+P24(f328(f328(f245(a877),x67951),f328(f328(f82(a877),x67952),f328(a118,x67953))))
% 81.29/80.92 [6812]~P24(f328(x68121,x68123))+~P24(f328(f328(f244(a877),x68123),x68122))+P24(f328(f328(f330(a877),f409(x68121,x68122)),f299(a877,f2(a877),x68122)))
% 81.29/80.92 [6850]~P24(f328(x68501,x68503))+P24(f328(x68501,f429(x68501,x68502)))+~P24(f328(f328(f330(a877),x68503),f299(a877,f2(a877),x68502)))
% 81.29/80.92 [6869]~P110(x68693)+~P24(f328(f328(f244(x68693),f328(f106(x68693),x68691)),f328(f106(x68693),x68692)))+P24(f328(f328(f244(a877),x68691),x68692))
% 81.29/80.92 [6870]~P111(x68703)+~P24(f328(f328(f244(x68703),f328(f108(x68703),x68701)),f328(f108(x68703),x68702)))+P24(f328(f328(f244(a1),x68701),x68702))
% 81.29/80.92 [6872]~P110(x68723)+~P24(f328(f328(f245(x68723),f328(f106(x68723),x68721)),f328(f106(x68723),x68722)))+P24(f328(f328(f245(a877),x68721),x68722))
% 81.29/80.92 [6873]~P111(x68733)+~P24(f328(f328(f245(x68733),f328(f108(x68733),x68731)),f328(f108(x68733),x68732)))+P24(f328(f328(f245(a1),x68731),x68732))
% 81.29/80.92 [6887]~P110(x68871)+~P24(f328(f328(f245(x68871),f79(x68871)),x68872))+P24(f328(f328(f245(x68871),f79(x68871)),f328(f328(f258(x68871),x68872),f328(a118,x68873))))
% 81.29/80.92 [6889]~P80(x68891)+~P24(f328(f328(f244(x68891),f328(f80(x68891),x68893)),f328(f80(x68891),x68892)))+P24(f328(f328(f244(x68891),x68892),x68893))
% 81.29/80.92 [6890]~P97(x68901)+~P24(f328(f328(f244(x68901),f328(f80(x68901),x68903)),f328(f80(x68901),x68902)))+P24(f328(f328(f244(x68901),x68902),x68903))
% 81.29/80.92 [6891]~P80(x68911)+~P24(f328(f328(f245(x68911),f328(f80(x68911),x68913)),f328(f80(x68911),x68912)))+P24(f328(f328(f245(x68911),x68912),x68913))
% 81.29/80.92 [6917]P24(f328(x69171,x69172))+~P24(f328(x69171,f430(x69171,x69173)))+~P24(f328(f328(f330(a877),x69172),f299(a877,f2(a877),x69173)))
% 81.29/80.92 [6936]~P63(x69361)+P24(f328(f328(f245(x69361),f356(x69363,x69362,x69361)),f79(x69361)))+P24(f328(f328(f244(x69361),x69362),x69363))
% 81.29/80.92 [6955]~E(f45(a877,x69553,x69552),f45(a877,x69551,x69552))+E(f328(f328(f81(a877),x69551),f328(f328(f82(a877),x69552),f376(x69551,x69552,x69553))),x69553)+~P24(f328(f328(f244(a877),x69551),x69553))
% 81.29/80.92 [6974]E(f328(x69741,f378(x69741,x69742,x69743)),f196(x69742))+~P24(f328(f62(x69743),f183(x69743,x69742,x69741)))+P24(f328(f62(x69743),f252(f885(x69743,a871))))
% 81.29/80.92 [7015]E(f328(f328(f6(x70151,a877),x70152),x70153),f2(a877))+~P24(f328(f62(x70151),x70153))+P24(f328(f328(f330(x70151),f822(x70152,x70153,x70151)),x70153))
% 81.29/80.92 [7016]E(f328(f328(f9(x70161,a877),x70162),x70163),f79(a877))+~P24(f328(f62(x70161),x70163))+P24(f328(f328(f330(x70161),f335(x70162,x70163,x70161)),x70163))
% 81.29/80.92 [7038]~P108(x70381)+~P24(f328(f328(f244(x70381),x70382),x70383))+P24(f328(f328(f244(f885(x70381,a871)),f328(f297(x70381),x70382)),f328(f297(x70381),x70383)))
% 81.29/80.92 [7039]~P106(x70391)+~P24(f328(f328(f244(x70391),x70393),x70392))+P24(f328(f328(f244(f885(x70391,a871)),f328(f300(x70391),x70392)),f328(f300(x70391),x70393)))
% 81.29/80.92 [7040]~P106(x70401)+~P24(f328(f328(f244(x70401),x70402),x70403))+P24(f328(f328(f244(f885(x70401,a871)),f328(f250(x70401),x70402)),f328(f250(x70401),x70403)))
% 81.29/80.92 [7041]~P108(x70411)+~P24(f328(f328(f244(x70411),x70413),x70412))+P24(f328(f328(f244(f885(x70411,a871)),f328(f251(x70411),x70412)),f328(f251(x70411),x70413)))
% 81.29/80.92 [7042]~P106(x70421)+~P24(f328(f328(f245(x70421),x70422),x70423))+P24(f328(f328(f245(f885(x70421,a871)),f328(f250(x70421),x70422)),f328(f250(x70421),x70423)))
% 81.29/80.92 [7050]~P27(x70501)+P24(f328(f328(f244(x70501),x70502),f41(x70501,x70503)))+P24(f328(f328(f330(x70501),f377(x70503,x70502,x70501)),x70503))
% 81.29/80.92 [7056]~P80(x70561)+P24(f328(f328(f244(x70561),f328(f328(f22(x70561),x70562),x70563)),f2(x70561)))+~P24(f328(f328(f244(x70561),x70562),x70563))
% 81.29/80.92 [7057]~P80(x70571)+P24(f328(f328(f245(x70571),f328(f328(f22(x70571),x70572),x70573)),f2(x70571)))+~P24(f328(f328(f245(x70571),x70572),x70573))
% 81.29/80.92 [7099]P24(f328(x70991,x70992))+P24(f328(f328(f244(a877),f430(x70991,x70993)),x70993))+~P24(f328(f328(f330(a877),x70992),f299(a877,f2(a877),x70993)))
% 81.29/80.92 [7139]~E(f328(f328(f6(x71391,a877),x71392),x71393),f79(a877))+~P24(f328(f62(x71391),x71393))+P24(f328(f328(f330(x71391),f821(x71392,x71393,x71391)),x71393))
% 81.29/80.92 [7140]~P24(f328(x71401,x71403))+P24(f328(f328(f244(a877),f429(x71401,x71402)),x71402))+~P24(f328(f328(f330(a877),x71403),f299(a877,f2(a877),x71402)))
% 81.29/80.92 [7180]~P27(x71801)+P24(f328(f328(f330(x71801),f684(x71803,x71802,x71801)),x71802))+P24(f328(f328(f244(x71801),f40(x71801,x71802)),x71803))
% 81.29/80.92 [7211]~E(f328(f328(f6(x72111,a877),x72112),x72113),f328(a118,f2(a877)))+~P24(f328(f62(x72111),x72113))+P24(f328(f328(f330(x72111),f824(x72112,x72113,x72111)),x72113))
% 81.29/80.92 [7222]E(x72221,f2(a877))+P24(f328(x72222,f45(a877,x72223,x72221)))+P24(f328(f328(f245(a877),f374(x72221,x72223,x72222)),x72221))
% 81.29/80.92 [7327]~P24(f328(x73271,x73272))+P24(f328(x73271,f45(a877,x73272,x73273)))+P24(f328(f328(f245(a877),f374(x73273,x73272,x73271)),x73273))
% 81.29/80.92 [7451]E(x74511,f119(x74512))+~P24(f328(f328(f330(f878(x74512)),x74511),f160(x74512,x74513)))+P24(f328(f328(f330(x74512),f625(x74513,x74511,x74512)),x74513))
% 81.29/80.92 [7473]~P106(x74731)+E(f328(f328(f116(f885(x74731,a871)),f328(f328(f306(x74731),x74732),f193(f885(x74731,a871)))),f302(x74731,x74732,x74733)),f328(f298(x74731,x74732),x74733))+~P24(f328(f328(f245(x74731),x74732),x74733))
% 81.29/80.92 [7496]~P106(x74961)+E(f328(f328(f116(f885(x74961,a871)),f328(f328(f306(x74961),x74962),f193(f885(x74961,a871)))),f301(x74961,x74962,x74963)),f299(x74961,x74962,x74963))+~P24(f328(f328(f244(x74961),x74962),x74963))
% 81.29/80.92 [7602]~P106(x76021)+P24(f328(f328(f244(x76021),x76022),x76023))+~P24(f328(f328(f244(f885(x76021,a871)),f328(f300(x76021),x76023)),f328(f300(x76021),x76022)))
% 81.29/80.92 [7603]~P108(x76031)+P24(f328(f328(f244(x76031),x76032),x76033))+~P24(f328(f328(f244(f885(x76031,a871)),f328(f251(x76031),x76033)),f328(f251(x76031),x76032)))
% 81.29/80.92 [7604]~P106(x76041)+P24(f328(f328(f244(x76041),x76042),x76043))+~P24(f328(f328(f244(f885(x76041,a871)),f328(f250(x76041),x76042)),f328(f250(x76041),x76043)))
% 81.29/80.92 [7605]~P108(x76051)+P24(f328(f328(f244(x76051),x76052),x76053))+~P24(f328(f328(f244(f885(x76051,a871)),f328(f297(x76051),x76052)),f328(f297(x76051),x76053)))
% 81.29/80.92 [7606]~P106(x76061)+P24(f328(f328(f245(x76061),x76062),x76063))+~P24(f328(f328(f245(f885(x76061,a871)),f328(f250(x76061),x76062)),f328(f250(x76061),x76063)))
% 81.29/80.92 [7629]~P80(x76291)+~P24(f328(f328(f244(x76291),f328(f328(f22(x76291),x76292),x76293)),f2(x76291)))+P24(f328(f328(f244(x76291),x76292),x76293))
% 81.29/80.92 [7630]~P80(x76301)+~P24(f328(f328(f245(x76301),f328(f328(f22(x76301),x76302),x76303)),f2(x76301)))+P24(f328(f328(f245(x76301),x76302),x76303))
% 81.29/80.92 [7786]E(x77861,f2(a877))+~E(f328(f141(a877,a877,f81(a877),x77862),x77863),f2(a877))+~P24(f328(f328(f330(a877),x77861),f328(f171(a877),x77863)))
% 81.29/80.92 [7790]~P27(x77901)+~P24(f328(f328(f244(x77901),f684(x77903,x77902,x77901)),x77903))+P24(f328(f328(f244(x77901),f40(x77901,x77902)),x77903))
% 81.29/80.92 [7944]P24(f328(f328(f244(a1),f2(a1)),f362(x79441,x79442,x79443)))+P24(f328(f328(x79442,f328(f328(f39(a1),x79441),x79443)),f45(a1,x79441,x79443)))+~P24(f328(f328(f245(a1),f2(a1)),x79443))
% 81.29/80.92 [8038]E(x80381,x80382)+~E(f328(f194(f878(x80383)),x80381),f328(f194(f878(x80383)),x80382))+~P24(f328(f328(f267(x80383,x80383,a871),a325),f605(x80383,x80381,x80382)))
% 81.29/80.92 [8106]~P38(x81062,x81063)+E(x81061,f193(f885(x81062,a871)))+~P24(f328(f328(f244(f885(x81062,a871)),x81061),f328(f282(x81062,x81062,x81063),x81061)))
% 81.29/80.92 [8136]~P64(x81361)+~P24(f328(f328(f244(x81361),x81362),f328(f328(f81(x81361),x81363),f460(x81363,x81362,x81361))))+P24(f328(f328(f244(x81361),x81362),x81363))
% 81.29/80.92 [8177]P48(x81771,x81772,x81773)+P24(f328(f328(f330(x81771),f612(x81773,x81772,x81771)),x81772))+P24(f328(f328(f330(f884(x81771,x81771)),f613(x81773,x81772,x81771)),x81773))
% 81.29/80.92 [8200]P24(f328(f328(x82002,f328(f328(f39(a1),x82001),x82003)),f45(a1,x82001,x82003)))+~P24(f328(f328(f245(a1),f2(a1)),x82003))+P24(f328(f328(f245(a1),f362(x82001,x82002,x82003)),x82003))
% 81.29/80.92 [8224]E(f328(f307(a877,a877,f328(f328(f7(a877,a877,a877),f22(a877)),x82241)),f328(f298(a877,x82242),x82243)),f193(f885(a877,a871)))+P24(f328(f328(f245(a877),x82241),x82243))+P24(f328(f328(f245(a877),x82242),x82243))
% 81.29/80.92 [8330]E(f328(f307(a877,a877,f328(f328(f7(a877,a877,a877),f22(a877)),x83301)),f328(f298(a877,x83302),x83303)),f328(f328(f306(a877),f2(a877)),f193(f885(a877,a871))))+P24(f328(f328(f245(a877),x83301),x83303))+~P24(f328(f328(f245(a877),x83302),x83303))
% 81.29/80.92 [8347]~P106(x83471)+E(f148(x83471,x83471,f5(x83471),x83472,x83473),x83473)+~P24(f328(f328(f330(x83471),x83472),f328(f171(x83471),x83473)))
% 81.29/80.92 [8361]P21(x83611,x83611,x83612,x83613)+~P24(f328(f62(x83611),x83613))+~P24(f328(f328(f244(f885(x83611,a871)),x83613),f328(f307(x83611,x83611,x83612),x83613)))
% 81.29/80.92 [8384]E(f328(f328(f81(a1),f328(f328(f82(a1),x83841),f363(x83842,x83843,x83841))),f362(x83842,x83843,x83841)),x83842)+P24(f328(f328(x83843,f328(f328(f39(a1),x83842),x83841)),f45(a1,x83842,x83841)))+~P24(f328(f328(f245(a1),f2(a1)),x83841))
% 81.29/80.92 [8626]~P24(f328(f328(x86261,f363(x86262,x86261,x86263)),f362(x86262,x86261,x86263)))+P24(f328(f328(x86261,f328(f328(f39(a1),x86262),x86263)),f45(a1,x86262,x86263)))+~P24(f328(f328(f245(a1),f2(a1)),x86263))
% 81.29/80.92 [9491]~P24(f328(f62(x94911),x94912))+~P24(f328(f328(f330(x94911),x94913),x94912))+P24(f328(f328(f245(a877),f328(f38(x94911),f328(f328(f22(f885(x94911,a871)),x94912),f328(f328(f306(x94911),x94913),f193(f885(x94911,a871)))))),f328(f38(x94911),x94912)))
% 81.29/80.92 [10090]P48(x100901,x100902,x100903)+~P24(f328(f328(f267(x100901,x100901,a871),f328(f328(f7(x100901,f885(x100901,a871),f885(x100901,a871)),f328(f328(f8(f885(a871,a871),f885(f885(x100901,a871),f885(x100901,a871)),x100901),f8(a871,a871,x100901)),f328(f328(f8(a871,f885(a871,a871),x100901),a326),f328(f328(f7(x100901,f885(x100901,a871),a871),f330(x100901)),x100902)))),f328(f328(f7(x100901,f885(x100901,a871),a871),f330(x100901)),x100902))),f613(x100903,x100902,x100901)))+P24(f328(f328(f330(x100901),f612(x100903,x100902,x100901)),x100902))
% 81.29/80.92 [5475]~P120(x54752)+E(x54751,f2(x54752))+E(f328(f328(f286(x54752),x54753),f328(f80(x54752),x54751)),f328(f80(x54752),f328(f328(f286(x54752),x54753),x54751)))
% 81.29/80.92 [5607]~E(x56073,f193(f885(x56071,a871)))+~E(x56072,f193(f885(x56071,a871)))+E(f328(f328(f116(f885(x56071,a871)),x56072),x56073),f193(f885(x56071,a871)))
% 81.29/80.92 [5665]~E(x56653,f2(a877))+~P24(f328(x56651,f2(a877)))+P24(f328(x56651,f328(f328(f39(a877),x56652),x56653)))
% 81.29/80.92 [5806]~P64(x58062)+E(x58061,f2(x58062))+E(f328(f328(f286(x58062),f328(f76(x58062),x58063)),f328(f76(x58062),x58061)),f328(f76(x58062),f328(f328(f286(x58062),x58063),x58061)))
% 81.29/80.92 [5974]~P24(f328(f62(x59741),x59743))+E(f328(f38(x59741),f328(f328(f306(x59741),x59742),x59743)),f328(a118,f328(f38(x59741),x59743)))+P24(f328(f328(f330(x59741),x59742),x59743))
% 81.29/80.92 [6048]~E(x60482,f2(a877))+P24(f328(x60481,f2(a877)))+~P24(f328(x60481,f328(f328(f39(a877),x60483),x60482)))
% 81.29/80.92 [6067]~P24(f328(f62(x60671),x60673))+E(f328(f38(x60671),f328(f328(f306(x60671),x60672),x60673)),f328(f38(x60671),x60673))+~P24(f328(f328(f330(x60671),x60672),x60673))
% 81.29/80.92 [6101]~P24(f328(f62(x61011),x61013))+E(f328(f38(x61011),f328(f328(f306(x61011),x61012),x61013)),f328(f328(f81(a877),f79(a877)),f328(f38(x61011),x61013)))+P24(f328(f328(f330(x61011),x61012),x61013))
% 81.29/80.92 [6220]E(f328(f328(f81(a877),x62201),f825(x62201,x62202,x62203)),x62202)+~P24(f328(x62203,f2(a877)))+P24(f328(x62203,f328(f328(f22(a877),x62202),x62201)))
% 81.29/80.92 [6221]E(f328(f328(f81(a877),x62211),f826(x62211,x62212,x62213)),x62212)+~P24(f328(x62213,f2(a877)))+P24(f328(x62213,f328(f328(f22(a877),x62212),x62211)))
% 81.29/80.92 [6268]~P27(x62681)+~P24(f328(f62(x62681),x62683))+E(f328(f328(f65(x62681,x62681,f116(x62681)),x62682),x62683),f328(f328(f116(x62681),x62682),f40(x62681,x62683)))
% 81.29/80.92 [6269]~P27(x62691)+~P24(f328(f62(x62691),x62693))+E(f328(f328(f65(x62691,x62691,f107(x62691)),x62692),x62693),f328(f328(f107(x62691),x62692),f41(x62691,x62693)))
% 81.29/80.92 [6275]~P96(x62751)+~E(f328(f109(x62751),x62752),f328(f109(x62751),x62753))+P31(x62751,f328(f109(x62751),f328(f328(f81(a1),x62752),f328(f80(a1),x62753))))
% 81.29/80.92 [6282]~P137(x62821)+E(f328(f328(f22(x62821),f328(f106(x62821),x62822)),f328(f106(x62821),x62823)),f328(f106(x62821),f328(f328(f22(a877),x62822),x62823)))+~P24(f328(f328(f244(a877),x62823),x62822))
% 81.29/80.92 [6370]E(f328(f328(f81(a877),x63701),f825(x63701,x63702,x63703)),x63702)+P24(f328(f328(f245(a877),x63702),x63701))+P24(f328(x63703,f328(f328(f22(a877),x63702),x63701)))
% 81.29/80.92 [6371]E(f328(f328(f81(a877),x63711),f826(x63711,x63712,x63713)),x63712)+P24(f328(f328(f245(a877),x63712),x63711))+P24(f328(x63713,f328(f328(f22(a877),x63712),x63711)))
% 81.29/80.92 [6386]~P111(x63861)+E(f328(f328(f82(x63861),f328(f76(x63861),x63862)),x63863),f328(f76(x63861),f328(f328(f82(x63861),x63862),x63863)))+~P24(f328(f328(f244(x63861),f2(x63861)),x63863))
% 81.29/80.92 [6387]~P63(x63871)+E(f328(f328(f286(x63871),f328(f76(x63871),x63872)),x63873),f328(f76(x63871),f328(f328(f286(x63871),x63872),x63873)))+~P24(f328(f328(f245(x63871),f2(x63871)),x63873))
% 81.29/80.92 [6395]~P78(x63951)+~P24(f328(f62(x63951),x63953))+E(f328(f328(f65(x63951,x63951,f116(x63951)),x63952),x63953),f10(x63951,f328(f328(f306(x63951),x63952),x63953)))
% 81.29/80.92 [6396]~P78(x63961)+~P24(f328(f62(x63961),x63963))+E(f328(f328(f65(x63961,x63961,f107(x63961)),x63962),x63963),f11(x63961,f328(f328(f306(x63961),x63962),x63963)))
% 81.29/80.92 [6397]~P106(x63971)+~P24(f328(f62(x63971),x63973))+E(f328(f328(f65(x63971,x63971,f242(x63971)),x63972),x63973),f14(x63971,f328(f328(f306(x63971),x63972),x63973)))
% 81.29/80.92 [6398]~P106(x63981)+~P24(f328(f62(x63981),x63983))+E(f328(f328(f65(x63981,x63981,f243(x63981)),x63982),x63983),f15(x63981,f328(f328(f306(x63981),x63982),x63983)))
% 81.29/80.92 [6443]E(x64431,f119(x64432))+~E(f179(x64432,x64433),f119(f878(x64432)))+~P24(f328(f328(f330(f878(x64432)),x64431),f328(f171(f878(x64432)),x64433)))
% 81.29/80.92 [6485]~P24(f328(f136(x64851),x64853))+P24(f328(f328(f330(x64851),x64852),f328(f171(x64851),x64853)))+P24(f328(f136(x64851),f328(f328(f150(x64851),x64852),x64853)))
% 81.29/80.92 [6496]~P98(x64961)+~P24(f328(f62(x64961),x64963))+E(f328(f64(x64961,f82(x64961)),f328(f328(f306(x64961),x64962),x64963)),f328(f328(f65(x64961,x64961,f82(x64961)),x64962),x64963))
% 81.29/80.92 [6519]~P106(x65191)+~P24(f328(f62(x65191),x65193))+E(f12(x65191,f242(x65191),f328(f328(f306(x65191),x65192),x65193)),f328(f328(f65(x65191,x65191,f242(x65191)),x65192),x65193))
% 81.29/80.92 [6520]~P106(x65201)+~P24(f328(f62(x65201),x65203))+E(f13(x65201,f243(x65201),f328(f328(f306(x65201),x65202),x65203)),f328(f328(f65(x65201,x65201,f243(x65201)),x65202),x65203))
% 81.29/80.92 [6522]P24(f328(x65221,f2(a877)))+~P24(f328(f328(f245(a877),x65222),x65223))+~P24(f328(x65221,f328(f328(f22(a877),x65222),x65223)))
% 81.29/80.92 [6541]~P87(x65411)+P24(f328(f328(f244(x65411),x65412),x65413))+~P24(f328(f328(f244(x65411),f328(f76(x65411),x65412)),x65413))
% 81.29/80.92 [6542]~P111(x65421)+P24(f328(f328(f245(x65421),x65422),x65423))+~P24(f328(f328(f245(x65421),f328(f76(x65421),x65422)),x65423))
% 81.29/80.92 [6559]E(x65591,f119(x65592))+E(f328(f140(x65592),f328(f328(f137(x65592),x65593),x65591)),f328(f328(f164(x65592),x65591),x65593))+~P24(f328(f328(f245(a877),x65593),f328(f194(f878(x65592)),x65591)))
% 81.29/80.92 [6611]~P24(f328(x66111,x66113))+P24(f328(x66111,f457(x66111,x66112)))+~P24(f328(f328(f330(a877),x66113),f328(f298(a877,f2(a877)),x66112)))
% 81.29/80.92 [6633]P24(f328(x66331,x66332))+~P24(f328(f328(f245(a877),x66332),x66333))+P24(f328(f328(f330(a877),f456(x66331,x66333)),f328(f298(a877,f2(a877)),x66333)))
% 81.29/80.92 [6648]~P110(x66481)+~P24(f328(f328(f244(x66481),f79(x66481)),x66482))+P24(f328(f328(f244(x66481),f79(x66481)),f328(f328(f258(x66481),x66482),x66483)))
% 81.29/80.92 [6650]~P110(x66501)+~P24(f328(f328(f244(x66501),f2(x66501)),x66502))+P24(f328(f328(f244(x66501),f2(x66501)),f328(f328(f258(x66501),x66502),x66503)))
% 81.29/80.92 [6652]~P110(x66521)+~P24(f328(f328(f245(x66521),f2(x66521)),x66522))+P24(f328(f328(f245(x66521),f2(x66521)),f328(f328(f258(x66521),x66522),x66523)))
% 81.29/80.92 [6677]~P24(f328(x66771,x66773))+~P24(f328(f328(f245(a877),x66773),x66772))+P24(f328(f328(f330(a877),f447(x66771,x66772)),f328(f298(a877,f2(a877)),x66772)))
% 81.29/80.92 [6684]P24(f328(f62(x66841),x66842))+~P24(f328(f62(x66841),x66843))+~P24(f328(f328(f244(f885(x66841,a871)),x66842),x66843))
% 81.29/80.92 [6692]P24(f328(x66921,x66922))+~P24(f328(x66921,f458(x66921,x66923)))+~P24(f328(f328(f330(a877),x66922),f328(f298(a877,f2(a877)),x66923)))
% 81.29/80.92 [6703]E(x67031,f2(a877))+P24(f328(x67032,f373(x67031,x67033,x67032)))+~P24(f328(x67032,f328(f328(f39(a877),x67033),x67031)))
% 81.29/80.92 [6711]~P123(x67112)+E(x67111,f2(x67112))+~E(f328(f328(f81(x67112),f328(f328(f82(x67112),x67113),x67113)),f328(f328(f82(x67112),x67111),x67111)),f2(x67112))
% 81.29/80.92 [6712]~P123(x67122)+E(x67121,f2(x67122))+~E(f328(f328(f81(x67122),f328(f328(f82(x67122),x67121),x67121)),f328(f328(f82(x67122),x67123),x67123)),f2(x67122))
% 81.29/80.92 [6757]E(x67571,f2(a877))+~P24(f328(x67572,f367(x67571,x67573,x67572)))+P24(f328(x67572,f328(f328(f39(a877),x67573),x67571)))
% 81.29/80.92 [6762]~P106(x67621)+~P29(x67621,x67623)+P29(x67621,f328(f328(f147(x67621,x67621,f5(x67621)),x67622),x67623))
% 81.29/80.92 [6805]P24(f328(x68051,f373(x68052,x68053,x68051)))+P24(f328(x68051,f2(a877)))+~P24(f328(x68051,f328(f328(f39(a877),x68053),x68052)))
% 81.29/80.92 [6811]~P96(x68111)+E(f328(f109(x68111),x68112),f328(f109(x68111),x68113))+~P31(x68111,f328(f109(x68111),f328(f328(f81(a1),x68112),f328(f80(a1),x68113))))
% 81.29/80.92 [6876]E(x68761,f2(a1))+E(x68762,f2(a1))+~P24(f328(f49(x68762,x68762),f328(f328(f257(a1,a1),x68763),x68761)))
% 81.29/80.92 [6877]E(x68771,f79(a1))+E(x68772,f2(a1))+~P24(f328(f49(x68772,x68772),f328(f328(f257(a1,a1),x68771),x68773)))
% 81.29/80.92 [6888]P24(f328(x68881,x68882))+P24(f328(f328(f245(a877),f458(x68881,x68883)),x68883))+~P24(f328(f328(f330(a877),x68882),f328(f298(a877,f2(a877)),x68883)))
% 81.29/80.92 [6912]~P24(f328(x69121,f825(x69123,x69122,x69121)))+~P24(f328(x69121,f2(a877)))+P24(f328(x69121,f328(f328(f22(a877),x69122),x69123)))
% 81.29/80.92 [6913]~P24(f328(x69131,f826(x69133,x69132,x69131)))+~P24(f328(x69131,f2(a877)))+P24(f328(x69131,f328(f328(f22(a877),x69132),x69133)))
% 81.29/80.92 [6914]~P24(f328(x69141,f367(x69143,x69142,x69141)))+~P24(f328(x69141,f2(a877)))+P24(f328(x69141,f328(f328(f39(a877),x69142),x69143)))
% 81.29/80.92 [6932]~P24(f328(x69321,x69323))+P24(f328(f328(f245(a877),f457(x69321,x69322)),x69322))+~P24(f328(f328(f330(a877),x69323),f328(f298(a877,f2(a877)),x69322)))
% 81.29/80.92 [6933]E(f328(f328(f22(a877),f328(f328(f22(a877),x69331),x69332)),f328(f328(f22(a877),x69333),x69332)),f328(f328(f22(a877),x69331),x69333))+~P24(f328(f328(f244(a877),x69332),x69331))+~P24(f328(f328(f244(a877),x69332),x69333))
% 81.29/80.92 [6968]~P80(x69681)+~P24(f328(f328(f244(x69681),f328(f80(x69681),x69683)),x69682))+P24(f328(f328(f244(x69681),f328(f80(x69681),x69682)),x69683))
% 81.29/80.92 [6970]~P87(x69701)+~P24(f328(f328(f244(x69701),f328(f76(x69701),x69702)),x69703))+P24(f328(f328(f244(x69701),f328(f80(x69701),x69702)),x69703))
% 81.29/80.92 [6972]~P80(x69721)+~P24(f328(f328(f245(x69721),f328(f80(x69721),x69723)),x69722))+P24(f328(f328(f245(x69721),f328(f80(x69721),x69722)),x69723))
% 81.29/80.92 [6973]~P111(x69731)+~P24(f328(f328(f245(x69731),f328(f76(x69731),x69732)),x69733))+P24(f328(f328(f245(x69731),f328(f80(x69731),x69732)),x69733))
% 81.29/80.92 [7009]~P24(f328(x70093,f825(x70092,x70091,x70093)))+P24(f328(f328(f245(a877),x70091),x70092))+P24(f328(x70093,f328(f328(f22(a877),x70091),x70092)))
% 81.29/80.92 [7010]~P24(f328(x70103,f826(x70102,x70101,x70103)))+P24(f328(f328(f245(a877),x70101),x70102))+P24(f328(x70103,f328(f328(f22(a877),x70101),x70102)))
% 81.29/80.92 [7060]~E(f795(x70603,x70602,x70601),f768(x70603,x70602,x70601))+E(f328(f328(f107(f885(x70601,a871)),x70602),f40(f885(x70601,a871),x70603)),f193(f885(x70601,a871)))+P24(f328(f328(f330(f885(x70601,a871)),x70602),x70603))
% 81.29/80.92 [7069]~P24(f328(f62(x70691),x70693))+P24(f328(f62(x70691),f41(f885(x70691,a871),x70692)))+~P24(f328(f328(f330(f885(x70691,a871)),x70693),x70692))
% 81.29/80.92 [7128]~P106(x71281)+E(f328(f328(f116(f885(x71281,a871)),f328(f298(x71281,x71282),x71283)),f328(f328(f306(x71281),x71283),f193(f885(x71281,a871)))),f299(x71281,x71282,x71283))+~P24(f328(f328(f244(x71281),x71282),x71283))
% 81.29/80.92 [7129]E(x71291,f2(a877))+P24(f328(f328(f245(a877),f368(x71291,x71293,x71292)),x71291))+P24(f328(x71292,f328(f328(f39(a877),x71293),x71291)))
% 81.29/80.92 [7164]E(x71641,x71642)+~P24(f328(f328(f244(f885(x71643,a871)),x71641),x71642))+P24(f328(f328(f245(f885(x71643,a871)),x71641),x71642))
% 81.29/80.92 [7177]E(x71771,x71772)+~E(f328(f194(f878(x71773)),x71771),f328(f194(f878(x71773)),x71772))+P24(f328(f328(f245(a877),f568(x71773,x71771,x71772)),f328(f194(f878(x71773)),x71772)))
% 81.29/80.92 [7223]P6(x72231,x72232,x72233)+~E(f328(f255(x72231,x72231),x72233),x72232)+~E(f328(f328(f285(x72231,x72231,x72231),f328(f283(x72231,x72231),x72233)),x72233),x72233)
% 81.29/80.92 [7295]~P24(f328(x72951,f2(a877)))+P24(f328(f328(f245(a877),f368(x72953,x72952,x72951)),x72953))+P24(f328(x72951,f328(f328(f39(a877),x72952),x72953)))
% 81.29/80.92 [7304]~P106(x73041)+E(f328(f328(f116(f885(x73041,a871)),f302(x73041,x73042,x73043)),f328(f328(f306(x73041),x73043),f193(f885(x73041,a871)))),f301(x73041,x73042,x73043))+~P24(f328(f328(f245(x73041),x73042),x73043))
% 81.29/80.92 [7405]~P24(f328(f62(x74051),x74053))+P24(f328(f328(f244(a877),f328(f38(x74051),x74052)),f328(f38(x74051),x74053)))+~P24(f328(f328(f244(f885(x74051,a871)),x74052),x74053))
% 81.29/80.92 [7406]~P24(f328(f62(x74061),x74063))+P24(f328(f328(f245(a877),f328(f38(x74061),x74062)),f328(f38(x74061),x74063)))+~P24(f328(f328(f245(f885(x74061,a871)),x74062),x74063))
% 81.29/80.92 [7444]~P24(f328(x74443,x74442))+P24(f328(f328(f200(x74441),x74442),f563(x74442,x74441,x74443)))+~P24(f328(f328(f200(f33(x74443,x74441)),x74442),x74442))
% 81.29/80.92 [7540]E(x75401,x75402)+~P24(f328(f328(f244(f885(x75403,a871)),x75402),x75401))+~P24(f328(f328(f244(f885(x75403,a871)),x75401),x75402))
% 81.29/80.92 [7543]~P106(x75431)+P29(x75431,x75432)+~P29(x75431,f328(f328(f147(x75431,x75431,f5(x75431)),x75433),x75432))
% 81.29/80.92 [7611]~P24(f328(f328(f245(a877),x76113),x76112))+~P24(f328(f328(f245(a877),x76113),x76111))+P24(f328(f328(f245(a877),f328(f328(f22(a877),x76111),x76112)),f328(f328(f22(a877),x76111),x76113)))
% 81.29/80.92 [7612]~P24(f328(f328(f244(a877),x76122),x76121))+~P24(f328(f328(f245(a877),x76121),x76123))+P24(f328(f328(f245(a877),f328(f328(f22(a877),x76121),x76122)),f328(f328(f22(a877),x76123),x76122)))
% 81.29/80.92 [7627]~P24(f328(f328(f245(a1),x76272),f2(a1)))+~P24(f328(f328(f244(a1),x76273),x76271))+P24(f328(f328(f244(a1),f328(f328(f39(a1),x76271),x76272)),f328(f328(f39(a1),x76273),x76272)))
% 81.29/80.92 [7645]~P24(f328(f328(f245(a877),f2(a877)),x76453))+~P24(f328(f328(f244(a877),x76453),x76452))+P24(f328(f328(f244(a877),f328(f328(f39(a877),x76451),x76452)),f328(f328(f39(a877),x76451),x76453)))
% 81.29/80.92 [7646]~P24(f328(f328(f245(a1),f2(a1)),x76462))+~P24(f328(f328(f244(a1),x76461),x76463))+P24(f328(f328(f244(a1),f328(f328(f39(a1),x76461),x76462)),f328(f328(f39(a1),x76463),x76462)))
% 81.29/80.92 [7650]~P24(f328(f328(f245(a877),f2(a877)),x76502))+~P24(f328(f328(f245(a877),x76501),x76503))+P24(f328(f328(f245(a877),f328(f328(f82(a877),x76501),x76502)),f328(f328(f82(a877),x76503),x76502)))
% 81.29/80.92 [7651]~P24(f328(f328(f245(a877),f2(a877)),x76511))+~P24(f328(f328(f245(a877),x76512),x76513))+P24(f328(f328(f245(a877),f328(f328(f82(a877),x76511),x76512)),f328(f328(f82(a877),x76511),x76513)))
% 81.29/80.92 [7652]~P24(f328(f328(f245(a1),f2(a1)),x76521))+~P24(f328(f328(f245(a1),x76522),x76523))+P24(f328(f328(f245(a1),f328(f328(f82(a1),x76521),x76522)),f328(f328(f82(a1),x76521),x76523)))
% 81.29/80.92 [7701]E(x77011,f2(a877))+E(f328(f328(f81(a877),f328(f328(f82(a877),x77011),f367(x77011,x77012,x77013))),f368(x77011,x77012,x77013)),x77012)+P24(f328(x77013,f328(f328(f39(a877),x77012),x77011)))
% 81.29/80.92 [7760]E(f328(f328(f81(a877),f328(f328(f82(a877),x77601),f367(x77601,x77602,x77603))),f368(x77601,x77602,x77603)),x77602)+~P24(f328(x77603,f2(a877)))+P24(f328(x77603,f328(f328(f39(a877),x77602),x77601)))
% 81.29/80.92 [7777]~P24(f328(f62(x77771),x77773))+P24(f328(f328(f330(x77771),f350(x77772,x77773,x77771)),x77773))+P24(f328(f328(f245(a877),f2(a877)),f328(f328(f9(x77771,a877),x77772),x77773)))
% 81.29/80.92 [7778]~P24(f328(f62(x77781),x77783))+P24(f328(f328(f330(x77781),f357(x77782,x77783,x77781)),x77783))+P24(f328(f328(f245(a877),f2(a877)),f328(f328(f9(x77781,a877),x77782),x77783)))
% 81.29/80.92 [8071]E(x80711,f193(f885(x80712,a871)))+E(x80711,f328(f328(f306(x80712),x80713),f193(f885(x80712,a871))))+~P24(f328(f328(f244(f885(x80712,a871)),x80711),f328(f328(f306(x80712),x80713),f193(f885(x80712,a871)))))
% 81.29/80.92 [8089]~P60(x80891)+P8(x80891,x80892,x80893)+P24(f328(f328(f330(f878(x80891)),f658(x80893,x80892,x80891)),f328(f171(f878(x80891)),f55(x80891,x80893,f56(x80891)))))
% 81.29/80.92 [8108]~P24(f328(f328(f245(a877),f2(a877)),x81083))+P24(f328(f328(f244(a877),x81081),x81082))+~P24(f328(f328(f244(a877),f328(f328(f82(a877),x81083),x81081)),f328(f328(f82(a877),x81083),x81082)))
% 81.29/80.92 [8109]~P24(f328(f328(f245(a877),f2(a877)),x81093))+P24(f328(f328(f244(a877),x81091),x81092))+~P24(f328(f328(f244(a877),f328(f328(f82(a877),x81091),x81093)),f328(f328(f82(a877),x81092),x81093)))
% 81.29/80.92 [8111]~P24(f328(f328(f245(a877),f2(a877)),x81113))+P24(f328(f328(f245(a877),x81111),x81112))+~P24(f328(f328(f245(a877),f328(f328(f258(a877),x81113),x81111)),f328(f328(f258(a877),x81113),x81112)))
% 81.29/80.92 [8138]~P60(x81381)+~P7(x81381,x81383,x81382)+P24(f328(f328(f330(f878(x81381)),f657(x81382,x81383,x81381)),f328(f171(f878(x81381)),f55(x81381,x81382,f56(x81381)))))
% 81.29/80.92 [8146]~P24(f328(x81461,x81463))+P24(f328(f328(f200(f33(x81461,x81462)),f563(x81463,x81462,x81461)),x81463))+~P24(f328(f328(f200(f33(x81461,x81462)),x81463),x81463))
% 81.29/80.92 [8155]~E(f328(f328(f107(f885(x81551,a871)),f768(x81553,x81552,x81551)),f795(x81553,x81552,x81551)),f193(f885(x81551,a871)))+E(f328(f328(f107(f885(x81551,a871)),x81552),f40(f885(x81551,a871),x81553)),f193(f885(x81551,a871)))+P24(f328(f328(f330(f885(x81551,a871)),x81552),x81553))
% 81.29/80.92 [8172]E(x81721,f119(x81722))+~E(f328(f141(f878(x81722),f878(x81722),f127(x81722),f119(x81722)),x81723),f119(x81722))+~P24(f328(f328(f330(f878(x81722)),x81721),f328(f171(f878(x81722)),x81723)))
% 81.29/80.92 [8229]E(x82291,f193(f885(f885(x82292,a871),a871)))+P24(f328(f328(f330(f885(x82292,a871)),f380(x82293,x82291,x82292)),x82291))+P24(f328(f328(f244(f885(x82292,a871)),f41(f885(x82292,a871),x82291)),x82293))
% 81.29/80.92 [8236]~P74(x82361)+~P75(x82361)+E(f328(f328(f6(a1,x82361),f328(f328(f8(a877,x82361,a1),x82362),a110)),f328(f307(a877,a1,f106(a1)),x82363)),f328(f328(f6(a877,x82361),x82362),x82363))
% 81.29/80.92 [8237]~P74(x82371)+~P75(x82371)+E(f328(f328(f9(a1,x82371),f328(f328(f8(a877,x82371,a1),x82372),a110)),f328(f307(a877,a1,f106(a1)),x82373)),f328(f328(f9(a877,x82371),x82372),x82373))
% 81.29/80.92 [8276]~P24(f328(f62(x82761),x82763))+~P24(f328(f328(f245(a877),f2(a877)),f328(x82762,f350(x82762,x82763,x82761))))+P24(f328(f328(f245(a877),f2(a877)),f328(f328(f9(x82761,a877),x82762),x82763)))
% 81.29/80.92 [8277]~P24(f328(f62(x82771),x82773))+~P24(f328(f328(f245(a877),f2(a877)),f328(x82772,f357(x82772,x82773,x82771))))+P24(f328(f328(f245(a877),f2(a877)),f328(f328(f9(x82771,a877),x82772),x82773)))
% 81.29/80.92 [8312]~P62(x83122)+E(x83121,f79(x83122))+E(f328(f328(f286(x83122),f328(f328(f22(x83122),f328(f328(f258(x83122),x83121),x83123)),f79(x83122))),f328(f328(f22(x83122),x83121),f79(x83122))),f328(f328(f6(a877,x83122),f328(f258(x83122),x83121)),f328(f298(a877,f2(a877)),x83123)))
% 81.29/80.92 [8370]E(x83701,f2(a877))+~P24(f328(x83703,f328(f328(f39(a877),x83702),x83701)))+P24(f328(f328(f245(a877),x83702),f328(f328(f82(a877),x83701),f328(a118,f373(x83701,x83702,x83703)))))
% 81.29/80.92 [8388]P24(f328(x83881,f2(a877)))+~P24(f328(x83881,f328(f328(f39(a877),x83882),x83883)))+P24(f328(f328(f245(a877),x83882),f328(f328(f82(a877),x83883),f328(a118,f373(x83883,x83882,x83881)))))
% 81.29/80.92 [8429]E(x84291,f2(a877))+~P24(f328(x84293,f328(f328(f39(a877),x84292),x84291)))+P24(f328(f328(f244(a877),f328(f328(f82(a877),x84291),f373(x84291,x84292,x84293))),x84292))
% 81.29/80.92 [8470]P24(f328(x84701,f2(a877)))+~P24(f328(x84701,f328(f328(f39(a877),x84703),x84702)))+P24(f328(f328(f244(a877),f328(f328(f82(a877),x84702),f373(x84702,x84703,x84701))),x84703))
% 81.29/80.92 [8473]~P106(x84731)+E(f328(f328(f147(x84731,x84731,f5(x84731)),x84732),x84733),f148(x84731,x84731,f5(x84731),x84732,x84733))+P24(f328(f328(f330(x84731),x84732),f328(f171(x84731),x84733)))
% 81.29/80.92 [8511]~E(f328(x85113,f724(x85112,x85113,x85111)),f328(x85113,f726(x85112,x85113,x85111)))+~P57(x85111,f328(x85113,f725(x85112,x85113,x85111)))+P57(x85111,f328(f328(f43(x85112,f885(x85111,f885(x85111,a871))),f252(f885(x85112,a871))),x85113))
% 81.29/80.92 [8519]E(x85191,f193(f885(f885(x85192,a871),a871)))+~P24(f328(f328(f244(f885(x85192,a871)),f380(x85193,x85191,x85192)),x85193))+P24(f328(f328(f244(f885(x85192,a871)),f41(f885(x85192,a871),x85191)),x85193))
% 81.29/80.92 [8577]~P64(x85771)+~P24(f328(f328(f245(x85771),x85772),x85773))+P24(f328(f328(f245(x85771),x85772),f328(f328(f286(x85771),f328(f328(f81(x85771),x85772),x85773)),f328(f328(f81(x85771),f79(x85771)),f79(x85771)))))
% 81.29/80.92 [8632]~P24(f328(f328(x86321,f490(x86321,x86323,x86322)),f491(x86321,x86323,x86322)))+P24(f328(f328(x86321,x86322),x86323))+~P24(f328(f316(f884(a1,a1),a52),f328(f328(f257(a1,a1),x86322),x86323)))
% 81.29/80.92 [8633]~P24(f328(f328(x86331,f492(x86331,x86333,x86332)),f494(x86331,x86333,x86332)))+P24(f328(f328(x86331,x86332),x86333))+~P24(f328(f316(f884(a1,a1),a57),f328(f328(f257(a1,a1),x86332),x86333)))
% 81.29/80.92 [8634]~P24(f328(f328(x86341,f495(x86341,x86343,x86342)),f496(x86341,x86343,x86342)))+P24(f328(f328(x86341,x86342),x86343))+~P24(f328(f316(f884(a1,a1),a232),f328(f328(f257(a1,a1),x86342),x86343)))
% 81.29/80.92 [8635]~P24(f328(f328(x86351,f497(x86351,x86353,x86352)),f498(x86351,x86353,x86352)))+P24(f328(f328(x86351,x86352),x86353))+~P24(f328(f316(f884(a877,a877),a227),f328(f328(f257(a877,a877),x86352),x86353)))
% 81.29/80.92 [8636]~P24(f328(f328(x86361,f586(x86361,x86363,x86362)),f588(x86361,x86363,x86362)))+P24(f328(f328(x86361,x86362),x86363))+~P24(f328(f316(f884(a1,a1),a182),f328(f328(f257(a1,a1),x86362),x86363)))
% 81.29/80.92 [8889]P24(f328(f328(x88891,x88892),x88893))+P24(f328(f316(f884(a877,a877),a227),f328(f328(f257(a877,a877),f497(x88891,x88893,x88892)),f498(x88891,x88893,x88892))))+~P24(f328(f316(f884(a877,a877),a227),f328(f328(f257(a877,a877),x88892),x88893)))
% 81.29/80.92 [8890]P24(f328(f328(x88901,x88902),x88903))+P24(f328(f316(f884(a1,a1),a52),f328(f328(f257(a1,a1),f490(x88901,x88903,x88902)),f491(x88901,x88903,x88902))))+~P24(f328(f316(f884(a1,a1),a52),f328(f328(f257(a1,a1),x88902),x88903)))
% 81.29/80.92 [8891]P24(f328(f328(x88911,x88912),x88913))+P24(f328(f316(f884(a1,a1),a57),f328(f328(f257(a1,a1),f492(x88911,x88913,x88912)),f494(x88911,x88913,x88912))))+~P24(f328(f316(f884(a1,a1),a57),f328(f328(f257(a1,a1),x88912),x88913)))
% 81.29/80.92 [8892]P24(f328(f328(x88921,x88922),x88923))+P24(f328(f316(f884(a1,a1),a232),f328(f328(f257(a1,a1),f495(x88921,x88923,x88922)),f496(x88921,x88923,x88922))))+~P24(f328(f316(f884(a1,a1),a232),f328(f328(f257(a1,a1),x88922),x88923)))
% 81.29/80.92 [8893]P24(f328(f328(x88931,x88932),x88933))+P24(f328(f316(f884(a1,a1),a182),f328(f328(f257(a1,a1),f586(x88931,x88933,x88932)),f588(x88931,x88933,x88932))))+~P24(f328(f316(f884(a1,a1),a182),f328(f328(f257(a1,a1),x88932),x88933)))
% 81.29/80.92 [9238]~P24(f328(f62(x92381),x92383))+P24(f328(f328(f330(f884(f885(x92381,a871),f885(x92381,a871))),f328(f328(f257(f885(x92381,a871),f885(x92381,a871)),x92382),x92383)),f303(x92381)))+~P24(f328(f328(f245(f885(x92381,a871)),x92382),x92383))
% 81.29/80.92 [9246]~P23(a872,f193(f885(f876(a872),a871)),f328(f328(f306(f876(a872)),f328(f328(f328(f93(a872),x92461),x92462),x92463)),f193(f885(f876(a872),a871))))+P20(a872,f193(f885(f876(a872),a871)),f328(f328(f306(f876(a872)),f328(f328(f328(f93(a872),x92461),x92462),x92463)),f193(f885(f876(a872),a871))))+~P20(a872,f193(f885(f876(a872),a871)),f328(f328(f306(f876(a872)),f328(a94,x92462)),f193(f885(f876(a872),a871))))
% 81.29/80.92 [9310]~P57(x93101,f328(x93103,f725(x93102,x93103,x93101)))+P57(x93101,f328(f328(f43(x93102,f885(x93101,f885(x93101,a871))),f252(f885(x93102,a871))),x93103))+~E(f328(f328(f107(f885(x93101,a871)),f263(x93101,x93101,f328(x93103,f724(x93102,x93103,x93101)))),f264(x93101,x93101,f328(x93103,f726(x93102,x93103,x93101)))),f193(f885(x93101,a871)))
% 81.29/80.92 [9506]P48(x95061,x95062,x95063)+P24(f328(f328(f330(f884(x95061,x95061)),f613(x95063,x95062,x95061)),x95063))+~P24(f328(f328(f330(f884(x95061,x95061)),f328(f328(f257(x95061,x95061),f612(x95063,x95062,x95061)),f612(x95063,x95062,x95061))),x95063))
% 81.29/80.92 [10091]P48(x100911,x100912,x100913)+~P24(f328(f328(f267(x100911,x100911,a871),f328(f328(f7(x100911,f885(x100911,a871),f885(x100911,a871)),f328(f328(f8(f885(a871,a871),f885(f885(x100911,a871),f885(x100911,a871)),x100911),f8(a871,a871,x100911)),f328(f328(f8(a871,f885(a871,a871),x100911),a326),f328(f328(f7(x100911,f885(x100911,a871),a871),f330(x100911)),x100912)))),f328(f328(f7(x100911,f885(x100911,a871),a871),f330(x100911)),x100912))),f613(x100913,x100912,x100911)))+~P24(f328(f328(f330(f884(x100911,x100911)),f328(f328(f257(x100911,x100911),f612(x100913,x100912,x100911)),f612(x100913,x100912,x100911))),x100913))
% 81.29/80.92 [5646]~P58(x56462)+E(x56461,f2(x56462))+E(f328(f328(f39(x56462),f328(f328(f82(x56462),x56463),x56461)),x56461),x56463)
% 81.29/80.92 [5647]~P58(x56472)+E(x56471,f2(x56472))+E(f328(f328(f39(x56472),f328(f328(f82(x56472),x56471),x56473)),x56471),x56473)
% 81.29/80.92 [6442]~P74(x64421)+~E(f328(x64422,f2(a877)),f2(x64421))+E(f328(f328(f6(a877,x64421),x64422),f328(f298(a877,f328(a118,f2(a877))),x64423)),f328(f328(f6(a877,x64421),x64422),f328(f298(a877,f2(a877)),x64423)))
% 81.29/80.92 [6572]~P58(x65722)+E(x65721,f2(x65722))+E(f328(f328(f39(x65722),f328(f328(f81(x65722),x65723),x65721)),x65721),f328(f328(f81(x65722),f328(f328(f39(x65722),x65723),x65721)),f79(x65722)))
% 81.29/80.92 [6573]~P58(x65732)+E(x65731,f2(x65732))+E(f328(f328(f39(x65732),f328(f328(f81(x65732),x65731),x65733)),x65731),f328(f328(f81(x65732),f328(f328(f39(x65732),x65733),x65731)),f79(x65732)))
% 81.29/80.92 [6793]~P24(f328(x67933,f2(a1)))+P24(f328(f328(f244(a877),x67931),x67932))+P24(f328(x67933,f328(f106(a1),f328(f328(f22(a877),x67932),x67931))))
% 81.29/80.92 [6894]P24(f328(f328(f245(a877),x68942),x68941))+P24(f328(f328(f244(a877),x68941),x68942))+P24(f328(x68943,f328(f106(a1),f328(f328(f22(a877),x68942),x68941))))
% 81.29/80.92 [6966]E(f328(f328(f81(a877),f328(f109(a877),x69661)),f328(f328(f81(a877),f328(f109(a877),x69662)),x69663)),f328(f328(f81(a877),f328(f109(a877),x69661)),x69663))+P24(f328(a199,f328(f109(a1),x69661)))+~P24(f328(a199,f328(f109(a1),x69662)))
% 81.29/80.92 [7047]~E(x70472,f328(f328(f39(a877),x70473),x70471))+~P24(f328(f328(f245(a877),f2(a877)),x70471))+P24(f328(f328(f244(a877),f328(f328(f82(a877),x70471),x70472)),x70473))
% 81.29/80.92 [7162]~P24(f328(f62(x71621),x71623))+~P24(f328(f62(x71621),x71622))+P24(f328(f62(x71621),f328(f328(f116(f885(x71621,a871)),x71622),x71623)))
% 81.29/80.92 [7457]~P106(x74571)+~P24(f328(f62(x74571),x74572))+E(f138(x74571,f328(f328(f22(f885(x74571,a871)),x74572),f328(f328(f306(x74571),x74573),f193(f885(x74571,a871))))),f169(x74571,x74573,f138(x74571,x74572)))
% 81.29/80.92 [7520]P24(f328(x75201,f2(a1)))+~P24(f328(f328(f245(a877),x75202),x75203))+~P24(f328(x75201,f328(f106(a1),f328(f328(f22(a877),x75202),x75203))))
% 81.29/80.92 [7537]~P24(f328(f62(x75371),x75372))+E(f328(f38(x75371),f328(f328(f22(f885(x75371,a871)),x75372),f328(f328(f306(x75371),x75373),f193(f885(x75371,a871))))),f328(f38(x75371),x75372))+P24(f328(f328(f330(x75371),x75373),x75372))
% 81.29/80.92 [7667]~P110(x76671)+~P24(f328(f328(f245(x76671),f79(x76671)),x76672))+P24(f328(f328(f245(x76671),f79(x76671)),f328(f328(f82(x76671),x76672),f328(f328(f258(x76671),x76672),x76673))))
% 81.29/80.92 [7712]~P24(f328(f62(x77121),x77123))+E(f328(f328(f22(a877),f328(f38(x77121),x77122)),f328(f38(x77121),x77123)),f328(f38(x77121),f328(f328(f22(f885(x77121,a871)),x77122),x77123)))+~P24(f328(f328(f244(f885(x77121,a871)),x77123),x77122))
% 81.29/80.92 [7769]~P24(f328(f328(f244(a877),x77692),x77693))+~P24(f328(f328(f244(a877),x77691),f328(f328(f22(a877),x77693),x77692)))+P24(f328(f328(f244(a877),f328(f328(f81(a877),x77691),x77692)),x77693))
% 81.29/80.92 [7820]P24(f328(f62(x78201),x78202))+~P24(f328(f62(x78201),x78203))+~P24(f328(f62(x78201),f328(f328(f22(f885(x78201,a871)),x78202),x78203)))
% 81.29/80.92 [7826]~P24(f328(f62(x78261),x78262))+E(f328(f38(x78261),f328(f328(f22(f885(x78261,a871)),x78262),f328(f328(f306(x78261),x78263),f193(f885(x78261,a871))))),f328(f328(f22(a877),f328(f38(x78261),x78262)),f79(a877)))+~P24(f328(f328(f330(x78261),x78263),x78262))
% 81.29/80.92 [7902]P57(x79021,x79022)+~P57(x79021,x79023)+~P24(f328(f328(f244(f885(x79021,f885(x79021,a871))),x79022),x79023))
% 81.29/80.92 [7943]~P24(f328(f328(f244(a877),x79433),x79432))+P24(f328(f328(f244(a877),x79431),f328(f328(f22(a877),x79432),x79433)))+~P24(f328(f328(f244(a877),f328(f328(f81(a877),x79431),x79433)),x79432))
% 81.29/80.92 [7961]P38(x79611,x79612)+~P38(x79611,x79613)+~P24(f328(f328(f244(f885(f884(x79611,x79611),a871)),x79612),x79613))
% 81.29/80.92 [7962]P55(x79621,x79622)+~P55(x79621,x79623)+~P24(f328(f328(f244(f885(f884(x79621,x79621),a871)),x79622),x79623))
% 81.29/80.92 [8207]~P110(x82071)+~P24(f328(f328(f245(x82071),f79(x82071)),x82072))+P24(f328(f328(f245(x82071),f328(f328(f258(x82071),x82072),x82073)),f328(f328(f82(x82071),x82072),f328(f328(f258(x82071),x82072),x82073))))
% 81.29/80.92 [8296]~P24(f328(x82961,f2(a1)))+~P24(f328(x82961,f328(f328(f22(a1),f328(f106(a1),x82962)),f328(f106(a1),x82963))))+P24(f328(x82961,f328(f106(a1),f328(f328(f22(a877),x82962),x82963))))
% 81.29/80.92 [8309]~P24(f328(f328(f244(a877),x83093),x83092))+P24(f328(x83091,f328(f328(f22(a1),f328(f106(a1),x83092)),f328(f106(a1),x83093))))+~P24(f328(x83091,f328(f106(a1),f328(f328(f22(a877),x83092),x83093))))
% 81.29/80.92 [8327]P24(f328(f328(f245(a877),x83271),x83272))+~P24(f328(x83273,f328(f328(f22(a1),f328(f106(a1),x83271)),f328(f106(a1),x83272))))+P24(f328(x83273,f328(f106(a1),f328(f328(f22(a877),x83271),x83272))))
% 81.29/80.92 [8381]~P123(x83812)+E(x83811,f2(x83812))+P24(f328(f328(f245(x83812),f2(x83812)),f328(f328(f81(x83812),f328(f328(f82(x83812),x83813),x83813)),f328(f328(f82(x83812),x83811),x83811))))
% 81.29/80.92 [8382]~P123(x83822)+E(x83821,f2(x83822))+P24(f328(f328(f245(x83822),f2(x83822)),f328(f328(f81(x83822),f328(f328(f82(x83822),x83821),x83821)),f328(f328(f82(x83822),x83823),x83823))))
% 81.29/80.92 [8491]~P24(f328(f328(f245(a877),f2(a877)),x84911))+~P24(f328(f328(f245(a1),x84912),x84913))+P24(f328(f328(f245(a1),f328(f328(f82(a1),f328(f106(a1),x84911)),x84912)),f328(f328(f82(a1),f328(f106(a1),x84911)),x84913)))
% 81.29/80.92 [8547]E(f328(f328(f107(f885(x85471,a871)),x85472),f40(f885(x85471,a871),x85473)),f193(f885(x85471,a871)))+P24(f328(f328(f330(f885(x85471,a871)),x85472),x85473))+P24(f328(f328(f330(f885(x85471,a871)),f768(x85473,x85472,x85471)),f328(f328(f306(f885(x85471,a871)),x85472),x85473)))
% 81.29/80.92 [8548]E(f328(f328(f107(f885(x85481,a871)),x85482),f40(f885(x85481,a871),x85483)),f193(f885(x85481,a871)))+P24(f328(f328(f330(f885(x85481,a871)),x85482),x85483))+P24(f328(f328(f330(f885(x85481,a871)),f795(x85483,x85482,x85481)),f328(f328(f306(f885(x85481,a871)),x85482),x85483)))
% 81.29/80.92 [8576]E(x85761,x85762)+~E(f328(f194(f878(x85763)),x85761),f328(f194(f878(x85763)),x85762))+P24(f328(f328(f330(f884(x85763,x85763)),f605(x85763,x85761,x85762)),f328(f171(f884(x85763,x85763)),f328(f328(f181(x85763,x85763),x85762),x85761))))
% 81.29/80.92 [8808]E(f304(x88081,x88082),f304(x88081,x88083))+~P24(f328(f328(f244(f885(f884(x88081,x88081),a871)),x88083),f304(x88081,x88082)))+~P24(f328(f328(f244(f885(f884(x88081,x88081),a871)),x88082),x88083))
% 81.29/80.92 [8868]~P48(x88681,f252(f885(x88681,a871)),x88683)+P24(f328(f328(f244(f885(f884(f878(x88681),f878(x88681)),a871)),f156(x88681,x88682)),f157(x88681,x88683)))+~P24(f328(f328(f244(f885(f884(x88681,x88681),a871)),x88682),x88683))
% 81.29/80.92 [9074]P38(x90741,x90742)+~P24(f328(f328(f330(x90741),x90743),f766(x90742,x90741)))+P24(f328(f328(f330(f884(x90741,x90741)),f328(f328(f257(x90741,x90741),f796(x90742,x90741,x90743)),x90743)),x90742))
% 81.29/80.92 [9108]~P24(f328(f62(x91081),x91082))+P24(f328(f62(f885(x91081,a871)),f328(f328(f61(x91081),x91082),x91083)))+~P24(f328(f328(f244(f885(f884(x91081,x91081),a871)),x91083),f328(f328(f265(x91081,x91081),x91082),f328(f16(f885(x91081,a871),x91081),x91082))))
% 81.29/80.92 [9143]P48(x91431,x91432,x91433)+P24(f328(f328(f330(x91431),f698(x91433,x91432,x91431)),x91432))+~P24(f328(f328(f244(f885(f884(x91431,x91431),a871)),x91433),f328(f328(f265(x91431,x91431),x91432),f328(f16(f885(x91431,a871),x91431),x91432))))
% 81.29/80.92 [9144]P48(x91441,x91442,x91443)+P24(f328(f328(f330(x91441),f702(x91442,x91443,x91441)),x91442))+~P24(f328(f328(f244(f885(f884(x91441,x91441),a871)),x91443),f328(f328(f265(x91441,x91441),x91442),f328(f16(f885(x91441,a871),x91441),x91442))))
% 81.29/80.92 [9179]~P64(x91791)+~P24(f328(f328(f245(x91791),x91792),x91793))+P24(f328(f328(f245(x91791),f328(f328(f286(x91791),f328(f328(f81(x91791),x91792),x91793)),f328(f328(f81(x91791),f79(x91791)),f79(x91791)))),x91793))
% 81.29/80.92 [9208]~P63(x92081)+P24(f328(f328(f244(x92081),x92082),x92083))+~P24(f328(f328(f244(x92081),f328(f328(f82(x92081),f356(x92083,x92082,x92081)),x92082)),x92083))
% 81.29/80.92 [9345]E(f328(f194(f878(f878(x93451))),f328(f135(f878(x93451),f328(f328(f8(a877,a871,f878(x93451)),f328(f245(a877),x93452)),f194(f878(x93451)))),f179(x93451,x93453))),f328(f194(f878(x93451)),f328(f328(f164(f878(x93451)),x93453),x93452)))+~P29(a877,f328(f168(a877),f328(f328(f153(f878(x93451),a877),f194(f878(x93451))),x93453)))+~P24(f328(f328(f245(a877),x93452),f328(f194(f878(f878(x93451))),x93453)))
% 81.29/80.92 [9452]~P38(x94521,x94522)+P22(x94521,f328(f328(f257(f885(f884(x94521,x94521),a871),f885(f884(x94521,x94521),a871)),x94522),x94523))+~P24(f328(f328(f244(f885(f884(x94521,x94521),a871)),f328(f328(f285(x94521,x94521,x94521),x94522),x94523)),x94522))
% 81.29/80.92 [9459]E(f328(f328(f153(f878(x94591),x94591),f328(f328(f7(f878(x94591),a877,x94591),f164(x94591)),x94592)),f328(f135(f878(x94591),f328(f328(f8(a877,a871,f878(x94591)),f328(f245(a877),x94592)),f194(f878(x94591)))),f179(x94591,x94593))),f328(f328(f164(f878(x94591)),x94593),x94592))+~P29(a877,f328(f168(a877),f328(f328(f153(f878(x94591),a877),f194(f878(x94591))),x94593)))+~P24(f328(f328(f245(a877),x94592),f328(f194(f878(f878(x94591))),x94593)))
% 81.29/80.92 [9593]P48(x95931,x95932,x95933)+~P24(f328(f328(f330(f884(x95931,x95931)),f328(f328(f257(x95931,x95931),f698(x95933,x95932,x95931)),f698(x95933,x95932,x95931))),x95933))+~P24(f328(f328(f244(f885(f884(x95931,x95931),a871)),x95933),f328(f328(f265(x95931,x95931),x95932),f328(f16(f885(x95931,a871),x95931),x95932))))
% 81.29/80.92 [9594]P48(x95941,x95942,x95943)+~P24(f328(f328(f330(f884(x95941,x95941)),f328(f328(f257(x95941,x95941),f702(x95942,x95943,x95941)),f702(x95942,x95943,x95941))),x95943))+~P24(f328(f328(f244(f885(f884(x95941,x95941),a871)),x95943),f328(f328(f265(x95941,x95941),x95942),f328(f16(f885(x95941,a871),x95941),x95942))))
% 81.29/80.92 [9766]~P137(x97661)+~P122(x97661)+E(f328(f328(f286(x97661),f328(f108(x97661),f328(f328(f74(f884(a1,a1),a1,x97662,f256(a1,a1)),f220(x97662)),x97663))),f328(f108(x97661),f328(f328(f74(f884(a1,a1),a1,x97662,f266(a1,a1)),f220(x97662)),x97663))),f233(x97662,x97661,x97663))
% 81.29/80.92 [9969]~E(x99693,f2(a877))+~E(f328(f194(f878(x99691)),f328(f328(f164(f878(x99691)),x99692),f649(x99693,x99691,x99692))),x99693)+E(f328(f328(f153(a877,f878(x99691)),f328(f328(f7(a877,f878(a877),f878(x99691)),f328(f328(f8(f885(a877,x99691),f885(f878(a877),f878(x99691)),a877),f153(a877,x99691)),f328(f7(a877,a877,x99691),f328(f328(f8(f878(x99691),f885(a877,x99691),a877),f164(x99691)),f328(f164(f878(x99691)),x99692))))),f138(a877,f328(f298(a877,f2(a877)),f328(f194(f878(f878(x99691))),x99692))))),f138(a877,f328(f298(a877,f2(a877)),x99693))),f179(x99691,x99692))
% 81.29/80.92 [9970]E(x99701,f119(f878(x99702)))+~E(f328(f194(f878(x99702)),f328(f328(f164(f878(x99702)),x99701),f649(x99703,x99702,x99701))),x99703)+E(f328(f328(f153(a877,f878(x99702)),f328(f328(f7(a877,f878(a877),f878(x99702)),f328(f328(f8(f885(a877,x99702),f885(f878(a877),f878(x99702)),a877),f153(a877,x99702)),f328(f7(a877,a877,x99702),f328(f328(f8(f878(x99702),f885(a877,x99702),a877),f164(x99702)),f328(f164(f878(x99702)),x99701))))),f138(a877,f328(f298(a877,f2(a877)),f328(f194(f878(f878(x99702))),x99701))))),f138(a877,f328(f298(a877,f2(a877)),x99703))),f179(x99702,x99701))
% 81.29/80.92 [9971]~E(x99713,f2(a877))+E(f328(f328(f153(a877,f878(x99711)),f328(f328(f7(a877,f878(a877),f878(x99711)),f328(f328(f8(f885(a877,x99711),f885(f878(a877),f878(x99711)),a877),f153(a877,x99711)),f328(f7(a877,a877,x99711),f328(f328(f8(f878(x99711),f885(a877,x99711),a877),f164(x99711)),f328(f164(f878(x99711)),x99712))))),f138(a877,f328(f298(a877,f2(a877)),f328(f194(f878(f878(x99711))),x99712))))),f138(a877,f328(f298(a877,f2(a877)),x99713))),f179(x99711,x99712))+P24(f328(f328(f245(a877),f649(x99713,x99711,x99712)),f328(f194(f878(f878(x99711))),x99712)))
% 81.29/80.92 [9972]E(x99721,f119(f878(x99722)))+E(f328(f328(f153(a877,f878(x99722)),f328(f328(f7(a877,f878(a877),f878(x99722)),f328(f328(f8(f885(a877,x99722),f885(f878(a877),f878(x99722)),a877),f153(a877,x99722)),f328(f7(a877,a877,x99722),f328(f328(f8(f878(x99722),f885(a877,x99722),a877),f164(x99722)),f328(f164(f878(x99722)),x99721))))),f138(a877,f328(f298(a877,f2(a877)),f328(f194(f878(f878(x99722))),x99721))))),f138(a877,f328(f298(a877,f2(a877)),x99723))),f179(x99722,x99721))+P24(f328(f328(f245(a877),f649(x99723,x99722,x99721)),f328(f194(f878(f878(x99722))),x99721)))
% 81.29/80.92 [7709]E(f328(f328(f81(a877),f328(f109(a877),x77091)),f328(f328(f81(a877),f328(f109(a877),x77092)),x77093)),f328(f328(f81(a877),f328(f109(a877),f328(f328(f81(a1),x77091),x77092))),x77093))+P24(f328(a199,f328(f109(a1),x77091)))+P24(f328(a199,f328(f109(a1),x77092)))
% 81.29/80.92 [8482]~P24(f328(f62(x84821),x84822))+~P24(f328(f328(f330(x84821),x84823),x84822))+E(f328(a118,f328(f38(x84821),f328(f328(f22(f885(x84821,a871)),x84822),f328(f328(f306(x84821),x84823),f193(f885(x84821,a871)))))),f328(f38(x84821),x84822))
% 81.29/80.92 [8501]~P24(f328(f62(x85011),x85012))+~P24(f328(f328(f330(x85011),x85013),x85012))+E(f328(f328(f81(a877),f79(a877)),f328(f38(x85011),f328(f328(f22(f885(x85011,a871)),x85012),f328(f328(f306(x85011),x85013),f193(f885(x85011,a871)))))),f328(f38(x85011),x85012))
% 81.29/80.92 [8585]~P106(x85851)+~P24(f328(f62(x85851),x85853))+E(f328(f328(f147(x85851,x85851,f5(x85851)),x85852),f138(x85851,f328(f328(f22(f885(x85851,a871)),x85853),f328(f328(f306(x85851),x85852),f193(f885(x85851,a871)))))),f138(x85851,f328(f328(f306(x85851),x85852),x85853)))
% 81.29/80.92 [8737]~P24(f328(f62(x87371),x87373))+~P24(f328(f62(x87371),x87372))+E(f328(f328(f81(a877),f328(f38(x87371),f328(f328(f116(f885(x87371,a871)),x87372),x87373))),f328(f38(x87371),f328(f328(f107(f885(x87371,a871)),x87372),x87373))),f328(f328(f81(a877),f328(f38(x87371),x87372)),f328(f38(x87371),x87373)))
% 81.29/80.92 [9917]~P21(x99171,f885(f885(x99171,a871),a871),f328(f328(f7(x99171,f885(f884(x99171,x99171),a871),f885(f885(x99171,a871),a871)),f328(f328(f8(f885(x99171,a871),f885(f885(f884(x99171,x99171),a871),f885(f885(x99171,a871),a871)),x99171),f61(x99171)),f328(f328(f7(x99171,f885(x99171,a871),f885(x99171,a871)),f306(x99171)),f193(f885(x99171,a871))))),x99173),x99172)+~P24(f328(f62(x99171),x99172))+E(f328(f38(f885(x99171,a871)),f328(f328(f61(x99171),x99172),x99173)),f328(f38(x99171),x99172))
% 81.29/80.92 [7977]~P96(x79771)+P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),x79773)))+E(f328(f328(f258(x79771),x79772),f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),x79773),x79773)),a103))),f79(x79771))
% 81.29/80.92 [9435]~P96(x94351)+~P24(f328(f328(f244(a1),f2(a1)),f328(f109(a1),x94353)))+E(f328(f328(f258(x94351),x94352),f328(f109(a877),f328(f328(f22(a1),f328(f328(f81(a1),x94353),x94353)),a103))),f328(f328(f87(x94351,x94351),f328(f328(f258(x94351),x94352),f328(f109(a877),x94353))),f328(f328(f18(x94351,x94351,x94351),f328(f328(f8(x94351,f885(x94351,x94351),x94351),f82(x94351)),f328(f82(x94351),x94352))),f5(x94351))))
% 81.29/80.92 [9823]~P24(f328(f136(x98231),x98233))+~P24(f328(f328(f330(x98231),x98232),f328(f171(x98231),x98233)))+E(f328(f328(f137(x98231),f328(f194(f878(x98231)),f176(x98231,f328(f328(f8(a871,a871,x98231),a323),f328(f328(f7(x98231,x98231,a871),a325),x98232)),f328(f168(x98231),x98233)))),f328(f168(x98231),x98233)),f328(f328(f150(x98231),x98232),f328(f168(x98231),f176(x98231,f328(f328(f8(a871,a871,x98231),a323),f328(f328(f7(x98231,x98231,a871),a325),x98232)),x98233))))
% 81.29/80.92 [9896]P24(f328(f328(f244(f885(f884(x98961,x98961),a871)),f304(x98961,x98962)),x98963))+~P24(f328(f328(f244(f885(f884(x98961,x98961),a871)),f304(x98961,f193(f885(f884(x98961,x98961),a871)))),x98963))+~P24(f328(f328(f244(f885(f884(x98961,x98961),a871)),f328(f328(f285(x98961,x98961,x98961),f328(f328(f107(f885(f884(x98961,x98961),a871)),f304(x98961,x98962)),x98963)),x98962)),x98963))
% 81.29/80.92 [9737]~P24(f328(f62(x97371),f328(f249(x97371),x97373)))+~P24(f328(f62(x97371),f328(f249(x97371),x97372)))+P24(f328(f62(x97371),f328(f249(x97371),f328(f328(f18(x97371,a871,a871),f328(f328(f8(a871,f885(a871,a871),x97371),a327),x97372)),x97373))))
% 81.29/80.92 [10033]P24(f328(f328(f244(f885(f884(x100331,x100331),a871)),f328(f328(f285(x100331,x100331,x100331),x100332),f304(x100331,x100332))),x100333))+~P24(f328(f328(f244(f885(f884(x100331,x100331),a871)),x100332),x100333))+~P24(f328(f328(f244(f885(f884(x100331,x100331),a871)),f328(f328(f285(x100331,x100331,x100331),f328(f328(f107(f885(f884(x100331,x100331),a871)),f328(f328(f285(x100331,x100331,x100331),x100332),f304(x100331,x100332))),x100333)),x100332)),x100333))
% 81.29/80.92 [9987]~P111(x99872)+E(x99871,f2(x99872))+~E(f328(f328(f81(x99872),f328(f328(f258(x99872),x99873),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x99872),x99871),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f2(x99872))
% 81.29/80.92 [9988]~P111(x99882)+E(x99881,f2(x99882))+~E(f328(f328(f81(x99882),f328(f328(f258(x99882),x99881),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x99882),x99883),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f2(x99882))
% 81.29/80.92 [9993]~P24(f328(f136(x99931),x99933))+~P24(f328(f328(f330(x99931),x99932),f328(f171(x99931),x99933)))+E(f328(f168(x99931),f328(f170(x99931),f328(f328(f137(x99931),f328(f194(f878(x99931)),f176(x99931,f328(f328(f8(a871,a871,x99931),a323),f328(f328(f7(x99931,x99931,a871),a325),x99932)),x99933))),x99933))),f176(x99931,f328(f328(f8(a871,a871,x99931),a323),f328(f328(f7(x99931,x99931,a871),a325),x99932)),f328(f168(x99931),x99933)))
% 81.29/80.92 [10078]~P111(x100782)+E(x100781,f2(x100782))+P24(f328(f328(f245(x100782),f2(x100782)),f328(f328(f81(x100782),f328(f328(f258(x100782),x100783),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x100782),x100781),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))))
% 81.29/80.92 [10079]~P111(x100792)+E(x100791,f2(x100792))+P24(f328(f328(f245(x100792),f2(x100792)),f328(f328(f81(x100792),f328(f328(f258(x100792),x100791),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x100792),x100793),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))))
% 81.29/80.92 [10122]~P111(x101221)+P24(f328(f328(f244(x101221),f2(x101221)),x101222))+~P24(f328(f328(f244(x101221),f2(x101221)),f328(f328(f258(x101221),x101222),f328(a118,f328(f328(f82(a877),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),x101223)))))
% 81.29/80.92 [5489]~P20(x54891,x54894,x54893)+P20(x54891,x54892,x54893)+~P20(x54891,x54892,x54894)
% 81.29/80.92 [4949]~E(x49492,f91(x49493,x49491))+P24(f328(x49491,x49492))+~P24(f328(x49491,x49494))
% 81.29/80.92 [6704]~P38(x67042,x67044)+~P38(x67041,x67043)+P38(f884(x67041,x67042),f320(x67041,x67042,x67043,x67044))
% 81.29/80.92 [5128]~P5(x51284,x51281)+~E(f328(x51281,x51282),f328(x51281,x51283))+P24(f328(f328(x51281,x51282),x51283))
% 81.29/80.92 [5302]~P5(x53024,x53021)+E(f328(x53021,x53022),f328(x53021,x53023))+~P24(f328(f328(x53021,x53022),x53023))
% 81.29/80.92 [5395]~P14(x53953,x53954,x53951)+E(f328(x53951,x53952),f328(f64(x53953,x53954),x53952))+~P24(f328(f62(x53953),x53952))
% 81.29/80.92 [5396]~P3(x53963,x53964,x53961)+E(f328(x53961,x53962),f328(f64(x53963,x53964),x53962))+~P24(f328(f62(x53963),x53962))
% 81.29/80.92 [5522]~P5(x55224,x55221)+~P24(f328(f328(x55221,x55223),x55222))+P24(f328(f328(x55221,x55222),x55223))
% 81.29/80.92 [5589]E(x55891,x55892)+~E(f328(f256(x55893,x55894),x55891),f328(f256(x55893,x55894),x55892))+~E(f328(f266(x55893,x55894),x55891),f328(f266(x55893,x55894),x55892))
% 81.29/80.92 [5614]E(x56141,x56142)+~P24(f328(f48(x56143,x56144),x56142))+~P24(f328(f48(x56143,x56144),x56141))
% 81.29/80.92 [5805]~P74(x58052)+E(f234(x58051,x58052,x58053,x58054),f2(x58052))+P24(f328(f62(x58051),x58054))
% 81.29/80.92 [5942]~P24(f328(f316(x59421,x59422),x59424))+P24(f328(f316(x59421,x59422),x59423))+~P24(f328(f328(x59422,x59423),x59424))
% 81.29/80.92 [7897]~P106(x78972)+~P24(f328(f136(x78971),x78974))+P24(f328(f136(x78971),f149(x78971,x78972,x78973,x78974)))
% 81.29/80.92 [8125]~P24(f328(f62(x81252),x81254))+~P24(f328(f62(x81251),x81253))+P24(f328(f62(f883(x81251,x81252)),f315(x81251,x81252,x81253,x81254)))
% 81.29/80.92 [8126]~P24(f328(f136(x81262),x81264))+~P24(f328(f136(x81261),x81263))+P24(f328(f136(f884(x81261,x81262)),f60(x81261,x81262,x81263,x81264)))
% 81.29/80.92 [8130]P24(f328(f328(f330(f878(x81301)),f328(f328(f127(x81301),x81302),x81303)),f160(x81301,x81304)))+~P24(f328(f328(f330(f878(x81301)),x81303),f160(x81301,x81304)))+~P24(f328(f328(f330(f878(x81301)),x81302),f160(x81301,x81304)))
% 81.29/80.92 [8450]P24(f328(x84501,x84502))+~E(x84503,f328(f236(x84504),x84502))+~P24(f328(x84501,f410(x84502,x84501,x84503,x84504)))
% 81.29/80.92 [8461]~P106(x84613)+~P24(f328(f136(x84611),f149(x84611,x84613,x84614,x84612)))+P24(f328(f136(x84611),x84612))
% 81.29/80.92 [8728]~P24(f328(f328(f330(f884(x87281,x87281)),f328(f328(f257(x87281,x87281),x87282),x87284)),f304(x87281,x87283)))+P24(f328(f328(f330(x87281),x87282),f317(x87281,x87283)))+~P24(f328(f328(f330(x87281),x87284),f317(x87281,x87283)))
% 81.29/80.92 [8748]~E(x87484,f328(f236(x87483),x87482))+P24(f328(x87481,x87482))+P24(f328(f328(f330(x87483),f410(x87482,x87481,x87484,x87483)),f235(x87483,x87484)))
% 81.29/80.92 [5112]~P74(x51122)+E(f328(f328(f6(x51121,x51122),x51123),x51124),f2(x51122))+P24(f328(f62(x51121),x51124))
% 81.29/80.92 [5115]~P75(x51152)+E(f328(f328(f9(x51151,x51152),x51153),x51154),f79(x51152))+P24(f328(f62(x51151),x51154))
% 81.29/80.92 [5266]~P69(x52663)+E(x52661,x52662)+~E(f328(f328(f81(x52663),x52664),x52661),f328(f328(f81(x52663),x52664),x52662))
% 81.29/80.92 [5267]~P70(x52673)+E(x52671,x52672)+~E(f328(f328(f81(x52673),x52674),x52671),f328(f328(f81(x52673),x52674),x52672))
% 81.29/80.92 [5269]~P69(x52693)+E(x52691,x52692)+~E(f328(f328(f81(x52693),x52691),x52694),f328(f328(f81(x52693),x52692),x52694))
% 81.29/80.92 [5348]~E(x53482,f328(f328(f306(x53481),x53483),x53484))+~P24(f328(f62(x53481),x53484))+P24(f328(f62(x53481),x53482))
% 81.29/80.92 [5391]~P27(x53913)+E(x53911,f193(f885(x53912,a871)))+E(f328(f328(f42(x53912,x53913),x53911),f328(f16(x53913,x53912),x53914)),x53914)
% 81.29/80.92 [5392]~P27(x53923)+E(x53921,f193(f885(x53922,a871)))+E(f328(f328(f43(x53922,x53923),x53921),f328(f16(x53923,x53922),x53924)),x53924)
% 81.29/80.92 [5602]~P108(x56023)+E(x56021,x56022)+~E(f299(x56023,x56024,x56021),f328(f328(f306(x56023),x56022),f193(f885(x56023,a871))))
% 81.29/80.92 [5603]~P108(x56033)+E(x56031,x56032)+~E(f299(x56033,x56031,x56032),f328(f328(f306(x56033),x56034),f193(f885(x56033,a871))))
% 81.29/80.92 [5663]~P36(x56633,x56631,x56634)+P36(x56633,x56631,f328(f328(f150(x56633),x56632),x56634))+P24(f328(x56631,x56632))
% 81.29/80.92 [5765]~P32(x57651,x57652,x57654)+~P24(f328(x57652,x57653))+P32(x57651,x57652,f328(f328(f150(x57651),x57653),x57654))
% 81.29/80.92 [5898]P24(f328(x58981,x58982))+~P24(f328(f262(x58983,x58981),x58984))+~P24(f328(f328(f330(x58983),x58982),x58984))
% 81.29/80.92 [5907]~P32(x59071,x59072,x59074)+~P32(x59071,x59072,x59073)+P32(x59071,x59072,f328(f328(f127(x59071),x59073),x59074))
% 81.29/80.92 [5917]P34(x59171,x59172,x59173)+~P34(x59171,x59172,f328(f328(f150(x59171),x59174),x59173))+P24(f328(x59172,x59174))
% 81.29/80.92 [5918]P36(x59181,x59182,x59183)+~P36(x59181,x59182,f328(f328(f150(x59181),x59184),x59183))+P24(f328(x59182,x59184))
% 81.29/80.92 [5931]E(x59311,x59312)+~P24(f328(f328(f200(x59313),x59314),x59312))+~P24(f328(f328(f200(x59313),x59314),x59311))
% 81.29/80.92 [5998]P34(x59981,x59982,x59983)+P34(x59981,x59982,x59984)+~P34(x59981,x59982,f328(f328(f127(x59981),x59984),x59983))
% 81.29/80.92 [6017]~P74(x60171)+E(f328(f328(f6(a877,x60171),x60172),f328(f298(a877,x60173),f328(a118,x60174))),f2(x60171))+~P24(f328(f328(f245(a877),x60174),x60173))
% 81.29/80.92 [6022]~P59(x60221)+~E(f45(x60221,x60222,x60223),f45(x60221,x60224,x60223))+E(f45(x60221,f328(f80(x60221),x60222),x60223),f45(x60221,f328(f80(x60221),x60224),x60223))
% 81.29/80.92 [6090]P24(f328(x60901,x60902))+~E(f328(f135(x60903,x60901),x60904),x60904)+~P24(f328(f328(f330(x60903),x60902),f328(f171(x60903),x60904)))
% 81.29/80.92 [6109]~E(f328(f328(f81(a877),x61093),x61092),f328(f328(f81(a877),x61091),x61094))+~P24(f328(f328(f245(a877),x61093),x61094))+P24(f328(f328(f245(a877),x61091),x61092))
% 81.29/80.92 [6113]P34(x61131,x61132,x61133)+~P24(f328(x61132,x61134))+~P24(f328(f328(f330(x61131),x61134),f328(f171(x61131),x61133)))
% 81.29/80.92 [6149]~P32(x61493,x61491,x61494)+P24(f328(x61491,x61492))+~P24(f328(f328(f330(x61493),x61492),f328(f171(x61493),x61494)))
% 81.29/80.92 [6151]~E(f328(f135(x61511,x61512),x61513),f119(x61511))+~P24(f328(x61512,x61514))+~P24(f328(f328(f330(x61511),x61514),f328(f171(x61511),x61513)))
% 81.29/80.92 [6152]~E(f176(x61523,x61521,x61524),x61524)+P24(f328(x61521,x61522))+~P24(f328(f328(f330(x61523),x61522),f328(f171(x61523),x61524)))
% 81.29/80.92 [6186]~E(x61864,f193(f885(x61862,a871)))+~E(x61863,f193(f885(x61861,a871)))+E(f315(x61861,x61862,x61863,x61864),f193(f885(f883(x61861,x61862),a871)))
% 81.29/80.92 [6330]P24(f328(x63301,x63302))+~P24(f328(f159(x63303,x63301),x63304))+~P24(f328(f328(f330(x63303),x63302),f328(f171(x63303),x63304)))
% 81.29/80.92 [6601]~P74(x66011)+E(f328(f328(f6(a877,x66011),x66012),f299(a877,x66013,f328(a118,x66014))),f2(x66011))+~P24(f328(f328(f245(a877),f328(a118,x66014)),x66013))
% 81.29/80.92 [6743]~P106(x67431)+E(f328(f328(f22(f885(x67431,a871)),f328(f298(x67431,x67432),x67433)),f328(f298(x67431,x67432),x67434)),f328(f298(x67431,x67434),x67433))+~P24(f328(f328(f244(x67431),x67432),x67434))
% 81.29/80.92 [7093]~P24(f328(f328(f330(f878(x70931)),x70934),f160(x70931,x70933)))+P24(f328(f328(f330(x70931),x70932),x70933))+~P24(f328(f328(f330(x70931),x70932),f328(f171(x70931),x70934)))
% 81.29/80.92 [7100]~P38(x71001,x71002)+P24(f328(f328(f330(x71001),f791(x71002,x71001,x71003)),x71003))+~P24(f328(f328(f330(x71001),x71004),x71003))
% 81.29/80.92 [7156]~P74(x71561)+E(f328(f328(f328(f66(x71561,x71562,f81(x71561)),x71563),f2(x71561)),x71564),f328(f328(f6(x71562,x71561),x71563),x71564))+~P24(f328(f62(x71562),x71564))
% 81.29/80.92 [7158]~P75(x71581)+E(f328(f328(f328(f66(x71581,x71582,f82(x71581)),x71583),f79(x71581)),x71584),f328(f328(f9(x71582,x71581),x71583),x71584))+~P24(f328(f62(x71582),x71584))
% 81.29/80.92 [7186]P21(x71861,x71862,x71863,x71864)+~E(f328(f38(x71862),f328(f307(x71861,x71862,x71863),x71864)),f328(f38(x71861),x71864))+~P24(f328(f62(x71861),x71864))
% 81.29/80.92 [7372]~P74(x73721)+E(f328(f328(f81(x73721),f328(x73722,x73723)),f328(f328(f6(a877,x73721),x73722),f301(a877,x73723,x73724))),f328(f328(f6(a877,x73721),x73722),f299(a877,x73723,x73724)))+~P24(f328(f328(f244(a877),x73723),x73724))
% 81.29/80.92 [7382]~P74(x73821)+~P21(x73822,x73821,x73823,x73824)+E(f328(f328(f6(x73821,x73821),f35(x73821)),f328(f307(x73822,x73821,x73823),x73824)),f328(f328(f6(x73822,x73821),x73823),x73824))
% 81.29/80.92 [7383]~P75(x73831)+~P21(x73832,x73831,x73833,x73834)+E(f328(f328(f9(x73831,x73831),f35(x73831)),f328(f307(x73832,x73831,x73833),x73834)),f328(f328(f9(x73832,x73831),x73833),x73834))
% 81.29/80.92 [7437]E(f328(f38(f883(x74371,x74372)),f315(x74371,x74372,x74373,x74374)),f328(f328(f81(a877),f328(f38(x74371),x74373)),f328(f38(x74372),x74374)))+~P24(f328(f62(x74372),x74374))+~P24(f328(f62(x74371),x74373))
% 81.29/80.92 [7521]E(x75211,x75212)+P24(f328(f328(f330(x75213),x75211),f328(f171(x75213),f169(x75213,x75212,x75214))))+~P24(f328(f328(f330(x75213),x75211),f328(f171(x75213),x75214)))
% 81.29/80.92 [7745]~P74(x77451)+E(f328(f328(f81(x77451),f328(f328(f6(a877,x77451),x77452),f328(f298(a877,x77453),x77454))),f328(x77452,x77454)),f328(f328(f6(a877,x77451),x77452),f328(f298(a877,x77453),f328(a118,x77454))))+P24(f328(f328(f245(a877),x77454),x77453))
% 81.29/80.92 [7798]~P21(x77981,x77982,x77983,f252(f885(x77981,a871)))+~P24(f328(f62(x77982),x77984))+P24(f328(f62(x77981),f328(f308(x77981,x77982,x77983),x77984)))
% 81.29/80.92 [7910]P24(f328(f328(f330(f878(x79101)),f328(f328(f150(x79101),x79102),x79103)),f160(x79101,x79104)))+~P24(f328(f328(f330(f878(x79101)),x79103),f160(x79101,x79104)))+~P24(f328(f328(f330(x79101),x79102),x79104))
% 81.29/80.92 [8001]~E(f328(f307(x80013,x80011,x80014),f252(f885(x80013,a871))),f252(f885(x80011,a871)))+P24(f328(f62(x80011),x80012))+~P24(f328(f62(x80013),f328(f308(x80013,x80011,x80014),x80012)))
% 81.29/80.92 [8097]~P21(x80971,x80973,x80974,x80972)+P24(f328(f62(x80971),x80972))+~P24(f328(f62(x80973),f328(f307(x80971,x80973,x80974),x80972)))
% 81.29/80.92 [8118]~E(x81182,x81183)+P24(f328(f328(f330(f884(x81181,x81181)),f328(f328(f257(x81181,x81181),x81182),x81183)),f254(x81181,x81184)))+~P24(f328(f328(f330(x81181),x81182),x81184))
% 81.29/80.92 [8157]~P74(x81571)+E(f328(f328(f81(x81571),f328(f328(f6(a877,x81571),x81572),f299(a877,x81573,x81574))),f328(x81572,f328(a118,x81574))),f328(f328(f6(a877,x81571),x81572),f299(a877,x81573,f328(a118,x81574))))+P24(f328(f328(f245(a877),f328(a118,x81574)),x81573))
% 81.29/80.92 [8221]P24(f328(x82211,x82212))+~P24(f328(x82211,f328(f328(f164(x82213),x82214),f578(x82211,x82214,x82213))))+~P24(f328(f328(f330(x82213),x82212),f328(f171(x82213),x82214)))
% 81.29/80.92 [8360]~P24(f328(f328(f330(x83601),x83602),f317(x83601,x83604)))+P24(f328(f328(f330(f878(x83601)),f328(f328(f150(x83601),x83602),x83603)),f317(f878(x83601),f156(x83601,x83604))))+~P24(f328(f328(f330(f878(x83601)),x83603),f317(f878(x83601),f156(x83601,x83604))))
% 81.29/80.92 [8373]~P21(x83732,x83733,x83734,f692(x83734,x83733,x83732,x83731))+P21(x83732,x83733,x83734,f41(f885(x83732,a871),x83731))+E(x83731,f193(f885(f885(x83732,a871),a871)))
% 81.29/80.92 [8646]E(x86461,x86462)+~P24(f328(f328(f330(f884(x86463,x86463)),f328(f328(f257(x86463,x86463),x86461),x86462)),f304(x86463,x86464)))+P24(f328(f328(f330(x86463),x86461),f328(f255(x86463,x86463),x86464)))
% 81.29/80.92 [8927]P21(x89272,x89273,x89274,f41(f885(x89272,a871),x89271))+E(x89271,f193(f885(f885(x89272,a871),a871)))+P24(f328(f328(f330(f885(x89272,a871)),f692(x89274,x89273,x89272,x89271)),x89271))
% 81.29/80.92 [9065]P24(f328(f62(x90651),x90652))+~P24(f328(f62(x90654),f328(f307(x90651,x90654,x90653),x90652)))+P24(f328(f328(f330(x90651),f714(x90653,x90654,x90652,x90651)),x90652))
% 81.29/80.92 [9157]~P27(x91572)+E(f328(f328(f65(x91571,x91572,f328(f328(f8(x91572,f885(x91572,x91572),x91571),f107(x91572)),x91573)),f252(x91572)),x91574),f328(f328(f42(x91571,x91572),x91574),x91573))+~P24(f328(f62(x91571),x91574))
% 81.29/80.92 [9158]~P27(x91582)+E(f328(f328(f65(x91581,x91582,f328(f328(f8(x91582,f885(x91582,x91582),x91581),f116(x91582)),x91583)),f193(x91582)),x91584),f328(f328(f43(x91581,x91582),x91584),x91583))+~P24(f328(f62(x91581),x91584))
% 81.29/80.92 [9241]P24(f328(x92411,x92412))+~P24(f328(x92411,f328(f328(f164(x92413),x92414),f675(x92412,x92411,x92414,x92413))))+~P24(f328(f328(f330(x92413),x92412),f328(f171(x92413),x92414)))
% 81.29/80.92 [9262]E(x92621,x92622)+~P24(f328(f328(f330(f884(x92623,x92623)),f328(f328(f257(x92623,x92623),x92621),x92622)),f304(x92623,x92624)))+P24(f328(f328(f330(f884(x92623,x92623)),f328(f328(f257(x92623,x92623),x92621),x92622)),f328(f328(f285(x92623,x92623,x92623),x92624),f304(x92623,x92624))))
% 81.29/80.92 [9311]~E(f328(f194(f878(x93111)),x93112),f328(f194(f878(x93111)),x93113))+~P24(f328(f328(f330(f884(f878(x93111),f878(x93111))),f328(f328(f257(f878(x93111),f878(x93111)),x93112),x93113)),f146(x93111,x93114)))+P24(f328(f328(f330(f884(f878(x93111),f878(x93111))),f328(f328(f257(f878(x93111),f878(x93111)),x93112),x93113)),f144(x93111,x93114)))
% 81.29/80.92 [9540]P32(x95401,f328(f328(f18(x95401,a871,a871),f328(f328(f8(a871,f885(a871,a871),x95401),a327),f328(f328(f8(a871,a871,x95401),a323),x95402))),f328(a325,x95403)),x95404)+~P24(f328(x95402,x95403))+~P36(x95401,x95402,f328(f328(f150(x95401),x95403),x95404))
% 81.29/80.92 [9699]~P32(x96991,f328(f328(f18(x96991,a871,a871),f328(f328(f8(a871,f885(a871,a871),x96991),a327),f328(f328(f8(a871,a871,x96991),a323),x96992))),f328(a325,x96993)),x96994)+~P24(f328(x96992,x96993))+P36(x96991,x96992,f328(f328(f150(x96991),x96993),x96994))
% 81.29/80.92 [9703]~P36(x97031,x97032,x97034)+~P32(x97031,f328(f328(f18(x97031,a871,a871),f328(f328(f8(a871,f885(a871,a871),x97031),a327),f328(f328(f8(a871,a871,x97031),a323),x97032))),f328(a325,x97033)),x97034)+P36(x97031,x97032,f328(f328(f150(x97031),x97033),x97034))
% 81.29/80.92 [9740]~P67(x97401)+E(f328(f328(f6(a877,x97401),f328(f328(f18(a877,x97401,x97401),f328(f328(f8(x97401,f885(x97401,x97401),a877),f22(x97401)),x97402)),f328(f328(f8(a877,x97401,a877),x97402),f328(f328(f7(a877,a877,a877),f81(a877)),f79(a877))))),f299(a877,x97403,x97404)),f2(x97401))+P24(f328(f328(f244(a877),x97403),x97404))
% 81.29/80.92 [9985]~P38(x99852,x99854)+~P21(x99852,x99851,x99853,f252(f885(x99852,a871)))+P38(x99851,f328(f307(f884(x99852,x99852),f884(x99851,x99851),f268(x99852,x99851,x99852,x99851,x99853,x99853)),x99854))
% 81.29/80.92 [10149]~E(f328(f194(f878(x101491)),x101493),f328(f194(f878(x101491)),x101492))+P24(f328(f328(f330(f884(f878(x101491),f878(x101491))),f328(f328(f257(f878(x101491),f878(x101491)),x101492),x101493)),f157(x101491,x101494)))+~P24(f328(f328(f267(x101491,x101491,a871),f328(f328(f7(x101491,f885(f884(x101491,x101491),a871),f885(x101491,a871)),f328(f328(f8(f885(x101491,f885(f885(f884(x101491,x101491),a871),a871)),f885(f885(f884(x101491,x101491),a871),f885(x101491,a871)),x101491),f7(x101491,f885(f884(x101491,x101491),a871),a871)),f328(f328(f8(f885(x101491,f884(x101491,x101491)),f885(x101491,f885(f885(f884(x101491,x101491),a871),a871)),x101491),f328(f8(f884(x101491,x101491),f885(f885(f884(x101491,x101491),a871),a871),x101491),f330(f884(x101491,x101491)))),f257(x101491,x101491)))),x101494)),f591(x101494,x101493,x101492,x101491)))
% 81.29/80.92 [5981]~E(x59814,x59812)+P24(f328(x59811,x59812))+P24(f328(f328(f200(f33(x59811,x59813)),x59812),x59814))
% 81.29/80.92 [6074]~P58(x60741)+~E(x60742,f2(x60741))+E(f328(f328(f39(x60741),f328(f328(f82(x60741),x60742),x60743)),f328(f328(f82(x60741),x60742),x60744)),f2(x60741))
% 81.29/80.92 [6112]E(x61121,f119(x61122))+E(x61123,f328(f328(f22(a877),f328(f194(f878(x61122)),x61121)),f79(a877)))+E(f143(x61122,f328(f328(f158(x61122,x61121),x61123),x61124)),f143(x61122,x61121))
% 81.29/80.92 [6140]E(x61401,x61402)+P24(f328(x61403,x61402))+~P24(f328(f328(f328(f306(x61404),x61401),x61403),x61402))
% 81.29/80.92 [6156]~P74(x61561)+~P24(f328(f136(x61562),x61564))+E(f328(f165(x61561),f328(f328(f153(x61562,x61561),x61563),x61564)),f328(f328(f6(x61562,x61561),x61563),f328(f171(x61562),x61564)))
% 81.29/80.92 [6179]~P75(x61792)+~P24(f328(f62(x61791),x61794))+E(f328(f328(f9(x61791,x61792),f328(f16(x61792,x61791),x61793)),x61794),f328(f328(f258(x61792),x61793),f328(f38(x61791),x61794)))
% 81.29/80.92 [6233]~P61(x62332)+E(x62331,f2(x62332))+E(f328(f328(f286(x62332),f328(f328(f82(x62332),x62333),x62331)),f328(f328(f82(x62332),x62334),x62331)),f328(f328(f286(x62332),x62333),x62334))
% 81.29/80.92 [6234]~P61(x62342)+E(x62341,f2(x62342))+E(f328(f328(f286(x62342),f328(f328(f82(x62342),x62341),x62343)),f328(f328(f82(x62342),x62341),x62344)),f328(f328(f286(x62342),x62343),x62344))
% 81.29/80.92 [6235]~P58(x62352)+E(x62351,f2(x62352))+E(f328(f328(f39(x62352),f328(f328(f82(x62352),x62353),x62351)),f328(f328(f82(x62352),x62354),x62351)),f328(f328(f39(x62352),x62353),x62354))
% 81.29/80.92 [6237]~P58(x62372)+E(x62371,f2(x62372))+E(f328(f328(f39(x62372),f328(f328(f82(x62372),x62371),x62373)),f328(f328(f82(x62372),x62371),x62374)),f328(f328(f39(x62372),x62373),x62374))
% 81.29/80.92 [6300]P24(f328(x63001,x63002))+~E(x63003,f328(f328(f81(a877),x63004),x63002))+~P24(f328(x63001,f328(f328(f22(a877),x63003),x63004)))
% 81.29/80.92 [6383]P23(x63831,x63832,x63833)+P30(x63831,f601(x63833,x63832,x63831),x63834)+~P24(f328(f328(f330(f876(x63831)),x63834),x63832))
% 81.29/80.92 [6385]~P24(f328(x63852,x63853))+~P24(f328(f159(x63851,x63852),x63854))+P24(f328(f159(x63851,x63852),f328(f328(f150(x63851),x63853),x63854)))
% 81.29/80.92 [6425]E(x64251,f119(x64252))+~E(x64253,f328(f328(f22(a877),f328(f194(f878(x64252)),x64251)),f79(a877)))+E(f143(x64252,f328(f328(f158(x64252,x64251),x64253),x64254)),x64254)
% 81.29/80.92 [6448]~P65(x64481)+~P24(f328(f328(f244(x64481),x64482),x64484))+P24(f328(f328(f244(x64481),x64482),f328(f328(f116(x64481),x64483),x64484)))
% 81.29/80.92 [6449]~P65(x64491)+~P24(f328(f328(f244(x64491),x64492),x64493))+P24(f328(f328(f244(x64491),x64492),f328(f328(f116(x64491),x64493),x64494)))
% 81.29/80.92 [6451]~P106(x64511)+~P24(f328(f328(f244(x64511),x64512),x64514))+P24(f328(f328(f244(x64511),x64512),f328(f328(f243(x64511),x64513),x64514)))
% 81.29/80.92 [6453]~P106(x64531)+~P24(f328(f328(f244(x64531),x64532),x64533))+P24(f328(f328(f244(x64531),x64532),f328(f328(f243(x64531),x64533),x64534)))
% 81.29/80.92 [6454]~P65(x64541)+~P24(f328(f328(f245(x64541),x64542),x64544))+P24(f328(f328(f245(x64541),x64542),f328(f328(f116(x64541),x64543),x64544)))
% 81.29/80.92 [6455]~P65(x64551)+~P24(f328(f328(f245(x64551),x64552),x64553))+P24(f328(f328(f245(x64551),x64552),f328(f328(f116(x64551),x64553),x64554)))
% 81.29/80.92 [6457]~P106(x64571)+~P24(f328(f328(f245(x64571),x64572),x64574))+P24(f328(f328(f245(x64571),x64572),f328(f328(f243(x64571),x64573),x64574)))
% 81.29/80.92 [6459]~P106(x64591)+~P24(f328(f328(f245(x64591),x64592),x64593))+P24(f328(f328(f245(x64591),x64592),f328(f328(f243(x64591),x64593),x64594)))
% 81.29/80.92 [6546]~E(f328(f328(f164(x65461),x65462),x65463),x65464)+E(f328(f328(f158(x65461,x65462),x65463),x65464),x65462)+~P24(f328(f328(f245(a877),x65463),f328(f194(f878(x65461)),x65462)))
% 81.29/80.92 [6563]E(x65631,x65632)+P24(f328(x65633,x65631))+~P24(f328(f328(f200(f33(x65633,x65634)),x65631),x65632))
% 81.29/80.92 [6587]P24(f328(x65871,x65872))+~P24(f328(x65873,x65872))+~P24(f328(f328(f244(f885(x65874,a871)),x65873),x65871))
% 81.29/80.92 [6619]~E(f328(f328(f158(x66191,x66192),x66193),x66194),x66192)+E(f328(f328(f164(x66191),x66192),x66193),x66194)+~P24(f328(f328(f245(a877),x66193),f328(f194(f878(x66191)),x66192)))
% 81.29/80.92 [6634]~P24(f328(f159(x66341,x66342),x66344))+~P24(f328(f159(x66341,x66342),x66343))+P24(f328(f159(x66341,x66342),f328(f328(f127(x66341),x66343),x66344)))
% 81.29/80.92 [6731]P30(x67311,x67312,x67313)+~P30(x67311,f328(a118,x67312),f607(x67312,x67314,x67311))+~P24(f328(f328(f330(f876(x67311)),x67313),x67314))
% 81.29/80.92 [6740]E(x67401,f193(f885(x67402,a871)))+E(x67403,f193(f885(x67404,a871)))+~E(f328(f328(f265(x67404,x67402),x67403),f328(f16(f885(x67402,a871),x67404),x67401)),f193(f885(f884(x67404,x67402),a871)))
% 81.29/80.92 [6759]E(x67591,x67592)+P24(f328(f328(f330(x67593),x67591),x67594))+~P24(f328(f328(f330(x67593),x67591),f328(f328(f306(x67593),x67592),x67594)))
% 81.29/80.92 [6776]~P106(x67761)+P24(f328(f328(f244(x67761),x67762),x67763))+~P24(f328(f328(f244(x67761),x67762),f328(f328(f242(x67761),x67764),x67763)))
% 81.29/80.92 [6778]~P106(x67781)+P24(f328(f328(f244(x67781),x67782),x67783))+~P24(f328(f328(f244(x67781),x67782),f328(f328(f242(x67781),x67783),x67784)))
% 81.29/80.92 [6780]~P102(x67801)+P24(f328(f328(f244(x67801),x67802),x67803))+~P24(f328(f328(f244(x67801),x67802),f328(f328(f107(x67801),x67804),x67803)))
% 81.29/80.92 [6782]~P102(x67821)+P24(f328(f328(f244(x67821),x67822),x67823))+~P24(f328(f328(f244(x67821),x67822),f328(f328(f107(x67821),x67823),x67824)))
% 81.29/80.92 [6783]~P106(x67831)+P24(f328(f328(f245(x67831),x67832),x67833))+~P24(f328(f328(f245(x67831),x67832),f328(f328(f242(x67831),x67834),x67833)))
% 81.29/80.92 [6784]~P106(x67841)+P24(f328(f328(f245(x67841),x67842),x67843))+~P24(f328(f328(f245(x67841),x67842),f328(f328(f242(x67841),x67843),x67844)))
% 81.29/80.92 [6806]~E(f328(f328(f164(x68061),x68063),x68064),x68062)+P24(f328(f328(f330(x68061),x68062),f328(f171(x68061),x68063)))+~P24(f328(f328(f245(a877),x68064),f328(f194(f878(x68061)),x68063)))
% 81.29/80.92 [6817]~P106(x68171)+~P29(x68171,f328(f328(f150(x68171),x68172),f328(f328(f150(x68171),x68173),x68174)))+P24(f328(f328(f244(x68171),x68172),x68173))
% 81.29/80.92 [6956]~P32(x69562,x69561,x69563)+P24(f328(x69561,f328(f328(f164(x69562),x69563),x69564)))+~P24(f328(f328(f245(a877),x69564),f328(f194(f878(x69562)),x69563)))
% 81.29/80.92 [6975]E(x69751,f2(a1))+E(f328(f328(f39(a1),x69752),x69751),x69753)+~P24(f328(f49(x69752,x69751),f328(f328(f257(a1,a1),x69753),x69754)))
% 81.29/80.92 [6996]E(f45(a1,x69962,x69961),x69963)+E(x69961,f2(a1))+~P24(f328(f49(x69962,x69961),f328(f328(f257(a1,a1),x69964),x69963)))
% 81.29/80.92 [7117]P24(f328(f328(f330(x71171),x71172),x71173))+~P24(f328(f328(f330(x71171),x71172),x71174))+~P24(f328(f328(f245(f885(x71171,a871)),x71174),x71173))
% 81.29/80.92 [7118]P24(f328(f328(f330(x71181),x71182),x71183))+~P24(f328(f328(f330(x71181),x71182),x71184))+~P24(f328(f328(f244(f885(x71181,a871)),x71184),x71183))
% 81.29/80.92 [7226]P34(x72261,x72262,x72263)+~P24(f328(x72262,f328(f328(f164(x72261),x72263),x72264)))+~P24(f328(f328(f245(a877),x72264),f328(f194(f878(x72261)),x72263)))
% 81.29/80.92 [7337]~P107(x73372)+~P24(f328(f328(f245(f885(x73371,x73372)),x73373),x73374))+P24(f328(f328(f244(f885(x73371,x73372)),x73373),x73374))
% 81.29/80.92 [7425]~P20(x74251,x74252,x74254)+P20(x74251,x74252,f328(f328(f306(f876(x74251)),x74253),x74254))+~P20(x74251,x74252,f328(f328(f306(f876(x74251)),x74253),f193(f885(f876(x74251),a871))))
% 81.29/80.92 [7470]~P24(f328(f328(f330(x74701),x74702),x74704))+P24(f328(f328(f330(x74701),x74702),f40(f885(x74701,a871),x74703)))+~P24(f328(f328(f330(f885(x74701,a871)),x74704),x74703))
% 81.29/80.92 [7482]P30(x74821,x74822,x74823)+P24(f328(f328(f330(f876(x74821)),f607(x74822,x74824,x74821)),x74824))+~P24(f328(f328(f330(f876(x74821)),x74823),x74824))
% 81.29/80.92 [7499]~P85(x74991)+~P24(f328(f328(f244(x74991),x74993),x74994))+P24(f328(f328(f244(x74991),f328(f328(f81(x74991),x74992),x74993)),f328(f328(f81(x74991),x74992),x74994)))
% 81.29/80.92 [7500]~P86(x75001)+~P24(f328(f328(f244(x75001),x75003),x75004))+P24(f328(f328(f244(x75001),f328(f328(f81(x75001),x75002),x75003)),f328(f328(f81(x75001),x75002),x75004)))
% 81.29/80.92 [7501]~P85(x75011)+~P24(f328(f328(f244(x75011),x75012),x75014))+P24(f328(f328(f244(x75011),f328(f328(f81(x75011),x75012),x75013)),f328(f328(f81(x75011),x75014),x75013)))
% 81.29/80.92 [7502]~P86(x75021)+~P24(f328(f328(f244(x75021),x75022),x75024))+P24(f328(f328(f244(x75021),f328(f328(f81(x75021),x75022),x75023)),f328(f328(f81(x75021),x75024),x75023)))
% 81.29/80.92 [7503]~P84(x75031)+~P24(f328(f328(f245(x75031),x75033),x75034))+P24(f328(f328(f245(x75031),f328(f328(f81(x75031),x75032),x75033)),f328(f328(f81(x75031),x75032),x75034)))
% 81.29/80.92 [7504]~P85(x75041)+~P24(f328(f328(f245(x75041),x75043),x75044))+P24(f328(f328(f245(x75041),f328(f328(f81(x75041),x75042),x75043)),f328(f328(f81(x75041),x75042),x75044)))
% 81.29/80.92 [7505]~P84(x75051)+~P24(f328(f328(f245(x75051),x75052),x75054))+P24(f328(f328(f245(x75051),f328(f328(f81(x75051),x75052),x75053)),f328(f328(f81(x75051),x75054),x75053)))
% 81.29/80.92 [7506]~P85(x75061)+~P24(f328(f328(f245(x75061),x75062),x75064))+P24(f328(f328(f245(x75061),f328(f328(f81(x75061),x75062),x75063)),f328(f328(f81(x75061),x75064),x75063)))
% 81.29/80.92 [7515]~P109(x75151)+~P94(x75151)+E(f328(f328(f22(x75151),f328(f328(f82(x75151),x75152),f328(f109(x75151),x75153))),f328(f328(f82(x75151),x75154),f328(f109(x75151),x75153))),f328(f328(f82(x75151),f328(f328(f22(x75151),x75152),x75154)),f328(f109(x75151),x75153)))
% 81.29/80.92 [7516]~P94(x75161)+~P140(x75161)+E(f328(f328(f81(x75161),f328(f328(f82(x75161),x75162),f328(f109(x75161),x75163))),f328(f328(f82(x75161),x75164),f328(f109(x75161),x75163))),f328(f328(f82(x75161),f328(f328(f81(x75161),x75162),x75164)),f328(f109(x75161),x75163)))
% 81.29/80.92 [7551]~P74(x75511)+E(f328(f328(f81(x75511),f328(x75512,x75513)),f328(f328(f6(a877,x75511),x75512),f299(a877,f328(a118,x75513),x75514))),f328(f328(f6(a877,x75511),x75512),f299(a877,x75513,x75514)))+~P24(f328(f328(f244(a877),x75513),x75514))
% 81.29/80.92 [7562]~P21(x75622,x75621,x75623,f328(f171(x75622),x75624))+~P24(f328(f136(x75622),x75624))+P24(f328(f136(x75621),f328(f328(f153(x75622,x75621),x75623),x75624)))
% 81.29/80.92 [7609]~P24(f328(f328(f244(a877),x76092),x76094))+~P24(f328(f328(f244(a877),x76091),x76093))+P24(f328(f328(f244(a877),f328(f328(f81(a877),x76091),x76092)),f328(f328(f81(a877),x76093),x76094)))
% 81.29/80.92 [7610]~P24(f328(f328(f244(a877),x76102),x76104))+~P24(f328(f328(f244(a877),x76101),x76103))+P24(f328(f328(f244(a877),f328(f328(f82(a877),x76101),x76102)),f328(f328(f82(a877),x76103),x76104)))
% 81.29/80.92 [7613]~P24(f328(f328(f245(a877),x76132),x76134))+~P24(f328(f328(f245(a877),x76131),x76133))+P24(f328(f328(f245(a877),f328(f328(f81(a877),x76131),x76132)),f328(f328(f81(a877),x76133),x76134)))
% 81.29/80.92 [7614]~P24(f328(f328(f244(a1),x76142),x76144))+~P24(f328(f328(f245(a1),x76141),x76143))+P24(f328(f328(f245(a1),f328(f328(f81(a1),x76141),x76142)),f328(f328(f81(a1),x76143),x76144)))
% 81.29/80.92 [7662]P24(f328(f328(f330(x76621),x76622),x76623))+~P24(f328(f328(f330(x76621),x76622),f41(f885(x76621,a871),x76624)))+~P24(f328(f328(f330(f885(x76621,a871)),x76623),x76624))
% 81.29/80.92 [7677]~P24(f328(x76771,f577(x76771,x76773,x76772)))+P24(f328(x76771,f328(f328(f164(x76772),x76773),x76774)))+~P24(f328(f328(f245(a877),x76774),f328(f194(f878(x76772)),x76773)))
% 81.29/80.92 [7682]P24(f328(x76821,x76822))+~P24(f328(f328(f330(x76824),x76822),f328(f171(x76824),x76823)))+P24(f328(f328(f245(a877),f578(x76821,x76823,x76824)),f328(f194(f878(x76824)),x76823)))
% 81.29/80.92 [7702]~P24(f328(f328(f200(x77022),x77023),x77024))+~P24(f328(f328(f200(f33(x77021,x77022)),x77024),x77023))+P24(f328(f328(f200(f33(x77021,x77022)),x77023),x77023))
% 81.29/80.92 [7731]~P107(x77311)+~P24(f328(f328(f245(f885(x77312,x77311)),x77314),x77313))+~P24(f328(f328(f244(f885(x77312,x77311)),x77313),x77314))
% 81.29/80.92 [7775]~P24(f328(x77754,x77752))+~P24(f328(f328(f330(x77751),x77752),x77753))+P24(f328(f328(f330(x77751),x77752),f328(f328(f107(f885(x77751,a871)),x77753),f328(f249(x77751),x77754))))
% 81.29/80.92 [7919]~P24(f328(f328(f330(x79191),x79193),x79194))+~P24(f328(f328(f245(f885(x79191,a871)),x79192),x79194))+P24(f328(f328(f245(f885(x79191,a871)),x79192),f328(f328(f306(x79191),x79193),x79194)))
% 81.29/80.92 [7921]E(f328(f328(f107(f885(x79211,a871)),x79212),x79213),f193(f885(x79211,a871)))+~E(f328(f328(f107(f885(x79211,a871)),f40(f885(x79211,a871),x79214)),x79213),f193(f885(x79211,a871)))+~P24(f328(f328(f330(f885(x79211,a871)),x79212),x79214))
% 81.29/80.92 [7997]P24(f328(f328(f330(x79971),x79972),x79973))+~P24(f328(f328(f244(f885(x79971,a871)),x79973),f328(f328(f306(x79971),x79972),x79974)))+P24(f328(f328(f244(f885(x79971,a871)),x79973),x79974))
% 81.29/80.92 [8019]P24(f328(f328(f330(x80192),f577(x80191,x80193,x80192)),f328(f171(x80192),x80193)))+P24(f328(x80191,f328(f328(f164(x80192),x80193),x80194)))+~P24(f328(f328(f245(a877),x80194),f328(f194(f878(x80192)),x80193)))
% 81.29/80.92 [8027]~P24(f328(f328(f244(f885(x80271,a871)),x80272),x80274))+P24(f328(f328(f244(f885(x80271,a871)),x80272),x80273))+~P24(f328(f328(f244(f885(x80271,a871)),x80274),x80273))
% 81.29/80.92 [8028]~P24(f328(f328(f245(f885(x80281,a871)),x80282),x80284))+~P24(f328(f328(f244(f885(x80281,a871)),x80284),x80283))+P24(f328(f328(f245(f885(x80281,a871)),x80282),x80283))
% 81.29/80.92 [8029]~P24(f328(f328(f244(f885(x80291,a871)),x80292),x80294))+~P24(f328(f328(f245(f885(x80291,a871)),x80294),x80293))+P24(f328(f328(f245(f885(x80291,a871)),x80292),x80293))
% 81.29/80.92 [8030]~P24(f328(f328(f245(f885(x80301,a871)),x80302),x80304))+P24(f328(f328(f245(f885(x80301,a871)),x80302),x80303))+~P24(f328(f328(f245(f885(x80301,a871)),x80304),x80303))
% 81.29/80.92 [8070]~P24(f328(f328(f330(x80701),x80704),x80703))+~P24(f328(f328(f245(f885(x80701,a871)),x80702),f328(f328(f306(x80701),x80704),x80703)))+P24(f328(f328(f245(f885(x80701,a871)),x80702),x80703))
% 81.29/80.92 [8082]~P85(x80821)+P24(f328(f328(f244(x80821),x80822),x80823))+~P24(f328(f328(f244(x80821),f328(f328(f81(x80821),x80824),x80822)),f328(f328(f81(x80821),x80824),x80823)))
% 81.29/80.92 [8084]~P85(x80841)+P24(f328(f328(f244(x80841),x80842),x80843))+~P24(f328(f328(f244(x80841),f328(f328(f81(x80841),x80842),x80844)),f328(f328(f81(x80841),x80843),x80844)))
% 81.29/80.92 [8086]~P85(x80861)+P24(f328(f328(f245(x80861),x80862),x80863))+~P24(f328(f328(f245(x80861),f328(f328(f81(x80861),x80864),x80862)),f328(f328(f81(x80861),x80864),x80863)))
% 81.29/80.92 [8088]~P85(x80881)+P24(f328(f328(f245(x80881),x80882),x80883))+~P24(f328(f328(f245(x80881),f328(f328(f81(x80881),x80882),x80884)),f328(f328(f81(x80881),x80883),x80884)))
% 81.29/80.92 [8137]P24(f328(x81371,x81372))+~E(f328(f328(f137(x81373),f328(f194(f878(x81373)),f176(x81373,x81371,x81374))),x81374),f119(x81373))+~P24(f328(f328(f330(x81373),x81372),f328(f171(x81373),x81374)))
% 81.29/80.92 [8263]P24(f328(x82631,x82632))+~P24(f328(f328(f330(x82633),x82632),f328(f171(x82633),x82634)))+P24(f328(f328(f245(a877),f328(f194(f878(x82633)),f328(f135(x82633,x82631),x82634))),f328(f194(f878(x82633)),x82634)))
% 81.29/80.92 [8389]E(x83891,x83892)+P24(f328(f328(f200(x83893),x83891),f565(x83892,x83891,x83893,x83894)))+~P24(f328(f328(f200(f33(x83894,x83893)),x83891),x83892))
% 81.29/80.92 [8419]~P24(f328(x84194,x84192))+P24(f328(f328(f200(x84191),x84192),f565(x84193,x84192,x84191,x84194)))+~P24(f328(f328(f200(f33(x84194,x84191)),x84192),x84193))
% 81.29/80.92 [8739]~P24(f328(x87391,f751(x87391,x87393,x87392,x87394)))+P24(f328(x87391,f328(f328(f164(x87392),x87393),x87394)))+~P24(f328(f328(f245(a877),x87394),f328(f194(f878(x87392)),x87393)))
% 81.29/80.92 [8763]~P21(x87634,x87633,x87631,f252(f885(x87634,a871)))+E(f328(x87631,f550(x87632,x87631,x87633,x87634)),x87632)+~P24(f328(f328(f330(x87633),x87632),f328(f307(x87634,x87633,x87631),f252(f885(x87634,a871)))))
% 81.29/80.92 [8828]E(f176(x88281,x88282,x88283),f328(f328(f174(x88281),x88284),x88283))+P24(f328(f328(f245(a877),f665(x88282,x88283,x88281,x88284)),x88284))+P24(f328(f328(f245(a877),x88284),f328(f194(f878(x88281)),x88283)))
% 81.29/80.92 [8831]E(f176(x88311,x88312,x88313),f328(f328(f174(x88311),x88314),x88313))+P24(f328(f328(f245(a877),f665(x88312,x88313,x88311,x88314)),x88314))+P24(f328(x88312,f328(f328(f164(x88311),x88313),x88314)))
% 81.29/80.92 [8860]P24(f328(x88601,x88602))+~P24(f328(f328(f330(x88604),x88602),f328(f171(x88604),x88603)))+P24(f328(f328(f245(a877),f675(x88602,x88601,x88603,x88604)),f328(f194(f878(x88604)),x88603)))
% 81.29/80.92 [8863]E(f176(x88631,x88632,x88633),f328(f328(f174(x88631),x88634),x88633))+P24(f328(f328(f245(a877),x88634),f328(f194(f878(x88631)),x88633)))+P24(f328(f328(f245(a877),f665(x88632,x88633,x88631,x88634)),f328(f194(f878(x88631)),x88633)))
% 81.29/80.92 [8870]E(f176(x88701,x88702,x88703),f328(f328(f174(x88701),x88704),x88703))+P24(f328(x88702,f328(f328(f164(x88701),x88703),x88704)))+P24(f328(f328(f245(a877),f665(x88702,x88703,x88701,x88704)),f328(f194(f878(x88701)),x88703)))
% 81.29/80.92 [8896]~P110(x88964)+P24(f328(f328(f330(x88961),f387(x88962,x88963,x88961,x88964)),x88963))+P24(f328(f328(f245(x88964),f2(x88964)),f328(f328(f9(x88961,x88964),x88962),x88963)))
% 81.29/80.92 [8897]~P110(x88974)+P24(f328(f328(f330(x88971),f388(x88972,x88973,x88971,x88974)),x88973))+P24(f328(f328(f244(x88974),f2(x88974)),f328(f328(f9(x88971,x88974),x88972),x88973)))
% 81.29/80.92 [8929]~P24(f328(f62(x89291),x89294))+P24(f328(f328(f330(x89291),f701(x89292,x89293,x89294,x89291)),x89294))+P24(f328(f62(f884(x89291,x89293)),f328(f328(f265(x89291,x89293),x89294),x89292)))
% 81.29/80.92 [8963]P24(f328(f328(f330(x89632),f751(x89631,x89633,x89632,x89634)),f328(f171(x89632),x89633)))+P24(f328(x89631,f328(f328(f164(x89632),x89633),x89634)))+~P24(f328(f328(f245(a877),x89634),f328(f194(f878(x89632)),x89633)))
% 81.29/80.92 [8978]E(x89781,x89782)+P24(f328(f328(f200(f33(x89783,x89784)),f565(x89781,x89782,x89784,x89783)),x89781))+~P24(f328(f328(f200(f33(x89783,x89784)),x89782),x89781))
% 81.29/80.92 [8999]~P24(f328(x89991,x89994))+P24(f328(f328(f200(f33(x89991,x89992)),f565(x89993,x89994,x89992,x89991)),x89993))+~P24(f328(f328(f200(f33(x89991,x89992)),x89994),x89993))
% 81.29/80.92 [9094]P24(f328(f328(f244(a877),x90944),f328(f194(f878(x90942)),f176(x90942,x90943,x90941))))+P24(f328(f328(f245(a877),f666(x90941,x90942,x90943,x90944)),x90944))+~P24(f328(f328(f244(a877),x90944),f328(f194(f878(x90942)),x90941)))
% 81.29/80.92 [9198]~E(f328(f328(f177(x91981,x91982),x91983),f715(x91984,x91983,x91982,x91981)),f328(f328(f177(x91981,x91982),x91984),f715(x91984,x91983,x91982,x91981)))+E(f328(f177(x91981,x91982),x91983),f328(f177(x91981,x91982),x91984))+~E(f328(f171(x91981),f328(f328(f153(f884(x91981,x91982),x91981),f256(x91981,x91982)),x91983)),f328(f171(x91981),f328(f328(f153(f884(x91981,x91982),x91981),f256(x91981,x91982)),x91984)))
% 81.29/80.92 [9244]E(f176(x92441,x92442,x92443),f328(f328(f174(x92441),x92444),x92443))+~P24(f328(x92442,f328(f328(f164(x92441),x92443),f665(x92442,x92443,x92441,x92444))))+P24(f328(f328(f245(a877),x92444),f328(f194(f878(x92441)),x92443)))
% 81.29/80.92 [9249]E(f176(x92491,x92492,x92493),f328(f328(f174(x92491),x92494),x92493))+~P24(f328(x92492,f328(f328(f164(x92491),x92493),f665(x92492,x92493,x92491,x92494))))+P24(f328(x92492,f328(f328(f164(x92491),x92493),x92494)))
% 81.29/80.92 [9256]~P24(f328(f62(x92561),x92563))+~P24(f328(f62(x92562),f328(x92564,f701(x92564,x92562,x92563,x92561))))+P24(f328(f62(f884(x92561,x92562)),f328(f328(f265(x92561,x92562),x92563),x92564)))
% 81.29/80.92 [9264]~P110(x92641)+~P24(f328(f328(f244(x92641),f2(x92641)),f328(x92643,f388(x92643,x92644,x92642,x92641))))+P24(f328(f328(f244(x92641),f2(x92641)),f328(f328(f9(x92642,x92641),x92643),x92644)))
% 81.29/80.92 [9265]~P110(x92651)+~P24(f328(f328(f245(x92651),f2(x92651)),f328(x92653,f387(x92653,x92654,x92652,x92651))))+P24(f328(f328(f245(x92651),f2(x92651)),f328(f328(f9(x92652,x92651),x92653),x92654)))
% 81.29/80.92 [9271]~E(f328(f194(f878(x92714)),x92712),f328(f194(f878(x92714)),x92713))+P24(f328(f328(f330(f884(f878(x92714),f878(x92714))),f328(f328(f257(f878(x92714),f878(x92714)),x92713),x92712)),f157(x92714,x92711)))+P24(f328(f328(f245(a877),f587(x92711,x92712,x92713,x92714)),f328(f194(f878(x92714)),x92713)))
% 81.29/80.92 [9325]~P24(f328(x93253,f328(f328(f164(x93252),x93254),f666(x93254,x93252,x93253,x93251))))+P24(f328(f328(f244(a877),x93251),f328(f194(f878(x93252)),f176(x93252,x93253,x93254))))+~P24(f328(f328(f244(a877),x93251),f328(f194(f878(x93252)),x93254)))
% 81.29/80.92 [9401]E(f328(f328(f174(x94011),f608(x94012,x94013,x94014,x94011)),x94013),f328(f328(f174(x94011),f608(x94012,x94013,x94014,x94011)),x94014))+~P24(f328(f328(f330(f884(f878(x94011),f878(x94011))),f328(f328(f257(f878(x94011),f878(x94011)),x94014),x94013)),f146(x94011,x94012)))+P24(f328(f328(f245(a877),f328(f194(f878(x94011)),x94014)),f328(f194(f878(x94011)),x94013)))
% 81.29/80.92 [9455]~P24(f328(f328(f245(a877),f2(a877)),x94553))+~P24(f328(f328(f245(a877),x94554),x94551))+P24(f328(f328(f245(a877),f328(f328(f81(a877),f328(f328(f82(a877),x94551),f45(a877,x94552,x94553))),x94554)),f328(f328(f82(a877),x94551),x94553)))
% 81.29/80.92 [9644]~P107(x96442)+~P24(f328(f328(f244(x96442),f328(x96443,f493(x96444,x96443,x96441,x96442))),f328(x96444,f493(x96444,x96443,x96441,x96442))))+P24(f328(f328(f244(f885(x96441,x96442)),x96443),x96444))
% 81.29/80.92 [9747]~P67(x97471)+E(f328(f328(f6(a877,x97471),f328(f328(f18(a877,x97471,x97471),f328(f328(f8(x97471,f885(x97471,x97471),a877),f22(x97471)),x97472)),f328(f328(f8(a877,x97471,a877),x97472),f328(f328(f7(a877,a877,a877),f81(a877)),f79(a877))))),f299(a877,x97473,x97474)),f328(f328(f22(x97471),f328(x97472,x97473)),f328(x97472,f328(f328(f81(a877),x97474),f79(a877)))))+~P24(f328(f328(f244(a877),x97473),x97474))
% 81.29/80.92 [6810]E(f328(f328(f127(x68101),x68102),x68103),x68104)+~E(x68103,f328(f328(f137(x68101),f328(f194(f878(x68101)),x68102)),x68104))+~E(f328(f328(f174(x68101),f328(f194(f878(x68101)),x68102)),x68104),x68102)
% 81.29/80.92 [6865]~P62(x68652)+E(x68651,f2(x68652))+E(f328(f328(f286(x68652),f328(f328(f258(x68652),x68653),x68654)),f328(f328(f258(x68652),x68651),x68654)),f328(f328(f258(x68652),f328(f328(f286(x68652),x68653),x68651)),x68654))
% 81.29/80.92 [6998]~E(f328(f194(f878(x69981)),x69983),f328(f194(f878(x69982)),x69984))+~P24(f328(f136(x69981),x69983))+E(f183(x69981,x69982,f328(f177(x69981,x69982),f328(f328(f181(x69981,x69982),x69983),x69984))),f328(f171(x69981),x69983))
% 81.29/80.92 [7017]~P102(x70171)+~P24(f328(f328(f244(x70171),x70173),x70174))+P24(f328(f328(f244(x70171),f328(f328(f107(x70171),x70172),x70173)),x70174))
% 81.29/80.92 [7018]~P102(x70181)+~P24(f328(f328(f244(x70181),x70182),x70184))+P24(f328(f328(f244(x70181),f328(f328(f107(x70181),x70182),x70183)),x70184))
% 81.29/80.92 [7020]~P106(x70201)+~P24(f328(f328(f244(x70201),x70203),x70204))+P24(f328(f328(f244(x70201),f328(f328(f242(x70201),x70202),x70203)),x70204))
% 81.29/80.92 [7022]~P106(x70221)+~P24(f328(f328(f244(x70221),x70222),x70224))+P24(f328(f328(f244(x70221),f328(f328(f242(x70221),x70222),x70223)),x70224))
% 81.29/80.92 [7023]~P102(x70231)+~P24(f328(f328(f245(x70231),x70233),x70234))+P24(f328(f328(f245(x70231),f328(f328(f107(x70231),x70232),x70233)),x70234))
% 81.29/80.92 [7024]~P102(x70241)+~P24(f328(f328(f245(x70241),x70242),x70244))+P24(f328(f328(f245(x70241),f328(f328(f107(x70241),x70242),x70243)),x70244))
% 81.29/80.92 [7026]~P106(x70261)+~P24(f328(f328(f245(x70261),x70263),x70264))+P24(f328(f328(f245(x70261),f328(f328(f242(x70261),x70262),x70263)),x70264))
% 81.29/80.92 [7028]~P106(x70281)+~P24(f328(f328(f245(x70281),x70282),x70284))+P24(f328(f328(f245(x70281),f328(f328(f242(x70281),x70282),x70283)),x70284))
% 81.29/80.92 [7048]~P24(f328(x70483,x70484))+~P24(f328(x70482,x70484))+P24(f328(f328(f328(f107(f885(x70481,a871)),x70482),x70483),x70484))
% 81.29/80.92 [7172]P20(x71721,x71722,x71723)+~P20(x71721,x71724,x71723)+~P24(f328(f328(f244(f885(f876(x71721),a871)),x71724),x71722))
% 81.29/80.92 [7173]P20(x71731,x71732,x71733)+~P20(x71731,x71732,x71734)+~P24(f328(f328(f244(f885(f876(x71731),a871)),x71733),x71734))
% 81.29/80.92 [7541]~P74(x75411)+E(f328(f328(f81(x75411),f328(x75412,x75413)),f328(f328(f6(a877,x75411),x75412),f328(f298(a877,f328(a118,x75413)),x75414))),f328(f328(f6(a877,x75411),x75412),f328(f298(a877,x75413),x75414)))+~P24(f328(f328(f245(a877),x75413),x75414))
% 81.29/80.92 [7570]~P106(x75701)+P24(f328(f328(f244(x75701),x75702),x75703))+~P24(f328(f328(f244(x75701),f328(f328(f243(x75701),x75704),x75702)),x75703))
% 81.29/80.92 [7572]~P106(x75721)+P24(f328(f328(f244(x75721),x75722),x75723))+~P24(f328(f328(f244(x75721),f328(f328(f243(x75721),x75722),x75724)),x75723))
% 81.29/80.92 [7574]~P65(x75741)+P24(f328(f328(f244(x75741),x75742),x75743))+~P24(f328(f328(f244(x75741),f328(f328(f116(x75741),x75744),x75742)),x75743))
% 81.29/80.92 [7576]~P65(x75761)+P24(f328(f328(f244(x75761),x75762),x75763))+~P24(f328(f328(f244(x75761),f328(f328(f116(x75761),x75762),x75764)),x75763))
% 81.29/80.92 [7577]~P106(x75771)+P24(f328(f328(f245(x75771),x75772),x75773))+~P24(f328(f328(f245(x75771),f328(f328(f243(x75771),x75774),x75772)),x75773))
% 81.29/80.92 [7578]~P106(x75781)+P24(f328(f328(f245(x75781),x75782),x75783))+~P24(f328(f328(f245(x75781),f328(f328(f243(x75781),x75782),x75784)),x75783))
% 81.29/80.92 [7654]~P24(f328(f328(f330(x76541),x76542),x76544))+P24(f328(f328(f330(x76541),x76542),x76543))+P24(f328(f328(f330(x76541),x76542),f328(f328(f22(f885(x76541,a871)),x76544),x76543)))
% 81.29/80.92 [7737]P24(f328(x77371,x77372))+P24(f328(x77373,x77372))+~P24(f328(f328(f328(f116(f885(x77374,a871)),x77373),x77371),x77372))
% 81.29/80.92 [7747]~P24(f328(f328(f330(x77471),x77472),x77474))+~P24(f328(f328(f330(x77471),x77472),x77473))+P24(f328(f328(f330(x77471),x77472),f328(f328(f107(f885(x77471,a871)),x77473),x77474)))
% 81.29/80.92 [7799]~P65(x77991)+~P24(f328(f62(x77991),x77994))+E(f328(f328(f65(x77991,x77991,f116(x77991)),x77992),f328(f328(f306(x77991),x77993),x77994)),f328(f328(f116(x77991),x77993),f328(f328(f65(x77991,x77991,f116(x77991)),x77992),x77994)))
% 81.29/80.92 [7800]~P102(x78001)+~P24(f328(f62(x78001),x78004))+E(f328(f328(f65(x78001,x78001,f107(x78001)),x78002),f328(f328(f306(x78001),x78003),x78004)),f328(f328(f107(x78001),x78003),f328(f328(f65(x78001,x78001,f107(x78001)),x78002),x78004)))
% 81.29/80.92 [7801]~P106(x78011)+~P24(f328(f62(x78011),x78014))+E(f328(f328(f65(x78011,x78011,f242(x78011)),x78012),f328(f328(f306(x78011),x78013),x78014)),f328(f328(f242(x78011),x78013),f328(f328(f65(x78011,x78011,f242(x78011)),x78012),x78014)))
% 81.29/80.92 [7802]~P106(x78021)+~P24(f328(f62(x78021),x78024))+E(f328(f328(f65(x78021,x78021,f243(x78021)),x78022),f328(f328(f306(x78021),x78023),x78024)),f328(f328(f243(x78021),x78023),f328(f328(f65(x78021,x78021,f243(x78021)),x78022),x78024)))
% 81.29/80.92 [7803]~P109(x78031)+~P94(x78031)+E(f328(f328(f22(x78031),f328(f328(f82(x78031),f328(f109(x78031),x78032)),x78033)),f328(f328(f82(x78031),f328(f109(x78031),x78032)),x78034)),f328(f328(f82(x78031),f328(f109(x78031),x78032)),f328(f328(f22(x78031),x78033),x78034)))
% 81.29/80.92 [7804]~P94(x78041)+~P140(x78041)+E(f328(f328(f81(x78041),f328(f328(f82(x78041),f328(f109(x78041),x78042)),x78043)),f328(f328(f82(x78041),f328(f109(x78041),x78042)),x78044)),f328(f328(f82(x78041),f328(f109(x78041),x78042)),f328(f328(f81(x78041),x78043),x78044)))
% 81.29/80.92 [7917]E(x79171,x79172)+P24(f328(f328(f330(x79173),x79171),f328(f171(x79173),x79174)))+~P24(f328(f328(f330(x79173),x79171),f328(f171(x79173),f328(f328(f150(x79173),x79172),x79174))))
% 81.29/80.92 [7942]~P60(x79421)+~E(f328(f194(f878(x79422)),x79423),f328(f194(f878(x79421)),f56(x79421)))+E(f328(f328(f177(x79421,x79422),f328(f328(f181(x79421,x79422),f56(x79421)),x79423)),x79424),f328(f236(x79422),f663(x79424,x79423,x79422,x79421)))
% 81.29/80.92 [8095]P52(x80951,x80952,x80953)+~P52(x80951,x80952,x80954)+~P24(f328(f328(f244(f885(f884(x80951,x80952),a871)),x80953),x80954))
% 81.29/80.92 [8140]P24(f328(f328(f330(x81401),x81402),x81403))+P24(f328(f328(f330(x81401),x81402),x81404))+~P24(f328(f328(f330(x81401),x81402),f328(f328(f116(f885(x81401,a871)),x81404),x81403)))
% 81.29/80.92 [8151]~P48(x81511,x81514,x81513)+~P24(f328(f328(f330(x81511),x81512),x81514))+P24(f328(f328(f330(f884(x81511,x81511)),f328(f328(f257(x81511,x81511),x81512),x81512)),x81513))
% 81.29/80.92 [8166]~P24(f328(f62(x81662),x81664))+~P24(f328(f62(x81661),x81663))+P24(f328(f62(f884(x81661,x81662)),f328(f328(f265(x81661,x81662),x81663),f328(f16(f885(x81662,a871),x81661),x81664))))
% 81.29/80.92 [8167]~P24(f328(f328(f330(x81671),x81672),x81674))+~P24(f328(f328(f244(f885(x81671,a871)),x81673),x81674))+P24(f328(f328(f244(f885(x81671,a871)),f328(f328(f306(x81671),x81672),x81673)),x81674))
% 81.29/80.92 [8175]~P75(x81752)+~P141(x81752)+E(f328(f328(f9(x81751,x81752),f328(f328(f8(a877,x81752,x81751),f106(x81752)),x81753)),x81754),f328(f106(x81752),f328(f328(f9(x81751,a877),x81753),x81754)))
% 81.29/80.92 [8176]~P137(x81762)+~P75(x81762)+E(f328(f328(f9(x81761,x81762),f328(f328(f8(a1,x81762,x81761),f108(x81762)),x81763)),x81764),f328(f108(x81762),f328(f328(f9(x81761,a1),x81763),x81764)))
% 81.29/80.92 [8202]E(f328(f328(f22(f885(x82021,a871)),x82022),f328(f328(f22(f885(x82021,a871)),x82023),x82024)),x82024)+~P24(f328(f328(f244(f885(x82021,a871)),x82022),x82023))+~P24(f328(f328(f244(f885(x82021,a871)),x82024),x82022))
% 81.29/80.92 [8297]~P24(f328(f62(x82971),x82974))+E(f328(f328(f22(a877),f328(f328(f6(x82971,a877),x82972),x82973)),f328(f328(f6(x82971,a877),x82972),x82974)),f328(f328(f6(x82971,a877),x82972),f328(f328(f22(f885(x82971,a871)),x82973),x82974)))+~P24(f328(f328(f244(f885(x82971,a871)),x82974),x82973))
% 81.29/80.92 [8454]~P6(x84541,x84544,x84543)+~P24(f328(f328(f330(x84541),x84542),x84544))+P24(f328(f328(f330(x84541),x84542),f328(f282(x84541,x84541,x84543),f328(f328(f306(x84541),x84542),f193(f885(x84541,a871))))))
% 81.29/80.92 [8517]~P24(f328(f328(f244(f885(x85171,a871)),x85172),x85173))+~P24(f328(f328(f244(f885(x85171,a871)),x85172),x85174))+P24(f328(f328(f244(f885(x85171,a871)),x85172),f328(f328(f107(f885(x85171,a871)),x85173),x85174)))
% 81.29/80.92 [8614]E(x86141,f193(f885(x86142,a871)))+P24(f328(f62(x86143),x86144))+~P24(f328(f62(f884(x86143,x86142)),f328(f328(f265(x86143,x86142),x86144),f328(f16(f885(x86142,a871),x86143),x86141))))
% 81.29/80.92 [8615]E(x86151,f193(f885(x86152,a871)))+P24(f328(f62(x86153),x86154))+~P24(f328(f62(f884(x86152,x86153)),f328(f328(f265(x86152,x86153),x86151),f328(f16(f885(x86153,a871),x86152),x86154))))
% 81.29/80.92 [8682]P24(f328(f328(f330(x86821),x86822),f317(x86821,x86823)))+~P24(f328(f328(f330(x86821),x86824),f317(x86821,x86823)))+~P24(f328(f328(f330(f884(x86821,x86821)),f328(f328(f257(x86821,x86821),x86822),x86824)),x86823))
% 81.29/80.92 [8734]~P38(x87341,x87344)+P24(f328(f328(f330(f884(x87341,x87341)),f328(f328(f257(x87341,x87341),x87343),x87342)),f304(x87341,x87344)))+P38(x87341,f328(f328(f306(f884(x87341,x87341)),f328(f328(f257(x87341,x87341),x87342),x87343)),x87344))
% 81.29/80.92 [8735]~P55(x87351,x87354)+P24(f328(f328(f330(f884(x87351,x87351)),f328(f328(f257(x87351,x87351),x87353),x87352)),f304(x87351,x87354)))+P55(x87351,f328(f328(f306(f884(x87351,x87351)),f328(f328(f257(x87351,x87351),x87352),x87353)),x87354))
% 81.29/80.92 [8813]~E(x88132,x88133)+~P24(f328(f328(f330(x88131),x88132),f328(f171(x88131),x88134)))+P24(f328(f328(f330(f884(x88131,x88131)),f328(f328(f257(x88131,x88131),x88132),x88133)),f328(f171(f884(x88131,x88131)),f328(f328(f181(x88131,x88131),x88134),x88134))))
% 81.29/80.92 [8894]~E(x88943,x88944)+P24(f328(f328(f267(x88941,x88941,a871),a325),x88942))+~P24(f328(f328(f330(f884(x88941,x88941)),x88942),f328(f171(f884(x88941,x88941)),f328(f328(f181(x88941,x88941),x88943),x88944))))
% 81.29/80.92 [8920]~P24(f328(x89204,x89202))+P24(f328(f328(f328(f328(a202,x89201),x89202),x89203),f566(x89203,x89202,x89201,x89204)))+~P24(f328(f328(f328(f328(a202,f33(x89204,x89201)),x89202),x89203),x89202))
% 81.29/80.92 [8947]P24(f328(f328(f330(f884(f878(x89471),f878(x89471))),f328(f328(f257(f878(x89471),f878(x89471)),x89472),x89473)),f146(x89471,x89474)))+~E(f328(f328(f174(x89471),f328(f194(f878(x89471)),x89472)),x89473),x89472)+~P24(f328(f328(f245(a877),f328(f194(f878(x89471)),x89472)),f328(f194(f878(x89471)),x89473)))
% 81.29/80.92 [9046]~P24(f328(f62(x90461),x90464))+P24(f328(f328(f330(x90461),f513(x90462,x90463,x90464,x90461)),x90464))+P24(f328(f62(x90463),f328(f328(f43(x90461,f885(x90463,a871)),x90464),x90462)))
% 81.29/80.92 [9047]~P24(f328(f62(x90471),x90474))+P24(f328(f328(f330(x90471),f721(x90472,x90473,x90474,x90471)),x90474))+P24(f328(f62(x90473),f328(f328(f43(x90471,f885(x90473,a871)),x90474),x90472)))
% 81.29/80.92 [9128]P24(f328(f328(f330(f884(x91281,x91281)),x91282),f328(f328(f285(x91281,x91281,x91281),x91283),f304(x91281,x91283))))+~P24(f328(f328(f245(a877),f2(a877)),x91284))+~P24(f328(f328(f330(f884(x91281,x91281)),x91282),f328(f328(f188(f884(x91281,x91281),a871),x91284),x91283)))
% 81.29/80.92 [9136]~P38(x91361,x91362)+~P24(f328(f328(f330(f884(x91361,x91361)),f328(f328(f257(x91361,x91361),x91364),x91363)),x91362))+~P24(f328(f328(f330(f884(x91361,x91361)),f328(f328(f257(x91361,x91361),x91363),x91364)),x91362))
% 81.29/80.92 [9263]~P24(f328(f62(x92631),x92634))+E(f328(f328(f6(x92631,a877),f328(f328(f8(f885(x92632,a871),a877,x92631),f38(x92632)),x92633)),x92634),f328(f38(f884(x92631,x92632)),f328(f328(f265(x92631,x92632),x92634),x92633)))+P24(f328(f328(f330(x92631),f704(x92633,x92632,x92634,x92631)),x92634))
% 81.29/80.92 [9267]~P24(f328(f136(x92671),x92672))+P24(f328(f136(x92671),f328(f328(f158(x92671,x92672),x92673),x92674)))+P24(f328(f328(f330(x92671),x92674),f328(f328(f22(f885(x92671,a871)),f328(f171(x92671),x92672)),f328(f328(f306(x92671),f328(f328(f164(x92671),x92672),x92673)),f193(f885(x92671,a871))))))
% 81.29/80.92 [9283]~P24(f328(f62(x92832),x92833))+~P24(f328(f62(x92831),f328(x92834,f513(x92834,x92831,x92833,x92832))))+P24(f328(f62(x92831),f328(f328(f43(x92832,f885(x92831,a871)),x92833),x92834)))
% 81.29/80.92 [9284]~P24(f328(f62(x92842),x92843))+~P24(f328(f62(x92841),f328(x92844,f721(x92844,x92841,x92843,x92842))))+P24(f328(f62(x92841),f328(f328(f43(x92842,f885(x92841,a871)),x92843),x92844)))
% 81.29/80.92 [9363]~P24(f328(f328(f330(f884(x93631,x93631)),x93632),f328(f328(f285(x93631,x93631,x93631),x93634),f304(x93631,x93634))))+P24(f328(f328(f330(f884(x93631,x93631)),x93632),f328(f328(f285(x93631,x93631,x93631),x93633),f304(x93631,x93633))))+~P24(f328(f328(f244(f885(f884(x93631,x93631),a871)),x93634),x93633))
% 81.29/80.92 [9370]E(f328(f328(f174(x93701),f608(x93704,x93703,x93702,x93701)),x93703),f328(f328(f174(x93701),f608(x93704,x93703,x93702,x93701)),x93702))+~P24(f328(f328(f330(f884(f878(x93701),f878(x93701))),f328(f328(f257(f878(x93701),f878(x93701)),x93702),x93703)),f146(x93701,x93704)))+E(f328(f328(f174(x93701),f328(f194(f878(x93701)),x93702)),x93703),x93702)
% 81.29/80.92 [9386]~P24(f328(f62(x93861),x93864))+E(f328(f328(f6(x93861,a877),f328(f328(f8(f885(x93862,a871),a877,x93861),f38(x93862)),x93863)),x93864),f328(f38(f884(x93861,x93862)),f328(f328(f265(x93861,x93862),x93864),x93863)))+~P24(f328(f62(x93862),f328(x93863,f704(x93863,x93862,x93864,x93861))))
% 81.29/80.92 [9390]~E(f328(f194(f878(x93901)),x93903),f328(f194(f878(x93901)),x93902))+P24(f328(f328(f330(f884(f878(x93901),f878(x93901))),f328(f328(f257(f878(x93901),f878(x93901)),x93902),x93903)),f157(x93901,x93904)))+P24(f328(f328(f330(f884(x93901,x93901)),f591(x93904,x93903,x93902,x93901)),f328(f171(f884(x93901,x93901)),f328(f328(f181(x93901,x93901),x93902),x93903))))
% 81.29/80.92 [9467]~P24(f328(f328(f330(f884(f878(x94671),f878(x94671))),f328(f328(f257(f878(x94671),f878(x94671)),x94672),x94673)),f146(x94671,x94674)))+E(f328(f328(f174(x94671),f328(f194(f878(x94671)),x94672)),x94673),x94672)+P24(f328(f328(f245(a877),f608(x94674,x94673,x94672,x94671)),f328(f328(f242(a877),f328(f194(f878(x94671)),x94672)),f328(f194(f878(x94671)),x94673))))
% 81.29/80.92 [9468]E(f328(f177(x94681,x94682),x94683),f328(f177(x94681,x94682),x94684))+~E(f328(f171(x94681),f328(f328(f153(f884(x94681,x94682),x94681),f256(x94681,x94682)),x94683)),f328(f171(x94681),f328(f328(f153(f884(x94681,x94682),x94681),f256(x94681,x94682)),x94684)))+P24(f328(f328(f330(x94681),f715(x94683,x94684,x94682,x94681)),f328(f171(x94681),f328(f328(f153(f884(x94681,x94682),x94681),f256(x94681,x94682)),x94684))))
% 81.29/80.92 [9484]~P24(f328(x94841,x94844))+P24(f328(f328(f328(f328(a202,f33(x94841,x94842)),f566(x94843,x94844,x94842,x94841)),x94843),x94844))+~P24(f328(f328(f328(f328(a202,f33(x94841,x94842)),x94844),x94843),x94844))
% 81.29/80.92 [9489]~P24(f328(f328(f330(f884(f878(x94891),f878(x94891))),f328(f328(f257(f878(x94891),f878(x94891)),x94892),x94893)),f146(x94891,x94894)))+P24(f328(f328(f245(a877),f328(f194(f878(x94891)),x94892)),f328(f194(f878(x94891)),x94893)))+P24(f328(f328(f245(a877),f608(x94894,x94893,x94892,x94891)),f328(f328(f242(a877),f328(f194(f878(x94891)),x94892)),f328(f194(f878(x94891)),x94893))))
% 81.29/80.92 [9784]~P24(f328(f328(f328(x97841,f502(x97841,x97844,x97843,x97842)),f504(x97841,x97844,x97843,x97842)),f505(x97841,x97844,x97843,x97842)))+P24(f328(f328(f328(x97841,x97842),x97843),x97844))+~P24(f328(f316(f884(f885(a1,f881(f878(a324))),f884(a1,a1)),a314),f328(f328(f257(f885(a1,f881(f878(a324))),f884(a1,a1)),x97842),f328(f328(f257(a1,a1),x97843),x97844))))
% 81.29/80.92 [9862]P24(f328(f328(f328(x98621,x98622),x98623),x98624))+P24(f328(f316(f884(f885(a1,f881(f878(a324))),f884(a1,a1)),a314),f328(f328(f257(f885(a1,f881(f878(a324))),f884(a1,a1)),f502(x98621,x98624,x98623,x98622)),f328(f328(f257(a1,a1),f504(x98621,x98624,x98623,x98622)),f505(x98621,x98624,x98623,x98622)))))+~P24(f328(f316(f884(f885(a1,f881(f878(a324))),f884(a1,a1)),a314),f328(f328(f257(f885(a1,f881(f878(a324))),f884(a1,a1)),x98622),f328(f328(f257(a1,a1),x98623),x98624))))
% 81.29/80.92 [9902]~P24(f328(f328(f330(f884(f878(x99021),f878(x99021))),f328(f328(f257(f878(x99021),f878(x99021)),x99022),x99023)),f146(x99021,x99024)))+E(f328(f328(f174(x99021),f328(f194(f878(x99021)),x99022)),x99023),x99022)+P24(f328(f328(f330(f884(x99021,x99021)),f328(f328(f257(x99021,x99021),f328(f328(f164(x99021),x99022),f608(x99024,x99023,x99022,x99021))),f328(f328(f164(x99021),x99023),f608(x99024,x99023,x99022,x99021)))),x99024))
% 81.29/80.92 [9905]~P24(f328(f328(f330(f884(f878(x99051),f878(x99051))),f328(f328(f257(f878(x99051),f878(x99051)),x99052),x99053)),f146(x99051,x99054)))+P24(f328(f328(f245(a877),f328(f194(f878(x99051)),x99052)),f328(f194(f878(x99051)),x99053)))+P24(f328(f328(f330(f884(x99051,x99051)),f328(f328(f257(x99051,x99051),f328(f328(f164(x99051),x99052),f608(x99054,x99053,x99052,x99051))),f328(f328(f164(x99051),x99053),f608(x99054,x99053,x99052,x99051)))),x99054))
% 81.29/80.92 [9962]~E(f328(f194(f878(x99621)),x99622),f328(f194(f878(x99621)),x99623))+P24(f328(f328(f330(f884(f878(x99621),f878(x99621))),f328(f328(f257(f878(x99621),f878(x99621)),x99622),x99623)),f157(x99621,x99624)))+~P24(f328(f328(f330(f884(x99621,x99621)),f328(f328(f257(x99621,x99621),f328(f328(f164(x99621),x99622),f587(x99624,x99623,x99622,x99621))),f328(f328(f164(x99621),x99623),f587(x99624,x99623,x99622,x99621)))),x99624))
% 81.29/80.92 [10099]~P74(x100991)+~P24(f328(f62(x100992),x100994))+E(f328(f165(x100991),f328(f328(f153(x100992,x100991),x100993),f91(f878(x100992),f328(f328(f18(f878(x100992),a871,a871),f328(f328(f8(a871,f885(a871,a871),f878(x100992)),a326),f328(f328(f7(f878(x100992),f885(x100992,a871),a871),f328(f328(f8(f885(x100992,a871),f885(f885(x100992,a871),a871),f878(x100992)),a325),f171(x100992))),x100994))),f136(x100992))))),f234(x100992,x100991,x100993,x100994))
% 81.29/80.92 [7384]~P61(x73842)+E(x73841,f2(x73842))+E(f328(f328(f286(x73842),f328(f328(f81(x73842),x73843),f328(f328(f82(x73842),x73844),x73841))),x73841),f328(f328(f81(x73842),x73844),f328(f328(f286(x73842),x73843),x73841)))
% 81.29/80.92 [7385]~P58(x73852)+E(x73851,f2(x73852))+E(f328(f328(f39(x73852),f328(f328(f81(x73852),x73853),f328(f328(f82(x73852),x73854),x73851))),x73851),f328(f328(f81(x73852),x73854),f328(f328(f39(x73852),x73853),x73851)))
% 81.29/80.92 [7386]~P58(x73862)+E(x73861,f2(x73862))+E(f328(f328(f39(x73862),f328(f328(f81(x73862),x73863),f328(f328(f82(x73862),x73861),x73864))),x73861),f328(f328(f81(x73862),x73864),f328(f328(f39(x73862),x73863),x73861)))
% 81.29/80.92 [7617]~P62(x76172)+E(x76171,f2(x76172))+E(f328(f328(f286(x76172),f328(f328(f22(x76172),x76173),f328(f328(f82(x76172),x76171),x76174))),x76171),f328(f328(f22(x76172),f328(f328(f286(x76172),x76173),x76171)),x76174))
% 81.29/80.92 [7618]~P61(x76182)+E(x76181,f2(x76182))+E(f328(f328(f286(x76182),f328(f328(f81(x76182),x76183),f328(f328(f82(x76182),x76184),x76181))),x76181),f328(f328(f81(x76182),f328(f328(f286(x76182),x76183),x76181)),x76184))
% 81.29/80.92 [7619]~P62(x76192)+E(x76191,f2(x76192))+E(f328(f328(f286(x76192),f328(f328(f81(x76192),x76193),f328(f328(f82(x76192),x76191),x76194))),x76191),f328(f328(f81(x76192),f328(f328(f286(x76192),x76193),x76191)),x76194))
% 81.29/80.92 [8325]~P24(f328(f159(x83251,x83253),x83254))+~P24(f328(f159(x83251,x83252),x83254))+P24(f328(f159(x83251,f328(f328(f107(f885(x83251,a871)),x83252),x83253)),x83254))
% 81.29/80.92 [8696]~E(f328(f328(f285(x86961,x86961,x86961),x86962),x86964),f193(f885(f884(x86961,x86961),a871)))+~E(f328(f328(f285(x86961,x86961,x86961),x86962),x86963),f193(f885(f884(x86961,x86961),a871)))+E(f328(f328(f285(x86961,x86961,x86961),x86962),f328(f328(f116(f885(f884(x86961,x86961),a871)),x86963),x86964)),f193(f885(f884(x86961,x86961),a871)))
% 81.29/80.92 [8814]~P24(f328(f328(f244(f885(x88141,a871)),x88143),x88144))+~P24(f328(f328(f244(f885(x88141,a871)),x88142),x88144))+P24(f328(f328(f244(f885(x88141,a871)),f328(f328(f116(f885(x88141,a871)),x88142),x88143)),x88144))
% 81.29/80.92 [9192]~P24(f328(f62(x91921),x91924))+~P24(f328(f62(x91921),x91923))+E(f328(f328(f22(a877),f328(f328(f81(a877),f328(f328(f6(x91921,a877),x91922),x91923)),f328(f328(f6(x91921,a877),x91922),x91924))),f328(f328(f6(x91921,a877),x91922),f328(f328(f107(f885(x91921,a871)),x91923),x91924))),f328(f328(f6(x91921,a877),x91922),f328(f328(f116(f885(x91921,a871)),x91923),x91924)))
% 81.29/80.92 [9280]~P24(f328(f328(f330(x92801),x92803),x92802))+~P24(f328(f328(f244(f885(x92801,a871)),x92802),f328(f328(f306(x92801),x92803),x92804)))+P24(f328(f328(f244(f885(x92801,a871)),f328(f328(f22(f885(x92801,a871)),x92802),f328(f328(f306(x92801),x92803),f193(f885(x92801,a871))))),x92804))
% 81.29/80.92 [9439]~P24(f328(f328(f330(x94391),x94393),x94392))+P24(f328(f328(f244(f885(x94391,a871)),x94392),f328(f328(f306(x94391),x94393),x94394)))+~P24(f328(f328(f244(f885(x94391,a871)),f328(f328(f22(f885(x94391,a871)),x94392),f328(f328(f306(x94391),x94393),f193(f885(x94391,a871))))),x94394))
% 81.29/80.92 [9529]~P24(f328(f328(f244(a877),x95291),x95293))+~P24(f328(f328(f245(a877),x95292),x95294))+P24(f328(f328(f330(f884(f884(a877,a877),f884(a877,a877))),f328(f328(f257(f884(a877,a877),f884(a877,a877)),f328(f328(f257(a877,a877),x95291),x95292)),f328(f328(f257(a877,a877),x95293),x95294))),a36))
% 81.29/80.92 [9530]~P24(f328(f328(f244(a877),x95302),x95304))+~P24(f328(f328(f244(a877),x95301),x95303))+P24(f328(f328(f330(f884(f884(a877,a877),f884(a877,a877))),f328(f328(f257(f884(a877,a877),f884(a877,a877)),f328(f328(f257(a877,a877),x95301),x95302)),f328(f328(f257(a877,a877),x95303),x95304))),a71))
% 81.29/80.92 [9821]~P24(f328(f328(f330(f878(x98211)),x98214),f160(x98211,x98213)))+~P24(f328(f328(f330(f878(x98211)),x98214),f160(x98211,x98212)))+P24(f328(f159(x98211,f328(f328(f107(f885(x98211,a871)),f328(f328(f7(x98211,f885(x98211,a871),a871),f330(x98211)),x98212)),f328(f328(f7(x98211,f885(x98211,a871),a871),f330(x98211)),x98213))),x98214))
% 81.29/80.92 [9927]~P21(x99271,f885(f885(x99271,a871),a871),f328(f328(f7(x99271,f885(f884(x99271,x99271),a871),f885(f885(x99271,a871),a871)),f328(f328(f8(f885(x99271,a871),f885(f885(f884(x99271,x99271),a871),f885(f885(x99271,a871),a871)),x99271),f61(x99271)),f328(f328(f7(x99271,f885(x99271,a871),f885(x99271,a871)),f306(x99271)),f193(f885(x99271,a871))))),x99273),x99272)+~P24(f328(f328(f330(x99271),x99274),x99272))+E(f328(f328(f22(f885(f885(x99271,a871),a871)),f328(f328(f61(x99271),x99272),x99273)),f328(f328(f61(x99271),f328(f328(f306(x99271),x99274),f193(f885(x99271,a871)))),x99273)),f328(f328(f61(x99271),f328(f328(f22(f885(x99271,a871)),x99272),f328(f328(f306(x99271),x99274),f193(f885(x99271,a871))))),x99273))
% 81.29/80.92 [10063]~P48(x100631,x100632,x100634)+~P24(f328(f328(f330(f884(x100631,x100631)),x100633),x100634))+P24(f328(f328(f267(x100631,x100631,a871),f328(f328(f7(x100631,f885(x100631,a871),f885(x100631,a871)),f328(f328(f8(f885(a871,a871),f885(f885(x100631,a871),f885(x100631,a871)),x100631),f8(a871,a871,x100631)),f328(f328(f8(a871,f885(a871,a871),x100631),a326),f328(f328(f7(x100631,f885(x100631,a871),a871),f330(x100631)),x100632)))),f328(f328(f7(x100631,f885(x100631,a871),a871),f330(x100631)),x100632))),x100633))
% 81.29/80.92 [10075]P24(f328(f62(x100751),x100752))+~P24(f328(f62(x100753),f328(f307(x100751,x100753,x100754),x100752)))+~P24(f328(f62(x100751),f328(f249(x100751),f328(f328(f18(x100751,a871,a871),f328(f328(f8(a871,f885(a871,a871),x100751),a326),f328(f328(f7(x100751,f885(x100751,a871),a871),f330(x100751)),x100752))),f328(f328(f7(x100751,x100753,a871),f328(f328(f8(x100753,f885(x100753,a871),x100751),a325),x100754)),f328(x100754,f714(x100754,x100753,x100752,x100751)))))))
% 81.29/80.92 [8077]~P62(x80772)+E(x80771,f2(x80772))+E(f328(f328(f286(x80772),f328(f328(f22(x80772),f328(f328(f82(x80772),x80771),x80773)),x80774)),x80771),f328(f328(f22(x80772),x80773),f328(f328(f286(x80772),x80774),x80771)))
% 81.29/80.92 [8078]~P62(x80782)+E(x80781,f2(x80782))+E(f328(f328(f286(x80782),f328(f328(f81(x80782),f328(f328(f82(x80782),x80781),x80783)),x80784)),x80781),f328(f328(f81(x80782),x80783),f328(f328(f286(x80782),x80784),x80781)))
% 81.29/80.92 [8977]~E(f328(f328(f285(x89771,x89771,x89771),x89773),x89774),f193(f885(f884(x89771,x89771),a871)))+~E(f328(f328(f285(x89771,x89771,x89771),x89772),x89774),f193(f885(f884(x89771,x89771),a871)))+E(f328(f328(f285(x89771,x89771,x89771),f328(f328(f116(f885(f884(x89771,x89771),a871)),x89772),x89773)),x89774),f193(f885(f884(x89771,x89771),a871)))
% 81.29/80.92 [10006]~P144(x100061)+~P144(x100062)+E(f328(f328(f313(x100061),f328(f328(f7(x100061,a105,f881(f878(a324))),f328(f328(f8(f885(x100062,f881(f878(a324))),f885(a105,f881(f878(a324))),x100061),f313(x100062)),f328(f328(f8(f885(x100062,f884(x100061,x100062)),f885(x100062,f881(f878(a324))),x100061),f328(f8(f884(x100061,x100062),f881(f878(a324)),x100062),x100063)),f257(x100061,x100062)))),x100064)),x100064),f328(f328(f313(f884(x100061,x100062)),x100063),x100064))
% 81.29/80.92 [9732]~P24(f328(f159(x97321,x97323),x97324))+~P24(f328(f159(x97321,x97322),x97324))+P24(f328(f159(x97321,f328(f328(f18(x97321,a871,a871),f328(f328(f8(a871,f885(a871,a871),x97321),a326),x97322)),x97323)),x97324))
% 81.29/80.92 [9998]P24(f328(x99981,f572(x99982,x99983,x99981,x99984)))+~P24(f328(f62(x99984),f328(f249(x99984),x99981)))+P24(f328(f62(x99983),f328(f249(x99983),f328(f328(f8(f885(x99984,a871),a871,x99983),f88(x99984)),f328(f328(f8(f885(x99984,a871),f885(x99984,a871),x99983),f328(f18(x99984,a871,a871),f328(f328(f8(a871,f885(a871,a871),x99984),a326),x99981))),x99982)))))
% 81.29/80.92 [10019]~P24(f328(f62(x100192),f328(f249(x100192),x100193)))+~P24(f328(f62(x100191),f328(f249(x100191),f328(f328(f7(x100191,x100192,a871),x100194),f572(x100194,x100191,x100193,x100192)))))+P24(f328(f62(x100191),f328(f249(x100191),f328(f328(f8(f885(x100192,a871),a871,x100191),f88(x100192)),f328(f328(f8(f885(x100192,a871),f885(x100192,a871),x100191),f328(f18(x100192,a871,a871),f328(f328(f8(a871,f885(a871,a871),x100192),a326),x100193))),x100194)))))
% 81.29/80.92 [6527]E(x65271,x65272)+~E(f328(x65273,x65271),f328(x65273,x65272))+~P21(x65274,x65275,x65273,f252(f885(x65274,a871)))
% 81.29/80.92 [6688]~E(f328(x66883,x66885),f196(x66882))+~E(f328(x66884,x66885),f196(x66882))+E(f328(f184(x66881,x66882,x66883,x66884),x66885),f196(x66882))
% 81.29/80.92 [7420]E(x74201,x74202)+~P21(x74203,x74204,x74205,f252(f885(x74203,a871)))+~E(f328(f307(x74203,x74204,x74205),x74201),f328(f307(x74203,x74204,x74205),x74202))
% 81.29/80.92 [7671]P21(x76712,x76713,f540(x76714,x76713,x76712,x76711),x76711)+~E(f328(f307(x76713,x76712,x76715),x76714),x76711)+E(x76711,f193(f885(x76712,a871)))
% 81.29/80.92 [8213]~P24(f328(f328(x82133,x82132),x82135))+~P24(f328(f328(x82133,x82134),x82132))+P24(f328(f328(f330(x82131),x82132),f295(x82131,x82133,x82134,x82135)))
% 81.29/80.92 [8214]~P24(f328(f328(x82143,x82142),x82145))+~P24(f328(f328(x82143,x82144),x82142))+P24(f328(f328(f330(x82141),x82142),f292(x82141,x82143,x82144,x82145)))
% 81.29/80.92 [8772]~P21(x87721,x87723,x87725,f252(f885(x87721,a871)))+~P21(x87723,x87722,x87724,f252(f885(x87723,a871)))+P21(x87721,x87722,f328(f74(x87723,x87722,x87721,x87724),x87725),f252(f885(x87721,a871)))
% 81.29/80.92 [9339]P24(f328(f328(f330(f884(x93391,x93391)),f328(f328(f257(x93391,x93391),x93392),x93393)),f304(x93391,x93394)))+~P24(f328(f328(f330(f884(x93391,x93391)),f328(f328(f257(x93391,x93391),x93392),x93395)),f304(x93391,x93394)))+~P24(f328(f328(f330(f884(x93391,x93391)),f328(f328(f257(x93391,x93391),x93395),x93393)),f304(x93391,x93394)))
% 81.29/80.92 [9377]~P106(x93772)+~P24(f328(f136(x93771),x93775))+P24(f328(f136(x93771),f148(x93771,x93772,x93773,x93774,x93775)))
% 81.29/80.92 [5357]~E(x53572,f119(x53571))+E(f328(f328(f127(x53571),x53572),x53573),f328(f328(f150(x53571),x53574),x53575))+~E(x53573,f328(f328(f150(x53571),x53574),x53575))
% 81.29/80.92 [5358]~E(x53582,f119(x53581))+E(f328(f328(f127(x53581),x53582),x53583),f328(f328(f150(x53581),x53584),x53585))+~E(f328(f328(f150(x53581),x53584),x53585),x53583)
% 81.29/80.92 [6483]~E(f328(f194(f878(x64831)),x64835),f328(f194(f878(x64832)),x64834))+E(f328(f328(f153(f884(x64831,x64832),x64832),f266(x64831,x64832)),x64833),x64834)+~E(f328(f328(f181(x64831,x64832),x64835),x64834),x64833)
% 81.29/80.92 [6484]~E(f328(f194(f878(x64841)),x64844),f328(f194(f878(x64842)),x64845))+E(f328(f328(f153(f884(x64841,x64842),x64841),f256(x64841,x64842)),x64843),x64844)+~E(f328(f328(f181(x64841,x64842),x64844),x64845),x64843)
% 81.29/80.92 [6957]~P106(x69571)+~P29(x69571,f328(f328(f153(x69572,x69571),x69573),x69575))+P29(x69571,f328(f328(f153(x69572,x69571),x69573),f328(f135(x69572,x69574),x69575)))
% 81.29/80.92 [7004]~P24(f328(x70043,x70045))+~P24(f328(f328(x70042,x70044),x70045))+P24(f328(f328(f98(x70041,x70042,x70043),x70044),x70045))
% 81.29/80.92 [7101]~P106(x71011)+P29(x71011,f328(f328(f153(x71012,x71011),x71013),f169(x71012,x71014,x71015)))+~P29(x71011,f328(f328(f153(x71012,x71011),x71013),x71015))
% 81.29/80.92 [7124]~P52(x71243,x71242,x71245)+~P52(x71241,x71243,x71244)+P52(x71241,x71242,f328(f328(f285(x71241,x71243,x71242),x71244),x71245))
% 81.29/80.92 [7216]E(x72161,x72162)+~P21(x72163,x72164,x72165,f252(f885(x72163,a871)))+~E(f328(f328(f153(x72163,x72164),x72165),x72161),f328(f328(f153(x72163,x72164),x72165),x72162))
% 81.29/80.92 [7370]~P24(f328(f328(f244(a877),x73701),f328(x73703,x73705)))+P24(f328(f328(f244(a877),x73701),f154(x73702,x73703,x73704)))+~P24(f328(f328(f330(x73702),x73705),f328(f171(x73702),x73704)))
% 81.29/80.92 [7371]~P24(f328(f328(f245(a877),x73711),f328(x73713,x73715)))+P24(f328(f328(f245(a877),x73711),f154(x73712,x73713,x73714)))+~P24(f328(f328(f330(x73712),x73715),f328(f171(x73712),x73714)))
% 81.29/80.92 [7774]~P108(x77741)+P24(f328(f328(f244(f885(x77741,a871)),f299(x77741,x77742,x77743)),f299(x77741,x77744,x77745)))+P24(f328(f328(f244(x77741),x77742),x77743))
% 81.29/80.92 [7797]~P27(x77971)+P24(f328(f328(f244(x77971),f328(f328(f42(x77972,x77971),x77973),x77974)),f328(x77974,x77975)))+~P24(f328(f328(f330(x77972),x77975),x77973))
% 81.29/80.92 [7863]~P21(x78631,x78632,x78634,x78633)+E(f328(f78(x78631,x78632,x78633,x78634),f328(x78634,x78635)),x78635)+~P24(f328(f328(f330(x78631),x78635),x78633))
% 81.29/80.92 [8065]~P24(f328(x80651,x80655))+P24(f328(x80651,f479(x80651,x80652,x80653,x80654)))+~P24(f328(f328(f330(x80654),x80655),x80653))
% 81.29/80.92 [8066]~P24(f328(x80661,x80665))+P24(f328(x80661,f479(x80661,x80662,x80663,x80664)))+~P24(f328(f328(f330(x80664),x80665),x80662))
% 81.29/80.92 [8164]P24(f328(f62(x81641),x81642))+~P24(f328(f62(x81643),x81644))+~P24(f328(f328(f244(f885(x81641,a871)),x81642),f328(f307(x81643,x81641,x81645),x81644)))
% 81.29/80.92 [8329]E(x83291,x83292)+~P21(x83293,x83294,x83295,f328(f328(f116(f885(x83293,a871)),f328(f171(x83293),x83291)),f328(f171(x83293),x83292)))+~E(f328(f328(f153(x83293,x83294),x83295),x83291),f328(f328(f153(x83293,x83294),x83295),x83292))
% 81.29/80.92 [8383]~P108(x83831)+~P24(f328(f328(f245(f885(x83831,a871)),f299(x83831,x83834,x83835)),f299(x83831,x83832,x83833)))+P24(f328(f328(f244(x83831),x83832),x83833))
% 81.29/80.92 [8452]~P21(x84521,x84524,x84525,f252(f885(x84521,a871)))+~P24(f328(f328(f330(x84524),f328(x84525,x84522)),f328(f307(x84521,x84524,x84525),x84523)))+P24(f328(f328(f330(x84521),x84522),x84523))
% 81.29/80.92 [8530]P24(f328(x85301,x85302))+~P24(f328(x85301,f413(x85301,x85303,x85304,x85305)))+~P24(f328(f328(f330(x85305),x85302),x85304))
% 81.29/80.92 [8531]P24(f328(x85311,x85312))+~P24(f328(x85311,f413(x85311,x85313,x85314,x85315)))+~P24(f328(f328(f330(x85315),x85312),x85313))
% 81.29/80.92 [8811]~P21(x88112,x88113,x88111,x88114)+E(f328(x88111,f328(f78(x88112,x88113,x88114,x88111),x88115)),x88115)+~P24(f328(f328(f330(x88113),x88115),f328(f307(x88112,x88113,x88111),x88114)))
% 81.29/80.92 [8915]E(x89151,f119(x89152))+E(f328(f328(f150(x89152),x89153),f589(x89154,x89153,x89155,x89151,x89152)),x89151)+~E(f328(f328(f127(x89152),x89151),x89155),f328(f328(f150(x89152),x89153),x89154))
% 81.29/80.92 [8916]E(x89161,f119(x89162))+E(f328(f328(f150(x89162),x89163),f590(x89164,x89161,x89165,x89163,x89162)),x89161)+~E(f328(f328(f127(x89162),x89161),x89164),f328(f328(f150(x89162),x89163),x89165))
% 81.29/80.92 [8933]E(f328(f328(f150(x89332),x89333),f589(x89334,x89333,x89331,x89335,x89332)),x89335)+~E(f328(f328(f127(x89332),x89335),x89331),f328(f328(f150(x89332),x89333),x89334))+E(x89331,f328(f328(f150(x89332),x89333),x89334))
% 81.29/80.92 [8934]E(f328(f328(f150(x89341),x89342),f590(x89344,x89345,x89343,x89342,x89341)),x89345)+~E(f328(f328(f127(x89341),x89345),x89344),f328(f328(f150(x89341),x89342),x89343))+E(f328(f328(f150(x89341),x89342),x89343),x89344)
% 81.29/80.92 [9016]~E(f328(f307(x90163,x90162,x90164),f252(f885(x90163,a871))),f252(f885(x90162,a871)))+~E(f328(f307(x90161,x90163,x90165),f252(f885(x90161,a871))),f252(f885(x90163,a871)))+E(f328(f307(x90161,x90162,f328(f74(x90163,x90162,x90161,x90164),x90165)),f252(f885(x90161,a871))),f252(f885(x90162,a871)))
% 81.29/80.92 [9383]E(x93831,f119(x93832))+~E(f328(f328(f127(x93832),x93831),x93833),f328(f328(f150(x93832),x93835),x93834))+E(f328(f328(f127(x93832),f590(x93833,x93831,x93834,x93835,x93832)),x93833),x93834)
% 81.29/80.92 [9384]E(x93841,f119(x93842))+~E(f328(f328(f127(x93842),x93841),x93845),f328(f328(f150(x93842),x93844),x93843))+E(f328(f328(f127(x93842),f589(x93843,x93844,x93845,x93841,x93842)),x93845),x93843)
% 81.29/80.92 [9391]E(f328(f328(f127(x93912),f589(x93914,x93913,x93911,x93915,x93912)),x93911),x93914)+~E(f328(f328(f127(x93912),x93915),x93911),f328(f328(f150(x93912),x93913),x93914))+E(x93911,f328(f328(f150(x93912),x93913),x93914))
% 81.29/80.92 [9392]~E(f328(f328(f127(x93921),x93925),x93924),f328(f328(f150(x93921),x93922),x93923))+E(f328(f328(f127(x93921),f590(x93924,x93925,x93923,x93922,x93921)),x93924),x93923)+E(f328(f328(f150(x93921),x93922),x93923),x93924)
% 81.29/80.92 [9393]E(f328(f328(f127(x93931),x93935),f593(x93933,x93932,x93934,x93935,x93931)),x93932)+E(f328(f328(f127(x93931),x93932),f592(x93933,x93932,x93934,x93935,x93931)),x93935)+~E(f328(f328(f127(x93931),x93935),x93934),f328(f328(f127(x93931),x93932),x93933))
% 81.29/80.92 [9425]~P106(x94251)+P29(x94251,f328(f328(f153(x94252,x94251),x94253),f148(x94252,x94251,x94253,x94254,x94255)))+~P29(x94251,f328(f328(f153(x94252,x94251),x94253),x94255))
% 81.29/80.92 [9436]~P56(x94365,x94361,x94364,x94363)+P24(f328(f328(x94361,x94362),f688(x94363,x94364,x94361,x94365,x94362)))+~P24(f328(f328(f330(x94365),x94362),x94364))
% 81.29/80.92 [9541]~P24(f328(f328(f330(f884(x95411,x95411)),f328(f328(f257(x95411,x95411),x95415),x95413)),f304(x95411,x95414)))+P24(f328(f328(f330(f884(x95411,x95411)),f328(f328(f257(x95411,x95411),x95412),x95413)),f328(f328(f285(x95411,x95411,x95411),x95414),f304(x95411,x95414))))+~P24(f328(f328(f330(f884(x95411,x95411)),f328(f328(f257(x95411,x95411),x95412),x95415)),f328(f328(f285(x95411,x95411,x95411),x95414),f304(x95411,x95414))))
% 81.29/80.92 [9542]~P24(f328(f328(f330(f884(x95421,x95421)),f328(f328(f257(x95421,x95421),x95422),x95425)),f304(x95421,x95424)))+P24(f328(f328(f330(f884(x95421,x95421)),f328(f328(f257(x95421,x95421),x95422),x95423)),f328(f328(f285(x95421,x95421,x95421),x95424),f304(x95421,x95424))))+~P24(f328(f328(f330(f884(x95421,x95421)),f328(f328(f257(x95421,x95421),x95425),x95423)),f328(f328(f285(x95421,x95421,x95421),x95424),f304(x95421,x95424))))
% 81.29/80.92 [9545]P24(f328(f328(f330(f884(f878(x95451),f878(x95451))),f328(f328(f257(f878(x95451),f878(x95451)),x95452),x95453)),f157(x95451,f304(x95451,x95454))))+~P24(f328(f328(f330(f884(f878(x95451),f878(x95451))),f328(f328(f257(f878(x95451),f878(x95451)),x95452),x95455)),f157(x95451,f304(x95451,x95454))))+~P24(f328(f328(f330(f884(f878(x95451),f878(x95451))),f328(f328(f257(f878(x95451),f878(x95451)),x95455),x95453)),f157(x95451,f304(x95451,x95454))))
% 81.29/80.92 [9549]E(f328(f328(f127(x95491),x95492),f592(x95493,x95492,x95494,x95495,x95491)),x95495)+E(f328(f328(f127(x95491),f593(x95493,x95492,x95494,x95495,x95491)),x95493),x95494)+~E(f328(f328(f127(x95491),x95492),x95493),f328(f328(f127(x95491),x95495),x95494))
% 81.29/80.92 [9550]E(f328(f328(f127(x95501),x95502),f593(x95503,x95504,x95505,x95502,x95501)),x95504)+E(f328(f328(f127(x95501),f592(x95503,x95504,x95505,x95502,x95501)),x95505),x95503)+~E(f328(f328(f127(x95501),x95502),x95505),f328(f328(f127(x95501),x95504),x95503))
% 81.29/80.92 [9604]P24(f328(f328(f330(f884(x96041,x96041)),f328(f328(f257(x96041,x96041),x96042),x96043)),f328(f328(f285(x96041,x96041,x96041),x96044),f304(x96041,x96044))))+~P24(f328(f328(f330(f884(x96041,x96041)),f328(f328(f257(x96041,x96041),x96042),x96045)),f328(f328(f285(x96041,x96041,x96041),x96044),f304(x96041,x96044))))+~P24(f328(f328(f330(f884(x96041,x96041)),f328(f328(f257(x96041,x96041),x96045),x96043)),f328(f328(f285(x96041,x96041,x96041),x96044),f304(x96041,x96044))))
% 81.29/80.92 [9631]P35(x96311,x96312,x96313,x96314,x96315)+~E(f328(f194(f878(x96311)),x96314),f328(f194(f878(x96312)),x96315))+~P24(f328(f328(f267(x96311,x96312,a871),x96313),f669(x96315,x96314,x96313,x96312,x96311)))
% 81.29/80.92 [9632]P35(x96321,x96322,x96323,x96324,x96325)+~E(f328(f194(f878(x96321)),x96324),f328(f194(f878(x96322)),x96325))+~P24(f328(f328(f267(x96321,x96322,a871),x96323),f676(x96323,x96325,x96324,x96322,x96321)))
% 81.29/80.92 [9637]E(f328(f328(f127(x96371),f592(x96372,x96373,x96374,x96375,x96371)),x96374),x96372)+~E(f328(f328(f127(x96371),x96373),x96372),f328(f328(f127(x96371),x96375),x96374))+E(f328(f328(f127(x96371),f593(x96372,x96373,x96374,x96375,x96371)),x96372),x96374)
% 81.29/80.92 [9650]~P106(x96502)+E(f328(f328(f147(x96501,x96502,x96503),x96504),x96505),f328(f328(f150(x96501),x96504),x96505))+P24(f328(f328(f330(x96501),f734(x96504,x96503,x96505,x96501,x96502)),f328(f171(x96501),x96505)))
% 81.29/80.92 [9655]~P56(x96551,x96554,x96553,x96552)+~P24(f328(f328(f330(x96551),x96555),x96553))+P24(f328(f328(f330(x96551),f688(x96552,x96553,x96554,x96551,x96555)),x96552))
% 81.29/80.92 [9775]~P24(f328(f328(f330(f884(f885(x97751,a871),f885(x97751,a871))),f328(f328(f257(f885(x97751,a871),f885(x97751,a871)),x97754),x97753)),f319(x97751,x97752)))+~P24(f328(f328(f330(x97751),x97755),x97754))+P24(f328(f328(f330(x97751),f753(x97752,x97753,x97754,x97751,x97755)),x97753))
% 81.29/80.92 [9787]~P106(x97872)+E(f328(f328(f147(x97871,x97872,x97873),x97874),x97875),f328(f328(f150(x97871),x97874),x97875))+~P24(f328(f328(f244(x97872),f328(x97873,x97874)),f328(x97873,f734(x97874,x97873,x97875,x97871,x97872))))
% 81.29/80.92 [9979]P35(x99791,x99792,x99793,x99794,x99795)+~E(f328(f194(f878(x99791)),x99794),f328(f194(f878(x99792)),x99795))+~P24(f328(f328(x99793,f328(f328(f164(x99791),x99794),f677(x99795,x99794,x99793,x99792,x99791))),f328(f328(f164(x99792),x99795),f677(x99795,x99794,x99793,x99792,x99791))))
% 81.29/80.92 [9980]P35(x99801,x99802,x99803,x99804,x99805)+~E(f328(f194(f878(x99801)),x99804),f328(f194(f878(x99802)),x99805))+~P24(f328(f328(x99803,f328(f328(f164(x99801),x99804),f728(x99803,x99805,x99802,x99804,x99801))),f328(f328(f164(x99802),x99805),f728(x99803,x99805,x99802,x99804,x99801))))
% 81.29/80.92 [6555]~P13(x65552,x65555,x65551)+~P24(f328(f62(x65552),x65554))+E(f328(x65551,f328(f328(f306(x65552),x65553),x65554)),f328(f328(f65(x65552,x65552,x65555),x65553),x65554))
% 81.29/80.92 [6556]~E(x65563,x65564)+~E(x65562,x65565)+E(f328(f328(f306(x65561),x65562),f328(f328(f306(x65561),x65563),f193(f885(x65561,a871)))),f328(f328(f306(x65561),x65564),f328(f328(f306(x65561),x65565),f193(f885(x65561,a871)))))
% 81.29/80.92 [6567]P24(f328(x65672,x65675))+E(f176(x65671,x65672,f328(f328(f127(x65671),x65673),x65674)),f176(x65671,x65672,x65673))+~P24(f328(f328(f330(x65671),x65675),f328(f171(x65671),x65673)))
% 81.29/80.92 [6604]E(f328(x66041,x66042),f193(f885(x66043,a871)))+~E(f328(f328(f43(x66044,f885(x66043,a871)),x66045),x66041),f193(f885(x66043,a871)))+~P24(f328(f328(f330(x66044),x66042),x66045))
% 81.29/80.92 [6605]E(f328(x66051,x66052),f252(f885(x66053,a871)))+~E(f328(f328(f42(x66054,f885(x66053,a871)),x66055),x66051),f252(f885(x66053,a871)))+~P24(f328(f328(f330(x66054),x66052),x66055))
% 81.29/80.92 [6906]~P24(f328(f328(f200(x69061),x69063),x69065))+~P24(f328(f328(f200(x69062),x69065),x69064))+P24(f328(f328(f200(f34(x69061,x69062)),x69063),x69064))
% 81.29/80.92 [7111]~E(x71112,x71114)+~P143(x71111)+E(f328(f328(f81(x71111),f328(f328(f82(x71111),x71112),x71113)),f328(f328(f82(x71111),x71114),x71115)),f328(f328(f81(x71111),f328(f328(f82(x71111),x71112),x71115)),f328(f328(f82(x71111),x71114),x71113)))
% 81.29/80.92 [7171]~P27(x71711)+~P24(f328(f328(f330(x71714),x71713),x71715))+P24(f328(f328(f244(x71711),f328(x71712,x71713)),f328(f328(f43(x71714,x71711),x71715),x71712)))
% 81.29/80.92 [7221]~P107(x72211)+P24(f328(f328(f244(x72211),f328(x72212,x72213)),f328(x72214,x72213)))+~P24(f328(f328(f244(f885(x72215,x72211)),x72212),x72214))
% 81.29/80.92 [7338]E(x73381,x73382)+E(x73383,x73381)+~E(f328(f328(f306(x73384),x73381),f328(f328(f306(x73384),x73385),f193(f885(x73384,a871)))),f328(f328(f306(x73384),x73382),f328(f328(f306(x73384),x73383),f193(f885(x73384,a871)))))
% 81.29/80.92 [7339]E(x73391,x73392)+E(x73393,x73391)+~E(f328(f328(f306(x73394),x73393),f328(f328(f306(x73394),x73392),f193(f885(x73394,a871)))),f328(f328(f306(x73394),x73395),f328(f328(f306(x73394),x73391),f193(f885(x73394,a871)))))
% 81.29/80.92 [7340]E(x73401,x73402)+E(x73401,x73403)+~E(f328(f328(f306(x73404),x73403),f328(f328(f306(x73404),x73402),f193(f885(x73404,a871)))),f328(f328(f306(x73404),x73405),f328(f328(f306(x73404),x73401),f193(f885(x73404,a871)))))
% 81.29/80.92 [7341]E(x73411,x73412)+E(x73411,x73413)+~E(f328(f328(f306(x73414),x73411),f328(f328(f306(x73414),x73415),f193(f885(x73414,a871)))),f328(f328(f306(x73414),x73412),f328(f328(f306(x73414),x73413),f193(f885(x73414,a871)))))
% 81.29/80.92 [7873]P21(x78731,x78732,x78733,x78734)+~P21(x78731,x78732,x78733,x78735)+~P24(f328(f328(f244(f885(x78731,a871)),x78734),x78735))
% 81.29/80.92 [7880]~P24(f328(f328(f244(a877),x78805),x78803))+~P24(f328(f328(f328(f328(a202,x78801),x78802),x78805),x78804))+P24(f328(f328(f328(f328(a202,x78801),x78802),x78803),x78804))
% 81.29/80.92 [7976]P24(f328(x79761,x79762))+~P24(f328(f328(f200(x79764),x79762),x79765))+P24(f328(f328(f200(f31(x79761,x79763,x79764)),x79762),x79765))
% 81.29/80.92 [8004]~P24(f328(x80041,x80044))+~P24(f328(f328(f200(x80042),x80044),x80045))+P24(f328(f328(f200(f31(x80041,x80042,x80043)),x80044),x80045))
% 81.29/80.92 [8055]E(x80551,x80552)+~E(f328(f307(x80553,x80554,x80555),x80551),f328(f307(x80553,x80554,x80555),x80552))+~P21(x80553,x80554,x80555,f328(f328(f116(f885(x80553,a871)),x80551),x80552))
% 81.29/80.92 [8129]P24(f328(x81292,x81294))+E(f328(f328(f137(x81291),f328(f194(f878(x81291)),f176(x81291,x81292,x81293))),x81293),f328(f328(f150(x81291),x81294),x81295))+~E(f328(f328(f127(x81291),f176(x81291,x81292,x81293)),f328(f328(f150(x81291),x81294),x81295)),x81293)
% 81.29/80.92 [8161]~P21(x81611,x81612,x81613,x81615)+~P21(x81611,x81612,x81613,x81614)+P21(x81611,x81612,x81613,f328(f328(f107(f885(x81611,a871)),x81614),x81615))
% 81.29/80.92 [8270]~P74(x82701)+E(f328(f328(f81(x82701),f328(x82702,x82703)),f328(f165(x82701),f328(f328(f153(x82704,x82701),x82702),f169(x82704,x82703,x82705)))),f328(f165(x82701),f328(f328(f153(x82704,x82701),x82702),x82705)))+~P24(f328(f328(f330(x82704),x82703),f328(f171(x82704),x82705)))
% 81.29/80.92 [8359]~P106(x83591)+~P29(x83591,f328(f328(f153(x83592,x83591),x83593),x83595))+P29(x83591,f328(f328(f153(x83592,x83591),x83593),f328(f328(f147(x83592,x83591,x83593),x83594),x83595)))
% 81.29/80.92 [8436]P24(f328(x84361,x84362))+P24(f328(f328(f200(x84363),x84362),x84364))+~P24(f328(f328(f200(f31(x84361,x84365,x84363)),x84362),x84364))
% 81.29/80.92 [8447]~P27(x84471)+P24(f328(f328(f244(x84471),f328(f328(f42(x84472,x84471),x84473),x84474)),f328(f328(f42(x84472,x84471),x84475),x84474)))+~P24(f328(f328(f244(f885(x84472,a871)),x84475),x84473))
% 81.29/80.92 [8448]~P27(x84481)+P24(f328(f328(f244(x84481),f328(f328(f43(x84482,x84481),x84483),x84484)),f328(f328(f43(x84482,x84481),x84485),x84484)))+~P24(f328(f328(f244(f885(x84482,a871)),x84483),x84485))
% 81.29/80.92 [8460]~P24(f328(x84604,x84602))+P24(f328(f328(f200(x84601),x84602),x84603))+~P24(f328(f328(f200(f31(x84604,x84601,x84605)),x84602),x84603))
% 81.29/80.92 [8484]~P106(x84843)+P24(f328(f136(x84841),x84842))+~P24(f328(f136(x84841),f328(f328(f147(x84841,x84843,x84844),x84845),x84842)))
% 81.29/80.92 [8494]P24(f328(f328(f200(x84941),x84942),x84943))+P24(f328(f328(f200(x84944),x84942),x84943))+~P24(f328(f328(f200(f31(x84945,x84941,x84944)),x84942),x84943))
% 81.29/80.92 [8625]~P106(x86251)+~P24(f328(f328(f330(x86252),x86253),f328(f171(x86252),x86254)))+~P24(f328(f136(x86252),f328(f328(f147(x86252,x86251,x86255),x86253),x86254)))
% 81.29/80.92 [8706]~P106(x87061)+P29(x87061,f328(f328(f153(x87062,x87061),x87063),x87064))+~P29(x87061,f328(f328(f153(x87062,x87061),x87063),f328(f328(f147(x87062,x87061,x87063),x87065),x87064)))
% 81.29/80.92 [8799]~P106(x87992)+E(f328(f328(f147(x87991,x87992,x87993),x87994),x87995),f148(x87991,x87992,x87993,x87994,x87995))+P24(f328(f328(f330(x87992),f328(x87993,x87994)),f328(f307(x87991,x87992,x87993),f328(f171(x87991),x87995))))
% 81.29/80.92 [8873]~P106(x88732)+E(f148(x88731,x88732,x88733,x88734,x88735),x88735)+~P24(f328(f328(f330(x88732),f328(x88733,x88734)),f328(f307(x88731,x88732,x88733),f328(f171(x88731),x88735))))
% 81.29/80.92 [8888]~P21(x88882,x88881,x88883,x88885)+P24(f328(f328(f245(f885(x88881,a871)),f328(f307(x88882,x88881,x88883),x88884)),f328(f307(x88882,x88881,x88883),x88885)))+~P24(f328(f328(f245(f885(x88882,a871)),x88884),x88885))
% 81.29/80.92 [9058]~P21(x90581,x90582,x90583,f252(f885(x90581,a871)))+~P24(f328(f328(f244(f885(x90582,a871)),x90584),f328(f307(x90581,x90582,x90583),x90585)))+P24(f328(f328(f244(f885(x90581,a871)),f328(f308(x90581,x90582,x90583),x90584)),x90585))
% 81.29/80.92 [9078]~E(f328(f307(x90783,x90781,x90784),f252(f885(x90783,a871))),f252(f885(x90781,a871)))+P24(f328(f328(f244(f885(x90781,a871)),x90782),f328(f307(x90783,x90781,x90784),x90785)))+~P24(f328(f328(f244(f885(x90783,a871)),f328(f308(x90783,x90781,x90784),x90782)),x90785))
% 81.29/80.92 [9102]~E(f328(f236(x91022),x91024),f328(f328(f177(x91021,x91022),x91025),x91023))+~P24(f328(f136(x91021),f328(f328(f153(f884(x91021,x91022),x91021),f256(x91021,x91022)),x91025)))+P24(f328(f328(f330(f884(x91021,x91022)),f328(f328(f257(x91021,x91022),x91023),x91024)),f328(f171(f884(x91021,x91022)),x91025)))
% 81.29/80.92 [9184]~P21(x91841,x91844,x91845,f252(f885(x91841,a871)))+~P24(f328(f328(f244(f885(x91844,a871)),f328(f307(x91841,x91844,x91845),x91842)),f328(f307(x91841,x91844,x91845),x91843)))+P24(f328(f328(f244(f885(x91841,a871)),x91842),x91843))
% 81.29/80.92 [9250]E(f328(f236(x92501),x92502),f328(f328(f177(x92503,x92501),x92504),x92505))+~P24(f328(f136(x92503),f328(f328(f153(f884(x92503,x92501),x92503),f256(x92503,x92501)),x92504)))+~P24(f328(f328(f330(f884(x92503,x92501)),f328(f328(f257(x92503,x92501),x92505),x92502)),f328(f171(f884(x92503,x92501)),x92504)))
% 81.29/80.92 [9252]E(f328(f328(f177(x92521,x92522),x92523),x92524),f328(f236(x92522),x92525))+~P24(f328(f136(x92521),f328(f328(f153(f884(x92521,x92522),x92521),f256(x92521,x92522)),x92523)))+~P24(f328(f328(f330(f884(x92521,x92522)),f328(f328(f257(x92521,x92522),x92524),x92525)),f328(f171(f884(x92521,x92522)),x92523)))
% 81.29/80.92 [9307]~P82(x93071)+~E(f328(x93073,f654(x93073,x93074,x93075,x93072,x93071)),f2(x93071))+E(f328(f165(x93071),f328(f328(f153(x93072,x93071),x93073),f328(f135(x93072,x93074),x93075))),f328(f165(x93071),f328(f328(f153(x93072,x93071),x93073),x93075)))
% 81.29/80.92 [9483]~P12(x94831,x94832,x94833)+~P24(f328(f62(x94831),x94835))+P24(f328(f67(x94831,x94832,x94833,x94834,x94835),f328(f328(f65(x94831,x94832,x94833),x94834),x94835)))
% 81.29/80.92 [9562]P24(f328(x95621,f800(x95622,x95621,x95623,x95624,x95625)))+~P24(f328(f328(f244(f885(x95625,a871)),x95624),x95623))+P24(f328(f328(f244(f885(x95625,a871)),f328(f328(f107(f885(x95625,a871)),x95624),f328(f249(x95625),x95621))),f328(f328(f107(f885(x95625,a871)),x95623),f328(f249(x95625),x95622))))
% 81.29/80.92 [9576]~P82(x95761)+~P24(f328(x95764,f654(x95763,x95764,x95765,x95762,x95761)))+E(f328(f165(x95761),f328(f328(f153(x95762,x95761),x95763),f328(f135(x95762,x95764),x95765))),f328(f165(x95761),f328(f328(f153(x95762,x95761),x95763),x95765)))
% 81.29/80.92 [9653]~P27(x96535)+P24(f328(f328(f330(x96531),f507(x96532,x96533,x96531,x96534,x96535)),x96533))+P24(f328(f328(f244(x96535),x96534),f328(f328(f42(x96531,x96535),x96533),x96532)))
% 81.29/80.92 [9656]~P82(x96561)+E(f328(f165(x96561),f328(f328(f153(x96562,x96561),x96563),f328(f135(x96562,x96564),x96565))),f328(f165(x96561),f328(f328(f153(x96562,x96561),x96563),x96565)))+P24(f328(f328(f330(x96562),f654(x96563,x96564,x96565,x96562,x96561)),f328(f171(x96562),x96565)))
% 81.29/80.92 [9666]~P24(f328(x96665,f800(x96665,x96663,x96664,x96662,x96661)))+~P24(f328(f328(f244(f885(x96661,a871)),x96662),x96664))+P24(f328(f328(f244(f885(x96661,a871)),f328(f328(f107(f885(x96661,a871)),x96662),f328(f249(x96661),x96663))),f328(f328(f107(f885(x96661,a871)),x96664),f328(f249(x96661),x96665))))
% 81.29/80.92 [9700]P35(x97001,x97002,x97003,x97004,x97005)+~E(f328(f194(f878(x97002)),x97005),f328(f194(f878(x97001)),x97004))+P24(f328(f328(f245(a877),f677(x97005,x97004,x97003,x97002,x97001)),f328(f194(f878(x97001)),x97004)))
% 81.29/80.92 [9701]P35(x97011,x97012,x97013,x97014,x97015)+~E(f328(f194(f878(x97012)),x97015),f328(f194(f878(x97011)),x97014))+P24(f328(f328(f245(a877),f728(x97013,x97015,x97012,x97014,x97011)),f328(f194(f878(x97011)),x97014)))
% 81.29/80.92 [9734]P24(f328(f328(f330(x97341),f800(x97342,x97343,x97344,x97345,x97341)),x97345))+~P24(f328(f328(f244(f885(x97341,a871)),x97345),x97344))+P24(f328(f328(f244(f885(x97341,a871)),f328(f328(f107(f885(x97341,a871)),x97345),f328(f249(x97341),x97343))),f328(f328(f107(f885(x97341,a871)),x97344),f328(f249(x97341),x97342))))
% 81.29/80.92 [9788]~P27(x97881)+~P24(f328(f328(f244(x97881),x97882),f328(x97885,f507(x97885,x97884,x97883,x97882,x97881))))+P24(f328(f328(f244(x97881),x97882),f328(f328(f42(x97883,x97881),x97884),x97885)))
% 81.29/80.92 [9819]~P75(x98191)+~P24(f328(f62(x98192),x98195))+E(f328(f328(f328(f66(x98191,x98192,f82(x98191)),f328(f328(f18(x98192,x98191,x98191),f328(f328(f8(x98191,f885(x98191,x98191),x98192),f82(x98191)),x98193)),x98194)),f79(x98191)),x98195),f328(f328(f82(x98191),f328(f328(f328(f66(x98191,x98192,f82(x98191)),x98193),f79(x98191)),x98195)),f328(f328(f328(f66(x98191,x98192,f82(x98191)),x98194),f79(x98191)),x98195)))
% 81.29/80.92 [9884]~P24(f328(f328(f330(f884(f885(x98841,a871),f885(x98841,a871))),f328(f328(f257(f885(x98841,a871),f885(x98841,a871)),x98845),x98844)),f319(x98841,x98843)))+~P24(f328(f328(f330(x98841),x98842),x98845))+P24(f328(f328(f330(f884(x98841,x98841)),f328(f328(f257(x98841,x98841),x98842),f753(x98843,x98844,x98845,x98841,x98842))),x98843))
% 81.29/80.92 [10016]~P24(f328(f328(f330(f884(f878(x100161),f878(x100161))),f328(f328(f257(f878(x100161),f878(x100161)),f328(f328(f127(x100161),x100165),x100162)),f328(f328(f127(x100161),x100165),x100163))),f146(x100161,x100164)))+P24(f328(f328(f330(f884(f878(x100161),f878(x100161))),f328(f328(f257(f878(x100161),f878(x100161)),x100162),x100163)),f146(x100161,x100164)))+P24(f328(f328(f330(f884(x100161,x100161)),f328(f328(f257(x100161,x100161),f621(x100164,x100163,x100162,x100165,x100161)),f621(x100164,x100163,x100162,x100165,x100161))),x100164))
% 81.29/80.92 [7151]~E(f328(f194(f878(x71511)),x71513),f328(f194(f878(x71512)),x71514))+E(f328(f328(f177(x71511,x71512),f328(f328(f181(x71511,x71512),x71513),x71514)),x71515),f196(x71512))+P24(f328(f328(f330(x71511),x71515),f328(f171(x71511),x71513)))
% 81.29/80.92 [7224]~E(x72243,x72245)+E(f328(f328(f164(x72241),f328(f328(f158(x72241,x72242),x72243),x72244)),x72245),x72244)+~P24(f328(f328(f245(a877),x72243),f328(f194(f878(x72241)),x72242)))
% 81.29/80.92 [7333]~E(f328(f328(f127(x73331),x73332),x73334),f328(f328(f127(x73331),x73333),x73335))+E(f328(f328(f174(x73331),f328(f194(f878(x73331)),x73332)),x73333),x73332)+P24(f328(f328(f244(a877),f328(f194(f878(x73331)),x73333)),f328(f194(f878(x73331)),x73332)))
% 81.29/80.92 [7350]~E(x73505,x73502)+P24(f328(x73501,x73502))+P24(f328(f328(f328(f328(a202,f33(x73501,x73503)),x73502),x73504),x73505))
% 81.29/80.92 [7834]~E(f328(f328(f127(x78341),x78342),x78344),f328(f328(f127(x78341),x78343),x78345))+E(f328(f328(f174(x78341),f328(f194(f878(x78341)),x78342)),x78343),x78342)+~P24(f328(f328(f244(a877),f328(f194(f878(x78341)),x78342)),f328(f194(f878(x78341)),x78343)))
% 81.29/80.92 [7858]~P24(f328(f62(x78581),f328(x78584,x78585)))+~P24(f328(f328(f330(x78582),x78585),x78583))+P24(f328(f62(x78581),f328(f328(f42(x78582,f885(x78581,a871)),x78583),x78584)))
% 81.29/80.92 [7911]~E(f328(f194(f878(x79111)),x79112),f328(f194(f878(x79113)),x79114))+~E(f328(f328(f177(x79111,x79113),f328(f328(f181(x79111,x79113),x79112),x79114)),x79115),f196(x79113))+~P24(f328(f328(f330(x79111),x79115),f328(f171(x79111),x79112)))
% 81.29/80.92 [8040]~P48(x80401,x80403,x80405)+~P48(x80401,x80402,x80404)+P48(x80401,f328(f328(f116(f885(x80401,a871)),x80402),x80403),f328(f328(f116(f885(f884(x80401,x80401),a871)),x80404),x80405))
% 81.29/80.92 [8041]~P48(x80411,x80413,x80415)+~P48(x80411,x80412,x80414)+P48(x80411,f328(f328(f107(f885(x80411,a871)),x80412),x80413),f328(f328(f107(f885(f884(x80411,x80411),a871)),x80414),x80415))
% 81.29/80.92 [8123]E(x81231,x81232)+P24(f328(x81233,x81231))+~P24(f328(f328(f328(f328(a202,f33(x81233,x81234)),x81231),x81235),x81232))
% 81.29/80.92 [8397]E(f328(f328(f257(x83971,x83972),f328(f328(f164(x83971),x83973),x83974)),f328(f328(f164(x83972),x83975),x83974)),f328(f328(f164(f884(x83971,x83972)),f328(f328(f181(x83971,x83972),x83973),x83975)),x83974))+~P24(f328(f328(f245(a877),x83974),f328(f194(f878(x83971)),x83973)))+~P24(f328(f328(f245(a877),x83974),f328(f194(f878(x83972)),x83975)))
% 81.29/80.92 [8558]~P48(x85581,x85583,x85584)+P24(f328(f328(f330(x85581),x85582),x85583))+~P24(f328(f328(f330(f884(x85581,x85581)),f328(f328(f257(x85581,x85581),x85585),x85582)),x85584))
% 81.29/80.92 [8559]~P48(x85591,x85593,x85594)+P24(f328(f328(f330(x85591),x85592),x85593))+~P24(f328(f328(f330(f884(x85591,x85591)),f328(f328(f257(x85591,x85591),x85592),x85595)),x85594))
% 81.29/80.92 [8560]~P6(x85601,x85603,x85604)+P24(f328(f328(f330(x85601),x85602),x85603))+~P24(f328(f328(f330(f884(x85601,x85601)),f328(f328(f257(x85601,x85601),x85605),x85602)),x85604))
% 81.29/80.92 [8561]~P6(x85611,x85613,x85614)+P24(f328(f328(f330(x85611),x85612),x85613))+~P24(f328(f328(f330(f884(x85611,x85611)),f328(f328(f257(x85611,x85611),x85612),x85615)),x85614))
% 81.29/80.92 [8821]~P6(x88211,x88215,x88212)+E(f328(f282(x88211,x88211,x88212),f328(f328(f306(x88211),x88213),f193(f885(x88211,a871)))),f328(f282(x88211,x88211,x88212),f328(f328(f306(x88211),x88214),f193(f885(x88211,a871)))))+~P24(f328(f328(f330(f884(x88211,x88211)),f328(f328(f257(x88211,x88211),x88213),x88214)),x88212))
% 81.29/80.92 [8903]~P24(f328(f328(f328(f328(a202,x89032),x89033),x89034),x89035))+~P24(f328(f328(f328(f328(a202,f33(x89031,x89032)),x89035),x89034),x89033))+P24(f328(f328(f328(f328(a202,f33(x89031,x89032)),x89033),x89034),x89033))
% 81.29/80.92 [9013]P24(f328(x90131,x90132))+~P24(f328(f328(f330(x90133),x90132),x90135))+P24(f328(f328(f330(x90133),f413(x90131,x90134,x90135,x90133)),f328(f328(f116(f885(x90133,a871)),x90135),x90134)))
% 81.29/80.92 [9014]P24(f328(x90141,x90142))+~P24(f328(f328(f330(x90143),x90142),x90144))+P24(f328(f328(f330(x90143),f413(x90141,x90144,x90145,x90143)),f328(f328(f116(f885(x90143,a871)),x90145),x90144)))
% 81.29/80.92 [9022]~P24(f328(x90222,x90225))+~P24(f328(f328(f330(x90221),x90225),x90224))+P24(f328(f328(f330(x90221),f479(x90222,x90223,x90224,x90221)),f328(f328(f116(f885(x90221,a871)),x90224),x90223)))
% 81.29/80.92 [9023]~P24(f328(x90232,x90235))+~P24(f328(f328(f330(x90231),x90235),x90233))+P24(f328(f328(f330(x90231),f479(x90232,x90233,x90234,x90231)),f328(f328(f116(f885(x90231,a871)),x90234),x90233)))
% 81.29/80.92 [9038]~P24(f328(f328(f244(f885(x90381,a871)),x90385),x90383))+~P24(f328(f328(f244(f885(x90381,a871)),x90382),x90384))+P24(f328(f328(f244(f885(x90381,a871)),f328(f328(f22(f885(x90381,a871)),x90382),x90383)),f328(f328(f22(f885(x90381,a871)),x90384),x90385)))
% 81.29/80.92 [9039]~P24(f328(f328(f244(f885(x90391,a871)),x90393),x90395))+~P24(f328(f328(f244(f885(x90391,a871)),x90392),x90394))+P24(f328(f328(f244(f885(x90391,a871)),f328(f328(f116(f885(x90391,a871)),x90392),x90393)),f328(f328(f116(f885(x90391,a871)),x90394),x90395)))
% 81.29/80.92 [9040]~P24(f328(f328(f244(f885(x90401,a871)),x90403),x90405))+~P24(f328(f328(f244(f885(x90401,a871)),x90402),x90404))+P24(f328(f328(f244(f885(x90401,a871)),f328(f328(f107(f885(x90401,a871)),x90402),x90403)),f328(f328(f107(f885(x90401,a871)),x90404),x90405)))
% 81.29/80.92 [9127]~E(f328(f194(f878(x91271)),x91273),f328(f194(f878(x91272)),x91274))+E(f328(f328(f177(x91271,x91272),f328(f328(f181(x91271,x91272),x91273),x91274)),x91275),f328(f236(x91272),f574(x91275,x91274,x91272,x91273,x91271)))+~P24(f328(f328(f330(x91271),x91275),f328(f171(x91271),x91273)))
% 81.29/80.92 [9131]P24(f328(f328(f330(f884(x91311,x91311)),f328(f328(f257(x91311,x91311),x91312),x91313)),f322(x91311,x91314,x91315)))+~P24(f328(f328(f244(a877),f328(x91314,x91312)),f328(x91314,x91313)))+~P24(f328(f328(f330(f884(x91311,x91311)),f328(f328(f257(x91311,x91311),x91312),x91313)),x91315))
% 81.29/80.92 [9317]P24(f328(f328(f330(f884(x93171,x93171)),f328(f328(f257(x93171,x93171),x93172),x93173)),f304(x93171,x93174)))+~P24(f328(f328(f330(f884(x93171,x93171)),f328(f328(f257(x93171,x93171),x93172),x93175)),f304(x93171,x93174)))+~P24(f328(f328(f330(f884(x93171,x93171)),f328(f328(f257(x93171,x93171),x93175),x93173)),x93174))
% 81.29/80.92 [9318]P24(f328(f328(f330(f884(x93181,x93181)),f328(f328(f257(x93181,x93181),x93182),x93183)),f304(x93181,x93184)))+~P24(f328(f328(f330(f884(x93181,x93181)),f328(f328(f257(x93181,x93181),x93185),x93183)),f304(x93181,x93184)))+~P24(f328(f328(f330(f884(x93181,x93181)),f328(f328(f257(x93181,x93181),x93182),x93185)),x93184))
% 81.29/80.92 [9414]E(x94141,x94142)+E(f328(a118,f774(x94143,x94144,x94141,x94142,x94145)),x94144)+~P24(f328(f328(f330(f884(x94145,x94145)),f328(f328(f257(x94145,x94145),x94142),x94141)),f328(f328(f188(f884(x94145,x94145),a871),x94144),x94143)))
% 81.29/80.92 [9415]E(x94151,x94152)+E(f328(a118,f776(x94153,x94154,x94151,x94152,x94155)),x94154)+~P24(f328(f328(f330(f884(x94155,x94155)),f328(f328(f257(x94155,x94155),x94152),x94151)),f328(f328(f188(f884(x94155,x94155),a871),x94154),x94153)))
% 81.29/80.92 [9416]E(x94161,f2(a877))+E(f328(a118,f774(x94162,x94161,x94163,x94164,x94165)),x94161)+~P24(f328(f328(f330(f884(x94165,x94165)),f328(f328(f257(x94165,x94165),x94164),x94163)),f328(f328(f188(f884(x94165,x94165),a871),x94161),x94162)))
% 81.29/80.92 [9417]E(x94171,f2(a877))+E(f328(a118,f776(x94172,x94171,x94173,x94174,x94175)),x94171)+~P24(f328(f328(f330(f884(x94175,x94175)),f328(f328(f257(x94175,x94175),x94174),x94173)),f328(f328(f188(f884(x94175,x94175),a871),x94171),x94172)))
% 81.29/80.92 [9433]P24(f328(f328(f330(f884(x94331,x94331)),f328(f328(f257(x94331,x94331),x94332),x94333)),f328(f328(f285(x94331,x94331,x94331),x94334),f304(x94331,x94334))))+~P24(f328(f328(f330(f884(x94331,x94331)),f328(f328(f257(x94331,x94331),x94332),x94335)),x94334))+~P24(f328(f328(f330(f884(x94331,x94331)),f328(f328(f257(x94331,x94331),x94335),x94333)),x94334))
% 81.29/80.92 [9440]~P24(f328(f328(f330(f884(x94401,x94401)),f328(f328(f257(x94401,x94401),x94402),x94405)),f304(x94401,x94404)))+P24(f328(f328(f330(f884(x94401,x94401)),f328(f328(f257(x94401,x94401),x94402),x94403)),f328(f328(f285(x94401,x94401,x94401),x94404),f304(x94401,x94404))))+~P24(f328(f328(f330(f884(x94401,x94401)),f328(f328(f257(x94401,x94401),x94405),x94403)),x94404))
% 81.29/80.92 [9479]~P6(x94791,x94795,x94792)+~P24(f328(f328(f330(f884(x94791,x94791)),f328(f328(f257(x94791,x94791),x94793),x94794)),x94792))+P24(f328(f328(f244(f885(x94791,a871)),f328(f282(x94791,x94791,x94792),f328(f328(f306(x94791),x94793),f193(f885(x94791,a871))))),f328(f282(x94791,x94791,x94792),f328(f328(f306(x94791),x94794),f193(f885(x94791,a871))))))
% 81.29/80.92 [9501]E(x95011,x95012)+P24(f328(f328(f328(f328(a202,x95013),x95011),x95014),f567(x95012,x95014,x95011,x95013,x95015)))+~P24(f328(f328(f328(f328(a202,f33(x95015,x95013)),x95011),x95014),x95012))
% 81.29/80.92 [9505]~P24(f328(x95055,x95052))+P24(f328(f328(f328(f328(a202,x95051),x95052),x95053),f567(x95054,x95053,x95052,x95051,x95055)))+~P24(f328(f328(f328(f328(a202,f33(x95055,x95051)),x95052),x95053),x95054))
% 81.29/80.92 [9534]P24(f328(f328(f330(f884(x95341,x95341)),f328(f328(f257(x95341,x95341),x95342),x95343)),f328(f328(f285(x95341,x95341,x95341),x95344),f304(x95341,x95344))))+~P24(f328(f328(f330(f884(x95341,x95341)),f328(f328(f257(x95341,x95341),x95342),x95345)),f328(f328(f285(x95341,x95341,x95341),x95344),f304(x95341,x95344))))+~P24(f328(f328(f330(f884(x95341,x95341)),f328(f328(f257(x95341,x95341),x95345),x95343)),x95344))
% 81.29/80.92 [9535]P24(f328(f328(f330(f884(x95351,x95351)),f328(f328(f257(x95351,x95351),x95352),x95353)),f328(f328(f285(x95351,x95351,x95351),x95354),f304(x95351,x95354))))+~P24(f328(f328(f330(f884(x95351,x95351)),f328(f328(f257(x95351,x95351),x95355),x95353)),f328(f328(f285(x95351,x95351,x95351),x95354),f304(x95351,x95354))))+~P24(f328(f328(f330(f884(x95351,x95351)),f328(f328(f257(x95351,x95351),x95352),x95355)),x95354))
% 81.29/80.92 [9585]~P24(f328(f67(x95851,x95851,x95854,x95852,x95853),x95855))+P24(f328(f328(f330(x95851),x95852),x95853))+P24(f328(f63(x95851,x95854,f328(f328(f306(x95851),x95852),x95853)),x95855))
% 81.29/80.92 [9624]~E(f328(f307(x96243,x96242,x96245),x96244),x96241)+E(x96241,f193(f885(x96242,a871)))+P24(f328(f328(f244(f885(x96243,a871)),f328(f307(x96242,x96243,f540(x96244,x96243,x96242,x96241)),x96241)),x96244))
% 81.29/80.92 [9669]~P27(x96695)+P24(f328(f328(f330(x96691),f518(x96692,x96693,x96694,x96691,x96695)),x96694))+P24(f328(f328(f244(x96695),f328(f328(f43(x96691,x96695),x96694),x96693)),x96692))
% 81.29/80.92 [9720]P35(x97201,x97202,x97203,x97204,x97205)+~E(f328(f194(f878(x97201)),x97204),f328(f194(f878(x97202)),x97205))+P24(f328(f328(f330(f884(x97201,x97202)),f669(x97205,x97204,x97203,x97202,x97201)),f328(f171(f884(x97201,x97202)),f328(f328(f181(x97201,x97202),x97204),x97205))))
% 81.29/80.92 [9721]P35(x97211,x97212,x97213,x97214,x97215)+~E(f328(f194(f878(x97211)),x97214),f328(f194(f878(x97212)),x97215))+P24(f328(f328(f330(f884(x97211,x97212)),f676(x97213,x97215,x97214,x97212,x97211)),f328(f171(f884(x97211,x97212)),f328(f328(f181(x97211,x97212),x97214),x97215))))
% 81.29/80.92 [9850]E(x98501,x98502)+P24(f328(f328(f328(f328(a202,f33(x98503,x98504)),f567(x98501,x98505,x98502,x98504,x98503)),x98505),x98501))+~P24(f328(f328(f328(f328(a202,f33(x98503,x98504)),x98502),x98505),x98501))
% 81.29/80.92 [9852]~P24(f328(x98521,x98525))+P24(f328(f328(f328(f328(a202,f33(x98521,x98522)),f567(x98523,x98524,x98525,x98522,x98521)),x98524),x98523))+~P24(f328(f328(f328(f328(a202,f33(x98521,x98522)),x98525),x98524),x98523))
% 81.29/80.92 [9860]E(x98601,x98602)+P24(f328(f328(f330(f884(x98603,x98603)),f328(f328(f257(x98603,x98603),x98601),f777(x98604,x98605,x98602,x98601,x98603))),x98604))+~P24(f328(f328(f330(f884(x98603,x98603)),f328(f328(f257(x98603,x98603),x98601),x98602)),f328(f328(f188(f884(x98603,x98603),a871),x98605),x98604)))
% 81.29/80.92 [9861]E(x98611,f2(a877))+P24(f328(f328(f330(f884(x98612,x98612)),f328(f328(f257(x98612,x98612),x98613),f777(x98614,x98611,x98615,x98613,x98612))),x98614))+~P24(f328(f328(f330(f884(x98612,x98612)),f328(f328(f257(x98612,x98612),x98613),x98615)),f328(f328(f188(f884(x98612,x98612),a871),x98611),x98614)))
% 81.29/80.92 [9907]~P27(x99071)+~P24(f328(f328(f244(x99071),f328(x99074,f518(x99075,x99074,x99073,x99072,x99071))),x99075))+P24(f328(f328(f244(x99071),f328(f328(f43(x99072,x99071),x99073),x99074)),x99075))
% 81.29/80.92 [9949]E(x99491,x99492)+P24(f328(f328(f330(f884(x99493,x99493)),f328(f328(f257(x99493,x99493),f775(x99494,x99495,x99491,x99492,x99493)),x99491)),x99494))+~P24(f328(f328(f330(f884(x99493,x99493)),f328(f328(f257(x99493,x99493),x99492),x99491)),f328(f328(f188(f884(x99493,x99493),a871),x99495),x99494)))
% 81.29/80.92 [9950]E(x99501,f2(a877))+P24(f328(f328(f330(f884(x99502,x99502)),f328(f328(f257(x99502,x99502),f775(x99503,x99501,x99504,x99505,x99502)),x99504)),x99503))+~P24(f328(f328(f330(f884(x99502,x99502)),f328(f328(f257(x99502,x99502),x99505),x99504)),f328(f328(f188(f884(x99502,x99502),a871),x99501),x99503)))
% 81.29/80.92 [9954]E(x99541,x99542)+P24(f328(f328(f330(f884(x99543,x99543)),f328(f328(f257(x99543,x99543),x99541),f775(x99544,x99545,x99542,x99541,x99543))),f328(f328(f188(f884(x99543,x99543),a871),f774(x99544,x99545,x99542,x99541,x99543)),x99544)))+~P24(f328(f328(f330(f884(x99543,x99543)),f328(f328(f257(x99543,x99543),x99541),x99542)),f328(f328(f188(f884(x99543,x99543),a871),x99545),x99544)))
% 81.29/80.92 [9955]E(x99551,f2(a877))+P24(f328(f328(f330(f884(x99552,x99552)),f328(f328(f257(x99552,x99552),x99553),f775(x99554,x99551,x99555,x99553,x99552))),f328(f328(f188(f884(x99552,x99552),a871),f774(x99554,x99551,x99555,x99553,x99552)),x99554)))+~P24(f328(f328(f330(f884(x99552,x99552)),f328(f328(f257(x99552,x99552),x99553),x99555)),f328(f328(f188(f884(x99552,x99552),a871),x99551),x99554)))
% 81.29/80.92 [10007]E(x100071,x100072)+P24(f328(f328(f330(f884(x100073,x100073)),f328(f328(f257(x100073,x100073),f777(x100074,x100075,x100071,x100072,x100073)),x100071)),f328(f328(f188(f884(x100073,x100073),a871),f776(x100074,x100075,x100071,x100072,x100073)),x100074)))+~P24(f328(f328(f330(f884(x100073,x100073)),f328(f328(f257(x100073,x100073),x100072),x100071)),f328(f328(f188(f884(x100073,x100073),a871),x100075),x100074)))
% 81.29/80.92 [10008]E(x100081,f2(a877))+P24(f328(f328(f330(f884(x100082,x100082)),f328(f328(f257(x100082,x100082),f777(x100083,x100081,x100084,x100085,x100082)),x100084)),f328(f328(f188(f884(x100082,x100082),a871),f776(x100083,x100081,x100084,x100085,x100082)),x100083)))+~P24(f328(f328(f330(f884(x100082,x100082)),f328(f328(f257(x100082,x100082),x100085),x100084)),f328(f328(f188(f884(x100082,x100082),a871),x100081),x100083)))
% 81.29/80.92 [10041]~P74(x100412)+~P24(f328(f62(x100411),x100415))+E(f328(f328(f6(x100411,x100412),f328(f328(f7(x100411,x100412,x100412),f328(f328(f18(x100411,x100412,f885(x100412,x100412)),f328(f328(f8(a871,f885(x100412,f885(x100412,x100412)),x100411),f102(x100412)),f328(f328(f7(x100411,f885(x100411,a871),a871),f330(x100411)),x100413))),x100414)),f2(x100412))),x100415),f328(f328(f6(x100411,x100412),x100414),f328(f328(f107(f885(x100411,a871)),x100415),x100413)))
% 81.29/80.92 [8622]~P74(x86221)+~P24(f328(f62(x86224),x86225))+E(f328(f328(f81(x86221),f328(x86222,x86223)),f328(f328(f6(x86224,x86221),x86222),f328(f328(f22(f885(x86224,a871)),x86225),f328(f328(f306(x86224),x86223),f193(f885(x86224,a871)))))),f328(f328(f6(x86224,x86221),x86222),f328(f328(f306(x86224),x86223),x86225)))
% 81.29/80.92 [8623]~P75(x86231)+~P24(f328(f62(x86234),x86235))+E(f328(f328(f82(x86231),f328(x86232,x86233)),f328(f328(f9(x86234,x86231),x86232),f328(f328(f22(f885(x86234,a871)),x86235),f328(f328(f306(x86234),x86233),f193(f885(x86234,a871)))))),f328(f328(f9(x86234,x86231),x86232),f328(f328(f306(x86234),x86233),x86235)))
% 81.29/80.92 [8942]~P106(x89422)+~P29(x89422,f328(f168(x89422),f328(f328(f153(x89421,x89422),x89424),x89425)))+E(f328(f135(x89421,f328(f328(f8(x89422,a871,x89421),f328(f245(x89422),x89423)),x89424)),x89425),f176(x89421,f328(f328(f8(x89422,a871,x89421),f328(f245(x89422),x89423)),x89424),x89425))
% 81.29/80.92 [8967]~P74(x89671)+E(f328(f328(f81(x89671),f328(f328(f6(a877,x89671),x89672),f299(a877,x89673,x89674))),f328(f328(f6(a877,x89671),x89672),f299(a877,f328(f328(f81(a877),x89674),f79(a877)),f328(f328(f81(a877),x89674),x89675)))),f328(f328(f6(a877,x89671),x89672),f299(a877,x89673,f328(f328(f81(a877),x89674),x89675))))+~P24(f328(f328(f244(a877),x89673),f328(f328(f81(a877),x89674),f79(a877))))
% 81.29/80.92 [8968]~P24(f328(f328(f330(x89681),x89684),x89685))+~P24(f328(f328(f244(f885(x89681,a871)),f328(f171(x89681),x89682)),x89685))+P24(f328(f328(f244(f885(x89681,a871)),f328(f171(x89681),f328(f328(f158(x89681,x89682),x89683),x89684))),x89685))
% 81.29/80.92 [9194]~P27(x91942)+~P24(f328(f62(x91941),x91945))+E(f328(f328(f65(x91941,x91942,f328(f328(f8(x91942,f885(x91942,x91942),x91941),f116(x91942)),x91943)),x91944),x91945),f328(f328(f116(x91942),x91944),f328(f328(f43(x91941,x91942),x91945),x91943)))
% 81.29/80.92 [9195]~P27(x91952)+~P24(f328(f62(x91951),x91955))+E(f328(f328(f65(x91951,x91952,f328(f328(f8(x91952,f885(x91952,x91952),x91951),f107(x91952)),x91953)),x91954),x91955),f328(f328(f107(x91952),x91954),f328(f328(f42(x91951,x91952),x91955),x91953)))
% 81.29/80.92 [9242]E(f328(x92421,x92422),f328(x92421,x92423))+P24(f328(f328(f245(a877),f328(x92421,x92422)),f328(x92421,x92423)))+~P24(f328(f328(f330(f884(x92424,x92424)),f328(f328(f257(x92424,x92424),x92422),x92423)),f152(x92424,f328(f328(f150(f885(x92424,a877)),x92421),x92425))))
% 81.29/80.92 [9274]~E(f328(x92744,x92742),f328(x92744,x92743))+~P24(f328(f328(f330(f884(x92741,x92741)),f328(f328(f257(x92741,x92741),x92742),x92743)),f152(x92741,x92745)))+P24(f328(f328(f330(f884(x92741,x92741)),f328(f328(f257(x92741,x92741),x92742),x92743)),f152(x92741,f328(f328(f150(f885(x92741,a877)),x92744),x92745))))
% 81.29/80.92 [9296]~P21(x92961,x92962,x92963,x92965)+P21(x92961,x92962,x92963,f328(f328(f306(x92961),x92964),x92965))+P24(f328(f328(f330(x92962),f328(x92963,x92964)),f328(f307(x92961,x92962,x92963),f328(f328(f22(f885(x92961,a871)),x92965),f328(f328(f306(x92961),x92964),f193(f885(x92961,a871)))))))
% 81.29/80.92 [9300]P24(f328(x93002,x93005))+~P24(f328(f328(f330(x93001),x93005),f328(f171(x93001),x93003)))+E(f328(f328(f137(x93001),f328(f194(f878(x93001)),f176(x93001,x93002,f328(f328(f127(x93001),x93003),x93004)))),f328(f328(f127(x93001),x93003),x93004)),f328(f328(f127(x93001),f328(f328(f137(x93001),f328(f194(f878(x93001)),f176(x93001,x93002,x93003))),x93003)),x93004))
% 81.29/80.92 [9303]~P24(f328(f328(f330(f884(x93031,x93031)),f328(f328(f257(x93031,x93031),x93032),x93033)),f152(x93031,x93035)))+~P24(f328(f328(f244(a877),f328(x93034,x93032)),f328(x93034,x93033)))+P24(f328(f328(f330(f884(x93031,x93031)),f328(f328(f257(x93031,x93031),x93032),x93033)),f152(x93031,f328(f328(f150(f885(x93031,a877)),x93034),x93035))))
% 81.29/80.92 [9368]P24(f328(f328(f330(f884(x93684,x93684)),f328(f328(f257(x93684,x93684),x93682),x93683)),f152(x93684,x93685)))+P24(f328(f328(f245(a877),f328(x93681,x93682)),f328(x93681,x93683)))+~P24(f328(f328(f330(f884(x93684,x93684)),f328(f328(f257(x93684,x93684),x93682),x93683)),f152(x93684,f328(f328(f150(f885(x93684,a877)),x93681),x93685))))
% 81.29/80.92 [9508]~P24(f328(f328(f330(f884(f878(x95081),f878(x95081))),f328(f328(f257(f878(x95081),f878(x95081)),x95082),x95084)),f157(x95081,x95085)))+~P24(f328(f328(f245(a877),x95083),f328(f194(f878(x95081)),x95082)))+P24(f328(f328(f330(f884(x95081,x95081)),f328(f328(f257(x95081,x95081),f328(f328(f164(x95081),x95082),x95083)),f328(f328(f164(x95081),x95084),x95083))),x95085))
% 81.29/80.92 [9748]E(x97481,f2(a1))+~P24(f328(f49(x97483,x97481),f328(f328(f257(a1,a1),x97484),x97485)))+P24(f328(f49(f328(f328(f82(a1),x97482),x97483),x97481),f328(f328(f257(a1,a1),f328(f328(f81(a1),f328(f328(f82(a1),x97482),x97484)),f328(f328(f39(a1),f328(f328(f82(a1),x97482),x97485)),x97481))),f45(a1,f328(f328(f82(a1),x97482),x97485),x97481))))
% 81.29/80.92 [9750]~P24(f328(f328(f245(a877),f2(a877)),x97503))+~P24(f328(f48(x97502,x97503),f328(f328(f257(a877,a877),x97504),x97505)))+P24(f328(f48(f328(f328(f82(a877),x97501),x97502),x97503),f328(f328(f257(a877,a877),f328(f328(f81(a877),f328(f328(f82(a877),x97501),x97504)),f328(f328(f39(a877),f328(f328(f82(a877),x97501),x97505)),x97503))),f45(a877,f328(f328(f82(a877),x97501),x97505),x97503))))
% 81.29/80.92 [10064]~P74(x100642)+~P24(f328(f62(x100641),x100644))+E(f328(f328(f6(x100641,x100642),x100643),f328(f249(x100641),f328(f328(f18(x100641,a871,a871),f328(f328(f8(a871,f885(a871,a871),x100641),a326),f328(f328(f7(x100641,f885(x100641,a871),a871),f330(x100641)),x100644))),f328(f328(f7(x100641,f885(x100641,a871),a871),f330(x100641)),x100645)))),f328(f328(f6(x100641,x100642),f328(f328(f7(x100641,x100642,x100642),f328(f328(f18(x100641,x100642,f885(x100642,x100642)),f328(f328(f8(a871,f885(x100642,f885(x100642,x100642)),x100641),f102(x100642)),f328(f328(f7(x100641,f885(x100641,a871),a871),f330(x100641)),x100645))),x100643)),f2(x100642))),x100644))
% 81.29/80.92 [8252]~E(f328(f328(f127(x82521),x82522),x82525),f328(f328(f127(x82521),x82523),x82524))+E(f328(f328(f127(x82521),f328(f328(f137(x82521),f328(f194(f878(x82521)),x82522)),x82523)),x82524),x82525)+P24(f328(f328(f244(a877),f328(f194(f878(x82521)),x82523)),f328(f194(f878(x82521)),x82522)))
% 81.29/80.92 [8451]~E(f328(f328(f127(x84512),x84513),x84511),f328(f328(f127(x84512),x84514),x84515))+E(x84511,f328(f328(f127(x84512),f328(f328(f137(x84512),f328(f194(f878(x84512)),x84513)),x84514)),x84515))+~P24(f328(f328(f244(a877),f328(f194(f878(x84512)),x84513)),f328(f194(f878(x84512)),x84514)))
% 81.29/80.92 [8541]~E(f328(f328(f81(a877),f328(f328(f82(a877),x85413),x85414)),x85411),f328(f328(f81(a877),f328(f328(f82(a877),x85412),x85414)),x85415))+~P24(f328(f328(f244(a877),x85413),x85412))+E(x85411,f328(f328(f81(a877),f328(f328(f82(a877),f328(f328(f22(a877),x85412),x85413)),x85414)),x85415))
% 81.29/80.92 [8542]~E(f328(f328(f81(a877),f328(f328(f82(a877),x85421),x85423)),x85424),f328(f328(f81(a877),f328(f328(f82(a877),x85422),x85423)),x85425))+~P24(f328(f328(f244(a877),x85422),x85421))+E(f328(f328(f81(a877),f328(f328(f82(a877),f328(f328(f22(a877),x85421),x85422)),x85423)),x85424),x85425)
% 81.29/80.92 [8699]E(f328(f328(f81(a877),f328(f328(f82(a877),x86991),x86992)),x86993),f328(f328(f81(a877),f328(f328(f82(a877),x86994),x86992)),x86995))+~P24(f328(f328(f244(a877),x86994),x86991))+~E(x86995,f328(f328(f81(a877),f328(f328(f82(a877),f328(f328(f22(a877),x86991),x86994)),x86992)),x86993))
% 81.29/80.92 [8700]E(f328(f328(f81(a877),f328(f328(f82(a877),x87001),x87002)),x87003),f328(f328(f81(a877),f328(f328(f82(a877),x87004),x87002)),x87005))+~P24(f328(f328(f244(a877),x87004),x87001))+~E(f328(f328(f81(a877),f328(f328(f82(a877),f328(f328(f22(a877),x87001),x87004)),x87002)),x87003),x87005)
% 81.29/80.92 [9561]~P61(x95612)+~P24(f328(f62(x95611),x95615))+E(f328(f328(f9(x95611,x95612),f328(f328(f18(x95611,x95612,x95612),f328(f328(f8(x95612,f885(x95612,x95612),x95611),f286(x95612)),x95613)),x95614)),x95615),f328(f328(f286(x95612),f328(f328(f9(x95611,x95612),x95613),x95615)),f328(f328(f9(x95611,x95612),x95614),x95615)))
% 81.29/80.92 [9684]~E(f778(x96845,x96844,x96843,x96842,x96841),f779(x96845,x96844,x96843,x96842,x96841))+P24(f328(f328(f330(f884(x96841,x96841)),f328(f328(f257(x96841,x96841),x96842),x96843)),f304(x96841,x96844)))+~P24(f328(f328(f330(f884(x96841,x96841)),f328(f328(f257(x96841,x96841),x96842),x96843)),f304(x96841,f328(f328(f116(f885(f884(x96841,x96841),a871)),x96844),x96845))))
% 81.29/80.92 [9685]~E(f784(x96855,x96854,x96853,x96852,x96851),f780(x96855,x96854,x96853,x96852,x96851))+P24(f328(f328(f330(f884(x96851,x96851)),f328(f328(f257(x96851,x96851),x96852),x96853)),f304(x96851,x96854)))+~P24(f328(f328(f330(f884(x96851,x96851)),f328(f328(f257(x96851,x96851),x96852),x96853)),f304(x96851,f328(f328(f116(f885(f884(x96851,x96851),a871)),x96854),x96855))))
% 81.29/80.92 [9895]P24(f328(f328(f330(f884(x98951,x98951)),f328(f328(f257(x98951,x98951),x98952),f780(x98955,x98954,x98953,x98952,x98951))),f304(x98951,x98954)))+P24(f328(f328(f330(f884(x98951,x98951)),f328(f328(f257(x98951,x98951),x98952),x98953)),f304(x98951,x98954)))+~P24(f328(f328(f330(f884(x98951,x98951)),f328(f328(f257(x98951,x98951),x98952),x98953)),f304(x98951,f328(f328(f116(f885(f884(x98951,x98951),a871)),x98954),x98955))))
% 81.29/80.92 [9976]P24(f328(f328(f330(f884(x99761,x99761)),f328(f328(f257(x99761,x99761),f779(x99765,x99764,x99763,x99762,x99761)),x99763)),f304(x99761,x99764)))+P24(f328(f328(f330(f884(x99761,x99761)),f328(f328(f257(x99761,x99761),x99762),x99763)),f304(x99761,x99764)))+~P24(f328(f328(f330(f884(x99761,x99761)),f328(f328(f257(x99761,x99761),x99762),x99763)),f304(x99761,f328(f328(f116(f885(f884(x99761,x99761),a871)),x99764),x99765))))
% 81.29/80.92 [10014]P24(f328(f328(f330(f884(x100141,x100141)),f328(f328(f257(x100141,x100141),x100142),x100143)),f304(x100141,x100144)))+P24(f328(f328(f330(f884(x100141,x100141)),f328(f328(f257(x100141,x100141),f778(x100145,x100144,x100143,x100142,x100141)),f779(x100145,x100144,x100143,x100142,x100141))),x100145))+~P24(f328(f328(f330(f884(x100141,x100141)),f328(f328(f257(x100141,x100141),x100142),x100143)),f304(x100141,f328(f328(f116(f885(f884(x100141,x100141),a871)),x100144),x100145))))
% 81.29/80.92 [10015]P24(f328(f328(f330(f884(x100151,x100151)),f328(f328(f257(x100151,x100151),x100152),x100153)),f304(x100151,x100154)))+P24(f328(f328(f330(f884(x100151,x100151)),f328(f328(f257(x100151,x100151),f780(x100155,x100154,x100153,x100152,x100151)),f784(x100155,x100154,x100153,x100152,x100151))),x100155))+~P24(f328(f328(f330(f884(x100151,x100151)),f328(f328(f257(x100151,x100151),x100152),x100153)),f304(x100151,f328(f328(f116(f885(f884(x100151,x100151),a871)),x100154),x100155))))
% 81.29/80.92 [10137]~P24(f328(f328(f330(f884(f878(x101371),f878(x101371))),f328(f328(f257(f878(x101371),f878(x101371)),x101374),x101375)),f157(x101371,x101372)))+~P24(f328(f328(f330(f884(x101371,x101371)),x101373),f328(f171(f884(x101371,x101371)),f328(f328(f181(x101371,x101371),x101374),x101375))))+P24(f328(f328(f267(x101371,x101371,a871),f328(f328(f7(x101371,f885(f884(x101371,x101371),a871),f885(x101371,a871)),f328(f328(f8(f885(x101371,f885(f885(f884(x101371,x101371),a871),a871)),f885(f885(f884(x101371,x101371),a871),f885(x101371,a871)),x101371),f7(x101371,f885(f884(x101371,x101371),a871),a871)),f328(f328(f8(f885(x101371,f884(x101371,x101371)),f885(x101371,f885(f885(f884(x101371,x101371),a871),a871)),x101371),f328(f8(f884(x101371,x101371),f885(f885(f884(x101371,x101371),a871),a871),x101371),f330(f884(x101371,x101371)))),f257(x101371,x101371)))),x101372)),x101373))
% 81.29/80.92 [9589]~P24(f328(f328(f244(a877),x95893),x95892))+~P24(f328(f328(f244(a877),f328(f328(f81(a877),f328(f328(f82(a877),x95893),x95894)),x95891)),f328(f328(f81(a877),f328(f328(f82(a877),x95892),x95894)),x95895)))+P24(f328(f328(f244(a877),x95891),f328(f328(f81(a877),f328(f328(f82(a877),f328(f328(f22(a877),x95892),x95893)),x95894)),x95895)))
% 81.29/80.92 [9590]~P24(f328(f328(f244(a877),x95903),x95902))+~P24(f328(f328(f245(a877),f328(f328(f81(a877),f328(f328(f82(a877),x95903),x95904)),x95901)),f328(f328(f81(a877),f328(f328(f82(a877),x95902),x95904)),x95905)))+P24(f328(f328(f245(a877),x95901),f328(f328(f81(a877),f328(f328(f82(a877),f328(f328(f22(a877),x95902),x95903)),x95904)),x95905)))
% 81.29/80.92 [9608]~P24(f328(f328(f244(a877),x96081),x96084))+P24(f328(f328(f244(a877),f328(f328(f81(a877),f328(f328(f82(a877),x96081),x96082)),x96083)),f328(f328(f81(a877),f328(f328(f82(a877),x96084),x96082)),x96085)))+~P24(f328(f328(f244(a877),x96083),f328(f328(f81(a877),f328(f328(f82(a877),f328(f328(f22(a877),x96084),x96081)),x96082)),x96085)))
% 81.29/80.92 [9609]~P24(f328(f328(f244(a877),x96091),x96094))+P24(f328(f328(f245(a877),f328(f328(f81(a877),f328(f328(f82(a877),x96091),x96092)),x96093)),f328(f328(f81(a877),f328(f328(f82(a877),x96094),x96092)),x96095)))+~P24(f328(f328(f245(a877),x96093),f328(f328(f81(a877),f328(f328(f82(a877),f328(f328(f22(a877),x96094),x96091)),x96092)),x96095)))
% 81.29/80.92 [9718]~P24(f328(f328(f244(a877),x97182),x97181))+~P24(f328(f328(f244(a877),f328(f328(f81(a877),f328(f328(f82(a877),x97181),x97183)),x97184)),f328(f328(f81(a877),f328(f328(f82(a877),x97182),x97183)),x97185)))+P24(f328(f328(f244(a877),f328(f328(f81(a877),f328(f328(f82(a877),f328(f328(f22(a877),x97181),x97182)),x97183)),x97184)),x97185))
% 81.29/80.92 [9719]~P24(f328(f328(f244(a877),x97192),x97191))+~P24(f328(f328(f245(a877),f328(f328(f81(a877),f328(f328(f82(a877),x97191),x97193)),x97194)),f328(f328(f81(a877),f328(f328(f82(a877),x97192),x97193)),x97195)))+P24(f328(f328(f245(a877),f328(f328(f81(a877),f328(f328(f82(a877),f328(f328(f22(a877),x97191),x97192)),x97193)),x97194)),x97195))
% 81.29/80.92 [9772]~P24(f328(f328(f244(a877),x97724),x97721))+P24(f328(f328(f244(a877),f328(f328(f81(a877),f328(f328(f82(a877),x97721),x97722)),x97723)),f328(f328(f81(a877),f328(f328(f82(a877),x97724),x97722)),x97725)))+~P24(f328(f328(f244(a877),f328(f328(f81(a877),f328(f328(f82(a877),f328(f328(f22(a877),x97721),x97724)),x97722)),x97723)),x97725))
% 81.29/80.92 [9773]~P24(f328(f328(f244(a877),x97734),x97731))+P24(f328(f328(f245(a877),f328(f328(f81(a877),f328(f328(f82(a877),x97731),x97732)),x97733)),f328(f328(f81(a877),f328(f328(f82(a877),x97734),x97732)),x97735)))+~P24(f328(f328(f245(a877),f328(f328(f81(a877),f328(f328(f82(a877),f328(f328(f22(a877),x97731),x97734)),x97732)),x97733)),x97735))
% 81.29/80.92 [9999]~P9(x99991,x99992,x99995,x99993)+~P24(f328(f328(f330(f884(x99991,x99991)),x99994),x99995))+P24(f328(f328(f267(x99991,x99991,a871),f328(f328(f7(x99991,f885(x99991,x99992),f885(x99991,a871)),f328(f328(f8(f885(x99992,a871),f885(f885(x99991,x99992),f885(x99991,a871)),x99991),f8(x99992,a871,x99991)),f328(f328(f8(x99992,f885(x99992,a871),x99991),a325),x99993))),x99993)),x99994))
% 81.29/80.92 [6798]~E(f328(x67984,x67985),f196(x67982))+E(f328(f184(x67981,x67982,x67983,x67984),x67985),f328(f236(x67982),x67986))+~E(f328(x67983,x67985),f328(f236(x67982),x67986))
% 81.29/80.92 [6895]~E(f328(x68953,x68956),f196(x68951))+E(f328(f238(f881(x68951),x68952,f196(x68951),x68953),f328(x68954,x68955)),f196(x68951))+~E(f328(x68954,x68955),f328(f236(x68952),x68956))
% 81.29/80.92 [7481]E(f328(x74811,x74812),f196(x74813))+~E(f328(f184(x74815,x74813,x74816,x74811),x74812),f328(f236(x74813),x74814))+E(f328(x74811,x74812),f328(f236(x74813),x74814))
% 81.29/80.92 [7514]~E(f328(f184(x75146,x75143,x75145,x75141),x75142),f328(f236(x75143),x75144))+E(f328(x75141,x75142),f328(f236(x75143),x75144))+E(f328(x75145,x75142),f328(f236(x75143),x75144))
% 81.29/80.92 [8410]~P15(x84106,x84101,x84102,x84104)+E(f328(f74(x84101,x84101,x84101,f328(x84102,x84103)),f328(x84104,x84105)),f328(f74(x84101,x84101,x84101,f328(x84104,x84105)),f328(x84102,x84103)))+~P24(f328(f62(x84106),x84105))
% 81.29/80.92 [8833]~P21(x88331,x88333,x88335,x88336)+~P21(x88333,x88332,x88334,f328(f307(x88331,x88333,x88335),x88336))+P21(x88331,x88332,f328(f74(x88333,x88332,x88331,x88334),x88335),x88336)
% 81.29/80.92 [9399]~P24(f328(f328(x93993,x93992),x93996))+~P24(f328(f328(x93994,x93995),x93992))+P24(f328(f328(f330(x93991),x93992),f296(x93991,x93993,x93994,x93995,x93996)))
% 81.29/80.92 [9400]~P24(f328(f328(x94004,x94002),x94006))+~P24(f328(f328(x94003,x94005),x94002))+P24(f328(f328(f330(x94001),x94002),f293(x94001,x94003,x94004,x94005,x94006)))
% 81.29/80.92 [9509]E(x95091,x95092)+E(x95093,x95094)+~P24(f328(f328(f330(f884(f878(x95095),f878(x95095))),f328(f328(f257(f878(x95095),f878(x95095)),f328(f328(f150(x95095),x95093),x95091)),f328(f328(f150(x95095),x95094),x95092))),f156(x95095,x95096)))
% 81.29/80.92 [9518]~E(x95182,x95184)+P24(f328(f328(f330(f884(f878(x95181),f878(x95181))),f328(f328(f257(f878(x95181),f878(x95181)),f328(f328(f150(x95181),x95182),x95183)),f328(f328(f150(x95181),x95184),x95185))),f144(x95181,x95186)))+~P24(f328(f328(f330(f884(f878(x95181),f878(x95181))),f328(f328(f257(f878(x95181),f878(x95181)),x95183),x95185)),f144(x95181,x95186)))
% 81.29/80.92 [9519]~E(x95192,x95194)+P24(f328(f328(f330(f884(f878(x95191),f878(x95191))),f328(f328(f257(f878(x95191),f878(x95191)),f328(f328(f150(x95191),x95192),x95193)),f328(f328(f150(x95191),x95194),x95195))),f146(x95191,x95196)))+~P24(f328(f328(f330(f884(f878(x95191),f878(x95191))),f328(f328(f257(f878(x95191),f878(x95191)),x95193),x95195)),f146(x95191,x95196)))
% 81.29/80.92 [9520]~E(x95202,x95204)+P24(f328(f328(f330(f884(f878(x95201),f878(x95201))),f328(f328(f257(f878(x95201),f878(x95201)),f328(f328(f150(x95201),x95202),x95203)),f328(f328(f150(x95201),x95204),x95205))),f156(x95201,x95206)))+~P24(f328(f328(f330(f884(f878(x95201),f878(x95201))),f328(f328(f257(f878(x95201),f878(x95201)),x95203),x95205)),f156(x95201,x95206)))
% 81.29/80.92 [9521]~E(x95212,x95214)+P24(f328(f328(f330(f884(f878(x95211),f878(x95211))),f328(f328(f257(f878(x95211),f878(x95211)),f328(f328(f127(x95211),x95212),x95213)),f328(f328(f127(x95211),x95214),x95215))),f156(x95211,x95216)))+~P24(f328(f328(f330(f884(f878(x95211),f878(x95211))),f328(f328(f257(f878(x95211),f878(x95211)),x95213),x95215)),f156(x95211,x95216)))
% 81.29/80.92 [9522]~E(x95223,x95225)+P24(f328(f328(f330(f884(f878(x95221),f878(x95221))),f328(f328(f257(f878(x95221),f878(x95221)),f328(f328(f127(x95221),x95222),x95223)),f328(f328(f127(x95221),x95224),x95225))),f156(x95221,x95226)))+~P24(f328(f328(f330(f884(f878(x95221),f878(x95221))),f328(f328(f257(f878(x95221),f878(x95221)),x95222),x95224)),f156(x95221,x95226)))
% 81.29/80.92 [9577]E(x95771,x95772)+P24(f328(f328(f330(f884(f878(x95773),f878(x95773))),f328(f328(f257(f878(x95773),f878(x95773)),x95771),x95772)),f156(x95773,x95774)))+~P24(f328(f328(f330(f884(f878(x95773),f878(x95773))),f328(f328(f257(f878(x95773),f878(x95773)),f328(f328(f150(x95773),x95775),x95771)),f328(f328(f150(x95773),x95776),x95772))),f156(x95773,x95774)))
% 81.29/80.92 [9722]~E(x97223,x97225)+P24(f328(f328(f330(f884(f878(x97221),f878(x97221))),f328(f328(f257(f878(x97221),f878(x97221)),f328(f328(f127(x97221),x97222),f328(f328(f150(x97221),x97223),f119(x97221)))),f328(f328(f127(x97221),x97224),f328(f328(f150(x97221),x97225),f119(x97221))))),f156(x97221,x97226)))+~P24(f328(f328(f330(f884(f878(x97221),f878(x97221))),f328(f328(f257(f878(x97221),f878(x97221)),x97222),x97224)),f156(x97221,x97226)))
% 81.29/80.92 [9738]E(f328(x97381,x97382),f196(x97383))+~E(f328(f238(f881(x97386),x97383,f196(x97386),x97384),f328(x97381,x97382)),f196(x97386))+E(f328(x97384,f361(x97382,x97381,x97384,x97385,x97386,x97383)),f196(x97386))
% 81.29/80.92 [9739]E(f328(x97391,x97392),f196(x97393))+~E(f328(f238(f881(x97396),x97393,f196(x97396),x97394),f328(x97391,x97392)),f196(x97396))+E(f328(f236(x97393),f361(x97392,x97391,x97394,x97395,x97396,x97393)),f328(x97391,x97392))
% 81.29/80.92 [9776]E(x97761,x97762)+E(x97763,x97764)+~P24(f328(f328(f330(f884(f878(x97765),f878(x97765))),f328(f328(f257(f878(x97765),f878(x97765)),f328(f328(f127(x97765),x97763),f328(f328(f150(x97765),x97761),f119(x97765)))),f328(f328(f127(x97765),x97764),f328(f328(f150(x97765),x97762),f119(x97765))))),f156(x97765,x97766)))
% 81.29/80.92 [9800]E(x98001,x98002)+~P24(f328(f328(f330(f884(f878(x98003),f878(x98003))),f328(f328(f257(f878(x98003),f878(x98003)),f328(f328(f127(x98003),x98001),f328(f328(f150(x98003),x98005),f119(x98003)))),f328(f328(f127(x98003),x98002),f328(f328(f150(x98003),x98006),f119(x98003))))),f156(x98003,x98004)))+P24(f328(f328(f330(f884(f878(x98003),f878(x98003))),f328(f328(f257(f878(x98003),f878(x98003)),x98001),x98002)),f156(x98003,x98004)))
% 81.29/80.92 [9836]~P24(f328(f328(f330(f884(f885(x98361,a871),f885(x98361,a871))),f328(f328(f257(f885(x98361,a871),f885(x98361,a871)),x98362),x98364)),f319(x98361,x98366)))+~P24(f328(f328(f330(f884(f885(x98361,a871),f885(x98361,a871))),f328(f328(f257(f885(x98361,a871),f885(x98361,a871)),x98363),x98365)),f319(x98361,x98366)))+P24(f328(f328(f330(f884(f885(x98361,a871),f885(x98361,a871))),f328(f328(f257(f885(x98361,a871),f885(x98361,a871)),f328(f328(f116(f885(x98361,a871)),x98362),x98363)),f328(f328(f116(f885(x98361,a871)),x98364),x98365))),f319(x98361,x98366)))
% 81.29/80.92 [5240]~E(f328(x52403,x52406),x52405)+~E(x52404,f328(f236(x52401),x52406))+E(f328(f328(f207(x52401,x52402),x52403),x52404),f328(f236(x52402),x52405))
% 81.29/80.92 [5655]~E(f328(f328(f127(x56551),x56556),x56553),x56555)+E(f328(f328(f127(x56551),x56552),x56553),f328(f328(f150(x56551),x56554),x56555))+~E(x56552,f328(f328(f150(x56551),x56554),x56556))
% 81.29/80.92 [5656]~E(f328(f328(f127(x56561),x56566),x56563),x56565)+E(f328(f328(f127(x56561),x56562),x56563),f328(f328(f127(x56561),x56564),x56565))+~E(x56562,f328(f328(f127(x56561),x56564),x56566))
% 81.29/80.92 [5658]E(f328(f328(f127(x56581),x56582),x56583),f328(f328(f150(x56581),x56584),x56585))+~E(f328(f328(f150(x56581),x56584),x56586),x56582)+~E(x56585,f328(f328(f127(x56581),x56586),x56583))
% 81.29/80.92 [5660]~E(f328(f328(f127(x56601),x56602),x56606),x56604)+E(f328(f328(f127(x56601),x56602),x56603),f328(f328(f127(x56601),x56604),x56605))+~E(x56603,f328(f328(f127(x56601),x56606),x56605))
% 81.29/80.92 [6792]E(f328(x67921,x67922),f328(x67923,x67922))+~E(f328(f328(f153(x67924,x67925),x67921),x67926),f328(f328(f153(x67924,x67925),x67923),x67926))+~P24(f328(f328(f330(x67924),x67922),f328(f171(x67924),x67926)))
% 81.29/80.92 [7174]~P15(x71744,x71745,x71746,x71741)+E(f328(f328(x71741,x71742),x71743),f328(f328(f65(x71744,x71745,x71746),x71743),x71742))+~P24(f328(f62(x71744),x71742))
% 81.29/80.92 [7240]~E(x72402,f328(x72404,x72406))+~P24(f328(f328(f330(x72403),x72406),x72405))+P24(f328(f328(f330(x72401),x72402),f328(f307(x72403,x72401,x72404),x72405)))
% 81.29/80.92 [7241]~E(f328(x72414,x72412),x72416)+~P24(f328(f328(f330(x72413),x72416),x72415))+P24(f328(f328(f330(x72411),x72412),f328(f308(x72411,x72413,x72414),x72415)))
% 81.29/80.92 [7692]~P33(x76921,x76922,x76924,x76926)+P33(x76921,x76922,f328(f328(f150(x76921),x76923),x76924),f328(f328(f150(x76921),x76925),x76926))+~P24(f328(f328(x76922,x76923),x76925))
% 81.29/80.92 [8707]~P54(x87074,x87075,x87071,x87072,x87076)+E(f328(x87071,f328(x87072,x87073)),x87073)+~P24(f328(f328(f330(x87075),x87073),x87076))
% 81.29/80.92 [9511]E(x95111,x95112)+E(f328(f194(f878(x95113)),x95114),f328(f194(f878(x95113)),x95115))+~P24(f328(f328(f330(f884(f878(x95113),f878(x95113))),f328(f328(f257(f878(x95113),f878(x95113)),f328(f328(f150(x95113),x95111),x95114)),f328(f328(f150(x95113),x95112),x95115))),f144(x95113,x95116)))
% 81.29/80.92 [9573]~P12(x95731,x95732,x95733)+E(f328(f328(f65(x95731,x95732,x95733),x95734),x95735),x95736)+~P24(f328(f67(x95731,x95732,x95733,x95734,x95735),x95736))
% 81.29/80.92 [9580]E(f328(f194(f878(x95801)),x95802),f328(f194(f878(x95801)),x95803))+P24(f328(f328(f330(f884(f878(x95801),f878(x95801))),f328(f328(f257(f878(x95801),f878(x95801)),x95802),x95803)),f144(x95801,x95804)))+~P24(f328(f328(f330(f884(f878(x95801),f878(x95801))),f328(f328(f257(f878(x95801),f878(x95801)),f328(f328(f150(x95801),x95805),x95802)),f328(f328(f150(x95801),x95806),x95803))),f144(x95801,x95804)))
% 81.29/80.92 [9602]~P24(f328(f328(f330(f884(x96021,x96021)),f328(f328(f257(x96021,x96021),x96022),x96024)),f304(x96021,x96026)))+P24(f328(f328(f330(f884(f878(x96021),f878(x96021))),f328(f328(f257(f878(x96021),f878(x96021)),f328(f328(f150(x96021),x96022),x96023)),f328(f328(f150(x96021),x96024),x96025))),f304(f878(x96021),f156(x96021,x96026))))+~P24(f328(f328(f330(f884(f878(x96021),f878(x96021))),f328(f328(f257(f878(x96021),f878(x96021)),x96023),x96025)),f304(f878(x96021),f156(x96021,x96026))))
% 81.29/80.92 [9782]~P24(f328(x97822,x97826))+~E(f328(f135(x97821,x97822),x97823),f328(f328(f150(x97821),x97824),x97825))+~P24(f328(f328(f330(x97821),x97826),f328(f171(x97821),f743(x97825,x97824,x97823,x97822,x97821))))
% 81.29/80.92 [9783]~P24(f328(x97834,x97836))+~E(f328(f328(f150(x97831),x97832),x97833),f328(f135(x97831,x97834),x97835))+~P24(f328(f328(f330(x97831),x97836),f328(f171(x97831),f745(x97835,x97834,x97833,x97832,x97831))))
% 81.29/80.92 [10092]~P74(x100922)+E(f328(f328(f6(x100921,x100922),f328(f328(f8(f885(x100923,a871),x100922,x100921),f328(f6(x100923,x100922),x100924)),f328(f328(f8(f885(x100923,a871),f885(x100923,a871),x100921),f249(x100923)),f328(f328(f8(f885(x100923,a871),f885(x100923,a871),x100921),f328(f18(x100923,a871,a871),f328(f328(f8(a871,f885(a871,a871),x100923),a326),f328(f328(f7(x100923,f885(x100923,a871),a871),f330(x100923)),x100925)))),f328(f7(x100923,x100921,a871),f328(f328(f8(x100921,f885(x100921,a871),x100923),a325),x100926)))))),f328(f307(x100923,x100921,x100926),x100925)),f328(f328(f6(x100923,x100922),x100924),x100925))+~P24(f328(f62(x100923),x100925))
% 81.29/80.92 [6849]~P106(x68493)+P24(f328(x68492,x68495))+E(f328(f135(x68491,x68492),f328(f328(f147(x68491,x68493,x68494),x68495),x68496)),f328(f135(x68491,x68492),x68496))
% 81.29/80.92 [6851]P24(f328(x68511,x68512))+~E(f166(x68513,x68511,x68514),f328(f328(f257(f878(x68513),f878(x68513)),x68515),x68516))+~P24(f328(f328(f330(x68513),x68512),f328(f171(x68513),x68515)))
% 81.29/80.92 [6892]~P24(f328(x68922,x68926))+~E(f166(x68921,x68922,x68923),f328(f328(f257(f878(x68921),f878(x68921)),x68924),x68925))+~P24(f328(f328(f330(x68921),x68926),f328(f171(x68921),x68925)))
% 81.29/80.92 [7558]~P11(x75581,x75582,x75583)+~P24(f328(f62(x75581),x75586))+E(f328(f328(f65(x75581,x75582,x75583),x75584),f328(f328(f306(x75581),x75585),x75586)),f328(f328(f65(x75581,x75582,x75583),f328(f328(x75583,x75585),x75584)),x75586))
% 81.29/80.92 [7608]~P106(x76082)+~P24(f328(f328(f244(x76082),f328(x76083,x76084)),f328(x76083,x76085)))+E(f328(f328(f147(x76081,x76082,x76083),x76084),f328(f328(f150(x76081),x76085),x76086)),f328(f328(f150(x76081),x76084),f328(f328(f150(x76081),x76085),x76086)))
% 81.29/80.92 [7723]E(x77231,x77232)+~E(f328(f328(f265(x77233,x77234),x77231),f328(f16(f885(x77234,a871),x77233),x77235)),f328(f328(f265(x77233,x77234),x77232),f328(f16(f885(x77234,a871),x77233),x77235)))+~P24(f328(f328(f330(x77234),x77236),x77235))
% 81.29/80.92 [7787]~P11(x77871,x77872,x77873)+~P24(f328(f62(x77871),x77876))+E(f328(f328(f65(x77871,x77872,x77873),x77874),f328(f328(f306(x77871),x77875),x77876)),f328(f328(x77873,x77875),f328(f328(f65(x77871,x77872,x77873),x77874),x77876)))
% 81.29/80.92 [7903]~P12(x79031,x79032,x79033)+~P24(f328(f62(x79031),x79036))+E(f328(f328(f65(x79031,x79032,x79033),f328(f328(x79033,x79034),x79035)),x79036),f328(f328(x79033,x79034),f328(f328(f65(x79031,x79032,x79033),x79035),x79036)))
% 81.29/80.92 [7972]~P16(x79722,x79725,x79726,x79721)+~P24(f328(f62(x79722),x79724))+E(f328(x79721,f328(f328(f306(x79722),x79723),x79724)),f328(f74(x79725,x79725,x79725,f328(x79721,x79724)),f328(x79726,x79723)))
% 81.29/80.92 [8010]~P106(x80102)+P24(f328(f328(f244(x80102),f328(x80103,x80104)),f328(x80103,x80105)))+E(f328(f328(f147(x80101,x80102,x80103),x80104),f328(f328(f150(x80101),x80105),x80106)),f328(f328(f150(x80101),x80105),f328(f328(f147(x80101,x80102,x80103),x80104),x80106)))
% 81.29/80.92 [8153]~E(f328(f194(f878(x81531)),x81535),f328(f194(f878(x81532)),x81536))+~E(f328(f194(f878(x81531)),x81533),f328(f194(f878(x81532)),x81534))+E(f328(f328(f127(f884(x81531,x81532)),f328(f328(f181(x81531,x81532),x81533),x81534)),f328(f328(f181(x81531,x81532),x81535),x81536)),f328(f328(f181(x81531,x81532),f328(f328(f127(x81531),x81533),x81535)),f328(f328(f127(x81532),x81534),x81536)))
% 81.29/80.92 [8267]~E(x82672,f328(f307(x82673,x82671,x82674),x82676))+P24(f328(f328(f244(f885(x82671,a871)),x82672),f328(f307(x82673,x82671,x82674),x82675)))+~P24(f328(f328(f244(f885(x82673,a871)),x82676),x82675))
% 81.29/80.92 [8368]~P106(x83685)+E(f328(x83681,x83682),f328(x83681,x83683))+E(f328(f328(f147(x83684,x83685,x83681),x83682),f328(f328(f147(x83684,x83685,x83681),x83683),x83686)),f328(f328(f147(x83684,x83685,x83681),x83683),f328(f328(f147(x83684,x83685,x83681),x83682),x83686)))
% 81.29/80.92 [8403]~P21(x84033,x84031,x84034,x84035)+P21(x84033,x84031,f328(f328(f328(f73(x84033,x84031),x84034),x84036),x84032),x84035)+P24(f328(f328(f330(x84031),x84032),f328(f307(x84033,x84031,x84034),x84035)))
% 81.29/80.92 [8550]~P24(f328(f328(f330(x85502),x85504),f328(x85506,x85503)))+~P24(f328(f328(f330(x85501),x85503),x85505))+P24(f328(f328(f330(f884(x85501,x85502)),f328(f328(f257(x85501,x85502),x85503),x85504)),f328(f328(f265(x85501,x85502),x85505),x85506)))
% 81.29/80.92 [9011]~P74(x90112)+~P21(x90114,x90111,x90115,x90116)+E(f328(f328(f6(x90111,x90112),x90113),f328(f307(x90114,x90111,x90115),x90116)),f328(f328(f6(x90114,x90112),f328(f74(x90111,x90112,x90114,x90113),x90115)),x90116))
% 81.29/80.92 [9012]~P75(x90122)+~P21(x90124,x90121,x90125,x90126)+E(f328(f328(f9(x90121,x90122),x90123),f328(f307(x90124,x90121,x90125),x90126)),f328(f328(f9(x90124,x90122),f328(f74(x90121,x90122,x90124,x90123),x90125)),x90126))
% 81.29/80.92 [9060]~P35(x90602,x90605,x90601,x90603,x90606)+P24(f328(f328(x90601,f328(f328(f164(x90602),x90603),x90604)),f328(f328(f164(x90605),x90606),x90604)))+~P24(f328(f328(f245(a877),x90604),f328(f194(f878(x90605)),x90606)))
% 81.29/80.92 [9061]~P35(x90612,x90615,x90611,x90613,x90616)+P24(f328(f328(x90611,f328(f328(f164(x90612),x90613),x90614)),f328(f328(f164(x90615),x90616),x90614)))+~P24(f328(f328(f245(a877),x90614),f328(f194(f878(x90612)),x90613)))
% 81.29/80.92 [9270]~P15(x92703,x92701,x92706,x92702)+~P24(f328(f62(x92703),x92704))+E(f328(f74(x92701,x92701,x92701,f328(x92702,f328(f328(f22(f885(x92703,a871)),x92704),f328(f328(f306(x92703),x92705),f193(f885(x92703,a871)))))),f328(x92706,x92705)),f328(x92702,f328(f328(f306(x92703),x92705),x92704)))
% 81.29/80.92 [9875]~E(f328(f307(x98752,x98754,x98756),f252(f885(x98752,a871))),f252(f885(x98754,a871)))+~E(f328(f307(x98751,x98753,x98755),f252(f885(x98751,a871))),f252(f885(x98753,a871)))+E(f328(f307(f884(x98751,x98752),f884(x98753,x98754),f268(x98751,x98753,x98752,x98754,x98755,x98756)),f252(f885(f884(x98751,x98752),a871))),f252(f885(f884(x98753,x98754),a871)))
% 81.29/80.92 [9925]~P21(x99253,x99254,x99255,f328(x99256,f716(x99256,x99255,x99254,x99253,x99252,x99251)))+P21(x99253,x99254,x99255,f328(f328(f42(x99252,f885(x99253,a871)),x99251),x99256))+E(x99251,f193(f885(x99252,a871)))
% 81.29/80.92 [9984]P21(x99846,x99845,x99844,f328(f328(f42(x99842,f885(x99846,a871)),x99841),x99843))+E(x99841,f193(f885(x99842,a871)))+P24(f328(f328(f330(x99842),f716(x99843,x99844,x99845,x99846,x99842,x99841)),x99841))
% 81.29/80.92 [9990]P24(f328(f328(f330(x99901),f749(x99902,x99903,x99904,x99905,x99906,x99901)),x99906))+P24(f328(f328(f244(f885(f884(x99901,x99904),a871)),f328(f328(f265(x99901,x99904),x99906),x99903)),f328(f328(f265(x99901,x99904),x99905),x99902)))+~P24(f328(f328(f244(f885(x99901,a871)),x99906),x99905))
% 81.29/80.92 [10028]P20(x100286,x100285,f328(f328(f306(f876(x100286)),f328(f328(f328(f93(x100286),x100281),x100283),x100282)),f193(f885(f876(x100286),a871))))+~P20(x100286,x100285,f328(f328(f306(f876(x100286)),f328(f328(f328(f93(x100286),x100284),x100283),x100282)),f193(f885(f876(x100286),a871))))+P24(f328(f328(x100281,f668(x100281,x100282,x100283,x100284,x100285,x100286)),f785(x100281,x100282,x100283,x100284,x100285,x100286)))
% 81.29/80.92 [10029]P20(x100296,x100295,f328(f328(f306(f876(x100296)),f328(f328(f328(f93(x100296),x100294),x100293),x100292)),f193(f885(f876(x100296),a871))))+~P20(x100296,x100295,f328(f328(f306(f876(x100296)),f328(f328(f328(f93(x100296),x100294),x100293),x100291)),f193(f885(f876(x100296),a871))))+P24(f328(f328(x100291,f830(x100292,x100291,x100293,x100294,x100295,x100296)),f840(x100292,x100291,x100293,x100294,x100295,x100296)))
% 81.29/80.92 [10067]~P20(x100671,x100672,f328(f328(f306(f876(x100671)),f328(f328(f328(f93(x100671),x100673),x100674),x100676)),f193(f885(f876(x100671),a871))))+P20(x100671,x100672,f328(f328(f306(f876(x100671)),f328(f328(f328(f93(x100671),x100673),x100674),x100675)),f193(f885(f876(x100671),a871))))+~P24(f328(f328(x100675,f830(x100675,x100676,x100674,x100673,x100672,x100671)),f840(x100675,x100676,x100674,x100673,x100672,x100671)))
% 81.29/80.92 [10068]~P20(x100681,x100682,f328(f328(f306(f876(x100681)),f328(f328(f328(f93(x100681),x100686),x100684),x100685)),f193(f885(f876(x100681),a871))))+P20(x100681,x100682,f328(f328(f306(f876(x100681)),f328(f328(f328(f93(x100681),x100683),x100684),x100685)),f193(f885(f876(x100681),a871))))+~P24(f328(f328(x100686,f668(x100683,x100685,x100684,x100686,x100682,x100681)),f785(x100683,x100685,x100684,x100686,x100682,x100681)))
% 81.29/80.92 [10104]~P24(f328(f328(f244(f885(x101042,a871)),f328(x101044,f749(x101046,x101044,x101042,x101045,x101043,x101041))),f328(x101046,f749(x101046,x101044,x101042,x101045,x101043,x101041))))+~P24(f328(f328(f244(f885(x101041,a871)),x101043),x101045))+P24(f328(f328(f244(f885(f884(x101041,x101042),a871)),f328(f328(f265(x101041,x101042),x101043),x101044)),f328(f328(f265(x101041,x101042),x101045),x101046)))
% 81.29/80.92 [7742]~P24(f328(x77421,x77425))+~P24(f328(x77426,x77424))+P24(f328(x77421,f328(f266(x77422,x77423),f328(f328(f257(x77422,x77423),x77424),x77425))))
% 81.29/80.92 [7743]~P24(f328(x77431,x77434))+~P24(f328(x77436,x77435))+P24(f328(x77431,f328(f256(x77432,x77433),f328(f328(f257(x77432,x77433),x77434),x77435))))
% 81.29/80.92 [7765]~E(f328(f194(f878(x77651)),x77653),f328(f194(f878(x77654)),x77655))+~E(f328(f328(f177(x77651,x77654),f328(f328(f181(x77651,x77654),x77653),x77655)),x77652),f328(f236(x77654),x77656))+P24(f328(f328(f330(x77651),x77652),f328(f171(x77651),x77653)))
% 81.29/80.92 [7792]~P24(f328(f328(x77924,x77926),x77925))+~P24(f328(f328(f330(x77921),x77926),x77923))+P24(f328(f328(f328(f43(x77921,f885(x77922,a871)),x77923),x77924),x77925))
% 81.29/80.92 [8101]~P24(f328(f328(f330(x81011),x81012),f328(x81015,x81016)))+~P24(f328(f328(f330(x81013),x81016),x81014))+P24(f328(f328(f330(x81011),x81012),f328(f328(f43(x81013,f885(x81011,a871)),x81014),x81015)))
% 81.29/80.92 [8145]P24(f328(f328(x81451,x81452),x81453))+~P24(f328(f328(x81454,x81452),x81453))+~P24(f328(f328(f244(f885(x81455,f885(x81456,a871))),x81454),x81451))
% 81.29/80.92 [8291]P24(f328(f328(x82911,x82912),x82913))+~P24(f328(f328(f330(x82914),x82912),x82915))+~P24(f328(f328(f328(f42(x82914,f885(x82916,a871)),x82915),x82911),x82913))
% 81.29/80.92 [8426]P24(f328(f328(f330(x84261),x84262),f328(x84263,x84264)))+~P24(f328(f328(f330(x84265),x84264),x84266))+~P24(f328(f328(f330(x84261),x84262),f328(f328(f42(x84265,f885(x84261,a871)),x84266),x84263)))
% 81.29/80.92 [8619]~P24(f328(f328(f328(f328(a202,x86191),x86193),x86194),x86196))+~P24(f328(f328(f328(f328(a202,x86192),x86196),x86194),x86195))+P24(f328(f328(f328(f328(a202,f34(x86191,x86192)),x86193),x86194),x86195))
% 81.29/80.92 [8689]~P9(x86894,x86895,x86896,x86891)+E(f328(x86891,x86892),f328(x86891,x86893))+~P24(f328(f328(f330(f884(x86894,x86894)),f328(f328(f257(x86894,x86894),x86892),x86893)),x86896))
% 81.29/80.92 [8720]P24(f328(f328(f244(f885(x87201,a871)),x87202),f328(x87203,x87204)))+~P24(f328(f328(f330(x87205),x87204),x87206))+~P24(f328(f328(f244(f885(x87201,a871)),x87202),f328(f328(f42(x87205,f885(x87201,a871)),x87206),x87203)))
% 81.29/80.92 [8749]~P52(x87493,x87494,f328(f283(x87494,x87493),x87495))+E(x87491,f193(f885(x87492,a871)))+E(f328(f328(f42(x87492,f885(x87493,a871)),x87491),f328(f328(f8(f885(x87494,a871),f885(x87493,a871),x87492),f282(x87494,x87493,x87495)),x87496)),f328(f282(x87494,x87493,x87495),f328(f328(f42(x87492,f885(x87494,a871)),x87491),x87496)))
% 81.29/80.92 [8824]P24(f328(f328(f330(x88241),x88242),f328(f282(x88243,x88241,x88244),x88245)))+~P24(f328(f328(f330(x88243),x88246),x88245))+~P24(f328(f328(f330(f884(x88243,x88241)),f328(f328(f257(x88243,x88241),x88246),x88242)),x88244))
% 81.29/80.92 [8941]P24(f328(x89411,x89412))+~P24(f328(f328(f328(f328(a202,x89414),x89412),x89415),x89416))+P24(f328(f328(f328(f328(a202,f31(x89411,x89413,x89414)),x89412),x89415),x89416))
% 81.29/80.92 [8958]~P24(f328(x89581,x89584))+~P24(f328(f328(f328(f328(a202,x89582),x89584),x89585),x89586))+P24(f328(f328(f328(f328(a202,f31(x89581,x89582,x89583)),x89584),x89585),x89586))
% 81.29/80.92 [9133]P24(f328(f328(f244(f885(x91331,a871)),f328(f282(x91332,x91331,x91333),x91334)),f328(f282(x91332,x91331,x91335),x91336)))+~P24(f328(f328(f244(f885(x91332,a871)),x91334),x91336))+~P24(f328(f328(f244(f885(f884(x91332,x91331),a871)),x91333),x91335))
% 81.29/80.92 [9221]P24(f328(x92211,x92212))+P24(f328(f328(f328(f328(a202,x92213),x92212),x92214),x92215))+~P24(f328(f328(f328(f328(a202,f31(x92211,x92216,x92213)),x92212),x92214),x92215))
% 81.29/80.92 [9226]~P24(f328(x92265,x92262))+P24(f328(f328(f328(f328(a202,x92261),x92262),x92263),x92264))+~P24(f328(f328(f328(f328(a202,f31(x92265,x92261,x92266)),x92262),x92263),x92264))
% 81.29/80.92 [9277]P24(f328(f328(f328(f328(a202,x92771),x92772),x92773),x92774))+P24(f328(f328(f328(f328(a202,x92775),x92772),x92773),x92774))+~P24(f328(f328(f328(f328(a202,f31(x92776,x92771,x92775)),x92772),x92773),x92774))
% 81.29/80.92 [9319]~P24(f328(f328(f330(x93192),x93196),x93194))+~P24(f328(f328(f244(f885(x93191,a871)),x93193),x93195))+P24(f328(f328(f244(f885(f884(x93191,x93192),a871)),f328(f328(f265(x93191,x93192),x93193),f328(f16(f885(x93192,a871),x93191),x93194))),f328(f328(f265(x93191,x93192),x93195),f328(f16(f885(x93192,a871),x93191),x93194))))
% 81.29/80.92 [9332]~P35(x93321,x93322,x93323,x93325,x93326)+P24(f328(f328(f267(x93321,x93322,a871),x93323),x93324))+~P24(f328(f328(f330(f884(x93321,x93322)),x93324),f328(f171(f884(x93321,x93322)),f328(f328(f181(x93321,x93322),x93325),x93326))))
% 81.29/80.92 [9465]~E(x94653,x94655)+P24(f328(f328(f330(f884(f878(x94651),f878(x94651))),f328(f328(f257(f878(x94651),f878(x94651)),f328(f328(f150(x94651),x94652),x94653)),f328(f328(f150(x94651),x94654),x94655))),f156(x94651,x94656)))+~P24(f328(f328(f330(f884(x94651,x94651)),f328(f328(f257(x94651,x94651),x94652),x94654)),x94656))
% 81.29/80.92 [9471]~E(f328(f194(f878(x94711)),x94715),f328(f194(f878(x94712)),x94716))+E(f186(x94711,x94712,f187(x94711,x94712,x94713,f328(f328(f22(f885(x94711,a871)),x94714),f328(f171(x94711),x94715))),x94715,x94716),f187(x94711,x94712,f186(x94711,x94712,x94713,x94715,x94716),x94714))+~P24(f328(f328(f244(f885(x94711,a871)),f328(f171(x94711),x94715)),x94714))
% 81.29/80.92 [9472]~E(f328(f194(f878(x94721)),x94723),f328(f194(f878(x94721)),x94725))+P24(f328(f328(f330(f884(f878(x94721),f878(x94721))),f328(f328(f257(f878(x94721),f878(x94721)),f328(f328(f150(x94721),x94722),x94723)),f328(f328(f150(x94721),x94724),x94725))),f144(x94721,x94726)))+~P24(f328(f328(f330(f884(x94721,x94721)),f328(f328(f257(x94721,x94721),x94722),x94724)),x94726))
% 81.29/80.92 [9502]P24(f328(f328(f330(f884(x95021,x95021)),f328(f328(f257(x95021,x95021),x95022),x95023)),f328(f328(f188(f884(x95021,x95021),a871),f328(a118,x95024)),x95025)))+~P24(f328(f328(f330(f884(x95021,x95021)),f328(f328(f257(x95021,x95021),x95026),x95023)),x95025))+~P24(f328(f328(f330(f884(x95021,x95021)),f328(f328(f257(x95021,x95021),x95022),x95026)),f328(f328(f188(f884(x95021,x95021),a871),x95024),x95025)))
% 81.29/80.92 [9503]P24(f328(f328(f330(f884(x95031,x95031)),f328(f328(f257(x95031,x95031),x95032),x95033)),f328(f328(f188(f884(x95031,x95031),a871),f328(a118,x95034)),x95035)))+~P24(f328(f328(f330(f884(x95031,x95031)),f328(f328(f257(x95031,x95031),x95032),x95036)),x95035))+~P24(f328(f328(f330(f884(x95031,x95031)),f328(f328(f257(x95031,x95031),x95036),x95033)),f328(f328(f188(f884(x95031,x95031),a871),x95034),x95035)))
% 81.29/80.92 [9507]~P24(f328(f328(f330(x95074),x95075),x95076))+P24(f328(f328(f244(f885(x95071,a871)),x95072),x95073))+~P24(f328(f328(f244(f885(f884(x95071,x95074),a871)),f328(f328(f265(x95071,x95074),x95072),f328(f16(f885(x95074,a871),x95071),x95076))),f328(f328(f265(x95071,x95074),x95073),f328(f16(f885(x95074,a871),x95071),x95076))))
% 81.29/80.92 [9551]E(x95511,x95512)+~P24(f328(f328(f330(f884(f878(x95513),f878(x95513))),f328(f328(f257(f878(x95513),f878(x95513)),f328(f328(f150(x95513),x95511),x95515)),f328(f328(f150(x95513),x95512),x95516))),f144(x95513,x95514)))+P24(f328(f328(f330(f884(x95513,x95513)),f328(f328(f257(x95513,x95513),x95511),x95512)),x95514))
% 81.29/80.92 [9552]E(x95521,x95522)+~P24(f328(f328(f330(f884(f878(x95523),f878(x95523))),f328(f328(f257(f878(x95523),f878(x95523)),f328(f328(f150(x95523),x95521),x95525)),f328(f328(f150(x95523),x95522),x95526))),f146(x95523,x95524)))+P24(f328(f328(f330(f884(x95523,x95523)),f328(f328(f257(x95523,x95523),x95521),x95522)),x95524))
% 81.29/80.92 [9553]E(x95531,x95532)+~P24(f328(f328(f330(f884(f878(x95533),f878(x95533))),f328(f328(f257(f878(x95533),f878(x95533)),f328(f328(f150(x95533),x95531),x95535)),f328(f328(f150(x95533),x95532),x95536))),f156(x95533,x95534)))+P24(f328(f328(f330(f884(x95533,x95533)),f328(f328(f257(x95533,x95533),x95531),x95532)),x95534))
% 81.29/80.92 [9588]P24(f328(f328(f330(f884(f878(x95881),f878(x95881))),f328(f328(f257(f878(x95881),f878(x95881)),f328(f328(f150(x95881),x95882),x95883)),f328(f328(f150(x95881),x95884),x95885))),f157(x95881,x95886)))+~P24(f328(f328(f330(f884(f878(x95881),f878(x95881))),f328(f328(f257(f878(x95881),f878(x95881)),x95883),x95885)),f157(x95881,x95886)))+~P24(f328(f328(f330(f884(x95881,x95881)),f328(f328(f257(x95881,x95881),x95882),x95884)),x95886))
% 81.29/80.92 [9606]P24(f328(x96061,x96062))+~P24(f328(x96061,f524(x96061,x96063,x96064,x96065,x96066)))+~P24(f328(f328(f330(x96066),x96062),f328(f328(f43(x96065,f885(x96066,a871)),x96064),x96063)))
% 81.29/80.92 [9611]~P24(f328(f328(f330(f884(f878(x96111),f878(x96111))),f328(f328(f257(f878(x96111),f878(x96111)),f328(f328(f150(x96111),x96112),x96115)),f328(f328(f150(x96111),x96113),x96116))),f144(x96111,x96114)))+P24(f328(f328(f330(f884(f878(x96111),f878(x96111))),f328(f328(f257(f878(x96111),f878(x96111)),x96115),x96116)),f144(x96111,x96114)))+P24(f328(f328(f330(f884(x96111,x96111)),f328(f328(f257(x96111,x96111),x96112),x96113)),x96114))
% 81.29/80.92 [9612]~P24(f328(f328(f330(f884(f878(x96121),f878(x96121))),f328(f328(f257(f878(x96121),f878(x96121)),f328(f328(f150(x96121),x96122),x96125)),f328(f328(f150(x96121),x96123),x96126))),f146(x96121,x96124)))+P24(f328(f328(f330(f884(f878(x96121),f878(x96121))),f328(f328(f257(f878(x96121),f878(x96121)),x96125),x96126)),f146(x96121,x96124)))+P24(f328(f328(f330(f884(x96121,x96121)),f328(f328(f257(x96121,x96121),x96122),x96123)),x96124))
% 81.29/80.92 [9613]~P24(f328(f328(f330(f884(f878(x96131),f878(x96131))),f328(f328(f257(f878(x96131),f878(x96131)),f328(f328(f150(x96131),x96132),x96135)),f328(f328(f150(x96131),x96133),x96136))),f156(x96131,x96134)))+P24(f328(f328(f330(f884(f878(x96131),f878(x96131))),f328(f328(f257(f878(x96131),f878(x96131)),x96135),x96136)),f156(x96131,x96134)))+P24(f328(f328(f330(f884(x96131,x96131)),f328(f328(f257(x96131,x96131),x96132),x96133)),x96134))
% 81.29/80.92 [9694]P24(f328(x96941,x96942))+P24(f328(f328(f330(x96943),f525(x96941,x96944,x96945,x96943,x96946)),x96945))+~P24(f328(f328(f330(x96946),x96942),f328(f328(f43(x96943,f885(x96946,a871)),x96945),x96944)))
% 81.29/80.92 [9705]~E(x97052,x97054)+P24(f328(f328(f330(f884(f878(x97051),f878(x97051))),f328(f328(f257(f878(x97051),f878(x97051)),f328(f328(f127(x97051),x97052),f328(f328(f150(x97051),x97053),f119(x97051)))),f328(f328(f127(x97051),x97054),f328(f328(f150(x97051),x97055),f119(x97051))))),f156(x97051,x97056)))+~P24(f328(f328(f330(f884(x97051,x97051)),f328(f328(f257(x97051,x97051),x97053),x97055)),x97056))
% 81.29/80.92 [9792]E(x97921,x97922)+~P24(f328(f328(f330(f884(f878(x97923),f878(x97923))),f328(f328(f257(f878(x97923),f878(x97923)),f328(f328(f127(x97923),x97925),f328(f328(f150(x97923),x97921),f119(x97923)))),f328(f328(f127(x97923),x97926),f328(f328(f150(x97923),x97922),f119(x97923))))),f156(x97923,x97924)))+P24(f328(f328(f330(f884(x97923,x97923)),f328(f328(f257(x97923,x97923),x97921),x97922)),x97924))
% 81.29/80.92 [9818]~P24(f328(f328(f330(f884(f878(x98181),f878(x98181))),f328(f328(f257(f878(x98181),f878(x98181)),f328(f328(f127(x98181),x98185),f328(f328(f150(x98181),x98182),f119(x98181)))),f328(f328(f127(x98181),x98186),f328(f328(f150(x98181),x98183),f119(x98181))))),f156(x98181,x98184)))+P24(f328(f328(f330(f884(f878(x98181),f878(x98181))),f328(f328(f257(f878(x98181),f878(x98181)),x98185),x98186)),f156(x98181,x98184)))+P24(f328(f328(f330(f884(x98181,x98181)),f328(f328(f257(x98181,x98181),x98182),x98183)),x98184))
% 81.29/80.92 [9837]P24(f328(x98371,x98372))+P24(f328(f328(f330(x98373),f524(x98371,x98374,x98375,x98376,x98373)),f328(x98374,f525(x98371,x98374,x98375,x98376,x98373))))+~P24(f328(f328(f330(x98373),x98372),f328(f328(f43(x98376,f885(x98373,a871)),x98375),x98374)))
% 81.29/80.92 [8839]~P12(x88393,x88394,x88391)+~P24(f328(f62(x88393),x88396))+E(f328(f328(x88391,x88392),f328(f328(f65(x88393,x88394,x88391),x88395),f328(f328(f22(f885(x88393,a871)),x88396),f328(f328(f306(x88393),x88392),f193(f885(x88393,a871)))))),f328(f328(f65(x88393,x88394,x88391),x88395),f328(f328(f306(x88393),x88392),x88396)))
% 81.29/80.92 [8924]~E(f328(f328(f177(x89241,x89242),x89244),x89245),f328(f236(x89242),x89246))+~P24(f328(f328(x89243,x89245),x89246))+E(f328(f328(f177(x89241,x89242),f328(f135(f884(x89241,x89242),f328(f267(x89241,x89242,a871),x89243)),x89244)),x89245),f328(f236(x89242),x89246))
% 81.29/80.92 [9140]~P24(f328(f328(f330(x91405),x91403),x91406))+P24(f328(f328(f244(f885(x91401,a871)),f328(x91402,x91403)),x91404))+~P24(f328(f328(f244(f885(x91401,a871)),f328(f328(f43(x91405,f885(x91401,a871)),x91406),x91402)),x91404))
% 81.29/80.92 [9765]~P6(x97651,x97655,x97654)+P24(f328(f328(f330(f884(x97651,x97651)),f328(f328(f257(x97651,x97651),x97652),x97653)),x97654))+~P24(f328(f328(f330(x97651),x97656),f328(f328(f107(f885(x97651,a871)),f328(f282(x97651,x97651,x97654),f328(f328(f306(x97651),x97652),f193(f885(x97651,a871))))),f328(f282(x97651,x97651,x97654),f328(f328(f306(x97651),x97653),f193(f885(x97651,a871)))))))
% 81.29/80.92 [8586]~P109(x85862)+~E(f328(f328(f81(x85862),f328(f328(f82(x85862),x85864),x85865)),x85861),f328(f328(f81(x85862),f328(f328(f82(x85862),x85863),x85865)),x85866))+E(x85861,f328(f328(f81(x85862),f328(f328(f82(x85862),f328(f328(f22(x85862),x85863),x85864)),x85865)),x85866))
% 81.29/80.92 [8587]~P109(x85871)+~E(f328(f328(f81(x85871),f328(f328(f82(x85871),x85872),x85874)),x85875),f328(f328(f81(x85871),f328(f328(f82(x85871),x85873),x85874)),x85876))+E(f328(f328(f81(x85871),f328(f328(f82(x85871),f328(f328(f22(x85871),x85872),x85873)),x85874)),x85875),x85876)
% 81.29/80.93 [8752]~P109(x87521)+E(f328(f328(f81(x87521),f328(f328(f82(x87521),x87522),x87523)),x87524),f328(f328(f81(x87521),f328(f328(f82(x87521),x87525),x87523)),x87526))+~E(x87526,f328(f328(f81(x87521),f328(f328(f82(x87521),f328(f328(f22(x87521),x87522),x87525)),x87523)),x87524))
% 81.29/80.93 [8753]~P109(x87531)+E(f328(f328(f81(x87531),f328(f328(f82(x87531),x87532),x87533)),x87534),f328(f328(f81(x87531),f328(f328(f82(x87531),x87535),x87533)),x87536))+~E(f328(f328(f81(x87531),f328(f328(f82(x87531),f328(f328(f22(x87531),x87532),x87535)),x87533)),x87534),x87536)
% 81.29/80.93 [9080]~P24(f328(f328(x90804,x90805),x90806))+~P24(f328(f328(x90803,x90805),x90806))+P24(f328(f328(f328(f328(f107(f885(x90801,f885(x90802,a871))),x90803),x90804),x90805),x90806))
% 81.29/80.93 [9340]P24(f328(f328(x93401,x93402),x93403))+P24(f328(f328(x93404,x93402),x93403))+~P24(f328(f328(f328(f328(f116(f885(x93405,f885(x93406,a871))),x93404),x93401),x93402),x93403))
% 81.29/80.93 [9626]~P132(x96261)+~P24(f328(f328(f244(x96261),f328(f328(f81(x96261),f328(f328(f82(x96261),x96264),x96265)),x96262)),f328(f328(f81(x96261),f328(f328(f82(x96261),x96263),x96265)),x96266)))+P24(f328(f328(f244(x96261),x96262),f328(f328(f81(x96261),f328(f328(f82(x96261),f328(f328(f22(x96261),x96263),x96264)),x96265)),x96266)))
% 81.29/80.93 [9627]~P132(x96271)+~P24(f328(f328(f245(x96271),f328(f328(f81(x96271),f328(f328(f82(x96271),x96274),x96275)),x96272)),f328(f328(f81(x96271),f328(f328(f82(x96271),x96273),x96275)),x96276)))+P24(f328(f328(f245(x96271),x96272),f328(f328(f81(x96271),f328(f328(f82(x96271),f328(f328(f22(x96271),x96273),x96274)),x96275)),x96276)))
% 81.29/80.93 [9648]~P132(x96481)+P24(f328(f328(f244(x96481),f328(f328(f81(x96481),f328(f328(f82(x96481),x96482),x96483)),x96484)),f328(f328(f81(x96481),f328(f328(f82(x96481),x96485),x96483)),x96486)))+~P24(f328(f328(f244(x96481),x96484),f328(f328(f81(x96481),f328(f328(f82(x96481),f328(f328(f22(x96481),x96485),x96482)),x96483)),x96486)))
% 81.29/80.93 [9649]~P132(x96491)+P24(f328(f328(f245(x96491),f328(f328(f81(x96491),f328(f328(f82(x96491),x96492),x96493)),x96494)),f328(f328(f81(x96491),f328(f328(f82(x96491),x96495),x96493)),x96496)))+~P24(f328(f328(f245(x96491),x96494),f328(f328(f81(x96491),f328(f328(f82(x96491),f328(f328(f22(x96491),x96495),x96492)),x96493)),x96496)))
% 81.29/80.93 [9753]~P132(x97531)+~P24(f328(f328(f244(x97531),f328(f328(f81(x97531),f328(f328(f82(x97531),x97532),x97534)),x97535)),f328(f328(f81(x97531),f328(f328(f82(x97531),x97533),x97534)),x97536)))+P24(f328(f328(f244(x97531),f328(f328(f81(x97531),f328(f328(f82(x97531),f328(f328(f22(x97531),x97532),x97533)),x97534)),x97535)),x97536))
% 81.29/80.93 [9754]~P132(x97541)+~P24(f328(f328(f245(x97541),f328(f328(f81(x97541),f328(f328(f82(x97541),x97542),x97544)),x97545)),f328(f328(f81(x97541),f328(f328(f82(x97541),x97543),x97544)),x97546)))+P24(f328(f328(f245(x97541),f328(f328(f81(x97541),f328(f328(f82(x97541),f328(f328(f22(x97541),x97542),x97543)),x97544)),x97545)),x97546))
% 81.29/80.93 [9802]~P132(x98021)+P24(f328(f328(f244(x98021),f328(f328(f81(x98021),f328(f328(f82(x98021),x98022),x98023)),x98024)),f328(f328(f81(x98021),f328(f328(f82(x98021),x98025),x98023)),x98026)))+~P24(f328(f328(f244(x98021),f328(f328(f81(x98021),f328(f328(f82(x98021),f328(f328(f22(x98021),x98022),x98025)),x98023)),x98024)),x98026))
% 81.29/80.93 [9803]~P132(x98031)+P24(f328(f328(f245(x98031),f328(f328(f81(x98031),f328(f328(f82(x98031),x98032),x98033)),x98034)),f328(f328(f81(x98031),f328(f328(f82(x98031),x98035),x98033)),x98036)))+~P24(f328(f328(f245(x98031),f328(f328(f81(x98031),f328(f328(f82(x98031),f328(f328(f22(x98031),x98032),x98035)),x98033)),x98034)),x98036))
% 81.29/80.93 [9977]~P74(x99772)+~P24(f328(f62(x99771),x99776))+E(f328(f328(f6(x99771,x99772),f328(f328(f18(x99771,x99772,x99772),f328(f328(f18(x99771,x99772,f885(x99772,x99772)),f328(f328(f8(a871,f885(x99772,f885(x99772,x99772)),x99771),f102(x99772)),x99773)),x99774)),x99775)),x99776),f328(f328(f81(x99772),f328(f328(f6(x99771,x99772),x99774),f328(f328(f107(f885(x99771,a871)),x99776),f328(f249(x99771),x99773)))),f328(f328(f6(x99771,x99772),x99775),f328(f328(f107(f885(x99771,a871)),x99776),f328(f80(f885(x99771,a871)),f328(f249(x99771),x99773))))))
% 81.29/80.93 [10037]P24(f328(f328(f330(x100372),x100374),x100376))+P24(f328(f328(f330(x100372),x100375),x100376))+E(f328(f308(x100371,x100372,f328(f328(f7(x100371,x100372,x100372),f328(f328(f7(x100371,x100372,f885(x100372,x100372)),f328(f328(f8(a871,f885(x100372,f885(x100372,x100372)),x100371),f102(x100372)),f328(f328(f7(x100371,f885(x100371,a871),a871),f330(x100371)),x100373))),x100374)),x100375)),x100376),f193(f885(x100371,a871)))
% 81.29/80.93 [10038]P24(f328(f328(f330(x100382),x100385),x100386))+~P24(f328(f328(f330(x100382),x100384),x100386))+E(f328(f308(x100381,x100382,f328(f328(f7(x100381,x100382,x100382),f328(f328(f7(x100381,x100382,f885(x100382,x100382)),f328(f328(f8(a871,f885(x100382,f885(x100382,x100382)),x100381),f102(x100382)),f328(f328(f7(x100381,f885(x100381,a871),a871),f330(x100381)),x100383))),x100384)),x100385)),x100386),x100383)
% 81.29/80.93 [10039]P24(f328(f328(f330(x100392),x100394),x100396))+~P24(f328(f328(f330(x100392),x100395),x100396))+E(f328(f308(x100391,x100392,f328(f328(f7(x100391,x100392,x100392),f328(f328(f7(x100391,x100392,f885(x100392,x100392)),f328(f328(f8(a871,f885(x100392,f885(x100392,x100392)),x100391),f102(x100392)),f328(f328(f7(x100391,f885(x100391,a871),a871),f330(x100391)),x100393))),x100394)),x100395)),x100396),f328(f80(f885(x100391,a871)),x100393))
% 81.29/80.93 [10040]~P24(f328(f328(f330(x100402),x100404),x100406))+~P24(f328(f328(f330(x100402),x100405),x100406))+E(f328(f308(x100401,x100402,f328(f328(f7(x100401,x100402,x100402),f328(f328(f7(x100401,x100402,f885(x100402,x100402)),f328(f328(f8(a871,f885(x100402,f885(x100402,x100402)),x100401),f102(x100402)),f328(f328(f7(x100401,f885(x100401,a871),a871),f330(x100401)),x100403))),x100404)),x100405)),x100406),f252(f885(x100401,a871)))
% 81.29/80.93 [10169]P20(x101691,x101692,f328(f328(f306(f876(x101691)),f328(f328(f328(f93(x101691),f328(x101693,x101694)),f328(a26,x101694)),f328(x101695,x101694))),f193(f885(f876(x101691),a871))))+~P24(f328(f328(f330(a874),x101694),x101696))+~P20(x101691,f328(f328(f116(f885(f876(x101691),a871)),x101692),f328(f307(a874,f876(x101691),f328(f328(f18(a874,f885(x101691,f885(a872,a871)),f876(x101691)),f328(f328(f18(a874,a873,f885(f885(x101691,f885(a872,a871)),f876(x101691))),f328(f328(f8(f885(x101691,f885(a872,a871)),f885(a873,f885(f885(x101691,f885(a872,a871)),f876(x101691))),a874),f93(x101691)),x101693)),a26)),x101695)),x101696)),f328(f307(a874,f876(x101691),f328(f328(f18(a874,f885(x101691,f885(a872,a871)),f876(x101691)),f328(f328(f18(a874,a873,f885(f885(x101691,f885(a872,a871)),f876(x101691))),f328(f328(f8(f885(x101691,f885(a872,a871)),f885(a873,f885(f885(x101691,f885(a872,a871)),f876(x101691))),a874),f93(x101691)),x101693)),f328(f328(f8(f881(a873),a873,a874),f240(a873)),a28))),x101695)),x101696))
% 81.29/80.93 [8616]E(x86161,x86162)+~P54(x86164,x86165,x86163,x86166,x86167)+~E(f328(x86163,x86161),f328(x86163,x86162))
% 81.29/80.93 [7000]E(f328(f238(f881(x70001),x70002,f196(x70001),x70003),f328(x70004,x70005)),f328(f236(x70001),x70006))+~E(f328(x70004,x70005),f328(f236(x70002),x70007))+~E(f328(x70003,x70007),f328(f236(x70001),x70006))
% 81.29/80.93 [8644]~P4(x86446,x86445,x86447,x86444,x86441)+E(f328(f328(x86441,x86442),x86443),x86444)+P24(f328(f62(x86445),x86443))
% 81.29/80.93 [9492]P42(x94921,x94922,x94923,x94924,x94925,f328(f328(x94923,x94926),x94927))+~E(f328(f328(x94923,x94926),x94927),x94924)+~E(x94925,f193(f885(x94921,a871)))
% 81.29/80.93 [9670]~P24(f328(x96706,x96703))+~P24(f328(f328(f330(f884(x96702,x96702)),f328(f328(f257(x96702,x96702),x96704),x96705)),f328(x96707,x96703)))+P24(f328(f328(f330(f884(f884(x96701,x96702),f884(x96701,x96702))),f328(f328(f257(f884(x96701,x96702),f884(x96701,x96702)),f328(f328(f257(x96701,x96702),x96703),x96704)),f328(f328(f257(x96701,x96702),x96703),x96705))),f280(x96701,x96702,x96706,x96707)))
% 81.29/80.93 [10094]~P42(x100942,x100947,x100943,x100946,x100941,f328(f328(x100943,x100945),x100944))+E(f328(f328(x100943,f398(x100944,x100945,x100941,x100946,x100943,x100947,x100942)),f399(x100944,x100945,x100941,x100946,x100943,x100947,x100942)),f328(f328(x100943,x100945),x100944))+E(x100941,f193(f885(x100942,a871)))
% 81.29/80.93 [10095]~P42(x100957,x100956,x100951,x100954,x100955,f328(f328(x100951,x100952),x100953))+E(f328(f328(x100951,f398(x100953,x100952,x100955,x100954,x100951,x100956,x100957)),f399(x100953,x100952,x100955,x100954,x100951,x100956,x100957)),f328(f328(x100951,x100952),x100953))+E(f328(f328(x100951,x100952),x100953),x100954)
% 81.29/80.93 [9178]~P35(x91781,x91782,x91783,x91785,x91787)+P35(x91781,x91782,x91783,f328(f328(f150(x91781),x91784),x91785),f328(f328(f150(x91782),x91786),x91787))+~P24(f328(f328(x91783,x91784),x91786))
% 81.29/80.93 [9196]P35(x91961,x91962,x91963,x91964,x91965)+~P35(x91961,x91962,x91963,f328(f328(f127(x91961),x91966),x91964),f328(f328(f127(x91962),x91967),x91965))+~E(f328(f194(f878(x91961)),x91966),f328(f194(f878(x91962)),x91967))
% 81.29/80.93 [9197]P35(x91971,x91972,x91973,x91974,x91975)+~P35(x91971,x91972,x91973,f328(f328(f127(x91971),x91974),x91976),f328(f328(f127(x91972),x91975),x91977))+~E(f328(f194(f878(x91971)),x91974),f328(f194(f878(x91972)),x91975))
% 81.29/80.93 [9402]~P35(x94021,x94022,x94023,x94025,x94027)+~P35(x94021,x94022,x94023,x94024,x94026)+P35(x94021,x94022,x94023,f328(f328(f127(x94021),x94024),x94025),f328(f328(f127(x94022),x94026),x94027))
% 81.29/80.93 [9742]~P24(f328(f67(x97421,x97424,x97425,x97426,x97423),x97427))+P24(f328(f67(x97421,x97424,x97425,x97426,f328(f328(f306(x97421),x97422),x97423)),f328(f328(x97425,x97422),x97427)))+P24(f328(f328(f330(x97421),x97422),x97423))
% 81.29/80.93 [9873]~P21(x98733,x98731,x98734,f252(f885(x98733,a871)))+E(f328(f328(f177(x98731,x98732),f328(f328(f153(f884(x98733,x98732),f884(x98731,x98732)),f328(f267(x98733,x98732,f884(x98731,x98732)),f328(f328(f8(x98731,f885(x98732,f884(x98731,x98732)),x98733),f257(x98731,x98732)),x98734))),x98735)),f328(x98734,x98736)),f328(f236(x98732),x98737))+~E(f328(f328(f177(x98733,x98732),x98735),x98736),f328(f236(x98732),x98737))
% 81.29/80.93 [10116]~P42(x101162,x101167,x101166,x101165,x101161,f328(f328(x101166,x101164),x101163))+E(x101161,f193(f885(x101162,a871)))+P24(f328(f328(f330(x101162),f398(x101163,x101164,x101161,x101165,x101166,x101167,x101162)),x101161))
% 81.29/80.93 [10117]~P42(x101175,x101177,x101171,x101174,x101176,f328(f328(x101171,x101172),x101173))+E(f328(f328(x101171,x101172),x101173),x101174)+P24(f328(f328(f330(x101175),f398(x101173,x101172,x101176,x101174,x101171,x101177,x101175)),x101176))
% 81.29/80.93 [6791]~E(x67915,x67917)+~E(x67916,x67914)+E(f328(f328(f328(f328(f73(x67911,f881(x67912)),x67913),x67914),f328(f236(x67912),x67915)),x67916),f328(f236(x67912),x67917))
% 81.29/80.93 [6916]E(x69161,x69162)+~E(f328(x69165,x69161),f328(f236(x69164),x69167))+E(f328(f328(f328(f328(f73(x69163,f881(x69164)),x69165),x69162),f328(f236(x69164),x69166)),x69161),f328(f236(x69164),x69167))
% 81.29/80.93 [7633]E(x76331,x76332)+~E(x76333,x76334)+~E(f328(f328(f328(f328(f73(x76335,f881(x76336)),x76337),x76334),f328(f236(x76336),x76331)),x76333),f328(f236(x76336),x76332))
% 81.29/80.93 [7698]E(x76981,x76982)+E(f328(x76983,x76984),f328(f236(x76985),x76981))+~E(f328(f328(f328(f328(f73(x76986,f881(x76985)),x76983),x76987),f328(f236(x76985),x76982)),x76984),f328(f236(x76985),x76981))
% 81.29/80.93 [7699]E(x76991,x76992)+E(f328(x76993,x76991),f328(f236(x76994),x76995))+~E(f328(f328(f328(f328(f73(x76996,f881(x76994)),x76993),x76992),f328(f236(x76994),x76997)),x76991),f328(f236(x76994),x76995))
% 81.29/80.93 [8864]~P17(x88644,x88645,x88646,x88647,x88641)+~P24(f328(f62(x88645),x88643))+E(f328(f328(x88641,x88642),x88643),f328(f328(f328(f66(x88644,x88645,x88646),x88642),x88647),x88643))
% 81.29/80.93 [8865]~P4(x88654,x88655,x88656,x88657,x88651)+~P24(f328(f62(x88655),x88653))+E(f328(f328(x88651,x88652),x88653),f328(f328(f328(f66(x88654,x88655,x88656),x88652),x88657),x88653))
% 81.29/80.93 [9458]~P20(x94581,x94582,f328(f328(f306(f876(x94581)),f328(f328(f328(f93(x94581),x94583),x94584),x94587)),f193(f885(f876(x94581),a871))))+P20(x94581,x94582,f328(f328(f306(f876(x94581)),f328(f328(f328(f93(x94581),x94583),f34(x94584,x94585)),x94586)),f193(f885(f876(x94581),a871))))+~P20(x94581,x94582,f328(f328(f306(f876(x94581)),f328(f328(f328(f93(x94581),x94587),x94585),x94586)),f193(f885(f876(x94581),a871))))
% 81.29/80.93 [9643]~P19(x96433,x96434,x96435,x96437,x96436,x96431)+~P24(f328(f62(x96434),x96432))+E(f328(x96431,x96432),f328(f328(f328(f66(x96433,x96434,x96435),x96436),x96437),x96432))
% 81.29/80.93 [9797]P42(x97971,x97972,x97973,x97974,x97975,f328(f328(x97973,x97976),x97977))+~P42(x97971,x97972,x97973,x97974,f328(f328(f22(f885(x97971,a871)),x97975),f328(f328(f306(x97971),x97976),f193(f885(x97971,a871)))),x97977)+~P24(f328(f328(f330(x97971),x97976),x97975))
% 81.29/80.93 [10069]~P20(x100691,x100692,f328(f328(f306(f876(x100691)),f328(f328(f328(f93(x100691),f98(x100691,x100693,x100694)),x100695),x100697)),f193(f885(f876(x100691),a871))))+P20(x100691,x100692,f328(f328(f306(f876(x100691)),f328(f328(f328(f93(x100691),x100693),f31(x100694,x100695,x100696)),x100697)),f193(f885(f876(x100691),a871))))+~P20(x100691,x100692,f328(f328(f306(f876(x100691)),f328(f328(f328(f93(x100691),f98(x100691,x100693,f328(f74(a871,a871,a872,a323),x100694))),x100696),x100697)),f193(f885(f876(x100691),a871))))
% 81.29/80.93 [10142]~P42(x101422,x101423,x101424,x101425,x101421,f328(f328(x101424,x101427),x101426))+P42(x101422,x101423,x101424,x101425,f328(f328(f22(f885(x101422,a871)),x101421),f328(f328(f306(x101422),f398(x101426,x101427,x101421,x101425,x101424,x101423,x101422)),f193(f885(x101422,a871)))),f399(x101426,x101427,x101421,x101425,x101424,x101423,x101422))+E(x101421,f193(f885(x101422,a871)))
% 81.29/80.93 [10143]~P42(x101435,x101436,x101431,x101434,x101437,f328(f328(x101431,x101432),x101433))+P42(x101435,x101436,x101431,x101434,f328(f328(f22(f885(x101435,a871)),x101437),f328(f328(f306(x101435),f398(x101433,x101432,x101437,x101434,x101431,x101436,x101435)),f193(f885(x101435,a871)))),f399(x101433,x101432,x101437,x101434,x101431,x101436,x101435))+E(f328(f328(x101431,x101432),x101433),x101434)
% 81.29/80.93 [9185]E(f186(x91851,x91852,x91853,x91854,f328(f328(f158(x91852,x91855),x91856),x91857)),f186(x91851,x91852,x91853,x91854,x91855))+~P24(f328(f328(f245(a877),x91856),f328(f194(f878(x91852)),x91855)))+~P24(f328(f328(f244(a877),f328(f194(f878(x91851)),x91854)),x91856))
% 81.29/80.93 [9480]P24(f328(f328(f244(f885(f884(x94801,x94802),a871)),f328(f328(f285(x94801,x94803,x94802),x94804),x94805)),f328(f328(f285(x94801,x94803,x94802),x94806),x94807)))+~P24(f328(f328(f244(f885(f884(x94803,x94802),a871)),x94805),x94807))+~P24(f328(f328(f244(f885(f884(x94801,x94803),a871)),x94804),x94806))
% 81.29/80.93 [9808]~P24(f328(f328(f330(x98081),x98086),x98085))+P24(f328(f67(x98081,x98082,x98083,x98084,x98085),f328(f328(x98083,x98086),x98087)))+~P24(f328(f67(x98081,x98082,x98083,x98084,f328(f328(f22(f885(x98081,a871)),x98085),f328(f328(f306(x98081),x98086),f193(f885(x98081,a871))))),x98087))
% 81.29/80.93 [10198]~P142(x101981)+~P21(f884(x101982,x101983),x101981,f328(f267(x101982,x101983,x101981),f328(f328(f7(x101982,f885(x101983,x101981),f885(x101983,x101981)),f328(f328(f8(f885(x101981,x101981),f885(f885(x101983,x101981),f885(x101983,x101981)),x101982),f8(x101981,x101981,x101983)),f328(f328(f8(x101981,f885(x101981,x101981),x101982),f82(x101981)),x101984))),x101985)),f328(f328(f265(x101982,x101983),x101986),f328(f16(f885(x101983,a871),x101982),x101987)))+E(f328(f328(f6(x101981,x101981),f35(x101981)),f328(f249(x101981),f328(f328(f8(f885(x101982,a871),a871,x101981),f88(x101982)),f328(f328(f8(f885(x101982,f885(x101983,a871)),f885(x101982,a871),x101981),f328(f8(f885(x101983,a871),a871,x101982),f88(x101983))),f328(f328(f7(x101981,f885(x101982,f885(x101983,a871)),f885(x101982,f885(x101983,a871))),f328(f328(f8(f885(x101982,f885(f885(x101983,a871),f885(x101983,a871))),f885(f885(x101982,f885(x101983,a871)),f885(x101982,f885(x101983,a871))),x101981),f18(x101982,f885(x101983,a871),f885(x101983,a871))),f328(f328(f8(f885(x101982,f885(x101983,f885(a871,a871))),f885(x101982,f885(f885(x101983,a871),f885(x101983,a871))),x101981),f328(f8(f885(x101983,f885(a871,a871)),f885(f885(x101983,a871),f885(x101983,a871)),x101982),f18(x101983,a871,a871))),f328(f328(f8(f885(x101982,f885(x101983,a871)),f885(x101982,f885(x101983,f885(a871,a871))),x101981),f328(f8(f885(x101983,a871),f885(x101983,f885(a871,a871)),x101982),f328(f8(a871,f885(a871,a871),x101983),a326))),f328(f328(f7(x101981,f885(x101982,f885(x101983,x101981)),f885(x101982,f885(x101983,a871))),f328(f328(f8(f885(f885(x101983,x101981),f885(x101983,a871)),f885(f885(x101982,f885(x101983,x101981)),f885(x101982,f885(x101983,a871))),x101981),f8(f885(x101983,x101981),f885(x101983,a871),x101982)),f328(f328(f8(f885(x101981,a871),f885(f885(x101983,x101981),f885(x101983,a871)),x101981),f8(x101981,a871,x101983)),a325))),f328(f328(f7(x101982,f885(x101983,x101981),f885(x101983,x101981)),f328(f328(f8(f885(x101981,x101981),f885(f885(x101983,x101981),f885(x101983,x101981)),x101982),f8(x101981,x101981,x101983)),f328(f328(f8(x101981,f885(x101981,x101981),x101982),f82(x101981)),x101984))),x101985)))))),f328(f328(f7(x101982,f885(x101983,a871),f885(x101983,a871)),f328(f328(f8(f885(a871,a871),f885(f885(x101983,a871),f885(x101983,a871)),x101982),f8(a871,a871,x101983)),f328(f328(f8(a871,f885(a871,a871),x101982),a326),f328(f328(f7(x101982,f885(x101982,a871),a871),f330(x101982)),x101986)))),f328(f328(f7(x101983,f885(x101983,a871),a871),f330(x101983)),x101987))))))),f328(f328(f82(x101981),f328(f328(f6(x101982,x101981),x101984),x101986)),f328(f328(f6(x101983,x101981),x101985),x101987)))
% 81.29/80.93 [9904]P51(x99041,x99042,x99043,x99044,x99045,x99046,x99047)+~P24(f328(f328(x99044,x99046),x99048))+~P24(f328(f328(x99045,x99048),x99047))
% 81.29/80.93 [9247]~P15(x92478,x92471,x92473,x92475)+~P24(f328(f62(x92478),x92476))+E(f328(f74(x92471,x92471,x92472,f328(x92473,x92474)),f328(f74(x92471,x92471,x92472,f328(x92475,x92476)),x92477)),f328(f74(x92471,x92471,x92472,f328(x92475,x92476)),f328(f74(x92471,x92471,x92472,f328(x92473,x92474)),x92477)))
% 81.29/80.93 [9633]~P18(x96337,x96332,x96335,x96338,x96336,x96331)+~P24(f328(f62(x96332),x96334))+E(f328(x96331,f328(f328(f306(x96332),x96333),x96334)),f328(f328(x96335,f328(x96336,x96333)),f328(x96331,x96334)))
% 81.29/80.93 [9751]~P21(x97512,x97514,x97516,x97518)+~P21(x97511,x97513,x97515,x97517)+P21(f884(x97511,x97512),f884(x97513,x97514),f268(x97511,x97513,x97512,x97514,x97515,x97516),f328(f328(f265(x97511,x97512),x97517),f328(f16(f885(x97512,a871),x97511),x97518)))
% 81.29/80.93 [9426]P24(f328(f328(f330(f884(x94261,x94262)),f328(f328(f257(x94261,x94262),x94263),x94264)),f328(f328(f285(x94261,x94265,x94262),x94266),x94267)))+~P24(f328(f328(f330(f884(x94261,x94265)),f328(f328(f257(x94261,x94265),x94263),x94268)),x94266))+~P24(f328(f328(f330(f884(x94265,x94262)),f328(f328(f257(x94265,x94262),x94268),x94264)),x94267))
% 81.29/80.93 [9614]~P24(f328(f328(f244(f885(f884(x96143,x96142),a871)),x96145),f328(f328(f265(x96143,x96142),x96148),f328(f16(f885(x96142,a871),x96143),x96147))))+~P24(f328(f328(f244(f885(f884(x96141,x96143),a871)),x96144),f328(f328(f265(x96141,x96143),x96146),f328(f16(f885(x96143,a871),x96141),x96148))))+P24(f328(f328(f244(f885(f884(x96141,x96142),a871)),f328(f328(f285(x96141,x96143,x96142),x96144),x96145)),f328(f328(f265(x96141,x96142),x96146),f328(f16(f885(x96142,a871),x96141),x96147))))
% 81.29/80.93 [9665]~E(x96653,x96655)+P24(f328(f328(f330(f884(f884(x96651,x96652),f884(x96651,x96652))),f328(f328(f257(f884(x96651,x96652),f884(x96651,x96652)),f328(f328(f257(x96651,x96652),x96653),x96654)),f328(f328(f257(x96651,x96652),x96655),x96656))),f320(x96651,x96652,x96657,x96658)))+~P24(f328(f328(f330(f884(x96652,x96652)),f328(f328(f257(x96652,x96652),x96654),x96656)),x96658))
% 81.29/80.93 [9774]E(x97741,x97742)+~P24(f328(f328(f330(f884(f884(x97743,x97745),f884(x97743,x97745))),f328(f328(f257(f884(x97743,x97745),f884(x97743,x97745)),f328(f328(f257(x97743,x97745),x97741),x97746)),f328(f328(f257(x97743,x97745),x97742),x97747))),f320(x97743,x97745,x97744,x97748)))+P24(f328(f328(f330(f884(x97743,x97743)),f328(f328(f257(x97743,x97743),x97741),x97742)),x97744))
% 81.29/80.93 [9791]~P24(f328(f328(f330(f884(f884(x97911,x97915),f884(x97911,x97915))),f328(f328(f257(f884(x97911,x97915),f884(x97911,x97915)),f328(f328(f257(x97911,x97915),x97912),x97916)),f328(f328(f257(x97911,x97915),x97913),x97917))),f320(x97911,x97915,x97914,x97918)))+P24(f328(f328(f330(f884(x97911,x97911)),f328(f328(f257(x97911,x97911),x97912),x97913)),x97914))+P24(f328(f328(f330(f884(x97915,x97915)),f328(f328(f257(x97915,x97915),x97916),x97917)),x97918))
% 81.29/80.93 [9695]~P19(x96957,x96955,x96951,x96958,x96952,x96954)+~P24(f328(f62(x96955),x96956))+E(f328(f328(x96951,f328(x96952,x96953)),f328(x96954,f328(f328(f22(f885(x96955,a871)),x96956),f328(f328(f306(x96955),x96953),f193(f885(x96955,a871)))))),f328(x96954,f328(f328(f306(x96955),x96953),x96956)))
% 81.29/80.93 [9204]~P24(f328(f328(f328(x92045,x92048),x92046),x92047))+~P24(f328(f328(f330(x92041),x92048),x92044))+P24(f328(f328(f328(f328(f43(x92041,f885(x92042,f885(x92043,a871))),x92044),x92045),x92046),x92047))
% 81.29/80.93 [9413]P24(f328(f328(f328(x94131,x94132),x94133),x94134))+~P24(f328(f328(f330(x94135),x94132),x94136))+~P24(f328(f328(f328(f328(f42(x94135,f885(x94137,f885(x94138,a871))),x94136),x94131),x94133),x94134))
% 81.29/80.93 [9607]~P17(x96073,x96072,x96074,x96078,x96071)+~P24(f328(f62(x96072),x96077))+E(f328(f328(x96071,f328(f328(f18(x96072,x96073,x96073),f328(f328(f8(x96073,f885(x96073,x96073),x96072),x96074),x96075)),x96076)),x96077),f328(f328(x96074,f328(f328(x96071,x96075),x96077)),f328(f328(x96071,x96076),x96077)))
% 81.29/80.93 [9881]~E(f328(f307(x98812,x98814,x98816),x98818),x988110)+~E(f328(f307(x98811,x98813,x98815),x98817),x98819)+E(f328(f307(f884(x98811,x98812),f884(x98813,x98814),f268(x98811,x98813,x98812,x98814,x98815,x98816)),f328(f328(f265(x98811,x98812),x98817),f328(f16(f885(x98812,a871),x98811),x98818))),f328(f328(f265(x98813,x98814),x98819),f328(f16(f885(x98814,a871),x98813),x988110)))
% 81.29/80.93 [9867]~P1(a5000)+~P2(a5000)+P20(a872,f328(f307(a874,f876(a872),f328(f328(f8(a873,f876(a872),a874),a94),a26)),f183(a874,a873,a28)),x98671)+~P24(f328(f328(f244(f885(f876(a872),a871)),x98671),f328(f307(a874,f876(a872),f328(f328(f8(a873,f876(a872),a874),a94),f328(f328(f8(f881(a873),a873,a874),f240(a873)),a28))),f183(a874,a873,a28))))
% 81.29/80.93 [6500]~P1(a5000)+~P2(a5000)+~P24(f328(a25,x65001))+P20(a872,f193(f885(f876(a872),a871)),f328(f328(f306(f876(a872)),f328(a94,x65001)),f193(f885(f876(a872),a871))))
% 81.29/80.93 [4834]~P106(x48342)+~P29(x48342,x48341)+P29(x48342,f120(x48342,x48341))+E(x48341,f119(x48342))
% 81.29/80.93 [4835]~P106(x48352)+~P29(x48352,x48351)+P29(x48352,f637(x48351,x48352))+E(x48351,f119(x48352))
% 81.29/80.93 [5067]~P27(x50672)+E(f10(x50672,x50671),f40(x50672,x50671))+E(x50671,f193(f885(x50672,a871)))+~P24(f328(f62(x50672),x50671))
% 81.29/80.93 [5068]~P27(x50682)+E(f11(x50682,x50681),f41(x50682,x50681))+E(x50681,f193(f885(x50682,a871)))+~P24(f328(f62(x50682),x50681))
% 81.29/80.93 [5228]~P106(x52282)+~P29(x52282,x52281)+E(x52281,f119(x52282))+E(f328(f328(f150(x52282),f670(x52281,x52282)),f637(x52281,x52282)),x52281)
% 81.29/80.93 [6026]~P78(x60262)+E(x60261,f193(f885(x60262,a871)))+P24(f328(f328(f244(x60262),f11(x60262,x60261)),f10(x60262,x60261)))+~P24(f328(f62(x60262),x60261))
% 81.29/80.93 [6038]~P40(x60382)+~P40(x60381)+E(x60381,x60382)+~E(f328(f307(a1,a877,a110),x60381),f328(f307(a1,a877,a110),x60382))
% 81.29/80.93 [9062]~P111(x90621)+~P24(f328(f328(f330(x90621),x90622),f115(x90621)))+P24(f328(f328(f245(x90621),f328(f328(f81(x90621),f328(f328(f81(x90621),f79(x90621)),x90622)),x90622)),f2(x90621)))+~P24(f328(f328(f245(x90621),x90622),f2(x90621)))
% 81.29/80.93 [9302]~P111(x93021)+~P24(f328(f328(f330(x93021),x93022),f115(x93021)))+~P24(f328(f328(f245(x93021),f328(f328(f81(x93021),f328(f328(f81(x93021),f79(x93021)),x93022)),x93022)),f2(x93021)))+P24(f328(f328(f245(x93021),x93022),f2(x93021)))
% 81.29/80.93 [4890]~P116(x48902)+~P142(x48902)+E(x48901,f2(a877))+E(f328(f328(f258(x48902),f2(x48902)),x48901),f2(x48902))
% 81.29/80.93 [4895]~P116(x48951)+~P142(x48951)+~E(x48952,f2(a877))+E(f328(f328(f258(x48951),f2(x48951)),x48952),f79(x48951))
% 81.29/80.93 [5054]~P139(x50542)+E(x50541,f79(x50542))+E(x50541,f328(f80(x50542),f79(x50542)))+~E(f328(f328(f82(x50542),x50541),x50541),f79(x50542))
% 81.29/80.93 [5311]~P91(x53112)+E(x53111,f2(x53112))+E(f83(x53112,x53111),f328(f80(x53112),f79(x53112)))+P24(f328(f328(f245(x53112),f2(x53112)),x53111))
% 81.29/80.93 [5547]~P91(x55472)+E(f83(x55472,x55471),f79(x55472))+E(x55471,f2(x55472))+~P24(f328(f328(f245(x55472),f2(x55472)),x55471))
% 81.29/80.93 [5556]E(x55561,x55562)+~E(f328(f109(a877),x55561),f328(f109(a877),x55562))+P24(f328(a199,f328(f109(a1),x55562)))+P24(f328(a199,f328(f109(a1),x55561)))
% 81.29/80.93 [5605]~P93(x56051)+~E(x56052,f2(x56051))+E(f328(f328(f81(x56051),x56052),x56052),f2(x56051))+~P24(f328(f328(f330(x56051),x56052),f115(x56051)))
% 81.29/80.93 [5643]E(x56431,f2(a1))+~E(f328(f328(f39(a1),x56432),x56431),f2(a1))+P24(f328(f328(f245(a1),x56431),x56432))+P24(f328(f328(f245(a1),x56432),x56431))
% 81.29/80.93 [5674]E(x56741,f2(a1))+~E(f328(f328(f39(a1),x56742),x56741),f2(a1))+P24(f328(f328(f244(a1),x56742),f2(a1)))+P24(f328(f328(f245(a1),x56742),x56741))
% 81.29/80.93 [5707]E(x57071,f2(a1))+~E(f328(f328(f39(a1),x57072),x57071),f2(a1))+P24(f328(f328(f244(a1),f2(a1)),x57072))+P24(f328(f328(f245(a1),x57071),x57072))
% 81.29/80.93 [5743]~P93(x57432)+E(x57431,f2(x57432))+~E(f328(f328(f81(x57432),x57431),x57431),f2(x57432))+~P24(f328(f328(f330(x57432),x57431),f115(x57432)))
% 81.29/80.93 [5803]E(f328(f109(a877),x58031),f328(f109(a877),x58032))+~E(f328(f109(a1),x58032),f2(a1))+P24(f328(a199,f328(f109(a1),x58032)))+~P24(f328(a199,f328(f109(a1),x58031)))
% 81.29/80.93 [5830]~E(f328(f109(a877),x58302),f328(f109(a877),x58301))+E(f328(f109(a1),x58301),f2(a1))+P24(f328(a199,f328(f109(a1),x58301)))+~P24(f328(a199,f328(f109(a1),x58302)))
% 81.29/80.93 [5839]~P106(x58392)+E(x58391,f193(f885(x58392,a871)))+~P24(f328(f62(x58392),x58391))+P24(f328(f328(f330(x58392),f14(x58392,x58391)),x58391))
% 81.29/80.93 [5840]~P106(x58402)+E(x58401,f193(f885(x58402,a871)))+~P24(f328(f62(x58402),x58401))+P24(f328(f328(f330(x58402),f15(x58402,x58401)),x58401))
% 81.29/80.93 [6006]~P111(x60061)+~P96(x60061)+P24(f328(f328(f244(x60061),f2(x60061)),f328(f109(x60061),x60062)))+~P24(f328(f328(f244(a1),a84),x60062))
% 81.29/80.93 [6007]~P111(x60071)+~P96(x60071)+P24(f328(f328(f245(x60071),f2(x60071)),f328(f109(x60071),x60072)))+~P24(f328(f328(f245(a1),a84),x60072))
% 81.29/80.93 [6025]~P111(x60251)+~P96(x60251)+E(f328(f76(x60251),f328(f109(x60251),x60252)),f328(f109(x60251),x60252))+P24(f328(f328(f245(x60251),f328(f109(x60251),x60252)),f2(x60251)))
% 81.29/80.93 [6065]E(x60651,x60652)+~E(f328(a110,x60651),f328(a110,x60652))+~P24(f328(f328(f244(a1),f2(a1)),x60652))+~P24(f328(f328(f244(a1),f2(a1)),x60651))
% 81.29/80.93 [6260]~P96(x62602)+~P111(x62602)+~P24(f328(f328(f244(x62602),f2(x62602)),f328(f109(x62602),x62601)))+P24(f328(f328(f244(a1),a84),x62601))
% 81.29/80.93 [6261]~P96(x62612)+~P111(x62612)+~P24(f328(f328(f245(x62612),f2(x62612)),f328(f109(x62612),x62611)))+P24(f328(f328(f245(a1),a84),x62611))
% 81.29/80.93 [6266]~P111(x62661)+~P96(x62661)+P24(f328(f328(f244(x62661),f328(f109(x62661),x62662)),f2(x62661)))+~P24(f328(f328(f244(a1),x62662),a84))
% 81.29/80.93 [6267]~P111(x62671)+~P96(x62671)+P24(f328(f328(f245(x62671),f328(f109(x62671),x62672)),f2(x62671)))+~P24(f328(f328(f245(a1),x62672),a84))
% 81.29/80.93 [6578]~P96(x65782)+~P111(x65782)+~P24(f328(f328(f244(x65782),f328(f109(x65782),x65781)),f2(x65782)))+P24(f328(f328(f244(a1),x65781),a84))
% 81.29/80.93 [6579]~P96(x65792)+~P111(x65792)+~P24(f328(f328(f245(x65792),f328(f109(x65792),x65791)),f2(x65792)))+P24(f328(f328(f245(a1),x65791),a84))
% 81.29/80.93 [6671]~P111(x66711)+~P96(x66711)+E(f328(f76(x66711),f328(f109(x66711),x66712)),f328(f80(x66711),f328(f109(x66711),x66712)))+~P24(f328(f328(f245(x66711),f328(f109(x66711),x66712)),f2(x66711)))
% 81.29/80.93 [6689]E(f328(f109(a877),x66891),f328(f109(a877),x66892))+~E(f328(f109(a1),x66892),f2(a1))+~P24(f328(f328(f244(a1),f328(f109(a1),x66891)),f2(a1)))+~P24(f328(a199,f328(f109(a1),x66891)))
% 81.29/80.93 [7564]~P106(x75642)+E(x75641,f193(f885(x75642,a871)))+~P24(f328(f62(x75642),x75641))+P24(f328(f328(f244(x75642),f12(x75642,f242(x75642),x75641)),f13(x75642,f243(x75642),x75641)))
% 81.29/80.93 [7879]~P28(x78791)+~P40(x78792)+P24(f328(f328(f330(a1),x78791),x78792))+~P24(f328(f328(f330(a877),f328(a110,x78791)),f328(f307(a1,a877,a110),x78792)))
% 81.29/80.93 [8156]~P60(x81562)+P24(f328(x81561,f196(x81562)))+~P24(f328(f58(f881(x81562)),x81561))+P24(f328(f58(x81562),f328(f328(f8(f881(x81562),a871,x81562),x81561),f236(x81562))))
% 81.29/80.93 [8624]~P60(x86241)+~P24(f328(x86242,f196(x86241)))+P24(f328(f59(f881(x86241)),x86242))+~P24(f328(f59(x86241),f328(f328(f8(f881(x86241),a871,x86241),x86242),f236(x86241))))
% 81.29/80.93 [5836]~P137(x58362)+E(x58361,f2(a1))+E(f328(f80(x58362),f328(f108(x58362),f328(f80(a1),x58361))),f328(f108(x58362),x58361))+~P24(f328(f328(f245(a1),x58361),f2(a1)))
% 81.29/80.93 [5909]~P93(x59091)+~P96(x59091)+~P31(x59091,f328(f109(x59091),x59092))+P31(x59091,f328(f109(x59091),f328(f328(f81(a1),x59092),x59092)))
% 81.29/80.93 [6248]~P76(x62482)+E(x62481,f193(f885(x62482,a871)))+E(f15(x62482,f328(f307(x62482,x62482,f80(x62482)),x62481)),f328(f80(x62482),f14(x62482,x62481)))+~P24(f328(f62(x62482),x62481))
% 81.29/80.93 [6249]~P76(x62492)+E(x62491,f193(f885(x62492,a871)))+E(f14(x62492,f328(f307(x62492,x62492,f80(x62492)),x62491)),f328(f80(x62492),f15(x62492,x62491)))+~P24(f328(f62(x62492),x62491))
% 81.29/80.93 [6281]~P93(x62811)+~P96(x62811)+P31(x62811,f328(f109(x62811),x62812))+~P31(x62811,f328(f109(x62811),f328(f328(f81(a1),x62812),x62812)))
% 81.29/80.93 [6372]E(x63721,f2(a1))+E(f328(a51,f50(f328(f80(a1),x63721),f328(f80(a1),x63722))),f46(x63721,x63722))+P24(f328(f328(f244(a1),f2(a1)),x63722))+~P24(f328(f328(f244(a1),f2(a1)),x63721))
% 81.29/80.93 [7390]~P1(a5000)+~P24(f328(a25,x73901))+P20(a872,x73902,f328(f328(f306(f876(a872)),f328(a94,x73901)),f193(f885(f876(a872),a871))))+P24(f328(f328(f330(a874),f539(x73901,x73902)),f183(a874,a873,a28)))
% 81.29/80.93 [8655]~P1(a5000)+~P24(f328(a25,x86552))+P20(a872,x86551,f328(f328(f306(f876(a872)),f328(a94,x86552)),f193(f885(f876(a872),a871))))+~P20(a872,x86551,f328(f328(f306(f876(a872)),f328(a94,f328(a26,f539(x86552,x86551)))),f193(f885(f876(a872),a871))))
% 81.29/80.93 [8669]~P40(x86692)+~P40(x86691)+P24(f328(f328(f245(f885(a877,a871)),f328(f307(a1,a877,a110),x86691)),f328(f307(a1,a877,a110),x86692)))+~P24(f328(f328(f245(f885(a1,a871)),x86691),x86692))
% 81.29/80.93 [8882]~E(f679(x88822,x88821),f680(x88822,x88821))+~P24(f328(f136(x88821),f681(x88822,x88821)))+~P24(f328(f136(f878(x88821)),x88822))+P24(f328(f136(x88821),f328(f141(f878(x88821),f878(x88821),f127(x88821),f119(x88821)),x88822)))
% 81.29/80.93 [8979]~P40(x89792)+~P40(x89791)+~P24(f328(f328(f244(f885(a877,a871)),f328(f307(a1,a877,a110),x89791)),f328(f307(a1,a877,a110),x89792)))+P24(f328(f328(f244(f885(a1,a871)),x89791),x89792))
% 81.29/80.93 [8980]~P40(x89802)+~P40(x89801)+~P24(f328(f328(f245(f885(a877,a871)),f328(f307(a1,a877,a110),x89801)),f328(f307(a1,a877,a110),x89802)))+P24(f328(f328(f245(f885(a1,a871)),x89801),x89802))
% 81.29/80.93 [8986]~E(f679(x89862,x89861),f680(x89862,x89861))+~P24(f328(f136(f878(x89861)),x89862))+P24(f328(f136(x89861),f328(f141(f878(x89861),f878(x89861),f127(x89861),f119(x89861)),x89862)))+P24(f328(f328(f330(f878(x89861)),f681(x89862,x89861)),f328(f171(f878(x89861)),x89862)))
% 81.29/80.93 [9029]~P24(f328(f136(x90291),f681(x90292,x90291)))+~P24(f328(f136(f878(x90291)),x90292))+P24(f328(f136(x90291),f328(f141(f878(x90291),f878(x90291),f127(x90291),f119(x90291)),x90292)))+P24(f328(f328(f330(f878(x90291)),f680(x90292,x90291)),f328(f171(f878(x90291)),x90292)))
% 81.29/80.93 [9030]~P24(f328(f136(x90301),f681(x90302,x90301)))+~P24(f328(f136(f878(x90301)),x90302))+P24(f328(f136(x90301),f328(f141(f878(x90301),f878(x90301),f127(x90301),f119(x90301)),x90302)))+P24(f328(f328(f330(f878(x90301)),f679(x90302,x90301)),f328(f171(f878(x90301)),x90302)))
% 81.29/80.93 [9105]~P24(f328(f136(f878(x91051)),x91052))+P24(f328(f136(x91051),f328(f141(f878(x91051),f878(x91051),f127(x91051),f119(x91051)),x91052)))+P24(f328(f328(f330(f878(x91051)),f680(x91052,x91051)),f328(f171(f878(x91051)),x91052)))+P24(f328(f328(f330(f878(x91051)),f681(x91052,x91051)),f328(f171(f878(x91051)),x91052)))
% 81.29/80.93 [9106]~P24(f328(f136(f878(x91061)),x91062))+P24(f328(f136(x91061),f328(f141(f878(x91061),f878(x91061),f127(x91061),f119(x91061)),x91062)))+P24(f328(f328(f330(f878(x91061)),f679(x91062,x91061)),f328(f171(f878(x91061)),x91062)))+P24(f328(f328(f330(f878(x91061)),f681(x91062,x91061)),f328(f171(f878(x91061)),x91062)))
% 81.29/80.93 [9119]~E(f328(f328(f107(f885(x91191,a871)),f328(f171(x91191),f680(x91192,x91191))),f328(f171(x91191),f679(x91192,x91191))),f193(f885(x91191,a871)))+~P24(f328(f136(x91191),f681(x91192,x91191)))+~P24(f328(f136(f878(x91191)),x91192))+P24(f328(f136(x91191),f328(f141(f878(x91191),f878(x91191),f127(x91191),f119(x91191)),x91192)))
% 81.29/80.93 [9181]~E(f328(f328(f107(f885(x91811,a871)),f328(f171(x91811),f680(x91812,x91811))),f328(f171(x91811),f679(x91812,x91811))),f193(f885(x91811,a871)))+~P24(f328(f136(f878(x91811)),x91812))+P24(f328(f136(x91811),f328(f141(f878(x91811),f878(x91811),f127(x91811),f119(x91811)),x91812)))+P24(f328(f328(f330(f878(x91811)),f681(x91812,x91811)),f328(f171(f878(x91811)),x91812)))
% 81.29/80.93 [9450]E(x94501,f2(a1))+E(x94502,f2(a1))+E(f328(f328(f87(a1,f884(a1,a1)),f328(f328(a225,x94502),x94501)),f328(f328(f18(a1,a1,f884(a1,a1)),f328(f328(f8(a1,f885(a1,f884(a1,a1)),a1),f257(a1,a1)),f328(f39(a1),x94502))),f328(f39(a1),x94501))),f223(x94502,x94501))+P24(f328(f328(f245(a1),x94501),f2(a1)))
% 81.29/80.93 [8217]~P96(x82172)+~P111(x82172)+~P24(f328(f328(f244(x82172),f328(f109(x82172),x82171)),f79(x82172)))+P24(f328(f328(f244(a1),x82171),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))
% 81.29/80.93 [8218]~P96(x82182)+~P111(x82182)+~P24(f328(f328(f245(x82182),f328(f109(x82182),x82181)),f79(x82182)))+P24(f328(f328(f245(a1),x82181),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))
% 81.29/80.93 [8496]~P111(x84961)+~P96(x84961)+P24(f328(f328(f244(x84961),f328(f109(x84961),x84962)),f79(x84961)))+~P24(f328(f328(f244(a1),x84962),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))
% 81.29/80.93 [8497]~P111(x84971)+~P96(x84971)+P24(f328(f328(f245(x84971),f328(f109(x84971),x84972)),f79(x84971)))+~P24(f328(f328(f245(a1),x84972),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))
% 81.29/80.93 [8694]~P96(x86942)+~P111(x86942)+~P24(f328(f328(f244(x86942),f79(x86942)),f328(f109(x86942),x86941)))+P24(f328(f328(f244(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),x86941))
% 81.29/80.93 [8695]~P96(x86952)+~P111(x86952)+~P24(f328(f328(f245(x86952),f79(x86952)),f328(f109(x86952),x86951)))+P24(f328(f328(f245(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),x86951))
% 81.29/80.93 [9068]~P111(x90681)+~P96(x90681)+P24(f328(f328(f244(x90681),f79(x90681)),f328(f109(x90681),x90682)))+~P24(f328(f328(f244(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),x90682))
% 81.29/80.93 [9069]~P111(x90691)+~P96(x90691)+P24(f328(f328(f245(x90691),f79(x90691)),f328(f109(x90691),x90692)))+~P24(f328(f328(f245(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),x90692))
% 81.29/80.93 [9579]~P139(x95792)+E(x95791,f79(x95792))+E(x95791,f328(f80(x95792),f79(x95792)))+~E(f328(f328(f258(x95792),x95791),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f79(x95792))
% 81.29/80.93 [9848]~P96(x98481)+~P63(x98481)+~P24(f328(f328(f245(x98481),f2(x98481)),x98482))+P24(f328(f328(f245(x98481),f2(x98481)),f328(f328(f286(x98481),x98482),f328(f109(x98481),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))))
% 81.29/80.93 [9913]~P96(x99131)+~P63(x99131)+P24(f328(f328(f245(x99131),f2(x99131)),x99132))+~P24(f328(f328(f245(x99131),f2(x99131)),f328(f328(f286(x99131),x99132),f328(f109(x99131),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))))
% 81.29/80.93 [10168]~P137(x101682)+E(x101681,f2(a1))+P24(f328(f328(f245(a1),x101681),f2(a1)))+E(f328(f328(f267(a1,a1,x101682),f328(f328(f7(a1,f885(a1,f885(x101682,x101682)),f885(a1,x101682)),f328(f328(f8(f885(f885(x101682,x101682),x101682),f885(f885(a1,f885(x101682,x101682)),f885(a1,x101682)),a1),f8(f885(x101682,x101682),x101682,a1)),f328(f328(f8(x101682,f885(f885(x101682,x101682),x101682),a1),f87(x101682,x101682)),f108(x101682)))),f328(f328(f7(a1,f885(x101682,x101682),f885(x101682,x101682)),f328(f328(f8(f885(x101682,f885(x101682,x101682)),f885(f885(x101682,x101682),f885(x101682,x101682)),a1),f18(x101682,x101682,x101682)),f328(f328(f7(a1,f885(x101682,x101682),f885(x101682,f885(x101682,x101682))),f328(f328(f8(f885(x101682,f885(x101682,x101682)),f885(f885(x101682,x101682),f885(x101682,f885(x101682,x101682))),a1),f8(x101682,f885(x101682,x101682),x101682)),f328(f328(f8(a871,f885(x101682,f885(x101682,x101682)),a1),f102(x101682)),f328(f328(f7(a1,a1,a871),a325),f2(a1))))),f328(f328(f18(x101682,x101682,x101682),f81(x101682)),f5(x101682))))),f328(f328(f7(x101682,x101682,x101682),f328(f328(f8(x101682,f885(x101682,x101682),x101682),f81(x101682)),f328(f328(f18(x101682,x101682,x101682),f81(x101682)),f5(x101682)))),f79(x101682))))),f46(x101681,f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f108(x101682),x101681))
% 81.29/80.93 [5223]~P60(x52233)+~P36(x52233,x52232,f56(x52233))+E(x52231,f735(x52232,x52233))+~P24(f328(x52232,x52231))
% 81.29/80.93 [5383]~P60(x53831)+P36(x53831,x53832,f56(x53831))+~E(f736(x53832,x53831,x53833),x53833)+~P24(f328(x53832,x53833))
% 81.29/80.93 [4861]~P93(x48613)+~P96(x48613)+E(x48611,x48612)+~E(f328(f109(x48613),x48611),f328(f109(x48613),x48612))
% 81.29/80.93 [6005]~P60(x60051)+P36(x60051,x60052,f56(x60051))+~P24(f328(x60052,x60053))+P24(f328(x60052,f736(x60052,x60051,x60053)))
% 81.29/80.93 [6015]~P24(f328(x60151,x60152))+~P24(f328(x60151,x60153))+~P24(f328(f328(f244(a877),x60153),f838(x60152,x60151)))+P24(f328(x60151,f2(a877)))
% 81.29/80.93 [6435]P146(x64352,x64351,x64353)+E(x64351,f2(a1))+P24(f328(f328(f244(a1),f2(a1)),f815(x64353,x64351,x64352)))+P24(f328(f328(f245(a1),x64351),f2(a1)))
% 81.29/80.93 [6436]P145(x64362,x64361,x64363)+E(x64361,f2(a1))+P24(f328(f328(f244(a1),f2(a1)),f818(x64363,x64361,x64362)))+P24(f328(f328(f245(a1),x64361),f2(a1)))
% 81.29/80.93 [6557]P145(x65571,x65572,x65573)+~P24(f328(x65571,x65573))+P24(f328(f328(f244(a1),f2(a1)),f818(x65573,x65572,x65571)))+P24(f328(f328(f245(a1),x65572),f2(a1)))
% 81.29/80.93 [6584]P146(x65841,x65842,x65843)+P24(f328(f328(f244(a1),f2(a1)),f815(x65843,x65842,x65841)))+~P24(f328(x65841,f2(a1)))+P24(f328(f328(f245(a1),x65842),f2(a1)))
% 81.29/80.93 [6612]P146(x66122,x66121,x66123)+E(x66121,f2(a1))+~P24(f328(x66122,f816(x66123,x66121,x66122)))+P24(f328(f328(f245(a1),x66121),f2(a1)))
% 81.29/80.93 [6613]P145(x66132,x66131,x66133)+E(x66131,f2(a1))+~P24(f328(x66132,f818(x66133,x66131,x66132)))+P24(f328(f328(f245(a1),x66131),f2(a1)))
% 81.29/80.93 [6714]~P106(x67141)+~P27(x67141)+~P24(f328(f328(f245(x67141),x67142),f40(x67141,x67143)))+P24(f328(f328(f245(x67141),x67142),f722(x67143,x67142,x67141)))
% 81.29/80.93 [6723]P145(x67231,x67232,x67233)+~P24(f328(x67231,x67233))+~P24(f328(x67231,f818(x67233,x67232,x67231)))+P24(f328(f328(f245(a1),x67232),f2(a1)))
% 81.29/80.93 [6755]P146(x67551,x67552,x67553)+~P24(f328(x67551,f816(x67553,x67552,x67551)))+~P24(f328(x67551,f2(a1)))+P24(f328(f328(f245(a1),x67552),f2(a1)))
% 81.29/80.93 [7005]P146(x70052,x70051,x70053)+E(x70051,f2(a1))+P24(f328(f328(f244(a1),f2(a1)),f815(x70053,x70051,x70052)))+P24(f328(f328(f245(a1),x70051),f814(x70053,x70051,x70052)))
% 81.29/80.93 [7006]P145(x70062,x70061,x70063)+E(x70061,f2(a1))+P24(f328(f328(f244(a1),f2(a1)),f818(x70063,x70061,x70062)))+P24(f328(f328(f245(a1),x70061),f823(x70063,x70061,x70062)))
% 81.29/80.93 [7123]P145(x71231,x71232,x71233)+~P24(f328(x71231,x71233))+P24(f328(f328(f244(a1),f2(a1)),f818(x71233,x71232,x71231)))+P24(f328(f328(f245(a1),x71232),f823(x71233,x71232,x71231)))
% 81.29/80.93 [7142]P146(x71421,x71422,x71423)+P24(f328(f328(f244(a1),f2(a1)),f815(x71423,x71422,x71421)))+P24(f328(f328(f245(a1),x71422),f814(x71423,x71422,x71421)))+~P24(f328(x71421,f2(a1)))
% 81.29/80.93 [7175]P146(x71752,x71751,x71753)+E(x71751,f2(a1))+~P24(f328(x71752,f816(x71753,x71751,x71752)))+P24(f328(f328(f245(a1),x71751),f814(x71753,x71751,x71752)))
% 81.29/80.93 [7176]P145(x71762,x71761,x71763)+E(x71761,f2(a1))+~P24(f328(x71762,f818(x71763,x71761,x71762)))+P24(f328(f328(f245(a1),x71761),f823(x71763,x71761,x71762)))
% 81.29/80.93 [7217]P146(x72172,x72171,x72173)+E(x72171,f2(a1))+P24(f328(f328(f244(a1),f2(a1)),f815(x72173,x72171,x72172)))+~P24(f328(x72172,f817(x72173,x72171,x72172)))
% 81.29/80.93 [7218]P145(x72182,x72181,x72183)+E(x72181,f2(a1))+P24(f328(f328(f244(a1),f2(a1)),f818(x72183,x72181,x72182)))+~P24(f328(x72182,f823(x72183,x72181,x72182)))
% 81.29/80.93 [7306]P145(x73061,x73062,x73063)+~P24(f328(x73061,x73063))+~P24(f328(x73061,f818(x73063,x73062,x73061)))+P24(f328(f328(f245(a1),x73062),f823(x73063,x73062,x73061)))
% 81.29/80.93 [7322]P146(x73221,x73222,x73223)+~P24(f328(x73221,f816(x73223,x73222,x73221)))+P24(f328(f328(f245(a1),x73222),f814(x73223,x73222,x73221)))+~P24(f328(x73221,f2(a1)))
% 81.29/80.93 [7326]P145(x73261,x73262,x73263)+~P24(f328(x73261,x73263))+P24(f328(f328(f244(a1),f2(a1)),f818(x73263,x73262,x73261)))+~P24(f328(x73261,f823(x73263,x73262,x73261)))
% 81.29/80.93 [7344]P146(x73441,x73442,x73443)+P24(f328(f328(f244(a1),f2(a1)),f815(x73443,x73442,x73441)))+~P24(f328(x73441,f817(x73443,x73442,x73441)))+~P24(f328(x73441,f2(a1)))
% 81.29/80.93 [7368]P146(x73682,x73681,x73683)+E(x73681,f2(a1))+~P24(f328(x73682,f816(x73683,x73681,x73682)))+~P24(f328(x73682,f817(x73683,x73681,x73682)))
% 81.29/80.93 [7369]P145(x73692,x73691,x73693)+E(x73691,f2(a1))+~P24(f328(x73692,f818(x73693,x73691,x73692)))+~P24(f328(x73692,f823(x73693,x73691,x73692)))
% 81.29/80.93 [7462]P145(x74621,x74622,x74623)+~P24(f328(x74621,x74623))+~P24(f328(x74621,f818(x74623,x74622,x74621)))+~P24(f328(x74621,f823(x74623,x74622,x74621)))
% 81.29/80.93 [7479]P146(x74791,x74792,x74793)+~P24(f328(x74791,f816(x74793,x74792,x74791)))+~P24(f328(x74791,f817(x74793,x74792,x74791)))+~P24(f328(x74791,f2(a1)))
% 81.29/80.93 [7524]P146(x75242,x75241,x75243)+E(x75241,f2(a1))+P24(f328(f328(f244(a1),f2(a1)),f815(x75243,x75241,x75242)))+P24(f328(f328(f244(a1),f814(x75243,x75241,x75242)),f2(a1)))
% 81.29/80.93 [7525]P145(x75252,x75251,x75253)+E(x75251,f2(a1))+P24(f328(f328(f244(a1),f2(a1)),f818(x75253,x75251,x75252)))+P24(f328(f328(f244(a1),f823(x75253,x75251,x75252)),f2(a1)))
% 81.29/80.93 [7526]~P137(x75261)+~P24(f328(f328(f330(x75261),x75263),f115(x75261)))+~P24(f328(f328(f330(x75261),x75262),f115(x75261)))+P24(f328(f328(f330(x75261),f328(f328(f22(x75261),x75262),x75263)),f115(x75261)))
% 81.29/80.93 [7527]~P137(x75271)+~P24(f328(f328(f330(x75271),x75273),f115(x75271)))+~P24(f328(f328(f330(x75271),x75272),f115(x75271)))+P24(f328(f328(f330(x75271),f328(f328(f81(x75271),x75272),x75273)),f115(x75271)))
% 81.29/80.93 [7528]~P141(x75281)+~P24(f328(f328(f330(x75281),x75283),f191(x75281)))+~P24(f328(f328(f330(x75281),x75282),f191(x75281)))+P24(f328(f328(f330(x75281),f328(f328(f81(x75281),x75282),x75283)),f191(x75281)))
% 81.29/80.93 [7529]~P137(x75291)+~P24(f328(f328(f330(x75291),x75293),f115(x75291)))+~P24(f328(f328(f330(x75291),x75292),f115(x75291)))+P24(f328(f328(f330(x75291),f328(f328(f82(x75291),x75292),x75293)),f115(x75291)))
% 81.29/80.93 [7530]~P141(x75301)+~P24(f328(f328(f330(x75301),x75303),f191(x75301)))+~P24(f328(f328(f330(x75301),x75302),f191(x75301)))+P24(f328(f328(f330(x75301),f328(f328(f82(x75301),x75302),x75303)),f191(x75301)))
% 81.29/80.93 [7531]~P89(x75311)+~P24(f328(f328(f244(x75311),x75313),f2(x75311)))+~P24(f328(f328(f244(x75311),x75312),f2(x75311)))+P24(f328(f328(f244(x75311),f328(f328(f81(x75311),x75312),x75313)),f2(x75311)))
% 81.29/80.93 [7532]~P89(x75321)+~P24(f328(f328(f244(x75321),x75323),f2(x75321)))+~P24(f328(f328(f245(x75321),x75322),f2(x75321)))+P24(f328(f328(f245(x75321),f328(f328(f81(x75321),x75322),x75323)),f2(x75321)))
% 81.29/80.93 [7533]~P89(x75331)+~P24(f328(f328(f244(x75331),x75332),f2(x75331)))+~P24(f328(f328(f245(x75331),x75333),f2(x75331)))+P24(f328(f328(f245(x75331),f328(f328(f81(x75331),x75332),x75333)),f2(x75331)))
% 81.29/80.93 [7534]~P89(x75341)+~P24(f328(f328(f245(x75341),x75343),f2(x75341)))+~P24(f328(f328(f245(x75341),x75342),f2(x75341)))+P24(f328(f328(f245(x75341),f328(f328(f81(x75341),x75342),x75343)),f2(x75341)))
% 81.29/80.93 [7560]P146(x75603,x75601,x75602)+E(x75601,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x75601),f816(x75602,x75601,x75603))),f815(x75602,x75601,x75603)),x75602)+P24(f328(f328(f245(a1),x75601),f2(a1)))
% 81.29/80.93 [7561]P145(x75613,x75611,x75612)+E(x75611,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x75611),f819(x75612,x75611,x75613))),f818(x75612,x75611,x75613)),x75612)+P24(f328(f328(f245(a1),x75611),f2(a1)))
% 81.29/80.93 [7643]P145(x76431,x76432,x76433)+~P24(f328(x76431,x76433))+P24(f328(f328(f244(a1),f2(a1)),f818(x76433,x76432,x76431)))+P24(f328(f328(f244(a1),f823(x76433,x76432,x76431)),f2(a1)))
% 81.29/80.93 [7672]P146(x76721,x76722,x76723)+P24(f328(f328(f244(a1),f2(a1)),f815(x76723,x76722,x76721)))+~P24(f328(x76721,f2(a1)))+P24(f328(f328(f244(a1),f814(x76723,x76722,x76721)),f2(a1)))
% 81.29/80.93 [7681]P145(x76813,x76811,x76812)+~P24(f328(x76813,x76812))+E(f328(f328(f81(a1),f328(f328(f82(a1),x76811),f819(x76812,x76811,x76813))),f818(x76812,x76811,x76813)),x76812)+P24(f328(f328(f245(a1),x76811),f2(a1)))
% 81.29/80.93 [7687]P146(x76872,x76871,x76873)+E(x76871,f2(a1))+~P24(f328(x76872,f816(x76873,x76871,x76872)))+P24(f328(f328(f244(a1),f814(x76873,x76871,x76872)),f2(a1)))
% 81.29/80.93 [7688]P145(x76882,x76881,x76883)+E(x76881,f2(a1))+~P24(f328(x76882,f818(x76883,x76881,x76882)))+P24(f328(f328(f244(a1),f823(x76883,x76881,x76882)),f2(a1)))
% 81.29/80.93 [7693]P146(x76933,x76931,x76932)+E(f328(f328(f81(a1),f328(f328(f82(a1),x76931),f816(x76932,x76931,x76933))),f815(x76932,x76931,x76933)),x76932)+~P24(f328(x76933,f2(a1)))+P24(f328(f328(f245(a1),x76931),f2(a1)))
% 81.29/80.93 [7748]P145(x77481,x77482,x77483)+~P24(f328(x77481,x77483))+~P24(f328(x77481,f818(x77483,x77482,x77481)))+P24(f328(f328(f244(a1),f823(x77483,x77482,x77481)),f2(a1)))
% 81.29/80.93 [7752]P146(x77521,x77522,x77523)+~P24(f328(x77521,f816(x77523,x77522,x77521)))+~P24(f328(x77521,f2(a1)))+P24(f328(f328(f244(a1),f814(x77523,x77522,x77521)),f2(a1)))
% 81.29/80.93 [7821]~P123(x78211)+~P24(f328(f328(f244(x78211),f328(f328(f82(x78211),x78213),x78212)),f2(x78211)))+P24(f328(f328(f244(x78211),x78212),f2(x78211)))+P24(f328(f328(f244(x78211),x78213),f2(x78211)))
% 81.29/80.93 [7822]~P63(x78221)+~P24(f328(f328(f244(x78221),f328(f328(f286(x78221),x78223),x78222)),f2(x78221)))+P24(f328(f328(f244(x78221),x78222),f2(x78221)))+P24(f328(f328(f244(x78221),x78223),f2(x78221)))
% 81.29/80.93 [7823]~P63(x78231)+~P24(f328(f328(f245(x78231),f328(f328(f286(x78231),x78233),x78232)),f2(x78231)))+P24(f328(f328(f245(x78231),x78232),f2(x78231)))+P24(f328(f328(f245(x78231),x78233),f2(x78231)))
% 81.29/80.93 [7937]P146(x79373,x79371,x79372)+E(x79371,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x79371),f816(x79372,x79371,x79373))),f815(x79372,x79371,x79373)),x79372)+P24(f328(f328(f245(a1),x79371),f814(x79372,x79371,x79373)))
% 81.29/80.93 [7938]P145(x79383,x79381,x79382)+E(x79381,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x79381),f819(x79382,x79381,x79383))),f818(x79382,x79381,x79383)),x79382)+P24(f328(f328(f245(a1),x79381),f823(x79382,x79381,x79383)))
% 81.29/80.93 [7950]P146(x79503,x79501,x79502)+E(x79501,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x79501),f817(x79502,x79501,x79503))),f814(x79502,x79501,x79503)),x79502)+P24(f328(f328(f244(a1),f2(a1)),f815(x79502,x79501,x79503)))
% 81.29/80.93 [7951]P145(x79513,x79511,x79512)+E(x79511,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x79511),f820(x79512,x79511,x79513))),f823(x79512,x79511,x79513)),x79512)+P24(f328(f328(f244(a1),f2(a1)),f818(x79512,x79511,x79513)))
% 81.29/80.93 [7995]P145(x79953,x79951,x79952)+~P24(f328(x79953,x79952))+E(f328(f328(f81(a1),f328(f328(f82(a1),x79951),f819(x79952,x79951,x79953))),f818(x79952,x79951,x79953)),x79952)+P24(f328(f328(f245(a1),x79951),f823(x79952,x79951,x79953)))
% 81.29/80.93 [8007]P146(x80073,x80071,x80072)+E(f328(f328(f81(a1),f328(f328(f82(a1),x80071),f816(x80072,x80071,x80073))),f815(x80072,x80071,x80073)),x80072)+P24(f328(f328(f245(a1),x80071),f814(x80072,x80071,x80073)))+~P24(f328(x80073,f2(a1)))
% 81.29/80.93 [8013]P145(x80133,x80131,x80132)+~P24(f328(x80133,x80132))+E(f328(f328(f81(a1),f328(f328(f82(a1),x80131),f820(x80132,x80131,x80133))),f823(x80132,x80131,x80133)),x80132)+P24(f328(f328(f244(a1),f2(a1)),f818(x80132,x80131,x80133)))
% 81.29/80.93 [8021]P146(x80213,x80211,x80212)+E(f328(f328(f81(a1),f328(f328(f82(a1),x80211),f817(x80212,x80211,x80213))),f814(x80212,x80211,x80213)),x80212)+P24(f328(f328(f244(a1),f2(a1)),f815(x80212,x80211,x80213)))+~P24(f328(x80213,f2(a1)))
% 81.29/80.93 [8032]P146(x80323,x80321,x80322)+E(x80321,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x80321),f816(x80322,x80321,x80323))),f815(x80322,x80321,x80323)),x80322)+~P24(f328(x80323,f817(x80322,x80321,x80323)))
% 81.29/80.93 [8033]P145(x80333,x80331,x80332)+E(x80331,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x80331),f819(x80332,x80331,x80333))),f818(x80332,x80331,x80333)),x80332)+~P24(f328(x80333,f823(x80332,x80331,x80333)))
% 81.29/80.93 [8034]P146(x80343,x80341,x80342)+E(x80341,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x80341),f817(x80342,x80341,x80343))),f814(x80342,x80341,x80343)),x80342)+~P24(f328(x80343,f816(x80342,x80341,x80343)))
% 81.29/80.93 [8035]P145(x80353,x80351,x80352)+E(x80351,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x80351),f820(x80352,x80351,x80353))),f823(x80352,x80351,x80353)),x80352)+~P24(f328(x80353,f818(x80352,x80351,x80353)))
% 81.29/80.93 [8093]P145(x80933,x80931,x80932)+~P24(f328(x80933,x80932))+E(f328(f328(f81(a1),f328(f328(f82(a1),x80931),f819(x80932,x80931,x80933))),f818(x80932,x80931,x80933)),x80932)+~P24(f328(x80933,f823(x80932,x80931,x80933)))
% 81.29/80.93 [8094]P145(x80943,x80941,x80942)+~P24(f328(x80943,x80942))+E(f328(f328(f81(a1),f328(f328(f82(a1),x80941),f820(x80942,x80941,x80943))),f823(x80942,x80941,x80943)),x80942)+~P24(f328(x80943,f818(x80942,x80941,x80943)))
% 81.29/80.93 [8104]P146(x81043,x81041,x81042)+E(f328(f328(f81(a1),f328(f328(f82(a1),x81041),f816(x81042,x81041,x81043))),f815(x81042,x81041,x81043)),x81042)+~P24(f328(x81043,f817(x81042,x81041,x81043)))+~P24(f328(x81043,f2(a1)))
% 81.29/80.93 [8105]P146(x81053,x81051,x81052)+E(f328(f328(f81(a1),f328(f328(f82(a1),x81051),f817(x81052,x81051,x81053))),f814(x81052,x81051,x81053)),x81052)+~P24(f328(x81053,f816(x81052,x81051,x81053)))+~P24(f328(x81053,f2(a1)))
% 81.29/80.93 [8210]P146(x82103,x82101,x82102)+E(x82101,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x82101),f816(x82102,x82101,x82103))),f815(x82102,x82101,x82103)),x82102)+P24(f328(f328(f244(a1),f814(x82102,x82101,x82103)),f2(a1)))
% 81.29/80.93 [8211]P145(x82113,x82111,x82112)+E(x82111,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x82111),f819(x82112,x82111,x82113))),f818(x82112,x82111,x82113)),x82112)+P24(f328(f328(f244(a1),f823(x82112,x82111,x82113)),f2(a1)))
% 81.29/80.93 [8251]P145(x82513,x82511,x82512)+~P24(f328(x82513,x82512))+E(f328(f328(f81(a1),f328(f328(f82(a1),x82511),f819(x82512,x82511,x82513))),f818(x82512,x82511,x82513)),x82512)+P24(f328(f328(f244(a1),f823(x82512,x82511,x82513)),f2(a1)))
% 81.29/80.93 [8256]P146(x82563,x82561,x82562)+E(f328(f328(f81(a1),f328(f328(f82(a1),x82561),f816(x82562,x82561,x82563))),f815(x82562,x82561,x82563)),x82562)+~P24(f328(x82563,f2(a1)))+P24(f328(f328(f244(a1),f814(x82562,x82561,x82563)),f2(a1)))
% 81.29/80.93 [8385]P146(x83853,x83851,x83852)+E(x83851,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x83851),f817(x83852,x83851,x83853))),f814(x83852,x83851,x83853)),x83852)+E(f328(f328(f81(a1),f328(f328(f82(a1),x83851),f816(x83852,x83851,x83853))),f815(x83852,x83851,x83853)),x83852)
% 81.29/80.93 [8386]P145(x83863,x83861,x83862)+E(x83861,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x83861),f820(x83862,x83861,x83863))),f823(x83862,x83861,x83863)),x83862)+E(f328(f328(f81(a1),f328(f328(f82(a1),x83861),f819(x83862,x83861,x83863))),f818(x83862,x83861,x83863)),x83862)
% 81.29/80.93 [8409]P145(x84093,x84091,x84092)+~P24(f328(x84093,x84092))+E(f328(f328(f81(a1),f328(f328(f82(a1),x84091),f820(x84092,x84091,x84093))),f823(x84092,x84091,x84093)),x84092)+E(f328(f328(f81(a1),f328(f328(f82(a1),x84091),f819(x84092,x84091,x84093))),f818(x84092,x84091,x84093)),x84092)
% 81.29/80.93 [8421]P146(x84213,x84211,x84212)+E(f328(f328(f81(a1),f328(f328(f82(a1),x84211),f817(x84212,x84211,x84213))),f814(x84212,x84211,x84213)),x84212)+E(f328(f328(f81(a1),f328(f328(f82(a1),x84211),f816(x84212,x84211,x84213))),f815(x84212,x84211,x84213)),x84212)+~P24(f328(x84213,f2(a1)))
% 81.29/80.93 [9073]~P123(x90731)+~E(x90733,f2(x90731))+~E(x90732,f2(x90731))+P24(f328(f328(f244(x90731),f328(f328(f81(x90731),f328(f328(f82(x90731),x90732),x90732)),f328(f328(f82(x90731),x90733),x90733))),f2(x90731)))
% 81.29/80.93 [10119]~P111(x101191)+~E(x101193,f2(x101191))+~E(x101192,f2(x101191))+P24(f328(f328(f244(x101191),f328(f328(f81(x101191),f328(f328(f258(x101191),x101192),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x101191),x101193),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))),f2(x101191)))
% 81.29/80.93 [4809]~E(x48093,x48091)+~P120(x48092)+E(x48091,f2(x48092))+E(f328(f328(f286(x48092),x48093),x48091),f79(x48092))
% 81.29/80.93 [4862]~P79(x48621)+~E(x48623,f193(x48621))+~E(x48622,f193(x48621))+E(f328(f328(f116(x48621),x48622),x48623),f193(x48621))
% 81.29/80.93 [4863]~P101(x48631)+~E(x48633,f252(x48631))+~E(x48632,f252(x48631))+E(f328(f328(f107(x48631),x48632),x48633),f252(x48631))
% 81.29/80.93 [4950]~P120(x49503)+E(x49501,x49502)+E(x49502,f2(x49503))+~E(f328(f328(f286(x49503),x49501),x49502),f79(x49503))
% 81.29/80.93 [4969]~P125(x49692)+E(x49691,f2(x49692))+E(x49693,f2(x49692))+~E(f328(f328(f82(x49692),x49693),x49691),f2(x49692))
% 81.29/80.93 [4970]~P138(x49702)+E(x49701,f2(x49702))+E(x49703,f2(x49702))+~E(f328(f328(f82(x49702),x49703),x49701),f2(x49702))
% 81.29/80.93 [5350]~P119(x53503)+E(x53501,x53502)+E(x53501,f328(f80(x53503),x53502))+~E(f328(f328(f82(x53503),x53501),x53501),f328(f328(f82(x53503),x53502),x53502))
% 81.29/80.93 [5390]~P97(x53901)+E(f328(f80(x53901),x53902),x53903)+~E(f328(f328(f116(x53901),x53902),x53903),f252(x53901))+~E(f328(f328(f107(x53901),x53902),x53903),f193(x53901))
% 81.29/80.93 [5469]~P111(x54693)+E(x54691,x54692)+P24(f328(f328(f245(x54693),x54692),x54691))+P24(f328(f328(f245(x54693),x54691),x54692))
% 81.29/80.93 [5470]~P106(x54703)+E(x54701,x54702)+P24(f328(f328(f245(x54703),x54702),x54701))+P24(f328(f328(f245(x54703),x54701),x54702))
% 81.29/80.93 [5471]~E(x54712,x54713)+~P106(x54711)+P24(f328(f328(f245(x54711),x54712),x54713))+P24(f328(f328(f244(x54711),x54712),x54713))
% 81.29/80.93 [5723]~P108(x57233)+E(x57231,x57232)+~P24(f328(f328(f244(x57233),x57232),x57231))+P24(f328(f328(f245(x57233),x57232),x57231))
% 81.29/80.93 [5725]~P106(x57253)+E(x57251,x57252)+~P24(f328(f328(f244(x57253),x57251),x57252))+P24(f328(f328(f245(x57253),x57251),x57252))
% 81.29/80.93 [5731]~P108(x57313)+E(x57311,x57312)+~P24(f328(f328(f244(x57313),x57311),x57312))+P24(f328(f328(f245(x57313),x57311),x57312))
% 81.29/80.93 [5833]P145(x58331,x58332,x58333)+~P24(f328(x58331,x58333))+P24(f328(f328(f245(a1),x58332),f2(a1)))+P24(f328(f328(f245(a1),f2(a1)),x58332))
% 81.29/80.93 [5880]P146(x58801,x58802,x58803)+~P24(f328(x58801,f2(a1)))+P24(f328(f328(f245(a1),x58802),f2(a1)))+P24(f328(f328(f245(a1),f2(a1)),x58802))
% 81.29/80.93 [5884]~P78(x58841)+E(f328(f328(f116(x58841),x58842),f11(x58841,x58843)),x58842)+~P24(f328(f62(x58841),x58843))+~P24(f328(f328(f330(x58841),x58842),x58843))
% 81.29/80.93 [5885]~P78(x58851)+E(f328(f328(f107(x58851),x58852),f10(x58851,x58853)),x58852)+~P24(f328(f62(x58851),x58853))+~P24(f328(f328(f330(x58851),x58852),x58853))
% 81.29/80.93 [5921]~P78(x59211)+E(f328(f328(f116(x59211),x59212),f10(x59211,x59213)),f10(x59211,x59213))+~P24(f328(f62(x59211),x59213))+~P24(f328(f328(f330(x59211),x59212),x59213))
% 81.29/80.93 [5922]~P78(x59221)+E(f328(f328(f107(x59221),x59222),f11(x59221,x59223)),f11(x59221,x59223))+~P24(f328(f62(x59221),x59223))+~P24(f328(f328(f330(x59221),x59222),x59223))
% 81.29/80.93 [5923]~P106(x59231)+E(f328(f328(f242(x59231),x59232),f14(x59231,x59233)),f14(x59231,x59233))+~P24(f328(f62(x59231),x59233))+~P24(f328(f328(f330(x59231),x59232),x59233))
% 81.29/80.93 [5924]~P106(x59241)+E(f328(f328(f243(x59241),x59242),f15(x59241,x59243)),f15(x59241,x59243))+~P24(f328(f62(x59241),x59243))+~P24(f328(f328(f330(x59241),x59242),x59243))
% 81.29/80.93 [5969]E(x59691,x59692)+~P108(x59693)+~P24(f328(f328(f244(x59693),x59692),x59691))+~P24(f328(f328(f244(x59693),x59691),x59692))
% 81.29/80.93 [6110]~P105(x61101)+P24(f328(f328(f245(x61101),x61103),x61102))+~P24(f328(f328(f244(x61101),x61103),x61102))+P24(f328(f328(f244(x61101),x61102),x61103))
% 81.29/80.93 [6131]~P106(x61311)+~P24(f328(f62(x61311),x61313))+P24(f328(f328(f244(x61311),x61312),f15(x61311,x61313)))+~P24(f328(f328(f330(x61311),x61312),x61313))
% 81.29/80.93 [6184]~P106(x61841)+E(f328(f328(f242(x61841),x61842),f13(x61841,f243(x61841),x61843)),x61842)+~P24(f328(f62(x61841),x61843))+~P24(f328(f328(f330(x61841),x61842),x61843))
% 81.29/80.93 [6185]~P106(x61851)+E(f328(f328(f243(x61851),x61852),f12(x61851,f242(x61851),x61853)),x61852)+~P24(f328(f62(x61851),x61853))+~P24(f328(f328(f330(x61851),x61852),x61853))
% 81.29/80.93 [6322]E(x63221,x63222)+~E(f328(f328(f22(a877),x63221),x63223),f328(f328(f22(a877),x63222),x63223))+~P24(f328(f328(f244(a877),x63223),x63221))+~P24(f328(f328(f244(a877),x63223),x63222))
% 81.29/80.93 [6351]~P106(x63511)+~P24(f328(f62(x63511),x63512))+~P24(f328(f328(f330(x63511),x63513),x63512))+P24(f328(f328(f244(x63511),f14(x63511,x63512)),x63513))
% 81.29/80.93 [6414]P146(x64142,x64141,x64143)+E(x64141,f2(a1))+P24(f328(f328(f245(a1),x64141),f814(x64143,x64141,x64142)))+P24(f328(f328(f245(a1),f2(a1)),x64141))
% 81.29/80.93 [6415]P145(x64152,x64151,x64153)+E(x64151,f2(a1))+P24(f328(f328(f245(a1),x64151),f823(x64153,x64151,x64152)))+P24(f328(f328(f245(a1),f2(a1)),x64151))
% 81.29/80.93 [6416]~P106(x64161)+E(f328(f328(f242(x64161),x64162),f12(x64161,f242(x64161),x64163)),f12(x64161,f242(x64161),x64163))+~P24(f328(f62(x64161),x64163))+~P24(f328(f328(f330(x64161),x64162),x64163))
% 81.29/80.93 [6417]~P106(x64171)+E(f328(f328(f243(x64171),x64172),f13(x64171,f243(x64171),x64173)),f13(x64171,f243(x64171),x64173))+~P24(f328(f62(x64171),x64173))+~P24(f328(f328(f330(x64171),x64172),x64173))
% 81.29/80.93 [6423]~P24(f328(x64231,x64232))+P24(f328(x64231,f371(x64232,x64231,x64233)))+P24(f328(x64231,f2(a877)))+~P24(f328(f328(f245(a877),x64232),x64233))
% 81.29/80.93 [6478]~P24(f328(x64781,x64782))+~P24(f328(f62(x64783),x64782))+P24(f328(x64781,f562(x64781,x64782,x64783)))+P24(f328(x64781,f193(f885(x64783,a871))))
% 81.29/80.93 [6491]~P111(x64911)+~P96(x64911)+P24(f328(f328(f244(x64911),f328(f109(x64911),x64912)),f328(f109(x64911),x64913)))+~P24(f328(f328(f244(a1),x64912),x64913))
% 81.29/80.93 [6492]~P111(x64921)+~P96(x64921)+P24(f328(f328(f245(x64921),f328(f109(x64921),x64922)),f328(f109(x64921),x64923)))+~P24(f328(f328(f245(a1),x64922),x64923))
% 81.29/80.93 [6495]~P24(f328(x64951,x64953))+~P24(f328(f62(x64952),x64953))+P24(f328(f62(x64952),f562(x64951,x64953,x64952)))+P24(f328(x64951,f193(f885(x64952,a871))))
% 81.29/80.93 [6529]P145(x65291,x65292,x65293)+~P24(f328(x65291,x65293))+P24(f328(f328(f245(a1),x65292),f823(x65293,x65292,x65291)))+P24(f328(f328(f245(a1),f2(a1)),x65292))
% 81.29/80.93 [6564]P146(x65641,x65642,x65643)+P24(f328(f328(f245(a1),x65642),f814(x65643,x65642,x65641)))+~P24(f328(x65641,f2(a1)))+P24(f328(f328(f245(a1),f2(a1)),x65642))
% 81.29/80.93 [6595]~P107(x65951)+~P94(x65951)+E(f328(f328(f242(x65951),f328(f109(x65951),x65952)),f328(f109(x65951),x65953)),f328(f109(x65951),x65953))+P24(f328(f328(f244(x65951),f328(f109(x65951),x65952)),f328(f109(x65951),x65953)))
% 81.29/80.93 [6596]~P107(x65961)+~P94(x65961)+E(f328(f328(f243(x65961),f328(f109(x65961),x65962)),f328(f109(x65961),x65963)),f328(f109(x65961),x65962))+P24(f328(f328(f244(x65961),f328(f109(x65961),x65962)),f328(f109(x65961),x65963)))
% 81.29/80.93 [6654]P146(x66542,x66541,x66543)+E(x66541,f2(a1))+~P24(f328(x66542,f817(x66543,x66541,x66542)))+P24(f328(f328(f245(a1),f2(a1)),x66541))
% 81.29/80.93 [6655]P145(x66552,x66551,x66553)+E(x66551,f2(a1))+~P24(f328(x66552,f823(x66553,x66551,x66552)))+P24(f328(f328(f245(a1),f2(a1)),x66551))
% 81.29/80.93 [6659]P24(f328(x66591,x66592))+~P24(f328(f62(x66593),x66592))+P24(f328(x66591,f381(x66591,x66592,x66593)))+~P24(f328(x66591,f193(f885(x66593,a871))))
% 81.29/80.93 [6679]P24(f328(x66791,x66792))+P24(f328(f62(x66793),f381(x66791,x66792,x66793)))+~P24(f328(f62(x66793),x66792))+~P24(f328(x66791,f193(f885(x66793,a871))))
% 81.29/80.93 [6744]P145(x67441,x67442,x67443)+~P24(f328(x67441,x67443))+~P24(f328(x67441,f823(x67443,x67442,x67441)))+P24(f328(f328(f245(a1),f2(a1)),x67442))
% 81.29/80.93 [6774]P146(x67741,x67742,x67743)+~P24(f328(x67741,f817(x67743,x67742,x67741)))+~P24(f328(x67741,f2(a1)))+P24(f328(f328(f245(a1),f2(a1)),x67742))
% 81.29/80.93 [6881]~P96(x68813)+~P111(x68813)+~P24(f328(f328(f244(x68813),f328(f109(x68813),x68811)),f328(f109(x68813),x68812)))+P24(f328(f328(f244(a1),x68811),x68812))
% 81.29/80.93 [6882]~P96(x68823)+~P111(x68823)+~P24(f328(f328(f245(x68823),f328(f109(x68823),x68821)),f328(f109(x68823),x68822)))+P24(f328(f328(f245(a1),x68821),x68822))
% 81.29/80.93 [6908]~P106(x69081)+~P29(x69081,x69083)+P29(x69081,f328(f328(f150(x69081),x69082),x69083))+~P24(f328(f328(f244(x69081),x69082),f641(x69083,x69082,x69081)))
% 81.29/80.93 [6909]~P106(x69091)+~P29(x69091,x69093)+P29(x69091,f328(f328(f150(x69091),x69092),x69093))+~P24(f328(f328(f244(x69091),x69092),f642(x69093,x69092,x69091)))
% 81.29/80.93 [6910]~P106(x69101)+~P29(x69101,x69103)+P29(x69101,f328(f328(f150(x69101),x69102),x69103))+~P24(f328(f328(f244(x69101),x69102),f740(x69102,x69103,x69101)))
% 81.29/80.93 [6994]P146(x69942,x69941,x69943)+E(x69941,f2(a1))+P24(f328(f328(f245(a1),x69941),f2(a1)))+P24(f328(f328(f245(a1),f815(x69943,x69941,x69942)),x69941))
% 81.29/80.93 [6995]P145(x69952,x69951,x69953)+E(x69951,f2(a1))+P24(f328(f328(f245(a1),x69951),f2(a1)))+P24(f328(f328(f245(a1),f818(x69953,x69951,x69952)),x69951))
% 81.29/80.93 [7036]P146(x70362,x70361,x70363)+E(x70361,f2(a1))+P24(f328(f328(f244(a1),f814(x70363,x70361,x70362)),f2(a1)))+P24(f328(f328(f245(a1),f2(a1)),x70361))
% 81.29/80.93 [7037]P145(x70372,x70371,x70373)+E(x70371,f2(a1))+P24(f328(f328(f244(a1),f823(x70373,x70371,x70372)),f2(a1)))+P24(f328(f328(f245(a1),f2(a1)),x70371))
% 81.29/80.93 [7059]~P106(x70591)+~P29(x70591,x70593)+E(f328(f328(f147(x70591,x70591,f5(x70591)),x70592),f169(x70591,x70592,x70593)),x70593)+~P24(f328(f328(f330(x70591),x70592),f328(f171(x70591),x70593)))
% 81.29/80.93 [7106]P145(x71061,x71062,x71063)+~P24(f328(x71061,x71063))+P24(f328(f328(f245(a1),x71062),f2(a1)))+P24(f328(f328(f245(a1),f818(x71063,x71062,x71061)),x71062))
% 81.29/80.93 [7112]~P107(x71121)+~P94(x71121)+E(f328(f328(f242(x71121),f328(f109(x71121),x71122)),f328(f109(x71121),x71123)),f328(f109(x71121),x71122))+~P24(f328(f328(f244(x71121),f328(f109(x71121),x71122)),f328(f109(x71121),x71123)))
% 81.29/80.93 [7113]~P107(x71131)+~P94(x71131)+E(f328(f328(f243(x71131),f328(f109(x71131),x71132)),f328(f109(x71131),x71133)),f328(f109(x71131),x71133))+~P24(f328(f328(f244(x71131),f328(f109(x71131),x71132)),f328(f109(x71131),x71133)))
% 81.29/80.93 [7127]P146(x71271,x71272,x71273)+~P24(f328(x71271,f2(a1)))+P24(f328(f328(f245(a1),x71272),f2(a1)))+P24(f328(f328(f245(a1),f815(x71273,x71272,x71271)),x71272))
% 81.29/80.93 [7135]P145(x71351,x71352,x71353)+~P24(f328(x71351,x71353))+P24(f328(f328(f244(a1),f823(x71353,x71352,x71351)),f2(a1)))+P24(f328(f328(f245(a1),f2(a1)),x71352))
% 81.29/80.93 [7159]P146(x71591,x71592,x71593)+~P24(f328(x71591,f2(a1)))+P24(f328(f328(f244(a1),f814(x71593,x71592,x71591)),f2(a1)))+P24(f328(f328(f245(a1),f2(a1)),x71592))
% 81.29/80.93 [7187]~P24(f328(x71871,x71872))+P24(f328(x71871,f2(a877)))+~P24(f328(f328(f245(a877),x71872),x71873))+P24(f328(f328(f245(a877),f371(x71872,x71871,x71873)),x71873))
% 81.29/80.93 [7204]~P106(x72041)+~P29(x72041,x72043)+P29(x72041,f328(f328(f150(x72041),x72042),x72043))+P24(f328(f328(f330(x72041),f641(x72043,x72042,x72041)),f328(f171(x72041),x72043)))
% 81.29/80.93 [7205]~P106(x72051)+~P29(x72051,x72053)+P29(x72051,f328(f328(f150(x72051),x72052),x72053))+P24(f328(f328(f330(x72051),f642(x72053,x72052,x72051)),f328(f171(x72051),x72053)))
% 81.29/80.93 [7206]~P106(x72061)+~P29(x72061,x72063)+P29(x72061,f328(f328(f150(x72061),x72062),x72063))+P24(f328(f328(f330(x72061),f740(x72062,x72063,x72061)),f328(f171(x72061),x72063)))
% 81.29/80.93 [7310]~P106(x73101)+~P27(x73101)+~P24(f328(f328(f245(x73101),x73103),f40(x73101,x73102)))+P24(f328(f328(f330(x73101),f722(x73102,x73103,x73101)),x73102))
% 81.29/80.93 [7477]~P106(x74771)+~P27(x74771)+~P24(f328(f328(f245(x74771),f41(x74771,x74773)),x74772))+P24(f328(f328(f330(x74771),f379(x74772,x74773,x74771)),x74773))
% 81.29/80.93 [7478]~P106(x74781)+~P27(x74781)+~P24(f328(f328(f245(x74781),f41(x74781,x74783)),x74782))+P24(f328(f328(f245(x74781),f379(x74782,x74783,x74781)),x74782))
% 81.29/80.93 [7490]P146(x74902,x74901,x74903)+E(x74901,f2(a1))+P24(f328(f328(f245(a1),x74901),f814(x74903,x74901,x74902)))+P24(f328(f328(f245(a1),f815(x74903,x74901,x74902)),x74901))
% 81.29/80.93 [7491]P145(x74912,x74911,x74913)+E(x74911,f2(a1))+P24(f328(f328(f245(a1),x74911),f823(x74913,x74911,x74912)))+P24(f328(f328(f245(a1),f818(x74913,x74911,x74912)),x74911))
% 81.29/80.93 [7581]P146(x75813,x75811,x75812)+E(x75811,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x75811),f817(x75812,x75811,x75813))),f814(x75812,x75811,x75813)),x75812)+P24(f328(f328(f245(a1),f2(a1)),x75811))
% 81.29/80.93 [7582]P145(x75823,x75821,x75822)+E(x75821,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x75821),f820(x75822,x75821,x75823))),f823(x75822,x75821,x75823)),x75822)+P24(f328(f328(f245(a1),f2(a1)),x75821))
% 81.29/80.93 [7585]~P131(x75851)+~P24(f328(f328(f244(x75851),x75853),f2(x75851)))+P24(f328(f328(f244(x75851),f328(f328(f82(x75851),x75852),x75853)),f2(x75851)))+~P24(f328(f328(f244(x75851),f2(x75851)),x75852))
% 81.29/80.93 [7587]~P131(x75871)+~P24(f328(f328(f244(x75871),x75872),f2(x75871)))+P24(f328(f328(f244(x75871),f328(f328(f82(x75871),x75872),x75873)),f2(x75871)))+~P24(f328(f328(f244(x75871),f2(x75871)),x75873))
% 81.29/80.93 [7588]~P123(x75881)+~P24(f328(f328(f244(x75881),x75883),f2(x75881)))+P24(f328(f328(f244(x75881),f328(f328(f82(x75881),x75882),x75883)),f2(x75881)))+~P24(f328(f328(f244(x75881),f2(x75881)),x75882))
% 81.29/80.93 [7589]~P123(x75891)+~P24(f328(f328(f244(x75891),x75892),f2(x75891)))+P24(f328(f328(f244(x75891),f328(f328(f82(x75891),x75892),x75893)),f2(x75891)))+~P24(f328(f328(f244(x75891),f2(x75891)),x75893))
% 81.29/80.93 [7590]~P63(x75901)+~P24(f328(f328(f244(x75901),x75903),f2(x75901)))+P24(f328(f328(f244(x75901),f328(f328(f286(x75901),x75902),x75903)),f2(x75901)))+~P24(f328(f328(f244(x75901),f2(x75901)),x75902))
% 81.29/80.93 [7591]~P63(x75911)+~P24(f328(f328(f244(x75911),x75912),f2(x75911)))+P24(f328(f328(f244(x75911),f328(f328(f286(x75911),x75912),x75913)),f2(x75911)))+~P24(f328(f328(f244(x75911),f2(x75911)),x75913))
% 81.29/80.93 [7592]~P64(x75921)+~P24(f328(f328(f244(x75921),x75922),f2(x75921)))+P24(f328(f328(f244(x75921),f328(f328(f286(x75921),x75922),x75923)),f2(x75921)))+~P24(f328(f328(f245(x75921),f2(x75921)),x75923))
% 81.29/80.93 [7593]~P64(x75931)+~P24(f328(f328(f245(x75931),x75933),f2(x75931)))+P24(f328(f328(f244(x75931),f328(f328(f286(x75931),x75932),x75933)),f2(x75931)))+~P24(f328(f328(f244(x75931),f2(x75931)),x75932))
% 81.29/80.93 [7595]~P127(x75951)+~P24(f328(f328(f245(x75951),x75953),f2(x75951)))+P24(f328(f328(f245(x75951),f328(f328(f82(x75951),x75952),x75953)),f2(x75951)))+~P24(f328(f328(f245(x75951),f2(x75951)),x75952))
% 81.29/80.93 [7596]~P127(x75961)+~P24(f328(f328(f245(x75961),x75962),f2(x75961)))+P24(f328(f328(f245(x75961),f328(f328(f82(x75961),x75962),x75963)),f2(x75961)))+~P24(f328(f328(f245(x75961),f2(x75961)),x75963))
% 81.29/80.93 [7597]~P63(x75971)+~P24(f328(f328(f245(x75971),x75973),f2(x75971)))+P24(f328(f328(f245(x75971),f328(f328(f286(x75971),x75972),x75973)),f2(x75971)))+~P24(f328(f328(f245(x75971),f2(x75971)),x75972))
% 81.29/80.93 [7598]~P63(x75981)+~P24(f328(f328(f245(x75981),x75982),f2(x75981)))+P24(f328(f328(f245(x75981),f328(f328(f286(x75981),x75982),x75983)),f2(x75981)))+~P24(f328(f328(f245(x75981),f2(x75981)),x75983))
% 81.29/80.93 [7599]~P64(x75991)+~P24(f328(f328(f245(x75991),x75993),f2(x75991)))+P24(f328(f328(f245(x75991),f328(f328(f286(x75991),x75992),x75993)),f2(x75991)))+~P24(f328(f328(f245(x75991),f2(x75991)),x75992))
% 81.29/80.93 [7600]~P64(x76001)+~P24(f328(f328(f245(x76001),x76002),f2(x76001)))+P24(f328(f328(f245(x76001),f328(f328(f286(x76001),x76002),x76003)),f2(x76001)))+~P24(f328(f328(f245(x76001),f2(x76001)),x76003))
% 81.29/80.93 [7615]P145(x76151,x76152,x76153)+~P24(f328(x76151,x76153))+P24(f328(f328(f245(a1),x76152),f823(x76153,x76152,x76151)))+P24(f328(f328(f245(a1),f818(x76153,x76152,x76151)),x76152))
% 81.29/80.93 [7628]P146(x76281,x76282,x76283)+P24(f328(f328(f245(a1),x76282),f814(x76283,x76282,x76281)))+~P24(f328(x76281,f2(a1)))+P24(f328(f328(f245(a1),f815(x76283,x76282,x76281)),x76282))
% 81.29/80.93 [7678]P146(x76782,x76781,x76783)+E(x76781,f2(a1))+~P24(f328(x76782,f817(x76783,x76781,x76782)))+P24(f328(f328(f245(a1),f815(x76783,x76781,x76782)),x76781))
% 81.29/80.93 [7679]P145(x76792,x76791,x76793)+E(x76791,f2(a1))+~P24(f328(x76792,f823(x76793,x76791,x76792)))+P24(f328(f328(f245(a1),f818(x76793,x76791,x76792)),x76791))
% 81.29/80.93 [7690]P145(x76903,x76901,x76902)+~P24(f328(x76903,x76902))+E(f328(f328(f81(a1),f328(f328(f82(a1),x76901),f820(x76902,x76901,x76903))),f823(x76902,x76901,x76903)),x76902)+P24(f328(f328(f245(a1),f2(a1)),x76901))
% 81.29/80.93 [7708]P146(x77083,x77081,x77082)+E(f328(f328(f81(a1),f328(f328(f82(a1),x77081),f817(x77082,x77081,x77083))),f814(x77082,x77081,x77083)),x77082)+~P24(f328(x77083,f2(a1)))+P24(f328(f328(f245(a1),f2(a1)),x77081))
% 81.29/80.93 [7733]~P24(f328(x77331,x77333))+~P24(f328(f62(x77332),x77333))+P24(f328(f328(f330(x77332),f553(x77331,x77333,x77332)),f562(x77331,x77333,x77332)))+P24(f328(x77331,f193(f885(x77332,a871))))
% 81.29/80.93 [7744]P145(x77441,x77442,x77443)+~P24(f328(x77441,x77443))+~P24(f328(x77441,f823(x77443,x77442,x77441)))+P24(f328(f328(f245(a1),f818(x77443,x77442,x77441)),x77442))
% 81.29/80.93 [7749]P146(x77491,x77492,x77493)+~P24(f328(x77491,f817(x77493,x77492,x77491)))+~P24(f328(x77491,f2(a1)))+P24(f328(f328(f245(a1),f815(x77493,x77492,x77491)),x77492))
% 81.29/80.93 [7852]~P123(x78521)+~P24(f328(f328(f244(x78521),f328(f328(f82(x78521),x78523),x78522)),f2(x78521)))+P24(f328(f328(f244(x78521),x78522),f2(x78521)))+P24(f328(f328(f244(x78521),f2(x78521)),x78522))
% 81.29/80.93 [7853]~P123(x78531)+~P24(f328(f328(f244(x78531),f328(f328(f82(x78531),x78532),x78533)),f2(x78531)))+P24(f328(f328(f244(x78531),x78532),f2(x78531)))+P24(f328(f328(f244(x78531),f2(x78531)),x78532))
% 81.29/80.93 [7854]~P63(x78541)+~P24(f328(f328(f244(x78541),f328(f328(f286(x78541),x78543),x78542)),f2(x78541)))+P24(f328(f328(f244(x78541),x78542),f2(x78541)))+P24(f328(f328(f244(x78541),f2(x78541)),x78542))
% 81.29/80.93 [7855]~P63(x78551)+~P24(f328(f328(f244(x78551),f328(f328(f286(x78551),x78552),x78553)),f2(x78551)))+P24(f328(f328(f244(x78551),x78552),f2(x78551)))+P24(f328(f328(f244(x78551),f2(x78551)),x78552))
% 81.29/80.93 [7856]~P63(x78561)+~P24(f328(f328(f245(x78561),f328(f328(f286(x78561),x78563),x78562)),f2(x78561)))+P24(f328(f328(f245(x78561),x78562),f2(x78561)))+P24(f328(f328(f245(x78561),f2(x78561)),x78562))
% 81.29/80.93 [7857]~P63(x78571)+~P24(f328(f328(f245(x78571),f328(f328(f286(x78571),x78572),x78573)),f2(x78571)))+P24(f328(f328(f245(x78571),x78572),f2(x78571)))+P24(f328(f328(f245(x78571),f2(x78571)),x78572))
% 81.29/80.93 [7881]~P123(x78811)+~P24(f328(f328(f244(x78811),f328(f328(f82(x78811),x78812),x78813)),f2(x78811)))+P24(f328(f328(f244(x78811),f2(x78811)),x78812))+P24(f328(f328(f244(x78811),f2(x78811)),x78813))
% 81.29/80.93 [7882]~P63(x78821)+~P24(f328(f328(f244(x78821),f328(f328(f286(x78821),x78822),x78823)),f2(x78821)))+P24(f328(f328(f244(x78821),f2(x78821)),x78822))+P24(f328(f328(f244(x78821),f2(x78821)),x78823))
% 81.29/80.93 [7883]~P63(x78831)+~P24(f328(f328(f245(x78831),f328(f328(f286(x78831),x78832),x78833)),f2(x78831)))+P24(f328(f328(f245(x78831),f2(x78831)),x78832))+P24(f328(f328(f245(x78831),f2(x78831)),x78833))
% 81.29/80.93 [7904]P146(x79042,x79041,x79043)+E(x79041,f2(a1))+P24(f328(f328(f244(a1),f814(x79043,x79041,x79042)),f2(a1)))+P24(f328(f328(f245(a1),f815(x79043,x79041,x79042)),x79041))
% 81.29/80.93 [7905]P145(x79052,x79051,x79053)+E(x79051,f2(a1))+P24(f328(f328(f244(a1),f823(x79053,x79051,x79052)),f2(a1)))+P24(f328(f328(f245(a1),f818(x79053,x79051,x79052)),x79051))
% 81.29/80.93 [7912]~P110(x79121)+~P24(f328(f328(f245(x79121),x79122),f79(x79121)))+P24(f328(f328(f245(x79121),f328(f328(f258(x79121),x79122),f328(a118,x79123))),f79(x79121)))+~P24(f328(f328(f245(x79121),f2(x79121)),x79122))
% 81.29/80.93 [7967]~P106(x79671)+~E(x79673,f119(x79671))+~P29(x79671,f328(f168(x79671),x79673))+E(f328(f141(x79671,x79671,f328(f7(x79671,x79671,x79671),f243(x79671)),x79672),f328(f168(x79671),x79673)),x79672)
% 81.29/80.93 [7969]P145(x79691,x79692,x79693)+~P24(f328(x79691,x79693))+P24(f328(f328(f244(a1),f823(x79693,x79692,x79691)),f2(a1)))+P24(f328(f328(f245(a1),f818(x79693,x79692,x79691)),x79692))
% 81.29/80.93 [7979]P146(x79791,x79792,x79793)+~P24(f328(x79791,f2(a1)))+P24(f328(f328(f244(a1),f814(x79793,x79792,x79791)),f2(a1)))+P24(f328(f328(f245(a1),f815(x79793,x79792,x79791)),x79792))
% 81.29/80.93 [8205]P146(x82053,x82051,x82052)+E(x82051,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x82051),f817(x82052,x82051,x82053))),f814(x82052,x82051,x82053)),x82052)+P24(f328(f328(f245(a1),f815(x82052,x82051,x82053)),x82051))
% 81.29/80.93 [8206]P145(x82063,x82061,x82062)+E(x82061,f2(a1))+E(f328(f328(f81(a1),f328(f328(f82(a1),x82061),f820(x82062,x82061,x82063))),f823(x82062,x82061,x82063)),x82062)+P24(f328(f328(f245(a1),f818(x82062,x82061,x82063)),x82061))
% 81.29/80.93 [8242]P145(x82423,x82421,x82422)+~P24(f328(x82423,x82422))+E(f328(f328(f81(a1),f328(f328(f82(a1),x82421),f820(x82422,x82421,x82423))),f823(x82422,x82421,x82423)),x82422)+P24(f328(f328(f245(a1),f818(x82422,x82421,x82423)),x82421))
% 81.29/80.93 [8243]~P74(x82431)+~P75(x82431)+~P40(x82433)+E(f328(f328(f6(a877,x82431),f328(f328(f8(a1,x82431,a877),x82432),f106(a1))),f328(f307(a1,a877,a110),x82433)),f328(f328(f6(a1,x82431),x82432),x82433))
% 81.29/80.93 [8244]~P74(x82441)+~P75(x82441)+~P40(x82443)+E(f328(f328(f9(a877,x82441),f328(f328(f8(a1,x82441,a877),x82442),f106(a1))),f328(f307(a1,a877,a110),x82443)),f328(f328(f9(a1,x82441),x82442),x82443))
% 81.29/80.93 [8253]P146(x82533,x82531,x82532)+E(f328(f328(f81(a1),f328(f328(f82(a1),x82531),f817(x82532,x82531,x82533))),f814(x82532,x82531,x82533)),x82532)+~P24(f328(x82533,f2(a1)))+P24(f328(f328(f245(a1),f815(x82532,x82531,x82533)),x82531))
% 81.29/80.93 [8272]~E(x82722,f2(a877))+~E(f328(f256(a877,a877),x82723),f2(a877))+~E(x82721,f328(f328(f81(a877),f328(f328(f82(a877),f328(f256(a877,a877),x82723)),x82722)),f328(f266(a877,a877),x82723)))+P24(f328(f48(x82721,x82722),x82723))
% 81.29/80.93 [8326]P24(f328(x83261,x83262))+~P24(f328(f328(f330(x83263),f386(x83261,x83262,x83263)),f381(x83261,x83262,x83263)))+~P24(f328(f62(x83263),x83262))+~P24(f328(x83261,f193(f885(x83263,a871))))
% 81.29/80.93 [8943]P24(f328(x89431,x89432))+~P24(f328(f62(x89433),x89432))+~P24(f328(x89431,f328(f328(f306(x89433),f386(x89431,x89432,x89433)),f381(x89431,x89432,x89433))))+~P24(f328(x89431,f193(f885(x89433,a871))))
% 81.29/80.93 [9177]P24(f328(f328(f244(a1),x91771),f2(a1)))+~P24(f328(f328(f245(a1),f328(f328(f81(a1),f328(f328(f82(a1),x91773),x91771)),x91772)),f2(a1)))+~P24(f328(f328(f244(a1),f2(a1)),x91772))+~P24(f328(f328(f245(a1),f2(a1)),x91773))
% 81.29/80.93 [5794]~P78(x57942)+E(x57941,f193(f885(x57942,a871)))+~P24(f328(f62(x57942),x57941))+E(f10(x57942,f328(f328(f306(x57942),x57943),x57941)),f328(f328(f116(x57942),x57943),f10(x57942,x57941)))
% 81.29/80.93 [5795]~P78(x57952)+E(x57951,f193(f885(x57952,a871)))+~P24(f328(f62(x57952),x57951))+E(f11(x57952,f328(f328(f306(x57952),x57953),x57951)),f328(f328(f107(x57952),x57953),f11(x57952,x57951)))
% 81.29/80.93 [5796]~P106(x57962)+E(x57961,f193(f885(x57962,a871)))+~P24(f328(f62(x57962),x57961))+E(f14(x57962,f328(f328(f306(x57962),x57963),x57961)),f328(f328(f242(x57962),x57963),f14(x57962,x57961)))
% 81.29/80.93 [5797]~P106(x57972)+E(x57971,f193(f885(x57972,a871)))+~P24(f328(f62(x57972),x57971))+E(f15(x57972,f328(f328(f306(x57972),x57973),x57971)),f328(f328(f243(x57972),x57973),f15(x57972,x57971)))
% 81.29/80.93 [6107]~P123(x61071)+~E(x61073,f2(x61071))+~E(x61072,f2(x61071))+E(f328(f328(f81(x61071),f328(f328(f82(x61071),x61072),x61072)),f328(f328(f82(x61071),x61073),x61073)),f2(x61071))
% 81.29/80.93 [6178]~P98(x61782)+E(x61781,f193(f885(x61782,a871)))+~P24(f328(f62(x61782),x61781))+E(f328(f64(x61782,f82(x61782)),f328(f328(f306(x61782),x61783),x61781)),f328(f328(f82(x61782),x61783),f328(f64(x61782,f82(x61782)),x61781)))
% 81.29/80.93 [6301]~P106(x63012)+E(x63011,f193(f885(x63012,a871)))+~P24(f328(f62(x63012),x63011))+E(f12(x63012,f242(x63012),f328(f328(f306(x63012),x63013),x63011)),f328(f328(f242(x63012),x63013),f12(x63012,f242(x63012),x63011)))
% 81.29/80.93 [6302]~P106(x63022)+E(x63021,f193(f885(x63022,a871)))+~P24(f328(f62(x63022),x63021))+E(f13(x63022,f243(x63022),f328(f328(f306(x63022),x63023),x63021)),f328(f328(f243(x63022),x63023),f13(x63022,f243(x63022),x63021)))
% 81.29/80.93 [6809]~P71(x68091)+~P24(f328(f62(x68091),x68093))+E(f328(f64(x68091,f82(x68091)),f328(f328(f306(x68091),x68092),x68093)),f328(f328(f65(x68091,x68091,f82(x68091)),x68092),x68093))+P24(f328(f328(f330(x68091),x68092),x68093))
% 81.29/80.93 [6886]~E(f328(f328(f81(a1),x68862),f328(f328(f82(a1),x68863),x68861)),x68863)+~P24(f328(f328(f245(a1),f2(a1)),x68863))+P24(f328(f328(f244(a1),f79(a1)),x68861))+~P24(f328(f328(f245(a1),x68862),x68863))
% 81.29/80.93 [6915]~E(f328(f328(f81(a1),x69152),f328(f328(f82(a1),x69153),x69151)),x69153)+P24(f328(f328(f244(a1),x69151),f79(a1)))+~P24(f328(f328(f244(a1),f2(a1)),x69152))+~P24(f328(f328(f245(a1),f2(a1)),x69153))
% 81.29/80.93 [6931]E(x69311,f2(a877))+~P24(f328(f48(x69313,x69311),x69312))+~P24(f328(f328(f245(a877),f2(a877)),x69311))+P24(f328(f328(f245(a877),f328(f266(a877,a877),x69312)),x69311))
% 81.29/80.93 [6961]~P135(x69611)+~P24(f328(f328(f244(x69611),x69612),f2(x69611)))+~P24(f328(f328(f244(x69611),x69613),f2(x69611)))+E(f328(f328(f82(x69611),f328(f76(x69611),x69612)),f328(f76(x69611),x69613)),f328(f76(x69611),f328(f328(f82(x69611),x69612),x69613)))
% 81.29/80.93 [7013]~P135(x70131)+~P24(f328(f328(f244(x70131),x70132),f2(x70131)))+E(f328(f328(f82(x70131),f328(f76(x70131),x70132)),f328(f76(x70131),x70133)),f328(f76(x70131),f328(f328(f82(x70131),x70132),x70133)))+~P24(f328(f328(f244(x70131),f2(x70131)),x70133))
% 81.29/80.93 [7014]~P135(x70141)+~P24(f328(f328(f244(x70141),x70143),f2(x70141)))+E(f328(f328(f82(x70141),f328(f76(x70141),x70142)),f328(f76(x70141),x70143)),f328(f76(x70141),f328(f328(f82(x70141),x70142),x70143)))+~P24(f328(f328(f244(x70141),f2(x70141)),x70142))
% 81.29/80.93 [7068]~P135(x70681)+E(f328(f328(f82(x70681),f328(f76(x70681),x70682)),f328(f76(x70681),x70683)),f328(f76(x70681),f328(f328(f82(x70681),x70682),x70683)))+~P24(f328(f328(f244(x70681),f2(x70681)),x70682))+~P24(f328(f328(f244(x70681),f2(x70681)),x70683))
% 81.29/80.93 [7085]~P132(x70851)+~P24(f328(f328(f244(x70851),x70853),f2(x70851)))+~P24(f328(f328(f244(x70851),x70852),f2(x70851)))+P24(f328(f328(f244(x70851),f2(x70851)),f328(f328(f82(x70851),x70852),x70853)))
% 81.29/80.93 [7086]~P123(x70861)+~P24(f328(f328(f244(x70861),x70863),f2(x70861)))+~P24(f328(f328(f244(x70861),x70862),f2(x70861)))+P24(f328(f328(f244(x70861),f2(x70861)),f328(f328(f82(x70861),x70862),x70863)))
% 81.29/80.93 [7087]~P63(x70871)+~P24(f328(f328(f244(x70871),x70873),f2(x70871)))+~P24(f328(f328(f244(x70871),x70872),f2(x70871)))+P24(f328(f328(f244(x70871),f2(x70871)),f328(f328(f286(x70871),x70872),x70873)))
% 81.29/80.93 [7088]~P64(x70881)+~P24(f328(f328(f245(x70881),x70883),f2(x70881)))+~P24(f328(f328(f244(x70881),x70882),f2(x70881)))+P24(f328(f328(f244(x70881),f2(x70881)),f328(f328(f286(x70881),x70882),x70883)))
% 81.29/80.93 [7089]~P123(x70891)+~P24(f328(f328(f245(x70891),x70893),f2(x70891)))+~P24(f328(f328(f245(x70891),x70892),f2(x70891)))+P24(f328(f328(f245(x70891),f2(x70891)),f328(f328(f82(x70891),x70892),x70893)))
% 81.29/80.93 [7090]~P63(x70901)+~P24(f328(f328(f245(x70901),x70903),f2(x70901)))+~P24(f328(f328(f245(x70901),x70902),f2(x70901)))+P24(f328(f328(f245(x70901),f2(x70901)),f328(f328(f286(x70901),x70902),x70903)))
% 81.29/80.93 [7091]~P64(x70911)+~P24(f328(f328(f245(x70911),x70913),f2(x70911)))+~P24(f328(f328(f245(x70911),x70912),f2(x70911)))+P24(f328(f328(f245(x70911),f2(x70911)),f328(f328(f286(x70911),x70912),x70913)))
% 81.29/80.93 [7092]~P110(x70921)+~P24(f328(f328(f245(a877),f2(a877)),x70923))+~P24(f328(f328(f245(x70921),f79(x70921)),x70922))+P24(f328(f328(f245(x70921),f79(x70921)),f328(f328(f258(x70921),x70922),x70923)))
% 81.29/80.93 [7189]~P131(x71891)+~P24(f328(f328(f244(x71891),f2(x71891)),x71893))+~P24(f328(f328(f244(x71891),f2(x71891)),x71892))+P24(f328(f328(f244(x71891),f2(x71891)),f328(f328(f82(x71891),x71892),x71893)))
% 81.29/80.93 [7190]~P132(x71901)+~P24(f328(f328(f244(x71901),f2(x71901)),x71903))+~P24(f328(f328(f244(x71901),f2(x71901)),x71902))+P24(f328(f328(f244(x71901),f2(x71901)),f328(f328(f82(x71901),x71902),x71903)))
% 81.29/80.93 [7191]~P123(x71911)+~P24(f328(f328(f244(x71911),f2(x71911)),x71913))+~P24(f328(f328(f244(x71911),f2(x71911)),x71912))+P24(f328(f328(f244(x71911),f2(x71911)),f328(f328(f82(x71911),x71912),x71913)))
% 81.29/80.93 [7192]~P63(x71921)+~P24(f328(f328(f244(x71921),f2(x71921)),x71923))+~P24(f328(f328(f244(x71921),f2(x71921)),x71922))+P24(f328(f328(f244(x71921),f2(x71921)),f328(f328(f286(x71921),x71922),x71923)))
% 81.29/80.93 [7193]~P64(x71931)+~P24(f328(f328(f245(x71931),f2(x71931)),x71933))+~P24(f328(f328(f244(x71931),f2(x71931)),x71932))+P24(f328(f328(f244(x71931),f2(x71931)),f328(f328(f286(x71931),x71932),x71933)))
% 81.29/80.93 [7194]~P110(x71941)+~P24(f328(f328(f245(x71941),f79(x71941)),x71943))+~P24(f328(f328(f245(x71941),f79(x71941)),x71942))+P24(f328(f328(f245(x71941),f79(x71941)),f328(f328(f82(x71941),x71942),x71943)))
% 81.29/80.93 [7197]~P89(x71971)+~P24(f328(f328(f245(x71971),f2(x71971)),x71973))+~P24(f328(f328(f245(x71971),f2(x71971)),x71972))+P24(f328(f328(f245(x71971),f2(x71971)),f328(f328(f81(x71971),x71972),x71973)))
% 81.29/80.93 [7198]~P127(x71981)+~P24(f328(f328(f245(x71981),f2(x71981)),x71983))+~P24(f328(f328(f245(x71981),f2(x71981)),x71982))+P24(f328(f328(f245(x71981),f2(x71981)),f328(f328(f82(x71981),x71982),x71983)))
% 81.29/80.93 [7199]~P63(x71991)+~P24(f328(f328(f245(x71991),f2(x71991)),x71993))+~P24(f328(f328(f245(x71991),f2(x71991)),x71992))+P24(f328(f328(f245(x71991),f2(x71991)),f328(f328(f286(x71991),x71992),x71993)))
% 81.29/80.93 [7200]~P64(x72001)+~P24(f328(f328(f245(x72001),f2(x72001)),x72003))+~P24(f328(f328(f245(x72001),f2(x72001)),x72002))+P24(f328(f328(f245(x72001),f2(x72001)),f328(f328(f286(x72001),x72002),x72003)))
% 81.29/80.93 [7271]~P78(x72711)+~P24(f328(f62(x72711),x72713))+E(f10(x72711,f328(f328(f306(x72711),x72712),x72713)),x72712)+~E(f328(f328(f22(f885(x72711,a871)),x72713),f328(f328(f306(x72711),x72712),f193(f885(x72711,a871)))),f193(f885(x72711,a871)))
% 81.29/80.93 [7272]~P78(x72721)+~P24(f328(f62(x72721),x72723))+E(f11(x72721,f328(f328(f306(x72721),x72722),x72723)),x72722)+~E(f328(f328(f22(f885(x72721,a871)),x72723),f328(f328(f306(x72721),x72722),f193(f885(x72721,a871)))),f193(f885(x72721,a871)))
% 81.29/80.93 [7273]~P106(x72731)+~P24(f328(f62(x72731),x72733))+E(f14(x72731,f328(f328(f306(x72731),x72732),x72733)),x72732)+~E(f328(f328(f22(f885(x72731,a871)),x72733),f328(f328(f306(x72731),x72732),f193(f885(x72731,a871)))),f193(f885(x72731,a871)))
% 81.29/80.93 [7274]~P106(x72741)+~P24(f328(f62(x72741),x72743))+E(f15(x72741,f328(f328(f306(x72741),x72742),x72743)),x72742)+~E(f328(f328(f22(f885(x72741,a871)),x72743),f328(f328(f306(x72741),x72742),f193(f885(x72741,a871)))),f193(f885(x72741,a871)))
% 81.29/80.93 [7275]~P123(x72751)+P24(f328(f328(f244(x72751),x72752),f2(x72751)))+P24(f328(f328(f244(x72751),f2(x72751)),x72753))+~P24(f328(f328(f244(x72751),f2(x72751)),f328(f328(f82(x72751),x72753),x72752)))
% 81.29/80.93 [7276]~P123(x72761)+P24(f328(f328(f244(x72761),x72762),f2(x72761)))+P24(f328(f328(f244(x72761),f2(x72761)),x72763))+~P24(f328(f328(f244(x72761),f2(x72761)),f328(f328(f82(x72761),x72762),x72763)))
% 81.29/80.93 [7277]~P63(x72771)+P24(f328(f328(f244(x72771),x72772),f2(x72771)))+P24(f328(f328(f244(x72771),f2(x72771)),x72773))+~P24(f328(f328(f244(x72771),f2(x72771)),f328(f328(f286(x72771),x72773),x72772)))
% 81.29/80.93 [7278]~P63(x72781)+P24(f328(f328(f244(x72781),x72782),f2(x72781)))+P24(f328(f328(f244(x72781),f2(x72781)),x72783))+~P24(f328(f328(f244(x72781),f2(x72781)),f328(f328(f286(x72781),x72782),x72783)))
% 81.29/80.93 [7279]~P123(x72791)+P24(f328(f328(f244(x72791),x72792),f2(x72791)))+P24(f328(f328(f244(x72791),f2(x72791)),x72792))+~P24(f328(f328(f244(x72791),f2(x72791)),f328(f328(f82(x72791),x72793),x72792)))
% 81.29/80.93 [7280]~P123(x72801)+P24(f328(f328(f244(x72801),x72802),f2(x72801)))+P24(f328(f328(f244(x72801),f2(x72801)),x72802))+~P24(f328(f328(f244(x72801),f2(x72801)),f328(f328(f82(x72801),x72802),x72803)))
% 81.29/80.93 [7281]~P63(x72811)+P24(f328(f328(f244(x72811),x72812),f2(x72811)))+P24(f328(f328(f244(x72811),f2(x72811)),x72812))+~P24(f328(f328(f244(x72811),f2(x72811)),f328(f328(f286(x72811),x72813),x72812)))
% 81.29/80.93 [7282]~P63(x72821)+P24(f328(f328(f244(x72821),x72822),f2(x72821)))+P24(f328(f328(f244(x72821),f2(x72821)),x72822))+~P24(f328(f328(f244(x72821),f2(x72821)),f328(f328(f286(x72821),x72822),x72823)))
% 81.29/80.93 [7283]~P63(x72831)+P24(f328(f328(f245(x72831),x72832),f2(x72831)))+P24(f328(f328(f245(x72831),f2(x72831)),x72833))+~P24(f328(f328(f245(x72831),f2(x72831)),f328(f328(f286(x72831),x72833),x72832)))
% 81.29/80.93 [7284]~P63(x72841)+P24(f328(f328(f245(x72841),x72842),f2(x72841)))+P24(f328(f328(f245(x72841),f2(x72841)),x72843))+~P24(f328(f328(f245(x72841),f2(x72841)),f328(f328(f286(x72841),x72842),x72843)))
% 81.29/80.93 [7285]~P63(x72851)+P24(f328(f328(f245(x72851),x72852),f2(x72851)))+P24(f328(f328(f245(x72851),f2(x72851)),x72852))+~P24(f328(f328(f245(x72851),f2(x72851)),f328(f328(f286(x72851),x72853),x72852)))
% 81.29/80.93 [7286]~P63(x72861)+P24(f328(f328(f245(x72861),x72862),f2(x72861)))+P24(f328(f328(f245(x72861),f2(x72861)),x72862))+~P24(f328(f328(f245(x72861),f2(x72861)),f328(f328(f286(x72861),x72862),x72863)))
% 81.29/80.93 [7376]~E(f328(f328(f107(f885(x73761,a871)),f328(f171(x73761),x73762)),f328(f171(x73761),x73763)),f193(f885(x73761,a871)))+~P24(f328(f136(x73761),x73763))+~P24(f328(f136(x73761),x73762))+P24(f328(f136(x73761),f328(f328(f127(x73761),x73762),x73763)))
% 81.29/80.93 [7377]~P106(x73771)+~P24(f328(f62(x73771),x73773))+E(f12(x73771,f242(x73771),f328(f328(f306(x73771),x73772),x73773)),x73772)+~E(f328(f328(f22(f885(x73771,a871)),x73773),f328(f328(f306(x73771),x73772),f193(f885(x73771,a871)))),f193(f885(x73771,a871)))
% 81.29/80.93 [7378]~P106(x73781)+~P24(f328(f62(x73781),x73783))+E(f13(x73781,f243(x73781),f328(f328(f306(x73781),x73782),x73783)),x73782)+~E(f328(f328(f22(f885(x73781,a871)),x73783),f328(f328(f306(x73781),x73782),f193(f885(x73781,a871)))),f193(f885(x73781,a871)))
% 81.29/80.93 [7395]~P87(x73951)+~P24(f328(f328(f244(x73951),x73952),x73953))+~P24(f328(f328(f244(x73951),f328(f80(x73951),x73952)),x73953))+P24(f328(f328(f244(x73951),f328(f76(x73951),x73952)),x73953))
% 81.29/80.93 [7396]~P111(x73961)+~P24(f328(f328(f245(x73961),x73962),x73963))+~P24(f328(f328(f245(x73961),f328(f80(x73961),x73962)),x73963))+P24(f328(f328(f245(x73961),f328(f76(x73961),x73962)),x73963))
% 81.29/80.93 [7467]~P127(x74671)+P24(f328(f328(f245(x74671),f2(x74671)),x74672))+~P24(f328(f328(f245(x74671),f2(x74671)),x74673))+~P24(f328(f328(f245(x74671),f2(x74671)),f328(f328(f82(x74671),x74673),x74672)))
% 81.29/80.93 [7468]~P127(x74681)+P24(f328(f328(f245(x74681),f2(x74681)),x74682))+~P24(f328(f328(f245(x74681),f2(x74681)),x74683))+~P24(f328(f328(f245(x74681),f2(x74681)),f328(f328(f82(x74681),x74682),x74683)))
% 81.29/80.93 [7767]E(x77671,x77672)+~P24(f328(f62(x77673),x77671))+~P24(f328(f328(f244(a877),f328(f38(x77673),x77671)),f328(f38(x77673),x77672)))+~P24(f328(f328(f244(f885(x77673,a871)),x77672),x77671))
% 81.29/80.93 [7908]~P24(f328(f328(f245(a1),x79081),f2(a1)))+~P24(f328(f328(f245(a1),f2(a1)),x79082))+~P24(f328(f328(f244(a1),x79082),x79083))+P24(f328(f328(f244(a1),f328(f328(f39(a1),x79081),x79082)),f328(f328(f39(a1),x79081),x79083)))
% 81.29/80.93 [7920]~P24(f328(f328(f244(a1),f2(a1)),x79201))+~P24(f328(f328(f245(a1),f2(a1)),x79203))+~P24(f328(f328(f244(a1),x79203),x79202))+P24(f328(f328(f244(a1),f328(f328(f39(a1),x79201),x79202)),f328(f328(f39(a1),x79201),x79203)))
% 81.29/80.93 [8060]E(f328(x80601,f340(x80602,x80601,x80603)),x80602)+~P24(f328(f328(f244(a1),x80602),f328(x80601,x80603)))+P24(f328(f328(f245(a877),f870(x80602,x80601,x80603)),x80603))+~P24(f328(f328(f244(a1),f328(x80601,f2(a877))),x80602))
% 81.29/80.93 [8061]E(f328(x80611,f341(x80612,x80611,x80613)),x80612)+~P24(f328(f328(f244(a1),x80612),f328(x80611,x80613)))+P24(f328(f328(f245(a877),f342(x80612,x80611,x80613)),x80613))+~P24(f328(f328(f244(a1),f328(x80611,f2(a877))),x80612))
% 81.29/80.93 [8165]~P24(f328(f62(x81651),x81653))+~P24(f328(f328(f245(a877),f328(f38(x81651),x81652)),f328(f38(x81651),x81653)))+~P24(f328(f328(f244(f885(x81651,a871)),x81652),x81653))+P24(f328(f328(f245(f885(x81651,a871)),x81652),x81653))
% 81.29/80.93 [8194]E(f328(f328(f81(a1),f431(x81943,x81941,x81942)),f432(x81943,x81941,x81942)),x81941)+E(f328(f328(f22(a1),x81941),x81942),x81941)+~P24(f328(f328(f245(a1),f2(a1)),x81942))+~P24(f328(f328(f330(a1),f328(f328(f22(a1),x81941),f79(a1))),x81943))
% 81.29/80.93 [8195]E(f328(f328(f22(a1),f433(x81953,x81951,x81952)),f434(x81953,x81951,x81952)),x81951)+E(f328(f328(f81(a1),x81951),x81952),x81951)+~P24(f328(f328(f245(a1),f2(a1)),x81952))+~P24(f328(f328(f330(a1),f328(f328(f81(a1),x81951),f79(a1))),x81953))
% 81.29/80.93 [8248]~P24(f328(f328(f244(a877),x82483),x82481))+P24(f328(f328(f244(a877),x82481),x82482))+~P24(f328(f328(f244(a877),x82483),x82482))+~P24(f328(f328(f244(a877),f328(f328(f22(a877),x82481),x82483)),f328(f328(f22(a877),x82482),x82483)))
% 81.29/80.93 [8249]~P24(f328(f328(f244(a877),x82493),x82491))+P24(f328(f328(f245(a877),x82491),x82492))+~P24(f328(f328(f244(a877),x82493),x82492))+~P24(f328(f328(f245(a877),f328(f328(f22(a877),x82491),x82493)),f328(f328(f22(a877),x82492),x82493)))
% 81.29/80.93 [8265]~P106(x82652)+E(x82651,f119(x82652))+~P29(x82652,f328(f168(x82652),x82651))+E(f328(f141(x82652,x82652,f328(f7(x82652,x82652,x82652),f243(x82652)),x82653),f328(f168(x82652),x82651)),f328(f328(f243(x82652),f328(f328(f164(x82652),x82651),f2(a877))),x82653))
% 81.29/80.93 [8331]E(f328(f328(f22(a1),x83311),x83312),x83311)+~P24(f328(f328(f245(a1),f2(a1)),x83312))+P24(f328(f328(f330(a1),f431(x83313,x83311,x83312)),x83313))+~P24(f328(f328(f330(a1),f328(f328(f22(a1),x83311),f79(a1))),x83313))
% 81.29/80.93 [8332]E(f328(f328(f81(a1),x83321),x83322),x83321)+~P24(f328(f328(f245(a1),f2(a1)),x83322))+P24(f328(f328(f330(a1),f433(x83323,x83321,x83322)),x83323))+~P24(f328(f328(f330(a1),f328(f328(f81(a1),x83321),f79(a1))),x83323))
% 81.29/80.93 [8407]~P24(f328(f328(f244(a1),x84071),f328(x84072,x84073)))+P24(f328(f328(f245(a877),f870(x84071,x84072,x84073)),x84073))+P24(f328(f328(f244(a877),f340(x84071,x84072,x84073)),x84073))+~P24(f328(f328(f244(a1),f328(x84072,f2(a877))),x84071))
% 81.29/80.93 [8408]~P24(f328(f328(f244(a1),x84081),f328(x84082,x84083)))+P24(f328(f328(f245(a877),f342(x84081,x84082,x84083)),x84083))+P24(f328(f328(f244(a877),f341(x84081,x84082,x84083)),x84083))+~P24(f328(f328(f244(a1),f328(x84082,f2(a877))),x84081))
% 81.29/80.93 [8487]E(f328(f328(f22(a1),x84871),x84872),x84871)+~P24(f328(f328(f245(a1),f2(a1)),x84872))+P24(f328(f328(f330(a1),f432(x84873,x84871,x84872)),f299(a1,f79(a1),x84872)))+~P24(f328(f328(f330(a1),f328(f328(f22(a1),x84871),f79(a1))),x84873))
% 81.29/80.93 [8488]E(f328(f328(f81(a1),x84881),x84882),x84881)+~P24(f328(f328(f245(a1),f2(a1)),x84882))+P24(f328(f328(f330(a1),f434(x84883,x84881,x84882)),f299(a1,f79(a1),x84882)))+~P24(f328(f328(f330(a1),f328(f328(f81(a1),x84881),f79(a1))),x84883))
% 81.29/80.93 [8617]~P110(x86171)+~P24(f328(f328(f245(x86171),x86172),f79(x86171)))+~P24(f328(f328(f245(x86171),f2(x86171)),x86172))+P24(f328(f328(f245(x86171),f328(f328(f82(x86171),x86172),f328(f328(f258(x86171),x86172),x86173))),f328(f328(f258(x86171),x86172),x86173)))
% 81.29/80.93 [8701]~P24(f328(x87011,x87012))+P24(f328(x87011,f2(a877)))+~P24(f328(f328(f245(a877),x87012),x87013))+~P24(f328(x87011,f45(a877,f328(a118,f371(x87012,x87011,x87013)),x87013)))
% 81.29/80.93 [8840]E(f498(x88401,x88402,x88403),f2(a877))+P24(f328(f328(x88401,x88403),x88402))+P24(f328(f328(x88401,f498(x88401,x88402,x88403)),f45(a877,f497(x88401,x88402,x88403),f498(x88401,x88402,x88403))))+~P24(f328(f316(f884(a877,a877),a227),f328(f328(f257(a877,a877),x88403),x88402)))
% 81.29/80.93 [8878]~P21(x88781,x88781,x88782,x88783)+E(f328(f307(x88781,x88781,x88782),x88783),x88783)+~P24(f328(f62(x88781),x88783))+~P24(f328(f328(f244(f885(x88781,a871)),f328(f307(x88781,x88781,x88782),x88783)),x88783))
% 81.29/80.93 [9118]P24(f328(f328(x91181,x91182),x91183))+~P24(f328(f328(f245(a1),f496(x91181,x91183,x91182)),f2(a1)))+P24(f328(f328(x91181,f328(f80(a1),f495(x91181,x91183,x91182))),f328(f80(a1),f496(x91181,x91183,x91182))))+~P24(f328(f316(f884(a1,a1),a232),f328(f328(f257(a1,a1),x91182),x91183)))
% 81.29/80.93 [9306]P24(f328(f328(x93061,x93062),x93063))+P24(f328(f328(x93061,f328(f328(f81(a1),f586(x93061,x93063,x93062)),f79(a1))),f588(x93061,x93063,x93062)))+~P24(f328(f328(f244(a1),f586(x93061,x93063,x93062)),f588(x93061,x93063,x93062)))+~P24(f328(f316(f884(a1,a1),a182),f328(f328(f257(a1,a1),x93062),x93063)))
% 81.29/80.93 [9727]~P60(x97272)+~P60(x97271)+~P24(f328(f59(f884(x97271,x97272)),x97273))+P24(f328(f59(x97271),f328(f328(f8(f885(x97272,a871),a871,x97271),f59(x97272)),f328(f328(f8(f885(x97272,f884(x97271,x97272)),f885(x97272,a871),x97271),f328(f8(f884(x97271,x97272),a871,x97272),x97273)),f257(x97271,x97272)))))
% 81.29/80.93 [9728]~P60(x97282)+~P60(x97281)+~P24(f328(f58(f884(x97281,x97282)),x97283))+P24(f328(f58(x97281),f328(f328(f8(f885(x97282,a871),a871,x97281),f58(x97282)),f328(f328(f8(f885(x97282,f884(x97281,x97282)),f885(x97282,a871),x97281),f328(f8(f884(x97281,x97282),a871,x97282),x97283)),f257(x97281,x97282)))))
% 81.29/80.93 [9828]~P60(x98282)+~P60(x98281)+P24(f328(f59(f884(x98281,x98282)),x98283))+~P24(f328(f59(x98281),f328(f328(f8(f885(x98282,a871),a871,x98281),f59(x98282)),f328(f328(f8(f885(x98282,f884(x98281,x98282)),f885(x98282,a871),x98281),f328(f8(f884(x98281,x98282),a871,x98282),x98283)),f257(x98281,x98282)))))
% 81.29/80.93 [9829]~P60(x98292)+~P60(x98291)+P24(f328(f58(f884(x98291,x98292)),x98293))+~P24(f328(f58(x98291),f328(f328(f8(f885(x98292,a871),a871,x98291),f58(x98292)),f328(f328(f8(f885(x98292,f884(x98291,x98292)),f885(x98292,a871),x98291),f328(f8(f884(x98291,x98292),a871,x98292),x98293)),f257(x98291,x98292)))))
% 81.29/80.93 [10004]E(f328(x100041,f340(x100042,x100041,x100043)),x100042)+~P24(f328(f328(f244(a1),x100042),f328(x100041,x100043)))+~P24(f328(f328(f244(a1),f328(f76(a1),f328(f328(f22(a1),f328(x100041,f328(f328(f81(a877),f870(x100042,x100041,x100043)),f79(a877)))),f328(x100041,f870(x100042,x100041,x100043))))),f79(a1)))+~P24(f328(f328(f244(a1),f328(x100041,f2(a877))),x100042))
% 81.29/80.93 [10005]E(f328(x100051,f341(x100052,x100051,x100053)),x100052)+~P24(f328(f328(f244(a1),x100052),f328(x100051,x100053)))+~P24(f328(f328(f244(a1),f328(f76(a1),f328(f328(f22(a1),f328(x100051,f328(f328(f81(a877),f342(x100052,x100051,x100053)),f79(a877)))),f328(x100051,f342(x100052,x100051,x100053))))),f79(a1)))+~P24(f328(f328(f244(a1),f328(x100051,f2(a877))),x100052))
% 81.29/80.93 [10009]~P24(f328(f328(f244(a1),x100091),f328(x100092,x100093)))+~P24(f328(f328(f244(a1),f328(f76(a1),f328(f328(f22(a1),f328(x100092,f328(f328(f81(a877),f870(x100091,x100092,x100093)),f79(a877)))),f328(x100092,f870(x100091,x100092,x100093))))),f79(a1)))+P24(f328(f328(f244(a877),f340(x100091,x100092,x100093)),x100093))+~P24(f328(f328(f244(a1),f328(x100092,f2(a877))),x100091))
% 81.29/80.93 [10010]~P24(f328(f328(f244(a1),x100101),f328(x100102,x100103)))+~P24(f328(f328(f244(a1),f328(f76(a1),f328(f328(f22(a1),f328(x100102,f328(f328(f81(a877),f342(x100101,x100102,x100103)),f79(a877)))),f328(x100102,f342(x100101,x100102,x100103))))),f79(a1)))+P24(f328(f328(f244(a877),f341(x100101,x100102,x100103)),x100103))+~P24(f328(f328(f244(a1),f328(x100102,f2(a877))),x100101))
% 81.29/80.93 [10065]E(x100651,x100652)+~E(f328(f141(f878(x100653),f878(x100653),f127(x100653),f119(x100653)),x100651),f328(f141(f878(x100653),f878(x100653),f127(x100653),f119(x100653)),x100652))+~E(f328(f194(f878(f878(x100653))),x100651),f328(f194(f878(f878(x100653))),x100652))+~P24(f328(f328(f267(f878(x100653),f878(x100653),a871),f328(f328(f7(f878(x100653),f885(f878(x100653),a877),f885(f878(x100653),a871)),f328(f328(f8(f885(a877,a871),f885(f885(f878(x100653),a877),f885(f878(x100653),a871)),f878(x100653)),f8(a877,a871,f878(x100653))),f328(f328(f8(a877,f885(a877,a871),f878(x100653)),a325),f194(f878(x100653))))),f194(f878(x100653)))),f651(x100651,x100652,x100653)))
% 81.29/80.93 [10066]E(x100661,x100662)+~E(f328(f141(f878(x100663),f878(x100663),f127(x100663),f119(x100663)),x100661),f328(f141(f878(x100663),f878(x100663),f127(x100663),f119(x100663)),x100662))+~E(f328(f194(f878(f878(x100663))),x100661),f328(f194(f878(f878(x100663))),x100662))+~P24(f328(f328(f267(f878(x100663),f878(x100663),a871),f328(f328(f7(f878(x100663),f885(f878(x100663),a877),f885(f878(x100663),a871)),f328(f328(f8(f885(a877,a871),f885(f885(f878(x100663),a877),f885(f878(x100663),a871)),f878(x100663)),f8(a877,a871,f878(x100663))),f328(f328(f8(a877,f885(a877,a871),f878(x100663)),a325),f194(f878(x100663))))),f194(f878(x100663)))),f652(x100662,x100661,x100663)))
% 81.29/80.93 [6796]~E(f79(a877),f2(a877))+~P24(f328(f62(x67961),x67963))+~P24(f328(f62(x67961),x67962))+E(f328(f328(f81(a877),f328(f38(x67961),x67962)),f328(f38(x67961),x67963)),f328(f38(x67961),f328(f328(f116(f885(x67961,a871)),x67962),x67963)))
% 81.29/80.93 [7207]~P102(x72071)+~P24(f328(f62(x72071),x72072))+~P24(f328(f328(f330(x72071),x72073),x72072))+P24(f328(f328(f244(x72071),f328(f64(x72071,f107(x72071)),x72072)),x72073))
% 81.29/80.93 [7208]~P106(x72081)+~P24(f328(f62(x72081),x72082))+~P24(f328(f328(f330(x72081),x72083),x72082))+P24(f328(f328(f244(x72081),f328(f64(x72081,f242(x72081)),x72082)),x72083))
% 81.29/80.93 [7461]~P24(f328(f62(x74611),x74613))+~P24(f328(f62(x74611),x74612))+~E(f328(f328(f107(f885(x74611,a871)),x74612),x74613),f193(f885(x74611,a871)))+E(f328(f328(f81(a877),f328(f38(x74611),x74612)),f328(f38(x74611),x74613)),f328(f38(x74611),f328(f328(f116(f885(x74611,a871)),x74612),x74613)))
% 81.29/80.93 [8254]~P38(x82541,x82543)+~P38(x82541,x82542)+~E(f328(f328(f107(f885(x82541,a871)),f328(f255(x82541,x82541),x82542)),f328(f253(x82541,x82541),x82543)),f193(f885(x82541,a871)))+P38(x82541,f328(f328(f116(f885(f884(x82541,x82541),a871)),x82542),x82543))
% 81.29/80.93 [8346]E(x83461,f328(f328(f39(a877),x83462),x83463))+~P24(f328(f328(f245(a877),f2(a877)),x83463))+~P24(f328(f328(f245(a877),x83462),f328(f328(f82(a877),x83463),f328(a118,x83461))))+~P24(f328(f328(f244(a877),f328(f328(f82(a877),x83463),x83461)),x83462))
% 81.29/80.93 [8485]~P24(f328(f62(x84851),x84852))+~P24(f328(f62(x84851),x84853))+E(f328(f328(f81(a877),f328(f38(x84851),x84852)),f328(f38(x84851),x84853)),f328(f38(x84851),f328(f328(f116(f885(x84851,a871)),x84852),x84853)))+P24(f328(f328(f330(x84851),f831(x84853,x84852,x84851)),f328(f328(f107(f885(x84851,a871)),x84852),x84853)))
% 81.29/80.93 [8852]~P123(x88522)+~E(x88521,f2(x88522))+~E(x88523,f2(x88522))+~P24(f328(f328(f245(x88522),f2(x88522)),f328(f328(f81(x88522),f328(f328(f82(x88522),x88523),x88523)),f328(f328(f82(x88522),x88521),x88521))))
% 81.29/80.93 [9385]~P38(x93851,x93853)+~P38(x93851,x93852)+P38(x93851,f328(f328(f116(f885(f884(x93851,x93851),a871)),x93852),x93853))+~P24(f328(f328(f244(f885(f884(x93851,x93851),a871)),f328(f328(f285(x93851,x93851,x93851),x93852),x93853)),x93852))
% 81.29/80.93 [9510]~P24(f328(x95101,x95103))+~P24(f328(f62(x95102),x95103))+P24(f328(x95101,f193(f885(x95102,a871))))+~P24(f328(x95101,f328(f328(f22(f885(x95102,a871)),f562(x95101,x95103,x95102)),f328(f328(f306(x95102),f553(x95101,x95103,x95102)),f193(f885(x95102,a871))))))
% 81.29/80.93 [9757]~P60(x97571)+~P60(x97572)+P7(x97571,f328(f328(f8(f885(x97572,x97571),a871,f878(x97571)),x97573),f328(f328(f8(f885(x97572,f881(x97571)),f885(x97572,x97571),f878(x97571)),f74(f881(x97571),x97571,x97572,f240(x97571))),f328(f328(f8(f878(f884(x97572,x97571)),f885(x97572,f881(x97571)),f878(x97571)),f177(x97572,x97571)),f328(f181(x97572,x97571),f56(x97572))))),f328(f194(f878(x97572)),f56(x97572)))+~P24(f328(f58(f885(x97572,x97571)),x97573))
% 81.29/80.93 [9758]~P60(x97581)+~P60(x97582)+P8(x97581,f328(f328(f8(f885(x97582,x97581),a871,f878(x97581)),x97583),f328(f328(f8(f885(x97582,f881(x97581)),f885(x97582,x97581),f878(x97581)),f74(f881(x97581),x97581,x97582,f240(x97581))),f328(f328(f8(f878(f884(x97582,x97581)),f885(x97582,f881(x97581)),f878(x97581)),f177(x97582,x97581)),f328(f181(x97582,x97581),f56(x97582))))),f328(f194(f878(x97582)),f56(x97582)))+~P24(f328(f59(f885(x97582,x97581)),x97583))
% 81.29/80.93 [9853]~P60(x98531)+~P60(x98532)+~P8(x98532,f328(f328(f8(f885(x98531,x98532),a871,f878(x98532)),x98533),f328(f328(f8(f885(x98531,f881(x98532)),f885(x98531,x98532),f878(x98532)),f74(f881(x98532),x98532,x98531,f240(x98532))),f328(f328(f8(f878(f884(x98531,x98532)),f885(x98531,f881(x98532)),f878(x98532)),f177(x98531,x98532)),f328(f181(x98531,x98532),f56(x98531))))),f328(f194(f878(x98531)),f56(x98531)))+P24(f328(f59(f885(x98531,x98532)),x98533))
% 81.29/80.93 [9854]~P60(x98541)+~P60(x98542)+~P7(x98542,f328(f328(f8(f885(x98541,x98542),a871,f878(x98542)),x98543),f328(f328(f8(f885(x98541,f881(x98542)),f885(x98541,x98542),f878(x98542)),f74(f881(x98542),x98542,x98541,f240(x98542))),f328(f328(f8(f878(f884(x98541,x98542)),f885(x98541,f881(x98542)),f878(x98542)),f177(x98541,x98542)),f328(f181(x98541,x98542),f56(x98541))))),f328(f194(f878(x98541)),f56(x98541)))+P24(f328(f58(f885(x98541,x98542)),x98543))
% 81.29/80.93 [8652]~P24(f328(f328(f245(a1),f2(a1)),x86523))+P24(f328(f328(f244(a1),f2(a1)),x86521))+~P24(f328(f328(f245(a1),x86522),x86523))+~P24(f328(f328(f244(a1),f2(a1)),f328(f328(f81(a1),f328(f328(f82(a1),x86523),x86521)),x86522)))
% 81.29/80.93 [8675]~P78(x86751)+~P24(f328(f62(x86751),x86752))+E(f328(f328(f22(f885(x86751,a871)),x86752),f328(f328(f306(x86751),x86753),f193(f885(x86751,a871)))),f193(f885(x86751,a871)))+E(f328(f328(f116(x86751),x86753),f10(x86751,f328(f328(f22(f885(x86751,a871)),x86752),f328(f328(f306(x86751),x86753),f193(f885(x86751,a871)))))),f10(x86751,f328(f328(f306(x86751),x86753),x86752)))
% 81.29/80.93 [8676]~P78(x86761)+~P24(f328(f62(x86761),x86762))+E(f328(f328(f22(f885(x86761,a871)),x86762),f328(f328(f306(x86761),x86763),f193(f885(x86761,a871)))),f193(f885(x86761,a871)))+E(f328(f328(f107(x86761),x86763),f11(x86761,f328(f328(f22(f885(x86761,a871)),x86762),f328(f328(f306(x86761),x86763),f193(f885(x86761,a871)))))),f11(x86761,f328(f328(f306(x86761),x86763),x86762)))
% 81.29/80.93 [8677]~P106(x86771)+~P24(f328(f62(x86771),x86772))+E(f328(f328(f22(f885(x86771,a871)),x86772),f328(f328(f306(x86771),x86773),f193(f885(x86771,a871)))),f193(f885(x86771,a871)))+E(f328(f328(f242(x86771),x86773),f14(x86771,f328(f328(f22(f885(x86771,a871)),x86772),f328(f328(f306(x86771),x86773),f193(f885(x86771,a871)))))),f14(x86771,f328(f328(f306(x86771),x86773),x86772)))
% 81.29/80.93 [8678]~P106(x86781)+~P24(f328(f62(x86781),x86782))+E(f328(f328(f22(f885(x86781,a871)),x86782),f328(f328(f306(x86781),x86783),f193(f885(x86781,a871)))),f193(f885(x86781,a871)))+E(f328(f328(f243(x86781),x86783),f15(x86781,f328(f328(f22(f885(x86781,a871)),x86782),f328(f328(f306(x86781),x86783),f193(f885(x86781,a871)))))),f15(x86781,f328(f328(f306(x86781),x86783),x86782)))
% 81.29/80.93 [8742]~P106(x87421)+~P24(f328(f62(x87421),x87422))+E(f328(f328(f22(f885(x87421,a871)),x87422),f328(f328(f306(x87421),x87423),f193(f885(x87421,a871)))),f193(f885(x87421,a871)))+E(f328(f328(f242(x87421),x87423),f12(x87421,f242(x87421),f328(f328(f22(f885(x87421,a871)),x87422),f328(f328(f306(x87421),x87423),f193(f885(x87421,a871)))))),f12(x87421,f242(x87421),f328(f328(f306(x87421),x87423),x87422)))
% 81.29/80.93 [8743]~P106(x87431)+~P24(f328(f62(x87431),x87432))+E(f328(f328(f22(f885(x87431,a871)),x87432),f328(f328(f306(x87431),x87433),f193(f885(x87431,a871)))),f193(f885(x87431,a871)))+E(f328(f328(f243(x87431),x87433),f13(x87431,f243(x87431),f328(f328(f22(f885(x87431,a871)),x87432),f328(f328(f306(x87431),x87433),f193(f885(x87431,a871)))))),f13(x87431,f243(x87431),f328(f328(f306(x87431),x87433),x87432)))
% 81.29/80.93 [9326]E(x93261,x93262)+~E(f328(f141(f878(x93263),f878(x93263),f127(x93263),f119(x93263)),x93261),f328(f141(f878(x93263),f878(x93263),f127(x93263),f119(x93263)),x93262))+~E(f328(f194(f878(f878(x93263))),x93261),f328(f194(f878(f878(x93263))),x93262))+P24(f328(f328(f330(f884(f878(x93263),f878(x93263))),f651(x93261,x93262,x93263)),f328(f171(f884(f878(x93263),f878(x93263))),f328(f328(f181(f878(x93263),f878(x93263)),x93262),x93261))))
% 81.29/80.93 [9327]E(x93271,x93272)+~E(f328(f141(f878(x93273),f878(x93273),f127(x93273),f119(x93273)),x93271),f328(f141(f878(x93273),f878(x93273),f127(x93273),f119(x93273)),x93272))+~E(f328(f194(f878(f878(x93273))),x93271),f328(f194(f878(f878(x93273))),x93272))+P24(f328(f328(f330(f884(f878(x93273),f878(x93273))),f652(x93272,x93271,x93273)),f328(f171(f884(f878(x93273),f878(x93273))),f328(f328(f181(f878(x93273),f878(x93273)),x93271),x93272))))
% 81.29/80.93 [10152]~P100(x101522)+E(x101521,f193(f885(x101522,a871)))+~P24(f328(f62(x101522),x101521))+E(f11(x101522,f328(f249(x101522),f328(f328(f8(f885(x101522,a871),a871,x101522),f88(x101522)),f328(f328(f7(x101522,f885(x101522,a871),f885(x101522,a871)),f328(f328(f8(f885(x101522,f885(a871,a871)),f885(f885(x101522,a871),f885(x101522,a871)),x101522),f18(x101522,a871,a871)),f328(f328(f8(f885(x101522,a871),f885(x101522,f885(a871,a871)),x101522),f328(f8(a871,f885(a871,a871),x101522),a326)),f328(f328(f7(x101522,f885(x101522,x101522),f885(x101522,a871)),f328(f328(f8(f885(x101522,a871),f885(f885(x101522,x101522),f885(x101522,a871)),x101522),f8(x101522,a871,x101522)),a325)),f328(f116(x101522),x101523))))),f328(f328(f7(x101522,f885(x101522,a871),a871),f330(x101522)),x101521))))),f328(f328(f116(x101522),x101523),f11(x101522,x101521)))
% 81.29/80.93 [10153]~P77(x101532)+E(x101531,f193(f885(x101532,a871)))+~P24(f328(f62(x101532),x101531))+E(f14(x101532,f328(f249(x101532),f328(f328(f8(f885(x101532,a871),a871,x101532),f88(x101532)),f328(f328(f7(x101532,f885(x101532,a871),f885(x101532,a871)),f328(f328(f8(f885(x101532,f885(a871,a871)),f885(f885(x101532,a871),f885(x101532,a871)),x101532),f18(x101532,a871,a871)),f328(f328(f8(f885(x101532,a871),f885(x101532,f885(a871,a871)),x101532),f328(f8(a871,f885(a871,a871),x101532),a326)),f328(f328(f7(x101532,f885(x101532,x101532),f885(x101532,a871)),f328(f328(f8(f885(x101532,a871),f885(f885(x101532,x101532),f885(x101532,a871)),x101532),f8(x101532,a871,x101532)),a325)),f328(f81(x101532),x101533))))),f328(f328(f7(x101532,f885(x101532,a871),a871),f330(x101532)),x101531))))),f328(f328(f81(x101532),x101533),f14(x101532,x101531)))
% 81.29/80.93 [10154]~P77(x101542)+E(x101541,f193(f885(x101542,a871)))+~P24(f328(f62(x101542),x101541))+E(f15(x101542,f328(f249(x101542),f328(f328(f8(f885(x101542,a871),a871,x101542),f88(x101542)),f328(f328(f7(x101542,f885(x101542,a871),f885(x101542,a871)),f328(f328(f8(f885(x101542,f885(a871,a871)),f885(f885(x101542,a871),f885(x101542,a871)),x101542),f18(x101542,a871,a871)),f328(f328(f8(f885(x101542,a871),f885(x101542,f885(a871,a871)),x101542),f328(f8(a871,f885(a871,a871),x101542),a326)),f328(f328(f7(x101542,f885(x101542,x101542),f885(x101542,a871)),f328(f328(f8(f885(x101542,a871),f885(f885(x101542,x101542),f885(x101542,a871)),x101542),f8(x101542,a871,x101542)),a325)),f328(f81(x101542),x101543))))),f328(f328(f7(x101542,f885(x101542,a871),a871),f330(x101542)),x101541))))),f328(f328(f81(x101542),x101543),f15(x101542,x101541)))
% 81.29/80.93 [10155]~P100(x101552)+E(x101551,f193(f885(x101552,a871)))+~P24(f328(f62(x101552),x101551))+E(f10(x101552,f328(f249(x101552),f328(f328(f8(f885(x101552,a871),a871,x101552),f88(x101552)),f328(f328(f7(x101552,f885(x101552,a871),f885(x101552,a871)),f328(f328(f8(f885(x101552,f885(a871,a871)),f885(f885(x101552,a871),f885(x101552,a871)),x101552),f18(x101552,a871,a871)),f328(f328(f8(f885(x101552,a871),f885(x101552,f885(a871,a871)),x101552),f328(f8(a871,f885(a871,a871),x101552),a326)),f328(f328(f7(x101552,f885(x101552,x101552),f885(x101552,a871)),f328(f328(f8(f885(x101552,a871),f885(f885(x101552,x101552),f885(x101552,a871)),x101552),f8(x101552,a871,x101552)),a325)),f328(f107(x101552),x101553))))),f328(f328(f7(x101552,f885(x101552,a871),a871),f330(x101552)),x101551))))),f328(f328(f107(x101552),x101553),f10(x101552,x101551)))
% 81.29/80.93 [10156]~P106(x101562)+E(x101561,f193(f885(x101562,a871)))+~P24(f328(f62(x101562),x101561))+E(f13(x101562,f243(x101562),f328(f249(x101562),f328(f328(f8(f885(x101562,a871),a871,x101562),f88(x101562)),f328(f328(f7(x101562,f885(x101562,a871),f885(x101562,a871)),f328(f328(f8(f885(x101562,f885(a871,a871)),f885(f885(x101562,a871),f885(x101562,a871)),x101562),f18(x101562,a871,a871)),f328(f328(f8(f885(x101562,a871),f885(x101562,f885(a871,a871)),x101562),f328(f8(a871,f885(a871,a871),x101562),a326)),f328(f328(f7(x101562,f885(x101562,x101562),f885(x101562,a871)),f328(f328(f8(f885(x101562,a871),f885(f885(x101562,x101562),f885(x101562,a871)),x101562),f8(x101562,a871,x101562)),a325)),f328(f242(x101562),x101563))))),f328(f328(f7(x101562,f885(x101562,a871),a871),f330(x101562)),x101561))))),f328(f328(f242(x101562),x101563),f13(x101562,f243(x101562),x101561)))
% 81.29/80.93 [10157]~P106(x101572)+E(x101571,f193(f885(x101572,a871)))+~P24(f328(f62(x101572),x101571))+E(f12(x101572,f242(x101572),f328(f249(x101572),f328(f328(f8(f885(x101572,a871),a871,x101572),f88(x101572)),f328(f328(f7(x101572,f885(x101572,a871),f885(x101572,a871)),f328(f328(f8(f885(x101572,f885(a871,a871)),f885(f885(x101572,a871),f885(x101572,a871)),x101572),f18(x101572,a871,a871)),f328(f328(f8(f885(x101572,a871),f885(x101572,f885(a871,a871)),x101572),f328(f8(a871,f885(a871,a871),x101572),a326)),f328(f328(f7(x101572,f885(x101572,x101572),f885(x101572,a871)),f328(f328(f8(f885(x101572,a871),f885(f885(x101572,x101572),f885(x101572,a871)),x101572),f8(x101572,a871,x101572)),a325)),f328(f243(x101572),x101573))))),f328(f328(f7(x101572,f885(x101572,a871),a871),f330(x101572)),x101571))))),f328(f328(f243(x101572),x101573),f12(x101572,f242(x101572),x101571)))
% 81.29/80.93 [9906]~P111(x99061)+~E(x99063,f2(x99061))+~E(x99062,f2(x99061))+E(f328(f328(f81(x99061),f328(f328(f258(x99061),x99062),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x99061),x99063),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f2(x99061))
% 81.29/80.93 [10049]~P110(x100491)+~P24(f328(f328(f244(x100491),f2(x100491)),x100493))+P24(f328(f328(f244(x100491),x100492),x100493))+~P24(f328(f328(f244(x100491),f328(f328(f258(x100491),x100492),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x100491),x100493),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))))
% 81.29/80.93 [10096]~P111(x100962)+~E(x100961,f2(x100962))+~E(x100963,f2(x100962))+~P24(f328(f328(f245(x100962),f2(x100962)),f328(f328(f81(x100962),f328(f328(f258(x100962),x100963),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103))))),f328(f328(f258(x100962),x100961),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))))
% 81.29/80.93 [9288]E(x92881,x92882)+~E(f629(x92881,x92882,x92884,x92883),f631(x92881,x92882,x92884,x92883))+P24(f328(f328(f330(f884(f878(x92883),f878(x92883))),f328(f328(f257(f878(x92883),f878(x92883)),x92882),x92881)),f146(x92883,x92884)))+P24(f328(f328(f330(f884(f878(x92883),f878(x92883))),f328(f328(f257(f878(x92883),f878(x92883)),x92881),x92882)),f146(x92883,x92884)))
% 81.29/80.93 [4848]~P61(x48482)+~E(x48484,f2(x48482))+~E(x48481,f2(x48482))+E(x48481,f328(f328(f286(x48482),x48483),x48484))
% 81.29/80.93 [4849]~P61(x48491)+~E(x48493,f2(x48491))+~E(x48494,f2(x48491))+E(f328(f328(f286(x48491),x48492),x48493),x48494)
% 81.29/80.93 [4959]~P61(x49592)+E(x49591,f2(x49592))+~E(x49593,f2(x49592))+~E(x49591,f328(f328(f286(x49592),x49594),x49593))
% 81.29/80.93 [4960]~P61(x49602)+E(x49601,f2(x49602))+~E(x49603,f2(x49602))+~E(f328(f328(f286(x49602),x49604),x49603),x49601)
% 81.29/80.93 [5135]~P120(x51352)+E(x51351,f2(x51352))+~E(f328(f328(f286(x51352),x51353),x51351),x51354)+E(x51353,f328(f328(f82(x51352),x51354),x51351))
% 81.29/80.93 [5137]~P120(x51372)+E(x51371,f2(x51372))+~E(f328(f328(f82(x51372),x51373),x51371),x51374)+E(x51373,f328(f328(f286(x51372),x51374),x51371))
% 81.29/80.93 [5138]~P61(x51382)+E(x51381,f2(x51382))+~E(f328(f328(f286(x51382),x51383),x51381),x51384)+E(x51383,f328(f328(f82(x51382),x51384),x51381))
% 81.29/80.93 [5139]~P61(x51392)+E(x51391,f2(x51392))+~E(f328(f328(f82(x51392),x51393),x51391),x51394)+E(x51393,f328(f328(f286(x51392),x51394),x51391))
% 81.29/80.93 [5140]~P120(x51402)+E(x51401,f2(x51402))+~E(x51403,f328(f328(f286(x51402),x51404),x51401))+E(f328(f328(f82(x51402),x51403),x51401),x51404)
% 81.29/80.93 [5142]~P120(x51422)+E(x51421,f2(x51422))+~E(x51423,f328(f328(f82(x51422),x51424),x51421))+E(f328(f328(f286(x51422),x51423),x51421),x51424)
% 81.29/80.93 [5143]~P61(x51432)+E(x51431,f2(x51432))+~E(x51433,f328(f328(f286(x51432),x51434),x51431))+E(f328(f328(f82(x51432),x51433),x51431),x51434)
% 81.29/80.93 [5144]~P61(x51442)+E(x51441,f2(x51442))+~E(x51443,f328(f328(f82(x51442),x51444),x51441))+E(f328(f328(f286(x51442),x51443),x51441),x51444)
% 81.29/80.93 [5177]~P61(x51772)+~E(x51771,f2(x51772))+~E(f328(f328(f82(x51772),x51771),x51774),x51773)+E(x51771,f328(f328(f286(x51772),x51773),x51774))
% 81.29/80.93 [5178]~P61(x51781)+~E(x51784,f2(x51781))+~E(x51782,f328(f328(f82(x51781),x51784),x51783))+E(f328(f328(f286(x51781),x51782),x51783),x51784)
% 81.29/80.93 [5251]~E(x52513,x52514)+~E(x52512,x52513)+~P108(x52511)+E(f299(x52511,x52512,x52513),f328(f328(f306(x52511),x52514),f193(f885(x52511,a871))))
% 81.29/80.93 [5459]~E(f143(x54592,x54591),x54594)+~E(f120(x54592,x54591),x54593)+E(x54591,f119(x54592))+E(f328(f328(f127(x54592),x54593),f328(f328(f150(x54592),x54594),f119(x54592))),x54591)
% 81.29/80.93 [6075]~P110(x60753)+E(x60751,x60752)+~E(f328(f328(f258(x60753),x60754),x60751),f328(f328(f258(x60753),x60754),x60752))+~P24(f328(f328(f245(x60753),f79(x60753)),x60754))
% 81.29/80.93 [6076]E(x60761,x60762)+~E(f328(f328(f306(x60763),x60764),x60761),f328(f328(f306(x60763),x60764),x60762))+P24(f328(f328(f330(x60763),x60764),x60762))+P24(f328(f328(f330(x60763),x60764),x60761))
% 81.29/80.93 [6114]E(f328(x61141,x61142),f79(a877))+~E(f328(f328(f9(x61143,a877),x61141),x61144),f79(a877))+~P24(f328(f62(x61143),x61144))+~P24(f328(f328(f330(x61143),x61142),x61144))
% 81.29/80.93 [6115]E(f328(x61151,x61152),f2(a877))+~E(f328(f328(f6(x61153,a877),x61151),x61154),f2(a877))+~P24(f328(f62(x61153),x61154))+~P24(f328(f328(f330(x61153),x61152),x61154))
% 81.29/80.93 [6334]~P108(x63341)+~P24(f328(f328(f244(x63341),x63344),x63343))+P24(f328(f328(f244(x63341),x63342),x63343))+~P24(f328(f328(f244(x63341),x63342),x63344))
% 81.29/80.93 [6335]~P105(x63351)+~P24(f328(f328(f244(x63351),x63352),x63354))+P24(f328(f328(f244(x63351),x63352),x63353))+~P24(f328(f328(f244(x63351),x63354),x63353))
% 81.29/80.93 [6336]~P108(x63361)+~P24(f328(f328(f245(x63361),x63364),x63363))+P24(f328(f328(f245(x63361),x63362),x63363))+~P24(f328(f328(f244(x63361),x63362),x63364))
% 81.29/80.93 [6337]~P108(x63371)+~P24(f328(f328(f245(x63371),x63372),x63374))+P24(f328(f328(f245(x63371),x63372),x63373))+~P24(f328(f328(f244(x63371),x63374),x63373))
% 81.29/80.93 [6338]~P108(x63381)+~P24(f328(f328(f245(x63381),x63384),x63383))+P24(f328(f328(f245(x63381),x63382),x63383))+~P24(f328(f328(f245(x63381),x63382),x63384))
% 81.29/80.93 [6339]~P105(x63391)+~P24(f328(f328(f245(x63391),x63392),x63394))+P24(f328(f328(f245(x63391),x63392),x63393))+~P24(f328(f328(f244(x63391),x63394),x63393))
% 81.29/80.93 [6340]~P105(x63401)+~P24(f328(f328(f245(x63401),x63404),x63403))+P24(f328(f328(f245(x63401),x63402),x63403))+~P24(f328(f328(f244(x63401),x63402),x63404))
% 81.29/80.93 [6341]~P105(x63411)+~P24(f328(f328(f245(x63411),x63412),x63414))+P24(f328(f328(f245(x63411),x63412),x63413))+~P24(f328(f328(f245(x63411),x63414),x63413))
% 81.29/80.93 [6424]~P36(x64244,x64243,x64242)+E(x64241,f807(x64242,x64243,x64244))+~P24(f328(x64243,x64241))+~P24(f328(f328(f330(x64244),x64241),f328(f171(x64244),x64242)))
% 81.29/80.93 [6570]~P27(x65701)+~P24(f328(f328(f244(x65701),x65702),f41(x65701,x65704)))+P24(f328(f328(f244(x65701),x65702),x65703))+~P24(f328(f328(f330(x65701),x65703),x65704))
% 81.29/80.93 [6717]~P106(x67171)+~P29(x67171,f328(f328(f150(x67171),x67172),x67174))+~P24(f328(f328(f330(x67171),x67173),f328(f171(x67171),x67174)))+P24(f328(f328(f244(x67171),x67172),x67173))
% 81.29/80.93 [6807]~P27(x68071)+~P24(f328(f328(f244(x68071),f40(x68071,x68074)),x68073))+P24(f328(f328(f244(x68071),x68072),x68073))+~P24(f328(f328(f330(x68071),x68072),x68074))
% 81.29/80.93 [7210]~P106(x72101)+E(f328(f328(f116(f885(x72101,a871)),f328(f298(x72101,x72102),x72103)),f328(f298(x72101,x72103),x72104)),f328(f298(x72101,x72102),x72104))+~P24(f328(f328(f244(x72101),x72103),x72104))+~P24(f328(f328(f244(x72101),x72102),x72103))
% 81.29/80.93 [7247]P36(x72471,x72472,x72473)+~E(f808(x72473,x72472,x72471,x72474),x72474)+~P24(f328(x72472,x72474))+~P24(f328(f328(f330(x72471),x72474),f328(f171(x72471),x72473)))
% 81.29/80.93 [7321]~P106(x73211)+E(f328(f328(f116(f885(x73211,a871)),f328(f298(x73211,x73212),x73213)),f299(x73211,x73213,x73214)),f299(x73211,x73212,x73214))+~P24(f328(f328(f244(x73211),x73213),x73214))+~P24(f328(f328(f244(x73211),x73212),x73213))
% 81.29/80.93 [7387]~P106(x73871)+E(f328(f328(f116(f885(x73871,a871)),f302(x73871,x73872,x73873)),f328(f298(x73871,x73873),x73874)),f302(x73871,x73872,x73874))+~P24(f328(f328(f244(x73871),x73873),x73874))+~P24(f328(f328(f245(x73871),x73872),x73873))
% 81.29/80.93 [7408]~P106(x74081)+E(f328(f328(f116(f885(x74081,a871)),f299(x74081,x74082,x74083)),f302(x74081,x74083,x74084)),f328(f298(x74081,x74082),x74084))+~P24(f328(f328(f244(x74081),x74082),x74083))+~P24(f328(f328(f245(x74081),x74083),x74084))
% 81.29/80.93 [7440]~P106(x74401)+E(f328(f328(f116(f885(x74401,a871)),f302(x74401,x74402,x74403)),f299(x74401,x74403,x74404)),f301(x74401,x74402,x74404))+~P24(f328(f328(f244(x74401),x74403),x74404))+~P24(f328(f328(f245(x74401),x74402),x74403))
% 81.29/80.93 [7441]~P106(x74411)+E(f328(f328(f116(f885(x74411,a871)),f301(x74411,x74412,x74413)),f302(x74411,x74413,x74414)),f302(x74411,x74412,x74414))+~P24(f328(f328(f244(x74411),x74412),x74413))+~P24(f328(f328(f245(x74411),x74413),x74414))
% 81.29/80.93 [7442]~P106(x74421)+E(f328(f328(f116(f885(x74421,a871)),f301(x74421,x74422,x74423)),f301(x74421,x74423,x74424)),f301(x74421,x74422,x74424))+~P24(f328(f328(f244(x74421),x74423),x74424))+~P24(f328(f328(f244(x74421),x74422),x74423))
% 81.29/80.93 [7443]~P106(x74431)+E(f328(f328(f116(f885(x74431,a871)),f299(x74431,x74432,x74433)),f301(x74431,x74433,x74434)),f299(x74431,x74432,x74434))+~P24(f328(f328(f244(x74431),x74433),x74434))+~P24(f328(f328(f244(x74431),x74432),x74433))
% 81.29/80.93 [8238]P21(x82381,x82382,f554(x82383,x82382,x82384,x82381),x82384)+~P24(f328(f62(x82382),x82383))+~P24(f328(f62(x82381),x82384))+~P24(f328(f328(f244(a877),f328(f38(x82381),x82384)),f328(f38(x82382),x82383)))
% 81.29/80.93 [8259]P36(x82591,x82592,x82593)+~P24(f328(x82592,x82594))+P24(f328(x82592,f808(x82593,x82592,x82591,x82594)))+~P24(f328(f328(f330(x82591),x82594),f328(f171(x82591),x82593)))
% 81.29/80.93 [8310]~P75(x83101)+~E(f328(x83103,f343(x83103,x83104,x83102,x83101)),f79(x83101))+E(f328(f328(f328(f66(x83101,x83102,f82(x83101)),x83103),f79(x83101)),x83104),f79(x83101))+~P24(f328(f62(x83102),x83104))
% 81.29/80.93 [8584]~P110(x85841)+~P24(f328(f328(f244(x85841),f2(x85841)),x85843))+P24(f328(f328(f244(x85841),x85842),x85843))+~P24(f328(f328(f244(x85841),f328(f328(f258(x85841),x85842),f328(a118,x85844))),f328(f328(f258(x85841),x85843),f328(a118,x85844))))
% 81.29/80.93 [8879]P36(x88791,x88792,x88793)+~P24(f328(x88792,x88794))+~P24(f328(f328(f330(x88791),x88794),f328(f171(x88791),x88793)))+P24(f328(f328(f330(x88791),f808(x88793,x88792,x88791,x88794)),f328(f171(x88791),x88793)))
% 81.29/80.93 [8964]~P75(x89641)+E(f328(f328(f328(f66(x89641,x89642,f82(x89641)),x89643),f79(x89641)),x89644),f79(x89641))+~P24(f328(f62(x89642),x89644))+P24(f328(f328(f330(x89642),f343(x89643,x89644,x89642,x89641)),x89644))
% 81.29/80.93 [9451]~P24(f328(f328(f244(a1),x94514),f2(a1)))+P24(f328(f328(f244(a1),f328(f328(f81(a1),f328(f328(f82(a1),x94511),f45(a1,x94512,x94513))),x94514)),f2(a1)))+~P24(f328(f328(f245(a1),f2(a1)),x94513))+~P24(f328(f328(f245(a1),x94511),x94514))
% 81.29/80.93 [9897]~P24(f328(f62(x98971),x98972))+~P24(f328(f328(f330(x98971),x98974),x98972))+~P24(f328(f328(f330(x98971),x98973),x98972))+P24(f328(f328(f245(a877),f328(f38(x98971),f328(f328(f22(f885(x98971,a871)),f328(f328(f22(f885(x98971,a871)),x98972),f328(f328(f306(x98971),x98973),f193(f885(x98971,a871))))),f328(f328(f306(x98971),x98974),f193(f885(x98971,a871)))))),f328(f38(x98971),x98972)))
% 81.29/80.93 [6920]~P102(x69201)+~P24(f328(f328(f244(x69201),x69202),x69204))+~P24(f328(f328(f244(x69201),x69202),x69203))+P24(f328(f328(f244(x69201),x69202),f328(f328(f107(x69201),x69203),x69204)))
% 81.29/80.93 [6923]~P106(x69231)+~P24(f328(f328(f244(x69231),x69232),x69234))+~P24(f328(f328(f244(x69231),x69232),x69233))+P24(f328(f328(f244(x69231),x69232),f328(f328(f242(x69231),x69233),x69234)))
% 81.29/80.93 [6924]~P106(x69241)+~P24(f328(f328(f245(x69241),x69242),x69244))+~P24(f328(f328(f245(x69241),x69242),x69243))+P24(f328(f328(f245(x69241),x69242),f328(f328(f242(x69241),x69243),x69244)))
% 81.29/80.93 [6943]~P62(x69432)+E(x69431,f2(x69432))+E(f328(f328(f286(x69432),f328(f328(f258(x69432),x69431),x69433)),f328(f328(f258(x69432),x69431),x69434)),f328(f328(f258(x69432),x69431),f328(f328(f22(a877),x69433),x69434)))+~P24(f328(f328(f244(a877),x69434),x69433))
% 81.29/80.93 [6988]~P106(x69881)+~P29(x69881,f328(f328(f150(x69881),x69883),x69884))+P29(x69881,f328(f328(f150(x69881),x69882),f328(f328(f150(x69881),x69883),x69884)))+~P24(f328(f328(f244(x69881),x69882),x69883))
% 81.29/80.93 [7029]~P89(x70291)+~P24(f328(f328(f244(x70291),f2(x70291)),x70294))+~P24(f328(f328(f244(x70291),x70292),x70293))+P24(f328(f328(f244(x70291),x70292),f328(f328(f81(x70291),x70293),x70294)))
% 81.29/80.93 [7030]~P89(x70301)+~P24(f328(f328(f244(x70301),f2(x70301)),x70303))+~P24(f328(f328(f244(x70301),x70302),x70304))+P24(f328(f328(f244(x70301),x70302),f328(f328(f81(x70301),x70303),x70304)))
% 81.29/80.93 [7031]~P110(x70311)+~P24(f328(f328(f245(x70311),f2(x70311)),x70313))+~P24(f328(f328(f245(x70311),x70312),x70314))+P24(f328(f328(f245(x70311),x70312),f328(f328(f81(x70311),x70313),x70314)))
% 81.29/80.93 [7032]~P89(x70321)+~P24(f328(f328(f244(x70321),x70322),x70324))+~P24(f328(f328(f245(x70321),f2(x70321)),x70323))+P24(f328(f328(f245(x70321),x70322),f328(f328(f81(x70321),x70323),x70324)))
% 81.29/80.93 [7033]~P89(x70331)+~P24(f328(f328(f244(x70331),f2(x70331)),x70333))+~P24(f328(f328(f245(x70331),x70332),x70334))+P24(f328(f328(f245(x70331),x70332),f328(f328(f81(x70331),x70333),x70334)))
% 81.29/80.93 [7072]~P106(x70721)+P24(f328(f328(f244(x70721),x70722),x70723))+P24(f328(f328(f244(x70721),x70722),x70724))+~P24(f328(f328(f244(x70721),x70722),f328(f328(f243(x70721),x70724),x70723)))
% 81.29/80.93 [7073]~P106(x70731)+P24(f328(f328(f245(x70731),x70732),x70733))+P24(f328(f328(f245(x70731),x70732),x70734))+~P24(f328(f328(f245(x70731),x70732),f328(f328(f243(x70731),x70734),x70733)))
% 81.29/80.93 [7360]~P108(x73602)+~P60(x73601)+~P24(f328(f328(f245(f885(x73601,x73602)),x73603),x73604))+P24(f328(f328(f244(f885(x73601,x73602)),x73603),x73604))
% 81.29/80.93 [7727]~P64(x77271)+~P24(f328(f328(f245(x77271),x77274),f2(x77271)))+~P24(f328(f328(f244(x77271),x77273),f328(f328(f286(x77271),x77272),x77274)))+P24(f328(f328(f244(x77271),x77272),f328(f328(f82(x77271),x77273),x77274)))
% 81.29/80.93 [7728]~P64(x77281)+~P24(f328(f328(f245(x77281),x77284),f2(x77281)))+~P24(f328(f328(f244(x77281),x77283),f328(f328(f82(x77281),x77282),x77284)))+P24(f328(f328(f244(x77281),x77282),f328(f328(f286(x77281),x77283),x77284)))
% 81.29/80.93 [7729]~P64(x77291)+~P24(f328(f328(f245(x77291),x77294),f2(x77291)))+~P24(f328(f328(f245(x77291),x77293),f328(f328(f286(x77291),x77292),x77294)))+P24(f328(f328(f245(x77291),x77292),f328(f328(f82(x77291),x77293),x77294)))
% 81.29/80.93 [7730]~P64(x77301)+~P24(f328(f328(f245(x77301),x77304),f2(x77301)))+~P24(f328(f328(f245(x77301),x77303),f328(f328(f82(x77301),x77302),x77304)))+P24(f328(f328(f245(x77301),x77302),f328(f328(f286(x77301),x77303),x77304)))
% 81.29/80.93 [7835]~P132(x78351)+~P24(f328(f328(f244(x78351),x78352),f2(x78351)))+~P24(f328(f328(f244(x78351),x78354),x78353))+P24(f328(f328(f244(x78351),f328(f328(f82(x78351),x78352),x78353)),f328(f328(f82(x78351),x78352),x78354)))
% 81.29/80.93 [7836]~P123(x78361)+~P24(f328(f328(f245(x78361),x78362),f2(x78361)))+~P24(f328(f328(f244(x78361),x78364),x78363))+P24(f328(f328(f244(x78361),f328(f328(f82(x78361),x78362),x78363)),f328(f328(f82(x78361),x78362),x78364)))
% 81.29/80.93 [7837]~P132(x78371)+~P24(f328(f328(f244(x78371),x78373),f2(x78371)))+~P24(f328(f328(f244(x78371),x78374),x78372))+P24(f328(f328(f244(x78371),f328(f328(f82(x78371),x78372),x78373)),f328(f328(f82(x78371),x78374),x78373)))
% 81.29/80.93 [7838]~P63(x78381)+~P24(f328(f328(f244(x78381),x78383),f2(x78381)))+~P24(f328(f328(f244(x78381),x78384),x78382))+P24(f328(f328(f244(x78381),f328(f328(f286(x78381),x78382),x78383)),f328(f328(f286(x78381),x78384),x78383)))
% 81.29/80.93 [7842]~P123(x78421)+~P24(f328(f328(f245(x78421),x78423),f2(x78421)))+~P24(f328(f328(f245(x78421),x78424),x78422))+P24(f328(f328(f245(x78421),f328(f328(f82(x78421),x78422),x78423)),f328(f328(f82(x78421),x78424),x78423)))
% 81.29/80.93 [7843]~P123(x78431)+~P24(f328(f328(f245(x78431),x78432),f2(x78431)))+~P24(f328(f328(f245(x78431),x78434),x78433))+P24(f328(f328(f245(x78431),f328(f328(f82(x78431),x78432),x78433)),f328(f328(f82(x78431),x78432),x78434)))
% 81.29/80.93 [7844]~P64(x78441)+~P24(f328(f328(f245(x78441),x78443),f2(x78441)))+~P24(f328(f328(f245(x78441),x78444),x78442))+P24(f328(f328(f245(x78441),f328(f328(f286(x78441),x78442),x78443)),f328(f328(f286(x78441),x78444),x78443)))
% 81.29/80.93 [7845]~P110(x78451)+~P24(f328(f328(f245(x78451),f79(x78451)),x78452))+~P24(f328(f328(f244(a877),x78453),x78454))+P24(f328(f328(f244(x78451),f328(f328(f258(x78451),x78452),x78453)),f328(f328(f258(x78451),x78452),x78454)))
% 81.29/80.93 [7846]~P110(x78461)+~P24(f328(f328(f244(x78461),f79(x78461)),x78462))+~P24(f328(f328(f244(a877),x78463),x78464))+P24(f328(f328(f244(x78461),f328(f328(f258(x78461),x78462),x78463)),f328(f328(f258(x78461),x78462),x78464)))
% 81.29/80.93 [7848]~P110(x78481)+~P24(f328(f328(f245(x78481),f79(x78481)),x78482))+~P24(f328(f328(f245(a877),x78483),x78484))+P24(f328(f328(f245(x78481),f328(f328(f258(x78481),x78482),x78483)),f328(f328(f258(x78481),x78482),x78484)))
% 81.29/80.93 [7875]P24(f328(f328(f245(a877),f2(a877)),f328(x78751,x78752)))+~P24(f328(f62(x78753),x78754))+~P24(f328(f328(f330(x78753),x78752),x78754))+~P24(f328(f328(f245(a877),f2(a877)),f328(f328(f9(x78753,a877),x78751),x78754)))
% 81.29/80.93 [7884]~P134(x78841)+~P24(f328(f328(f244(x78841),x78843),x78844))+~P24(f328(f328(f244(x78841),f2(x78841)),x78842))+P24(f328(f328(f244(x78841),f328(f328(f82(x78841),x78842),x78843)),f328(f328(f82(x78841),x78842),x78844)))
% 81.29/80.93 [7885]~P133(x78851)+~P24(f328(f328(f244(x78851),x78853),x78854))+~P24(f328(f328(f244(x78851),f2(x78851)),x78852))+P24(f328(f328(f244(x78851),f328(f328(f82(x78851),x78852),x78853)),f328(f328(f82(x78851),x78852),x78854)))
% 81.29/80.93 [7886]~P123(x78861)+~P24(f328(f328(f245(x78861),f2(x78861)),x78862))+~P24(f328(f328(f244(x78861),x78863),x78864))+P24(f328(f328(f244(x78861),f328(f328(f82(x78861),x78862),x78863)),f328(f328(f82(x78861),x78862),x78864)))
% 81.29/80.93 [7887]~P134(x78871)+~P24(f328(f328(f244(x78871),x78872),x78874))+~P24(f328(f328(f244(x78871),f2(x78871)),x78873))+P24(f328(f328(f244(x78871),f328(f328(f82(x78871),x78872),x78873)),f328(f328(f82(x78871),x78874),x78873)))
% 81.29/80.93 [7888]~P63(x78881)+~P24(f328(f328(f244(x78881),x78882),x78884))+~P24(f328(f328(f244(x78881),f2(x78881)),x78883))+P24(f328(f328(f244(x78881),f328(f328(f286(x78881),x78882),x78883)),f328(f328(f286(x78881),x78884),x78883)))
% 81.29/80.93 [7889]~P110(x78891)+~P24(f328(f328(f244(x78891),x78892),x78894))+~P24(f328(f328(f244(x78891),f2(x78891)),x78892))+P24(f328(f328(f244(x78891),f328(f328(f258(x78891),x78892),x78893)),f328(f328(f258(x78891),x78894),x78893)))
% 81.29/80.93 [7891]~P127(x78911)+~P24(f328(f328(f245(x78911),x78913),x78914))+~P24(f328(f328(f245(x78911),f2(x78911)),x78912))+P24(f328(f328(f245(x78911),f328(f328(f82(x78911),x78912),x78913)),f328(f328(f82(x78911),x78912),x78914)))
% 81.29/80.93 [7892]~P118(x78921)+~P24(f328(f328(f245(x78921),x78923),x78924))+~P24(f328(f328(f245(x78921),f2(x78921)),x78922))+P24(f328(f328(f245(x78921),f328(f328(f82(x78921),x78922),x78923)),f328(f328(f82(x78921),x78922),x78924)))
% 81.29/80.93 [7893]~P123(x78931)+~P24(f328(f328(f245(x78931),x78932),x78934))+~P24(f328(f328(f245(x78931),f2(x78931)),x78933))+P24(f328(f328(f245(x78931),f328(f328(f82(x78931),x78932),x78933)),f328(f328(f82(x78931),x78934),x78933)))
% 81.29/80.93 [7894]~P127(x78941)+~P24(f328(f328(f245(x78941),x78942),x78944))+~P24(f328(f328(f245(x78941),f2(x78941)),x78943))+P24(f328(f328(f245(x78941),f328(f328(f82(x78941),x78942),x78943)),f328(f328(f82(x78941),x78944),x78943)))
% 81.29/80.93 [7895]~P123(x78951)+~P24(f328(f328(f245(x78951),x78953),x78954))+~P24(f328(f328(f245(x78951),f2(x78951)),x78952))+P24(f328(f328(f245(x78951),f328(f328(f82(x78951),x78952),x78953)),f328(f328(f82(x78951),x78952),x78954)))
% 81.29/80.93 [7896]~P64(x78961)+~P24(f328(f328(f245(x78961),x78962),x78964))+~P24(f328(f328(f245(x78961),f2(x78961)),x78963))+P24(f328(f328(f245(x78961),f328(f328(f286(x78961),x78962),x78963)),f328(f328(f286(x78961),x78964),x78963)))
% 81.29/80.93 [7939]~P107(x79392)+P24(f328(f328(f245(f885(x79391,x79392)),x79394),x79393))+~P24(f328(f328(f244(f885(x79391,x79392)),x79394),x79393))+P24(f328(f328(f244(f885(x79391,x79392)),x79393),x79394))
% 81.29/80.93 [7981]P24(f328(f328(f330(x79811),x79812),x79813))+P24(f328(f328(f330(x79811),x79812),x79814))+~P24(f328(f328(f244(f885(x79811,a871)),x79814),x79813))+P24(f328(f328(f245(f885(x79811,a871)),x79814),f328(f328(f306(x79811),x79812),x79813)))
% 81.29/80.93 [8143]P24(f328(f328(f330(x81431),x81432),x81433))+P24(f328(f328(f330(x81431),x81432),x81434))+~P24(f328(f328(f245(f885(x81431,a871)),x81434),f328(f328(f306(x81431),x81432),x81433)))+P24(f328(f328(f244(f885(x81431,a871)),x81434),x81433))
% 81.29/80.93 [8152]~P60(x81521)+P7(x81521,x81522,x81523)+~P24(f328(x81522,x81524))+~P24(f328(f328(f330(f878(x81521)),x81524),f328(f171(f878(x81521)),f55(x81521,x81523,f56(x81521)))))
% 81.29/80.93 [8162]~P8(x81623,x81621,x81624)+~P60(x81623)+P24(f328(x81621,x81622))+~P24(f328(f328(f330(f878(x81623)),x81622),f328(f171(f878(x81623)),f55(x81623,x81624,f56(x81623)))))
% 81.29/80.93 [8215]~P123(x82151)+P24(f328(f328(f245(x82151),x82153),x82152))+P24(f328(f328(f245(x82151),x82152),x82153))+~P24(f328(f328(f245(x82151),f328(f328(f82(x82151),x82154),x82152)),f328(f328(f82(x82151),x82154),x82153)))
% 81.29/80.93 [8216]~P123(x82161)+P24(f328(f328(f245(x82161),x82163),x82162))+P24(f328(f328(f245(x82161),x82162),x82163))+~P24(f328(f328(f245(x82161),f328(f328(f82(x82161),x82162),x82164)),f328(f328(f82(x82161),x82163),x82164)))
% 81.29/80.93 [8227]~P123(x82271)+P24(f328(f328(f245(x82271),x82274),f2(x82271)))+P24(f328(f328(f245(x82271),x82272),x82273))+~P24(f328(f328(f245(x82271),f328(f328(f82(x82271),x82272),x82274)),f328(f328(f82(x82271),x82273),x82274)))
% 81.29/80.93 [8228]~P123(x82281)+P24(f328(f328(f245(x82281),x82284),f2(x82281)))+P24(f328(f328(f245(x82281),x82282),x82283))+~P24(f328(f328(f245(x82281),f328(f328(f82(x82281),x82284),x82282)),f328(f328(f82(x82281),x82284),x82283)))
% 81.29/80.93 [8232]~P123(x82321)+P24(f328(f328(f245(x82321),x82322),x82323))+P24(f328(f328(f245(x82321),f2(x82321)),x82324))+~P24(f328(f328(f245(x82321),f328(f328(f82(x82321),x82324),x82323)),f328(f328(f82(x82321),x82324),x82322)))
% 81.29/80.93 [8233]~P123(x82331)+P24(f328(f328(f245(x82331),x82332),x82333))+P24(f328(f328(f245(x82331),f2(x82331)),x82334))+~P24(f328(f328(f245(x82331),f328(f328(f82(x82331),x82333),x82334)),f328(f328(f82(x82331),x82332),x82334)))
% 81.29/80.93 [8246]~P123(x82461)+P24(f328(f328(f245(x82461),x82462),f2(x82461)))+P24(f328(f328(f245(x82461),f2(x82461)),x82462))+~P24(f328(f328(f245(x82461),f328(f328(f82(x82461),x82463),x82462)),f328(f328(f82(x82461),x82464),x82462)))
% 81.29/80.93 [8247]~P123(x82471)+P24(f328(f328(f245(x82471),x82472),f2(x82471)))+P24(f328(f328(f245(x82471),f2(x82471)),x82472))+~P24(f328(f328(f245(x82471),f328(f328(f82(x82471),x82472),x82473)),f328(f328(f82(x82471),x82472),x82474)))
% 81.29/80.93 [8273]~P123(x82731)+~P24(f328(f328(f245(x82731),x82734),f2(x82731)))+P24(f328(f328(f244(x82731),x82732),x82733))+~P24(f328(f328(f244(x82731),f328(f328(f82(x82731),x82734),x82733)),f328(f328(f82(x82731),x82734),x82732)))
% 81.29/80.93 [8274]~P123(x82741)+~P24(f328(f328(f245(x82741),x82744),f2(x82741)))+P24(f328(f328(f245(x82741),x82742),x82743))+~P24(f328(f328(f245(x82741),f328(f328(f82(x82741),x82744),x82743)),f328(f328(f82(x82741),x82744),x82742)))
% 81.29/80.93 [8286]~P110(x82863)+~P24(f328(f328(f245(x82863),f79(x82863)),x82864))+P24(f328(f328(f244(a877),x82861),x82862))+~P24(f328(f328(f244(x82863),f328(f328(f258(x82863),x82864),x82861)),f328(f328(f258(x82863),x82864),x82862)))
% 81.29/80.93 [8288]~P110(x82883)+~P24(f328(f328(f245(x82883),f79(x82883)),x82884))+P24(f328(f328(f245(a877),x82881),x82882))+~P24(f328(f328(f245(x82883),f328(f328(f258(x82883),x82884),x82881)),f328(f328(f258(x82883),x82884),x82882)))
% 81.29/80.93 [8298]~P123(x82981)+P24(f328(f328(f244(x82981),x82982),x82983))+~P24(f328(f328(f245(x82981),f2(x82981)),x82984))+~P24(f328(f328(f244(x82981),f328(f328(f82(x82981),x82984),x82982)),f328(f328(f82(x82981),x82984),x82983)))
% 81.29/80.93 [8299]~P127(x82991)+P24(f328(f328(f244(x82991),x82992),x82993))+~P24(f328(f328(f245(x82991),f2(x82991)),x82994))+~P24(f328(f328(f244(x82991),f328(f328(f82(x82991),x82994),x82992)),f328(f328(f82(x82991),x82994),x82993)))
% 81.29/80.93 [8300]~P127(x83001)+P24(f328(f328(f244(x83001),x83002),x83003))+~P24(f328(f328(f245(x83001),f2(x83001)),x83004))+~P24(f328(f328(f244(x83001),f328(f328(f82(x83001),x83002),x83004)),f328(f328(f82(x83001),x83003),x83004)))
% 81.29/80.93 [8301]~P123(x83011)+P24(f328(f328(f245(x83011),x83012),x83013))+~P24(f328(f328(f245(x83011),f2(x83011)),x83014))+~P24(f328(f328(f245(x83011),f328(f328(f82(x83011),x83014),x83012)),f328(f328(f82(x83011),x83014),x83013)))
% 81.29/80.93 [8302]~P127(x83021)+P24(f328(f328(f245(x83021),x83022),x83023))+~P24(f328(f328(f244(x83021),f2(x83021)),x83024))+~P24(f328(f328(f245(x83021),f328(f328(f82(x83021),x83024),x83022)),f328(f328(f82(x83021),x83024),x83023)))
% 81.29/80.93 [8303]~P128(x83031)+P24(f328(f328(f245(x83031),x83032),x83033))+~P24(f328(f328(f244(x83031),f2(x83031)),x83034))+~P24(f328(f328(f245(x83031),f328(f328(f82(x83031),x83034),x83032)),f328(f328(f82(x83031),x83034),x83033)))
% 81.29/80.93 [8304]~P110(x83041)+~P24(f328(f328(f244(x83041),f2(x83041)),x83043))+P24(f328(f328(f245(x83041),x83042),x83043))+~P24(f328(f328(f245(x83041),f328(f328(f258(x83041),x83042),x83044)),f328(f328(f258(x83041),x83043),x83044)))
% 81.29/80.93 [8305]~P127(x83051)+P24(f328(f328(f245(x83051),x83052),x83053))+~P24(f328(f328(f244(x83051),f2(x83051)),x83054))+~P24(f328(f328(f245(x83051),f328(f328(f82(x83051),x83052),x83054)),f328(f328(f82(x83051),x83053),x83054)))
% 81.29/80.93 [8306]~P128(x83061)+P24(f328(f328(f245(x83061),x83062),x83063))+~P24(f328(f328(f244(x83061),f2(x83061)),x83064))+~P24(f328(f328(f245(x83061),f328(f328(f82(x83061),x83062),x83064)),f328(f328(f82(x83061),x83063),x83064)))
% 81.29/80.93 [8349]P24(f328(f328(f330(x83491),x83492),x83493))+~P24(f328(f328(f244(f885(x83491,a871)),x83493),x83494))+~P24(f328(f328(f245(f885(x83491,a871)),x83493),x83494))+P24(f328(f328(f245(f885(x83491,a871)),x83493),f328(f328(f306(x83491),x83492),x83494)))
% 81.29/80.93 [8607]~P60(x86071)+~P95(x86072)+~E(f328(x86073,f809(x86074,x86073,x86071,x86072)),f328(x86074,f809(x86074,x86073,x86071,x86072)))+P24(f328(f328(f92(f885(x86071,x86072)),x86073),x86074))
% 81.29/80.93 [8722]E(f328(f328(f22(a1),f436(x87221,x87222,x87223,x87224)),f437(x87221,x87222,x87223,x87224)),x87224)+~P24(f328(f328(f245(a1),f2(a1)),x87223))+~P24(f328(f328(f244(a1),x87221),x87224))+P24(f328(f328(f244(a1),x87221),f328(f328(f81(a1),x87224),x87223)))
% 81.29/80.93 [8723]E(f328(f328(f22(a1),f452(x87231,x87232,x87233,x87234)),f453(x87231,x87232,x87233,x87234)),x87234)+~P24(f328(f328(f245(a1),f2(a1)),x87233))+~P24(f328(f328(f245(a1),x87231),x87234))+P24(f328(f328(f245(a1),x87231),f328(f328(f81(a1),x87234),x87233)))
% 81.29/80.93 [8859]~E(f328(f328(f164(x88591),x88593),f634(x88594,x88593,x88591,x88592)),f328(f328(f164(x88591),x88594),f634(x88594,x88593,x88591,x88592)))+E(f328(f328(f174(x88591),x88592),x88593),f328(f328(f174(x88591),x88592),x88594))+~P24(f328(f328(f244(a877),x88592),f328(f194(f878(x88591)),x88593)))+~P24(f328(f328(f244(a877),x88592),f328(f194(f878(x88591)),x88594)))
% 81.29/80.93 [8930]~P24(f328(f328(f245(a1),f2(a1)),x89303))+~P24(f328(f328(f244(a1),x89301),x89304))+P24(f328(f328(f330(a1),f436(x89301,x89302,x89303,x89304)),x89302))+P24(f328(f328(f244(a1),x89301),f328(f328(f81(a1),x89304),x89303)))
% 81.29/80.93 [8931]~P24(f328(f328(f245(a1),f2(a1)),x89313))+~P24(f328(f328(f245(a1),x89311),x89314))+P24(f328(f328(f330(a1),f452(x89311,x89312,x89313,x89314)),x89312))+P24(f328(f328(f245(a1),x89311),f328(f328(f81(a1),x89314),x89313)))
% 81.29/80.93 [8973]~P102(x89731)+~P24(f328(f62(x89731),x89733))+~P24(f328(f328(f330(x89731),x89734),x89733))+P24(f328(f328(f244(x89731),f328(f328(f65(x89731,x89731,f107(x89731)),x89732),x89733)),f328(f328(f107(x89731),x89734),x89732)))
% 81.29/80.93 [8974]~P106(x89741)+~P24(f328(f62(x89741),x89743))+~P24(f328(f328(f330(x89741),x89744),x89743))+P24(f328(f328(f244(x89741),f328(f328(f65(x89741,x89741,f242(x89741)),x89742),x89743)),f328(f328(f242(x89741),x89744),x89742)))
% 81.29/80.93 [9021]E(f328(f328(f174(x90211),x90212),x90213),f328(f328(f174(x90211),x90212),x90214))+P24(f328(f328(f245(a877),f634(x90213,x90214,x90211,x90212)),x90212))+~P24(f328(f328(f244(a877),x90212),f328(f194(f878(x90211)),x90213)))+~P24(f328(f328(f244(a877),x90212),f328(f194(f878(x90211)),x90214)))
% 81.29/80.93 [9026]~P24(f328(f328(f245(a1),f2(a1)),x90263))+~P24(f328(f328(f244(a1),x90261),x90262))+P24(f328(f328(f330(a1),f437(x90261,x90264,x90263,x90262)),f299(a1,f79(a1),x90263)))+P24(f328(f328(f244(a1),x90261),f328(f328(f81(a1),x90262),x90263)))
% 81.29/80.93 [9027]~P24(f328(f328(f245(a1),f2(a1)),x90273))+~P24(f328(f328(f245(a1),x90271),x90272))+P24(f328(f328(f330(a1),f453(x90271,x90274,x90273,x90272)),f299(a1,f79(a1),x90273)))+P24(f328(f328(f245(a1),x90271),f328(f328(f81(a1),x90272),x90273)))
% 81.29/80.93 [9190]~E(f328(f177(x91901,x91902),x91903),f328(f177(x91901,x91902),x91904))+E(f328(f171(f884(x91901,x91902)),x91903),f328(f171(f884(x91901,x91902)),x91904))+~P24(f328(f136(x91901),f328(f328(f153(f884(x91901,x91902),x91901),f256(x91901,x91902)),x91904)))+~P24(f328(f136(x91901),f328(f328(f153(f884(x91901,x91902),x91901),f256(x91901,x91902)),x91903)))
% 81.29/80.93 [9202]E(f328(f177(x92021,x92022),x92023),f328(f177(x92021,x92022),x92024))+~E(f328(f171(f884(x92021,x92022)),x92023),f328(f171(f884(x92021,x92022)),x92024))+~P24(f328(f136(x92021),f328(f328(f153(f884(x92021,x92022),x92021),f256(x92021,x92022)),x92024)))+~P24(f328(f136(x92021),f328(f328(f153(f884(x92021,x92022),x92021),f256(x92021,x92022)),x92023)))
% 81.29/80.93 [9346]~P65(x93461)+~P24(f328(f62(x93461),x93464))+P24(f328(f328(f330(x93461),f847(x93462,x93463,x93464,x93461)),x93464))+P24(f328(f328(f244(x93461),f328(f328(f65(x93461,x93461,f116(x93461)),x93462),x93464)),f328(f328(f116(x93461),x93463),x93462)))
% 81.29/80.93 [9347]~P106(x93471)+~P24(f328(f62(x93471),x93474))+P24(f328(f328(f330(x93471),f475(x93472,x93473,x93474,x93471)),x93474))+P24(f328(f328(f244(x93471),f328(f328(f65(x93471,x93471,f243(x93471)),x93472),x93474)),f328(f328(f243(x93471),x93473),x93472)))
% 81.29/80.93 [9469]~P65(x94691)+~P24(f328(f62(x94691),x94693))+~P24(f328(f328(f244(x94691),f847(x94692,x94694,x94693,x94691)),x94694))+P24(f328(f328(f244(x94691),f328(f328(f65(x94691,x94691,f116(x94691)),x94692),x94693)),f328(f328(f116(x94691),x94694),x94692)))
% 81.29/80.93 [9470]~P106(x94701)+~P24(f328(f62(x94701),x94703))+~P24(f328(f328(f244(x94701),f475(x94702,x94704,x94703,x94701)),x94704))+P24(f328(f328(f244(x94701),f328(f328(f65(x94701,x94701,f243(x94701)),x94702),x94703)),f328(f328(f243(x94701),x94704),x94702)))
% 81.29/80.93 [9473]~P24(f328(f328(f244(a1),f2(a1)),x94734))+~P24(f328(f328(f245(a1),f2(a1)),x94733))+~P24(f328(f328(f245(a1),x94734),x94731))+P24(f328(f328(f245(a1),f328(f328(f81(a1),f328(f328(f82(a1),x94731),f45(a1,x94732,x94733))),x94734)),f328(f328(f82(a1),x94731),x94733)))
% 81.29/80.93 [9865]E(x98651,x98652)+P24(f328(f328(f330(f884(f878(x98653),f878(x98653))),f328(f328(f257(f878(x98653),f878(x98653)),x98652),x98651)),f146(x98653,x98654)))+P24(f328(f328(f330(f884(f878(x98653),f878(x98653))),f328(f328(f257(f878(x98653),f878(x98653)),x98651),x98652)),f146(x98653,x98654)))+~P24(f328(f328(f330(f884(x98653,x98653)),f328(f328(f257(x98653,x98653),f629(x98651,x98652,x98654,x98653)),f631(x98651,x98652,x98654,x98653))),x98654))
% 81.29/80.93 [9866]E(x98661,x98662)+P24(f328(f328(f330(f884(f878(x98663),f878(x98663))),f328(f328(f257(f878(x98663),f878(x98663)),x98662),x98661)),f146(x98663,x98664)))+P24(f328(f328(f330(f884(f878(x98663),f878(x98663))),f328(f328(f257(f878(x98663),f878(x98663)),x98661),x98662)),f146(x98663,x98664)))+~P24(f328(f328(f330(f884(x98663,x98663)),f328(f328(f257(x98663,x98663),f631(x98661,x98662,x98664,x98663)),f629(x98661,x98662,x98664,x98663))),x98664))
% 81.29/80.93 [7430]~P65(x74301)+~P24(f328(f328(f244(x74301),x74303),x74304))+~P24(f328(f328(f244(x74301),x74302),x74304))+P24(f328(f328(f244(x74301),f328(f328(f116(x74301),x74302),x74303)),x74304))
% 81.29/80.93 [7433]~P106(x74331)+~P24(f328(f328(f244(x74331),x74333),x74334))+~P24(f328(f328(f244(x74331),x74332),x74334))+P24(f328(f328(f244(x74331),f328(f328(f243(x74331),x74332),x74333)),x74334))
% 81.29/80.93 [7434]~P106(x74341)+~P24(f328(f328(f245(x74341),x74343),x74344))+~P24(f328(f328(f245(x74341),x74342),x74344))+P24(f328(f328(f245(x74341),f328(f328(f243(x74341),x74342),x74343)),x74344))
% 81.29/80.93 [7750]~E(x77501,x77503)+E(f138(a877,f328(f298(a877,x77501),x77502)),f328(f328(f150(a877),x77503),x77504))+~E(f138(a877,f328(f298(a877,f328(f328(f81(a877),x77501),f79(a877))),x77502)),x77504)+~P24(f328(f328(f245(a877),x77501),x77502))
% 81.29/80.93 [7761]~P106(x77611)+P24(f328(f328(f244(x77611),x77612),x77613))+P24(f328(f328(f244(x77611),x77614),x77613))+~P24(f328(f328(f244(x77611),f328(f328(f242(x77611),x77614),x77612)),x77613))
% 81.29/80.93 [7762]~P106(x77621)+P24(f328(f328(f245(x77621),x77622),x77623))+P24(f328(f328(f245(x77621),x77624),x77623))+~P24(f328(f328(f245(x77621),f328(f328(f242(x77621),x77624),x77622)),x77623))
% 81.29/80.93 [8042]~P63(x80421)+~P24(f328(f328(f245(x80421),f2(x80421)),x80423))+~P24(f328(f328(f244(x80421),x80422),f328(f328(f286(x80421),x80424),x80423)))+P24(f328(f328(f244(x80421),f328(f328(f82(x80421),x80422),x80423)),x80424))
% 81.29/80.93 [8043]~P64(x80431)+~P24(f328(f328(f245(x80431),f2(x80431)),x80433))+~P24(f328(f328(f244(x80431),x80432),f328(f328(f286(x80431),x80434),x80433)))+P24(f328(f328(f244(x80431),f328(f328(f82(x80431),x80432),x80433)),x80434))
% 81.29/80.93 [8044]~P63(x80441)+~P24(f328(f328(f245(x80441),f2(x80441)),x80443))+~P24(f328(f328(f244(x80441),x80442),f328(f328(f82(x80441),x80444),x80443)))+P24(f328(f328(f244(x80441),f328(f328(f286(x80441),x80442),x80443)),x80444))
% 81.29/80.93 [8046]~P64(x80461)+~P24(f328(f328(f245(x80461),f2(x80461)),x80463))+~P24(f328(f328(f244(x80461),x80462),f328(f328(f82(x80461),x80464),x80463)))+P24(f328(f328(f244(x80461),f328(f328(f286(x80461),x80462),x80463)),x80464))
% 81.29/80.93 [8047]~P63(x80471)+~P24(f328(f328(f245(x80471),f2(x80471)),x80473))+~P24(f328(f328(f245(x80471),x80472),f328(f328(f286(x80471),x80474),x80473)))+P24(f328(f328(f245(x80471),f328(f328(f82(x80471),x80472),x80473)),x80474))
% 81.29/80.93 [8048]~P64(x80481)+~P24(f328(f328(f245(x80481),f2(x80481)),x80483))+~P24(f328(f328(f245(x80481),x80482),f328(f328(f286(x80481),x80484),x80483)))+P24(f328(f328(f245(x80481),f328(f328(f82(x80481),x80482),x80483)),x80484))
% 81.29/80.93 [8049]~P63(x80491)+~P24(f328(f328(f245(x80491),f2(x80491)),x80493))+~P24(f328(f328(f245(x80491),x80492),f328(f328(f82(x80491),x80494),x80493)))+P24(f328(f328(f245(x80491),f328(f328(f286(x80491),x80492),x80493)),x80494))
% 81.29/80.93 [8051]~P64(x80511)+~P24(f328(f328(f245(x80511),f2(x80511)),x80513))+~P24(f328(f328(f245(x80511),x80512),f328(f328(f82(x80511),x80514),x80513)))+P24(f328(f328(f245(x80511),f328(f328(f286(x80511),x80512),x80513)),x80514))
% 81.29/80.93 [8184]~P63(x81841)+~P24(f328(f328(f245(x81841),f2(x81841)),x81844))+P24(f328(f328(f244(x81841),x81842),f328(f328(f82(x81841),x81843),x81844)))+~P24(f328(f328(f244(x81841),f328(f328(f286(x81841),x81842),x81844)),x81843))
% 81.29/80.93 [8185]~P63(x81851)+~P24(f328(f328(f245(x81851),f2(x81851)),x81854))+P24(f328(f328(f244(x81851),x81852),f328(f328(f286(x81851),x81853),x81854)))+~P24(f328(f328(f244(x81851),f328(f328(f82(x81851),x81852),x81854)),x81853))
% 81.29/80.93 [8187]~P64(x81871)+~P24(f328(f328(f245(x81871),f2(x81871)),x81874))+P24(f328(f328(f244(x81871),x81872),f328(f328(f82(x81871),x81873),x81874)))+~P24(f328(f328(f244(x81871),f328(f328(f286(x81871),x81872),x81874)),x81873))
% 81.29/80.93 [8188]~P64(x81881)+~P24(f328(f328(f245(x81881),f2(x81881)),x81884))+P24(f328(f328(f244(x81881),x81882),f328(f328(f286(x81881),x81883),x81884)))+~P24(f328(f328(f244(x81881),f328(f328(f82(x81881),x81882),x81884)),x81883))
% 81.29/80.93 [8189]~P63(x81891)+~P24(f328(f328(f245(x81891),f2(x81891)),x81894))+P24(f328(f328(f245(x81891),x81892),f328(f328(f82(x81891),x81893),x81894)))+~P24(f328(f328(f245(x81891),f328(f328(f286(x81891),x81892),x81894)),x81893))
% 81.29/80.93 [8190]~P63(x81901)+~P24(f328(f328(f245(x81901),f2(x81901)),x81904))+P24(f328(f328(f245(x81901),x81902),f328(f328(f286(x81901),x81903),x81904)))+~P24(f328(f328(f245(x81901),f328(f328(f82(x81901),x81902),x81904)),x81903))
% 81.29/80.93 [8192]~P64(x81921)+~P24(f328(f328(f245(x81921),f2(x81921)),x81924))+P24(f328(f328(f245(x81921),x81922),f328(f328(f82(x81921),x81923),x81924)))+~P24(f328(f328(f245(x81921),f328(f328(f286(x81921),x81922),x81924)),x81923))
% 81.29/80.93 [8193]~P64(x81931)+~P24(f328(f328(f245(x81931),f2(x81931)),x81934))+P24(f328(f328(f245(x81931),x81932),f328(f328(f286(x81931),x81933),x81934)))+~P24(f328(f328(f245(x81931),f328(f328(f82(x81931),x81932),x81934)),x81933))
% 81.29/80.93 [8353]~P64(x83531)+~P24(f328(f328(f245(x83531),x83533),f2(x83531)))+~P24(f328(f328(f244(x83531),f328(f328(f286(x83531),x83534),x83533)),x83532))+P24(f328(f328(f244(x83531),f328(f328(f82(x83531),x83532),x83533)),x83534))
% 81.29/80.93 [8354]~P64(x83541)+~P24(f328(f328(f245(x83541),x83543),f2(x83541)))+~P24(f328(f328(f244(x83541),f328(f328(f82(x83541),x83544),x83543)),x83542))+P24(f328(f328(f244(x83541),f328(f328(f286(x83541),x83542),x83543)),x83544))
% 81.29/80.93 [8355]~P64(x83551)+~P24(f328(f328(f245(x83551),x83553),f2(x83551)))+~P24(f328(f328(f245(x83551),f328(f328(f286(x83551),x83554),x83553)),x83552))+P24(f328(f328(f245(x83551),f328(f328(f82(x83551),x83552),x83553)),x83554))
% 81.29/80.93 [8356]~P64(x83561)+~P24(f328(f328(f245(x83561),x83563),f2(x83561)))+~P24(f328(f328(f245(x83561),f328(f328(f82(x83561),x83564),x83563)),x83562))+P24(f328(f328(f245(x83561),f328(f328(f286(x83561),x83562),x83563)),x83564))
% 81.29/80.93 [8366]~P24(f328(x83661,x83664))+~P24(f328(f328(f245(a877),x83662),f328(f328(f82(a877),x83663),f328(a118,x83664))))+P24(f328(x83661,f328(f328(f39(a877),x83662),x83663)))+~P24(f328(f328(f244(a877),f328(f328(f82(a877),x83663),x83664)),x83662))
% 81.29/80.93 [8581]~P65(x85811)+~P24(f328(f62(x85811),x85814))+~P24(f328(f328(f330(x85811),x85812),x85814))+P24(f328(f328(f244(x85811),f328(f328(f116(x85811),x85812),x85813)),f328(f328(f65(x85811,x85811,f116(x85811)),x85813),x85814)))
% 81.29/80.93 [8582]~P106(x85821)+~P24(f328(f62(x85821),x85824))+~P24(f328(f328(f330(x85821),x85822),x85824))+P24(f328(f328(f244(x85821),f328(f328(f243(x85821),x85822),x85823)),f328(f328(f65(x85821,x85821,f243(x85821)),x85823),x85824)))
% 81.29/80.93 [8724]~P24(f328(f62(x87241),x87242))+E(f328(f38(x87241),f328(f328(f22(f885(x87241,a871)),x87242),f328(f328(f306(x87241),x87243),x87244))),f328(f328(f22(a877),f328(f38(x87241),f328(f328(f22(f885(x87241,a871)),x87242),x87244))),f79(a877)))+P24(f328(f328(f330(x87241),x87243),x87244))+~P24(f328(f328(f330(x87241),x87243),x87242))
% 81.29/80.93 [8795]E(f328(f328(f81(a1),f442(x87951,x87952,x87953,x87954)),f443(x87951,x87952,x87953,x87954)),x87954)+~P24(f328(f328(f245(a1),f2(a1)),x87953))+~P24(f328(f328(f244(a1),x87954),x87951))+P24(f328(f328(f244(a1),f328(f328(f22(a1),x87954),x87953)),x87951))
% 81.29/80.93 [8796]E(f328(f328(f81(a1),f454(x87961,x87962,x87963,x87964)),f455(x87961,x87962,x87963,x87964)),x87964)+~P24(f328(f328(f245(a1),f2(a1)),x87963))+~P24(f328(f328(f245(a1),x87964),x87961))+P24(f328(f328(f245(a1),f328(f328(f22(a1),x87964),x87963)),x87961))
% 81.29/80.93 [9006]~P24(f328(f328(f245(a1),f2(a1)),x90063))+~P24(f328(f328(f244(a1),x90064),x90061))+P24(f328(f328(f330(a1),f442(x90061,x90062,x90063,x90064)),x90062))+P24(f328(f328(f244(a1),f328(f328(f22(a1),x90064),x90063)),x90061))
% 81.29/80.93 [9007]~P24(f328(f328(f245(a1),f2(a1)),x90073))+~P24(f328(f328(f245(a1),x90074),x90071))+P24(f328(f328(f330(a1),f454(x90071,x90072,x90073,x90074)),x90072))+P24(f328(f328(f245(a1),f328(f328(f22(a1),x90074),x90073)),x90071))
% 81.29/80.93 [9092]~P24(f328(f328(f245(a1),f2(a1)),x90922))+~P24(f328(f328(f244(a1),x90921),x90923))+P24(f328(f328(f330(a1),f443(x90923,x90924,x90922,x90921)),f299(a1,f79(a1),x90922)))+P24(f328(f328(f244(a1),f328(f328(f22(a1),x90921),x90922)),x90923))
% 81.29/80.93 [9093]~P24(f328(f328(f245(a1),f2(a1)),x90932))+~P24(f328(f328(f245(a1),x90931),x90933))+P24(f328(f328(f330(a1),f455(x90933,x90934,x90932,x90931)),f299(a1,f79(a1),x90932)))+P24(f328(f328(f245(a1),f328(f328(f22(a1),x90931),x90932)),x90933))
% 81.29/80.93 [9109]~P24(f328(f328(f244(a1),f2(a1)),x91094))+~P24(f328(f328(f245(a1),f2(a1)),x91093))+~P24(f328(f328(f245(a1),x91094),x91091))+P24(f328(f328(f244(a1),f2(a1)),f328(f328(f81(a1),f328(f328(f82(a1),x91091),f45(a1,x91092,x91093))),x91094)))
% 81.29/80.93 [9173]~P102(x91731)+~P24(f328(f62(x91731),x91734))+~P24(f328(f328(f244(x91731),x91732),f846(x91733,x91732,x91734,x91731)))+P24(f328(f328(f244(x91731),f328(f328(f107(x91731),x91732),x91733)),f328(f328(f65(x91731,x91731,f107(x91731)),x91733),x91734)))
% 81.29/80.93 [9174]~P106(x91741)+~P24(f328(f62(x91741),x91744))+~P24(f328(f328(f244(x91741),x91742),f463(x91743,x91742,x91744,x91741)))+P24(f328(f328(f244(x91741),f328(f328(f242(x91741),x91742),x91743)),f328(f328(f65(x91741,x91741,f242(x91741)),x91743),x91744)))
% 81.29/80.93 [9189]~P24(f328(f328(f244(a1),x91894),f2(a1)))+~P24(f328(f328(f245(a1),f2(a1)),x91892))+~P24(f328(f328(f245(a1),x91891),x91894))+P24(f328(f328(f245(a1),f328(f328(f82(a1),x91891),x91892)),f328(f328(f81(a1),f328(f328(f82(a1),x91891),f45(a1,x91893,x91892))),x91894)))
% 81.29/80.93 [9211]P24(f328(f62(x92111),x92112))+~P24(f328(f62(x92111),x92113))+~P24(f328(f328(f330(f885(x92111,a871)),x92112),f328(f328(f61(x92111),x92113),x92114)))+~P24(f328(f328(f244(f885(f884(x92111,x92111),a871)),x92114),f328(f328(f265(x92111,x92111),x92113),f328(f16(f885(x92111,a871),x92111),x92113))))
% 81.29/80.93 [9239]~P102(x92391)+~P24(f328(f62(x92391),x92394))+P24(f328(f328(f330(x92391),f846(x92392,x92393,x92394,x92391)),x92394))+P24(f328(f328(f244(x92391),f328(f328(f107(x92391),x92393),x92392)),f328(f328(f65(x92391,x92391,f107(x92391)),x92392),x92394)))
% 81.29/80.93 [9240]~P106(x92401)+~P24(f328(f62(x92401),x92404))+P24(f328(f328(f330(x92401),f463(x92402,x92403,x92404,x92401)),x92404))+P24(f328(f328(f244(x92401),f328(f328(f242(x92401),x92403),x92402)),f328(f328(f65(x92401,x92401,f242(x92401)),x92402),x92404)))
% 81.29/80.93 [9635]~P24(f328(f62(x96352),x96354))+~P24(f328(f62(x96351),x96353))+~P24(f328(f328(f244(a877),f328(f38(x96352),x96354)),f328(f38(x96351),x96353)))+P24(f328(f328(f244(f885(x96351,a871)),f328(f307(x96352,x96351,f554(x96353,x96351,x96354,x96352)),x96354)),x96353))
% 81.29/80.93 [9287]~P24(f328(f328(f330(x92871),x92872),x92874))+P24(f328(f328(f330(x92871),x92872),x92873))+~P24(f328(f328(f245(f885(x92871,a871)),x92874),f328(f328(f306(x92871),x92872),x92873)))+P24(f328(f328(f245(f885(x92871,a871)),f328(f328(f22(f885(x92871,a871)),x92874),f328(f328(f306(x92871),x92872),f193(f885(x92871,a871))))),x92873))
% 81.29/80.93 [9447]~P24(f328(f328(f330(x94471),x94472),x94474))+P24(f328(f328(f330(x94471),x94472),x94473))+P24(f328(f328(f245(f885(x94471,a871)),x94474),f328(f328(f306(x94471),x94472),x94473)))+~P24(f328(f328(f245(f885(x94471,a871)),f328(f328(f22(f885(x94471,a871)),x94474),f328(f328(f306(x94471),x94472),f193(f885(x94471,a871))))),x94473))
% 81.29/80.93 [9476]P24(f328(f328(f330(x94761),x94762),x94763))+~P24(f328(f328(f244(f885(x94761,a871)),x94764),x94763))+P24(f328(f328(f245(f885(x94761,a871)),x94764),f328(f328(f306(x94761),x94762),x94763)))+~P24(f328(f328(f245(f885(x94761,a871)),f328(f328(f22(f885(x94761,a871)),x94764),f328(f328(f306(x94761),x94762),f193(f885(x94761,a871))))),x94763))
% 81.29/80.93 [9481]~P24(f328(f328(f330(x94811),x94813),x94812))+~P24(f328(f328(f245(f885(x94811,a871)),x94812),x94814))+P24(f328(f328(f245(f885(x94811,a871)),x94812),f328(f328(f306(x94811),x94813),x94814)))+~P24(f328(f328(f245(f885(x94811,a871)),f328(f328(f22(f885(x94811,a871)),x94812),f328(f328(f306(x94811),x94813),f193(f885(x94811,a871))))),x94814))
% 81.29/80.93 [9494]~P24(f328(f328(f244(f885(x94941,a871)),x94942),x94944))+~P24(f328(f328(f245(f885(x94941,a871)),x94942),x94944))+P24(f328(f328(f245(f885(x94941,a871)),x94942),f328(f328(f306(x94941),x94943),x94944)))+~P24(f328(f328(f245(f885(x94941,a871)),f328(f328(f22(f885(x94941,a871)),x94942),f328(f328(f306(x94941),x94943),f193(f885(x94941,a871))))),x94944))
% 81.29/80.93 [9538]~P108(x95382)+~P60(x95381)+~P24(f328(f328(f244(f885(x95381,x95382)),x95383),x95384))+P24(f328(f59(x95381),f328(f328(f18(x95381,x95382,a871),f328(f328(f8(x95382,f885(x95382,a871),x95381),f244(x95382)),x95383)),x95384)))
% 81.29/80.93 [9680]~P108(x96802)+~P60(x96801)+P24(f328(f328(f244(f885(x96801,x96802)),x96803),x96804))+~P24(f328(f59(x96801),f328(f328(f18(x96801,x96802,a871),f328(f328(f8(x96802,f885(x96802,a871),x96801),f244(x96802)),x96803)),x96804)))
% 81.29/80.93 [9849]E(f328(f328(f164(x98491),f328(f328(f164(f878(x98491)),f179(x98491,x98492)),x98493)),x98494),f328(f328(f164(x98491),f328(f328(f164(f878(x98491)),x98492),x98494)),x98493))+~P24(f328(f328(f245(a877),x98493),f328(f194(f878(f878(x98491))),f179(x98491,x98492))))+~P29(a877,f328(f168(a877),f328(f328(f153(f878(x98491),a877),f194(f878(x98491))),x98492)))+~P24(f328(f328(f245(a877),x98494),f328(f194(f878(f878(x98491))),f328(f135(f878(x98491),f328(f328(f8(a877,a871,f878(x98491)),f328(f245(a877),x98493)),f194(f878(x98491)))),x98492))))
% 81.29/80.93 [9879]~P24(f328(f328(f330(f884(a877,a877)),x98794),x98791))+~P24(f328(f328(f330(f884(f884(a877,a877),f884(a877,a877))),f328(f328(f257(f884(a877,a877),f884(a877,a877)),x98794),x98792)),a36))+~P24(f328(f328(f330(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f328(f328(f257(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),x98791),x98793)),a69))+P24(f328(f328(f330(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f328(f328(f257(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),x98791),f328(f328(f306(f884(a877,a877)),x98792),x98793))),a69))
% 81.29/80.93 [9880]~P24(f328(f328(f330(f884(a877,a877)),x98804),x98801))+~P24(f328(f328(f330(f884(f884(a877,a877),f884(a877,a877))),f328(f328(f257(f884(a877,a877),f884(a877,a877)),x98804),x98802)),a71))+~P24(f328(f328(f330(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f328(f328(f257(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),x98801),x98803)),a72))+P24(f328(f328(f330(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f328(f328(f257(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),x98801),f328(f328(f306(f884(a877,a877)),x98802),x98803))),a72))
% 81.29/80.93 [9764]~P108(x97642)+~P60(x97641)+~P24(f328(f328(f245(f885(x97641,x97642)),x97643),x97644))+P24(f328(f58(x97641),f328(f328(f8(a871,a871,x97641),a323),f328(f328(f18(x97641,x97642,a871),f328(f328(f8(x97642,f885(x97642,a871),x97641),a325),x97643)),x97644))))
% 81.29/80.93 [9893]~P24(f328(f328(f330(f884(a877,a877)),x98934),x98933))+~P24(f328(f328(f330(f884(f884(a877,a877),f884(a877,a877))),f328(f328(f257(f884(a877,a877),f884(a877,a877)),x98931),x98934)),a36))+~P24(f328(f328(f330(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f328(f328(f257(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),x98932),x98933)),a37))+P24(f328(f328(f330(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f328(f328(f257(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),f328(f328(f306(f884(a877,a877)),x98931),x98932)),x98933)),a37))
% 81.29/80.93 [9894]~P24(f328(f328(f330(f884(a877,a877)),x98944),x98943))+~P24(f328(f328(f330(f884(f884(a877,a877),f884(a877,a877))),f328(f328(f257(f884(a877,a877),f884(a877,a877)),x98941),x98944)),a71))+~P24(f328(f328(f330(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f328(f328(f257(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),x98942),x98943)),a70))+P24(f328(f328(f330(f884(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871))),f328(f328(f257(f885(f884(a877,a877),a871),f885(f884(a877,a877),a871)),f328(f328(f306(f884(a877,a877)),x98941),x98942)),x98943)),a70))
% 81.29/80.93 [6024]~P5(x60244,x60241)+~P24(f328(f328(x60241,x60242),x60245))+P24(f328(f328(x60241,x60242),x60243))+~P24(f328(f328(x60241,x60245),x60243))
% 81.29/80.93 [5285]~P67(x52855)+E(x52851,x52852)+~E(x52853,x52854)+~E(f328(f328(f22(x52855),x52853),x52854),f328(f328(f22(x52855),x52851),x52852))
% 81.29/80.93 [6132]~P13(x61325,x61321,x61323)+E(f328(f328(x61321,x61322),f328(x61323,x61324)),f328(x61323,x61324))+~P24(f328(f62(x61325),x61324))+~P24(f328(f328(f330(x61325),x61322),x61324))
% 81.29/80.93 [6325]~P80(x63251)+~E(f328(f328(f22(x63251),x63254),x63255),f328(f328(f22(x63251),x63252),x63253))+~P24(f328(f328(f244(x63251),x63254),x63255))+P24(f328(f328(f244(x63251),x63252),x63253))
% 81.29/80.93 [6327]~P80(x63271)+~E(f328(f328(f22(x63271),x63274),x63275),f328(f328(f22(x63271),x63272),x63273))+~P24(f328(f328(f245(x63271),x63274),x63275))+P24(f328(f328(f245(x63271),x63272),x63273))
% 81.29/80.93 [7288]~E(x72882,f328(f328(f150(x72881),x72884),x72885))+P24(f328(f328(f330(f878(x72881)),x72882),f160(x72881,x72883)))+~P24(f328(f328(f330(f878(x72881)),x72885),f160(x72881,x72883)))+~P24(f328(f328(f330(x72881),x72884),x72883))
% 81.29/80.93 [7703]~E(f328(f194(f878(x77031)),x77033),f328(f194(f878(x77032)),x77034))+~E(f328(f328(f153(f884(x77031,x77032),x77032),f266(x77031,x77032)),x77035),x77034)+~E(f328(f328(f153(f884(x77031,x77032),x77031),f256(x77031,x77032)),x77035),x77033)+E(f328(f328(f181(x77031,x77032),x77033),x77034),x77035)
% 81.29/80.93 [8039]~P108(x80391)+P24(f328(f328(f245(f885(x80391,a871)),f299(x80391,x80392,x80393)),f299(x80391,x80394,x80395)))+~P24(f328(f328(f244(x80391),x80394),x80395))+P24(f328(f328(f244(x80391),x80392),x80393))
% 81.29/80.93 [8135]~P108(x81351)+P24(f328(f328(f244(f885(x81351,a871)),f299(x81351,x81352,x81353)),f299(x81351,x81354,x81355)))+~P24(f328(f328(f244(x81351),x81353),x81355))+~P24(f328(f328(f244(x81351),x81354),x81352))
% 81.29/80.93 [8261]~P106(x82611)+P24(f328(f328(f244(x82611),x82612),x82613))+P24(f328(f328(f244(x82611),x82614),x82613))+~P24(f328(f328(f244(f885(x82611,a871)),f328(f298(x82611,x82613),x82612)),f328(f298(x82611,x82614),x82615)))
% 81.29/80.93 [8262]~P106(x82621)+P24(f328(f328(f244(x82621),x82622),x82623))+P24(f328(f328(f244(x82621),x82622),x82624))+~P24(f328(f328(f244(f885(x82621,a871)),f328(f298(x82621,x82623),x82622)),f328(f298(x82621,x82625),x82624)))
% 81.29/80.93 [8502]~P108(x85021)+~P24(f328(f328(f244(f885(x85021,a871)),f299(x85021,x85024,x85022)),f299(x85021,x85025,x85023)))+P24(f328(f328(f244(x85021),x85022),x85023))+~P24(f328(f328(f244(x85021),x85024),x85022))
% 81.29/80.93 [8503]~P108(x85031)+~P24(f328(f328(f245(f885(x85031,a871)),f299(x85031,x85034,x85032)),f299(x85031,x85035,x85033)))+P24(f328(f328(f244(x85031),x85032),x85033))+~P24(f328(f328(f244(x85031),x85034),x85032))
% 81.29/80.93 [8504]~P108(x85041)+~P24(f328(f328(f244(f885(x85041,a871)),f299(x85041,x85043,x85044)),f299(x85041,x85042,x85045)))+P24(f328(f328(f244(x85041),x85042),x85043))+~P24(f328(f328(f244(x85041),x85043),x85044))
% 81.29/80.93 [8505]~P108(x85051)+~P24(f328(f328(f245(f885(x85051,a871)),f299(x85051,x85053,x85054)),f299(x85051,x85052,x85055)))+P24(f328(f328(f244(x85051),x85052),x85053))+~P24(f328(f328(f244(x85051),x85053),x85054))
% 81.29/80.93 [6023]~P13(x60232,x60235,x60233)+E(x60231,f193(f885(x60232,a871)))+~P24(f328(f62(x60232),x60231))+E(f328(x60233,f328(f328(f306(x60232),x60234),x60231)),f328(f328(x60235,x60234),f328(x60233,x60231)))
% 81.29/80.93 [6794]~E(x67941,x67942)+~E(f328(f328(f107(f885(x67943,a871)),x67944),x67945),f193(f885(x67943,a871)))+~P24(f328(f328(f330(x67943),x67942),x67945))+~P24(f328(f328(f330(x67943),x67941),x67944))
% 81.29/80.93 [6875]~P14(x68752,x68755,x68751)+~P24(f328(f62(x68752),x68754))+E(f328(x68751,f328(f328(f306(x68752),x68753),x68754)),f328(f328(f65(x68752,x68752,x68755),x68753),x68754))+P24(f328(f328(f330(x68752),x68753),x68754))
% 81.29/80.93 [6939]~P74(x69392)+~P24(f328(f62(x69391),x69395))+E(f328(f328(f6(x69391,x69392),x69393),f328(f328(f306(x69391),x69394),x69395)),f328(f328(f81(x69392),f328(x69393,x69394)),f328(f328(f6(x69391,x69392),x69393),x69395)))+P24(f328(f328(f330(x69391),x69394),x69395))
% 81.29/80.93 [6941]~P75(x69412)+~P24(f328(f62(x69411),x69415))+E(f328(f328(f9(x69411,x69412),x69413),f328(f328(f306(x69411),x69414),x69415)),f328(f328(f82(x69412),f328(x69413,x69414)),f328(f328(f9(x69411,x69412),x69413),x69415)))+P24(f328(f328(f330(x69411),x69414),x69415))
% 81.29/80.93 [7446]~P14(x74462,x74465,x74461)+~P24(f328(f62(x74462),x74464))+E(f328(x74461,f328(f328(f306(x74462),x74463),x74464)),x74463)+~E(f328(f328(f22(f885(x74462,a871)),x74464),f328(f328(f306(x74462),x74463),f193(f885(x74462,a871)))),f193(f885(x74462,a871)))
% 81.29/80.93 [7754]~P24(f328(x77541,x77543))+~P24(f328(f328(f200(x77542),x77543),x77545))+~P24(f328(f328(f200(f33(x77541,x77542)),x77545),x77544))+P24(f328(f328(f200(f33(x77541,x77542)),x77543),x77544))
% 81.29/80.93 [7806]~P65(x78061)+~P24(f328(f328(f244(x78061),x78063),x78065))+~P24(f328(f328(f244(x78061),x78062),x78064))+P24(f328(f328(f244(x78061),f328(f328(f116(x78061),x78062),x78063)),f328(f328(f116(x78061),x78064),x78065)))
% 81.29/80.93 [7807]~P86(x78071)+~P24(f328(f328(f244(x78071),x78073),x78075))+~P24(f328(f328(f244(x78071),x78072),x78074))+P24(f328(f328(f244(x78071),f328(f328(f81(x78071),x78072),x78073)),f328(f328(f81(x78071),x78074),x78075)))
% 81.29/80.93 [7808]~P102(x78081)+~P24(f328(f328(f244(x78081),x78083),x78085))+~P24(f328(f328(f244(x78081),x78082),x78084))+P24(f328(f328(f244(x78081),f328(f328(f107(x78081),x78082),x78083)),f328(f328(f107(x78081),x78084),x78085)))
% 81.29/80.93 [7809]~P106(x78091)+~P24(f328(f328(f244(x78091),x78093),x78095))+~P24(f328(f328(f244(x78091),x78092),x78094))+P24(f328(f328(f244(x78091),f328(f328(f242(x78091),x78092),x78093)),f328(f328(f242(x78091),x78094),x78095)))
% 81.29/80.93 [7810]~P106(x78101)+~P24(f328(f328(f244(x78101),x78103),x78105))+~P24(f328(f328(f244(x78101),x78102),x78104))+P24(f328(f328(f244(x78101),f328(f328(f243(x78101),x78102),x78103)),f328(f328(f243(x78101),x78104),x78105)))
% 81.29/80.93 [7811]~P84(x78111)+~P24(f328(f328(f244(x78111),x78113),x78115))+~P24(f328(f328(f245(x78111),x78112),x78114))+P24(f328(f328(f245(x78111),f328(f328(f81(x78111),x78112),x78113)),f328(f328(f81(x78111),x78114),x78115)))
% 81.29/80.93 [7812]~P84(x78121)+~P24(f328(f328(f244(x78121),x78122),x78124))+~P24(f328(f328(f245(x78121),x78123),x78125))+P24(f328(f328(f245(x78121),f328(f328(f81(x78121),x78122),x78123)),f328(f328(f81(x78121),x78124),x78125)))
% 81.29/80.93 [7813]~P84(x78131)+~P24(f328(f328(f245(x78131),x78133),x78135))+~P24(f328(f328(f245(x78131),x78132),x78134))+P24(f328(f328(f245(x78131),f328(f328(f81(x78131),x78132),x78133)),f328(f328(f81(x78131),x78134),x78135)))
% 81.29/80.93 [7949]~P143(x79495)+E(x79491,x79492)+E(x79493,x79494)+~E(f328(f328(f81(x79495),f328(f328(f82(x79495),x79493),x79491)),f328(f328(f82(x79495),x79494),x79492)),f328(f328(f81(x79495),f328(f328(f82(x79495),x79493),x79492)),f328(f328(f82(x79495),x79494),x79491)))
% 81.29/80.93 [8090]P30(x80901,x80902,x80903)+~P23(x80901,x80904,x80905)+~P30(x80901,x80902,f609(x80905,x80904,x80901,x80902))+~P24(f328(f328(f330(f876(x80901)),x80903),x80905))
% 81.29/80.93 [8159]~P106(x81594)+~P24(f328(f136(x81591),x81593))+P24(f328(f328(f330(x81591),x81592),f328(f171(x81591),x81593)))+P24(f328(f136(x81591),f328(f328(f147(x81591,x81594,x81595),x81592),x81593)))
% 81.29/80.93 [8307]~P67(x83071)+E(f328(f328(f22(x83071),f328(f328(f6(a877,x83071),x83072),f328(f298(a877,x83073),x83074))),f328(f328(f6(a877,x83071),x83072),f328(f298(a877,x83073),x83075))),f328(f328(f6(a877,x83071),x83072),f328(f298(a877,x83075),x83074)))+~P24(f328(f328(f244(a877),x83075),x83074))+~P24(f328(f328(f244(a877),x83073),x83075))
% 81.29/80.93 [8308]~P74(x83081)+E(f328(f328(f81(x83081),f328(f328(f6(a877,x83081),x83082),f328(f298(a877,x83083),x83084))),f328(f328(f6(a877,x83081),x83082),f328(f298(a877,x83084),x83085))),f328(f328(f6(a877,x83081),x83082),f328(f298(a877,x83083),x83085)))+~P24(f328(f328(f244(a877),x83084),x83085))+~P24(f328(f328(f244(a877),x83083),x83084))
% 81.29/80.93 [8638]~P62(x86382)+E(x86381,f2(x86382))+E(x86383,f2(x86382))+E(f328(f328(f286(x86382),f328(f328(f22(x86382),f328(f328(f82(x86382),x86384),x86381)),f328(f328(f82(x86382),x86385),x86383))),f328(f328(f82(x86382),x86383),x86381)),f328(f328(f22(x86382),f328(f328(f286(x86382),x86384),x86383)),f328(f328(f286(x86382),x86385),x86381)))
% 81.29/80.93 [8639]~P62(x86392)+E(x86391,f2(x86392))+E(x86393,f2(x86392))+E(f328(f328(f286(x86392),f328(f328(f81(x86392),f328(f328(f82(x86392),x86394),x86391)),f328(f328(f82(x86392),x86395),x86393))),f328(f328(f82(x86392),x86393),x86391)),f328(f328(f81(x86392),f328(f328(f286(x86392),x86394),x86393)),f328(f328(f286(x86392),x86395),x86391)))
% 81.29/80.93 [8648]~E(x86482,f328(x86483,x86481))+E(x86481,f550(x86482,x86483,x86484,x86485))+~P21(x86485,x86484,x86483,f252(f885(x86485,a871)))+~P24(f328(f328(f330(x86484),x86482),f328(f307(x86485,x86484,x86483),f252(f885(x86485,a871)))))
% 81.29/80.93 [8844]~P111(x88441)+~P24(f328(f328(f245(x88441),f328(f76(x88441),x88442)),x88444))+P24(f328(f328(f245(x88441),f328(f328(f82(x88441),f328(f76(x88441),x88442)),f328(f76(x88441),x88443))),f328(f328(f82(x88441),x88444),x88445)))+~P24(f328(f328(f245(x88441),f328(f76(x88441),x88443)),x88445))
% 81.29/80.93 [8861]~P23(x88611,x88615,x88614)+P30(x88611,x88612,x88613)+P24(f328(f328(f330(f876(x88611)),f609(x88614,x88615,x88611,x88612)),x88615))+~P24(f328(f328(f330(f876(x88611)),x88613),x88614))
% 81.29/80.93 [8965]~P21(x89651,x89653,x89655,x89652)+~P24(f328(f62(x89653),x89654))+P24(f328(f328(f244(a877),f328(f38(x89651),x89652)),f328(f38(x89653),x89654)))+~P24(f328(f328(f244(f885(x89653,a871)),f328(f307(x89651,x89653,x89655),x89652)),x89654))
% 81.29/80.93 [9035]~P74(x90352)+~P21(x90351,x90351,x90354,x90355)+~P24(f328(f62(x90351),x90355))+E(f328(f328(f6(x90351,x90352),f328(f74(x90351,x90352,x90351,x90353),x90354)),x90355),f328(f328(f6(x90351,x90352),x90353),f328(f307(x90351,x90351,x90354),x90355)))
% 81.29/80.93 [9036]~P75(x90362)+~P21(x90361,x90361,x90364,x90365)+~P24(f328(f62(x90361),x90365))+E(f328(f328(f9(x90361,x90362),f328(f74(x90361,x90362,x90361,x90363),x90364)),x90365),f328(f328(f9(x90361,x90362),x90363),f328(f307(x90361,x90361,x90364),x90365)))
% 81.29/80.93 [9150]~P38(x91501,x91502)+~P24(f328(f328(f330(x91501),x91503),x91504))+~P24(f328(f328(f330(x91501),x91505),x91504))+~P24(f328(f328(f330(f884(x91501,x91501)),f328(f328(f257(x91501,x91501),x91505),f791(x91502,x91501,x91504))),x91502))
% 81.29/80.93 [9188]~P21(x91882,x91883,x91885,x91881)+E(x91881,f193(f885(x91882,a871)))+E(f328(f307(x91883,x91882,f552(x91884,x91883,x91882,x91881)),x91884),x91881)+~P24(f328(f328(f244(f885(x91883,a871)),f328(f307(x91882,x91883,x91885),x91881)),x91884))
% 81.29/80.93 [9662]~P106(x96625)+~P27(x96625)+P24(f328(f328(f330(x96621),f517(x96622,x96623,x96621,x96624,x96625)),x96623))+~P24(f328(f328(f245(x96625),x96624),f328(f328(f43(x96621,x96625),x96623),x96622)))
% 81.29/80.93 [9667]~P106(x96671)+~P27(x96671)+P24(f328(f328(f245(x96671),x96672),f328(x96673,f517(x96673,x96674,x96675,x96672,x96671))))+~P24(f328(f328(f245(x96671),x96672),f328(f328(f43(x96675,x96671),x96674),x96673)))
% 81.29/80.93 [9744]~P71(x97441)+~P24(f328(f67(x97441,x97441,f82(x97441),x97442,x97443),x97445))+P24(f328(f328(f330(x97441),x97442),x97443))+P24(f328(f67(x97441,x97441,f82(x97441),x97444,f328(f328(f306(x97441),x97442),x97443)),f328(f328(f82(x97441),x97444),x97445)))
% 81.29/80.93 [9963]~P74(x99632)+~P24(f328(f62(x99631),x99635))+E(f328(f328(f6(x99631,x99632),f328(f328(f7(x99631,x99632,x99632),f328(f328(f18(x99631,x99632,f885(x99632,x99632)),f328(f328(f8(a871,f885(x99632,f885(x99632,x99632)),x99631),f102(x99632)),f328(a325,x99633))),x99634)),f2(x99632))),x99635),f2(x99632))+P24(f328(f328(f330(x99631),x99633),x99635))
% 81.29/80.93 [9964]~P75(x99642)+~P24(f328(f62(x99641),x99645))+E(f328(f328(f9(x99641,x99642),f328(f328(f7(x99641,x99642,x99642),f328(f328(f18(x99641,x99642,f885(x99642,x99642)),f328(f328(f8(a871,f885(x99642,f885(x99642,x99642)),x99641),f102(x99642)),f328(a325,x99643))),x99644)),f79(x99642))),x99645),f79(x99642))+P24(f328(f328(f330(x99641),x99643),x99645))
% 81.29/80.93 [9965]~P74(x99652)+~P24(f328(f62(x99651),x99655))+E(f328(f328(f6(x99651,x99652),f328(f328(f7(x99651,x99652,x99652),f328(f328(f18(x99651,x99652,f885(x99652,x99652)),f328(f328(f8(a871,f885(x99652,f885(x99652,x99652)),x99651),f102(x99652)),f328(a325,x99653))),x99654)),f2(x99652))),x99655),f328(x99654,x99653))+~P24(f328(f328(f330(x99651),x99653),x99655))
% 81.29/80.93 [9966]~P75(x99662)+~P24(f328(f62(x99661),x99665))+E(f328(f328(f9(x99661,x99662),f328(f328(f7(x99661,x99662,x99662),f328(f328(f18(x99661,x99662,f885(x99662,x99662)),f328(f328(f8(a871,f885(x99662,f885(x99662,x99662)),x99661),f102(x99662)),f328(a325,x99663))),x99664)),f79(x99662))),x99665),f328(x99664,x99663))+~P24(f328(f328(f330(x99661),x99663),x99665))
% 81.29/80.93 [10023]~P74(x100232)+~P24(f328(f62(x100231),x100235))+E(f328(f328(f6(x100231,x100232),f328(f328(f7(x100231,x100232,x100232),f328(f328(f18(x100231,x100232,f885(x100232,x100232)),f328(f328(f8(a871,f885(x100232,f885(x100232,x100232)),x100231),f102(x100232)),f328(f328(f7(x100231,x100231,a871),a325),x100233))),x100234)),f2(x100232))),x100235),f2(x100232))+P24(f328(f328(f330(x100231),x100233),x100235))
% 81.29/80.93 [10024]~P75(x100242)+~P24(f328(f62(x100241),x100245))+E(f328(f328(f9(x100241,x100242),f328(f328(f7(x100241,x100242,x100242),f328(f328(f18(x100241,x100242,f885(x100242,x100242)),f328(f328(f8(a871,f885(x100242,f885(x100242,x100242)),x100241),f102(x100242)),f328(f328(f7(x100241,x100241,a871),a325),x100243))),x100244)),f79(x100242))),x100245),f79(x100242))+P24(f328(f328(f330(x100241),x100243),x100245))
% 81.29/80.93 [10026]~P74(x100262)+~P24(f328(f62(x100261),x100265))+E(f328(f328(f6(x100261,x100262),f328(f328(f7(x100261,x100262,x100262),f328(f328(f18(x100261,x100262,f885(x100262,x100262)),f328(f328(f8(a871,f885(x100262,f885(x100262,x100262)),x100261),f102(x100262)),f328(f328(f7(x100261,x100261,a871),a325),x100263))),x100264)),f2(x100262))),x100265),f328(x100264,x100263))+~P24(f328(f328(f330(x100261),x100263),x100265))
% 81.29/80.93 [10027]~P75(x100272)+~P24(f328(f62(x100271),x100275))+E(f328(f328(f9(x100271,x100272),f328(f328(f7(x100271,x100272,x100272),f328(f328(f18(x100271,x100272,f885(x100272,x100272)),f328(f328(f8(a871,f885(x100272,f885(x100272,x100272)),x100271),f102(x100272)),f328(f328(f7(x100271,x100271,a871),a325),x100273))),x100274)),f79(x100272))),x100275),f328(x100274,x100273))+~P24(f328(f328(f330(x100271),x100273),x100275))
% 81.29/80.93 [7805]~P67(x78052)+~P24(f328(f62(x78051),x78054))+E(f328(f328(f6(x78051,x78052),x78053),f328(f328(f22(f885(x78051,a871)),x78054),f328(f328(f306(x78051),x78055),f193(f885(x78051,a871))))),f328(f328(f6(x78051,x78052),x78053),x78054))+P24(f328(f328(f330(x78051),x78055),x78054))
% 81.29/80.93 [8313]~P109(x83132)+~P24(f328(f62(x83131),x83134))+E(f328(f328(f6(x83131,x83132),x83133),f328(f328(f22(f885(x83131,a871)),x83134),f328(f328(f306(x83131),x83135),f193(f885(x83131,a871))))),f328(f328(f22(x83132),f328(f328(f6(x83131,x83132),x83133),x83134)),f328(x83133,x83135)))+~P24(f328(f328(f330(x83131),x83135),x83134))
% 81.29/80.93 [8314]~P67(x83142)+~P24(f328(f62(x83141),x83144))+E(f328(f328(f6(x83141,x83142),x83143),f328(f328(f22(f885(x83141,a871)),x83144),f328(f328(f306(x83141),x83145),f193(f885(x83141,a871))))),f328(f328(f22(x83142),f328(f328(f6(x83141,x83142),x83143),x83144)),f328(x83143,x83145)))+~P24(f328(f328(f330(x83141),x83145),x83144))
% 81.29/80.93 [8345]~P67(x83451)+~P24(f328(f62(x83452),x83454))+E(f328(f328(f22(x83451),f328(f328(f6(x83452,x83451),x83453),x83454)),f328(f328(f6(x83452,x83451),x83453),x83455)),f328(f328(f6(x83452,x83451),x83453),f328(f328(f22(f885(x83452,a871)),x83454),x83455)))+~P24(f328(f328(f244(f885(x83452,a871)),x83455),x83454))
% 81.29/80.93 [8365]P24(f328(f62(x83651),f328(x83652,x83653)))+~P24(f328(f62(x83654),x83655))+~P24(f328(f328(f330(x83654),x83653),x83655))+~P24(f328(f62(x83651),f328(f328(f43(x83654,f885(x83651,a871)),x83655),x83652)))
% 81.29/80.93 [8807]~P6(x88071,x88075,x88074)+~E(f328(f282(x88071,x88071,x88074),f328(f328(f306(x88071),x88072),f193(f885(x88071,a871)))),f328(f282(x88071,x88071,x88074),f328(f328(f306(x88071),x88073),f193(f885(x88071,a871)))))+~P24(f328(f328(f330(x88071),x88073),x88075))+P24(f328(f328(f330(f884(x88071,x88071)),f328(f328(f257(x88071,x88071),x88072),x88073)),x88074))
% 81.29/80.93 [9107]~P24(f328(x91071,x91075))+P24(f328(x91071,f468(x91071,x91072,x91073,x91074)))+P24(f328(x91071,f459(x91071,x91072,x91073,x91074)))+~P24(f328(f328(f330(x91074),x91075),f328(f328(f116(f885(x91074,a871)),x91073),x91072)))
% 81.29/80.93 [9292]~P24(f328(x92921,x92925))+P24(f328(x92921,f459(x92921,x92922,x92923,x92924)))+P24(f328(f328(f330(x92924),f468(x92921,x92922,x92923,x92924)),x92922))+~P24(f328(f328(f330(x92924),x92925),f328(f328(f116(f885(x92924,a871)),x92923),x92922)))
% 81.29/80.93 [9293]~P24(f328(x92931,x92935))+P24(f328(x92931,f468(x92931,x92932,x92933,x92934)))+P24(f328(f328(f330(x92934),f459(x92931,x92932,x92933,x92934)),x92933))+~P24(f328(f328(f330(x92934),x92935),f328(f328(f116(f885(x92934,a871)),x92933),x92932)))
% 81.29/80.93 [9299]P24(f328(x92991,x92992))+~P24(f328(x92991,f444(x92991,x92993,x92994,x92995)))+~P24(f328(x92991,f435(x92991,x92993,x92994,x92995)))+~P24(f328(f328(f330(x92995),x92992),f328(f328(f116(f885(x92995,a871)),x92994),x92993)))
% 81.29/80.93 [9341]E(x93411,x93412)+~P24(f328(f328(f330(f884(x93413,x93413)),f328(f328(f257(x93413,x93413),x93411),x93412)),f304(x93413,x93415)))+P24(f328(f328(f330(x93413),x93411),x93414))+~P24(f328(f328(f244(f885(f884(x93413,x93413),a871)),x93415),f328(f328(f265(x93413,x93413),x93414),f328(f16(f885(x93413,a871),x93413),x93414))))
% 81.29/80.93 [9360]P24(f328(x93601,x93602))+~P24(f328(x93601,f435(x93601,x93604,x93605,x93603)))+P24(f328(f328(f330(x93603),f444(x93601,x93604,x93605,x93603)),x93604))+~P24(f328(f328(f330(x93603),x93602),f328(f328(f116(f885(x93603,a871)),x93605),x93604)))
% 81.29/80.93 [9361]P24(f328(x93611,x93612))+~P24(f328(x93611,f444(x93611,x93614,x93615,x93613)))+P24(f328(f328(f330(x93613),f435(x93611,x93614,x93615,x93613)),x93615))+~P24(f328(f328(f330(x93613),x93612),f328(f328(f116(f885(x93613,a871)),x93615),x93614)))
% 81.29/80.93 [9421]P24(f328(x94211,x94212))+P24(f328(f328(f330(x94213),f444(x94211,x94214,x94215,x94213)),x94214))+P24(f328(f328(f330(x94213),f435(x94211,x94214,x94215,x94213)),x94215))+~P24(f328(f328(f330(x94213),x94212),f328(f328(f116(f885(x94213,a871)),x94215),x94214)))
% 81.29/80.93 [9423]~P24(f328(x94232,x94235))+P24(f328(f328(f330(x94231),f468(x94232,x94233,x94234,x94231)),x94233))+P24(f328(f328(f330(x94231),f459(x94232,x94233,x94234,x94231)),x94234))+~P24(f328(f328(f330(x94231),x94235),f328(f328(f116(f885(x94231,a871)),x94234),x94233)))
% 81.29/80.93 [9571]~P6(x95711,x95715,x95714)+~P24(f328(f328(f330(x95711),x95713),x95715))+P24(f328(f328(f330(f884(x95711,x95711)),f328(f328(f257(x95711,x95711),x95712),x95713)),x95714))+~P24(f328(f328(f244(f885(x95711,a871)),f328(f282(x95711,x95711,x95714),f328(f328(f306(x95711),x95713),f193(f885(x95711,a871))))),f328(f282(x95711,x95711,x95714),f328(f328(f306(x95711),x95712),f193(f885(x95711,a871))))))
% 81.29/80.93 [9692]~P106(x96925)+~P27(x96925)+P24(f328(f328(f330(x96921),f510(x96922,x96923,x96924,x96921,x96925)),x96924))+~P24(f328(f328(f245(x96925),f328(f328(f42(x96921,x96925),x96924),x96923)),x96922))
% 81.29/80.93 [9724]~P86(x97245)+~P82(x97245)+P24(f328(f328(f330(x97241),f630(x97242,x97243,x97244,x97241,x97245)),f328(f171(x97241),x97244)))+P24(f328(f328(f244(x97245),f328(f165(x97245),f328(f328(f153(x97241,x97245),x97243),x97244))),f328(f165(x97245),f328(f328(f153(x97241,x97245),x97242),x97244))))
% 81.29/80.93 [9838]~P106(x98381)+~P27(x98381)+P24(f328(f328(f245(x98381),f328(x98382,f510(x98383,x98382,x98384,x98385,x98381))),x98383))+~P24(f328(f328(f245(x98381),f328(f328(f42(x98385,x98381),x98384),x98382)),x98383))
% 81.29/80.93 [9982]~P86(x99821)+~P82(x99821)+~P24(f328(f328(f244(x99821),f328(x99823,f630(x99825,x99823,x99824,x99822,x99821))),f328(x99825,f630(x99825,x99823,x99824,x99822,x99821))))+P24(f328(f328(f244(x99821),f328(f165(x99821),f328(f328(f153(x99822,x99821),x99823),x99824))),f328(f165(x99821),f328(f328(f153(x99822,x99821),x99825),x99824))))
% 81.29/80.93 [8657]~P74(x86571)+~P24(f328(f62(x86574),x86575))+~P24(f328(f328(f330(x86574),x86573),x86575))+E(f328(f328(f81(x86571),f328(x86572,x86573)),f328(f328(f6(x86574,x86571),x86572),f328(f328(f22(f885(x86574,a871)),x86575),f328(f328(f306(x86574),x86573),f193(f885(x86574,a871)))))),f328(f328(f6(x86574,x86571),x86572),x86575))
% 81.29/80.93 [8658]~P75(x86581)+~P24(f328(f62(x86584),x86585))+~P24(f328(f328(f330(x86584),x86583),x86585))+E(f328(f328(f82(x86581),f328(x86582,x86583)),f328(f328(f9(x86584,x86581),x86582),f328(f328(f22(f885(x86584,a871)),x86585),f328(f328(f306(x86584),x86583),f193(f885(x86584,a871)))))),f328(f328(f9(x86584,x86581),x86582),x86585))
% 81.29/80.93 [8713]~P14(x87131,x87134,x87135)+~P24(f328(f62(x87131),x87132))+E(f328(f328(f22(f885(x87131,a871)),x87132),f328(f328(f306(x87131),x87133),f193(f885(x87131,a871)))),f193(f885(x87131,a871)))+E(f328(f328(x87134,x87133),f328(x87135,f328(f328(f22(f885(x87131,a871)),x87132),f328(f328(f306(x87131),x87133),f193(f885(x87131,a871)))))),f328(x87135,f328(f328(f306(x87131),x87133),x87132)))
% 81.29/80.93 [9087]~P74(x90871)+~P24(f328(f62(x90872),x90875))+~P24(f328(f62(x90872),x90874))+E(f328(f328(f81(x90871),f328(f328(f6(x90872,x90871),x90873),f328(f328(f116(f885(x90872,a871)),x90874),x90875))),f328(f328(f6(x90872,x90871),x90873),f328(f328(f107(f885(x90872,a871)),x90874),x90875))),f328(f328(f81(x90871),f328(f328(f6(x90872,x90871),x90873),x90874)),f328(f328(f6(x90872,x90871),x90873),x90875)))
% 81.29/80.93 [9089]~P75(x90891)+~P24(f328(f62(x90892),x90895))+~P24(f328(f62(x90892),x90894))+E(f328(f328(f82(x90891),f328(f328(f9(x90892,x90891),x90893),f328(f328(f116(f885(x90892,a871)),x90894),x90895))),f328(f328(f9(x90892,x90891),x90893),f328(f328(f107(f885(x90892,a871)),x90894),x90895))),f328(f328(f82(x90891),f328(f328(f9(x90892,x90891),x90893),x90894)),f328(f328(f9(x90892,x90891),x90893),x90895)))
% 81.29/80.93 [9230]~P67(x92301)+~P24(f328(f62(x92302),x92305))+~P24(f328(f62(x92302),x92304))+E(f328(f328(f22(x92301),f328(f328(f81(x92301),f328(f328(f6(x92302,x92301),x92303),x92304)),f328(f328(f6(x92302,x92301),x92303),x92305))),f328(f328(f6(x92302,x92301),x92303),f328(f328(f107(f885(x92302,a871)),x92304),x92305))),f328(f328(f6(x92302,x92301),x92303),f328(f328(f116(f885(x92302,a871)),x92304),x92305)))
% 81.29/80.93 [9432]~P21(x94321,x94322,x94323,x94325)+~P21(x94321,x94322,x94323,x94324)+P21(x94321,x94322,x94323,f328(f328(f116(f885(x94321,a871)),x94324),x94325))+~E(f328(f328(f107(f885(x94322,a871)),f328(f307(x94321,x94322,x94323),f328(f328(f22(f885(x94321,a871)),x94324),x94325))),f328(f307(x94321,x94322,x94323),f328(f328(f22(f885(x94321,a871)),x94325),x94324))),f193(f885(x94322,a871)))
% 81.29/80.93 [9546]E(x95461,f2(a1))+~P24(f328(f328(f245(a1),f2(a1)),x95463))+~P24(f328(f49(x95462,x95461),f328(f328(f257(a1,a1),x95464),x95465)))+P24(f328(f49(x95462,f328(f328(f82(a1),x95461),x95463)),f328(f328(f257(a1,a1),f328(f328(f39(a1),x95464),x95463)),f328(f328(f81(a1),f328(f328(f82(a1),x95461),f45(a1,x95464,x95463))),x95465))))
% 81.29/80.93 [9554]~P24(f328(f328(f245(a877),f2(a877)),x95543))+~P24(f328(f328(f245(a877),f2(a877)),x95542))+~P24(f328(f48(x95541,x95542),f328(f328(f257(a877,a877),x95544),x95545)))+P24(f328(f48(x95541,f328(f328(f82(a877),x95542),x95543)),f328(f328(f257(a877,a877),f328(f328(f39(a877),x95544),x95543)),f328(f328(f81(a877),f328(f328(f82(a877),x95542),f45(a877,x95544,x95543))),x95545))))
% 81.29/80.93 [9603]~P75(x96031)+~P24(f328(f62(x96032),x96035))+~P24(f328(f62(x96032),x96034))+E(f328(f328(f82(x96031),f328(f328(f328(f66(x96031,x96032,f82(x96031)),x96033),f79(x96031)),f328(f328(f116(f885(x96032,a871)),x96034),x96035))),f328(f328(f328(f66(x96031,x96032,f82(x96031)),x96033),f79(x96031)),f328(f328(f107(f885(x96032,a871)),x96034),x96035))),f328(f328(f82(x96031),f328(f328(f328(f66(x96031,x96032,f82(x96031)),x96033),f79(x96031)),x96034)),f328(f328(f328(f66(x96031,x96032,f82(x96031)),x96033),f79(x96031)),x96035)))
% 81.29/80.93 [9605]~E(f328(f328(f174(x96051),x96055),x96052),f328(f328(f174(x96051),x96055),x96053))+P24(f328(f328(f330(f884(f878(x96051),f878(x96051))),f328(f328(f257(f878(x96051),f878(x96051)),x96052),x96053)),f146(x96051,x96054)))+~P24(f328(f328(f245(a877),x96055),f328(f328(f242(a877),f328(f194(f878(x96051)),x96052)),f328(f194(f878(x96051)),x96053))))+~P24(f328(f328(f330(f884(x96051,x96051)),f328(f328(f257(x96051,x96051),f328(f328(f164(x96051),x96052),x96055)),f328(f328(f164(x96051),x96053),x96055))),x96054))
% 81.29/80.93 [9712]~P86(x97125)+~P141(x97125)+P24(f328(f328(f330(x97121),f868(x97122,x97123,x97124,x97121,x97125)),x97124))+P24(f328(f328(f244(x97125),f328(f328(f6(x97121,x97125),x97123),x97124)),f328(f328(f82(x97125),f328(f106(x97125),f328(f38(x97121),x97124))),x97122)))
% 81.29/80.93 [9909]~P86(x99091)+~P141(x99091)+~P24(f328(f328(f244(x99091),f328(x99093,f868(x99095,x99093,x99094,x99092,x99091))),x99095))+P24(f328(f328(f244(x99091),f328(f328(f6(x99092,x99091),x99093),x99094)),f328(f328(f82(x99091),f328(f106(x99091),f328(f38(x99092),x99094))),x99095)))
% 81.29/80.93 [8685]E(f328(f328(f127(x86851),x86852),x86853),f328(f328(f127(x86851),x86854),x86855))+~E(f328(f328(f174(x86851),f328(f194(f878(x86851)),x86852)),x86854),x86852)+~E(f328(f328(f127(x86851),f328(f328(f137(x86851),f328(f194(f878(x86851)),x86852)),x86854)),x86855),x86853)+P24(f328(f328(f244(a877),f328(f194(f878(x86851)),x86854)),f328(f194(f878(x86851)),x86852)))
% 81.29/80.93 [8806]E(f328(f328(f127(x88061),x88062),x88063),f328(f328(f127(x88061),x88064),x88065))+~E(f328(f328(f174(x88061),f328(f194(f878(x88061)),x88062)),x88064),x88062)+~E(x88063,f328(f328(f127(x88061),f328(f328(f137(x88061),f328(f194(f878(x88061)),x88062)),x88064)),x88065))+~P24(f328(f328(f244(a877),f328(f194(f878(x88061)),x88062)),f328(f194(f878(x88061)),x88064)))
% 81.29/80.93 [10045]~P24(f328(x100455,x100454))+~P24(f328(f62(x100452),f328(f249(x100452),x100455)))+P24(f328(f62(x100451),f328(f249(x100451),f328(f328(f7(x100451,x100452,a871),x100453),x100454))))+~P24(f328(f62(x100451),f328(f249(x100451),f328(f328(f8(f885(x100452,a871),a871,x100451),f88(x100452)),f328(f328(f8(f885(x100452,a871),f885(x100452,a871),x100451),f328(f18(x100452,a871,a871),f328(f328(f8(a871,f885(a871,a871),x100452),a326),x100455))),x100453)))))
% 81.29/80.93 [8480]~P15(x84805,x84801,x84806,x84802)+E(f328(f74(x84801,x84801,x84801,f328(x84802,x84803)),f328(x84802,x84804)),f328(f74(x84801,x84801,x84801,f328(x84802,x84804)),f328(x84802,x84803)))+~P24(f328(f62(x84805),x84804))+~P24(f328(f62(x84805),x84803))
% 81.29/80.93 [7860]~P21(x78601,x78602,x78604,x78603)+~E(f328(x78604,x78606),x78605)+E(f328(f78(x78601,x78602,x78603,x78604),x78605),x78606)+~P24(f328(f328(f330(x78601),x78606),x78603))
% 81.29/80.93 [8059]~P16(x80596,x80591,x80594,x80592)+E(f328(f74(x80591,x80591,x80591,f328(x80592,x80593)),f328(x80594,x80595)),f328(x80592,x80593))+~P24(f328(f62(x80596),x80593))+~P24(f328(f328(f330(x80596),x80595),x80593))
% 81.29/80.93 [9278]~P15(x92783,x92781,x92786,x92782)+E(f328(f74(x92781,x92781,x92781,f328(x92782,f328(f328(f22(f885(x92783,a871)),x92784),f328(f328(f306(x92783),x92785),f193(f885(x92783,a871)))))),f328(x92786,x92785)),f328(x92782,x92784))+~P24(f328(f62(x92783),x92784))+~P24(f328(f328(f330(x92783),x92785),x92784))
% 81.29/80.93 [6944]~P59(x69441)+~E(f45(x69441,x69443,x69444),f45(x69441,x69446,x69444))+~E(f45(x69441,x69442,x69444),f45(x69441,x69445,x69444))+E(f45(x69441,f328(f328(f22(x69441),x69442),x69443),x69444),f45(x69441,f328(f328(f22(x69441),x69445),x69446),x69444))
% 81.29/80.93 [6945]~P58(x69451)+~E(f45(x69451,x69453,x69454),f45(x69451,x69456,x69454))+~E(f45(x69451,x69452,x69454),f45(x69451,x69455,x69454))+E(f45(x69451,f328(f328(f81(x69451),x69452),x69453),x69454),f45(x69451,f328(f328(f81(x69451),x69455),x69456),x69454))
% 81.29/80.93 [6946]~P58(x69461)+~E(f45(x69461,x69463,x69464),f45(x69461,x69466,x69464))+~E(f45(x69461,x69462,x69464),f45(x69461,x69465,x69464))+E(f45(x69461,f328(f328(f82(x69461),x69462),x69463),x69464),f45(x69461,f328(f328(f82(x69461),x69465),x69466),x69464))
% 81.29/80.93 [7756]~P12(x77561,x77562,x77563)+~P24(f328(f62(x77561),x77566))+E(f328(f328(f65(x77561,x77562,x77563),x77564),f328(f328(f306(x77561),x77565),x77566)),f328(f328(f65(x77561,x77562,x77563),f328(f328(x77563,x77565),x77564)),x77566))+P24(f328(f328(f330(x77561),x77565),x77566))
% 81.29/80.93 [7818]~P27(x78181)+P24(f328(f328(f244(x78181),x78182),f328(x78183,x78184)))+~P24(f328(f328(f330(x78185),x78184),x78186))+~P24(f328(f328(f244(x78181),x78182),f328(f328(f42(x78185,x78181),x78186),x78183)))
% 81.29/80.93 [7978]~P12(x79781,x79782,x79783)+~P24(f328(f62(x79781),x79786))+E(f328(f328(f65(x79781,x79782,x79783),x79784),f328(f328(f306(x79781),x79785),x79786)),f328(f328(x79783,x79785),f328(f328(f65(x79781,x79782,x79783),x79784),x79786)))+P24(f328(f328(f330(x79781),x79785),x79786))
% 81.29/80.93 [8075]~P106(x80753)+~P24(f328(x80752,x80755))+~P29(x80753,f328(f328(f153(x80751,x80753),x80754),x80756))+E(f328(f135(x80751,x80752),f328(f328(f147(x80751,x80753,x80754),x80755),x80756)),f328(f328(f147(x80751,x80753,x80754),x80755),f328(f135(x80751,x80752),x80756)))
% 81.29/80.93 [8098]E(x80981,x80982)+E(x80983,f2(a1))+~P24(f328(f49(x80984,x80983),f328(f328(f257(a1,a1),x80985),x80982)))+~P24(f328(f49(x80984,x80983),f328(f328(f257(a1,a1),x80986),x80981)))
% 81.29/80.93 [8099]E(x80991,x80992)+E(x80993,f2(a1))+~P24(f328(f49(x80994,x80993),f328(f328(f257(a1,a1),x80992),x80995)))+~P24(f328(f49(x80994,x80993),f328(f328(f257(a1,a1),x80991),x80996)))
% 81.29/80.93 [8119]~P15(x81192,x81195,x81196,x81191)+~P24(f328(f62(x81192),x81194))+E(f328(x81191,f328(f328(f306(x81192),x81193),x81194)),f328(f74(x81195,x81195,x81195,f328(x81191,x81194)),f328(x81196,x81193)))+P24(f328(f328(f330(x81192),x81193),x81194))
% 81.29/80.93 [8348]~P16(x83485,x83481,x83486,x83482)+E(f328(f74(x83481,x83481,x83481,f328(x83482,x83483)),f328(x83482,x83484)),f328(x83482,x83483))+~P24(f328(f62(x83485),x83483))+~P24(f328(f328(f244(f885(x83485,a871)),x83484),x83483))
% 81.29/80.93 [9478]~P21(x94781,x94782,x94784,x94783)+~P24(f328(f328(f330(x94782),x94785),f328(f307(x94781,x94782,x94784),x94783)))+P24(f328(f328(f330(x94781),f328(f78(x94781,x94782,x94783,x94784),x94785)),x94786))+~P24(f328(f328(f244(f885(x94781,a871)),x94783),x94786))
% 81.29/80.93 [9851]~P74(x98512)+~E(f570(x98511,x98513,x98515,x98516,x98514,x98512),f571(x98511,x98513,x98515,x98516,x98514,x98512))+~P24(f328(f62(x98514),x98516))+E(f328(f328(f6(x98511,x98512),x98513),f328(f307(x98514,x98511,x98515),x98516)),f328(f328(f6(x98514,x98512),f328(f74(x98511,x98512,x98514,x98513),x98515)),x98516))
% 81.29/80.93 [9889]~P74(x98896)+E(f328(x98891,f570(x98892,x98893,x98891,x98894,x98895,x98896)),f328(x98891,f571(x98892,x98893,x98891,x98894,x98895,x98896)))+E(f328(f328(f6(x98892,x98896),x98893),f328(f307(x98895,x98892,x98891),x98894)),f328(f328(f6(x98895,x98896),f328(f74(x98892,x98896,x98895,x98893),x98891)),x98894))+~P24(f328(f62(x98895),x98894))
% 81.29/80.93 [9931]~P74(x99312)+~E(f328(x99313,f328(x99315,f571(x99311,x99313,x99315,x99316,x99314,x99312))),f2(x99312))+~P24(f328(f62(x99314),x99316))+E(f328(f328(f6(x99311,x99312),x99313),f328(f307(x99314,x99311,x99315),x99316)),f328(f328(f6(x99314,x99312),f328(f74(x99311,x99312,x99314,x99313),x99315)),x99316))
% 81.29/80.93 [9991]~P74(x99912)+~P24(f328(f62(x99914),x99916))+E(f328(f328(f6(x99911,x99912),x99913),f328(f307(x99914,x99911,x99915),x99916)),f328(f328(f6(x99914,x99912),f328(f74(x99911,x99912,x99914,x99913),x99915)),x99916))+P24(f328(f328(f330(x99914),f571(x99911,x99913,x99915,x99916,x99914,x99912)),x99916))
% 81.29/80.93 [9992]~P74(x99922)+~P24(f328(f62(x99924),x99926))+E(f328(f328(f6(x99921,x99922),x99923),f328(f307(x99924,x99921,x99925),x99926)),f328(f328(f6(x99924,x99922),f328(f74(x99921,x99922,x99924,x99923),x99925)),x99926))+P24(f328(f328(f330(x99924),f570(x99921,x99923,x99925,x99926,x99924,x99922)),x99926))
% 81.29/80.93 [10105]~P75(x101051)+~P24(f328(f62(x101052),x101056))+E(f328(f328(f328(f66(x101051,x101052,f82(x101051)),f328(f328(f18(x101052,f885(x101053,a871),x101051),f328(f328(f7(x101052,x101051,f885(f885(x101053,a871),x101051)),f328(f328(f8(f885(x101053,x101051),f885(x101051,f885(f885(x101053,a871),x101051)),x101052),f66(x101051,x101053,f82(x101051))),x101054)),f79(x101051))),x101055)),f79(x101051)),x101056),f328(f328(f328(f66(x101051,f884(x101052,x101053),f82(x101051)),f328(f267(x101052,x101053,x101051),x101054)),f79(x101051)),f328(f328(f265(x101052,x101053),x101056),x101055)))+P24(f328(f328(f330(x101052),f706(x101054,x101055,x101053,x101056,x101052,x101051)),x101056))
% 81.29/80.93 [10123]~P75(x101231)+~P24(f328(f62(x101232),x101236))+E(f328(f328(f328(f66(x101231,x101232,f82(x101231)),f328(f328(f18(x101232,f885(x101233,a871),x101231),f328(f328(f7(x101232,x101231,f885(f885(x101233,a871),x101231)),f328(f328(f8(f885(x101233,x101231),f885(x101231,f885(f885(x101233,a871),x101231)),x101232),f66(x101231,x101233,f82(x101231))),x101234)),f79(x101231))),x101235)),f79(x101231)),x101236),f328(f328(f328(f66(x101231,f884(x101232,x101233),f82(x101231)),f328(f267(x101232,x101233,x101231),x101234)),f79(x101231)),f328(f328(f265(x101232,x101233),x101236),x101235)))+~P24(f328(f62(x101233),f328(x101235,f706(x101234,x101235,x101233,x101236,x101232,x101231))))
% 81.29/80.93 [8260]~P16(x82602,x82605,x82606,x82601)+~P24(f328(f62(x82602),x82604))+~P24(f328(f62(x82602),x82603))+E(f328(x82601,f328(f328(f116(f885(x82602,a871)),x82603),x82604)),f328(f74(x82605,x82605,x82605,f328(x82601,x82603)),f328(x82601,x82604)))
% 81.29/80.93 [8481]~P27(x84811)+P24(f328(f328(f244(x84811),f328(x84812,x84813)),x84814))+~P24(f328(f328(f330(x84815),x84813),x84816))+~P24(f328(f328(f244(x84811),f328(f328(f43(x84815,x84811),x84816),x84812)),x84814))
% 81.29/80.93 [8885]~P21(x88852,x88851,x88853,x88856)+E(f328(f328(f22(f885(x88851,a871)),f328(f307(x88852,x88851,x88853),x88854)),f328(f307(x88852,x88851,x88853),x88855)),f328(f307(x88852,x88851,x88853),f328(f328(f22(f885(x88852,a871)),x88854),x88855)))+~P24(f328(f328(f244(f885(x88852,a871)),x88855),x88856))+~P24(f328(f328(f244(f885(x88852,a871)),x88854),x88856))
% 81.29/80.93 [8886]~P21(x88862,x88861,x88863,x88866)+E(f328(f328(f107(f885(x88861,a871)),f328(f307(x88862,x88861,x88863),x88864)),f328(f307(x88862,x88861,x88863),x88865)),f328(f307(x88862,x88861,x88863),f328(f328(f107(f885(x88862,a871)),x88864),x88865)))+~P24(f328(f328(f244(f885(x88862,a871)),x88865),x88866))+~P24(f328(f328(f244(f885(x88862,a871)),x88864),x88866))
% 81.29/80.93 [8923]~P24(f328(x89231,x89233))+~P24(f328(f328(f328(f328(a202,x89232),x89233),x89234),x89236))+~P24(f328(f328(f328(f328(a202,f33(x89231,x89232)),x89236),x89234),x89235))+P24(f328(f328(f328(f328(a202,f33(x89231,x89232)),x89233),x89234),x89235))
% 81.29/80.93 [9152]E(x91521,x91522)+~P52(x91523,x91524,x91525)+~P24(f328(f328(f330(f884(x91523,x91524)),f328(f328(f257(x91523,x91524),x91526),x91522)),x91525))+~P24(f328(f328(f330(f884(x91523,x91524)),f328(f328(f257(x91523,x91524),x91526),x91521)),x91525))
% 81.29/80.93 [9926]~P71(x99261)+~E(f328(x99263,f344(x99264,x99266,x99263,x99265,x99262,x99261)),f328(x99266,f344(x99264,x99266,x99263,x99265,x99262,x99261)))+~P24(f328(f62(x99262),x99265))+E(f328(f328(f328(f66(x99261,x99262,f82(x99261)),x99263),x99264),x99265),f328(f328(f328(f66(x99261,x99262,f82(x99261)),x99266),x99264),x99265))
% 81.29/80.93 [9989]~P71(x99891)+~P24(f328(f62(x99892),x99895))+E(f328(f328(f328(f66(x99891,x99892,f82(x99891)),x99893),x99894),x99895),f328(f328(f328(f66(x99891,x99892,f82(x99891)),x99896),x99894),x99895))+P24(f328(f328(f330(x99892),f344(x99894,x99893,x99896,x99895,x99892,x99891)),x99895))
% 81.29/80.93 [8698]~P71(x86981)+~P24(f328(f62(x86982),x86986))+P24(f328(f328(f330(x86982),x86985),x86986))+E(f328(f328(f328(f66(x86981,x86982,f82(x86981)),x86983),x86984),f328(f328(f306(x86982),x86985),x86986)),f328(f328(f82(x86981),f328(x86983,x86985)),f328(f328(f328(f66(x86981,x86982,f82(x86981)),x86983),x86984),x86986)))
% 81.29/80.93 [8744]~P6(x87441,x87446,x87443)+~P9(x87441,f885(x87442,a871),x87443,x87445)+~P24(f328(f328(f330(x87441),x87444),x87446))+E(f328(f328(f43(x87441,f885(x87442,a871)),f328(f282(x87441,x87441,x87443),f328(f328(f306(x87441),x87444),f193(f885(x87441,a871))))),x87445),f328(x87445,x87444))
% 81.29/80.93 [8862]~P12(x88623,x88624,x88621)+~P24(f328(f62(x88623),x88626))+~P24(f328(f328(f330(x88623),x88622),x88626))+E(f328(f328(x88621,x88622),f328(f328(f65(x88623,x88624,x88621),x88625),f328(f328(f22(f885(x88623,a871)),x88626),f328(f328(f306(x88623),x88622),f193(f885(x88623,a871)))))),f328(f328(f65(x88623,x88624,x88621),x88625),x88626))
% 81.29/80.93 [9165]~P15(x91653,x91651,x91656,x91652)+~P24(f328(f62(x91653),x91655))+~P24(f328(f62(x91653),x91654))+E(f328(f74(x91651,x91651,x91651,f328(x91652,f328(f328(f116(f885(x91653,a871)),x91654),x91655))),f328(x91652,f328(f328(f107(f885(x91653,a871)),x91654),x91655))),f328(f74(x91651,x91651,x91651,f328(x91652,x91654)),f328(x91652,x91655)))
% 81.29/80.93 [9498]~E(x94983,f328(f328(f158(x94981,x94982),x94985),x94986))+P24(f328(f328(f330(f884(f878(x94981),f878(x94981))),f328(f328(f257(f878(x94981),f878(x94981)),x94982),x94983)),f156(x94981,x94984)))+~P24(f328(f328(f245(a877),x94985),f328(f194(f878(x94981)),x94982)))+~P24(f328(f328(f330(f884(x94981,x94981)),f328(f328(f257(x94981,x94981),f328(f328(f164(x94981),x94982),x94985)),x94986)),x94984))
% 81.29/80.93 [10002]~P74(x100022)+~P24(f328(f62(x100021),x100026))+P24(f328(f328(f330(x100021),f705(x100024,x100025,x100023,x100026,x100021,x100022)),x100026))+E(f328(f328(f6(x100021,x100022),f328(f328(f18(x100021,f885(x100023,a871),x100022),f328(f328(f8(f885(x100023,x100022),f885(f885(x100023,a871),x100022),x100021),f6(x100023,x100022)),x100024)),x100025)),x100026),f328(f328(f6(f884(x100021,x100023),x100022),f328(f267(x100021,x100023,x100022),x100024)),f328(f328(f265(x100021,x100023),x100026),x100025)))
% 81.29/80.93 [10003]~P75(x100032)+~P24(f328(f62(x100031),x100036))+P24(f328(f328(f330(x100031),f703(x100034,x100035,x100033,x100036,x100031,x100032)),x100036))+E(f328(f328(f9(x100031,x100032),f328(f328(f18(x100031,f885(x100033,a871),x100032),f328(f328(f8(f885(x100033,x100032),f885(f885(x100033,a871),x100032),x100031),f9(x100033,x100032)),x100034)),x100035)),x100036),f328(f328(f9(f884(x100031,x100033),x100032),f328(f267(x100031,x100033,x100032),x100034)),f328(f328(f265(x100031,x100033),x100036),x100035)))
% 81.29/80.93 [10042]~P74(x100422)+~P24(f328(f62(x100421),x100426))+~P24(f328(f62(x100423),f328(x100425,f705(x100424,x100425,x100423,x100426,x100421,x100422))))+E(f328(f328(f6(x100421,x100422),f328(f328(f18(x100421,f885(x100423,a871),x100422),f328(f328(f8(f885(x100423,x100422),f885(f885(x100423,a871),x100422),x100421),f6(x100423,x100422)),x100424)),x100425)),x100426),f328(f328(f6(f884(x100421,x100423),x100422),f328(f267(x100421,x100423,x100422),x100424)),f328(f328(f265(x100421,x100423),x100426),x100425)))
% 81.29/80.93 [10043]~P75(x100432)+~P24(f328(f62(x100431),x100436))+~P24(f328(f62(x100433),f328(x100435,f703(x100434,x100435,x100433,x100436,x100431,x100432))))+E(f328(f328(f9(x100431,x100432),f328(f328(f18(x100431,f885(x100433,a871),x100432),f328(f328(f8(f885(x100433,x100432),f885(f885(x100433,a871),x100432),x100431),f9(x100433,x100432)),x100434)),x100435)),x100436),f328(f328(f9(f884(x100431,x100433),x100432),f328(f267(x100431,x100433,x100432),x100434)),f328(f328(f265(x100431,x100433),x100436),x100435)))
% 81.29/80.93 [10025]~P75(x100252)+~P24(f328(f62(x100251),x100256))+P24(f328(f328(f330(x100251),x100253),x100256))+E(f328(f328(f9(x100251,x100252),f328(f328(f7(x100251,x100252,x100252),f328(f328(f18(x100251,x100252,f885(x100252,x100252)),f328(f328(f8(a871,f885(x100252,f885(x100252,x100252)),x100251),f102(x100252)),f328(f328(f7(x100251,x100251,a871),a325),x100253))),x100254)),x100255)),x100256),f328(f328(f258(x100252),x100255),f328(f38(x100251),x100256)))
% 81.29/80.93 [10030]~P75(x100302)+~P24(f328(f62(x100301),x100306))+~P24(f328(f328(f330(x100301),x100303),x100306))+E(f328(f328(f9(x100301,x100302),f328(f328(f7(x100301,x100302,x100302),f328(f328(f18(x100301,x100302,f885(x100302,x100302)),f328(f328(f8(a871,f885(x100302,f885(x100302,x100302)),x100301),f102(x100302)),f328(f328(f7(x100301,x100301,a871),a325),x100303))),x100304)),x100305)),x100306),f328(f328(f82(x100302),f328(x100304,x100303)),f328(f328(f258(x100302),x100305),f328(f328(f22(a877),f328(f38(x100301),x100306)),f79(a877)))))
% 81.29/80.93 [10097]~P24(f328(f62(x100971),x100975))+~P24(f328(f62(x100972),x100973))+P24(f328(f328(f330(x100972),f564(x100976,x100974,x100973,x100972,x100975,x100971)),x100973))+E(f328(f328(f6(x100971,a877),f328(f328(f8(f885(x100972,a871),a877,x100971),f38(x100972)),f328(f328(f8(f885(x100972,a871),f885(x100972,a871),x100971),f249(x100972)),f328(f328(f8(f885(x100972,a871),f885(x100972,a871),x100971),f328(f18(x100972,a871,a871),f328(f328(f8(a871,f885(a871,a871),x100972),a326),f328(f328(f7(x100972,f885(x100972,a871),a871),f330(x100972)),x100973)))),x100974)))),x100975),f328(f328(f82(a877),x100976),f328(f38(x100972),x100973)))
% 81.29/80.93 [10098]~P24(f328(f62(x100981),x100985))+~P24(f328(f62(x100982),x100983))+P24(f328(f328(f330(x100982),f573(x100986,x100984,x100983,x100982,x100985,x100981)),x100983))+E(f328(f328(f6(x100981,a877),f328(f328(f8(f885(x100982,a871),a877,x100981),f38(x100982)),f328(f328(f8(f885(x100982,a871),f885(x100982,a871),x100981),f249(x100982)),f328(f328(f8(f885(x100982,a871),f885(x100982,a871),x100981),f328(f18(x100982,a871,a871),f328(f328(f8(a871,f885(a871,a871),x100982),a326),f328(f328(f7(x100982,f885(x100982,a871),a871),f330(x100982)),x100983)))),x100984)))),x100985),f328(f328(f6(x100982,a877),x100986),x100983))
% 81.29/80.93 [10129]~P24(f328(f62(x101292),x101293))+~P24(f328(f62(x101291),x101295))+~E(f328(f38(x101291),f328(f249(x101291),f328(f328(f18(x101291,a871,a871),f328(f328(f8(a871,f885(a871,a871),x101291),a326),f328(f328(f7(x101291,f885(x101291,a871),a871),f330(x101291)),x101295))),f328(f328(f7(x101291,x101292,a871),x101294),f564(x101296,x101294,x101293,x101292,x101295,x101291))))),x101296)+E(f328(f328(f6(x101291,a877),f328(f328(f8(f885(x101292,a871),a877,x101291),f38(x101292)),f328(f328(f8(f885(x101292,a871),f885(x101292,a871),x101291),f249(x101292)),f328(f328(f8(f885(x101292,a871),f885(x101292,a871),x101291),f328(f18(x101292,a871,a871),f328(f328(f8(a871,f885(a871,a871),x101292),a326),f328(f328(f7(x101292,f885(x101292,a871),a871),f330(x101292)),x101293)))),x101294)))),x101295),f328(f328(f82(a877),x101296),f328(f38(x101292),x101293)))
% 81.29/80.93 [10131]~P24(f328(f62(x101312),x101313))+~P24(f328(f62(x101311),x101315))+~E(f328(f38(x101311),f328(f249(x101311),f328(f328(f18(x101311,a871,a871),f328(f328(f8(a871,f885(a871,a871),x101311),a326),f328(f328(f7(x101311,f885(x101311,a871),a871),f330(x101311)),x101315))),f328(f328(f7(x101311,x101312,a871),x101314),f573(x101316,x101314,x101313,x101312,x101315,x101311))))),f328(x101316,f573(x101316,x101314,x101313,x101312,x101315,x101311)))+E(f328(f328(f6(x101311,a877),f328(f328(f8(f885(x101312,a871),a877,x101311),f38(x101312)),f328(f328(f8(f885(x101312,a871),f885(x101312,a871),x101311),f249(x101312)),f328(f328(f8(f885(x101312,a871),f885(x101312,a871),x101311),f328(f18(x101312,a871,a871),f328(f328(f8(a871,f885(a871,a871),x101312),a326),f328(f328(f7(x101312,f885(x101312,a871),a871),f330(x101312)),x101313)))),x101314)))),x101315),f328(f328(f6(x101312,a877),x101316),x101313))
% 81.29/80.93 [9779]E(x97791,x97792)+~P12(x97793,x97794,x97795)+~P24(f328(f67(x97793,x97794,x97795,x97796,x97797),x97792))+~P24(f328(f67(x97793,x97794,x97795,x97796,x97797),x97791))
% 81.29/80.93 [9574]P24(f328(x95741,x95742))+~P24(f328(f328(f330(x95747),x95742),f328(x95746,x95744)))+~P24(f328(x95741,f523(x95741,x95746,x95745,x95743,x95747)))+~P24(f328(f328(f330(x95743),x95744),x95745))
% 81.29/80.93 [10017]~P12(x100177,x100176,x100171)+E(f328(f328(x100171,x100172),f849(x100172,x100173,x100174,x100175,x100171,x100176,x100177)),x100173)+~P24(f328(f67(x100177,x100176,x100171,x100175,x100174),x100173))+~P24(f328(f328(f330(x100177),x100172),x100174))
% 81.29/80.93 [10082]~P12(x100821,x100822,x100823)+~P24(f328(f67(x100821,x100822,x100823,x100824,x100825),x100827))+P24(f328(f67(x100821,x100822,x100823,x100824,f328(f328(f22(f885(x100821,a871)),x100825),f328(f328(f306(x100821),x100826),f193(f885(x100821,a871))))),f849(x100826,x100827,x100825,x100824,x100823,x100822,x100821)))+~P24(f328(f328(f330(x100821),x100826),x100825))
% 81.29/80.93 [9474]~P71(x94741)+~P21(x94745,x94742,x94746,x94747)+~P24(f328(f62(x94745),x94747))+E(f328(f328(f328(f66(x94741,x94742,f82(x94741)),x94743),x94744),f328(f307(x94745,x94742,x94746),x94747)),f328(f328(f328(f66(x94741,x94745,f82(x94741)),f328(f74(x94742,x94741,x94745,x94743),x94746)),x94744),x94747))
% 81.29/80.93 [9598]~E(f328(f328(f306(x95981),x95985),x95986),f328(f328(f306(x95981),x95982),x95983))+~P24(f328(f67(x95981,x95981,x95984,x95982,x95983),x95987))+P24(f328(f328(f330(x95981),x95982),x95983))+P24(f328(f63(x95981,x95984,f328(f328(f306(x95981),x95985),x95986)),x95987))
% 81.29/80.93 [9679]P24(f328(x96791,x96792))+~P24(f328(f328(f330(x96793),x96792),f328(x96794,x96797)))+~P24(f328(f328(f330(x96796),x96797),x96795))+P24(f328(f328(f330(x96793),f523(x96791,x96794,x96795,x96796,x96793)),f328(f328(f43(x96796,f885(x96793,a871)),x96795),x96794)))
% 81.29/80.93 [9693]~P21(x96932,x96931,x96935,x96934)+~P21(x96931,x96933,x96936,f328(f307(x96932,x96931,x96935),x96934))+E(f328(f328(f74(x96931,x96932,x96933,f78(x96932,x96931,x96934,x96935)),f78(x96931,x96933,f328(f307(x96932,x96931,x96935),x96934),x96936)),x96937),f328(f78(x96932,x96933,x96934,f328(f74(x96931,x96933,x96932,x96936),x96935)),x96937))+~P24(f328(f328(f330(x96933),x96937),f328(f307(x96931,x96933,x96936),f328(f307(x96932,x96931,x96935),x96934))))
% 81.29/80.93 [10018]~P12(x100187,x100186,x100181)+E(f328(f328(x100181,x100182),f856(x100183,x100184,x100182,x100185,x100181,x100186,x100187)),x100183)+P24(f328(f328(f330(x100187),x100182),x100184))+~P24(f328(f67(x100187,x100186,x100181,x100185,f328(f328(f306(x100187),x100182),x100184)),x100183))
% 81.29/80.93 [10081]~P12(x100811,x100814,x100815)+P24(f328(f67(x100811,x100814,x100815,x100816,x100813),f856(x100817,x100813,x100812,x100816,x100815,x100814,x100811)))+P24(f328(f328(f330(x100811),x100812),x100813))+~P24(f328(f67(x100811,x100814,x100815,x100816,f328(f328(f306(x100811),x100812),x100813)),x100817))
% 81.29/80.93 [9761]E(x97611,f2(a1))+~P24(f328(f49(x97613,x97611),f328(f328(f257(a1,a1),x97615),x97617)))+~P24(f328(f49(x97612,x97611),f328(f328(f257(a1,a1),x97614),x97616)))+P24(f328(f49(f328(f328(f81(a1),x97612),x97613),x97611),f328(f328(f257(a1,a1),f328(f328(f81(a1),f328(f328(f81(a1),x97614),x97615)),f328(f328(f39(a1),f328(f328(f81(a1),x97616),x97617)),x97611))),f45(a1,f328(f328(f81(a1),x97616),x97617),x97611))))
% 81.29/80.93 [9763]~P24(f328(f328(f245(a877),f2(a877)),x97633))+~P24(f328(f48(x97632,x97633),f328(f328(f257(a877,a877),x97635),x97637)))+~P24(f328(f48(x97631,x97633),f328(f328(f257(a877,a877),x97634),x97636)))+P24(f328(f48(f328(f328(f81(a877),x97631),x97632),x97633),f328(f328(f257(a877,a877),f328(f328(f81(a877),f328(f328(f81(a877),x97634),x97635)),f328(f328(f39(a877),f328(f328(f81(a877),x97636),x97637)),x97633))),f45(a877,f328(f328(f81(a877),x97636),x97637),x97633))))
% 81.29/80.93 [10128]~P74(x101282)+~P24(f328(f62(x101283),x101285))+~P24(f328(f62(x101281),x101287))+E(f328(f328(f6(x101281,x101282),f328(f328(f18(x101281,f885(x101283,a871),x101282),f328(f328(f8(f885(x101283,x101282),f885(f885(x101283,a871),x101282),x101281),f6(x101283,x101282)),x101284)),f328(f328(f8(f885(x101283,a871),f885(x101283,a871),x101281),f249(x101283)),f328(f328(f8(f885(x101283,a871),f885(x101283,a871),x101281),f328(f18(x101283,a871,a871),f328(f328(f8(a871,f885(a871,a871),x101283),a326),f328(f328(f7(x101283,f885(x101283,a871),a871),f330(x101283)),x101285)))),x101286)))),x101287),f328(f328(f6(x101283,x101282),f328(f328(f18(x101283,f885(x101281,a871),x101282),f328(f328(f8(f885(x101281,x101282),f885(f885(x101281,a871),x101282),x101283),f6(x101281,x101282)),f328(f7(x101281,x101283,x101282),x101284))),f328(f328(f8(f885(x101281,a871),f885(x101281,a871),x101283),f249(x101281)),f328(f328(f8(f885(x101281,a871),f885(x101281,a871),x101283),f328(f18(x101281,a871,a871),f328(f328(f8(a871,f885(a871,a871),x101281),a326),f328(f328(f7(x101281,f885(x101281,a871),a871),f330(x101281)),x101287)))),f328(f7(x101281,x101283,a871),x101286))))),x101285))
% 81.29/80.93 [9634]~P18(x96347,x96346,x96341,x96348,x96342,x96344)+E(f328(f328(x96341,f328(x96342,x96343)),f328(x96344,x96345)),f328(x96344,x96345))+~P24(f328(f62(x96346),x96345))+~P24(f328(f328(f330(x96346),x96343),x96345))
% 81.29/80.93 [9638]~P10(x96386,x96381,x96382,x96388,x96383,x96384)+~P6(x96386,x96387,x96388)+P9(x96381,x96382,x96383,f328(x96384,x96385))+~P24(f328(f328(f330(x96386),x96385),x96387))
% 81.29/80.93 [8076]~P30(x80768,x80767,f328(f328(f328(f93(x80768),x80764),x80766),x80761))+P24(f328(f328(x80761,x80762),x80763))+~P24(f328(f328(x80764,x80762),x80765))+~P24(f328(f328(f328(f328(a202,x80766),x80765),x80767),x80763))
% 81.29/80.93 [9260]~P15(x92607,x92601,x92608,x92603)+~P24(f328(f62(x92607),x92605))+~P24(f328(f62(x92607),x92604))+E(f328(f74(x92601,x92601,x92602,f328(x92603,x92604)),f328(f74(x92601,x92601,x92602,f328(x92603,x92605)),x92606)),f328(f74(x92601,x92601,x92602,f328(x92603,x92605)),f328(f74(x92601,x92601,x92602,f328(x92603,x92604)),x92606)))
% 81.29/80.93 [9268]~P35(x92681,x92682,x92683,x92684,x92687)+P35(x92681,x92682,x92683,f328(f328(f158(x92681,x92684),x92685),x92686),f328(f328(f158(x92682,x92687),x92685),x92688))+~P24(f328(f328(x92683,x92686),x92688))+~P24(f328(f328(f245(a877),x92685),f328(f194(f878(x92681)),x92684)))
% 81.29/80.93 [9269]~P35(x92691,x92692,x92693,x92694,x92697)+P35(x92691,x92692,x92693,f328(f328(f158(x92691,x92694),x92695),x92696),f328(f328(f158(x92692,x92697),x92695),x92698))+~P24(f328(f328(x92693,x92696),x92698))+~P24(f328(f328(f245(a877),x92695),f328(f194(f878(x92692)),x92697)))
% 81.29/80.93 [9348]~P21(x93482,x93482,x93485,x93486)+~P17(x93483,x93482,x93487,x93488,x93481)+~P24(f328(f62(x93482),x93486))+E(f328(f328(x93481,f328(f74(x93482,x93483,x93482,x93484),x93485)),x93486),f328(f328(x93481,x93484),f328(f307(x93482,x93482,x93485),x93486)))
% 81.29/80.93 [9636]~P19(x96367,x96362,x96365,x96368,x96366,x96361)+~P24(f328(f62(x96362),x96364))+E(f328(x96361,f328(f328(f306(x96362),x96363),x96364)),f328(f328(x96365,f328(x96366,x96363)),f328(x96361,x96364)))+P24(f328(f328(f330(x96362),x96363),x96364))
% 81.29/80.93 [9645]~P18(x96456,x96455,x96451,x96457,x96458,x96452)+E(f328(f328(x96451,f328(x96452,x96453)),f328(x96452,x96454)),f328(x96452,x96454))+~P24(f328(f62(x96455),x96454))+~P24(f328(f328(f244(f885(x96455,a871)),x96453),x96454))
% 81.29/80.93 [9245]P24(f328(f328(f330(f884(f878(x92451),f878(x92451))),f328(f328(f257(f878(x92451),f878(x92451)),x92452),x92453)),f156(x92451,x92454)))+~E(x92453,f328(f328(f127(x92451),x92455),f328(f328(f150(x92451),x92456),x92457)))+~E(x92452,f328(f328(f127(x92451),x92455),f328(f328(f150(x92451),x92458),x92457)))+~P24(f328(f328(f330(f884(x92451,x92451)),f328(f328(f257(x92451,x92451),x92458),x92456)),x92454))
% 81.29/80.93 [9641]~P18(x96416,x96412,x96415,x96417,x96418,x96411)+~P24(f328(f62(x96412),x96414))+~P24(f328(f62(x96412),x96413))+E(f328(x96411,f328(f328(f116(f885(x96412,a871)),x96413),x96414)),f328(f328(x96415,f328(x96411,x96413)),f328(x96411,x96414)))
% 81.29/80.93 [10166]~P21(x101664,x101662,x101665,x101668)+E(f328(f328(f42(x101661,f885(x101662,a871)),x101663),f328(f328(f8(f885(x101664,a871),f885(x101662,a871),x101661),f307(x101664,x101662,x101665)),x101666)),f328(f307(x101664,x101662,x101665),f328(f328(f42(x101661,f885(x101664,a871)),x101663),x101666)))+~P24(f328(f328(f330(x101661),x101667),x101663))+P24(f328(f328(f330(x101661),f557(x101667,x101666,x101663,x101661,x101668,x101665,x101662,x101664)),x101663))
% 81.29/80.93 [10187]~P21(x101874,x101872,x101875,x101877)+E(f328(f328(f42(x101871,f885(x101872,a871)),x101873),f328(f328(f8(f885(x101874,a871),f885(x101872,a871),x101871),f307(x101874,x101872,x101875)),x101876)),f328(f307(x101874,x101872,x101875),f328(f328(f42(x101871,f885(x101874,a871)),x101873),x101876)))+~P24(f328(f328(f330(x101871),x101878),x101873))+~P24(f328(f328(f244(f885(x101874,a871)),f328(x101876,f557(x101878,x101876,x101873,x101871,x101877,x101875,x101872,x101874))),x101877))
% 81.29/80.93 [9702]~P19(x97027,x97025,x97021,x97028,x97022,x97024)+~P24(f328(f62(x97025),x97026))+~P24(f328(f328(f330(x97025),x97023),x97026))+E(f328(f328(x97021,f328(x97022,x97023)),f328(x97024,f328(f328(f22(f885(x97025,a871)),x97026),f328(f328(f306(x97025),x97023),f193(f885(x97025,a871)))))),f328(x97024,x97026))
% 81.29/80.93 [9710]~P19(x97106,x97103,x97101,x97107,x97108,x97102)+~P24(f328(f62(x97103),x97105))+~P24(f328(f62(x97103),x97104))+E(f328(f328(x97101,f328(x97102,f328(f328(f116(f885(x97103,a871)),x97104),x97105))),f328(x97102,f328(f328(f107(f885(x97103,a871)),x97104),x97105))),f328(f328(x97101,f328(x97102,x97104)),f328(x97102,x97105)))
% 81.29/80.93 [9801]P42(x98011,x98012,x98013,x98014,x98015,f328(f328(x98013,x98016),x98017))+~P42(x98011,x98012,x98013,x98014,f328(f328(f22(f885(x98011,a871)),x98015),f328(f328(f306(x98011),x98018),f193(f885(x98011,a871)))),x98019)+~E(f328(f328(x98013,x98016),x98017),f328(f328(x98013,x98018),x98019))+~P24(f328(f328(f330(x98011),x98018),x98015))
% 81.29/80.93 [10202]P20(x102021,x102022,f328(f328(f306(f876(x102021)),f328(f328(f328(f93(x102021),f328(x102023,f483(x102024,x102025,x102026,x102027,x102023,x102022,x102021,x102028,x102029))),f328(x102027,f483(x102024,x102025,x102026,x102027,x102023,x102022,x102021,x102028,x102029))),f328(x102026,f483(x102024,x102025,x102026,x102027,x102023,x102022,x102021,x102028,x102029)))),f193(f885(f876(x102021),a871))))+~P24(f328(f62(x102029),x102028))+~P20(x102021,x102022,f328(f307(x102029,f876(x102021),f328(f328(f18(x102029,f885(x102021,f885(a872,a871)),f876(x102021)),f328(f328(f18(x102029,a873,f885(f885(x102021,f885(a872,a871)),f876(x102021))),f328(f328(f8(f885(x102021,f885(a872,a871)),f885(a873,f885(f885(x102021,f885(a872,a871)),f876(x102021))),x102029),f93(x102021)),x102023)),x102027)),x102026)),x102028))+P20(x102021,x102022,f328(f307(x102029,f876(x102021),f328(f328(f18(x102029,f885(x102021,f885(a872,a871)),f876(x102021)),f328(f328(f18(x102029,a873,f885(f885(x102021,f885(a872,a871)),f876(x102021))),f328(f328(f8(f885(x102021,f885(a872,a871)),f885(a873,f885(f885(x102021,f885(a872,a871)),f876(x102021))),x102029),f93(x102021)),x102025)),x102027)),x102024)),x102028))
% 81.29/80.93 [10203]~P20(x102031,x102032,f328(f328(f306(f876(x102031)),f328(f328(f328(f93(x102031),f328(x102034,f483(x102036,x102034,x102038,x102035,x102039,x102032,x102031,x102037,x102033))),f328(x102035,f483(x102036,x102034,x102038,x102035,x102039,x102032,x102031,x102037,x102033))),f328(x102036,f483(x102036,x102034,x102038,x102035,x102039,x102032,x102031,x102037,x102033)))),f193(f885(f876(x102031),a871))))+~P24(f328(f62(x102033),x102037))+~P20(x102031,x102032,f328(f307(x102033,f876(x102031),f328(f328(f18(x102033,f885(x102031,f885(a872,a871)),f876(x102031)),f328(f328(f18(x102033,a873,f885(f885(x102031,f885(a872,a871)),f876(x102031))),f328(f328(f8(f885(x102031,f885(a872,a871)),f885(a873,f885(f885(x102031,f885(a872,a871)),f876(x102031))),x102033),f93(x102031)),x102039)),x102035)),x102038)),x102037))+P20(x102031,x102032,f328(f307(x102033,f876(x102031),f328(f328(f18(x102033,f885(x102031,f885(a872,a871)),f876(x102031)),f328(f328(f18(x102033,a873,f885(f885(x102031,f885(a872,a871)),f876(x102031))),f328(f328(f8(f885(x102031,f885(a872,a871)),f885(a873,f885(f885(x102031,f885(a872,a871)),f876(x102031))),x102033),f93(x102031)),x102034)),x102035)),x102036)),x102037))
% 81.29/80.93 [9736]~P10(x97366,x97367,x97368,x97369,x973610,x97361)+E(f328(f328(x97361,x97362),x97363),f328(f328(x97361,x97364),x97365))+~P24(f328(f328(f330(f884(x97367,x97367)),f328(f328(f257(x97367,x97367),x97363),x97365)),x973610))+~P24(f328(f328(f330(f884(x97366,x97366)),f328(f328(f257(x97366,x97366),x97362),x97364)),x97369))
% 81.29/80.93 [9350]~P78(x93502)+E(x93501,f193(f885(x93502,a871)))+~P24(f328(f62(x93502),x93501))+P24(f328(f328(f330(x93502),f10(x93502,x93501)),x93501))+~P24(f328(f328(f330(x93502),f328(f328(f116(x93502),f667(x93501,x93502)),f678(x93501,x93502))),f328(f328(f306(x93502),f667(x93501,x93502)),f328(f328(f306(x93502),f678(x93501,x93502)),f193(f885(x93502,a871))))))
% 81.29/80.93 [9351]~P78(x93512)+E(x93511,f193(f885(x93512,a871)))+~P24(f328(f62(x93512),x93511))+P24(f328(f328(f330(x93512),f11(x93512,x93511)),x93511))+~P24(f328(f328(f330(x93512),f328(f328(f107(x93512),f832(x93511,x93512)),f834(x93511,x93512))),f328(f328(f306(x93512),f832(x93511,x93512)),f328(f328(f306(x93512),f834(x93511,x93512)),f193(f885(x93512,a871))))))
% 81.29/80.93 [9382]~P71(x93822)+E(x93821,f193(f885(x93822,a871)))+~P24(f328(f62(x93822),x93821))+P24(f328(f328(f330(x93822),f328(f64(x93822,f82(x93822)),x93821)),x93821))+~P24(f328(f328(f330(x93822),f328(f328(f82(x93822),f865(x93821,x93822)),f867(x93821,x93822))),f328(f328(f306(x93822),f865(x93821,x93822)),f328(f328(f306(x93822),f867(x93821,x93822)),f193(f885(x93822,a871))))))
% 81.29/80.93 [9388]~P106(x93882)+E(x93881,f193(f885(x93882,a871)))+~P24(f328(f62(x93882),x93881))+P24(f328(f328(f330(x93882),f12(x93882,f242(x93882),x93881)),x93881))+~P24(f328(f328(f330(x93882),f328(f328(f242(x93882),f397(x93881,x93882)),f400(x93881,x93882))),f328(f328(f306(x93882),f397(x93881,x93882)),f328(f328(f306(x93882),f400(x93881,x93882)),f193(f885(x93882,a871))))))
% 81.29/80.93 [9389]~P106(x93892)+E(x93891,f193(f885(x93892,a871)))+~P24(f328(f62(x93892),x93891))+P24(f328(f328(f330(x93892),f13(x93892,f243(x93892),x93891)),x93891))+~P24(f328(f328(f330(x93892),f328(f328(f243(x93892),f471(x93891,x93892)),f472(x93891,x93892))),f328(f328(f306(x93892),f471(x93891,x93892)),f328(f328(f306(x93892),f472(x93891,x93892)),f193(f885(x93892,a871))))))
% 81.29/80.93 [6515]~P89(x65152)+E(x65151,f2(x65152))+~E(f328(f328(f81(x65152),x65153),x65151),f2(x65152))+~P24(f328(f328(f244(x65152),f2(x65152)),x65153))+~P24(f328(f328(f244(x65152),f2(x65152)),x65151))
% 81.29/80.93 [6516]~P89(x65162)+E(x65161,f2(x65162))+~E(f328(f328(f81(x65162),x65161),x65163),f2(x65162))+~P24(f328(f328(f244(x65162),f2(x65162)),x65163))+~P24(f328(f328(f244(x65162),f2(x65162)),x65161))
% 81.29/80.93 [7046]~P106(x70462)+~P29(x70462,x70461)+E(x70461,f119(x70462))+~P24(f328(f328(f330(x70462),x70463),f328(f171(x70462),f637(x70461,x70462))))+P24(f328(f328(f244(x70462),f670(x70461,x70462)),x70463))
% 81.29/80.93 [7212]~P106(x72121)+E(f14(x72121,x72122),x72123)+~P24(f328(f62(x72121),x72122))+~P24(f328(f328(f244(x72121),x72123),f461(x72123,x72122,x72121)))+~P24(f328(f328(f330(x72121),x72123),x72122))
% 81.29/80.93 [7243]~P106(x72431)+~P29(x72431,x72432)+~P29(x72431,x72433)+P29(x72431,f328(f328(f127(x72431),x72432),x72433))+P24(f328(f328(f330(x72431),f643(x72433,x72432,x72431)),f328(f171(x72431),x72432)))
% 81.29/80.93 [7244]~P106(x72441)+~P29(x72441,x72442)+~P29(x72441,x72443)+P29(x72441,f328(f328(f127(x72441),x72442),x72443))+P24(f328(f328(f330(x72441),f644(x72443,x72442,x72441)),f328(f171(x72441),x72443)))
% 81.29/80.93 [7300]~P106(x73001)+E(f14(x73001,x73002),x73003)+~P24(f328(f62(x73001),x73002))+P24(f328(f328(f330(x73001),f461(x73003,x73002,x73001)),x73002))+~P24(f328(f328(f330(x73001),x73003),x73002))
% 81.29/80.93 [7301]~P106(x73011)+E(f15(x73011,x73012),x73013)+~P24(f328(f62(x73011),x73012))+P24(f328(f328(f330(x73011),f462(x73013,x73012,x73011)),x73012))+~P24(f328(f328(f330(x73011),x73013),x73012))
% 81.29/80.93 [7878]~P106(x78781)+E(f15(x78781,x78782),x78783)+~P24(f328(f62(x78781),x78782))+~P24(f328(f328(f330(x78781),x78783),x78782))+~P24(f328(f328(f244(x78781),f462(x78783,x78782,x78781)),x78783))
% 81.29/80.93 [8208]~P106(x82081)+~P29(x82081,x82082)+~P29(x82081,x82083)+P29(x82081,f328(f328(f127(x82081),x82082),x82083))+~P24(f328(f328(f244(x82081),f643(x82083,x82082,x82081)),f644(x82083,x82082,x82081)))
% 81.29/80.93 [8989]~P78(x89892)+E(x89891,f193(f885(x89892,a871)))+~E(f328(f328(f116(x89892),f328(x89893,f414(x89891,x89893,x89892))),f328(x89893,f417(x89891,x89893,x89892))),f328(x89893,f328(f328(f116(x89892),f414(x89891,x89893,x89892)),f417(x89891,x89893,x89892))))+E(f10(x89892,f328(f307(x89892,x89892,x89893),x89891)),f328(x89893,f10(x89892,x89891)))+~P24(f328(f62(x89892),x89891))
% 81.29/80.93 [8990]~P78(x89902)+E(x89901,f193(f885(x89902,a871)))+~E(f328(f328(f107(x89902),f328(x89903,f415(x89901,x89903,x89902))),f328(x89903,f416(x89901,x89903,x89902))),f328(x89903,f328(f328(f107(x89902),f415(x89901,x89903,x89902)),f416(x89901,x89903,x89902))))+E(f11(x89902,f328(f307(x89902,x89902,x89903),x89901)),f328(x89903,f11(x89902,x89901)))+~P24(f328(f62(x89902),x89901))
% 81.29/80.93 [8991]~P106(x89912)+E(x89911,f193(f885(x89912,a871)))+~E(f328(f328(f242(x89912),f328(x89913,f411(x89911,x89913,x89912))),f328(x89913,f412(x89911,x89913,x89912))),f328(x89913,f328(f328(f242(x89912),f411(x89911,x89913,x89912)),f412(x89911,x89913,x89912))))+E(f14(x89912,f328(f307(x89912,x89912,x89913),x89911)),f328(x89913,f14(x89912,x89911)))+~P24(f328(f62(x89912),x89911))
% 81.29/80.93 [8992]~P106(x89922)+E(x89921,f193(f885(x89922,a871)))+~E(f328(f328(f243(x89922),f328(x89923,f466(x89921,x89923,x89922))),f328(x89923,f474(x89921,x89923,x89922))),f328(x89923,f328(f328(f243(x89922),f466(x89921,x89923,x89922)),f474(x89921,x89923,x89922))))+E(f15(x89922,f328(f307(x89922,x89922,x89923),x89921)),f328(x89923,f15(x89922,x89921)))+~P24(f328(f62(x89922),x89921))
% 81.29/80.93 [9063]~P106(x90632)+E(x90631,f193(f885(x90632,a871)))+~E(f328(f328(f242(x90632),f328(x90633,f403(x90631,x90633,x90632))),f328(x90633,f405(x90631,x90633,x90632))),f328(x90633,f328(f328(f242(x90632),f403(x90631,x90633,x90632)),f405(x90631,x90633,x90632))))+E(f12(x90632,f242(x90632),f328(f307(x90632,x90632,x90633),x90631)),f328(x90633,f12(x90632,f242(x90632),x90631)))+~P24(f328(f62(x90632),x90631))
% 81.29/80.93 [9064]~P106(x90642)+E(x90641,f193(f885(x90642,a871)))+~E(f328(f328(f243(x90642),f328(x90643,f467(x90641,x90643,x90642))),f328(x90643,f473(x90641,x90643,x90642))),f328(x90643,f328(f328(f243(x90642),f467(x90641,x90643,x90642)),f473(x90641,x90643,x90642))))+E(f13(x90642,f243(x90642),f328(f307(x90642,x90642,x90643),x90641)),f328(x90643,f13(x90642,f243(x90642),x90641)))+~P24(f328(f62(x90642),x90641))
% 81.29/80.93 [6531]~P71(x65312)+E(x65311,f193(f885(x65312,a871)))+~P24(f328(f62(x65312),x65311))+E(f328(f64(x65312,f82(x65312)),f328(f328(f306(x65312),x65313),x65311)),f328(f328(f82(x65312),x65313),f328(f64(x65312,f82(x65312)),x65311)))+P24(f328(f328(f330(x65312),x65313),x65311))
% 81.29/80.93 [7052]~P78(x70522)+E(f328(f328(f116(x70522),f10(x70522,x70521)),f10(x70522,x70523)),f10(x70522,x70523))+E(x70521,f193(f885(x70522,a871)))+~P24(f328(f62(x70522),x70523))+~P24(f328(f328(f244(f885(x70522,a871)),x70521),x70523))
% 81.29/80.93 [7053]~P78(x70532)+E(f328(f328(f107(x70532),f11(x70532,x70531)),f11(x70532,x70533)),f11(x70532,x70533))+E(x70531,f193(f885(x70532,a871)))+~P24(f328(f62(x70532),x70533))+~P24(f328(f328(f244(f885(x70532,a871)),x70531),x70533))
% 81.29/80.93 [7054]~P106(x70542)+E(f328(f328(f242(x70542),f14(x70542,x70541)),f14(x70542,x70543)),f14(x70542,x70543))+E(x70541,f193(f885(x70542,a871)))+~P24(f328(f62(x70542),x70543))+~P24(f328(f328(f244(f885(x70542,a871)),x70541),x70543))
% 81.29/80.93 [7055]~P106(x70552)+E(f328(f328(f243(x70552),f15(x70552,x70551)),f15(x70552,x70553)),f15(x70552,x70553))+E(x70551,f193(f885(x70552,a871)))+~P24(f328(f62(x70552),x70553))+~P24(f328(f328(f244(f885(x70552,a871)),x70551),x70553))
% 81.29/80.93 [7352]~P106(x73522)+E(x73521,f193(f885(x73522,a871)))+~P24(f328(f62(x73522),x73523))+P24(f328(f328(f244(x73522),f14(x73522,x73523)),f14(x73522,x73521)))+~P24(f328(f328(f244(f885(x73522,a871)),x73521),x73523))
% 81.29/80.93 [7353]~P106(x73532)+E(x73531,f193(f885(x73532,a871)))+~P24(f328(f62(x73532),x73533))+P24(f328(f328(f244(x73532),f15(x73532,x73531)),f15(x73532,x73533)))+~P24(f328(f328(f244(f885(x73532,a871)),x73531),x73533))
% 81.29/80.93 [7412]~P78(x74121)+E(f10(x74121,x74122),x74123)+~P24(f328(f62(x74121),x74122))+~E(f328(f328(f22(f885(x74121,a871)),x74122),f328(f328(f306(x74121),x74123),f193(f885(x74121,a871)))),f193(f885(x74121,a871)))+~P24(f328(f328(f330(x74121),x74123),x74122))
% 81.29/80.93 [7413]~P78(x74131)+E(f11(x74131,x74132),x74133)+~P24(f328(f62(x74131),x74132))+~E(f328(f328(f22(f885(x74131,a871)),x74132),f328(f328(f306(x74131),x74133),f193(f885(x74131,a871)))),f193(f885(x74131,a871)))+~P24(f328(f328(f330(x74131),x74133),x74132))
% 81.29/80.93 [7414]~P106(x74141)+E(f14(x74141,x74142),x74143)+~P24(f328(f62(x74141),x74142))+~E(f328(f328(f22(f885(x74141,a871)),x74142),f328(f328(f306(x74141),x74143),f193(f885(x74141,a871)))),f193(f885(x74141,a871)))+~P24(f328(f328(f330(x74141),x74143),x74142))
% 81.29/80.93 [7415]~P106(x74151)+E(f15(x74151,x74152),x74153)+~P24(f328(f62(x74151),x74152))+~E(f328(f328(f22(f885(x74151,a871)),x74152),f328(f328(f306(x74151),x74153),f193(f885(x74151,a871)))),f193(f885(x74151,a871)))+~P24(f328(f328(f330(x74151),x74153),x74152))
% 81.29/80.93 [7511]~P106(x75111)+E(f12(x75111,f242(x75111),x75112),x75113)+~P24(f328(f62(x75111),x75112))+~E(f328(f328(f22(f885(x75111,a871)),x75112),f328(f328(f306(x75111),x75113),f193(f885(x75111,a871)))),f193(f885(x75111,a871)))+~P24(f328(f328(f330(x75111),x75113),x75112))
% 81.29/80.93 [7512]~P106(x75121)+E(f13(x75121,f243(x75121),x75122),x75123)+~P24(f328(f62(x75121),x75122))+~E(f328(f328(f22(f885(x75121,a871)),x75122),f328(f328(f306(x75121),x75123),f193(f885(x75121,a871)))),f193(f885(x75121,a871)))+~P24(f328(f328(f330(x75121),x75123),x75122))
% 81.29/80.93 [7548]~P102(x75482)+E(x75481,f193(f885(x75482,a871)))+~P24(f328(f62(x75482),x75481))+~P24(f328(f328(f244(x75482),x75483),f863(x75483,x75481,x75482)))+P24(f328(f328(f244(x75482),x75483),f328(f64(x75482,f107(x75482)),x75481)))
% 81.29/80.93 [7549]~P106(x75492)+E(x75491,f193(f885(x75492,a871)))+~P24(f328(f62(x75492),x75491))+~P24(f328(f328(f244(x75492),x75493),f391(x75493,x75491,x75492)))+P24(f328(f328(f244(x75492),x75493),f328(f64(x75492,f242(x75492)),x75491)))
% 81.29/80.93 [7550]~P106(x75502)+E(x75501,f193(f885(x75502,a871)))+~P24(f328(f62(x75502),x75501))+~P24(f328(f328(f245(x75502),x75503),f393(x75503,x75501,x75502)))+P24(f328(f328(f245(x75502),x75503),f328(f64(x75502,f242(x75502)),x75501)))
% 81.29/80.93 [7635]~P102(x76352)+E(x76351,f193(f885(x76352,a871)))+~P24(f328(f62(x76352),x76351))+P24(f328(f328(f330(x76352),f863(x76353,x76351,x76352)),x76351))+P24(f328(f328(f244(x76352),x76353),f328(f64(x76352,f107(x76352)),x76351)))
% 81.29/80.93 [7636]~P106(x76362)+E(x76361,f193(f885(x76362,a871)))+~P24(f328(f62(x76362),x76361))+P24(f328(f328(f330(x76362),f391(x76363,x76361,x76362)),x76361))+P24(f328(f328(f244(x76362),x76363),f328(f64(x76362,f242(x76362)),x76361)))
% 81.29/80.93 [7637]~P106(x76372)+E(x76371,f193(f885(x76372,a871)))+~P24(f328(f62(x76372),x76371))+P24(f328(f328(f330(x76372),f393(x76373,x76371,x76372)),x76371))+P24(f328(f328(f245(x76372),x76373),f328(f64(x76372,f242(x76372)),x76371)))
% 81.29/80.93 [7758]~P106(x77582)+E(x77581,f193(f885(x77582,a871)))+E(f328(f328(f242(x77582),f12(x77582,f242(x77582),x77581)),f12(x77582,f242(x77582),x77583)),f12(x77582,f242(x77582),x77583))+~P24(f328(f62(x77582),x77583))+~P24(f328(f328(f244(f885(x77582,a871)),x77581),x77583))
% 81.29/80.93 [7759]~P106(x77592)+E(x77591,f193(f885(x77592,a871)))+E(f328(f328(f243(x77592),f13(x77592,f243(x77592),x77591)),f13(x77592,f243(x77592),x77593)),f13(x77592,f243(x77592),x77593))+~P24(f328(f62(x77592),x77593))+~P24(f328(f328(f244(f885(x77592,a871)),x77591),x77593))
% 81.29/80.93 [7957]~E(f337(x79571,x79573,x79572),f338(x79571,x79573,x79572))+~E(f328(f38(x79572),f339(x79571,x79573,x79572)),x79571)+E(f328(f328(f82(a877),x79571),f328(f38(f885(x79572,a871)),x79573)),f328(f38(x79572),f40(f885(x79572,a871),x79573)))+~P24(f328(f62(x79572),f40(f885(x79572,a871),x79573)))+~P24(f328(f62(f885(x79572,a871)),x79573))
% 81.29/80.93 [8141]~P106(x81412)+E(x81411,f193(f885(x81412,a871)))+~P24(f328(f62(x81412),x81413))+P24(f328(f328(f244(x81412),f328(f64(x81412,f242(x81412)),x81413)),f328(f64(x81412,f242(x81412)),x81411)))+~P24(f328(f328(f244(f885(x81412,a871)),x81411),x81413))
% 81.29/80.93 [8449]~E(f337(x84491,x84493,x84492),f338(x84491,x84493,x84492))+E(f328(f328(f82(a877),x84491),f328(f38(f885(x84492,a871)),x84493)),f328(f38(x84492),f40(f885(x84492,a871),x84493)))+P24(f328(f328(f330(f885(x84492,a871)),f339(x84491,x84493,x84492)),x84493))+~P24(f328(f62(x84492),f40(f885(x84492,a871),x84493)))+~P24(f328(f62(f885(x84492,a871)),x84493))
% 81.29/80.93 [8477]~E(f328(f38(x84772),f339(x84771,x84773,x84772)),x84771)+E(f328(f328(f82(a877),x84771),f328(f38(f885(x84772,a871)),x84773)),f328(f38(x84772),f40(f885(x84772,a871),x84773)))+P24(f328(f328(f330(f885(x84772,a871)),f338(x84771,x84773,x84772)),x84773))+~P24(f328(f62(x84772),f40(f885(x84772,a871),x84773)))+~P24(f328(f62(f885(x84772,a871)),x84773))
% 81.29/80.93 [8478]~E(f328(f38(x84782),f339(x84781,x84783,x84782)),x84781)+E(f328(f328(f82(a877),x84781),f328(f38(f885(x84782,a871)),x84783)),f328(f38(x84782),f40(f885(x84782,a871),x84783)))+P24(f328(f328(f330(f885(x84782,a871)),f337(x84781,x84783,x84782)),x84783))+~P24(f328(f62(x84782),f40(f885(x84782,a871),x84783)))+~P24(f328(f62(f885(x84782,a871)),x84783))
% 81.29/80.93 [8506]~E(f328(f38(x85062),f339(x85061,x85063,x85062)),x85061)+~E(f328(f328(f107(f885(x85062,a871)),f338(x85061,x85063,x85062)),f337(x85061,x85063,x85062)),f193(f885(x85062,a871)))+E(f328(f328(f82(a877),x85061),f328(f38(f885(x85062,a871)),x85063)),f328(f38(x85062),f40(f885(x85062,a871),x85063)))+~P24(f328(f62(f885(x85062,a871)),x85063))+~P24(f328(f62(x85062),f40(f885(x85062,a871),x85063)))
% 81.29/80.93 [8750]E(f328(f328(f82(a877),x87501),f328(f38(f885(x87502,a871)),x87503)),f328(f38(x87502),f40(f885(x87502,a871),x87503)))+P24(f328(f328(f330(f885(x87502,a871)),f339(x87501,x87503,x87502)),x87503))+P24(f328(f328(f330(f885(x87502,a871)),f338(x87501,x87503,x87502)),x87503))+~P24(f328(f62(f885(x87502,a871)),x87503))+~P24(f328(f62(x87502),f40(f885(x87502,a871),x87503)))
% 81.29/80.93 [8751]E(f328(f328(f82(a877),x87511),f328(f38(f885(x87512,a871)),x87513)),f328(f38(x87512),f40(f885(x87512,a871),x87513)))+P24(f328(f328(f330(f885(x87512,a871)),f339(x87511,x87513,x87512)),x87513))+P24(f328(f328(f330(f885(x87512,a871)),f337(x87511,x87513,x87512)),x87513))+~P24(f328(f62(f885(x87512,a871)),x87513))+~P24(f328(f62(x87512),f40(f885(x87512,a871),x87513)))
% 81.29/80.93 [8776]~E(f328(f328(f107(f885(x87762,a871)),f338(x87761,x87763,x87762)),f337(x87761,x87763,x87762)),f193(f885(x87762,a871)))+E(f328(f328(f82(a877),x87761),f328(f38(f885(x87762,a871)),x87763)),f328(f38(x87762),f40(f885(x87762,a871),x87763)))+~P24(f328(f62(f885(x87762,a871)),x87763))+P24(f328(f328(f330(f885(x87762,a871)),f339(x87761,x87763,x87762)),x87763))+~P24(f328(f62(x87762),f40(f885(x87762,a871),x87763)))
% 81.29/80.93 [9037]~P98(x90372)+E(x90371,f193(f885(x90372,a871)))+~E(f328(f328(f82(x90372),f328(x90373,f420(x90371,x90373,x90372))),f328(x90373,f421(x90371,x90373,x90372))),f328(x90373,f328(f328(f82(x90372),f420(x90371,x90373,x90372)),f421(x90371,x90373,x90372))))+~P24(f328(f62(x90372),x90371))+E(f328(f64(x90372,f82(x90372)),f328(f307(x90372,x90372,x90373),x90371)),f328(x90373,f328(f64(x90372,f82(x90372)),x90371)))
% 81.29/80.93 [9961]P24(f328(f328(x99611,x99612),x99613))+P24(f328(f328(f245(a1),f492(x99611,x99613,x99612)),f494(x99611,x99613,x99612)))+P24(f328(f328(f244(a1),f494(x99611,x99613,x99612)),f2(a1)))+P24(f328(f328(x99611,f492(x99611,x99613,x99612)),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f494(x99611,x99613,x99612))))+~P24(f328(f316(f884(a1,a1),a57),f328(f328(f257(a1,a1),x99612),x99613)))
% 81.29/80.93 [9967]P24(f328(f328(x99671,x99672),x99673))+P24(f328(f328(f244(a1),f491(x99671,x99673,x99672)),f2(a1)))+P24(f328(f328(x99671,f490(x99671,x99673,x99672)),f328(f328(f82(a1),f328(f109(a1),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f491(x99671,x99673,x99672))))+P24(f328(f328(f244(a1),f2(a1)),f328(f328(f81(a1),f490(x99671,x99673,x99672)),f491(x99671,x99673,x99672))))+~P24(f328(f316(f884(a1,a1),a52),f328(f328(f257(a1,a1),x99672),x99673)))
% 81.29/80.93 [7928]~P111(x79281)+~P24(f328(f328(f244(x79281),x79282),f79(x79281)))+~P24(f328(f328(f244(x79281),f2(x79281)),x79282))+~P24(f328(f328(f244(x79281),f2(x79281)),x79283))+P24(f328(f328(f244(x79281),f328(f328(f82(x79281),x79282),x79283)),x79283))
% 81.29/80.93 [7929]~P111(x79291)+~P24(f328(f328(f244(x79291),x79293),f79(x79291)))+~P24(f328(f328(f244(x79291),f2(x79291)),x79293))+~P24(f328(f328(f244(x79291),f2(x79291)),x79292))+P24(f328(f328(f244(x79291),f328(f328(f82(x79291),x79292),x79293)),x79292))
% 81.29/80.93 [8292]~P106(x82922)+E(x82921,f193(f885(x82922,a871)))+~P24(f328(f62(x82922),x82921))+P24(f328(f328(f330(x82922),f394(x82923,x82921,x82922)),x82921))+~P24(f328(f328(f244(x82922),f328(f64(x82922,f242(x82922)),x82921)),x82923))
% 81.29/80.93 [8293]~P106(x82932)+E(x82931,f193(f885(x82932,a871)))+~P24(f328(f62(x82932),x82931))+P24(f328(f328(f330(x82932),f395(x82933,x82931,x82932)),x82931))+~P24(f328(f328(f245(x82932),f328(f64(x82932,f242(x82932)),x82931)),x82933))
% 81.29/80.93 [8294]~P106(x82942)+E(x82941,f193(f885(x82942,a871)))+~P24(f328(f62(x82942),x82941))+P24(f328(f328(f244(x82942),f394(x82943,x82941,x82942)),x82943))+~P24(f328(f328(f244(x82942),f328(f64(x82942,f242(x82942)),x82941)),x82943))
% 81.29/80.93 [8295]~P106(x82952)+E(x82951,f193(f885(x82952,a871)))+~P24(f328(f62(x82952),x82951))+P24(f328(f328(f245(x82952),f395(x82953,x82951,x82952)),x82953))+~P24(f328(f328(f245(x82952),f328(f64(x82952,f242(x82952)),x82951)),x82953))
% 81.29/80.93 [8379]~P24(f328(x83791,x83793))+P24(f328(x83791,f449(x83791,x83792)))+P24(f328(x83791,f448(x83791,x83792)))+~P24(f328(f328(f245(a1),f2(a1)),x83792))+P24(f328(x83791,f328(f328(f22(a1),f448(x83791,x83792)),f328(f328(f82(a1),f450(x83791,x83792)),x83792))))
% 81.29/80.93 [8601]~P24(f328(x86011,x86013))+P24(f328(x86011,f448(x86011,x86012)))+~P24(f328(f328(f245(a1),f2(a1)),x86012))+P24(f328(f328(f330(a1),f449(x86011,x86012)),f299(a1,f79(a1),x86012)))+P24(f328(x86011,f328(f328(f22(a1),f448(x86011,x86012)),f328(f328(f82(a1),f450(x86011,x86012)),x86012))))
% 81.29/80.93 [8798]~P24(f328(x87981,x87983))+~P24(f328(x87981,f448(x87981,x87982)))+P24(f328(x87981,f449(x87981,x87982)))+~P24(f328(f328(f245(a1),f2(a1)),x87982))+~P24(f328(x87981,f328(f328(f22(a1),f448(x87981,x87982)),f328(f328(f82(a1),f450(x87981,x87982)),x87982))))
% 81.29/80.93 [8921]~P24(f328(x89211,x89213))+~P24(f328(x89211,f448(x89211,x89212)))+~P24(f328(f328(f245(a1),f2(a1)),x89212))+P24(f328(f328(f330(a1),f449(x89211,x89212)),f299(a1,f79(a1),x89212)))+~P24(f328(x89211,f328(f328(f22(a1),f448(x89211,x89212)),f328(f328(f82(a1),f450(x89211,x89212)),x89212))))
% 81.29/80.93 [8709]~P78(x87091)+~P24(f328(f62(x87091),x87092))+E(f328(f328(f22(f885(x87091,a871)),x87092),f328(f328(f306(x87091),x87093),f193(f885(x87091,a871)))),f193(f885(x87091,a871)))+~P24(f328(f328(f330(x87091),x87093),x87092))+E(f328(f328(f116(x87091),x87093),f10(x87091,f328(f328(f22(f885(x87091,a871)),x87092),f328(f328(f306(x87091),x87093),f193(f885(x87091,a871)))))),f10(x87091,x87092))
% 81.29/80.93 [8710]~P78(x87101)+~P24(f328(f62(x87101),x87102))+E(f328(f328(f22(f885(x87101,a871)),x87102),f328(f328(f306(x87101),x87103),f193(f885(x87101,a871)))),f193(f885(x87101,a871)))+~P24(f328(f328(f330(x87101),x87103),x87102))+E(f328(f328(f107(x87101),x87103),f11(x87101,f328(f328(f22(f885(x87101,a871)),x87102),f328(f328(f306(x87101),x87103),f193(f885(x87101,a871)))))),f11(x87101,x87102))
% 81.29/80.93 [8711]~P106(x87111)+~P24(f328(f62(x87111),x87112))+E(f328(f328(f22(f885(x87111,a871)),x87112),f328(f328(f306(x87111),x87113),f193(f885(x87111,a871)))),f193(f885(x87111,a871)))+~P24(f328(f328(f330(x87111),x87113),x87112))+E(f328(f328(f242(x87111),x87113),f14(x87111,f328(f328(f22(f885(x87111,a871)),x87112),f328(f328(f306(x87111),x87113),f193(f885(x87111,a871)))))),f14(x87111,x87112))
% 81.29/80.93 [8712]~P106(x87121)+~P24(f328(f62(x87121),x87122))+E(f328(f328(f22(f885(x87121,a871)),x87122),f328(f328(f306(x87121),x87123),f193(f885(x87121,a871)))),f193(f885(x87121,a871)))+~P24(f328(f328(f330(x87121),x87123),x87122))+E(f328(f328(f243(x87121),x87123),f15(x87121,f328(f328(f22(f885(x87121,a871)),x87122),f328(f328(f306(x87121),x87123),f193(f885(x87121,a871)))))),f15(x87121,x87122))
% 81.29/80.93 [8770]~P106(x87701)+~P24(f328(f62(x87701),x87702))+E(f328(f328(f22(f885(x87701,a871)),x87702),f328(f328(f306(x87701),x87703),f193(f885(x87701,a871)))),f193(f885(x87701,a871)))+~P24(f328(f328(f330(x87701),x87703),x87702))+E(f328(f328(f242(x87701),x87703),f12(x87701,f242(x87701),f328(f328(f22(f885(x87701,a871)),x87702),f328(f328(f306(x87701),x87703),f193(f885(x87701,a871)))))),f12(x87701,f242(x87701),x87702))
% 81.29/80.93 [8771]~P106(x87711)+~P24(f328(f62(x87711),x87712))+E(f328(f328(f22(f885(x87711,a871)),x87712),f328(f328(f306(x87711),x87713),f193(f885(x87711,a871)))),f193(f885(x87711,a871)))+~P24(f328(f328(f330(x87711),x87713),x87712))+E(f328(f328(f243(x87711),x87713),f13(x87711,f243(x87711),f328(f328(f22(f885(x87711,a871)),x87712),f328(f328(f306(x87711),x87713),f193(f885(x87711,a871)))))),f13(x87711,f243(x87711),x87712))
% 81.29/80.93 [8785]~P78(x87851)+~P24(f328(f62(x87851),x87853))+~P24(f328(f62(x87851),x87852))+E(f328(f328(f107(f885(x87851,a871)),x87852),x87853),f193(f885(x87851,a871)))+E(f328(f328(f116(x87851),f10(x87851,f328(f328(f116(f885(x87851,a871)),x87852),x87853))),f10(x87851,f328(f328(f107(f885(x87851,a871)),x87852),x87853))),f328(f328(f116(x87851),f10(x87851,x87852)),f10(x87851,x87853)))
% 81.29/80.93 [8786]~P78(x87861)+~P24(f328(f62(x87861),x87863))+~P24(f328(f62(x87861),x87862))+E(f328(f328(f107(f885(x87861,a871)),x87862),x87863),f193(f885(x87861,a871)))+E(f328(f328(f107(x87861),f11(x87861,f328(f328(f116(f885(x87861,a871)),x87862),x87863))),f11(x87861,f328(f328(f107(f885(x87861,a871)),x87862),x87863))),f328(f328(f107(x87861),f11(x87861,x87862)),f11(x87861,x87863)))
% 81.29/80.93 [8787]~P106(x87871)+~P24(f328(f62(x87871),x87873))+~P24(f328(f62(x87871),x87872))+E(f328(f328(f107(f885(x87871,a871)),x87872),x87873),f193(f885(x87871,a871)))+E(f328(f328(f242(x87871),f14(x87871,f328(f328(f116(f885(x87871,a871)),x87872),x87873))),f14(x87871,f328(f328(f107(f885(x87871,a871)),x87872),x87873))),f328(f328(f242(x87871),f14(x87871,x87872)),f14(x87871,x87873)))
% 81.29/80.93 [8788]~P106(x87881)+~P24(f328(f62(x87881),x87883))+~P24(f328(f62(x87881),x87882))+E(f328(f328(f107(f885(x87881,a871)),x87882),x87883),f193(f885(x87881,a871)))+E(f328(f328(f243(x87881),f15(x87881,f328(f328(f116(f885(x87881,a871)),x87882),x87883))),f15(x87881,f328(f328(f107(f885(x87881,a871)),x87882),x87883))),f328(f328(f243(x87881),f15(x87881,x87882)),f15(x87881,x87883)))
% 81.29/80.93 [9009]~P106(x90091)+~P24(f328(f62(x90091),x90093))+~P24(f328(f62(x90091),x90092))+E(f328(f328(f107(f885(x90091,a871)),x90092),x90093),f193(f885(x90091,a871)))+E(f328(f328(f242(x90091),f12(x90091,f242(x90091),f328(f328(f116(f885(x90091,a871)),x90092),x90093))),f12(x90091,f242(x90091),f328(f328(f107(f885(x90091,a871)),x90092),x90093))),f328(f328(f242(x90091),f12(x90091,f242(x90091),x90092)),f12(x90091,f242(x90091),x90093)))
% 81.29/80.93 [9010]~P106(x90101)+~P24(f328(f62(x90101),x90103))+~P24(f328(f62(x90101),x90102))+E(f328(f328(f107(f885(x90101,a871)),x90102),x90103),f193(f885(x90101,a871)))+E(f328(f328(f243(x90101),f13(x90101,f243(x90101),f328(f328(f116(f885(x90101,a871)),x90102),x90103))),f13(x90101,f243(x90101),f328(f328(f107(f885(x90101,a871)),x90102),x90103))),f328(f328(f243(x90101),f13(x90101,f243(x90101),x90102)),f13(x90101,f243(x90101),x90103)))
% 81.29/80.93 [9798]~P110(x97983)+E(x97981,x97982)+~P24(f328(f328(f244(x97983),f2(x97983)),x97982))+~P24(f328(f328(f244(x97983),f2(x97983)),x97981))+~E(f328(f328(f258(x97983),x97981),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))),f328(f328(f258(x97983),x97982),f328(f109(a877),f328(f328(f81(a1),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)),f328(f328(f22(a1),f328(f328(f81(a1),a84),a84)),a103)))))
% 81.29/80.93 [6329]E(f821(x63291,x63292,x63293),x63294)+E(f328(x63291,x63294),f2(a877))+~E(f328(f328(f6(x63293,a877),x63291),x63292),f79(a877))+~P24(f328(f62(x63293),x63292))+~P24(f328(f328(f330(x63293),x63294),x63292))
% 81.29/80.93 [6393]E(f824(x63931,x63932,x63933),x63934)+E(f328(x63931,x63934),f2(a877))+~E(f328(f328(f6(x63933,a877),x63931),x63932),f328(a118,f2(a877)))+~P24(f328(f62(x63933),x63932))+~P24(f328(f328(f330(x63933),x63934),x63932))
% 81.29/80.93 [6499]~P106(x64991)+~P27(x64991)+P24(f328(f328(f245(x64991),x64992),f40(x64991,x64993)))+~P24(f328(f328(f245(x64991),x64992),x64994))+~P24(f328(f328(f330(x64991),x64994),x64993))
% 81.29/80.93 [6674]~P106(x66741)+~P27(x66741)+~P24(f328(f328(f245(x66741),x66744),x66743))+P24(f328(f328(f245(x66741),f41(x66741,x66742)),x66743))+~P24(f328(f328(f330(x66741),x66744),x66742))
% 81.29/80.93 [6930]~P110(x69303)+E(x69301,x69302)+~E(f328(f328(f258(x69303),x69301),f328(a118,x69304)),f328(f328(f258(x69303),x69302),f328(a118,x69304)))+~P24(f328(f328(f244(x69303),f2(x69303)),x69302))+~P24(f328(f328(f244(x69303),f2(x69303)),x69301))
% 81.29/80.93 [7141]~E(f829(x71412,x71413,x71411,x71414),x71414)+~E(f328(x71412,x71414),f79(a877))+E(f328(f328(f6(x71411,a877),x71412),x71413),f79(a877))+~P24(f328(f62(x71411),x71413))+~P24(f328(f328(f330(x71411),x71414),x71413))
% 81.29/80.93 [7148]~P112(x71484)+~P125(x71484)+E(f328(x71481,f336(x71481,x71482,x71483,x71484)),f2(x71484))+~E(f328(f328(f9(x71483,x71484),x71481),x71482),f2(x71484))+~P24(f328(f62(x71483),x71482))
% 81.29/80.93 [7234]~E(f827(x72342,x72343,x72341,x72344),x72344)+~E(f328(x72342,x72344),f328(a118,f2(a877)))+E(f328(f328(f6(x72341,a877),x72342),x72343),f328(a118,f2(a877)))+~P24(f328(f62(x72341),x72343))+~P24(f328(f328(f330(x72341),x72344),x72343))
% 81.29/80.93 [7968]~E(f328(x79682,x79684),f79(a877))+~E(f328(x79682,f829(x79682,x79683,x79681,x79684)),f2(a877))+E(f328(f328(f6(x79681,a877),x79682),x79683),f79(a877))+~P24(f328(f62(x79681),x79683))+~P24(f328(f328(f330(x79681),x79684),x79683))
% 81.29/80.93 [8012]~E(f328(x80122,x80124),f328(a118,f2(a877)))+~E(f328(x80122,f827(x80122,x80123,x80121,x80124)),f2(a877))+E(f328(f328(f6(x80121,a877),x80122),x80123),f328(a118,f2(a877)))+~P24(f328(f62(x80121),x80123))+~P24(f328(f328(f330(x80121),x80124),x80123))
% 81.29/80.93 [8571]~P106(x85711)+~P29(x85711,x85714)+P29(x85711,x85712)+~E(x85712,f328(f328(f150(x85711),x85713),x85714))+~P24(f328(f328(f244(x85711),x85713),f674(x85712,x85711,x85714,x85713)))
% 81.29/80.93 [8605]E(x86051,x86052)+E(f328(f328(f22(a1),f424(x86053,x86052,x86054,x86051)),f425(x86053,x86052,x86054,x86051)),x86051)+~E(f328(f328(f81(a1),x86051),x86054),x86052)+~P24(f328(f328(f245(a1),f2(a1)),x86054))+~P24(f328(f328(f330(a1),x86052),x86053))
% 81.29/80.93 [8606]E(x86061,x86062)+E(f328(f328(f81(a1),f426(x86063,x86062,x86064,x86061)),f427(x86063,x86062,x86064,x86061)),x86061)+~E(f328(f328(f22(a1),x86061),x86064),x86062)+~P24(f328(f328(f245(a1),f2(a1)),x86064))+~P24(f328(f328(f330(a1),x86062),x86063))
% 81.29/80.93 [8783]E(f328(x87831,f384(x87832,x87831,x87833,x87834)),x87832)+P24(f328(f328(f244(a877),x87834),f385(x87832,x87831,x87833,x87834)))+~P24(f328(f328(f244(a1),x87832),f328(x87831,x87833)))+~P24(f328(f328(f245(a877),x87834),x87833))+~P24(f328(f328(f244(a1),f328(x87831,x87834)),x87832))
% 81.29/80.93 [8784]~P106(x87841)+~P29(x87841,x87843)+P29(x87841,x87842)+~E(x87842,f328(f328(f150(x87841),x87844),x87843))+P24(f328(f328(f330(x87841),f674(x87842,x87841,x87843,x87844)),f328(f171(x87841),x87843)))
% 81.29/80.93 [8802]~P112(x88024)+~P125(x88024)+~E(f328(f328(f9(x88021,x88024),x88022),x88023),f2(x88024))+~P24(f328(f62(x88021),x88023))+P24(f328(f328(f330(x88021),f336(x88022,x88023,x88021,x88024)),x88023))
% 81.29/80.93 [8836]~E(f328(x88362,x88364),f79(a877))+E(f328(f328(f6(x88361,a877),x88362),x88363),f79(a877))+~P24(f328(f62(x88361),x88363))+~P24(f328(f328(f330(x88361),x88364),x88363))+P24(f328(f328(f330(x88361),f829(x88362,x88363,x88361,x88364)),x88363))
% 81.29/80.93 [8845]E(x88451,x88452)+~E(f328(f328(f81(a1),x88452),x88454),x88451)+~P24(f328(f328(f245(a1),f2(a1)),x88454))+~P24(f328(f328(f330(a1),x88451),x88453))+P24(f328(f328(f330(a1),f424(x88453,x88451,x88454,x88452)),x88453))
% 81.29/80.93 [8846]E(x88461,x88462)+~E(f328(f328(f22(a1),x88462),x88464),x88461)+~P24(f328(f328(f245(a1),f2(a1)),x88464))+~P24(f328(f328(f330(a1),x88461),x88463))+P24(f328(f328(f330(a1),f426(x88463,x88461,x88464,x88462)),x88463))
% 81.29/80.93 [8848]~E(f328(x88482,x88484),f328(a118,f2(a877)))+E(f328(f328(f6(x88481,a877),x88482),x88483),f328(a118,f2(a877)))+~P24(f328(f62(x88481),x88483))+~P24(f328(f328(f330(x88481),x88484),x88483))+P24(f328(f328(f330(x88481),f827(x88482,x88483,x88481,x88484)),x88483))
% 81.29/80.93 [8853]P56(x88532,x88533,x88534,x88531)+E(x88531,f193(f885(x88532,a871)))+~P24(f328(f62(x88532),x88534))+~P24(f328(f62(x88532),x88531))+P24(f328(f328(f330(x88532),f691(x88531,x88534,x88533,x88532)),x88534))
% 81.29/80.93 [8935]E(x89351,x89352)+~E(f328(f328(f81(a1),x89352),x89354),x89351)+~P24(f328(f328(f245(a1),f2(a1)),x89354))+~P24(f328(f328(f330(a1),x89351),x89353))+P24(f328(f328(f330(a1),f425(x89353,x89351,x89354,x89352)),f299(a1,f79(a1),x89354)))
% 81.29/80.93 [8936]E(x89361,x89362)+~E(f328(f328(f22(a1),x89362),x89364),x89361)+~P24(f328(f328(f245(a1),f2(a1)),x89364))+~P24(f328(f328(f330(a1),x89361),x89363))+P24(f328(f328(f330(a1),f427(x89363,x89361,x89364,x89362)),f299(a1,f79(a1),x89364)))
% 81.29/80.93 [9015]P24(f328(f328(f244(a877),x90151),f384(x90152,x90153,x90154,x90151)))+~P24(f328(f328(f244(a1),x90152),f328(x90153,x90154)))+P24(f328(f328(f244(a877),x90151),f385(x90152,x90153,x90154,x90151)))+~P24(f328(f328(f245(a877),x90151),x90154))+~P24(f328(f328(f244(a1),f328(x90153,x90151)),x90152))
% 81.29/80.93 [9125]E(f328(x91251,f384(x91252,x91251,x91253,x91254)),x91252)+~P24(f328(f328(f244(a1),x91252),f328(x91251,x91253)))+P24(f328(f328(f245(a877),f385(x91252,x91251,x91253,x91254)),x91253))+~P24(f328(f328(f245(a877),x91254),x91253))+~P24(f328(f328(f244(a1),f328(x91251,x91254)),x91252))
% 81.29/80.93 [9257]~P24(f328(f328(f244(a1),x92572),f328(x92573,x92574)))+P24(f328(f328(f244(a877),x92571),f385(x92572,x92573,x92574,x92571)))+P24(f328(f328(f244(a877),f384(x92572,x92573,x92574,x92571)),x92574))+~P24(f328(f328(f245(a877),x92571),x92574))+~P24(f328(f328(f244(a1),f328(x92573,x92571)),x92572))
% 81.29/80.93 [9258]~P24(f328(f328(f244(a1),x92582),f328(x92583,x92584)))+P24(f328(f328(f244(a877),x92581),f384(x92582,x92583,x92584,x92581)))+P24(f328(f328(f245(a877),f385(x92582,x92583,x92584,x92581)),x92584))+~P24(f328(f328(f245(a877),x92581),x92584))+~P24(f328(f328(f244(a1),f328(x92583,x92581)),x92582))
% 81.29/80.93 [9365]~P24(f328(f328(f244(a1),x93651),f328(x93652,x93653)))+P24(f328(f328(f245(a877),f385(x93651,x93652,x93653,x93654)),x93653))+~P24(f328(f328(f245(a877),x93654),x93653))+~P24(f328(f328(f244(a1),f328(x93652,x93654)),x93651))+P24(f328(f328(f244(a877),f384(x93651,x93652,x93653,x93654)),x93653))
% 81.29/80.93 [9442]E(x94421,f193(f885(x94422,a871)))+~P24(f328(f62(x94422),x94424))+~P24(f328(f62(x94422),x94421))+P24(f328(f328(f330(f884(f885(x94422,a871),f885(x94422,a871))),f328(f328(f257(f885(x94422,a871),f885(x94422,a871)),x94424),x94421)),f319(x94422,x94423)))+P24(f328(f328(f330(x94422),f693(x94423,x94421,x94424,x94422)),x94424))
% 81.29/80.93 [9443]E(x94431,f193(f885(x94432,a871)))+~P24(f328(f62(x94432),x94434))+~P24(f328(f62(x94432),x94431))+P24(f328(f328(f330(f884(f885(x94432,a871),f885(x94432,a871))),f328(f328(f257(f885(x94432,a871),f885(x94432,a871)),x94434),x94431)),f319(x94432,x94433)))+P24(f328(f328(f330(x94432),f752(x94433,x94431,x94434,x94432)),x94434))
% 81.29/80.93 [10106]E(f328(x101061,f384(x101062,x101061,x101063,x101064)),x101062)+~P24(f328(f328(f244(a1),x101062),f328(x101061,x101063)))+~P24(f328(f328(f244(a1),f328(f76(a1),f328(f328(f22(a1),f328(x101061,f328(f328(f81(a877),f385(x101062,x101061,x101063,x101064)),f79(a877)))),f328(x101061,f385(x101062,x101061,x101063,x101064))))),f79(a1)))+~P24(f328(f328(f245(a877),x101064),x101063))+~P24(f328(f328(f244(a1),f328(x101061,x101064)),x101062))
% 81.29/80.93 [10107]~P24(f328(f328(f244(a1),x101072),f328(x101073,x101074)))+P24(f328(f328(f244(a877),x101071),f384(x101072,x101073,x101074,x101071)))+~P24(f328(f328(f244(a1),f328(f76(a1),f328(f328(f22(a1),f328(x101073,f328(f328(f81(a877),f385(x101072,x101073,x101074,x101071)),f79(a877)))),f328(x101073,f385(x101072,x101073,x101074,x101071))))),f79(a1)))+~P24(f328(f328(f245(a877),x101071),x101074))+~P24(f328(f328(f244(a1),f328(x101073,x101071)),x101072))
% 81.29/80.93 [10108]~P24(f328(f328(f244(a1),x101081),f328(x101082,x101083)))+~P24(f328(f328(f244(a1),f328(f76(a1),f328(f328(f22(a1),f328(x101082,f328(f328(f81(a877),f385(x101081,x101082,x101083,x101084)),f79(a877)))),f328(x101082,f385(x101081,x101082,x101083,x101084))))),f79(a1)))+~P24(f328(f328(f245(a877),x101084),x101083))+~P24(f328(f328(f244(a1),f328(x101082,x101084)),x101081))+P24(f328(f328(f244(a877),f384(x101081,x101082,x101083,x101084)),x101083))
% 81.29/80.93 [7201]~P63(x72011)+P24(f328(f328(f245(x72011),x72012),f2(x72011)))+~P24(f328(f328(f244(x72011),x72013),f2(x72011)))+P24(f328(f328(f245(x72011),f2(x72011)),x72012))+P24(f328(f328(f244(x72011),x72013),f328(f328(f286(x72011),x72014),x72012)))
% 81.29/80.93 [7202]~P63(x72021)+P24(f328(f328(f245(x72021),x72022),f2(x72021)))+~P24(f328(f328(f245(x72021),x72023),f2(x72021)))+P24(f328(f328(f245(x72021),f2(x72021)),x72022))+P24(f328(f328(f245(x72021),x72023),f328(f328(f286(x72021),x72024),x72022)))
% 81.29/80.93 [7452]~P63(x74521)+P24(f328(f328(f244(x74521),x74522),f2(x74521)))+P24(f328(f328(f245(x74521),x74523),f2(x74521)))+P24(f328(f328(f245(x74521),f2(x74521)),x74523))+~P24(f328(f328(f244(x74521),x74522),f328(f328(f286(x74521),x74524),x74523)))
% 81.29/80.93 [7453]~P63(x74531)+P24(f328(f328(f245(x74531),x74532),f2(x74531)))+P24(f328(f328(f245(x74531),x74533),f2(x74531)))+P24(f328(f328(f245(x74531),f2(x74531)),x74533))+~P24(f328(f328(f245(x74531),x74532),f328(f328(f286(x74531),x74534),x74533)))
% 81.29/80.93 [7568]E(x75681,x75682)+~E(f328(f328(f164(x75683),x75684),x75681),f328(f328(f164(x75683),x75684),x75682))+~P24(f328(f136(x75683),x75684))+~P24(f328(f328(f245(a877),x75682),f328(f194(f878(x75683)),x75684)))+~P24(f328(f328(f245(a877),x75681),f328(f194(f878(x75683)),x75684)))
% 81.29/80.93 [7930]~P63(x79301)+~P24(f328(f328(f244(x79301),x79303),f2(x79301)))+P24(f328(f328(f245(x79301),f2(x79301)),x79302))+~P24(f328(f328(f244(x79301),x79304),f328(f328(f82(x79301),x79303),x79302)))+P24(f328(f328(f244(x79301),x79303),f328(f328(f286(x79301),x79304),x79302)))
% 81.29/80.93 [7931]~P63(x79311)+~P24(f328(f328(f245(x79311),x79313),f2(x79311)))+P24(f328(f328(f245(x79311),f2(x79311)),x79312))+~P24(f328(f328(f245(x79311),x79314),f328(f328(f82(x79311),x79313),x79312)))+P24(f328(f328(f245(x79311),x79313),f328(f328(f286(x79311),x79314),x79312)))
% 81.29/80.93 [7932]~P63(x79321)+~P24(f328(f328(f245(x79321),x79322),f2(x79321)))+P24(f328(f328(f245(x79321),f2(x79321)),x79322))+~P24(f328(f328(f244(x79321),x79324),f328(f328(f82(x79321),x79323),x79322)))+P24(f328(f328(f244(x79321),x79323),f328(f328(f286(x79321),x79324),x79322)))
% 81.29/80.93 [7933]~P63(x79331)+~P24(f328(f328(f245(x79331),x79332),f2(x79331)))+P24(f328(f328(f245(x79331),f2(x79331)),x79332))+~P24(f328(f328(f244(x79331),x79334),f328(f328(f286(x79331),x79333),x79332)))+P24(f328(f328(f244(x79331),x79333),f328(f328(f82(x79331),x79334),x79332)))
% 81.29/80.93 [7934]~P63(x79341)+~P24(f328(f328(f245(x79341),x79342),f2(x79341)))+P24(f328(f328(f245(x79341),f2(x79341)),x79342))+~P24(f328(f328(f245(x79341),x79344),f328(f328(f82(x79341),x79343),x79342)))+P24(f328(f328(f245(x79341),x79343),f328(f328(f286(x79341),x79344),x79342)))
% 81.29/80.93 [7935]~P63(x79351)+~P24(f328(f328(f245(x79351),x79352),f2(x79351)))+P24(f328(f328(f245(x79351),f2(x79351)),x79352))+~P24(f328(f328(f245(x79351),x79354),f328(f328(f286(x79351),x79353),x79352)))+P24(f328(f328(f245(x79351),x79353),f328(f328(f82(x79351),x79354),x79352)))
% 81.29/80.93 [8080]~P106(x80801)+~P29(x80801,x80802)+~P24(f328(f328(f244(a877),x80803),x80804))+P24(f328(f328(f244(x80801),f328(f328(f164(x80801),x80802),x80803)),f328(f328(f164(x80801),x80802),x80804)))+~P24(f328(f328(f245(a877),x80804),f328(f194(f878(x80801)),x80802)))
% 81.29/80.93 [8131]~P110(x81311)+~P24(f328(f328(f244(x81311),x81312),f79(x81311)))+~P24(f328(f328(f244(x81311),f2(x81311)),x81312))+~P24(f328(f328(f244(a877),x81314),x81313))+P24(f328(f328(f244(x81311),f328(f328(f258(x81311),x81312),x81313)),f328(f328(f258(x81311),x81312),x81314)))
% 81.29/80.93 [8132]~P110(x81321)+~P24(f328(f328(f245(x81321),x81322),f79(x81321)))+~P24(f328(f328(f245(x81321),f2(x81321)),x81322))+~P24(f328(f328(f245(a877),x81324),x81323))+P24(f328(f328(f245(x81321),f328(f328(f258(x81321),x81322),x81323)),f328(f328(f258(x81321),x81322),x81324)))
% 81.29/80.93 [8133]~P110(x81331)+~P24(f328(f328(f244(x81331),f2(x81331)),x81332))+~P24(f328(f328(f245(a877),f2(a877)),x81333))+~P24(f328(f328(f245(x81331),x81332),x81334))+P24(f328(f328(f245(x81331),f328(f328(f258(x81331),x81332),x81333)),f328(f328(f258(x81331),x81334),x81333)))
% 81.29/80.93 [8154]~P106(x81541)+~P29(x81541,f328(f168(x81541),x81542))+~P24(f328(f328(f244(a877),x81544),x81543))+P24(f328(f328(f244(x81541),f328(f328(f164(x81541),x81542),x81543)),f328(f328(f164(x81541),x81542),x81544)))+~P24(f328(f328(f245(a877),x81543),f328(f194(f878(x81541)),x81542)))
% 81.29/80.93 [8401]~P63(x84011)+~P24(f328(f328(f244(x84011),x84012),f2(x84011)))+~P24(f328(f328(f244(x84011),x84013),x84014))+~P24(f328(f328(f245(x84011),f2(x84011)),f328(f328(f82(x84011),x84013),x84014)))+P24(f328(f328(f244(x84011),f328(f328(f286(x84011),x84012),x84013)),f328(f328(f286(x84011),x84012),x84014)))
% 81.29/80.93 [8402]~P64(x84021)+~P24(f328(f328(f245(x84021),x84022),f2(x84021)))+~P24(f328(f328(f245(x84021),x84023),x84024))+~P24(f328(f328(f245(x84021),f2(x84021)),f328(f328(f82(x84021),x84023),x84024)))+P24(f328(f328(f245(x84021),f328(f328(f286(x84021),x84022),x84023)),f328(f328(f286(x84021),x84022),x84024)))
% 81.29/80.93 [8412]~P64(x84121)+~P24(f328(f328(f244(x84121),x84124),x84123))+~P24(f328(f328(f244(x84121),f2(x84121)),x84122))+~P24(f328(f328(f245(x84121),f2(x84121)),f328(f328(f82(x84121),x84123),x84124)))+P24(f328(f328(f244(x84121),f328(f328(f286(x84121),x84122),x84123)),f328(f328(f286(x84121),x84122),x84124)))
% 81.29/80.93 [8413]~P64(x84131)+~P24(f328(f328(f245(x84131),x84134),x84133))+~P24(f328(f328(f245(x84131),f2(x84131)),x84132))+~P24(f328(f328(f245(x84131),f2(x84131)),f328(f328(f82(x84131),x84133),x84134)))+P24(f328(f328(f245(x84131),f328(f328(f286(x84131),x84132),x84133)),f328(f328(f286(x84131),x84132),x84134)))
% 81.29/80.93 [8521]P24(f328(x85211,x85212))+~P24(f328(f62(x85214),x85212))+P24(f328(x85211,f585(x85211,x85213,x85212,x85214)))+~P24(f328(x85211,f193(f885(x85214,a871))))+~P24(f328(f328(f244(f885(x85214,a871)),x85212),x85213))
% 81.29/80.93 [8529]P24(f328(x85291,x85292))+P24(f328(f62(x85293),f585(x85291,x85294,x85292,x85293)))+~P24(f328(f62(x85293),x85292))+~P24(f328(x85291,f193(f885(x85293,a871))))+~P24(f328(f328(f244(f885(x85293,a871)),x85292),x85294))
% 81.29/80.93 [8778]E(f328(f328(f81(a1),f438(x87781,x87782,x87783,x87784)),f439(x87781,x87782,x87783,x87784)),x87784)+~P24(f328(f328(f245(a1),f2(a1)),x87783))+~P24(f328(f328(f245(a1),x87782),x87784))+~P24(f328(f328(f330(a1),x87782),x87781))+P24(f328(f328(f245(a1),x87782),f328(f328(f22(a1),x87784),x87783)))
% 81.29/80.93 [8995]~P24(f328(f328(f245(a1),f2(a1)),x89953))+~P24(f328(f328(f245(a1),x89952),x89954))+~P24(f328(f328(f330(a1),x89952),x89951))+P24(f328(f328(f330(a1),f438(x89951,x89952,x89953,x89954)),x89951))+P24(f328(f328(f245(a1),x89952),f328(f328(f22(a1),x89954),x89953)))
% 81.29/80.93 [9008]P24(f328(x90081,x90082))+~P24(f328(f62(x90083),x90082))+P24(f328(f328(f330(x90083),f579(x90081,x90084,x90082,x90083)),x90084))+~P24(f328(x90081,f193(f885(x90083,a871))))+~P24(f328(f328(f244(f885(x90083,a871)),x90082),x90084))
% 81.29/80.93 [9025]E(f328(f328(f81(a1),f418(x90251,x90252,x90253,x90254)),f419(x90251,x90252,x90253,x90254)),x90254)+~P24(f328(f328(f245(a1),f2(a1)),x90253))+~P24(f328(f328(f244(a1),x90252),x90254))+P24(f328(f328(f244(a1),x90252),f328(f328(f22(a1),x90254),x90253)))+~P24(f328(f328(f330(a1),f328(f328(f22(a1),x90252),f79(a1))),x90251))
% 81.29/80.93 [9077]~P24(f328(f328(f245(a1),f2(a1)),x90773))+~P24(f328(f328(f245(a1),x90771),x90772))+~P24(f328(f328(f330(a1),x90771),x90774))+P24(f328(f328(f330(a1),f439(x90774,x90771,x90773,x90772)),f299(a1,f79(a1),x90773)))+P24(f328(f328(f245(a1),x90771),f328(f328(f22(a1),x90772),x90773)))
% 81.29/80.93 [9172]~P24(f328(f328(f245(a1),f2(a1)),x91723))+~P24(f328(f328(f244(a1),x91722),x91724))+P24(f328(f328(f330(a1),f418(x91721,x91722,x91723,x91724)),x91721))+P24(f328(f328(f244(a1),x91722),f328(f328(f22(a1),x91724),x91723)))+~P24(f328(f328(f330(a1),f328(f328(f22(a1),x91722),f79(a1))),x91721))
% 81.29/80.93 [9212]~P24(f328(f328(f245(a1),f2(a1)),x92123))+~P24(f328(f328(f244(a1),x92121),x92122))+P24(f328(f328(f330(a1),f419(x92124,x92121,x92123,x92122)),f299(a1,f79(a1),x92123)))+P24(f328(f328(f244(a1),x92121),f328(f328(f22(a1),x92122),x92123)))+~P24(f328(f328(f330(a1),f328(f328(f22(a1),x92121),f79(a1))),x92124))
% 81.29/80.93 [9445]P24(f328(x94451,x94452))+~P24(f328(f328(f330(x94453),f579(x94451,x94454,x94452,x94453)),f585(x94451,x94454,x94452,x94453)))+~P24(f328(f62(x94453),x94452))+~P24(f328(x94451,f193(f885(x94453,a871))))+~P24(f328(f328(f244(f885(x94453,a871)),x94452),x94454))
% 81.29/80.93 [9659]P24(f328(x96591,x96592))+~P24(f328(f62(x96593),x96592))+~P24(f328(x96591,f328(f328(f306(x96593),f579(x96591,x96594,x96592,x96593)),f585(x96591,x96594,x96592,x96593))))+~P24(f328(x96591,f193(f885(x96593,a871))))+~P24(f328(f328(f244(f885(x96593,a871)),x96592),x96594))
% 81.29/80.93 [7704]~P63(x77041)+P24(f328(f328(f245(x77041),x77042),f2(x77041)))+~P24(f328(f328(f244(x77041),f2(x77041)),x77044))+P24(f328(f328(f245(x77041),f2(x77041)),x77042))+P24(f328(f328(f244(x77041),f328(f328(f286(x77041),x77043),x77042)),x77044))
% 81.29/80.93 [7705]~P63(x77051)+P24(f328(f328(f245(x77051),x77052),f2(x77051)))+P24(f328(f328(f245(x77051),f2(x77051)),x77052))+~P24(f328(f328(f245(x77051),f2(x77051)),x77054))+P24(f328(f328(f245(x77051),f328(f328(f286(x77051),x77053),x77052)),x77054))
% 81.29/80.93 [7984]~P24(f328(f328(f244(a1),x79844),f2(a1)))+~E(x79842,f328(f328(f81(a1),f328(f328(f82(a1),x79841),x79843)),x79844))+P24(f328(f328(f245(a1),f2(a1)),x79841))+~P24(f328(f328(f245(a1),x79841),x79844))+P24(f328(f49(x79842,x79841),f328(f328(f257(a1,a1),x79843),x79844)))
% 81.29/80.93 [8023]~P24(f328(x80231,x80234))+P24(f328(x80231,f864(x80232,x80231,x80233)))+~P24(f328(f328(f244(a1),f2(a1)),x80232))+~P24(f328(f328(f245(a1),f2(a1)),x80233))+P24(f328(x80231,f328(f328(f22(a1),x80234),f328(f328(f82(a1),x80232),x80233))))
% 81.29/80.93 [8024]~P24(f328(x80241,x80244))+P24(f328(x80241,f869(x80242,x80241,x80243)))+~P24(f328(f328(f244(a1),f2(a1)),x80242))+~P24(f328(f328(f245(a1),f2(a1)),x80243))+P24(f328(x80241,f328(f328(f81(a1),x80244),f328(f328(f82(a1),x80242),x80243))))
% 81.29/80.93 [8025]~P63(x80251)+P24(f328(f328(f245(x80251),x80252),f2(x80251)))+P24(f328(f328(f245(x80251),f2(x80251)),x80252))+P24(f328(f328(f244(x80251),f2(x80251)),x80253))+~P24(f328(f328(f244(x80251),f328(f328(f286(x80251),x80254),x80252)),x80253))
% 81.29/80.93 [8026]~P63(x80261)+P24(f328(f328(f245(x80261),x80262),f2(x80261)))+P24(f328(f328(f245(x80261),f2(x80261)),x80262))+P24(f328(f328(f245(x80261),f2(x80261)),x80263))+~P24(f328(f328(f245(x80261),f328(f328(f286(x80261),x80264),x80262)),x80263))
% 81.29/80.93 [8074]~E(x80741,f328(f328(f81(a1),f328(f328(f82(a1),x80742),x80743)),x80744))+~P24(f328(f328(f244(a1),f2(a1)),x80744))+~P24(f328(f328(f245(a1),f2(a1)),x80742))+~P24(f328(f328(f245(a1),x80744),x80742))+P24(f328(f49(x80741,x80742),f328(f328(f257(a1,a1),x80743),x80744)))
% 81.29/80.93 [8198]~P63(x81981)+P24(f328(f328(f245(x81981),x81982),f2(x81981)))+~P24(f328(f328(f244(x81981),f2(x81981)),x81984))+~P24(f328(f328(f244(x81981),x81983),f328(f328(f82(x81981),x81984),x81982)))+P24(f328(f328(f244(x81981),f328(f328(f286(x81981),x81983),x81982)),x81984))
% 81.29/80.93 [8199]~P63(x81991)+P24(f328(f328(f245(x81991),x81992),f2(x81991)))+~P24(f328(f328(f245(x81991),f2(x81991)),x81994))+~P24(f328(f328(f245(x81991),x81993),f328(f328(f82(x81991),x81994),x81992)))+P24(f328(f328(f245(x81991),f328(f328(f286(x81991),x81993),x81992)),x81994))
% 81.29/80.93 [8280]~P63(x82801)+P24(f328(f328(f245(x82801),x82802),f2(x82801)))+~P24(f328(f328(f244(x82801),x82803),f2(x82801)))+P24(f328(f328(f244(x82801),x82803),f328(f328(f286(x82801),x82804),x82802)))+~P24(f328(f328(f244(x82801),f328(f328(f82(x82801),x82803),x82802)),x82804))
% 81.29/80.93 [8281]~P63(x82811)+P24(f328(f328(f245(x82811),x82812),f2(x82811)))+~P24(f328(f328(f245(x82811),x82813),f2(x82811)))+P24(f328(f328(f245(x82811),x82813),f328(f328(f286(x82811),x82814),x82812)))+~P24(f328(f328(f245(x82811),f328(f328(f82(x82811),x82813),x82812)),x82814))
% 81.29/80.93 [8438]~P63(x84381)+~P24(f328(f328(f245(x84381),x84382),f2(x84381)))+P24(f328(f328(f245(x84381),f2(x84381)),x84382))+~P24(f328(f328(f244(x84381),f328(f328(f286(x84381),x84384),x84382)),x84383))+P24(f328(f328(f244(x84381),f328(f328(f82(x84381),x84383),x84382)),x84384))
% 81.29/80.93 [8439]~P63(x84391)+~P24(f328(f328(f245(x84391),x84392),f2(x84391)))+P24(f328(f328(f245(x84391),f2(x84391)),x84392))+~P24(f328(f328(f244(x84391),f328(f328(f82(x84391),x84394),x84392)),x84393))+P24(f328(f328(f244(x84391),f328(f328(f286(x84391),x84393),x84392)),x84394))
% 81.29/80.93 [8440]~P63(x84401)+~P24(f328(f328(f245(x84401),x84402),f2(x84401)))+P24(f328(f328(f245(x84401),f2(x84401)),x84402))+~P24(f328(f328(f245(x84401),f328(f328(f286(x84401),x84404),x84402)),x84403))+P24(f328(f328(f245(x84401),f328(f328(f82(x84401),x84403),x84402)),x84404))
% 81.29/80.93 [8441]~P63(x84411)+~P24(f328(f328(f245(x84411),x84412),f2(x84411)))+P24(f328(f328(f245(x84411),f2(x84411)),x84412))+~P24(f328(f328(f245(x84411),f328(f328(f82(x84411),x84414),x84412)),x84413))+P24(f328(f328(f245(x84411),f328(f328(f286(x84411),x84413),x84412)),x84414))
% 81.29/80.93 [8464]~P63(x84641)+~P24(f328(f328(f244(x84641),f2(x84641)),x84644))+P24(f328(f328(f245(x84641),f2(x84641)),x84642))+~P24(f328(f328(f244(x84641),f328(f328(f82(x84641),x84644),x84642)),x84643))+P24(f328(f328(f244(x84641),f328(f328(f286(x84641),x84643),x84642)),x84644))
% 81.29/80.93 [8465]~P63(x84651)+~P24(f328(f328(f245(x84651),f2(x84651)),x84654))+P24(f328(f328(f245(x84651),f2(x84651)),x84652))+~P24(f328(f328(f245(x84651),f328(f328(f82(x84651),x84654),x84652)),x84653))+P24(f328(f328(f245(x84651),f328(f328(f286(x84651),x84653),x84652)),x84654))
% 81.29/80.93 [8537]~P63(x85371)+~P24(f328(f328(f245(x85371),x85374),f2(x85371)))+~P24(f328(f328(f244(x85371),x85373),f328(f328(f82(x85371),x85372),x85374)))+P24(f328(f328(f244(x85371),x85372),f328(f328(f286(x85371),x85373),x85374)))+~P24(f328(f328(f244(x85371),f328(f328(f82(x85371),x85372),x85374)),x85373))
% 81.29/80.93 [8538]~P63(x85381)+~P24(f328(f328(f244(x85381),x85382),f2(x85381)))+~P24(f328(f328(f244(x85381),x85383),f328(f328(f82(x85381),x85382),x85384)))+P24(f328(f328(f244(x85381),x85382),f328(f328(f286(x85381),x85383),x85384)))+~P24(f328(f328(f244(x85381),f328(f328(f82(x85381),x85382),x85384)),x85383))
% 81.29/80.93 [8539]~P63(x85391)+~P24(f328(f328(f245(x85391),x85394),f2(x85391)))+~P24(f328(f328(f245(x85391),x85393),f328(f328(f82(x85391),x85392),x85394)))+P24(f328(f328(f245(x85391),x85392),f328(f328(f286(x85391),x85393),x85394)))+~P24(f328(f328(f245(x85391),f328(f328(f82(x85391),x85392),x85394)),x85393))
% 81.29/80.93 [8540]~P63(x85401)+~P24(f328(f328(f245(x85401),x85402),f2(x85401)))+~P24(f328(f328(f245(x85401),x85403),f328(f328(f82(x85401),x85402),x85404)))+P24(f328(f328(f245(x85401),x85402),f328(f328(f286(x85401),x85403),x85404)))+~P24(f328(f328(f245(x85401),f328(f328(f82(x85401),x85402),x85404)),x85403))
% 81.29/80.93 [8653]~P63(x86531)+~P24(f328(f328(f245(x86531),x86533),f2(x86531)))+~P24(f328(f328(f244(x86531),x86532),f328(f328(f82(x86531),x86534),x86533)))+~P24(f328(f328(f244(x86531),f328(f328(f82(x86531),x86534),x86533)),x86532))+P24(f328(f328(f244(x86531),f328(f328(f286(x86531),x86532),x86533)),x86534))
% 81.29/80.93 [8654]~P63(x86541)+~P24(f328(f328(f245(x86541),x86543),f2(x86541)))+~P24(f328(f328(f245(x86541),x86542),f328(f328(f82(x86541),x86544),x86543)))+~P24(f328(f328(f245(x86541),f328(f328(f82(x86541),x86544),x86543)),x86542))+P24(f328(f328(f245(x86541),f328(f328(f286(x86541),x86542),x86543)),x86544))
% 81.29/80.93 [8670]~P63(x86701)+~P24(f328(f328(f244(x86701),f2(x86701)),x86704))+~P24(f328(f328(f244(x86701),x86702),f328(f328(f82(x86701),x86704),x86703)))+~P24(f328(f328(f244(x86701),f328(f328(f82(x86701),x86704),x86703)),x86702))+P24(f328(f328(f244(x86701),f328(f328(f286(x86701),x86702),x86703)),x86704))
% 81.29/80.93 [8671]~P63(x86711)+~P24(f328(f328(f245(x86711),f2(x86711)),x86714))+~P24(f328(f328(f245(x86711),x86712),f328(f328(f82(x86711),x86714),x86713)))+~P24(f328(f328(f245(x86711),f328(f328(f82(x86711),x86714),x86713)),x86712))+P24(f328(f328(f245(x86711),f328(f328(f286(x86711),x86712),x86713)),x86714))
% 81.29/80.93 [8838]E(f328(f328(f22(a1),f440(x88381,x88382,x88383,x88384)),f441(x88381,x88382,x88383,x88384)),x88384)+~P24(f328(f328(f245(a1),f2(a1)),x88383))+~P24(f328(f328(f330(a1),x88382),x88381))+~P24(f328(f328(f245(a1),x88384),x88382))+P24(f328(f328(f245(a1),f328(f328(f81(a1),x88384),x88383)),x88382))
% 81.29/80.93 [8917]~P24(f328(x89171,x89172))+~P24(f328(f328(f244(a1),f2(a1)),x89173))+~P24(f328(f328(f245(a1),f2(a1)),x89174))+~P24(f328(x89171,f328(f328(f22(a1),f864(x89173,x89171,x89174)),x89174)))+P24(f328(x89171,f328(f328(f22(a1),x89172),f328(f328(f82(a1),x89173),x89174))))
% 81.29/80.93 [8918]~P24(f328(x89181,x89182))+~P24(f328(f328(f244(a1),f2(a1)),x89183))+~P24(f328(f328(f245(a1),f2(a1)),x89184))+~P24(f328(x89181,f328(f328(f81(a1),f869(x89183,x89181,x89184)),x89184)))+P24(f328(x89181,f328(f328(f81(a1),x89182),f328(f328(f82(a1),x89183),x89184))))
% 81.29/80.93 [9071]~P24(f328(f328(f245(a1),f2(a1)),x90713))+~P24(f328(f328(f330(a1),x90712),x90711))+~P24(f328(f328(f245(a1),x90714),x90712))+P24(f328(f328(f330(a1),f440(x90711,x90712,x90713,x90714)),x90711))+P24(f328(f328(f245(a1),f328(f328(f81(a1),x90714),x90713)),x90712))
% 81.29/80.93 [9091]E(f328(f328(f22(a1),f422(x90911,x90912,x90913,x90914)),f423(x90911,x90912,x90913,x90914)),x90914)+~P24(f328(f328(f245(a1),f2(a1)),x90913))+~P24(f328(f328(f244(a1),x90914),x90912))+~P24(f328(f328(f330(a1),f328(f328(f81(a1),x90912),f79(a1))),x90911))+P24(f328(f328(f244(a1),f328(f328(f81(a1),x90914),x90913)),x90912))
% 81.29/80.93 [9117]~P24(f328(f328(f245(a1),f2(a1)),x91172))+~P24(f328(f328(f330(a1),x91173),x91174))+~P24(f328(f328(f245(a1),x91171),x91173))+P24(f328(f328(f330(a1),f441(x91174,x91173,x91172,x91171)),f299(a1,f79(a1),x91172)))+P24(f328(f328(f245(a1),f328(f328(f81(a1),x91171),x91172)),x91173))
% 81.29/80.93 [9207]~P24(f328(f328(f245(a1),f2(a1)),x92073))+~P24(f328(f328(f244(a1),x92074),x92072))+P24(f328(f328(f330(a1),f422(x92071,x92072,x92073,x92074)),x92071))+~P24(f328(f328(f330(a1),f328(f328(f81(a1),x92072),f79(a1))),x92071))+P24(f328(f328(f244(a1),f328(f328(f81(a1),x92074),x92073)),x92072))
% 81.29/80.93 [9253]~P24(f328(f328(f245(a1),f2(a1)),x92532))+~P24(f328(f328(f244(a1),x92531),x92533))+P24(f328(f328(f330(a1),f423(x92534,x92533,x92532,x92531)),f299(a1,f79(a1),x92532)))+~P24(f328(f328(f330(a1),f328(f328(f81(a1),x92533),f79(a1))),x92534))+P24(f328(f328(f244(a1),f328(f328(f81(a1),x92531),x92532)),x92533))
% 81.29/80.93 [9537]~P38(x95371,x95373)+~P22(x95371,x95374)+P38(x95371,f328(f328(f116(f885(f884(x95371,x95371),a871)),x95372),x95373))+~P24(f328(f328(f244(f885(f884(x95371,x95371),a871)),x95372),f328(f256(f885(f884(x95371,x95371),a871),f885(f884(x95371,x95371),a871)),x95374)))+~P24(f328(f328(f244(f885(f884(x95371,x95371),a871)),x95373),f328(f266(f885(f884(x95371,x95371),a871),f885(f884(x95371,x95371),a871)),x95374)))
% 81.29/80.93 [9825]~E(f328(f502(x98251,x98254,x98253,x98252),f505(x98251,x98254,x98253,x98252)),f196(f878(a324)))+P24(f328(f328(f245(a1),f504(x98251,x98254,x98253,x98252)),f505(x98251,x98254,x98253,x98252)))+P24(f328(f328(f328(x98251,x98252),x98253),x98254))+P24(f328(f328(f328(x98251,f502(x98251,x98254,x98253,x98252)),f504(x98251,x98254,x98253,x98252)),f328(f328(f81(a1),f505(x98251,x98254,x98253,x98252)),f79(a1))))+~P24(f328(f316(f884(f885(a1,f881(f878(a324))),f884(a1,a1)),a314),f328(f328(f257(f885(a1,f881(f878(a324))),f884(a1,a1)),x98252),f328(f328(f257(a1,a1),x98253),x98254))))
% 81.29/80.93 [9930]~P14(x99302,x99304,x99303)+E(x99301,f193(f885(x99302,a871)))+~P24(f328(f62(x99302),x99301))+P24(f328(f328(f330(x99302),f328(x99303,x99301)),x99301))+~P24(f328(f328(f330(x99302),f328(f328(x99304,f537(x99301,x99303,x99304,x99302)),f549(x99301,x99303,x99304,x99302))),f328(f328(f306(x99302),f537(x99301,x99303,x99304,x99302)),f328(f328(f306(x99302),f549(x99301,x99303,x99304,x99302)),f193(f885(x99302,a871))))))
% 81.29/80.93 [9858]~P108(x98582)+~P60(x98581)+~P24(f328(f328(f244(f885(x98581,x98582)),x98583),x98584))+P24(f328(f328(f245(f885(x98581,x98582)),x98583),x98584))+~P24(f328(f58(x98581),f328(f328(f8(a871,a871,x98581),a323),f328(f328(f18(x98581,x98582,a871),f328(f328(f8(x98582,f885(x98582,a871),x98581),a325),x98583)),x98584))))
% 81.29/80.93 [9453]~P52(x94531,x94531,x94534)+P24(f328(f328(f330(f884(x94531,x94531)),f328(f328(f257(x94531,x94531),x94532),x94533)),f304(x94531,x94534)))+P24(f328(f328(f330(f884(x94531,x94531)),f328(f328(f257(x94531,x94531),x94533),x94532)),f304(x94531,x94534)))+~P24(f328(f328(f330(f884(x94531,x94531)),f328(f328(f257(x94531,x94531),x94535),x94532)),f304(x94531,x94534)))+~P24(f328(f328(f330(f884(x94531,x94531)),f328(f328(f257(x94531,x94531),x94535),x94533)),f304(x94531,x94534)))
% 81.29/80.93 [5612]E(x56121,f2(a877))+~E(f328(f38(x56122),x56125),x56121)+E(f328(f38(x56122),x56123),f328(a118,x56121))+~E(x56123,f328(f328(f306(x56122),x56124),x56125))+P24(f328(f328(f330(x56122),x56124),x56125))
% 81.29/80.93 [5737]~P62(x57372)+E(x57371,f2(x57372))+E(x57373,f2(x57372))+~E(f328(f328(f286(x57372),x57374),x57373),f328(f328(f286(x57372),x57375),x57371))+E(f328(f328(f82(x57372),x57374),x57371),f328(f328(f82(x57372),x57375),x57373))
% 81.29/80.93 [5738]~P62(x57382)+E(x57381,f2(x57382))+E(x57383,f2(x57382))+~E(f328(f328(f82(x57382),x57384),x57383),f328(f328(f82(x57382),x57385),x57381))+E(f328(f328(f286(x57382),x57384),x57381),f328(f328(f286(x57382),x57385),x57383))
% 81.29/80.93 [5804]~E(f328(f38(x58041),x58045),x58043)+~E(x58045,f193(f885(x58041,a871)))+E(f328(f38(x58041),x58042),f328(a118,x58043))+~E(x58042,f328(f328(f306(x58041),x58044),x58045))+P24(f328(f328(f330(x58041),x58044),x58045))
% 81.29/80.93 [6033]~P112(x60332)+~E(f328(x60333,x60335),f2(x60332))+E(f328(f328(f9(x60331,x60332),x60333),x60334),f2(x60332))+~P24(f328(f62(x60331),x60334))+~P24(f328(f328(f330(x60331),x60335),x60334))
% 81.29/80.93 [6406]~P106(x64063)+E(x64061,x64062)+~E(f328(f298(x64063,x64064),x64061),f328(f298(x64063,x64065),x64062))+~P24(f328(f328(f245(x64063),x64065),x64062))+~P24(f328(f328(f245(x64063),x64064),x64061))
% 81.29/80.93 [6407]~P106(x64073)+E(x64071,x64072)+~E(f328(f298(x64073,x64071),x64074),f328(f298(x64073,x64072),x64075))+~P24(f328(f328(f245(x64073),x64072),x64075))+~P24(f328(f328(f245(x64073),x64071),x64074))
% 81.29/80.93 [7469]~P106(x74691)+~P29(x74691,f328(f328(f127(x74691),x74694),x74695))+~P24(f328(f328(f330(x74691),x74693),f328(f171(x74691),x74695)))+~P24(f328(f328(f330(x74691),x74692),f328(f171(x74691),x74694)))+P24(f328(f328(f244(x74691),x74692),x74693))
% 81.29/80.93 [8573]~P108(x85731)+~P24(f328(f328(f245(f885(x85731,a871)),f299(x85731,x85735,x85732)),f299(x85731,x85734,x85733)))+~P24(f328(f328(f244(x85731),x85735),x85732))+P24(f328(f328(f245(x85731),x85732),x85733))+P24(f328(f328(f245(x85731),x85734),x85735))
% 81.29/80.93 [9973]~P13(x99732,x99735,x99733)+E(x99731,f193(f885(x99732,a871)))+~E(f328(f328(x99735,f328(x99734,f464(x99731,x99734,x99733,x99735,x99732))),f328(x99734,f465(x99731,x99734,x99733,x99735,x99732))),f328(x99734,f328(f328(x99735,f464(x99731,x99734,x99733,x99735,x99732)),f465(x99731,x99734,x99733,x99735,x99732))))+E(f328(x99733,f328(f307(x99732,x99732,x99734),x99731)),f328(x99734,f328(x99733,x99731)))+~P24(f328(f62(x99732),x99731))
% 81.29/80.93 [6403]~P14(x64032,x64035,x64033)+E(x64031,f193(f885(x64032,a871)))+~P24(f328(f62(x64032),x64031))+E(f328(x64033,f328(f328(f306(x64032),x64034),x64031)),f328(f328(x64035,x64034),f328(x64033,x64031)))+P24(f328(f328(f330(x64032),x64034),x64031))
% 81.29/80.93 [7225]~P13(x72252,x72253,x72254)+E(f328(f328(x72253,f328(x72254,x72251)),f328(x72254,x72255)),f328(x72254,x72255))+E(x72251,f193(f885(x72252,a871)))+~P24(f328(f62(x72252),x72255))+~P24(f328(f328(f244(f885(x72252,a871)),x72251),x72255))
% 81.29/80.93 [7445]~P60(x74454)+~P95(x74455)+E(f328(x74451,x74452),f328(x74453,x74452))+~P24(f328(f328(f330(x74454),x74452),f328(f171(x74454),f56(x74454))))+~P24(f328(f328(f92(f885(x74454,x74455)),x74451),x74453))
% 81.29/80.93 [7601]~P14(x76014,x76015,x76011)+E(f328(x76011,x76012),x76013)+~P24(f328(f62(x76014),x76012))+~E(f328(f328(f22(f885(x76014,a871)),x76012),f328(f328(f306(x76014),x76013),f193(f885(x76014,a871)))),f193(f885(x76014,a871)))+~P24(f328(f328(f330(x76014),x76013),x76012))
% 81.29/80.93 [7686]E(x76861,x76862)+~E(f328(f194(f878(x76863)),x76862),f328(f194(f878(x76864)),x76865))+~E(f328(f194(f878(x76863)),x76861),f328(f194(f878(x76864)),x76865))+~E(f328(f177(x76864,x76863),f328(f328(f181(x76864,x76863),x76865),x76861)),f328(f177(x76864,x76863),f328(f328(f181(x76864,x76863),x76865),x76862)))+~P24(f328(f136(x76864),x76865))
% 81.29/80.93 [8544]E(x85441,x85442)+~P6(x85443,x85444,x85445)+E(f328(f328(f107(f885(x85443,a871)),x85441),x85442),f193(f885(x85443,a871)))+~P24(f328(f328(f330(f885(x85443,a871)),x85442),f328(f328(f61(x85443),x85444),x85445)))+~P24(f328(f328(f330(f885(x85443,a871)),x85441),f328(f328(f61(x85443),x85444),x85445)))
% 81.29/80.93 [9335]~P74(x93352)+~E(f328(x93353,f843(x93353,x93354,x93355,x93351,x93352)),f2(x93352))+E(f328(f328(f6(x93351,x93352),x93353),x93354),f328(f328(f6(x93351,x93352),x93353),x93355))+~P24(f328(f62(x93351),x93355))+~P24(f328(f328(f244(f885(x93351,a871)),x93354),x93355))
% 81.29/80.93 [9336]~P74(x93362)+~E(f328(x93363,f844(x93363,x93364,x93365,x93361,x93362)),f2(x93362))+E(f328(f328(f6(x93361,x93362),x93363),x93364),f328(f328(f6(x93361,x93362),x93363),x93365))+~P24(f328(f62(x93361),x93365))+~P24(f328(f328(f244(f885(x93361,a871)),x93364),x93365))
% 81.29/80.93 [9337]~P75(x93372)+~E(f328(x93373,f351(x93373,x93374,x93375,x93371,x93372)),f79(x93372))+E(f328(f328(f9(x93371,x93372),x93373),x93374),f328(f328(f9(x93371,x93372),x93373),x93375))+~P24(f328(f62(x93371),x93375))+~P24(f328(f328(f244(f885(x93371,a871)),x93374),x93375))
% 81.29/80.93 [9338]~P75(x93382)+~E(f328(x93383,f354(x93383,x93384,x93385,x93381,x93382)),f79(x93382))+E(f328(f328(f9(x93381,x93382),x93383),x93384),f328(f328(f9(x93381,x93382),x93383),x93385))+~P24(f328(f62(x93381),x93385))+~P24(f328(f328(f244(f885(x93381,a871)),x93384),x93385))
% 81.29/80.93 [9806]~P89(x98061)+~P24(f328(f62(x98062),x98065))+~P24(f328(f328(f244(x98061),f2(x98061)),f328(x98063,f833(x98063,x98064,x98065,x98062,x98061))))+P24(f328(f328(f244(x98061),f328(f328(f6(x98062,x98061),x98063),x98064)),f328(f328(f6(x98062,x98061),x98063),x98065)))+~P24(f328(f328(f244(f885(x98062,a871)),x98064),x98065))
% 81.29/80.93 [7466]E(x74661,f2(a877))+P24(f328(x74662,x74663))+~E(x74664,f328(f328(f81(a877),f328(f328(f82(a877),x74661),x74663)),x74665))+~P24(f328(f328(f245(a877),x74665),x74661))+~P24(f328(x74662,f328(f328(f39(a877),x74664),x74661)))
% 81.29/80.93 [7542]E(x75421,f2(a877))+P24(f328(x75422,x75423))+~P24(f328(x75422,f45(a877,x75424,x75421)))+~E(x75424,f328(f328(f81(a877),f328(f328(f82(a877),x75421),x75425)),x75423))+~P24(f328(f328(f245(a877),x75423),x75421))
% 81.29/80.93 [7831]~P62(x78313)+E(f328(x78311,x78312),f2(x78313))+~P24(f328(f62(x78314),x78315))+E(f328(f328(f9(x78314,x78313),x78311),f328(f328(f22(f885(x78314,a871)),x78315),f328(f328(f306(x78314),x78312),f193(f885(x78314,a871))))),f328(f328(f9(x78314,x78313),x78311),x78315))+P24(f328(f328(f330(x78314),x78312),x78315))
% 81.29/80.93 [8239]~P74(x82391)+~P24(f328(f62(x82392),x82395))+~P24(f328(f62(x82392),x82394))+~E(f328(f328(f107(f885(x82392,a871)),x82394),x82395),f193(f885(x82392,a871)))+E(f328(f328(f81(x82391),f328(f328(f6(x82392,x82391),x82393),x82394)),f328(f328(f6(x82392,x82391),x82393),x82395)),f328(f328(f6(x82392,x82391),x82393),f328(f328(f116(f885(x82392,a871)),x82394),x82395)))
% 81.29/80.93 [8241]~P75(x82411)+~P24(f328(f62(x82412),x82415))+~P24(f328(f62(x82412),x82414))+~E(f328(f328(f107(f885(x82412,a871)),x82414),x82415),f193(f885(x82412,a871)))+E(f328(f328(f82(x82411),f328(f328(f9(x82412,x82411),x82413),x82414)),f328(f328(f9(x82412,x82411),x82413),x82415)),f328(f328(f9(x82412,x82411),x82413),f328(f328(f116(f885(x82412,a871)),x82414),x82415)))
% 81.29/80.93 [8334]~P62(x83343)+E(f328(x83341,x83342),f2(x83343))+~P24(f328(f62(x83344),x83345))+E(f328(f328(f9(x83344,x83343),x83341),f328(f328(f22(f885(x83344,a871)),x83345),f328(f328(f306(x83344),x83342),f193(f885(x83344,a871))))),f328(f328(f286(x83343),f328(f328(f9(x83344,x83343),x83341),x83345)),f328(x83341,x83342)))+~P24(f328(f328(f330(x83344),x83342),x83345))
% 81.29/80.93 [9050]~P6(x90501,x90505,x90504)+~E(f328(f328(f61(x90501),f328(f328(f306(x90501),x90502),f193(f885(x90501,a871)))),x90504),f328(f328(f61(x90501),f328(f328(f306(x90501),x90503),f193(f885(x90501,a871)))),x90504))+~P24(f328(f328(f330(x90501),x90503),x90505))+~P24(f328(f328(f330(x90501),x90502),x90505))+P24(f328(f328(f330(f884(x90501,x90501)),f328(f328(f257(x90501,x90501),x90502),x90503)),x90504))
% 81.29/80.93 [9070]~P6(x90701,x90705,x90703)+E(f328(f328(f61(x90701),f328(f328(f306(x90701),x90702),f193(f885(x90701,a871)))),x90703),f328(f328(f61(x90701),f328(f328(f306(x90701),x90704),f193(f885(x90701,a871)))),x90703))+~P24(f328(f328(f330(x90701),x90704),x90705))+~P24(f328(f328(f330(x90701),x90702),x90705))+~P24(f328(f328(f330(f884(x90701,x90701)),f328(f328(f257(x90701,x90701),x90702),x90704)),x90703))
% 81.29/80.93 [9364]~P75(x93641)+~P24(f328(f62(x93642),x93645))+~P24(f328(f62(x93642),x93644))+~E(f328(f328(f107(f885(x93642,a871)),x93644),x93645),f193(f885(x93642,a871)))+E(f328(f328(f82(x93641),f328(f328(f328(f66(x93641,x93642,f82(x93641)),x93643),f79(x93641)),x93644)),f328(f328(f328(f66(x93641,x93642,f82(x93641)),x93643),f79(x93641)),x93645)),f328(f328(f328(f66(x93641,x93642,f82(x93641)),x93643),f79(x93641)),f328(f328(f116(f885(x93642,a871)),x93644),x93645)))
% 81.29/80.93 [9373]~P74(x93731)+~E(f328(x93733,f835(x93733,x93735,x93734,x93732,x93731)),f2(x93731))+~P24(f328(f62(x93732),x93734))+~P24(f328(f62(x93732),x93735))+E(f328(f328(f81(x93731),f328(f328(f6(x93732,x93731),x93733),x93734)),f328(f328(f6(x93732,x93731),x93733),x93735)),f328(f328(f6(x93732,x93731),x93733),f328(f328(f116(f885(x93732,a871)),x93734),x93735)))
% 81.29/80.93 [9374]~P74(x93741)+~E(f328(x93743,f836(x93743,x93745,x93744,x93742,x93741)),f2(x93741))+~P24(f328(f62(x93742),x93744))+~P24(f328(f62(x93742),x93745))+E(f328(f328(f81(x93741),f328(f328(f6(x93742,x93741),x93743),x93744)),f328(f328(f6(x93742,x93741),x93743),x93745)),f328(f328(f6(x93742,x93741),x93743),f328(f328(f116(f885(x93742,a871)),x93744),x93745)))
% 81.29/80.93 [9375]~P75(x93751)+~E(f328(x93753,f352(x93753,x93755,x93754,x93752,x93751)),f79(x93751))+~P24(f328(f62(x93752),x93754))+~P24(f328(f62(x93752),x93755))+E(f328(f328(f82(x93751),f328(f328(f9(x93752,x93751),x93753),x93754)),f328(f328(f9(x93752,x93751),x93753),x93755)),f328(f328(f9(x93752,x93751),x93753),f328(f328(f116(f885(x93752,a871)),x93754),x93755)))
% 81.29/80.93 [9376]~P75(x93761)+~E(f328(x93763,f353(x93763,x93765,x93764,x93762,x93761)),f79(x93761))+~P24(f328(f62(x93762),x93764))+~P24(f328(f62(x93762),x93765))+E(f328(f328(f82(x93761),f328(f328(f9(x93762,x93761),x93763),x93764)),f328(f328(f9(x93762,x93761),x93763),x93765)),f328(f328(f9(x93762,x93761),x93763),f328(f328(f116(f885(x93762,a871)),x93764),x93765)))
% 81.29/80.93 [9581]~P75(x95811)+~E(f328(x95813,f866(x95813,x95815,x95814,x95812,x95811)),f79(x95811))+~P24(f328(f62(x95812),x95814))+~P24(f328(f62(x95812),x95815))+E(f328(f328(f82(x95811),f328(f328(f328(f66(x95811,x95812,f82(x95811)),x95813),f79(x95811)),x95814)),f328(f328(f328(f66(x95811,x95812,f82(x95811)),x95813),f79(x95811)),x95815)),f328(f328(f328(f66(x95811,x95812,f82(x95811)),x95813),f79(x95811)),f328(f328(f116(f885(x95812,a871)),x95814),x95815)))
% 81.29/80.93 [9686]~P74(x96862)+E(f328(f328(f6(x96861,x96862),x96863),x96864),f328(f328(f6(x96861,x96862),x96863),x96865))+~P24(f328(f62(x96861),x96865))+~P24(f328(f328(f244(f885(x96861,a871)),x96864),x96865))+P24(f328(f328(f330(x96861),f843(x96863,x96864,x96865,x96861,x96862)),f328(f328(f22(f885(x96861,a871)),x96865),x96864)))
% 81.29/80.93 [9687]~P74(x96872)+E(f328(f328(f6(x96871,x96872),x96873),x96874),f328(f328(f6(x96871,x96872),x96873),x96875))+~P24(f328(f62(x96871),x96875))+~P24(f328(f328(f244(f885(x96871,a871)),x96874),x96875))+P24(f328(f328(f330(x96871),f844(x96873,x96874,x96875,x96871,x96872)),f328(f328(f22(f885(x96871,a871)),x96875),x96874)))
% 81.29/80.93 [9688]~P75(x96882)+E(f328(f328(f9(x96881,x96882),x96883),x96884),f328(f328(f9(x96881,x96882),x96883),x96885))+~P24(f328(f62(x96881),x96885))+~P24(f328(f328(f244(f885(x96881,a871)),x96884),x96885))+P24(f328(f328(f330(x96881),f351(x96883,x96884,x96885,x96881,x96882)),f328(f328(f22(f885(x96881,a871)),x96885),x96884)))
% 81.29/80.93 [9689]~P75(x96892)+E(f328(f328(f9(x96891,x96892),x96893),x96894),f328(f328(f9(x96891,x96892),x96893),x96895))+~P24(f328(f62(x96891),x96895))+~P24(f328(f328(f244(f885(x96891,a871)),x96894),x96895))+P24(f328(f328(f330(x96891),f354(x96893,x96894,x96895,x96891,x96892)),f328(f328(f22(f885(x96891,a871)),x96895),x96894)))
% 81.29/80.93 [9706]~P74(x97061)+~P24(f328(f62(x97062),x97064))+~P24(f328(f62(x97062),x97065))+E(f328(f328(f81(x97061),f328(f328(f6(x97062,x97061),x97063),x97064)),f328(f328(f6(x97062,x97061),x97063),x97065)),f328(f328(f6(x97062,x97061),x97063),f328(f328(f116(f885(x97062,a871)),x97064),x97065)))+P24(f328(f328(f330(x97062),f835(x97063,x97065,x97064,x97062,x97061)),f328(f328(f107(f885(x97062,a871)),x97064),x97065)))
% 81.29/80.93 [9707]~P74(x97071)+~P24(f328(f62(x97072),x97074))+~P24(f328(f62(x97072),x97075))+E(f328(f328(f81(x97071),f328(f328(f6(x97072,x97071),x97073),x97074)),f328(f328(f6(x97072,x97071),x97073),x97075)),f328(f328(f6(x97072,x97071),x97073),f328(f328(f116(f885(x97072,a871)),x97074),x97075)))+P24(f328(f328(f330(x97072),f836(x97073,x97075,x97074,x97072,x97071)),f328(f328(f107(f885(x97072,a871)),x97074),x97075)))
% 81.29/80.93 [9708]~P75(x97081)+~P24(f328(f62(x97082),x97084))+~P24(f328(f62(x97082),x97085))+E(f328(f328(f82(x97081),f328(f328(f9(x97082,x97081),x97083),x97084)),f328(f328(f9(x97082,x97081),x97083),x97085)),f328(f328(f9(x97082,x97081),x97083),f328(f328(f116(f885(x97082,a871)),x97084),x97085)))+P24(f328(f328(f330(x97082),f352(x97083,x97085,x97084,x97082,x97081)),f328(f328(f107(f885(x97082,a871)),x97084),x97085)))
% 81.29/80.93 [9709]~P75(x97091)+~P24(f328(f62(x97092),x97094))+~P24(f328(f62(x97092),x97095))+E(f328(f328(f82(x97091),f328(f328(f9(x97092,x97091),x97093),x97094)),f328(f328(f9(x97092,x97091),x97093),x97095)),f328(f328(f9(x97092,x97091),x97093),f328(f328(f116(f885(x97092,a871)),x97094),x97095)))+P24(f328(f328(f330(x97092),f353(x97093,x97095,x97094,x97092,x97091)),f328(f328(f107(f885(x97092,a871)),x97094),x97095)))
% 81.29/80.93 [9716]~P89(x97165)+~P24(f328(f62(x97161),x97164))+P24(f328(f328(f244(x97165),f328(f328(f6(x97161,x97165),x97162),x97163)),f328(f328(f6(x97161,x97165),x97162),x97164)))+~P24(f328(f328(f244(f885(x97161,a871)),x97163),x97164))+P24(f328(f328(f330(x97161),f833(x97162,x97163,x97164,x97161,x97165)),f328(f328(f22(f885(x97161,a871)),x97164),x97163)))
% 81.29/80.93 [9770]~P75(x97701)+~P24(f328(f62(x97702),x97704))+~P24(f328(f62(x97702),x97705))+E(f328(f328(f82(x97701),f328(f328(f328(f66(x97701,x97702,f82(x97701)),x97703),f79(x97701)),x97704)),f328(f328(f328(f66(x97701,x97702,f82(x97701)),x97703),f79(x97701)),x97705)),f328(f328(f328(f66(x97701,x97702,f82(x97701)),x97703),f79(x97701)),f328(f328(f116(f885(x97702,a871)),x97704),x97705)))+P24(f328(f328(f330(x97702),f866(x97703,x97705,x97704,x97702,x97701)),f328(f328(f107(f885(x97702,a871)),x97704),x97705)))
% 81.29/80.93 [8738]~P14(x87381,x87384,x87385)+~P24(f328(f62(x87381),x87382))+E(f328(f328(f22(f885(x87381,a871)),x87382),f328(f328(f306(x87381),x87383),f193(f885(x87381,a871)))),f193(f885(x87381,a871)))+~P24(f328(f328(f330(x87381),x87383),x87382))+E(f328(f328(x87384,x87383),f328(x87385,f328(f328(f22(f885(x87381,a871)),x87382),f328(f328(f306(x87381),x87383),f193(f885(x87381,a871)))))),f328(x87385,x87382))
% 81.29/80.93 [8812]~P14(x88121,x88124,x88125)+~P24(f328(f62(x88121),x88123))+~P24(f328(f62(x88121),x88122))+E(f328(f328(f107(f885(x88121,a871)),x88122),x88123),f193(f885(x88121,a871)))+E(f328(f328(x88124,f328(x88125,f328(f328(f116(f885(x88121,a871)),x88122),x88123))),f328(x88125,f328(f328(f107(f885(x88121,a871)),x88122),x88123))),f328(f328(x88124,f328(x88125,x88122)),f328(x88125,x88123)))
% 81.29/80.93 [9378]~P24(f328(f328(f244(a1),x93784),f2(a1)))+~P24(f328(f328(f245(a1),x93783),x93785))+P24(f328(f328(f244(a1),x93781),x93782))+~P24(f328(f328(f245(a1),x93783),x93784))+~P24(f328(f328(f244(a1),f328(f328(f81(a1),f328(f328(f82(a1),x93783),x93782)),x93785)),f328(f328(f81(a1),f328(f328(f82(a1),x93783),x93781)),x93784)))
% 81.29/80.93 [9380]~P24(f328(f328(f244(a1),f2(a1)),x93805))+P24(f328(f328(f244(a1),x93801),x93802))+~P24(f328(f328(f245(a1),x93803),x93804))+~P24(f328(f328(f245(a1),x93805),x93804))+~P24(f328(f328(f244(a1),f328(f328(f81(a1),f328(f328(f82(a1),x93804),x93801)),x93805)),f328(f328(f81(a1),f328(f328(f82(a1),x93804),x93802)),x93803)))
% 81.29/80.93 [9490]~P62(x94905)+E(f328(x94901,f355(x94901,x94902,x94903,x94904,x94905)),f2(x94905))+~P24(f328(f62(x94904),x94903))+~P24(f328(f62(x94904),x94902))+E(f328(f328(f286(x94905),f328(f328(f82(x94905),f328(f328(f9(x94904,x94905),x94901),x94903)),f328(f328(f9(x94904,x94905),x94901),x94902))),f328(f328(f9(x94904,x94905),x94901),f328(f328(f107(f885(x94904,a871)),x94903),x94902))),f328(f328(f9(x94904,x94905),x94901),f328(f328(f116(f885(x94904,a871)),x94903),x94902)))
% 81.29/80.93 [9762]~P62(x97621)+~P24(f328(f62(x97622),x97624))+~P24(f328(f62(x97622),x97625))+E(f328(f328(f286(x97621),f328(f328(f82(x97621),f328(f328(f9(x97622,x97621),x97623),x97624)),f328(f328(f9(x97622,x97621),x97623),x97625))),f328(f328(f9(x97622,x97621),x97623),f328(f328(f107(f885(x97622,a871)),x97624),x97625))),f328(f328(f9(x97622,x97621),x97623),f328(f328(f116(f885(x97622,a871)),x97624),x97625)))+P24(f328(f328(f330(x97622),f355(x97623,x97625,x97624,x97622,x97621)),f328(f328(f107(f885(x97622,a871)),x97624),x97625)))
% 81.29/80.93 [9090]E(f328(f328(f127(x90901),x90902),x90903),f328(f328(f127(x90901),x90904),x90905))+~E(f328(f328(f174(x90901),f328(f194(f878(x90901)),x90904)),x90902),x90904)+~E(f328(f328(f174(x90901),f328(f194(f878(x90901)),x90902)),x90904),x90902)+~E(x90905,f328(f328(f127(x90901),f328(f328(f137(x90901),f328(f194(f878(x90901)),x90904)),x90902)),x90903))+~E(f328(f328(f127(x90901),f328(f328(f137(x90901),f328(f194(f878(x90901)),x90902)),x90904)),x90905),x90903)
% 81.29/80.93 [9488]~P106(x94882)+E(f328(f328(f147(x94881,x94882,x94883),x94884),f169(x94881,x94884,x94885)),x94885)+~P29(x94882,f328(f328(f153(x94881,x94882),x94883),x94885))+~P24(f328(f328(f330(x94881),x94884),f328(f171(x94881),x94885)))+~E(f328(f140(x94881),f328(f135(x94881,f328(f328(f8(x94882,a871,x94881),f328(a325,f328(x94883,x94884))),x94883)),x94885)),x94884)
% 81.29/80.93 [9822]~P71(x98221)+~P24(f328(f67(x98221,x98221,f82(x98221),x98222,x98223),x98225))+~P24(f328(f328(f330(x98221),x98224),x98223))+P24(f328(f328(f330(x98221),x98222),x98223))+P24(f328(f67(x98221,x98221,f82(x98221),x98224,f328(f328(f306(x98221),x98222),f328(f328(f22(f885(x98221,a871)),x98223),f328(f328(f306(x98221),x98224),f193(f885(x98221,a871)))))),x98225))
% 81.29/80.93 [7233]E(x72331,x72332)+~P21(x72334,x72335,x72333,x72336)+~E(f328(x72333,x72331),f328(x72333,x72332))+~P24(f328(f328(f330(x72334),x72332),x72336))+~P24(f328(f328(f330(x72334),x72331),x72336))
% 81.29/80.93 [6494]~P143(x64944)+E(x64941,x64942)+~E(x64945,x64946)+E(x64943,f2(x64944))+~E(f328(f328(f81(x64944),x64945),f328(f328(f82(x64944),x64943),x64941)),f328(f328(f81(x64944),x64946),f328(f328(f82(x64944),x64943),x64942)))
% 81.29/80.93 [7523]~P106(x75231)+~P27(x75231)+~P24(f328(f328(f245(x75231),x75232),f328(x75235,x75236)))+~P24(f328(f328(f330(x75233),x75236),x75234))+P24(f328(f328(f245(x75231),x75232),f328(f328(f43(x75233,x75231),x75234),x75235)))
% 81.29/80.93 [8209]~P106(x82091)+~P27(x82091)+~P24(f328(f328(f245(x82091),f328(x82094,x82096)),x82095))+~P24(f328(f328(f330(x82092),x82096),x82093))+P24(f328(f328(f245(x82091),f328(f328(f42(x82092,x82091),x82093),x82094)),x82095))
% 81.29/80.93 [8471]~P15(x84712,x84715,x84716,x84711)+~P24(f328(f62(x84712),x84714))+~P24(f328(f62(x84712),x84713))+~E(f328(f328(f107(f885(x84712,a871)),x84713),x84714),f193(f885(x84712,a871)))+E(f328(x84711,f328(f328(f116(f885(x84712,a871)),x84713),x84714)),f328(f74(x84715,x84715,x84715,f328(x84711,x84713)),f328(x84711,x84714)))
% 81.29/80.93 [8782]E(x87821,x87822)+~P54(x87824,x87825,x87826,x87823,x87827)+~E(f328(x87823,x87821),f328(x87823,x87822))+~P24(f328(f328(f330(x87825),x87822),x87827))+~P24(f328(f328(f330(x87825),x87821),x87827))
% 81.29/80.93 [10073]~P24(f328(x100732,x100734))+~E(x100735,f328(f135(x100731,x100732),x100737))+E(f328(f135(x100731,x100732),x100733),f328(f328(f150(x100731),x100734),x100735))+~E(x100733,f328(f328(f127(x100731),x100736),f328(f328(f150(x100731),x100734),x100737)))+P24(f328(x100732,f746(x100735,x100734,x100733,x100732,x100731,x100736,x100737)))
% 81.29/80.93 [10074]~P24(f328(x100744,x100742))+~E(x100743,f328(f135(x100741,x100744),x100747))+E(f328(f328(f150(x100741),x100742),x100743),f328(f135(x100741,x100744),x100745))+~E(x100745,f328(f328(f127(x100741),x100746),f328(f328(f150(x100741),x100742),x100747)))+P24(f328(x100744,f748(x100745,x100744,x100743,x100742,x100741,x100746,x100747)))
% 81.29/80.93 [10109]~P24(f328(x101092,x101094))+~E(x101095,f328(f135(x101091,x101092),x101097))+E(f328(f135(x101091,x101092),x101093),f328(f328(f150(x101091),x101094),x101095))+~E(x101093,f328(f328(f127(x101091),x101096),f328(f328(f150(x101091),x101094),x101097)))+P24(f328(f328(f330(x101091),f746(x101095,x101094,x101093,x101092,x101091,x101096,x101097)),f328(f171(x101091),x101096)))
% 81.29/80.93 [10110]~P24(f328(x101104,x101102))+~E(x101103,f328(f135(x101101,x101104),x101107))+E(f328(f328(f150(x101101),x101102),x101103),f328(f135(x101101,x101104),x101105))+~E(x101105,f328(f328(f127(x101101),x101106),f328(f328(f150(x101101),x101102),x101107)))+P24(f328(f328(f330(x101101),f748(x101105,x101104,x101103,x101102,x101101,x101106,x101107)),f328(f171(x101101),x101106)))
% 81.29/80.93 [10113]~P6(x101131,x101137,x101136)+~P9(x101131,f885(x101135,a871),x101136,x101134)+P24(f328(f328(f330(x101131),f545(x101132,x101133,x101134,x101135,x101136,x101137,x101131)),x101137))+~P24(f328(f328(f330(f885(x101131,a871)),x101133),f328(f328(f61(x101131),x101137),x101136)))+P24(f328(f328(f330(f885(x101135,a871)),f328(f328(f43(x101131,f885(x101135,a871)),x101133),x101134)),x101132))
% 81.29/80.93 [10159]~P6(x101592,x101596,x101597)+~P9(x101592,f885(x101591,a871),x101597,x101594)+~P24(f328(f328(f330(f885(x101592,a871)),x101593),f328(f328(f61(x101592),x101596),x101597)))+~P24(f328(f328(f330(f885(x101591,a871)),f328(x101594,f545(x101595,x101593,x101594,x101591,x101597,x101596,x101592))),x101595))+P24(f328(f328(f330(f885(x101591,a871)),f328(f328(f43(x101592,f885(x101591,a871)),x101593),x101594)),x101595))
% 81.29/80.93 [8378]~P75(x83782)+~P21(x83781,x83785,x83788,x83784)+~E(x83783,f328(f74(x83785,x83782,x83781,x83786),x83788))+~E(x83787,f328(f307(x83781,x83785,x83788),x83784))+E(f328(f328(f9(x83781,x83782),x83783),x83784),f328(f328(f9(x83785,x83782),x83786),x83787))
% 81.29/80.93 [10162]~P75(x101622)+~P21(x101625,x101621,x101628,x101627)+~E(f328(x101626,f576(x101623,x101626,x101624,x101627,x101628,x101621,x101625,x101622)),f328(f328(f74(x101621,x101622,x101625,x101623),x101628),f576(x101623,x101626,x101624,x101627,x101628,x101621,x101625,x101622)))+~E(x101624,f328(f307(x101625,x101621,x101628),x101627))+E(f328(f328(f9(x101621,x101622),x101623),x101624),f328(f328(f9(x101625,x101622),x101626),x101627))
% 81.29/80.93 [10164]~P74(x101642)+~P21(x101641,x101645,x101648,x101644)+~E(x101647,f328(f307(x101641,x101645,x101648),x101644))+E(f328(f328(f6(x101641,x101642),x101643),x101644),f328(f328(f6(x101645,x101642),x101646),x101647))+P24(f328(f328(f330(x101641),f756(x101646,x101643,x101647,x101644,x101648,x101645,x101641,x101642)),x101644))
% 81.29/80.93 [10165]~P75(x101652)+~P21(x101651,x101655,x101658,x101654)+~E(x101657,f328(f307(x101651,x101655,x101658),x101654))+E(f328(f328(f9(x101651,x101652),x101653),x101654),f328(f328(f9(x101655,x101652),x101656),x101657))+P24(f328(f328(f330(x101651),f576(x101656,x101653,x101657,x101654,x101658,x101655,x101651,x101652)),x101654))
% 81.29/80.93 [10170]~P74(x101702)+~P21(x101705,x101701,x101708,x101707)+~E(x101704,f328(f307(x101705,x101701,x101708),x101707))+~E(f328(x101706,f756(x101703,x101706,x101704,x101707,x101708,x101701,x101705,x101702)),f328(x101703,f328(x101708,f756(x101703,x101706,x101704,x101707,x101708,x101701,x101705,x101702))))+E(f328(f328(f6(x101701,x101702),x101703),x101704),f328(f328(f6(x101705,x101702),x101706),x101707))
% 81.29/80.93 [9543]~E(f328(f194(f878(x95432)),x95435),f328(f194(f878(x95431)),x95433))+~E(f328(f194(f878(x95432)),x95434),f328(f194(f878(x95431)),x95433))+~E(f328(f328(f328(f73(x95431,f881(x95432)),f328(f177(x95431,x95432),f328(f328(f181(x95431,x95432),x95433),x95434))),x95436),f328(f236(x95432),x95437)),f328(f328(f328(f73(x95431,f881(x95432)),f328(f177(x95431,x95432),f328(f328(f181(x95431,x95432),x95433),x95435))),x95436),f328(f236(x95432),x95438)))+E(f328(f177(x95431,x95432),f328(f328(f181(x95431,x95432),x95433),x95434)),f328(f177(x95431,x95432),f328(f328(f181(x95431,x95432),x95433),x95435)))+P24(f328(f328(f330(x95431),x95436),f328(f171(x95431),x95433)))
% 81.29/80.93 [9654]~P19(x96546,x96542,x96545,x96547,x96548,x96541)+~P24(f328(f62(x96542),x96544))+~P24(f328(f62(x96542),x96543))+~E(f328(f328(f107(f885(x96542,a871)),x96543),x96544),f193(f885(x96542,a871)))+E(f328(x96541,f328(f328(f116(f885(x96542,a871)),x96543),x96544)),f328(f328(x96545,f328(x96541,x96543)),f328(x96541,x96544)))
% 81.29/80.93 [10060]~P19(x100608,x100602,x100605,x100607,x100606,x100601)+~E(f328(x100606,f845(x100604,x100603,x100601,x100606,x100607,x100605,x100602)),x100607)+~P24(f328(f62(x100602),x100603))+~P24(f328(f62(x100602),x100604))+E(f328(x100601,f328(f328(f116(f885(x100602,a871)),x100603),x100604)),f328(f328(x100605,f328(x100601,x100603)),f328(x100601,x100604)))
% 81.29/80.93 [10118]~P19(x101188,x101182,x101185,x101187,x101186,x101181)+~P24(f328(f62(x101182),x101183))+~P24(f328(f62(x101182),x101184))+E(f328(x101181,f328(f328(f116(f885(x101182,a871)),x101183),x101184)),f328(f328(x101185,f328(x101181,x101183)),f328(x101181,x101184)))+P24(f328(f328(f330(x101182),f845(x101184,x101183,x101181,x101186,x101187,x101185,x101182)),f328(f328(f107(f885(x101182,a871)),x101183),x101184)))
% 81.29/80.93 [9811]~P6(x98114,x98118,x98115)+~P6(x98111,x98119,x98113)+~P10(x98111,x98114,f885(x98112,a871),x98113,x98115,x98117)+P9(x98111,f885(x98112,a871),x98113,f328(f328(f8(f885(x98114,f885(x98112,a871)),f885(x98112,a871),x98111),f328(f43(x98114,f885(x98112,a871)),f328(f282(x98114,x98114,x98115),f328(f328(f306(x98114),x98116),f193(f885(x98114,a871)))))),x98117))+~P24(f328(f328(f330(x98114),x98116),x98118))
% 81.29/80.93 [5419]~P106(x54193)+~P29(x54193,x54191)+E(x54191,f719(x54192,x54193))+~E(f328(f171(x54193),x54191),x54192)+~P24(f328(f62(x54193),x54192))+~P24(f328(f136(x54193),x54191))
% 81.29/80.93 [5039]~P136(x50392)+~P125(x50392)+~P126(x50392)+~P116(x50392)+E(x50391,f2(x50392))+~E(f328(f328(f258(x50392),x50391),x50393),f2(x50392))
% 81.29/80.93 [5040]~P136(x50402)+~P125(x50402)+~P126(x50402)+~P116(x50402)+~E(x50401,f2(a877))+~E(f328(f328(f258(x50402),x50403),x50401),f2(x50402))
% 81.29/80.93 [6476]~P89(x64761)+~E(x64763,f2(x64761))+~E(x64762,f2(x64761))+E(f328(f328(f81(x64761),x64762),x64763),f2(x64761))+~P24(f328(f328(f244(x64761),f2(x64761)),x64763))+~P24(f328(f328(f244(x64761),f2(x64761)),x64762))
% 81.29/80.93 [8843]~E(f328(f256(a877,a877),x88433),f2(a877))+~E(x88431,f328(f328(f81(a877),f328(f328(f82(a877),f328(f256(a877,a877),x88433)),x88432)),f328(f266(a877,a877),x88433)))+P24(f328(f48(x88431,x88432),x88433))+~P24(f328(f328(f244(a877),f328(f266(a877,a877),x88433)),f2(a877)))+P24(f328(f328(f245(a877),f2(a877)),x88432))+~P24(f328(f328(f245(a877),x88432),f328(f266(a877,a877),x88433)))
% 81.29/80.93 [8851]E(x88511,f2(a877))+~E(x88512,f328(f328(f81(a877),f328(f328(f82(a877),f328(f256(a877,a877),x88513)),x88511)),f328(f266(a877,a877),x88513)))+P24(f328(f48(x88512,x88511),x88513))+~P24(f328(f328(f245(a877),f2(a877)),x88511))+~P24(f328(f328(f244(a877),f2(a877)),f328(f266(a877,a877),x88513)))+~P24(f328(f328(f245(a877),f328(f266(a877,a877),x88513)),x88511))
% 81.29/80.93 [8869]~E(f328(f256(a877,a877),x88693),f2(a877))+~E(x88691,f328(f328(f81(a877),f328(f328(f82(a877),f328(f256(a877,a877),x88693)),x88692)),f328(f266(a877,a877),x88693)))+P24(f328(f48(x88691,x88692),x88693))+~P24(f328(f328(f245(a877),f2(a877)),x88692))+~P24(f328(f328(f244(a877),f2(a877)),f328(f266(a877,a877),x88693)))+~P24(f328(f328(f245(a877),f328(f266(a877,a877),x88693)),x88692))
% 81.29/80.93 [6859]~P78(x68592)+E(x68591,f193(f885(x68592,a871)))+E(x68593,f193(f885(x68592,a871)))+~P24(f328(f62(x68592),x68591))+~P24(f328(f62(x68592),x68593))+E(f10(x68592,f328(f328(f116(f885(x68592,a871)),x68593),x68591)),f328(f328(f116(x68592),f10(x68592,x68593)),f10(x68592,x68591)))
% 81.29/80.93 [6860]~P78(x68602)+E(x68601,f193(f885(x68602,a871)))+E(x68603,f193(f885(x68602,a871)))+~P24(f328(f62(x68602),x68601))+~P24(f328(f62(x68602),x68603))+E(f11(x68602,f328(f328(f116(f885(x68602,a871)),x68603),x68601)),f328(f328(f107(x68602),f11(x68602,x68603)),f11(x68602,x68601)))
% 81.29/80.93 [6861]~P106(x68612)+E(x68611,f193(f885(x68612,a871)))+E(x68613,f193(f885(x68612,a871)))+~P24(f328(f62(x68612),x68611))+~P24(f328(f62(x68612),x68613))+E(f14(x68612,f328(f328(f116(f885(x68612,a871)),x68613),x68611)),f328(f328(f242(x68612),f14(x68612,x68613)),f14(x68612,x68611)))
% 81.29/80.93 [6862]~P106(x68622)+E(x68621,f193(f885(x68622,a871)))+E(x68623,f193(f885(x68622,a871)))+~P24(f328(f62(x68622),x68621))+~P24(f328(f62(x68622),x68623))+E(f15(x68622,f328(f328(f116(f885(x68622,a871)),x68623),x68621)),f328(f328(f243(x68622),f15(x68622,x68623)),f15(x68622,x68621)))
% 81.29/80.93 [7498]~P98(x74982)+E(x74981,f193(f885(x74982,a871)))+E(x74983,f193(f885(x74982,a871)))+~P24(f328(f62(x74982),x74981))+~P24(f328(f62(x74982),x74983))+E(f328(f328(f82(x74982),f328(f64(x74982,f82(x74982)),x74983)),f328(f64(x74982,f82(x74982)),x74981)),f328(f64(x74982,f82(x74982)),f328(f328(f116(f885(x74982,a871)),x74983),x74981)))
% 81.29/80.93 [7655]~P106(x76552)+E(x76551,f193(f885(x76552,a871)))+E(x76553,f193(f885(x76552,a871)))+~P24(f328(f62(x76552),x76551))+~P24(f328(f62(x76552),x76553))+E(f328(f328(f242(x76552),f12(x76552,f242(x76552),x76553)),f12(x76552,f242(x76552),x76551)),f12(x76552,f242(x76552),f328(f328(f116(f885(x76552,a871)),x76553),x76551)))
% 81.29/80.93 [7656]~P106(x76562)+E(x76561,f193(f885(x76562,a871)))+E(x76563,f193(f885(x76562,a871)))+~P24(f328(f62(x76562),x76561))+~P24(f328(f62(x76562),x76563))+E(f328(f328(f243(x76562),f13(x76562,f243(x76562),x76563)),f13(x76562,f243(x76562),x76561)),f13(x76562,f243(x76562),f328(f328(f116(f885(x76562,a871)),x76563),x76561)))
% 81.29/80.93 [8691]~P24(f328(x86911,x86913))+P24(f328(x86911,f451(x86911,x86912)))+P24(f328(x86911,f448(x86911,x86912)))+~P24(f328(f328(f245(a1),f2(a1)),x86912))+~P24(f328(f328(f330(a1),x86913),f299(a1,f79(a1),x86912)))+P24(f328(x86911,f328(f328(f22(a1),f448(x86911,x86912)),f328(f328(f82(a1),f450(x86911,x86912)),x86912))))
% 81.29/80.93 [8988]~P24(f328(x89881,x89883))+~P24(f328(x89881,f448(x89881,x89882)))+P24(f328(x89881,f451(x89881,x89882)))+~P24(f328(f328(f245(a1),f2(a1)),x89882))+~P24(f328(f328(f330(a1),x89883),f299(a1,f79(a1),x89882)))+~P24(f328(x89881,f328(f328(f22(a1),f448(x89881,x89882)),f328(f328(f82(a1),f450(x89881,x89882)),x89882))))
% 81.29/80.93 [10193]~P100(x101932)+E(x101931,f193(f885(x101932,a871)))+E(x101933,f193(f885(x101932,a871)))+~P24(f328(f62(x101932),x101931))+~P24(f328(f62(x101932),x101933))+E(f11(x101932,f328(f249(x101932),f328(f328(f8(f885(x101932,a871),a871,x101932),f88(x101932)),f328(f328(f8(f885(x101932,f885(x101932,a871)),f885(x101932,a871),x101932),f328(f8(f885(x101932,a871),a871,x101932),f88(x101932))),f328(f328(f7(x101932,f885(x101932,f885(x101932,a871)),f885(x101932,f885(x101932,a871))),f328(f328(f8(f885(x101932,f885(f885(x101932,a871),f885(x101932,a871))),f885(f885(x101932,f885(x101932,a871)),f885(x101932,f885(x101932,a871))),x101932),f18(x101932,f885(x101932,a871),f885(x101932,a871))),f328(f328(f8(f885(x101932,f885(x101932,f885(a871,a871))),f885(x101932,f885(f885(x101932,a871),f885(x101932,a871))),x101932),f328(f8(f885(x101932,f885(a871,a871)),f885(f885(x101932,a871),f885(x101932,a871)),x101932),f18(x101932,a871,a871))),f328(f328(f8(f885(x101932,f885(x101932,a871)),f885(x101932,f885(x101932,f885(a871,a871))),x101932),f328(f8(f885(x101932,a871),f885(x101932,f885(a871,a871)),x101932),f328(f8(a871,f885(a871,a871),x101932),a326))),f328(f328(f7(x101932,f885(x101932,f885(x101932,x101932)),f885(x101932,f885(x101932,a871))),f328(f328(f8(f885(f885(x101932,x101932),f885(x101932,a871)),f885(f885(x101932,f885(x101932,x101932)),f885(x101932,f885(x101932,a871))),x101932),f8(f885(x101932,x101932),f885(x101932,a871),x101932)),f328(f328(f8(f885(x101932,a871),f885(f885(x101932,x101932),f885(x101932,a871)),x101932),f8(x101932,a871,x101932)),a325))),f116(x101932)))))),f328(f328(f7(x101932,f885(x101932,a871),f885(x101932,a871)),f328(f328(f8(f885(a871,a871),f885(f885(x101932,a871),f885(x101932,a871)),x101932),f8(a871,a871,x101932)),f328(f328(f8(a871,f885(a871,a871),x101932),a326),f328(f328(f7(x101932,f885(x101932,a871),a871),f330(x101932)),x101933)))),f328(f328(f7(x101932,f885(x101932,a871),a871),f330(x101932)),x101931))))))),f328(f328(f116(x101932),f11(x101932,x101933)),f11(x101932,x101931)))
% 81.29/80.93 [10194]~P100(x101942)+E(x101941,f193(f885(x101942,a871)))+E(x101943,f193(f885(x101942,a871)))+~P24(f328(f62(x101942),x101941))+~P24(f328(f62(x101942),x101943))+E(f10(x101942,f328(f249(x101942),f328(f328(f8(f885(x101942,a871),a871,x101942),f88(x101942)),f328(f328(f8(f885(x101942,f885(x101942,a871)),f885(x101942,a871),x101942),f328(f8(f885(x101942,a871),a871,x101942),f88(x101942))),f328(f328(f7(x101942,f885(x101942,f885(x101942,a871)),f885(x101942,f885(x101942,a871))),f328(f328(f8(f885(x101942,f885(f885(x101942,a871),f885(x101942,a871))),f885(f885(x101942,f885(x101942,a871)),f885(x101942,f885(x101942,a871))),x101942),f18(x101942,f885(x101942,a871),f885(x101942,a871))),f328(f328(f8(f885(x101942,f885(x101942,f885(a871,a871))),f885(x101942,f885(f885(x101942,a871),f885(x101942,a871))),x101942),f328(f8(f885(x101942,f885(a871,a871)),f885(f885(x101942,a871),f885(x101942,a871)),x101942),f18(x101942,a871,a871))),f328(f328(f8(f885(x101942,f885(x101942,a871)),f885(x101942,f885(x101942,f885(a871,a871))),x101942),f328(f8(f885(x101942,a871),f885(x101942,f885(a871,a871)),x101942),f328(f8(a871,f885(a871,a871),x101942),a326))),f328(f328(f7(x101942,f885(x101942,f885(x101942,x101942)),f885(x101942,f885(x101942,a871))),f328(f328(f8(f885(f885(x101942,x101942),f885(x101942,a871)),f885(f885(x101942,f885(x101942,x101942)),f885(x101942,f885(x101942,a871))),x101942),f8(f885(x101942,x101942),f885(x101942,a871),x101942)),f328(f328(f8(f885(x101942,a871),f885(f885(x101942,x101942),f885(x101942,a871)),x101942),f8(x101942,a871,x101942)),a325))),f107(x101942)))))),f328(f328(f7(x101942,f885(x101942,a871),f885(x101942,a871)),f328(f328(f8(f885(a871,a871),f885(f885(x101942,a871),f885(x101942,a871)),x101942),f8(a871,a871,x101942)),f328(f328(f8(a871,f885(a871,a871),x101942),a326),f328(f328(f7(x101942,f885(x101942,a871),a871),f330(x101942)),x101943)))),f328(f328(f7(x101942,f885(x101942,a871),a871),f330(x101942)),x101941))))))),f328(f328(f107(x101942),f10(x101942,x101943)),f10(x101942,x101941)))
% 81.29/80.93 [10195]~P106(x101952)+E(x101951,f193(f885(x101952,a871)))+E(x101953,f193(f885(x101952,a871)))+~P24(f328(f62(x101952),x101951))+~P24(f328(f62(x101952),x101953))+E(f13(x101952,f243(x101952),f328(f249(x101952),f328(f328(f8(f885(x101952,a871),a871,x101952),f88(x101952)),f328(f328(f8(f885(x101952,f885(x101952,a871)),f885(x101952,a871),x101952),f328(f8(f885(x101952,a871),a871,x101952),f88(x101952))),f328(f328(f7(x101952,f885(x101952,f885(x101952,a871)),f885(x101952,f885(x101952,a871))),f328(f328(f8(f885(x101952,f885(f885(x101952,a871),f885(x101952,a871))),f885(f885(x101952,f885(x101952,a871)),f885(x101952,f885(x101952,a871))),x101952),f18(x101952,f885(x101952,a871),f885(x101952,a871))),f328(f328(f8(f885(x101952,f885(x101952,f885(a871,a871))),f885(x101952,f885(f885(x101952,a871),f885(x101952,a871))),x101952),f328(f8(f885(x101952,f885(a871,a871)),f885(f885(x101952,a871),f885(x101952,a871)),x101952),f18(x101952,a871,a871))),f328(f328(f8(f885(x101952,f885(x101952,a871)),f885(x101952,f885(x101952,f885(a871,a871))),x101952),f328(f8(f885(x101952,a871),f885(x101952,f885(a871,a871)),x101952),f328(f8(a871,f885(a871,a871),x101952),a326))),f328(f328(f7(x101952,f885(x101952,f885(x101952,x101952)),f885(x101952,f885(x101952,a871))),f328(f328(f8(f885(f885(x101952,x101952),f885(x101952,a871)),f885(f885(x101952,f885(x101952,x101952)),f885(x101952,f885(x101952,a871))),x101952),f8(f885(x101952,x101952),f885(x101952,a871),x101952)),f328(f328(f8(f885(x101952,a871),f885(f885(x101952,x101952),f885(x101952,a871)),x101952),f8(x101952,a871,x101952)),a325))),f242(x101952)))))),f328(f328(f7(x101952,f885(x101952,a871),f885(x101952,a871)),f328(f328(f8(f885(a871,a871),f885(f885(x101952,a871),f885(x101952,a871)),x101952),f8(a871,a871,x101952)),f328(f328(f8(a871,f885(a871,a871),x101952),a326),f328(f328(f7(x101952,f885(x101952,a871),a871),f330(x101952)),x101953)))),f328(f328(f7(x101952,f885(x101952,a871),a871),f330(x101952)),x101951))))))),f328(f328(f242(x101952),f13(x101952,f243(x101952),x101953)),f13(x101952,f243(x101952),x101951)))
% 81.29/80.93 [10196]~P106(x101962)+E(x101961,f193(f885(x101962,a871)))+E(x101963,f193(f885(x101962,a871)))+~P24(f328(f62(x101962),x101961))+~P24(f328(f62(x101962),x101963))+E(f12(x101962,f242(x101962),f328(f249(x101962),f328(f328(f8(f885(x101962,a871),a871,x101962),f88(x101962)),f328(f328(f8(f885(x101962,f885(x101962,a871)),f885(x101962,a871),x101962),f328(f8(f885(x101962,a871),a871,x101962),f88(x101962))),f328(f328(f7(x101962,f885(x101962,f885(x101962,a871)),f885(x101962,f885(x101962,a871))),f328(f328(f8(f885(x101962,f885(f885(x101962,a871),f885(x101962,a871))),f885(f885(x101962,f885(x101962,a871)),f885(x101962,f885(x101962,a871))),x101962),f18(x101962,f885(x101962,a871),f885(x101962,a871))),f328(f328(f8(f885(x101962,f885(x101962,f885(a871,a871))),f885(x101962,f885(f885(x101962,a871),f885(x101962,a871))),x101962),f328(f8(f885(x101962,f885(a871,a871)),f885(f885(x101962,a871),f885(x101962,a871)),x101962),f18(x101962,a871,a871))),f328(f328(f8(f885(x101962,f885(x101962,a871)),f885(x101962,f885(x101962,f885(a871,a871))),x101962),f328(f8(f885(x101962,a871),f885(x101962,f885(a871,a871)),x101962),f328(f8(a871,f885(a871,a871),x101962),a326))),f328(f328(f7(x101962,f885(x101962,f885(x101962,x101962)),f885(x101962,f885(x101962,a871))),f328(f328(f8(f885(f885(x101962,x101962),f885(x101962,a871)),f885(f885(x101962,f885(x101962,x101962)),f885(x101962,f885(x101962,a871))),x101962),f8(f885(x101962,x101962),f885(x101962,a871),x101962)),f328(f328(f8(f885(x101962,a871),f885(f885(x101962,x101962),f885(x101962,a871)),x101962),f8(x101962,a871,x101962)),a325))),f243(x101962)))))),f328(f328(f7(x101962,f885(x101962,a871),f885(x101962,a871)),f328(f328(f8(f885(a871,a871),f885(f885(x101962,a871),f885(x101962,a871)),x101962),f8(a871,a871,x101962)),f328(f328(f8(a871,f885(a871,a871),x101962),a326),f328(f328(f7(x101962,f885(x101962,a871),a871),f330(x101962)),x101963)))),f328(f328(f7(x101962,f885(x101962,a871),a871),f330(x101962)),x101961))))))),f328(f328(f243(x101962),f12(x101962,f242(x101962),x101963)),f12(x101962,f242(x101962),x101961)))
% 81.29/80.93 [7184]~P110(x71843)+E(x71841,x71842)+~E(f328(f328(f258(x71843),x71841),x71844),f328(f328(f258(x71843),x71842),x71844))+~P24(f328(f328(f244(x71843),f2(x71843)),x71842))+~P24(f328(f328(f244(x71843),f2(x71843)),x71841))+~P24(f328(f328(f245(a877),f2(a877)),x71844))
% 81.29/80.93 [7458]~P106(x74582)+E(x74581,f193(f885(x74582,a871)))+~P24(f328(f62(x74582),x74581))+~P24(f328(f328(f330(x74582),x74584),x74581))+P24(f328(f328(f244(x74582),x74583),x74584))+~P24(f328(f328(f244(x74582),x74583),f328(f64(x74582,f242(x74582)),x74581)))
% 81.29/80.93 [7459]~P102(x74592)+E(x74591,f193(f885(x74592,a871)))+~P24(f328(f62(x74592),x74591))+~P24(f328(f328(f330(x74592),x74594),x74591))+P24(f328(f328(f244(x74592),x74593),x74594))+~P24(f328(f328(f244(x74592),x74593),f328(f64(x74592,f107(x74592)),x74591)))
% 81.29/80.93 [7460]~P106(x74602)+E(x74601,f193(f885(x74602,a871)))+~P24(f328(f62(x74602),x74601))+~P24(f328(f328(f330(x74602),x74604),x74601))+P24(f328(f328(f245(x74602),x74603),x74604))+~P24(f328(f328(f245(x74602),x74603),f328(f64(x74602,f242(x74602)),x74601)))
% 81.29/80.93 [7358]E(x73581,f2(a1))+E(f328(f328(f39(a1),x73582),x73581),x73583)+~P24(f328(f328(f244(a1),x73584),f2(a1)))+~E(x73582,f328(f328(f81(a1),f328(f328(f82(a1),x73581),x73583)),x73584))+P24(f328(f328(f245(a1),f2(a1)),x73581))+~P24(f328(f328(f245(a1),x73581),x73584))
% 81.29/80.93 [7373]E(f45(a1,x73732,x73731),x73733)+E(x73731,f2(a1))+~P24(f328(f328(f244(a1),x73733),f2(a1)))+~E(x73732,f328(f328(f81(a1),f328(f328(f82(a1),x73731),x73734)),x73733))+P24(f328(f328(f245(a1),f2(a1)),x73731))+~P24(f328(f328(f245(a1),x73731),x73733))
% 81.29/80.93 [7497]E(x74971,f2(a1))+E(f328(f328(f39(a1),x74972),x74971),x74973)+~E(x74972,f328(f328(f81(a1),f328(f328(f82(a1),x74971),x74973)),x74974))+~P24(f328(f328(f244(a1),f2(a1)),x74974))+~P24(f328(f328(f245(a1),f2(a1)),x74971))+~P24(f328(f328(f245(a1),x74974),x74971))
% 81.29/80.93 [7519]E(f45(a1,x75192,x75191),x75193)+E(x75191,f2(a1))+~E(x75192,f328(f328(f81(a1),f328(f328(f82(a1),x75191),x75194)),x75193))+~P24(f328(f328(f244(a1),f2(a1)),x75193))+~P24(f328(f328(f245(a1),f2(a1)),x75191))+~P24(f328(f328(f245(a1),x75193),x75191))
% 81.29/80.93 [7659]~P106(x76592)+E(x76591,f193(f885(x76592,a871)))+~P24(f328(f62(x76592),x76591))+~P24(f328(f328(f244(x76592),x76594),x76593))+~P24(f328(f328(f330(x76592),x76594),x76591))+P24(f328(f328(f244(x76592),f328(f64(x76592,f242(x76592)),x76591)),x76593))
% 81.29/80.93 [7660]~P106(x76602)+E(x76601,f193(f885(x76602,a871)))+~P24(f328(f62(x76602),x76601))+~P24(f328(f328(f245(x76602),x76604),x76603))+~P24(f328(f328(f330(x76602),x76604),x76601))+P24(f328(f328(f245(x76602),f328(f64(x76602,f242(x76602)),x76601)),x76603))
% 81.29/80.93 [8234]~P24(f328(f328(f244(a1),x82344),f2(a1)))+~E(x82341,f328(f328(f81(a1),f328(f328(f82(a1),x82342),x82343)),x82344))+~P24(f328(f328(f244(a1),f2(a1)),x82344))+~P24(f328(f328(f245(a1),x82344),x82342))+~P24(f328(f328(f245(a1),x82342),x82344))+P24(f328(f49(x82341,x82342),f328(f328(f257(a1,a1),x82343),x82344)))
% 81.29/80.93 [9182]~P60(x91823)+~P60(x91824)+E(x91821,x91822)+~E(f328(f194(f878(x91823)),x91822),f328(f194(f878(x91824)),f56(x91824)))+~E(f328(f194(f878(x91823)),x91821),f328(f194(f878(x91824)),f56(x91824)))+~E(f328(f74(f881(x91823),x91823,x91824,f240(x91823)),f328(f177(x91824,x91823),f328(f328(f181(x91824,x91823),f56(x91824)),x91821))),f328(f74(f881(x91823),x91823,x91824,f240(x91823)),f328(f177(x91824,x91823),f328(f328(f181(x91824,x91823),f56(x91824)),x91822))))
% 81.29/80.93 [8398]~P108(x83981)+P24(f328(f328(f245(f885(x83981,a871)),f299(x83981,x83982,x83983)),f299(x83981,x83984,x83985)))+~P24(f328(f328(f244(x83981),x83984),x83982))+~P24(f328(f328(f244(x83981),x83984),x83985))+~P24(f328(f328(f244(x83981),x83983),x83985))+~P24(f328(f328(f245(x83981),x83983),x83985))
% 81.29/80.93 [8399]~P108(x83991)+P24(f328(f328(f245(f885(x83991,a871)),f299(x83991,x83992,x83993)),f299(x83991,x83994,x83995)))+~P24(f328(f328(f244(x83991),x83993),x83995))+~P24(f328(f328(f244(x83991),x83994),x83995))+~P24(f328(f328(f244(x83991),x83994),x83992))+~P24(f328(f328(f245(x83991),x83994),x83992))
% 81.29/80.93 [9248]P56(x92482,x92483,x92484,x92481)+E(x92481,f193(f885(x92482,a871)))+~P24(f328(f62(x92482),x92484))+~P24(f328(f62(x92482),x92481))+~P24(f328(f328(x92483,f691(x92481,x92484,x92483,x92482)),x92485))+~P24(f328(f328(f330(x92482),x92485),x92481))
% 81.29/80.93 [9396]~E(x93963,x93965)+~P74(x93961)+~P75(x93961)+~P40(x93963)+E(f328(f328(f6(a1,x93961),x93962),x93963),f328(f328(f6(a1,x93961),x93964),x93965))+P24(f328(f328(f244(a1),f2(a1)),f560(x93962,x93964,x93963,x93965,x93961)))
% 81.29/80.93 [9397]~E(x93973,x93975)+~P74(x93971)+~P75(x93971)+~P40(x93973)+E(f328(f328(f9(a1,x93971),x93972),x93973),f328(f328(f9(a1,x93971),x93974),x93975))+P24(f328(f328(f244(a1),f2(a1)),f555(x93972,x93974,x93973,x93975,x93971)))
% 81.29/80.93 [9564]~E(x95645,x95643)+~P74(x95641)+~P75(x95641)+~P40(x95645)+~E(f328(x95642,f560(x95644,x95642,x95645,x95643,x95641)),f328(x95644,f560(x95644,x95642,x95645,x95643,x95641)))+E(f328(f328(f6(a1,x95641),x95642),x95643),f328(f328(f6(a1,x95641),x95644),x95645))
% 81.29/80.93 [9565]~E(x95655,x95653)+~P74(x95651)+~P75(x95651)+~P40(x95655)+~E(f328(x95652,f555(x95654,x95652,x95655,x95653,x95651)),f328(x95654,f555(x95654,x95652,x95655,x95653,x95651)))+E(f328(f328(f9(a1,x95651),x95652),x95653),f328(f328(f9(a1,x95651),x95654),x95655))
% 81.29/80.93 [9651]~P80(x96513)+E(f328(x96511,x96512),f2(x96513))+~E(f328(f328(f6(x96514,x96513),x96511),x96515),f2(x96513))+~P24(f328(f62(x96514),x96515))+P24(f328(f328(f330(x96514),f500(x96512,x96511,x96515,x96514,x96513)),x96515))+~P24(f328(f328(f330(x96514),x96512),x96515))
% 81.29/80.93 [9786]~P80(x97863)+E(f328(x97861,x97862),f2(x97863))+~E(f328(f328(f6(x97864,x97863),x97861),x97865),f2(x97863))+~P24(f328(f62(x97864),x97865))+~P24(f328(f328(f330(x97864),x97862),x97865))+~P24(f328(f328(f244(x97863),f2(x97863)),f328(x97861,f500(x97862,x97861,x97865,x97864,x97863))))
% 81.29/80.93 [8315]~P134(x83151)+~P24(f328(f328(f244(x83151),x83153),x83155))+~P24(f328(f328(f244(x83151),x83152),x83154))+~P24(f328(f328(f244(x83151),f2(x83151)),x83153))+~P24(f328(f328(f244(x83151),f2(x83151)),x83154))+P24(f328(f328(f244(x83151),f328(f328(f82(x83151),x83152),x83153)),f328(f328(f82(x83151),x83154),x83155)))
% 81.29/80.93 [8316]~P134(x83161)+~P24(f328(f328(f244(x83161),x83163),x83165))+~P24(f328(f328(f244(x83161),x83162),x83164))+~P24(f328(f328(f244(x83161),f2(x83161)),x83163))+~P24(f328(f328(f244(x83161),f2(x83161)),x83162))+P24(f328(f328(f244(x83161),f328(f328(f82(x83161),x83162),x83163)),f328(f328(f82(x83161),x83164),x83165)))
% 81.29/80.93 [8317]~P64(x83171)+~P24(f328(f328(f245(x83171),f2(x83171)),x83175))+~P24(f328(f328(f244(x83171),x83175),x83173))+~P24(f328(f328(f244(x83171),x83172),x83174))+~P24(f328(f328(f244(x83171),f2(x83171)),x83172))+P24(f328(f328(f244(x83171),f328(f328(f286(x83171),x83172),x83173)),f328(f328(f286(x83171),x83174),x83175)))
% 81.29/80.93 [8318]~P127(x83181)+~P24(f328(f328(f244(x83181),x83183),x83185))+~P24(f328(f328(f244(x83181),f2(x83181)),x83182))+~P24(f328(f328(f245(x83181),x83182),x83184))+~P24(f328(f328(f245(x83181),f2(x83181)),x83183))+P24(f328(f328(f245(x83181),f328(f328(f82(x83181),x83182),x83183)),f328(f328(f82(x83181),x83184),x83185)))
% 81.29/80.93 [8319]~P127(x83191)+~P24(f328(f328(f244(x83191),x83192),x83194))+~P24(f328(f328(f244(x83191),f2(x83191)),x83193))+~P24(f328(f328(f245(x83191),x83193),x83195))+~P24(f328(f328(f245(x83191),f2(x83191)),x83192))+P24(f328(f328(f245(x83191),f328(f328(f82(x83191),x83192),x83193)),f328(f328(f82(x83191),x83194),x83195)))
% 81.29/80.93 [8320]~P127(x83201)+~P24(f328(f328(f244(x83201),f2(x83201)),x83203))+~P24(f328(f328(f244(x83201),f2(x83201)),x83202))+~P24(f328(f328(f245(x83201),x83203),x83205))+~P24(f328(f328(f245(x83201),x83202),x83204))+P24(f328(f328(f245(x83201),f328(f328(f82(x83201),x83202),x83203)),f328(f328(f82(x83201),x83204),x83205)))
% 81.29/80.93 [8321]~P127(x83211)+~P24(f328(f328(f244(x83211),f2(x83211)),x83213))+~P24(f328(f328(f245(x83211),x83213),x83215))+~P24(f328(f328(f245(x83211),x83212),x83214))+~P24(f328(f328(f245(x83211),f2(x83211)),x83214))+P24(f328(f328(f245(x83211),f328(f328(f82(x83211),x83212),x83213)),f328(f328(f82(x83211),x83214),x83215)))
% 81.29/80.93 [8322]~P64(x83221)+~P24(f328(f328(f244(x83221),x83225),x83223))+~P24(f328(f328(f244(x83221),f2(x83221)),x83222))+~P24(f328(f328(f245(x83221),x83222),x83224))+~P24(f328(f328(f245(x83221),f2(x83221)),x83225))+P24(f328(f328(f245(x83221),f328(f328(f286(x83221),x83222),x83223)),f328(f328(f286(x83221),x83224),x83225)))
% 81.29/80.93 [8323]~P64(x83231)+~P24(f328(f328(f244(x83231),x83232),x83234))+~P24(f328(f328(f245(x83231),x83235),x83233))+~P24(f328(f328(f245(x83231),f2(x83231)),x83235))+~P24(f328(f328(f245(x83231),f2(x83231)),x83232))+P24(f328(f328(f245(x83231),f328(f328(f286(x83231),x83232),x83233)),f328(f328(f286(x83231),x83234),x83235)))
% 81.29/80.93 [9690]~P84(x96905)+~P74(x96905)+E(x96901,f193(f885(x96902,a871)))+~P24(f328(f62(x96902),x96901))+P24(f328(f328(f330(x96902),f747(x96903,x96904,x96901,x96902,x96905)),x96901))+P24(f328(f328(f245(x96905),f328(f328(f6(x96902,x96905),x96904),x96901)),f328(f328(f6(x96902,x96905),x96903),x96901)))
% 81.29/80.93 [9807]~P86(x98071)+~P74(x98071)+~P24(f328(f62(x98072),x98075))+~P24(f328(f328(f244(x98071),f2(x98071)),f328(x98073,f839(x98073,x98074,x98075,x98072,x98071))))+P24(f328(f328(f244(x98071),f328(f328(f6(x98072,x98071),x98073),x98074)),f328(f328(f6(x98072,x98071),x98073),x98075)))+~P24(f328(f328(f244(f885(x98072,a871)),x98074),x98075))
% 81.29/80.93 [9978]~P84(x99783)+~P74(x99783)+E(x99781,f193(f885(x99782,a871)))+~P24(f328(f62(x99782),x99781))+~P24(f328(f328(f245(x99783),f328(x99784,f747(x99785,x99784,x99781,x99782,x99783))),f328(x99785,f747(x99785,x99784,x99781,x99782,x99783))))+P24(f328(f328(f245(x99783),f328(f328(f6(x99782,x99783),x99784),x99781)),f328(f328(f6(x99782,x99783),x99785),x99781)))
% 81.29/80.93 [7043]~P13(x70432,x70435,x70434)+E(x70431,f193(f885(x70432,a871)))+E(x70433,f193(f885(x70432,a871)))+~P24(f328(f62(x70432),x70431))+~P24(f328(f62(x70432),x70433))+E(f328(x70434,f328(f328(f116(f885(x70432,a871)),x70433),x70431)),f328(f328(x70435,f328(x70434,x70433)),f328(x70434,x70431)))
% 81.29/80.93 [7625]~P146(x76251,x76254,x76253)+P24(f328(x76251,x76252))+~P24(f328(f328(f245(a1),x76254),f2(a1)))+~P24(f328(f328(f244(a1),x76255),f2(a1)))+~E(x76253,f328(f328(f81(a1),f328(f328(f82(a1),x76254),x76252)),x76255))+~P24(f328(f328(f245(a1),x76254),x76255))
% 81.29/80.93 [7626]~P145(x76261,x76264,x76263)+P24(f328(x76261,x76262))+~P24(f328(f328(f245(a1),x76264),f2(a1)))+~P24(f328(f328(f244(a1),x76262),f2(a1)))+~E(x76263,f328(f328(f81(a1),f328(f328(f82(a1),x76264),x76265)),x76262))+~P24(f328(f328(f245(a1),x76264),x76262))
% 81.29/80.93 [7668]~P146(x76681,x76684,x76683)+P24(f328(x76681,x76682))+~E(x76683,f328(f328(f81(a1),f328(f328(f82(a1),x76684),x76682)),x76685))+~P24(f328(f328(f244(a1),f2(a1)),x76685))+~P24(f328(f328(f245(a1),f2(a1)),x76684))+~P24(f328(f328(f245(a1),x76685),x76684))
% 81.29/80.93 [7669]~P145(x76691,x76694,x76693)+P24(f328(x76691,x76692))+~E(x76693,f328(f328(f81(a1),f328(f328(f82(a1),x76694),x76695)),x76692))+~P24(f328(f328(f244(a1),f2(a1)),x76692))+~P24(f328(f328(f245(a1),f2(a1)),x76694))+~P24(f328(f328(f245(a1),x76692),x76694))
% 81.29/80.93 [8612]P24(f328(f328(x86121,x86122),x86123))+~P24(f328(f328(x86121,f328(f328(f39(a1),x86124),x86125)),f45(a1,x86124,x86125)))+~P24(f328(f328(f245(a1),x86125),f2(a1)))+~P24(f328(f328(f244(a1),x86123),f2(a1)))+~E(x86124,f328(f328(f81(a1),f328(f328(f82(a1),x86125),x86122)),x86123))+~P24(f328(f328(f245(a1),x86125),x86123))
% 81.29/80.93 [8621]P24(f328(f328(x86211,x86212),x86213))+~P24(f328(f328(x86211,f328(f328(f39(a1),x86214),x86215)),f45(a1,x86214,x86215)))+~E(x86214,f328(f328(f81(a1),f328(f328(f82(a1),x86215),x86212)),x86213))+~P24(f328(f328(f244(a1),f2(a1)),x86213))+~P24(f328(f328(f245(a1),f2(a1)),x86215))+~P24(f328(f328(f245(a1),x86213),x86215))
% 81.29/80.93 [8857]E(x88571,x88572)+~P53(x88573,x88575,x88574)+~P24(f328(f328(f330(x88573),x88572),x88575))+~P24(f328(f328(f330(x88573),x88571),x88575))+P24(f328(f328(f330(f884(x88573,x88573)),f328(f328(f257(x88573,x88573),x88571),x88572)),x88574))+P24(f328(f328(f330(f884(x88573,x88573)),f328(f328(f257(x88573,x88573),x88572),x88571)),x88574))
% 81.29/80.93 [9717]~P86(x97175)+~P74(x97175)+~P24(f328(f62(x97171),x97174))+P24(f328(f328(f244(x97175),f328(f328(f6(x97171,x97175),x97172),x97173)),f328(f328(f6(x97171,x97175),x97172),x97174)))+~P24(f328(f328(f244(f885(x97171,a871)),x97173),x97174))+P24(f328(f328(f330(x97171),f839(x97172,x97173,x97174,x97171,x97175)),f328(f328(f22(f885(x97171,a871)),x97174),x97173)))
% 81.29/80.93 [9814]E(x98141,f193(f885(x98142,a871)))+~P24(f328(f62(x98142),x98143))+~P24(f328(f62(x98142),x98141))+P24(f328(f328(f330(f884(f885(x98142,a871),f885(x98142,a871))),f328(f328(f257(f885(x98142,a871),f885(x98142,a871)),x98143),x98141)),f319(x98142,x98144)))+~P24(f328(f328(f330(x98142),x98145),x98141))+~P24(f328(f328(f330(f884(x98142,x98142)),f328(f328(f257(x98142,x98142),f693(x98144,x98141,x98143,x98142)),x98145)),x98144))
% 81.29/80.93 [9815]E(x98151,f193(f885(x98152,a871)))+~P24(f328(f62(x98152),x98153))+~P24(f328(f62(x98152),x98151))+P24(f328(f328(f330(f884(f885(x98152,a871),f885(x98152,a871))),f328(f328(f257(f885(x98152,a871),f885(x98152,a871)),x98153),x98151)),f319(x98152,x98154)))+~P24(f328(f328(f330(x98152),x98155),x98151))+~P24(f328(f328(f330(f884(x98152,x98152)),f328(f328(f257(x98152,x98152),f752(x98154,x98151,x98153,x98152)),x98155)),x98154))
% 81.29/80.93 [9983]~P80(x99831)+~E(f328(f328(f6(x99835,x99831),x99832),x99836),x99834)+~P24(f328(f62(x99835),x99836))+P24(f328(f328(f330(x99835),f501(x99833,x99834,x99832,x99836,x99835,x99831)),x99836))+P24(f328(f328(f244(x99831),f328(x99832,x99833)),x99834))+~P24(f328(f328(f330(x99835),x99833),x99836))
% 81.29/80.93 [10031]~P80(x100311)+~E(f328(f328(f6(x100315,x100311),x100312),x100316),x100314)+~P24(f328(f62(x100315),x100316))+~P24(f328(f328(f330(x100315),x100313),x100316))+~P24(f328(f328(f244(x100311),f2(x100311)),f328(x100312,f501(x100313,x100314,x100312,x100316,x100315,x100311))))+P24(f328(f328(f244(x100311),f328(x100312,x100313)),x100314))
% 81.29/80.93 [10145]~E(x101455,x101458)+~E(x101454,x101457)+~P107(x101451)+~P74(x101452)+E(f328(f328(f6(x101451,x101452),x101453),f328(f298(x101451,x101454),x101455)),f328(f328(f6(x101451,x101452),x101456),f328(f298(x101451,x101457),x101458)))+P24(f328(f328(f244(x101451),x101454),f476(x101453,x101456,x101455,x101458,x101454,x101457,x101451,x101452)))
% 81.29/80.93 [10161]~E(x101617,x101614)+~E(x101618,x101615)+~P107(x101611)+~P74(x101612)+~E(f328(x101613,f476(x101616,x101613,x101618,x101615,x101617,x101614,x101611,x101612)),f328(x101616,f476(x101616,x101613,x101618,x101615,x101617,x101614,x101611,x101612)))+E(f328(f328(f6(x101611,x101612),x101613),f328(f298(x101611,x101614),x101615)),f328(f328(f6(x101611,x101612),x101616),f328(f298(x101611,x101617),x101618)))
% 81.29/80.93 [10163]~E(x101634,x101637)+~E(x101635,x101638)+~P107(x101631)+~P74(x101632)+E(f328(f328(f6(x101631,x101632),x101633),f328(f298(x101631,x101634),x101635)),f328(f328(f6(x101631,x101632),x101636),f328(f298(x101631,x101637),x101638)))+P24(f328(f328(f245(x101631),f476(x101633,x101636,x101635,x101638,x101634,x101637,x101631,x101632)),x101635))
% 81.29/80.93 [9820]~P6(x98205,x98209,x98206)+~P6(x98201,x982010,x98203)+~P10(x98201,x98205,f885(x98202,a871),x98203,x98206,x98208)+~P24(f328(f328(f330(x98205),x98207),x98209))+~P24(f328(f328(f330(x98201),x98204),x982010))+E(f328(f328(f43(x98201,f885(x98202,a871)),f328(f282(x98201,x98201,x98203),f328(f328(f306(x98201),x98204),f193(f885(x98201,a871))))),f328(f328(f8(f885(x98205,f885(x98202,a871)),f885(x98202,a871),x98201),f328(f43(x98205,f885(x98202,a871)),f328(f282(x98205,x98205,x98206),f328(f328(f306(x98205),x98207),f193(f885(x98205,a871)))))),x98208)),f328(f328(x98208,x98204),x98207))
% 81.29/80.93 [5585]~P106(x55853)+~P29(x55853,x55852)+~P29(x55853,x55851)+E(x55851,x55852)+~E(f328(f171(x55853),x55851),f328(f171(x55853),x55852))+~P24(f328(f136(x55853),x55852))+~P24(f328(f136(x55853),x55851))
% 81.29/80.93 [4922]~P136(x49222)+~P125(x49222)+~P126(x49222)+~P116(x49222)+~E(x49223,f2(x49222))+E(x49221,f2(a877))+E(f328(f328(f258(x49222),x49223),x49221),f2(x49222))
% 81.29/80.93 [9123]E(x91231,f2(a877))+~E(x91232,f328(f328(f81(a877),f328(f328(f82(a877),f328(f256(a877,a877),x91233)),x91231)),f328(f266(a877,a877),x91233)))+P24(f328(f48(x91232,x91231),x91233))+~P24(f328(f328(f244(a877),f328(f266(a877,a877),x91233)),f2(a877)))+~P24(f328(f328(f244(a877),f2(a877)),f328(f266(a877,a877),x91233)))+~P24(f328(f328(f245(a877),x91231),f328(f266(a877,a877),x91233)))+~P24(f328(f328(f245(a877),f328(f266(a877,a877),x91233)),x91231))
% 81.29/80.93 [9132]~E(f328(f256(a877,a877),x91323),f2(a877))+~E(x91321,f328(f328(f81(a877),f328(f328(f82(a877),f328(f256(a877,a877),x91323)),x91322)),f328(f266(a877,a877),x91323)))+P24(f328(f48(x91321,x91322),x91323))+~P24(f328(f328(f244(a877),f328(f266(a877,a877),x91323)),f2(a877)))+~P24(f328(f328(f244(a877),f2(a877)),f328(f266(a877,a877),x91323)))+~P24(f328(f328(f245(a877),x91322),f328(f266(a877,a877),x91323)))+~P24(f328(f328(f245(a877),f328(f266(a877,a877),x91323)),x91322))
% 81.29/80.93 [7980]~P71(x79802)+E(x79801,f193(f885(x79802,a871)))+E(x79803,f193(f885(x79802,a871)))+~P24(f328(f62(x79802),x79801))+~P24(f328(f62(x79802),x79803))+~E(f328(f328(f107(f885(x79802,a871)),x79803),x79801),f193(f885(x79802,a871)))+E(f328(f328(f82(x79802),f328(f64(x79802,f82(x79802)),x79803)),f328(f64(x79802,f82(x79802)),x79801)),f328(f64(x79802,f82(x79802)),f328(f328(f116(f885(x79802,a871)),x79803),x79801)))
% 81.29/80.93 [7764]E(x77641,f2(a1))+E(f328(f328(f39(a1),x77642),x77641),x77643)+~P24(f328(f328(f244(a1),x77644),f2(a1)))+~E(x77642,f328(f328(f81(a1),f328(f328(f82(a1),x77641),x77643)),x77644))+~P24(f328(f328(f244(a1),f2(a1)),x77644))+~P24(f328(f328(f245(a1),x77644),x77641))+~P24(f328(f328(f245(a1),x77641),x77644))
% 81.29/80.93 [7771]E(f45(a1,x77712,x77711),x77713)+E(x77711,f2(a1))+~P24(f328(f328(f244(a1),x77713),f2(a1)))+~E(x77712,f328(f328(f81(a1),f328(f328(f82(a1),x77711),x77714)),x77713))+~P24(f328(f328(f244(a1),f2(a1)),x77713))+~P24(f328(f328(f245(a1),x77713),x77711))+~P24(f328(f328(f245(a1),x77711),x77713))
% 81.29/80.93 [7676]~P14(x76762,x76765,x76764)+E(x76761,f193(f885(x76762,a871)))+E(x76763,f193(f885(x76762,a871)))+~P24(f328(f62(x76762),x76761))+~P24(f328(f62(x76762),x76763))+~E(f328(f328(f107(f885(x76762,a871)),x76763),x76761),f193(f885(x76762,a871)))+E(f328(x76764,f328(f328(f116(f885(x76762,a871)),x76763),x76761)),f328(f328(x76765,f328(x76764,x76763)),f328(x76764,x76761)))
% 81.29/80.93 [9369]~P21(x93693,x93691,x93695,x93694)+~P21(x93691,x93693,x93696,x93692)+E(f328(f38(x93691),x93692),f328(f38(x93693),x93694))+~P24(f328(f62(x93693),x93694))+~P24(f328(f62(x93691),x93692))+~P24(f328(f328(f244(f885(x93693,a871)),f328(f307(x93691,x93693,x93696),x93692)),x93694))+~P24(f328(f328(f244(f885(x93691,a871)),f328(f307(x93693,x93691,x93695),x93694)),x93692))
% 81.29/80.93 [9313]~P24(f328(f328(f245(a1),f328(f328(f81(a1),f328(f328(f82(a1),x93135),x93131)),x93136)),f2(a1)))+~E(f328(f328(f81(a1),f328(f328(f82(a1),x93133),x93132)),x93134),f328(f328(f81(a1),f328(f328(f82(a1),x93135),x93131)),x93136))+~P24(f328(f328(f244(a1),f2(a1)),x93136))+~P24(f328(f328(f245(a1),f2(a1)),x93135))+~P24(f328(f328(f244(a1),x93135),x93133))+~P24(f328(f328(f245(a1),x93134),x93133))+P24(f328(f328(f244(a1),x93131),x93132))
% 81.29/80.93 [9076]~E(f328(f328(f81(a1),f328(f328(f82(a1),x90763),x90761)),x90764),f328(f328(f81(a1),f328(f328(f82(a1),x90765),x90762)),x90766))+~P24(f328(f328(f244(a1),f2(a1)),x90764))+~P24(f328(f328(f245(a1),f2(a1)),x90765))+~P24(f328(f328(f244(a1),x90765),x90763))+~P24(f328(f328(f245(a1),x90766),x90765))+P24(f328(f328(f244(a1),x90761),x90762))+~P24(f328(f328(f244(a1),f2(a1)),f328(f328(f81(a1),f328(f328(f82(a1),x90765),x90762)),x90766)))
% 81.29/80.93 [9254]~P129(x92541)+~E(f328(f328(f81(x92541),x92542),x92544),f79(x92541))+~P24(f328(f328(f244(x92541),x92545),x92546))+~P24(f328(f328(f244(x92541),x92543),x92546))+~P24(f328(f328(f244(x92541),f2(x92541)),x92544))+~P24(f328(f328(f244(x92541),f2(x92541)),x92542))+P24(f328(f328(f244(x92541),f328(f328(f81(x92541),f328(f328(f82(x92541),x92542),x92543)),f328(f328(f82(x92541),x92544),x92545))),x92546))
% 81.29/80.93 [9255]~P130(x92551)+~E(f328(f328(f81(x92551),x92552),x92554),f79(x92551))+~P24(f328(f328(f244(x92551),f2(x92551)),x92554))+~P24(f328(f328(f244(x92551),f2(x92551)),x92552))+~P24(f328(f328(f245(x92551),x92555),x92556))+~P24(f328(f328(f245(x92551),x92553),x92556))+P24(f328(f328(f245(x92551),f328(f328(f81(x92551),f328(f328(f82(x92551),x92552),x92553)),f328(f328(f82(x92551),x92554),x92555))),x92556))
% 81.29/80.93 [10076]~P6(x100767,x100766,x100765)+E(x100761,x100762)+~P9(x100767,f885(x100764,a871),x100765,x100763)+E(f328(x100763,f543(x100761,x100762,x100763,x100764,x100765,x100766,x100767)),f328(x100763,f544(x100761,x100762,x100763,x100764,x100765,x100766,x100767)))+~E(f328(f328(f43(x100767,f885(x100764,a871)),x100761),x100763),f328(f328(f43(x100767,f885(x100764,a871)),x100762),x100763))+~P24(f328(f328(f330(f885(x100767,a871)),x100762),f328(f328(f61(x100767),x100766),x100765)))+~P24(f328(f328(f330(f885(x100767,a871)),x100761),f328(f328(f61(x100767),x100766),x100765)))
% 81.29/80.93 [10111]~P6(x101113,x101117,x101116)+E(x101111,x101112)+~P9(x101113,f885(x101115,a871),x101116,x101114)+~E(f328(f328(f43(x101113,f885(x101115,a871)),x101111),x101114),f328(f328(f43(x101113,f885(x101115,a871)),x101112),x101114))+P24(f328(f328(f330(x101113),f544(x101111,x101112,x101114,x101115,x101116,x101117,x101113)),x101117))+~P24(f328(f328(f330(f885(x101113,a871)),x101112),f328(f328(f61(x101113),x101117),x101116)))+~P24(f328(f328(f330(f885(x101113,a871)),x101111),f328(f328(f61(x101113),x101117),x101116)))
% 81.29/80.93 [10112]~P6(x101123,x101127,x101126)+E(x101121,x101122)+~P9(x101123,f885(x101125,a871),x101126,x101124)+~E(f328(f328(f43(x101123,f885(x101125,a871)),x101121),x101124),f328(f328(f43(x101123,f885(x101125,a871)),x101122),x101124))+P24(f328(f328(f330(x101123),f543(x101121,x101122,x101124,x101125,x101126,x101127,x101123)),x101127))+~P24(f328(f328(f330(f885(x101123,a871)),x101122),f328(f328(f61(x101123),x101127),x101126)))+~P24(f328(f328(f330(f885(x101123,a871)),x101121),f328(f328(f61(x101123),x101127),x101126)))
% 81.29/80.93 [10178]E(x101781,x101782)+~P6(x101783,x101786,x101787)+~P9(x101783,f885(x101784,a871),x101787,x101785)+~E(f328(f328(f43(x101783,f885(x101784,a871)),x101781),x101785),f328(f328(f43(x101783,f885(x101784,a871)),x101782),x101785))+~P24(f328(f328(f330(f884(x101783,x101783)),f328(f328(f257(x101783,x101783),f544(x101781,x101782,x101785,x101784,x101787,x101786,x101783)),f543(x101781,x101782,x101785,x101784,x101787,x101786,x101783))),x101787))+~P24(f328(f328(f330(f885(x101783,a871)),x101782),f328(f328(f61(x101783),x101786),x101787)))+~P24(f328(f328(f330(f885(x101783,a871)),x101781),f328(f328(f61(x101783),x101786),x101787)))
% 81.29/80.93 [9075]~P6(x90751,x90757,x90754)+~E(x90755,x90756)+~P24(f328(f328(f330(x90751),x90753),x90756))+~P24(f328(f328(f330(x90751),x90752),x90755))+~P24(f328(f328(f330(f885(x90751,a871)),x90756),f328(f328(f61(x90751),x90757),x90754)))+~P24(f328(f328(f330(f885(x90751,a871)),x90755),f328(f328(f61(x90751),x90757),x90754)))+P24(f328(f328(f330(f884(x90751,x90751)),f328(f328(f257(x90751,x90751),x90752),x90753)),x90754))
% 81.29/80.93 [9210]E(x92101,x92102)+~P6(x92103,x92104,x92105)+~P24(f328(f328(f330(x92103),x92106),x92102))+~P24(f328(f328(f330(x92103),x92107),x92101))+~P24(f328(f328(f330(f885(x92103,a871)),x92102),f328(f328(f61(x92103),x92104),x92105)))+~P24(f328(f328(f330(f885(x92103,a871)),x92101),f328(f328(f61(x92103),x92104),x92105)))+~P24(f328(f328(f330(f884(x92103,x92103)),f328(f328(f257(x92103,x92103),x92107),x92106)),x92105))
% 81.29/80.93 [10200]~P6(x102009,x102008,x102007)+~P6(x102001,x1020011,x1020010)+~P10(x102001,x102009,f885(x102006,a871),x1020010,x102007,x102005)+P24(f328(f328(f330(x102001),f546(x102002,x102003,x102004,x102005,x102006,x102007,x102008,x102009,x1020010,x1020011,x102001)),x1020011))+~P24(f328(f328(f330(f885(x102009,a871)),x102003),f328(f328(f61(x102009),x102008),x102007)))+~P24(f328(f328(f330(f885(x102001,a871)),x102004),f328(f328(f61(x102001),x1020011),x1020010)))+P24(f328(f328(f330(f885(x102006,a871)),f328(f328(f43(x102001,f885(x102006,a871)),x102004),f328(f328(f8(f885(x102009,f885(x102006,a871)),f885(x102006,a871),x102001),f328(f43(x102009,f885(x102006,a871)),x102003)),x102005))),x102002))
% 81.29/80.93 [10201]~P6(x1020111,x1020110,x102019)+~P6(x102011,x102018,x102017)+~P10(x1020111,x102011,f885(x102016,a871),x102019,x102017,x102015)+P24(f328(f328(f330(x102011),f547(x102012,x102013,x102014,x102015,x102016,x102017,x102018,x102011,x102019,x1020110,x1020111)),x102018))+~P24(f328(f328(f330(f885(x1020111,a871)),x102014),f328(f328(f61(x1020111),x1020110),x102019)))+~P24(f328(f328(f330(f885(x102011,a871)),x102013),f328(f328(f61(x102011),x102018),x102017)))+P24(f328(f328(f330(f885(x102016,a871)),f328(f328(f43(x1020111,f885(x102016,a871)),x102014),f328(f328(f8(f885(x102011,f885(x102016,a871)),f885(x102016,a871),x1020111),f328(f43(x102011,f885(x102016,a871)),x102013)),x102015))),x102012))
% 81.29/80.93 [10204]~P6(x102042,x102048,x102049)+~P6(x102044,x1020410,x1020411)+~P10(x102042,x102044,f885(x102041,a871),x102049,x1020411,x102046)+~P24(f328(f328(f330(f885(x102042,a871)),x102043),f328(f328(f61(x102042),x102048),x102049)))+~P24(f328(f328(f330(f885(x102044,a871)),x102045),f328(f328(f61(x102044),x1020410),x1020411)))+~P24(f328(f328(f330(f885(x102041,a871)),f328(f328(x102046,f546(x102047,x102045,x102043,x102046,x102041,x1020411,x1020410,x102044,x102049,x102048,x102042)),f547(x102047,x102045,x102043,x102046,x102041,x1020411,x1020410,x102044,x102049,x102048,x102042))),x102047))+P24(f328(f328(f330(f885(x102041,a871)),f328(f328(f43(x102042,f885(x102041,a871)),x102043),f328(f328(f8(f885(x102044,f885(x102041,a871)),f885(x102041,a871),x102042),f328(f43(x102044,f885(x102041,a871)),x102045)),x102046))),x102047))
% 81.29/80.93 [9110]E(x91101,x91102)+~P106(x91104)+~P21(x91103,x91104,x91105,f328(f328(f116(f885(x91103,a871)),f328(f171(x91103),x91101)),f328(f171(x91103),x91102)))+~E(f328(f171(x91103),x91101),f328(f171(x91103),x91102))+~P29(x91104,f328(f328(f153(x91103,x91104),x91105),x91102))+~P29(x91104,f328(f328(f153(x91103,x91104),x91105),x91101))+~P24(f328(f136(x91104),f328(f328(f153(x91103,x91104),x91105),x91102)))+~P24(f328(f136(x91104),f328(f328(f153(x91103,x91104),x91105),x91101)))
% 81.29/80.93 %EqnAxiom
% 81.29/80.93 [1]E(x11,x11)
% 81.29/80.93 [2]E(x22,x21)+~E(x21,x22)
% 81.29/80.93 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 81.29/80.93 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 81.29/80.93 [5]~E(x51,x52)+E(f106(x51),f106(x52))
% 81.29/80.93 [6]~E(x61,x62)+E(f22(x61),f22(x62))
% 81.29/80.93 [7]~E(x71,x72)+E(f193(x71),f193(x72))
% 81.29/80.93 [8]~E(x81,x82)+E(f328(x81,x83),f328(x82,x83))
% 81.29/80.93 [9]~E(x91,x92)+E(f328(x93,x91),f328(x93,x92))
% 81.29/80.93 [10]~E(x101,x102)+E(f32(x101),f32(x102))
% 81.29/80.93 [11]~E(x111,x112)+E(f38(x111),f38(x112))
% 81.29/80.93 [12]~E(x121,x122)+E(f85(x121),f85(x122))
% 81.29/80.93 [13]~E(x131,x132)+E(f885(x131,x133),f885(x132,x133))
% 81.29/80.93 [14]~E(x141,x142)+E(f885(x143,x141),f885(x143,x142))
% 81.29/80.93 [15]~E(x151,x152)+E(f876(x151),f876(x152))
% 81.29/80.93 [16]~E(x161,x162)+E(f547(x161,x163,x164,x165,x166,x167,x168,x169,x1610,x1611,x1612),f547(x162,x163,x164,x165,x166,x167,x168,x169,x1610,x1611,x1612))
% 81.29/80.93 [17]~E(x171,x172)+E(f547(x173,x171,x174,x175,x176,x177,x178,x179,x1710,x1711,x1712),f547(x173,x172,x174,x175,x176,x177,x178,x179,x1710,x1711,x1712))
% 81.29/80.93 [18]~E(x181,x182)+E(f547(x183,x184,x181,x185,x186,x187,x188,x189,x1810,x1811,x1812),f547(x183,x184,x182,x185,x186,x187,x188,x189,x1810,x1811,x1812))
% 81.29/80.93 [19]~E(x191,x192)+E(f547(x193,x194,x195,x191,x196,x197,x198,x199,x1910,x1911,x1912),f547(x193,x194,x195,x192,x196,x197,x198,x199,x1910,x1911,x1912))
% 81.29/80.93 [20]~E(x201,x202)+E(f547(x203,x204,x205,x206,x201,x207,x208,x209,x2010,x2011,x2012),f547(x203,x204,x205,x206,x202,x207,x208,x209,x2010,x2011,x2012))
% 81.29/80.93 [21]~E(x211,x212)+E(f547(x213,x214,x215,x216,x217,x211,x218,x219,x2110,x2111,x2112),f547(x213,x214,x215,x216,x217,x212,x218,x219,x2110,x2111,x2112))
% 81.29/80.93 [22]~E(x221,x222)+E(f547(x223,x224,x225,x226,x227,x228,x221,x229,x2210,x2211,x2212),f547(x223,x224,x225,x226,x227,x228,x222,x229,x2210,x2211,x2212))
% 81.29/80.93 [23]~E(x231,x232)+E(f547(x233,x234,x235,x236,x237,x238,x239,x231,x2310,x2311,x2312),f547(x233,x234,x235,x236,x237,x238,x239,x232,x2310,x2311,x2312))
% 81.29/80.93 [24]~E(x241,x242)+E(f547(x243,x244,x245,x246,x247,x248,x249,x2410,x241,x2411,x2412),f547(x243,x244,x245,x246,x247,x248,x249,x2410,x242,x2411,x2412))
% 81.29/80.93 [25]~E(x251,x252)+E(f547(x253,x254,x255,x256,x257,x258,x259,x2510,x2511,x251,x2512),f547(x253,x254,x255,x256,x257,x258,x259,x2510,x2511,x252,x2512))
% 81.29/80.93 [26]~E(x261,x262)+E(f547(x263,x264,x265,x266,x267,x268,x269,x2610,x2611,x2612,x261),f547(x263,x264,x265,x266,x267,x268,x269,x2610,x2611,x2612,x262))
% 81.29/80.93 [27]~E(x271,x272)+E(f107(x271),f107(x272))
% 81.29/80.93 [28]~E(x281,x282)+E(f242(x281),f242(x282))
% 81.29/80.93 [29]~E(x291,x292)+E(f116(x291),f116(x292))
% 81.29/80.93 [30]~E(x301,x302)+E(f243(x301),f243(x302))
% 81.29/80.93 [31]~E(x311,x312)+E(f108(x311),f108(x312))
% 81.29/80.93 [32]~E(x321,x322)+E(f35(x321),f35(x322))
% 81.29/80.93 [33]~E(x331,x332)+E(f79(x331),f79(x332))
% 81.29/80.93 [34]~E(x341,x342)+E(f82(x341),f82(x342))
% 81.29/80.93 [35]~E(x351,x352)+E(f546(x351,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512),f546(x352,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512))
% 81.29/80.93 [36]~E(x361,x362)+E(f546(x363,x361,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612),f546(x363,x362,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612))
% 81.29/80.93 [37]~E(x371,x372)+E(f546(x373,x374,x371,x375,x376,x377,x378,x379,x3710,x3711,x3712),f546(x373,x374,x372,x375,x376,x377,x378,x379,x3710,x3711,x3712))
% 81.29/80.93 [38]~E(x381,x382)+E(f546(x383,x384,x385,x381,x386,x387,x388,x389,x3810,x3811,x3812),f546(x383,x384,x385,x382,x386,x387,x388,x389,x3810,x3811,x3812))
% 81.29/80.93 [39]~E(x391,x392)+E(f546(x393,x394,x395,x396,x391,x397,x398,x399,x3910,x3911,x3912),f546(x393,x394,x395,x396,x392,x397,x398,x399,x3910,x3911,x3912))
% 81.29/80.93 [40]~E(x401,x402)+E(f546(x403,x404,x405,x406,x407,x401,x408,x409,x4010,x4011,x4012),f546(x403,x404,x405,x406,x407,x402,x408,x409,x4010,x4011,x4012))
% 81.29/80.93 [41]~E(x411,x412)+E(f546(x413,x414,x415,x416,x417,x418,x411,x419,x4110,x4111,x4112),f546(x413,x414,x415,x416,x417,x418,x412,x419,x4110,x4111,x4112))
% 81.29/80.93 [42]~E(x421,x422)+E(f546(x423,x424,x425,x426,x427,x428,x429,x421,x4210,x4211,x4212),f546(x423,x424,x425,x426,x427,x428,x429,x422,x4210,x4211,x4212))
% 81.29/80.93 [43]~E(x431,x432)+E(f546(x433,x434,x435,x436,x437,x438,x439,x4310,x431,x4311,x4312),f546(x433,x434,x435,x436,x437,x438,x439,x4310,x432,x4311,x4312))
% 81.29/80.93 [44]~E(x441,x442)+E(f546(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x441,x4412),f546(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x442,x4412))
% 81.29/80.93 [45]~E(x451,x452)+E(f546(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x451),f546(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x452))
% 81.29/80.93 [46]~E(x461,x462)+E(f117(x461),f117(x462))
% 81.29/80.93 [47]~E(x471,x472)+E(f330(x471),f330(x472))
% 81.29/80.93 [48]~E(x481,x482)+E(f878(x481),f878(x482))
% 81.29/80.93 [49]~E(x491,x492)+E(f4(x491),f4(x492))
% 81.29/80.93 [50]~E(x501,x502)+E(f62(x501),f62(x502))
% 81.29/80.93 [51]~E(x511,x512)+E(f286(x511),f286(x512))
% 81.29/80.93 [52]~E(x521,x522)+E(f881(x521),f881(x522))
% 81.29/80.93 [53]~E(x531,x532)+E(f167(x531),f167(x532))
% 81.29/80.93 [54]~E(x541,x542)+E(f879(x541),f879(x542))
% 81.29/80.93 [55]~E(x551,x552)+E(f109(x551),f109(x552))
% 81.29/80.93 [56]~E(x561,x562)+E(f245(x561),f245(x562))
% 81.29/80.93 [57]~E(x571,x572)+E(f188(x571,x573),f188(x572,x573))
% 81.29/80.93 [58]~E(x581,x582)+E(f188(x583,x581),f188(x583,x582))
% 81.29/80.93 [59]~E(x591,x592)+E(f257(x591,x593),f257(x592,x593))
% 81.29/80.93 [60]~E(x601,x602)+E(f257(x603,x601),f257(x603,x602))
% 81.29/80.93 [61]~E(x611,x612)+E(f80(x611),f80(x612))
% 81.29/80.93 [62]~E(x621,x622)+E(f7(x621,x623,x624),f7(x622,x623,x624))
% 81.29/80.93 [63]~E(x631,x632)+E(f7(x633,x631,x634),f7(x633,x632,x634))
% 81.29/80.93 [64]~E(x641,x642)+E(f7(x643,x644,x641),f7(x643,x644,x642))
% 81.29/80.93 [65]~E(x651,x652)+E(f194(x651),f194(x652))
% 81.29/80.93 [66]~E(x661,x662)+E(f244(x661),f244(x662))
% 81.29/80.93 [67]~E(x671,x672)+E(f415(x671,x673,x674),f415(x672,x673,x674))
% 81.29/80.93 [68]~E(x681,x682)+E(f415(x683,x681,x684),f415(x683,x682,x684))
% 81.29/80.93 [69]~E(x691,x692)+E(f415(x693,x694,x691),f415(x693,x694,x692))
% 81.29/80.93 [70]~E(x701,x702)+E(f8(x701,x703,x704),f8(x702,x703,x704))
% 81.29/80.93 [71]~E(x711,x712)+E(f8(x713,x711,x714),f8(x713,x712,x714))
% 81.29/80.93 [72]~E(x721,x722)+E(f8(x723,x724,x721),f8(x723,x724,x722))
% 81.29/80.93 [73]~E(x731,x732)+E(f306(x731),f306(x732))
% 81.29/80.93 [74]~E(x741,x742)+E(f18(x741,x743,x744),f18(x742,x743,x744))
% 81.29/80.93 [75]~E(x751,x752)+E(f18(x753,x751,x754),f18(x753,x752,x754))
% 81.29/80.93 [76]~E(x761,x762)+E(f18(x763,x764,x761),f18(x763,x764,x762))
% 81.29/80.93 [77]~E(x771,x772)+E(f307(x771,x773,x774),f307(x772,x773,x774))
% 81.29/80.93 [78]~E(x781,x782)+E(f307(x783,x781,x784),f307(x783,x782,x784))
% 81.29/80.93 [79]~E(x791,x792)+E(f307(x793,x794,x791),f307(x793,x794,x792))
% 81.29/80.93 [80]~E(x801,x802)+E(f122(x801,x803,x804),f122(x802,x803,x804))
% 81.29/80.93 [81]~E(x811,x812)+E(f122(x813,x811,x814),f122(x813,x812,x814))
% 81.29/80.93 [82]~E(x821,x822)+E(f122(x823,x824,x821),f122(x823,x824,x822))
% 81.29/80.93 [83]~E(x831,x832)+E(f884(x831,x833),f884(x832,x833))
% 81.29/80.93 [84]~E(x841,x842)+E(f884(x843,x841),f884(x843,x842))
% 81.29/80.93 [85]~E(x851,x852)+E(f416(x851,x853,x854),f416(x852,x853,x854))
% 81.29/80.93 [86]~E(x861,x862)+E(f416(x863,x861,x864),f416(x863,x862,x864))
% 81.29/80.93 [87]~E(x871,x872)+E(f416(x873,x874,x871),f416(x873,x874,x872))
% 81.29/80.93 [88]~E(x881,x882)+E(f298(x881,x883),f298(x882,x883))
% 81.29/80.93 [89]~E(x891,x892)+E(f298(x893,x891),f298(x893,x892))
% 81.29/80.93 [90]~E(x901,x902)+E(f45(x901,x903,x904),f45(x902,x903,x904))
% 81.29/80.93 [91]~E(x911,x912)+E(f45(x913,x911,x914),f45(x913,x912,x914))
% 81.29/80.93 [92]~E(x921,x922)+E(f45(x923,x924,x921),f45(x923,x924,x922))
% 81.29/80.93 [93]~E(x931,x932)+E(f6(x931,x933),f6(x932,x933))
% 81.29/80.93 [94]~E(x941,x942)+E(f6(x943,x941),f6(x943,x942))
% 81.29/80.93 [95]~E(x951,x952)+E(f288(x951,x953),f288(x952,x953))
% 81.29/80.93 [96]~E(x961,x962)+E(f288(x963,x961),f288(x963,x962))
% 81.29/80.93 [97]~E(x971,x972)+E(f249(x971),f249(x972))
% 81.29/80.93 [98]~E(x981,x982)+E(f61(x981),f61(x982))
% 81.29/80.93 [99]~E(x991,x992)+E(f127(x991),f127(x992))
% 81.29/80.93 [100]~E(x1001,x1002)+E(f81(x1001),f81(x1002))
% 81.29/80.93 [101]~E(x1011,x1012)+E(f883(x1011,x1013),f883(x1012,x1013))
% 81.29/80.93 [102]~E(x1021,x1022)+E(f883(x1023,x1021),f883(x1023,x1022))
% 81.29/80.93 [103]~E(x1031,x1032)+E(f160(x1031,x1033),f160(x1032,x1033))
% 81.29/80.93 [104]~E(x1041,x1042)+E(f160(x1043,x1041),f160(x1043,x1042))
% 81.29/80.93 [105]~E(x1051,x1052)+E(f337(x1051,x1053,x1054),f337(x1052,x1053,x1054))
% 81.29/80.93 [106]~E(x1061,x1062)+E(f337(x1063,x1061,x1064),f337(x1063,x1062,x1064))
% 81.29/80.93 [107]~E(x1071,x1072)+E(f337(x1073,x1074,x1071),f337(x1073,x1074,x1072))
% 81.29/80.93 [108]~E(x1081,x1082)+E(f146(x1081,x1083),f146(x1082,x1083))
% 81.29/80.93 [109]~E(x1091,x1092)+E(f146(x1093,x1091),f146(x1093,x1092))
% 81.29/80.93 [110]~E(x1101,x1102)+E(f136(x1101),f136(x1102))
% 81.29/80.93 [111]~E(x1111,x1112)+E(f92(x1111),f92(x1112))
% 81.29/80.93 [112]~E(x1121,x1122)+E(f171(x1121),f171(x1122))
% 81.29/80.93 [113]~E(x1131,x1132)+E(f235(x1131,x1133),f235(x1132,x1133))
% 81.29/80.93 [114]~E(x1141,x1142)+E(f235(x1143,x1141),f235(x1143,x1142))
% 81.29/80.93 [115]~E(x1151,x1152)+E(f284(x1151,x1153),f284(x1152,x1153))
% 81.29/80.93 [116]~E(x1161,x1162)+E(f284(x1163,x1161),f284(x1163,x1162))
% 81.29/80.93 [117]~E(x1171,x1172)+E(f119(x1171),f119(x1172))
% 81.29/80.93 [118]~E(x1181,x1182)+E(f176(x1181,x1183,x1184),f176(x1182,x1183,x1184))
% 81.29/80.93 [119]~E(x1191,x1192)+E(f176(x1193,x1191,x1194),f176(x1193,x1192,x1194))
% 81.29/80.93 [120]~E(x1201,x1202)+E(f176(x1203,x1204,x1201),f176(x1203,x1204,x1202))
% 81.29/80.93 [121]~E(x1211,x1212)+E(f120(x1211,x1213),f120(x1212,x1213))
% 81.29/80.93 [122]~E(x1221,x1222)+E(f120(x1223,x1221),f120(x1223,x1222))
% 81.29/80.93 [123]~E(x1231,x1232)+E(f153(x1231,x1233),f153(x1232,x1233))
% 81.29/80.93 [124]~E(x1241,x1242)+E(f153(x1243,x1241),f153(x1243,x1242))
% 81.29/80.93 [125]~E(x1251,x1252)+E(f33(x1251,x1253),f33(x1252,x1253))
% 81.29/80.93 [126]~E(x1261,x1262)+E(f33(x1263,x1261),f33(x1263,x1262))
% 81.29/80.93 [127]~E(x1271,x1272)+E(f30(x1271,x1273,x1274),f30(x1272,x1273,x1274))
% 81.29/80.93 [128]~E(x1281,x1282)+E(f30(x1283,x1281,x1284),f30(x1283,x1282,x1284))
% 81.29/80.93 [129]~E(x1291,x1292)+E(f30(x1293,x1294,x1291),f30(x1293,x1294,x1292))
% 81.29/80.93 [130]~E(x1301,x1302)+E(f137(x1301),f137(x1302))
% 81.29/80.93 [131]~E(x1311,x1312)+E(f183(x1311,x1313,x1314),f183(x1312,x1313,x1314))
% 81.29/80.93 [132]~E(x1321,x1322)+E(f183(x1323,x1321,x1324),f183(x1323,x1322,x1324))
% 81.29/80.93 [133]~E(x1331,x1332)+E(f183(x1333,x1334,x1331),f183(x1333,x1334,x1332))
% 81.29/80.93 [134]~E(x1341,x1342)+E(f814(x1341,x1343,x1344),f814(x1342,x1343,x1344))
% 81.29/80.93 [135]~E(x1351,x1352)+E(f814(x1353,x1351,x1354),f814(x1353,x1352,x1354))
% 81.29/80.93 [136]~E(x1361,x1362)+E(f814(x1363,x1364,x1361),f814(x1363,x1364,x1362))
% 81.29/80.93 [137]~E(x1371,x1372)+E(f829(x1371,x1373,x1374,x1375),f829(x1372,x1373,x1374,x1375))
% 81.29/80.93 [138]~E(x1381,x1382)+E(f829(x1383,x1381,x1384,x1385),f829(x1383,x1382,x1384,x1385))
% 81.29/80.93 [139]~E(x1391,x1392)+E(f829(x1393,x1394,x1391,x1395),f829(x1393,x1394,x1392,x1395))
% 81.29/80.93 [140]~E(x1401,x1402)+E(f829(x1403,x1404,x1405,x1401),f829(x1403,x1404,x1405,x1402))
% 81.29/80.93 [141]~E(x1411,x1412)+E(f12(x1411,x1413,x1414),f12(x1412,x1413,x1414))
% 81.29/80.93 [142]~E(x1421,x1422)+E(f12(x1423,x1421,x1424),f12(x1423,x1422,x1424))
% 81.29/80.93 [143]~E(x1431,x1432)+E(f12(x1433,x1434,x1431),f12(x1433,x1434,x1432))
% 81.29/80.93 [144]~E(x1441,x1442)+E(f304(x1441,x1443),f304(x1442,x1443))
% 81.29/80.93 [145]~E(x1451,x1452)+E(f304(x1453,x1451),f304(x1453,x1452))
% 81.29/80.93 [146]~E(x1461,x1462)+E(f159(x1461,x1463),f159(x1462,x1463))
% 81.29/80.93 [147]~E(x1471,x1472)+E(f159(x1473,x1471),f159(x1473,x1472))
% 81.29/80.93 [148]~E(x1481,x1482)+E(f451(x1481,x1483),f451(x1482,x1483))
% 81.29/80.93 [149]~E(x1491,x1492)+E(f451(x1493,x1491),f451(x1493,x1492))
% 81.29/80.93 [150]~E(x1501,x1502)+E(f588(x1501,x1503,x1504),f588(x1502,x1503,x1504))
% 81.29/80.93 [151]~E(x1511,x1512)+E(f588(x1513,x1511,x1514),f588(x1513,x1512,x1514))
% 81.29/80.93 [152]~E(x1521,x1522)+E(f588(x1523,x1524,x1521),f588(x1523,x1524,x1522))
% 81.29/80.93 [153]~E(x1531,x1532)+E(f39(x1531),f39(x1532))
% 81.29/80.93 [154]~E(x1541,x1542)+E(f111(x1541),f111(x1542))
% 81.29/80.93 [155]~E(x1551,x1552)+E(f113(x1551),f113(x1552))
% 81.29/80.93 [156]~E(x1561,x1562)+E(f329(x1561),f329(x1562))
% 81.29/80.93 [157]~E(x1571,x1572)+E(f73(x1571,x1573),f73(x1572,x1573))
% 81.29/80.93 [158]~E(x1581,x1582)+E(f73(x1583,x1581),f73(x1583,x1582))
% 81.29/80.93 [159]~E(x1591,x1592)+E(f196(x1591),f196(x1592))
% 81.29/80.93 [160]~E(x1601,x1602)+E(f265(x1601,x1603),f265(x1602,x1603))
% 81.29/80.93 [161]~E(x1611,x1612)+E(f265(x1613,x1611),f265(x1613,x1612))
% 81.29/80.93 [162]~E(x1621,x1622)+E(f40(x1621,x1623),f40(x1622,x1623))
% 81.29/80.93 [163]~E(x1631,x1632)+E(f40(x1633,x1631),f40(x1633,x1632))
% 81.29/80.93 [164]~E(x1641,x1642)+E(f156(x1641,x1643),f156(x1642,x1643))
% 81.29/80.93 [165]~E(x1651,x1652)+E(f156(x1653,x1651),f156(x1653,x1652))
% 81.29/80.93 [166]~E(x1661,x1662)+E(f5(x1661),f5(x1662))
% 81.29/80.93 [167]~E(x1671,x1672)+E(f285(x1671,x1673,x1674),f285(x1672,x1673,x1674))
% 81.29/80.93 [168]~E(x1681,x1682)+E(f285(x1683,x1681,x1684),f285(x1683,x1682,x1684))
% 81.29/80.93 [169]~E(x1691,x1692)+E(f285(x1693,x1694,x1691),f285(x1693,x1694,x1692))
% 81.29/80.93 [170]~E(x1701,x1702)+E(f252(x1701),f252(x1702))
% 81.29/80.93 [171]~E(x1711,x1712)+E(f282(x1711,x1713,x1714),f282(x1712,x1713,x1714))
% 81.29/80.93 [172]~E(x1721,x1722)+E(f282(x1723,x1721,x1724),f282(x1723,x1722,x1724))
% 81.29/80.93 [173]~E(x1731,x1732)+E(f282(x1733,x1734,x1731),f282(x1733,x1734,x1732))
% 81.29/80.93 [174]~E(x1741,x1742)+E(f150(x1741),f150(x1742))
% 81.29/80.93 [175]~E(x1751,x1752)+E(f135(x1751,x1753),f135(x1752,x1753))
% 81.29/80.93 [176]~E(x1761,x1762)+E(f135(x1763,x1761),f135(x1763,x1762))
% 81.29/80.93 [177]~E(x1771,x1772)+E(f65(x1771,x1773,x1774),f65(x1772,x1773,x1774))
% 81.29/80.93 [178]~E(x1781,x1782)+E(f65(x1783,x1781,x1784),f65(x1783,x1782,x1784))
% 81.29/80.93 [179]~E(x1791,x1792)+E(f65(x1793,x1794,x1791),f65(x1793,x1794,x1792))
% 81.29/80.93 [180]~E(x1801,x1802)+E(f158(x1801,x1803),f158(x1802,x1803))
% 81.29/80.93 [181]~E(x1811,x1812)+E(f158(x1813,x1811),f158(x1813,x1812))
% 81.29/80.93 [182]~E(x1821,x1822)+E(f267(x1821,x1823,x1824),f267(x1822,x1823,x1824))
% 81.29/80.93 [183]~E(x1831,x1832)+E(f267(x1833,x1831,x1834),f267(x1833,x1832,x1834))
% 81.29/80.93 [184]~E(x1841,x1842)+E(f267(x1843,x1844,x1841),f267(x1843,x1844,x1842))
% 81.29/80.93 [185]~E(x1851,x1852)+E(f206(x1851,x1853,x1854,x1855),f206(x1852,x1853,x1854,x1855))
% 81.29/80.93 [186]~E(x1861,x1862)+E(f206(x1863,x1861,x1864,x1865),f206(x1863,x1862,x1864,x1865))
% 81.29/80.93 [187]~E(x1871,x1872)+E(f206(x1873,x1874,x1871,x1875),f206(x1873,x1874,x1872,x1875))
% 81.29/80.93 [188]~E(x1881,x1882)+E(f206(x1883,x1884,x1885,x1881),f206(x1883,x1884,x1885,x1882))
% 81.29/80.93 [189]~E(x1891,x1892)+E(f34(x1891,x1893),f34(x1892,x1893))
% 81.29/80.93 [190]~E(x1901,x1902)+E(f34(x1903,x1901),f34(x1903,x1902))
% 81.29/80.93 [191]~E(x1911,x1912)+E(f164(x1911),f164(x1912))
% 81.29/80.93 [192]~E(x1921,x1922)+E(f823(x1921,x1923,x1924),f823(x1922,x1923,x1924))
% 81.29/80.93 [193]~E(x1931,x1932)+E(f823(x1933,x1931,x1934),f823(x1933,x1932,x1934))
% 81.29/80.93 [194]~E(x1941,x1942)+E(f823(x1943,x1944,x1941),f823(x1943,x1944,x1942))
% 81.29/80.93 [195]~E(x1951,x1952)+E(f315(x1951,x1953,x1954,x1955),f315(x1952,x1953,x1954,x1955))
% 81.29/80.93 [196]~E(x1961,x1962)+E(f315(x1963,x1961,x1964,x1965),f315(x1963,x1962,x1964,x1965))
% 81.29/80.93 [197]~E(x1971,x1972)+E(f315(x1973,x1974,x1971,x1975),f315(x1973,x1974,x1972,x1975))
% 81.29/80.93 [198]~E(x1981,x1982)+E(f315(x1983,x1984,x1985,x1981),f315(x1983,x1984,x1985,x1982))
% 81.29/80.93 [199]~E(x1991,x1992)+E(f187(x1991,x1993,x1994,x1995),f187(x1992,x1993,x1994,x1995))
% 81.29/80.93 [200]~E(x2001,x2002)+E(f187(x2003,x2001,x2004,x2005),f187(x2003,x2002,x2004,x2005))
% 81.29/80.93 [201]~E(x2011,x2012)+E(f187(x2013,x2014,x2011,x2015),f187(x2013,x2014,x2012,x2015))
% 81.29/80.93 [202]~E(x2021,x2022)+E(f187(x2023,x2024,x2025,x2021),f187(x2023,x2024,x2025,x2022))
% 81.29/80.93 [203]~E(x2031,x2032)+E(f807(x2031,x2033,x2034),f807(x2032,x2033,x2034))
% 81.29/80.93 [204]~E(x2041,x2042)+E(f807(x2043,x2041,x2044),f807(x2043,x2042,x2044))
% 81.29/80.93 [205]~E(x2051,x2052)+E(f807(x2053,x2054,x2051),f807(x2053,x2054,x2052))
% 81.29/80.93 [206]~E(x2061,x2062)+E(f165(x2061),f165(x2062))
% 81.29/80.93 [207]~E(x2071,x2072)+E(f87(x2071,x2073),f87(x2072,x2073))
% 81.29/80.93 [208]~E(x2081,x2082)+E(f87(x2083,x2081),f87(x2083,x2082))
% 81.29/80.93 [209]~E(x2091,x2092)+E(f50(x2091,x2093),f50(x2092,x2093))
% 81.29/80.93 [210]~E(x2101,x2102)+E(f50(x2103,x2101),f50(x2103,x2102))
% 81.29/80.93 [211]~E(x2111,x2112)+E(f289(x2111,x2113,x2114),f289(x2112,x2113,x2114))
% 81.29/80.93 [212]~E(x2121,x2122)+E(f289(x2123,x2121,x2124),f289(x2123,x2122,x2124))
% 81.29/80.93 [213]~E(x2131,x2132)+E(f289(x2133,x2134,x2131),f289(x2133,x2134,x2132))
% 81.29/80.93 [214]~E(x2141,x2142)+E(f736(x2141,x2143,x2144),f736(x2142,x2143,x2144))
% 81.29/80.93 [215]~E(x2151,x2152)+E(f736(x2153,x2151,x2154),f736(x2153,x2152,x2154))
% 81.29/80.93 [216]~E(x2161,x2162)+E(f736(x2163,x2164,x2161),f736(x2163,x2164,x2162))
% 81.29/80.93 [217]~E(x2171,x2172)+E(f169(x2171,x2173,x2174),f169(x2172,x2173,x2174))
% 81.29/80.93 [218]~E(x2181,x2182)+E(f169(x2183,x2181,x2184),f169(x2183,x2182,x2184))
% 81.29/80.93 [219]~E(x2191,x2192)+E(f169(x2193,x2194,x2191),f169(x2193,x2194,x2192))
% 81.29/80.93 [220]~E(x2201,x2202)+E(f269(x2201,x2203,x2204,x2205),f269(x2202,x2203,x2204,x2205))
% 81.29/80.93 [221]~E(x2211,x2212)+E(f269(x2213,x2211,x2214,x2215),f269(x2213,x2212,x2214,x2215))
% 81.29/80.93 [222]~E(x2221,x2222)+E(f269(x2223,x2224,x2221,x2225),f269(x2223,x2224,x2222,x2225))
% 81.29/80.93 [223]~E(x2231,x2232)+E(f269(x2233,x2234,x2235,x2231),f269(x2233,x2234,x2235,x2232))
% 81.29/80.93 [224]~E(x2241,x2242)+E(f250(x2241),f250(x2242))
% 81.29/80.93 [225]~E(x2251,x2252)+E(f31(x2251,x2253,x2254),f31(x2252,x2253,x2254))
% 81.29/80.93 [226]~E(x2261,x2262)+E(f31(x2263,x2261,x2264),f31(x2263,x2262,x2264))
% 81.29/80.93 [227]~E(x2271,x2272)+E(f31(x2273,x2274,x2271),f31(x2273,x2274,x2272))
% 81.29/80.93 [228]~E(x2281,x2282)+E(f299(x2281,x2283,x2284),f299(x2282,x2283,x2284))
% 81.29/80.93 [229]~E(x2291,x2292)+E(f299(x2293,x2291,x2294),f299(x2293,x2292,x2294))
% 81.29/80.93 [230]~E(x2301,x2302)+E(f299(x2303,x2304,x2301),f299(x2303,x2304,x2302))
% 81.29/80.93 [231]~E(x2311,x2312)+E(f836(x2311,x2313,x2314,x2315,x2316),f836(x2312,x2313,x2314,x2315,x2316))
% 81.29/80.93 [232]~E(x2321,x2322)+E(f836(x2323,x2321,x2324,x2325,x2326),f836(x2323,x2322,x2324,x2325,x2326))
% 81.29/80.93 [233]~E(x2331,x2332)+E(f836(x2333,x2334,x2331,x2335,x2336),f836(x2333,x2334,x2332,x2335,x2336))
% 81.29/80.93 [234]~E(x2341,x2342)+E(f836(x2343,x2344,x2345,x2341,x2346),f836(x2343,x2344,x2345,x2342,x2346))
% 81.29/80.93 [235]~E(x2351,x2352)+E(f836(x2353,x2354,x2355,x2356,x2351),f836(x2353,x2354,x2355,x2356,x2352))
% 81.29/80.93 [236]~E(x2361,x2362)+E(f301(x2361,x2363,x2364),f301(x2362,x2363,x2364))
% 81.29/80.93 [237]~E(x2371,x2372)+E(f301(x2373,x2371,x2374),f301(x2373,x2372,x2374))
% 81.29/80.93 [238]~E(x2381,x2382)+E(f301(x2383,x2384,x2381),f301(x2383,x2384,x2382))
% 81.29/80.93 [239]~E(x2391,x2392)+E(f74(x2391,x2393,x2394,x2395),f74(x2392,x2393,x2394,x2395))
% 81.29/80.93 [240]~E(x2401,x2402)+E(f74(x2403,x2401,x2404,x2405),f74(x2403,x2402,x2404,x2405))
% 81.29/80.93 [241]~E(x2411,x2412)+E(f74(x2413,x2414,x2411,x2415),f74(x2413,x2414,x2412,x2415))
% 81.29/80.93 [242]~E(x2421,x2422)+E(f74(x2423,x2424,x2425,x2421),f74(x2423,x2424,x2425,x2422))
% 81.29/80.93 [243]~E(x2431,x2432)+E(f43(x2431,x2433),f43(x2432,x2433))
% 81.29/80.93 [244]~E(x2441,x2442)+E(f43(x2443,x2441),f43(x2443,x2442))
% 81.29/80.93 [245]~E(x2451,x2452)+E(f154(x2451,x2453,x2454),f154(x2452,x2453,x2454))
% 81.29/80.93 [246]~E(x2461,x2462)+E(f154(x2463,x2461,x2464),f154(x2463,x2462,x2464))
% 81.29/80.93 [247]~E(x2471,x2472)+E(f154(x2473,x2474,x2471),f154(x2473,x2474,x2472))
% 81.29/80.93 [248]~E(x2481,x2482)+E(f256(x2481,x2483),f256(x2482,x2483))
% 81.29/80.93 [249]~E(x2491,x2492)+E(f256(x2493,x2491),f256(x2493,x2492))
% 81.29/80.93 [250]~E(x2501,x2502)+E(f88(x2501),f88(x2502))
% 81.29/80.93 [251]~E(x2511,x2512)+E(f174(x2511),f174(x2512))
% 81.29/80.93 [252]~E(x2521,x2522)+E(f809(x2521,x2523,x2524,x2525),f809(x2522,x2523,x2524,x2525))
% 81.29/80.93 [253]~E(x2531,x2532)+E(f809(x2533,x2531,x2534,x2535),f809(x2533,x2532,x2534,x2535))
% 81.29/80.93 [254]~E(x2541,x2542)+E(f809(x2543,x2544,x2541,x2545),f809(x2543,x2544,x2542,x2545))
% 81.29/80.93 [255]~E(x2551,x2552)+E(f809(x2553,x2554,x2555,x2551),f809(x2553,x2554,x2555,x2552))
% 81.29/80.93 [256]~E(x2561,x2562)+E(f258(x2561),f258(x2562))
% 81.29/80.93 [257]~E(x2571,x2572)+E(f181(x2571,x2573),f181(x2572,x2573))
% 81.29/80.93 [258]~E(x2581,x2582)+E(f181(x2583,x2581),f181(x2583,x2582))
% 81.29/80.93 [259]~E(x2591,x2592)+E(f168(x2591),f168(x2592))
% 81.29/80.93 [260]~E(x2601,x2602)+E(f140(x2601),f140(x2602))
% 81.29/80.93 [261]~E(x2611,x2612)+E(f10(x2611,x2613),f10(x2612,x2613))
% 81.29/80.93 [262]~E(x2621,x2622)+E(f10(x2623,x2621),f10(x2623,x2622))
% 81.29/80.93 [263]~E(x2631,x2632)+E(f151(x2631,x2633),f151(x2632,x2633))
% 81.29/80.93 [264]~E(x2641,x2642)+E(f151(x2643,x2641),f151(x2643,x2642))
% 81.29/80.93 [265]~E(x2651,x2652)+E(f283(x2651,x2653),f283(x2652,x2653))
% 81.29/80.93 [266]~E(x2661,x2662)+E(f283(x2663,x2661),f283(x2663,x2662))
% 81.29/80.93 [267]~E(x2671,x2672)+E(f197(x2671),f197(x2672))
% 81.29/80.93 [268]~E(x2681,x2682)+E(f11(x2681,x2683),f11(x2682,x2683))
% 81.29/80.93 [269]~E(x2691,x2692)+E(f11(x2693,x2691),f11(x2693,x2692))
% 81.29/80.93 [270]~E(x2701,x2702)+E(f121(x2701),f121(x2702))
% 81.29/80.93 [271]~E(x2711,x2712)+E(f141(x2711,x2713,x2714,x2715),f141(x2712,x2713,x2714,x2715))
% 81.29/80.93 [272]~E(x2721,x2722)+E(f141(x2723,x2721,x2724,x2725),f141(x2723,x2722,x2724,x2725))
% 81.29/80.93 [273]~E(x2731,x2732)+E(f141(x2733,x2734,x2731,x2735),f141(x2733,x2734,x2732,x2735))
% 81.29/80.93 [274]~E(x2741,x2742)+E(f141(x2743,x2744,x2745,x2741),f141(x2743,x2744,x2745,x2742))
% 81.29/80.93 [275]~E(x2751,x2752)+E(f86(x2751,x2753),f86(x2752,x2753))
% 81.29/80.93 [276]~E(x2761,x2762)+E(f86(x2763,x2761),f86(x2763,x2762))
% 81.29/80.93 [277]~E(x2771,x2772)+E(f316(x2771,x2773),f316(x2772,x2773))
% 81.29/80.93 [278]~E(x2781,x2782)+E(f316(x2783,x2781),f316(x2783,x2782))
% 81.29/80.93 [279]~E(x2791,x2792)+E(f236(x2791),f236(x2792))
% 81.29/80.93 [280]~E(x2801,x2802)+E(f413(x2801,x2803,x2804,x2805),f413(x2802,x2803,x2804,x2805))
% 81.29/80.93 [281]~E(x2811,x2812)+E(f413(x2813,x2811,x2814,x2815),f413(x2813,x2812,x2814,x2815))
% 81.29/80.93 [282]~E(x2821,x2822)+E(f413(x2823,x2824,x2821,x2825),f413(x2823,x2824,x2822,x2825))
% 81.29/80.93 [283]~E(x2831,x2832)+E(f413(x2833,x2834,x2835,x2831),f413(x2833,x2834,x2835,x2832))
% 81.29/80.93 [284]~E(x2841,x2842)+E(f91(x2841,x2843),f91(x2842,x2843))
% 81.29/80.93 [285]~E(x2851,x2852)+E(f91(x2853,x2851),f91(x2853,x2852))
% 81.29/80.93 [286]~E(x2861,x2862)+E(f9(x2861,x2863),f9(x2862,x2863))
% 81.29/80.93 [287]~E(x2871,x2872)+E(f9(x2873,x2871),f9(x2873,x2872))
% 81.29/80.93 [288]~E(x2881,x2882)+E(f15(x2881,x2883),f15(x2882,x2883))
% 81.29/80.93 [289]~E(x2891,x2892)+E(f15(x2893,x2891),f15(x2893,x2892))
% 81.29/80.93 [290]~E(x2901,x2902)+E(f76(x2901),f76(x2902))
% 81.29/80.93 [291]~E(x2911,x2912)+E(f598(x2911,x2913,x2914),f598(x2912,x2913,x2914))
% 81.29/80.93 [292]~E(x2921,x2922)+E(f598(x2923,x2921,x2924),f598(x2923,x2922,x2924))
% 81.29/80.93 [293]~E(x2931,x2932)+E(f598(x2933,x2934,x2931),f598(x2933,x2934,x2932))
% 81.29/80.93 [294]~E(x2941,x2942)+E(f450(x2941,x2943),f450(x2942,x2943))
% 81.29/80.93 [295]~E(x2951,x2952)+E(f450(x2953,x2951),f450(x2953,x2952))
% 81.29/80.93 [296]~E(x2961,x2962)+E(f16(x2961,x2963),f16(x2962,x2963))
% 81.29/80.93 [297]~E(x2971,x2972)+E(f16(x2973,x2971),f16(x2973,x2972))
% 81.29/80.93 [298]~E(x2981,x2982)+E(f49(x2981,x2983),f49(x2982,x2983))
% 81.29/80.93 [299]~E(x2991,x2992)+E(f49(x2993,x2991),f49(x2993,x2992))
% 81.29/80.93 [300]~E(x3001,x3002)+E(f56(x3001),f56(x3002))
% 81.29/80.93 [301]~E(x3011,x3012)+E(f170(x3011),f170(x3012))
% 81.29/80.93 [302]~E(x3021,x3022)+E(f317(x3021,x3023),f317(x3022,x3023))
% 81.29/80.93 [303]~E(x3031,x3032)+E(f317(x3033,x3031),f317(x3033,x3032))
% 81.29/80.93 [304]~E(x3041,x3042)+E(f59(x3041),f59(x3042))
% 81.29/80.93 [305]~E(x3051,x3052)+E(f859(x3051),f859(x3052))
% 81.29/80.93 [306]~E(x3061,x3062)+E(f361(x3061,x3063,x3064,x3065,x3066,x3067),f361(x3062,x3063,x3064,x3065,x3066,x3067))
% 81.29/80.93 [307]~E(x3071,x3072)+E(f361(x3073,x3071,x3074,x3075,x3076,x3077),f361(x3073,x3072,x3074,x3075,x3076,x3077))
% 81.29/80.93 [308]~E(x3081,x3082)+E(f361(x3083,x3084,x3081,x3085,x3086,x3087),f361(x3083,x3084,x3082,x3085,x3086,x3087))
% 81.29/80.93 [309]~E(x3091,x3092)+E(f361(x3093,x3094,x3095,x3091,x3096,x3097),f361(x3093,x3094,x3095,x3092,x3096,x3097))
% 81.29/80.93 [310]~E(x3101,x3102)+E(f361(x3103,x3104,x3105,x3106,x3101,x3107),f361(x3103,x3104,x3105,x3106,x3102,x3107))
% 81.29/80.93 [311]~E(x3111,x3112)+E(f361(x3113,x3114,x3115,x3116,x3117,x3111),f361(x3113,x3114,x3115,x3116,x3117,x3112))
% 81.29/80.93 [312]~E(x3121,x3122)+E(f195(x3121,x3123,x3124,x3125),f195(x3122,x3123,x3124,x3125))
% 81.29/80.93 [313]~E(x3131,x3132)+E(f195(x3133,x3131,x3134,x3135),f195(x3133,x3132,x3134,x3135))
% 81.29/80.93 [314]~E(x3141,x3142)+E(f195(x3143,x3144,x3141,x3145),f195(x3143,x3144,x3142,x3145))
% 81.29/80.93 [315]~E(x3151,x3152)+E(f195(x3153,x3154,x3155,x3151),f195(x3153,x3154,x3155,x3152))
% 81.29/80.93 [316]~E(x3161,x3162)+E(f815(x3161,x3163,x3164),f815(x3162,x3163,x3164))
% 81.29/80.93 [317]~E(x3171,x3172)+E(f815(x3173,x3171,x3174),f815(x3173,x3172,x3174))
% 81.29/80.93 [318]~E(x3181,x3182)+E(f815(x3183,x3184,x3181),f815(x3183,x3184,x3182))
% 81.29/80.93 [319]~E(x3191,x3192)+E(f805(x3191,x3193,x3194),f805(x3192,x3193,x3194))
% 81.29/80.93 [320]~E(x3201,x3202)+E(f805(x3203,x3201,x3204),f805(x3203,x3202,x3204))
% 81.29/80.93 [321]~E(x3211,x3212)+E(f805(x3213,x3214,x3211),f805(x3213,x3214,x3212))
% 81.29/80.93 [322]~E(x3221,x3222)+E(f179(x3221,x3223),f179(x3222,x3223))
% 81.29/80.93 [323]~E(x3231,x3232)+E(f179(x3233,x3231),f179(x3233,x3232))
% 81.29/80.93 [324]~E(x3241,x3242)+E(f211(x3241,x3243),f211(x3242,x3243))
% 81.29/80.93 [325]~E(x3251,x3252)+E(f211(x3253,x3251),f211(x3253,x3252))
% 81.29/80.93 [326]~E(x3261,x3262)+E(f302(x3261,x3263,x3264),f302(x3262,x3263,x3264))
% 81.29/80.93 [327]~E(x3271,x3272)+E(f302(x3273,x3271,x3274),f302(x3273,x3272,x3274))
% 81.29/80.93 [328]~E(x3281,x3282)+E(f302(x3283,x3284,x3281),f302(x3283,x3284,x3282))
% 81.29/80.93 [329]~E(x3291,x3292)+E(f449(x3291,x3293),f449(x3292,x3293))
% 81.29/80.93 [330]~E(x3301,x3302)+E(f449(x3303,x3301),f449(x3303,x3302))
% 81.29/80.93 [331]~E(x3311,x3312)+E(f177(x3311,x3313),f177(x3312,x3313))
% 81.29/80.93 [332]~E(x3321,x3322)+E(f177(x3323,x3321),f177(x3323,x3322))
% 81.29/80.93 [333]~E(x3331,x3332)+E(f701(x3331,x3333,x3334,x3335),f701(x3332,x3333,x3334,x3335))
% 81.29/80.93 [334]~E(x3341,x3342)+E(f701(x3343,x3341,x3344,x3345),f701(x3343,x3342,x3344,x3345))
% 81.29/80.93 [335]~E(x3351,x3352)+E(f701(x3353,x3354,x3351,x3355),f701(x3353,x3354,x3352,x3355))
% 81.29/80.93 [336]~E(x3361,x3362)+E(f701(x3363,x3364,x3365,x3361),f701(x3363,x3364,x3365,x3362))
% 81.29/80.93 [337]~E(x3371,x3372)+E(f788(x3371,x3373,x3374,x3375,x3376),f788(x3372,x3373,x3374,x3375,x3376))
% 81.29/80.93 [338]~E(x3381,x3382)+E(f788(x3383,x3381,x3384,x3385,x3386),f788(x3383,x3382,x3384,x3385,x3386))
% 81.29/80.93 [339]~E(x3391,x3392)+E(f788(x3393,x3394,x3391,x3395,x3396),f788(x3393,x3394,x3392,x3395,x3396))
% 81.29/80.93 [340]~E(x3401,x3402)+E(f788(x3403,x3404,x3405,x3401,x3406),f788(x3403,x3404,x3405,x3402,x3406))
% 81.29/80.93 [341]~E(x3411,x3412)+E(f788(x3413,x3414,x3415,x3416,x3411),f788(x3413,x3414,x3415,x3416,x3412))
% 81.29/80.93 [342]~E(x3421,x3422)+E(f319(x3421,x3423),f319(x3422,x3423))
% 81.29/80.93 [343]~E(x3431,x3432)+E(f319(x3433,x3431),f319(x3433,x3432))
% 81.29/80.93 [344]~E(x3441,x3442)+E(f178(x3441,x3443),f178(x3442,x3443))
% 81.29/80.93 [345]~E(x3451,x3452)+E(f178(x3453,x3451),f178(x3453,x3452))
% 81.29/80.93 [346]~E(x3461,x3462)+E(f321(x3461,x3463),f321(x3462,x3463))
% 81.29/80.93 [347]~E(x3471,x3472)+E(f321(x3473,x3471),f321(x3473,x3472))
% 81.29/80.93 [348]~E(x3481,x3482)+E(f223(x3481,x3483),f223(x3482,x3483))
% 81.29/80.93 [349]~E(x3491,x3492)+E(f223(x3493,x3491),f223(x3493,x3492))
% 81.29/80.93 [350]~E(x3501,x3502)+E(f504(x3501,x3503,x3504,x3505),f504(x3502,x3503,x3504,x3505))
% 81.29/80.93 [351]~E(x3511,x3512)+E(f504(x3513,x3511,x3514,x3515),f504(x3513,x3512,x3514,x3515))
% 81.29/80.93 [352]~E(x3521,x3522)+E(f504(x3523,x3524,x3521,x3525),f504(x3523,x3524,x3522,x3525))
% 81.29/80.93 [353]~E(x3531,x3532)+E(f504(x3533,x3534,x3535,x3531),f504(x3533,x3534,x3535,x3532))
% 81.29/80.93 [354]~E(x3541,x3542)+E(f554(x3541,x3543,x3544,x3545),f554(x3542,x3543,x3544,x3545))
% 81.29/80.93 [355]~E(x3551,x3552)+E(f554(x3553,x3551,x3554,x3555),f554(x3553,x3552,x3554,x3555))
% 81.29/80.93 [356]~E(x3561,x3562)+E(f554(x3563,x3564,x3561,x3565),f554(x3563,x3564,x3562,x3565))
% 81.29/80.93 [357]~E(x3571,x3572)+E(f554(x3573,x3574,x3575,x3571),f554(x3573,x3574,x3575,x3572))
% 81.29/80.93 [358]~E(x3581,x3582)+E(f308(x3581,x3583,x3584),f308(x3582,x3583,x3584))
% 81.29/80.93 [359]~E(x3591,x3592)+E(f308(x3593,x3591,x3594),f308(x3593,x3592,x3594))
% 81.29/80.93 [360]~E(x3601,x3602)+E(f308(x3603,x3604,x3601),f308(x3603,x3604,x3602))
% 81.29/80.93 [361]~E(x3611,x3612)+E(f143(x3611,x3613),f143(x3612,x3613))
% 81.29/80.93 [362]~E(x3621,x3622)+E(f143(x3623,x3621),f143(x3623,x3622))
% 81.29/80.93 [363]~E(x3631,x3632)+E(f29(x3631,x3633,x3634),f29(x3632,x3633,x3634))
% 81.29/80.93 [364]~E(x3641,x3642)+E(f29(x3643,x3641,x3644),f29(x3643,x3642,x3644))
% 81.29/80.93 [365]~E(x3651,x3652)+E(f29(x3653,x3654,x3651),f29(x3653,x3654,x3652))
% 81.29/80.93 [366]~E(x3661,x3662)+E(f838(x3661,x3663),f838(x3662,x3663))
% 81.29/80.93 [367]~E(x3671,x3672)+E(f838(x3673,x3671),f838(x3673,x3672))
% 81.29/80.93 [368]~E(x3681,x3682)+E(f432(x3681,x3683,x3684),f432(x3682,x3683,x3684))
% 81.29/80.93 [369]~E(x3691,x3692)+E(f432(x3693,x3691,x3694),f432(x3693,x3692,x3694))
% 81.29/80.93 [370]~E(x3701,x3702)+E(f432(x3703,x3704,x3701),f432(x3703,x3704,x3702))
% 81.29/80.93 [371]~E(x3711,x3712)+E(f780(x3711,x3713,x3714,x3715,x3716),f780(x3712,x3713,x3714,x3715,x3716))
% 81.29/80.93 [372]~E(x3721,x3722)+E(f780(x3723,x3721,x3724,x3725,x3726),f780(x3723,x3722,x3724,x3725,x3726))
% 81.29/80.93 [373]~E(x3731,x3732)+E(f780(x3733,x3734,x3731,x3735,x3736),f780(x3733,x3734,x3732,x3735,x3736))
% 81.29/80.93 [374]~E(x3741,x3742)+E(f780(x3743,x3744,x3745,x3741,x3746),f780(x3743,x3744,x3745,x3742,x3746))
% 81.29/80.93 [375]~E(x3751,x3752)+E(f780(x3753,x3754,x3755,x3756,x3751),f780(x3753,x3754,x3755,x3756,x3752))
% 81.29/80.93 [376]~E(x3761,x3762)+E(f661(x3761,x3763),f661(x3762,x3763))
% 81.29/80.93 [377]~E(x3771,x3772)+E(f661(x3773,x3771),f661(x3773,x3772))
% 81.29/80.93 [378]~E(x3781,x3782)+E(f444(x3781,x3783,x3784,x3785),f444(x3782,x3783,x3784,x3785))
% 81.29/80.93 [379]~E(x3791,x3792)+E(f444(x3793,x3791,x3794,x3795),f444(x3793,x3792,x3794,x3795))
% 81.29/80.93 [380]~E(x3801,x3802)+E(f444(x3803,x3804,x3801,x3805),f444(x3803,x3804,x3802,x3805))
% 81.29/80.93 [381]~E(x3811,x3812)+E(f444(x3813,x3814,x3815,x3811),f444(x3813,x3814,x3815,x3812))
% 81.29/80.93 [382]~E(x3821,x3822)+E(f180(x3821),f180(x3822))
% 81.29/80.93 [383]~E(x3831,x3832)+E(f55(x3831,x3833,x3834),f55(x3832,x3833,x3834))
% 81.29/80.93 [384]~E(x3841,x3842)+E(f55(x3843,x3841,x3844),f55(x3843,x3842,x3844))
% 81.29/80.93 [385]~E(x3851,x3852)+E(f55(x3853,x3854,x3851),f55(x3853,x3854,x3852))
% 81.29/80.93 [386]~E(x3861,x3862)+E(f679(x3861,x3863),f679(x3862,x3863))
% 81.29/80.93 [387]~E(x3871,x3872)+E(f679(x3873,x3871),f679(x3873,x3872))
% 81.29/80.93 [388]~E(x3881,x3882)+E(f762(x3881,x3883,x3884,x3885,x3886),f762(x3882,x3883,x3884,x3885,x3886))
% 81.29/80.93 [389]~E(x3891,x3892)+E(f762(x3893,x3891,x3894,x3895,x3896),f762(x3893,x3892,x3894,x3895,x3896))
% 81.29/80.93 [390]~E(x3901,x3902)+E(f762(x3903,x3904,x3901,x3905,x3906),f762(x3903,x3904,x3902,x3905,x3906))
% 81.29/80.93 [391]~E(x3911,x3912)+E(f762(x3913,x3914,x3915,x3911,x3916),f762(x3913,x3914,x3915,x3912,x3916))
% 81.29/80.93 [392]~E(x3921,x3922)+E(f762(x3923,x3924,x3925,x3926,x3921),f762(x3923,x3924,x3925,x3926,x3922))
% 81.29/80.93 [393]~E(x3931,x3932)+E(f138(x3931,x3933),f138(x3932,x3933))
% 81.29/80.93 [394]~E(x3941,x3942)+E(f138(x3943,x3941),f138(x3943,x3942))
% 81.29/80.93 [395]~E(x3951,x3952)+E(f93(x3951),f93(x3952))
% 81.29/80.93 [396]~E(x3961,x3962)+E(f406(x3961,x3963),f406(x3962,x3963))
% 81.29/80.93 [397]~E(x3971,x3972)+E(f406(x3973,x3971),f406(x3973,x3972))
% 81.29/80.93 [398]~E(x3981,x3982)+E(f14(x3981,x3983),f14(x3982,x3983))
% 81.29/80.93 [399]~E(x3991,x3992)+E(f14(x3993,x3991),f14(x3993,x3992))
% 81.29/80.93 [400]~E(x4001,x4002)+E(f251(x4001),f251(x4002))
% 81.29/80.93 [401]~E(x4011,x4012)+E(f152(x4011,x4013),f152(x4012,x4013))
% 81.29/80.93 [402]~E(x4021,x4022)+E(f152(x4023,x4021),f152(x4023,x4022))
% 81.29/80.93 [403]~E(x4031,x4032)+E(f532(x4031),f532(x4032))
% 81.29/80.93 [404]~E(x4041,x4042)+E(f41(x4041,x4043),f41(x4042,x4043))
% 81.29/80.93 [405]~E(x4051,x4052)+E(f41(x4053,x4051),f41(x4053,x4052))
% 81.29/80.93 [406]~E(x4061,x4062)+E(f64(x4061,x4063),f64(x4062,x4063))
% 81.29/80.93 [407]~E(x4071,x4072)+E(f64(x4073,x4071),f64(x4073,x4072))
% 81.29/80.93 [408]~E(x4081,x4082)+E(f463(x4081,x4083,x4084,x4085),f463(x4082,x4083,x4084,x4085))
% 81.29/80.93 [409]~E(x4091,x4092)+E(f463(x4093,x4091,x4094,x4095),f463(x4093,x4092,x4094,x4095))
% 81.29/80.93 [410]~E(x4101,x4102)+E(f463(x4103,x4104,x4101,x4105),f463(x4103,x4104,x4102,x4105))
% 81.29/80.93 [411]~E(x4111,x4112)+E(f463(x4113,x4114,x4115,x4111),f463(x4113,x4114,x4115,x4112))
% 81.29/80.93 [412]~E(x4121,x4122)+E(f496(x4121,x4123,x4124),f496(x4122,x4123,x4124))
% 81.29/80.93 [413]~E(x4131,x4132)+E(f496(x4133,x4131,x4134),f496(x4133,x4132,x4134))
% 81.29/80.93 [414]~E(x4141,x4142)+E(f496(x4143,x4144,x4141),f496(x4143,x4144,x4142))
% 81.29/80.93 [415]~E(x4151,x4152)+E(f566(x4151,x4153,x4154,x4155),f566(x4152,x4153,x4154,x4155))
% 81.29/80.93 [416]~E(x4161,x4162)+E(f566(x4163,x4161,x4164,x4165),f566(x4163,x4162,x4164,x4165))
% 81.29/80.93 [417]~E(x4171,x4172)+E(f566(x4173,x4174,x4171,x4175),f566(x4173,x4174,x4172,x4175))
% 81.29/80.93 [418]~E(x4181,x4182)+E(f566(x4183,x4184,x4185,x4181),f566(x4183,x4184,x4185,x4182))
% 81.29/80.93 [419]~E(x4191,x4192)+E(f305(x4191),f305(x4192))
% 81.29/80.93 [420]~E(x4201,x4202)+E(f297(x4201),f297(x4202))
% 81.29/80.93 [421]~E(x4211,x4212)+E(f653(x4211,x4213,x4214),f653(x4212,x4213,x4214))
% 81.29/80.93 [422]~E(x4221,x4222)+E(f653(x4223,x4221,x4224),f653(x4223,x4222,x4224))
% 81.29/80.93 [423]~E(x4231,x4232)+E(f653(x4233,x4234,x4231),f653(x4233,x4234,x4232))
% 81.29/80.93 [424]~E(x4241,x4242)+E(f470(x4241,x4243),f470(x4242,x4243))
% 81.29/80.93 [425]~E(x4251,x4252)+E(f470(x4253,x4251),f470(x4253,x4252))
% 81.29/80.93 [426]~E(x4261,x4262)+E(f13(x4261,x4263,x4264),f13(x4262,x4263,x4264))
% 81.29/80.93 [427]~E(x4271,x4272)+E(f13(x4273,x4271,x4274),f13(x4273,x4272,x4274))
% 81.29/80.93 [428]~E(x4281,x4282)+E(f13(x4283,x4284,x4281),f13(x4283,x4284,x4282))
% 81.29/80.93 [429]~E(x4291,x4292)+E(f818(x4291,x4293,x4294),f818(x4292,x4293,x4294))
% 81.29/80.93 [430]~E(x4301,x4302)+E(f818(x4303,x4301,x4304),f818(x4303,x4302,x4304))
% 81.29/80.93 [431]~E(x4311,x4312)+E(f818(x4313,x4314,x4311),f818(x4313,x4314,x4312))
% 81.29/80.93 [432]~E(x4321,x4322)+E(f200(x4321),f200(x4322))
% 81.29/80.93 [433]~E(x4331,x4332)+E(f147(x4331,x4333,x4334),f147(x4332,x4333,x4334))
% 81.29/80.93 [434]~E(x4341,x4342)+E(f147(x4343,x4341,x4344),f147(x4343,x4342,x4344))
% 81.29/80.93 [435]~E(x4351,x4352)+E(f147(x4353,x4354,x4351),f147(x4353,x4354,x4352))
% 81.29/80.93 [436]~E(x4361,x4362)+E(f623(x4361,x4363,x4364,x4365,x4366,x4367,x4368,x4369),f623(x4362,x4363,x4364,x4365,x4366,x4367,x4368,x4369))
% 81.29/80.93 [437]~E(x4371,x4372)+E(f623(x4373,x4371,x4374,x4375,x4376,x4377,x4378,x4379),f623(x4373,x4372,x4374,x4375,x4376,x4377,x4378,x4379))
% 81.29/80.93 [438]~E(x4381,x4382)+E(f623(x4383,x4384,x4381,x4385,x4386,x4387,x4388,x4389),f623(x4383,x4384,x4382,x4385,x4386,x4387,x4388,x4389))
% 81.29/80.93 [439]~E(x4391,x4392)+E(f623(x4393,x4394,x4395,x4391,x4396,x4397,x4398,x4399),f623(x4393,x4394,x4395,x4392,x4396,x4397,x4398,x4399))
% 81.29/80.93 [440]~E(x4401,x4402)+E(f623(x4403,x4404,x4405,x4406,x4401,x4407,x4408,x4409),f623(x4403,x4404,x4405,x4406,x4402,x4407,x4408,x4409))
% 81.29/80.93 [441]~E(x4411,x4412)+E(f623(x4413,x4414,x4415,x4416,x4417,x4411,x4418,x4419),f623(x4413,x4414,x4415,x4416,x4417,x4412,x4418,x4419))
% 81.29/80.93 [442]~E(x4421,x4422)+E(f623(x4423,x4424,x4425,x4426,x4427,x4428,x4421,x4429),f623(x4423,x4424,x4425,x4426,x4427,x4428,x4422,x4429))
% 81.29/80.93 [443]~E(x4431,x4432)+E(f623(x4433,x4434,x4435,x4436,x4437,x4438,x4439,x4431),f623(x4433,x4434,x4435,x4436,x4437,x4438,x4439,x4432))
% 81.29/80.93 [444]~E(x4441,x4442)+E(f281(x4441),f281(x4442))
% 81.29/80.93 [445]~E(x4451,x4452)+E(f665(x4451,x4453,x4454,x4455),f665(x4452,x4453,x4454,x4455))
% 81.29/80.93 [446]~E(x4461,x4462)+E(f665(x4463,x4461,x4464,x4465),f665(x4463,x4462,x4464,x4465))
% 81.29/80.93 [447]~E(x4471,x4472)+E(f665(x4473,x4474,x4471,x4475),f665(x4473,x4474,x4472,x4475))
% 81.29/80.93 [448]~E(x4481,x4482)+E(f665(x4483,x4484,x4485,x4481),f665(x4483,x4484,x4485,x4482))
% 81.29/80.93 [449]~E(x4491,x4492)+E(f42(x4491,x4493),f42(x4492,x4493))
% 81.29/80.93 [450]~E(x4501,x4502)+E(f42(x4503,x4501),f42(x4503,x4502))
% 81.29/80.93 [451]~E(x4511,x4512)+E(f268(x4511,x4513,x4514,x4515,x4516,x4517),f268(x4512,x4513,x4514,x4515,x4516,x4517))
% 81.29/80.93 [452]~E(x4521,x4522)+E(f268(x4523,x4521,x4524,x4525,x4526,x4527),f268(x4523,x4522,x4524,x4525,x4526,x4527))
% 81.29/80.93 [453]~E(x4531,x4532)+E(f268(x4533,x4534,x4531,x4535,x4536,x4537),f268(x4533,x4534,x4532,x4535,x4536,x4537))
% 81.29/80.93 [454]~E(x4541,x4542)+E(f268(x4543,x4544,x4545,x4541,x4546,x4547),f268(x4543,x4544,x4545,x4542,x4546,x4547))
% 81.29/80.93 [455]~E(x4551,x4552)+E(f268(x4553,x4554,x4555,x4556,x4551,x4557),f268(x4553,x4554,x4555,x4556,x4552,x4557))
% 81.29/80.93 [456]~E(x4561,x4562)+E(f268(x4563,x4564,x4565,x4566,x4567,x4561),f268(x4563,x4564,x4565,x4566,x4567,x4562))
% 81.29/80.93 [457]~E(x4571,x4572)+E(f816(x4571,x4573,x4574),f816(x4572,x4573,x4574))
% 81.29/80.93 [458]~E(x4581,x4582)+E(f816(x4583,x4581,x4584),f816(x4583,x4582,x4584))
% 81.29/80.93 [459]~E(x4591,x4592)+E(f816(x4593,x4594,x4591),f816(x4593,x4594,x4592))
% 81.29/80.93 [460]~E(x4601,x4602)+E(f184(x4601,x4603,x4604,x4605),f184(x4602,x4603,x4604,x4605))
% 81.29/80.93 [461]~E(x4611,x4612)+E(f184(x4613,x4611,x4614,x4615),f184(x4613,x4612,x4614,x4615))
% 81.29/80.93 [462]~E(x4621,x4622)+E(f184(x4623,x4624,x4621,x4625),f184(x4623,x4624,x4622,x4625))
% 81.29/80.93 [463]~E(x4631,x4632)+E(f184(x4633,x4634,x4635,x4631),f184(x4633,x4634,x4635,x4632))
% 81.29/80.93 [464]~E(x4641,x4642)+E(f204(x4641,x4643,x4644,x4645),f204(x4642,x4643,x4644,x4645))
% 81.29/80.93 [465]~E(x4651,x4652)+E(f204(x4653,x4651,x4654,x4655),f204(x4653,x4652,x4654,x4655))
% 81.29/80.93 [466]~E(x4661,x4662)+E(f204(x4663,x4664,x4661,x4665),f204(x4663,x4664,x4662,x4665))
% 81.29/80.93 [467]~E(x4671,x4672)+E(f204(x4673,x4674,x4675,x4671),f204(x4673,x4674,x4675,x4672))
% 81.29/80.93 [468]~E(x4681,x4682)+E(f587(x4681,x4683,x4684,x4685),f587(x4682,x4683,x4684,x4685))
% 81.29/80.93 [469]~E(x4691,x4692)+E(f587(x4693,x4691,x4694,x4695),f587(x4693,x4692,x4694,x4695))
% 81.29/80.93 [470]~E(x4701,x4702)+E(f587(x4703,x4704,x4701,x4705),f587(x4703,x4704,x4702,x4705))
% 81.29/80.93 [471]~E(x4711,x4712)+E(f587(x4713,x4714,x4715,x4711),f587(x4713,x4714,x4715,x4712))
% 81.29/80.93 [472]~E(x4721,x4722)+E(f407(x4721,x4723),f407(x4722,x4723))
% 81.29/80.93 [473]~E(x4731,x4732)+E(f407(x4733,x4731),f407(x4733,x4732))
% 81.29/80.93 [474]~E(x4741,x4742)+E(f115(x4741),f115(x4742))
% 81.29/80.93 [475]~E(x4751,x4752)+E(f83(x4751,x4753),f83(x4752,x4753))
% 81.29/80.93 [476]~E(x4761,x4762)+E(f83(x4763,x4761),f83(x4763,x4762))
% 81.29/80.93 [477]~E(x4771,x4772)+E(f802(x4771,x4773,x4774,x4775,x4776,x4777),f802(x4772,x4773,x4774,x4775,x4776,x4777))
% 81.29/80.93 [478]~E(x4781,x4782)+E(f802(x4783,x4781,x4784,x4785,x4786,x4787),f802(x4783,x4782,x4784,x4785,x4786,x4787))
% 81.29/80.93 [479]~E(x4791,x4792)+E(f802(x4793,x4794,x4791,x4795,x4796,x4797),f802(x4793,x4794,x4792,x4795,x4796,x4797))
% 81.29/80.93 [480]~E(x4801,x4802)+E(f802(x4803,x4804,x4805,x4801,x4806,x4807),f802(x4803,x4804,x4805,x4802,x4806,x4807))
% 81.29/80.93 [481]~E(x4811,x4812)+E(f802(x4813,x4814,x4815,x4816,x4811,x4817),f802(x4813,x4814,x4815,x4816,x4812,x4817))
% 81.29/80.93 [482]~E(x4821,x4822)+E(f802(x4823,x4824,x4825,x4826,x4827,x4821),f802(x4823,x4824,x4825,x4826,x4827,x4822))
% 81.29/80.93 [483]~E(x4831,x4832)+E(f477(x4831,x4833,x4834),f477(x4832,x4833,x4834))
% 81.29/80.93 [484]~E(x4841,x4842)+E(f477(x4843,x4841,x4844),f477(x4843,x4842,x4844))
% 81.29/80.93 [485]~E(x4851,x4852)+E(f477(x4853,x4854,x4851),f477(x4853,x4854,x4852))
% 81.29/80.93 [486]~E(x4861,x4862)+E(f636(x4861,x4863,x4864,x4865),f636(x4862,x4863,x4864,x4865))
% 81.29/80.93 [487]~E(x4871,x4872)+E(f636(x4873,x4871,x4874,x4875),f636(x4873,x4872,x4874,x4875))
% 81.29/80.93 [488]~E(x4881,x4882)+E(f636(x4883,x4884,x4881,x4885),f636(x4883,x4884,x4882,x4885))
% 81.29/80.93 [489]~E(x4891,x4892)+E(f636(x4893,x4894,x4895,x4891),f636(x4893,x4894,x4895,x4892))
% 81.29/80.93 [490]~E(x4901,x4902)+E(f303(x4901),f303(x4902))
% 81.29/80.93 [491]~E(x4911,x4912)+E(f338(x4911,x4913,x4914),f338(x4912,x4913,x4914))
% 81.29/80.93 [492]~E(x4921,x4922)+E(f338(x4923,x4921,x4924),f338(x4923,x4922,x4924))
% 81.29/80.93 [493]~E(x4931,x4932)+E(f338(x4933,x4934,x4931),f338(x4933,x4934,x4932))
% 81.29/80.93 [494]~E(x4941,x4942)+E(f803(x4941,x4943,x4944,x4945,x4946,x4947),f803(x4942,x4943,x4944,x4945,x4946,x4947))
% 81.29/80.93 [495]~E(x4951,x4952)+E(f803(x4953,x4951,x4954,x4955,x4956,x4957),f803(x4953,x4952,x4954,x4955,x4956,x4957))
% 81.29/80.93 [496]~E(x4961,x4962)+E(f803(x4963,x4964,x4961,x4965,x4966,x4967),f803(x4963,x4964,x4962,x4965,x4966,x4967))
% 81.29/80.93 [497]~E(x4971,x4972)+E(f803(x4973,x4974,x4975,x4971,x4976,x4977),f803(x4973,x4974,x4975,x4972,x4976,x4977))
% 81.29/80.93 [498]~E(x4981,x4982)+E(f803(x4983,x4984,x4985,x4986,x4981,x4987),f803(x4983,x4984,x4985,x4986,x4982,x4987))
% 81.29/80.93 [499]~E(x4991,x4992)+E(f803(x4993,x4994,x4995,x4996,x4997,x4991),f803(x4993,x4994,x4995,x4996,x4997,x4992))
% 81.29/80.93 [500]~E(x5001,x5002)+E(f657(x5001,x5003,x5004),f657(x5002,x5003,x5004))
% 81.29/80.93 [501]~E(x5011,x5012)+E(f657(x5013,x5011,x5014),f657(x5013,x5012,x5014))
% 81.29/80.93 [502]~E(x5021,x5022)+E(f657(x5023,x5024,x5021),f657(x5023,x5024,x5022))
% 81.29/80.93 [503]~E(x5031,x5032)+E(f47(x5031,x5033),f47(x5032,x5033))
% 81.29/80.93 [504]~E(x5041,x5042)+E(f47(x5043,x5041),f47(x5043,x5042))
% 81.29/80.93 [505]~E(x5051,x5052)+E(f755(x5051,x5053,x5054),f755(x5052,x5053,x5054))
% 81.29/80.93 [506]~E(x5061,x5062)+E(f755(x5063,x5061,x5064),f755(x5063,x5062,x5064))
% 81.29/80.93 [507]~E(x5071,x5072)+E(f755(x5073,x5074,x5071),f755(x5073,x5074,x5072))
% 81.29/80.93 [508]~E(x5081,x5082)+E(f66(x5081,x5083,x5084),f66(x5082,x5083,x5084))
% 81.29/80.93 [509]~E(x5091,x5092)+E(f66(x5093,x5091,x5094),f66(x5093,x5092,x5094))
% 81.29/80.93 [510]~E(x5101,x5102)+E(f66(x5103,x5104,x5101),f66(x5103,x5104,x5102))
% 81.29/80.93 [511]~E(x5111,x5112)+E(f240(x5111),f240(x5112))
% 81.29/80.93 [512]~E(x5121,x5122)+E(f276(x5121,x5123),f276(x5122,x5123))
% 81.29/80.93 [513]~E(x5131,x5132)+E(f276(x5133,x5131),f276(x5133,x5132))
% 81.29/80.93 [514]~E(x5141,x5142)+E(f48(x5141,x5143),f48(x5142,x5143))
% 81.29/80.93 [515]~E(x5151,x5152)+E(f48(x5153,x5151),f48(x5153,x5152))
% 81.29/80.93 [516]~E(x5161,x5162)+E(f98(x5161,x5163,x5164),f98(x5162,x5163,x5164))
% 81.29/80.93 [517]~E(x5171,x5172)+E(f98(x5173,x5171,x5174),f98(x5173,x5172,x5174))
% 81.29/80.93 [518]~E(x5181,x5182)+E(f98(x5183,x5184,x5181),f98(x5183,x5184,x5182))
% 81.29/80.93 [519]~E(x5191,x5192)+E(f266(x5191,x5193),f266(x5192,x5193))
% 81.29/80.93 [520]~E(x5201,x5202)+E(f266(x5203,x5201),f266(x5203,x5202))
% 81.29/80.93 [521]~E(x5211,x5212)+E(f362(x5211,x5213,x5214),f362(x5212,x5213,x5214))
% 81.29/80.93 [522]~E(x5221,x5222)+E(f362(x5223,x5221,x5224),f362(x5223,x5222,x5224))
% 81.29/80.93 [523]~E(x5231,x5232)+E(f362(x5233,x5234,x5231),f362(x5233,x5234,x5232))
% 81.29/80.93 [524]~E(x5241,x5242)+E(f254(x5241,x5243),f254(x5242,x5243))
% 81.29/80.93 [525]~E(x5251,x5252)+E(f254(x5253,x5251),f254(x5253,x5252))
% 81.29/80.93 [526]~E(x5261,x5262)+E(f608(x5261,x5263,x5264,x5265),f608(x5262,x5263,x5264,x5265))
% 81.29/80.93 [527]~E(x5271,x5272)+E(f608(x5273,x5271,x5274,x5275),f608(x5273,x5272,x5274,x5275))
% 81.29/80.93 [528]~E(x5281,x5282)+E(f608(x5283,x5284,x5281,x5285),f608(x5283,x5284,x5282,x5285))
% 81.29/80.93 [529]~E(x5291,x5292)+E(f608(x5293,x5294,x5295,x5291),f608(x5293,x5294,x5295,x5292))
% 81.29/80.93 [530]~E(x5301,x5302)+E(f54(x5301,x5303),f54(x5302,x5303))
% 81.29/80.93 [531]~E(x5311,x5312)+E(f54(x5313,x5311),f54(x5313,x5312))
% 81.29/80.93 [532]~E(x5321,x5322)+E(f817(x5321,x5323,x5324),f817(x5322,x5323,x5324))
% 81.29/80.93 [533]~E(x5331,x5332)+E(f817(x5333,x5331,x5334),f817(x5333,x5332,x5334))
% 81.29/80.93 [534]~E(x5341,x5342)+E(f817(x5343,x5344,x5341),f817(x5343,x5344,x5342))
% 81.29/80.93 [535]~E(x5351,x5352)+E(f279(x5351,x5353),f279(x5352,x5353))
% 81.29/80.93 [536]~E(x5361,x5362)+E(f279(x5363,x5361),f279(x5363,x5362))
% 81.29/80.93 [537]~E(x5371,x5372)+E(f492(x5371,x5373,x5374),f492(x5372,x5373,x5374))
% 81.29/80.93 [538]~E(x5381,x5382)+E(f492(x5383,x5381,x5384),f492(x5383,x5382,x5384))
% 81.29/80.93 [539]~E(x5391,x5392)+E(f492(x5393,x5394,x5391),f492(x5393,x5394,x5392))
% 81.29/80.93 [540]~E(x5401,x5402)+E(f505(x5401,x5403,x5404,x5405),f505(x5402,x5403,x5404,x5405))
% 81.29/80.93 [541]~E(x5411,x5412)+E(f505(x5413,x5411,x5414,x5415),f505(x5413,x5412,x5414,x5415))
% 81.29/80.93 [542]~E(x5421,x5422)+E(f505(x5423,x5424,x5421,x5425),f505(x5423,x5424,x5422,x5425))
% 81.29/80.93 [543]~E(x5431,x5432)+E(f505(x5433,x5434,x5435,x5431),f505(x5433,x5434,x5435,x5432))
% 81.29/80.93 [544]~E(x5441,x5442)+E(f253(x5441,x5443),f253(x5442,x5443))
% 81.29/80.93 [545]~E(x5451,x5452)+E(f253(x5453,x5451),f253(x5453,x5452))
% 81.29/80.93 [546]~E(x5461,x5462)+E(f801(x5461,x5463,x5464,x5465,x5466,x5467),f801(x5462,x5463,x5464,x5465,x5466,x5467))
% 81.29/80.93 [547]~E(x5471,x5472)+E(f801(x5473,x5471,x5474,x5475,x5476,x5477),f801(x5473,x5472,x5474,x5475,x5476,x5477))
% 81.29/80.93 [548]~E(x5481,x5482)+E(f801(x5483,x5484,x5481,x5485,x5486,x5487),f801(x5483,x5484,x5482,x5485,x5486,x5487))
% 81.29/80.93 [549]~E(x5491,x5492)+E(f801(x5493,x5494,x5495,x5491,x5496,x5497),f801(x5493,x5494,x5495,x5492,x5496,x5497))
% 81.29/80.93 [550]~E(x5501,x5502)+E(f801(x5503,x5504,x5505,x5506,x5501,x5507),f801(x5503,x5504,x5505,x5506,x5502,x5507))
% 81.29/80.93 [551]~E(x5511,x5512)+E(f801(x5513,x5514,x5515,x5516,x5517,x5511),f801(x5513,x5514,x5515,x5516,x5517,x5512))
% 81.29/80.93 [552]~E(x5521,x5522)+E(f606(x5521,x5523,x5524,x5525),f606(x5522,x5523,x5524,x5525))
% 81.29/80.93 [553]~E(x5531,x5532)+E(f606(x5533,x5531,x5534,x5535),f606(x5533,x5532,x5534,x5535))
% 81.29/80.93 [554]~E(x5541,x5542)+E(f606(x5543,x5544,x5541,x5545),f606(x5543,x5544,x5542,x5545))
% 81.29/80.93 [555]~E(x5551,x5552)+E(f606(x5553,x5554,x5555,x5551),f606(x5553,x5554,x5555,x5552))
% 81.29/80.93 [556]~E(x5561,x5562)+E(f203(x5561,x5563,x5564,x5565),f203(x5562,x5563,x5564,x5565))
% 81.29/80.93 [557]~E(x5571,x5572)+E(f203(x5573,x5571,x5574,x5575),f203(x5573,x5572,x5574,x5575))
% 81.29/80.93 [558]~E(x5581,x5582)+E(f203(x5583,x5584,x5581,x5585),f203(x5583,x5584,x5582,x5585))
% 81.29/80.93 [559]~E(x5591,x5592)+E(f203(x5593,x5594,x5595,x5591),f203(x5593,x5594,x5595,x5592))
% 81.29/80.93 [560]~E(x5601,x5602)+E(f149(x5601,x5603,x5604,x5605),f149(x5602,x5603,x5604,x5605))
% 81.29/80.93 [561]~E(x5611,x5612)+E(f149(x5613,x5611,x5614,x5615),f149(x5613,x5612,x5614,x5615))
% 81.29/80.93 [562]~E(x5621,x5622)+E(f149(x5623,x5624,x5621,x5625),f149(x5623,x5624,x5622,x5625))
% 81.29/80.93 [563]~E(x5631,x5632)+E(f149(x5633,x5634,x5635,x5631),f149(x5633,x5634,x5635,x5632))
% 81.29/80.93 [564]~E(x5641,x5642)+E(f705(x5641,x5643,x5644,x5645,x5646,x5647),f705(x5642,x5643,x5644,x5645,x5646,x5647))
% 81.29/80.93 [565]~E(x5651,x5652)+E(f705(x5653,x5651,x5654,x5655,x5656,x5657),f705(x5653,x5652,x5654,x5655,x5656,x5657))
% 81.29/80.93 [566]~E(x5661,x5662)+E(f705(x5663,x5664,x5661,x5665,x5666,x5667),f705(x5663,x5664,x5662,x5665,x5666,x5667))
% 81.29/80.93 [567]~E(x5671,x5672)+E(f705(x5673,x5674,x5675,x5671,x5676,x5677),f705(x5673,x5674,x5675,x5672,x5676,x5677))
% 81.29/80.93 [568]~E(x5681,x5682)+E(f705(x5683,x5684,x5685,x5686,x5681,x5687),f705(x5683,x5684,x5685,x5686,x5682,x5687))
% 81.29/80.93 [569]~E(x5691,x5692)+E(f705(x5693,x5694,x5695,x5696,x5697,x5691),f705(x5693,x5694,x5695,x5696,x5697,x5692))
% 81.29/80.93 [570]~E(x5701,x5702)+E(f676(x5701,x5703,x5704,x5705,x5706),f676(x5702,x5703,x5704,x5705,x5706))
% 81.29/80.93 [571]~E(x5711,x5712)+E(f676(x5713,x5711,x5714,x5715,x5716),f676(x5713,x5712,x5714,x5715,x5716))
% 81.29/80.93 [572]~E(x5721,x5722)+E(f676(x5723,x5724,x5721,x5725,x5726),f676(x5723,x5724,x5722,x5725,x5726))
% 81.29/80.93 [573]~E(x5731,x5732)+E(f676(x5733,x5734,x5735,x5731,x5736),f676(x5733,x5734,x5735,x5732,x5736))
% 81.29/80.93 [574]~E(x5741,x5742)+E(f676(x5743,x5744,x5745,x5746,x5741),f676(x5743,x5744,x5745,x5746,x5742))
% 81.29/80.93 [575]~E(x5751,x5752)+E(f394(x5751,x5753,x5754),f394(x5752,x5753,x5754))
% 81.29/80.93 [576]~E(x5761,x5762)+E(f394(x5763,x5761,x5764),f394(x5763,x5762,x5764))
% 81.29/80.93 [577]~E(x5771,x5772)+E(f394(x5773,x5774,x5771),f394(x5773,x5774,x5772))
% 81.29/80.93 [578]~E(x5781,x5782)+E(f67(x5781,x5783,x5784,x5785,x5786),f67(x5782,x5783,x5784,x5785,x5786))
% 81.29/80.93 [579]~E(x5791,x5792)+E(f67(x5793,x5791,x5794,x5795,x5796),f67(x5793,x5792,x5794,x5795,x5796))
% 81.29/80.93 [580]~E(x5801,x5802)+E(f67(x5803,x5804,x5801,x5805,x5806),f67(x5803,x5804,x5802,x5805,x5806))
% 81.29/80.93 [581]~E(x5811,x5812)+E(f67(x5813,x5814,x5815,x5811,x5816),f67(x5813,x5814,x5815,x5812,x5816))
% 81.29/80.93 [582]~E(x5821,x5822)+E(f67(x5823,x5824,x5825,x5826,x5821),f67(x5823,x5824,x5825,x5826,x5822))
% 81.29/80.93 [583]~E(x5831,x5832)+E(f310(x5831,x5833,x5834),f310(x5832,x5833,x5834))
% 81.29/80.93 [584]~E(x5841,x5842)+E(f310(x5843,x5841,x5844),f310(x5843,x5842,x5844))
% 81.29/80.93 [585]~E(x5851,x5852)+E(f310(x5853,x5854,x5851),f310(x5853,x5854,x5852))
% 81.29/80.93 [586]~E(x5861,x5862)+E(f46(x5861,x5863),f46(x5862,x5863))
% 81.29/80.93 [587]~E(x5871,x5872)+E(f46(x5873,x5871),f46(x5873,x5872))
% 81.29/80.93 [588]~E(x5881,x5882)+E(f216(x5881),f216(x5882))
% 81.29/80.93 [589]~E(x5891,x5892)+E(f313(x5891),f313(x5892))
% 81.29/80.93 [590]~E(x5901,x5902)+E(f644(x5901,x5903,x5904),f644(x5902,x5903,x5904))
% 81.29/80.93 [591]~E(x5911,x5912)+E(f644(x5913,x5911,x5914),f644(x5913,x5912,x5914))
% 81.29/80.93 [592]~E(x5921,x5922)+E(f644(x5923,x5924,x5921),f644(x5923,x5924,x5922))
% 81.29/80.93 [593]~E(x5931,x5932)+E(f751(x5931,x5933,x5934,x5935),f751(x5932,x5933,x5934,x5935))
% 81.29/80.93 [594]~E(x5941,x5942)+E(f751(x5943,x5941,x5944,x5945),f751(x5943,x5942,x5944,x5945))
% 81.29/80.93 [595]~E(x5951,x5952)+E(f751(x5953,x5954,x5951,x5955),f751(x5953,x5954,x5952,x5955))
% 81.29/80.93 [596]~E(x5961,x5962)+E(f751(x5963,x5964,x5965,x5961),f751(x5963,x5964,x5965,x5962))
% 81.29/80.93 [597]~E(x5971,x5972)+E(f166(x5971,x5973,x5974),f166(x5972,x5973,x5974))
% 81.29/80.93 [598]~E(x5981,x5982)+E(f166(x5983,x5981,x5984),f166(x5983,x5982,x5984))
% 81.29/80.93 [599]~E(x5991,x5992)+E(f166(x5993,x5994,x5991),f166(x5993,x5994,x5992))
% 81.29/80.93 [600]~E(x6001,x6002)+E(f157(x6001,x6003),f157(x6002,x6003))
% 81.29/80.93 [601]~E(x6011,x6012)+E(f157(x6013,x6011),f157(x6013,x6012))
% 81.29/80.93 [602]~E(x6021,x6022)+E(f218(x6021,x6023,x6024,x6025),f218(x6022,x6023,x6024,x6025))
% 81.29/80.93 [603]~E(x6031,x6032)+E(f218(x6033,x6031,x6034,x6035),f218(x6033,x6032,x6034,x6035))
% 81.29/80.93 [604]~E(x6041,x6042)+E(f218(x6043,x6044,x6041,x6045),f218(x6043,x6044,x6042,x6045))
% 81.29/80.93 [605]~E(x6051,x6052)+E(f218(x6053,x6054,x6055,x6051),f218(x6053,x6054,x6055,x6052))
% 81.29/80.93 [606]~E(x6061,x6062)+E(f163(x6061,x6063,x6064,x6065),f163(x6062,x6063,x6064,x6065))
% 81.29/80.93 [607]~E(x6071,x6072)+E(f163(x6073,x6071,x6074,x6075),f163(x6073,x6072,x6074,x6075))
% 81.29/80.93 [608]~E(x6081,x6082)+E(f163(x6083,x6084,x6081,x6085),f163(x6083,x6084,x6082,x6085))
% 81.29/80.93 [609]~E(x6091,x6092)+E(f163(x6093,x6094,x6095,x6091),f163(x6093,x6094,x6095,x6092))
% 81.29/80.93 [610]~E(x6101,x6102)+E(f142(x6101,x6103),f142(x6102,x6103))
% 81.29/80.93 [611]~E(x6111,x6112)+E(f142(x6113,x6111),f142(x6113,x6112))
% 81.29/80.93 [612]~E(x6121,x6122)+E(f638(x6121,x6123),f638(x6122,x6123))
% 81.29/80.93 [613]~E(x6131,x6132)+E(f638(x6133,x6131),f638(x6133,x6132))
% 81.29/80.93 [614]~E(x6141,x6142)+E(f261(x6141,x6143,x6144),f261(x6142,x6143,x6144))
% 81.29/80.93 [615]~E(x6151,x6152)+E(f261(x6153,x6151,x6154),f261(x6153,x6152,x6154))
% 81.29/80.93 [616]~E(x6161,x6162)+E(f261(x6163,x6164,x6161),f261(x6163,x6164,x6162))
% 81.29/80.93 [617]~E(x6171,x6172)+E(f228(x6171,x6173),f228(x6172,x6173))
% 81.29/80.93 [618]~E(x6181,x6182)+E(f228(x6183,x6181),f228(x6183,x6182))
% 81.29/80.93 [619]~E(x6191,x6192)+E(f131(x6191,x6193),f131(x6192,x6193))
% 81.29/80.93 [620]~E(x6201,x6202)+E(f131(x6203,x6201),f131(x6203,x6202))
% 81.29/80.93 [621]~E(x6211,x6212)+E(f486(x6211,x6213,x6214),f486(x6212,x6213,x6214))
% 81.29/80.93 [622]~E(x6221,x6222)+E(f486(x6223,x6221,x6224),f486(x6223,x6222,x6224))
% 81.29/80.93 [623]~E(x6231,x6232)+E(f486(x6233,x6234,x6231),f486(x6233,x6234,x6232))
% 81.29/80.93 [624]~E(x6241,x6242)+E(f414(x6241,x6243,x6244),f414(x6242,x6243,x6244))
% 81.29/80.93 [625]~E(x6251,x6252)+E(f414(x6253,x6251,x6254),f414(x6253,x6252,x6254))
% 81.29/80.93 [626]~E(x6261,x6262)+E(f414(x6263,x6264,x6261),f414(x6263,x6264,x6262))
% 81.29/80.93 [627]~E(x6271,x6272)+E(f359(x6271,x6273,x6274),f359(x6272,x6273,x6274))
% 81.29/80.93 [628]~E(x6281,x6282)+E(f359(x6283,x6281,x6284),f359(x6283,x6282,x6284))
% 81.29/80.93 [629]~E(x6291,x6292)+E(f359(x6293,x6294,x6291),f359(x6293,x6294,x6292))
% 81.29/80.93 [630]~E(x6301,x6302)+E(f78(x6301,x6303,x6304,x6305),f78(x6302,x6303,x6304,x6305))
% 81.29/80.93 [631]~E(x6311,x6312)+E(f78(x6313,x6311,x6314,x6315),f78(x6313,x6312,x6314,x6315))
% 81.29/80.93 [632]~E(x6321,x6322)+E(f78(x6323,x6324,x6321,x6325),f78(x6323,x6324,x6322,x6325))
% 81.29/80.93 [633]~E(x6331,x6332)+E(f78(x6333,x6334,x6335,x6331),f78(x6333,x6334,x6335,x6332))
% 81.29/80.93 [634]~E(x6341,x6342)+E(f820(x6341,x6343,x6344),f820(x6342,x6343,x6344))
% 81.29/80.93 [635]~E(x6351,x6352)+E(f820(x6353,x6351,x6354),f820(x6353,x6352,x6354))
% 81.29/80.93 [636]~E(x6361,x6362)+E(f820(x6363,x6364,x6361),f820(x6363,x6364,x6362))
% 81.29/80.93 [637]~E(x6371,x6372)+E(f845(x6371,x6373,x6374,x6375,x6376,x6377,x6378),f845(x6372,x6373,x6374,x6375,x6376,x6377,x6378))
% 81.29/80.93 [638]~E(x6381,x6382)+E(f845(x6383,x6381,x6384,x6385,x6386,x6387,x6388),f845(x6383,x6382,x6384,x6385,x6386,x6387,x6388))
% 81.29/80.93 [639]~E(x6391,x6392)+E(f845(x6393,x6394,x6391,x6395,x6396,x6397,x6398),f845(x6393,x6394,x6392,x6395,x6396,x6397,x6398))
% 81.29/80.93 [640]~E(x6401,x6402)+E(f845(x6403,x6404,x6405,x6401,x6406,x6407,x6408),f845(x6403,x6404,x6405,x6402,x6406,x6407,x6408))
% 81.29/80.93 [641]~E(x6411,x6412)+E(f845(x6413,x6414,x6415,x6416,x6411,x6417,x6418),f845(x6413,x6414,x6415,x6416,x6412,x6417,x6418))
% 81.29/80.93 [642]~E(x6421,x6422)+E(f845(x6423,x6424,x6425,x6426,x6427,x6421,x6428),f845(x6423,x6424,x6425,x6426,x6427,x6422,x6428))
% 81.29/80.93 [643]~E(x6431,x6432)+E(f845(x6433,x6434,x6435,x6436,x6437,x6438,x6431),f845(x6433,x6434,x6435,x6436,x6437,x6438,x6432))
% 81.29/80.93 [644]~E(x6441,x6442)+E(f553(x6441,x6443,x6444),f553(x6442,x6443,x6444))
% 81.29/80.93 [645]~E(x6451,x6452)+E(f553(x6453,x6451,x6454),f553(x6453,x6452,x6454))
% 81.29/80.93 [646]~E(x6461,x6462)+E(f553(x6463,x6464,x6461),f553(x6463,x6464,x6462))
% 81.29/80.93 [647]~E(x6471,x6472)+E(f63(x6471,x6473,x6474),f63(x6472,x6473,x6474))
% 81.29/80.93 [648]~E(x6481,x6482)+E(f63(x6483,x6481,x6484),f63(x6483,x6482,x6484))
% 81.29/80.93 [649]~E(x6491,x6492)+E(f63(x6493,x6494,x6491),f63(x6493,x6494,x6492))
% 81.29/80.93 [650]~E(x6501,x6502)+E(f607(x6501,x6503,x6504),f607(x6502,x6503,x6504))
% 81.29/80.93 [651]~E(x6511,x6512)+E(f607(x6513,x6511,x6514),f607(x6513,x6512,x6514))
% 81.29/80.93 [652]~E(x6521,x6522)+E(f607(x6523,x6524,x6521),f607(x6523,x6524,x6522))
% 81.29/80.93 [653]~E(x6531,x6532)+E(f96(x6531),f96(x6532))
% 81.29/80.93 [654]~E(x6541,x6542)+E(f255(x6541,x6543),f255(x6542,x6543))
% 81.29/80.93 [655]~E(x6551,x6552)+E(f255(x6553,x6551),f255(x6553,x6552))
% 81.29/80.93 [656]~E(x6561,x6562)+E(f44(x6561),f44(x6562))
% 81.29/80.93 [657]~E(x6571,x6572)+E(f175(x6571,x6573,x6574),f175(x6572,x6573,x6574))
% 81.29/80.93 [658]~E(x6581,x6582)+E(f175(x6583,x6581,x6584),f175(x6583,x6582,x6584))
% 81.29/80.93 [659]~E(x6591,x6592)+E(f175(x6593,x6594,x6591),f175(x6593,x6594,x6592))
% 81.29/80.93 [660]~E(x6601,x6602)+E(f391(x6601,x6603,x6604),f391(x6602,x6603,x6604))
% 81.29/80.93 [661]~E(x6611,x6612)+E(f391(x6613,x6611,x6614),f391(x6613,x6612,x6614))
% 81.29/80.93 [662]~E(x6621,x6622)+E(f391(x6623,x6624,x6621),f391(x6623,x6624,x6622))
% 81.29/80.93 [663]~E(x6631,x6632)+E(f777(x6631,x6633,x6634,x6635,x6636),f777(x6632,x6633,x6634,x6635,x6636))
% 81.29/80.93 [664]~E(x6641,x6642)+E(f777(x6643,x6641,x6644,x6645,x6646),f777(x6643,x6642,x6644,x6645,x6646))
% 81.29/80.93 [665]~E(x6651,x6652)+E(f777(x6653,x6654,x6651,x6655,x6656),f777(x6653,x6654,x6652,x6655,x6656))
% 81.29/80.93 [666]~E(x6661,x6662)+E(f777(x6663,x6664,x6665,x6661,x6666),f777(x6663,x6664,x6665,x6662,x6666))
% 81.29/80.93 [667]~E(x6671,x6672)+E(f777(x6673,x6674,x6675,x6676,x6671),f777(x6673,x6674,x6675,x6676,x6672))
% 81.29/80.93 [668]~E(x6681,x6682)+E(f352(x6681,x6683,x6684,x6685,x6686),f352(x6682,x6683,x6684,x6685,x6686))
% 81.29/80.93 [669]~E(x6691,x6692)+E(f352(x6693,x6691,x6694,x6695,x6696),f352(x6693,x6692,x6694,x6695,x6696))
% 81.29/80.93 [670]~E(x6701,x6702)+E(f352(x6703,x6704,x6701,x6705,x6706),f352(x6703,x6704,x6702,x6705,x6706))
% 81.29/80.93 [671]~E(x6711,x6712)+E(f352(x6713,x6714,x6715,x6711,x6716),f352(x6713,x6714,x6715,x6712,x6716))
% 81.29/80.93 [672]~E(x6721,x6722)+E(f352(x6723,x6724,x6725,x6726,x6721),f352(x6723,x6724,x6725,x6726,x6722))
% 81.29/80.93 [673]~E(x6731,x6732)+E(f309(x6731,x6733),f309(x6732,x6733))
% 81.29/80.93 [674]~E(x6741,x6742)+E(f309(x6743,x6741),f309(x6743,x6742))
% 81.29/80.93 [675]~E(x6751,x6752)+E(f614(x6751,x6753,x6754,x6755),f614(x6752,x6753,x6754,x6755))
% 81.29/80.93 [676]~E(x6761,x6762)+E(f614(x6763,x6761,x6764,x6765),f614(x6763,x6762,x6764,x6765))
% 81.29/80.93 [677]~E(x6771,x6772)+E(f614(x6773,x6774,x6771,x6775),f614(x6773,x6774,x6772,x6775))
% 81.29/80.93 [678]~E(x6781,x6782)+E(f614(x6783,x6784,x6785,x6781),f614(x6783,x6784,x6785,x6782))
% 81.29/80.93 [679]~E(x6791,x6792)+E(f238(x6791,x6793,x6794,x6795),f238(x6792,x6793,x6794,x6795))
% 81.29/80.93 [680]~E(x6801,x6802)+E(f238(x6803,x6801,x6804,x6805),f238(x6803,x6802,x6804,x6805))
% 81.29/80.93 [681]~E(x6811,x6812)+E(f238(x6813,x6814,x6811,x6815),f238(x6813,x6814,x6812,x6815))
% 81.29/80.93 [682]~E(x6821,x6822)+E(f238(x6823,x6824,x6825,x6821),f238(x6823,x6824,x6825,x6822))
% 81.29/80.93 [683]~E(x6831,x6832)+E(f300(x6831),f300(x6832))
% 81.29/80.93 [684]~E(x6841,x6842)+E(f723(x6841,x6843),f723(x6842,x6843))
% 81.29/80.93 [685]~E(x6851,x6852)+E(f723(x6853,x6851),f723(x6853,x6852))
% 81.29/80.93 [686]~E(x6861,x6862)+E(f502(x6861,x6863,x6864,x6865),f502(x6862,x6863,x6864,x6865))
% 81.29/80.93 [687]~E(x6871,x6872)+E(f502(x6873,x6871,x6874,x6875),f502(x6873,x6872,x6874,x6875))
% 81.29/80.93 [688]~E(x6881,x6882)+E(f502(x6883,x6884,x6881,x6885),f502(x6883,x6884,x6882,x6885))
% 81.29/80.93 [689]~E(x6891,x6892)+E(f502(x6893,x6894,x6895,x6891),f502(x6893,x6894,x6895,x6892))
% 81.29/80.93 [690]~E(x6901,x6902)+E(f191(x6901),f191(x6902))
% 81.29/80.93 [691]~E(x6911,x6912)+E(f672(x6911,x6913),f672(x6912,x6913))
% 81.29/80.93 [692]~E(x6921,x6922)+E(f672(x6923,x6921),f672(x6923,x6922))
% 81.29/80.93 [693]~E(x6931,x6932)+E(f481(x6931,x6933,x6934),f481(x6932,x6933,x6934))
% 81.29/80.93 [694]~E(x6941,x6942)+E(f481(x6943,x6941,x6944),f481(x6943,x6942,x6944))
% 81.29/80.93 [695]~E(x6951,x6952)+E(f481(x6953,x6954,x6951),f481(x6953,x6954,x6952))
% 81.29/80.93 [696]~E(x6961,x6962)+E(f822(x6961,x6963,x6964),f822(x6962,x6963,x6964))
% 81.29/80.93 [697]~E(x6971,x6972)+E(f822(x6973,x6971,x6974),f822(x6973,x6972,x6974))
% 81.29/80.93 [698]~E(x6981,x6982)+E(f822(x6983,x6984,x6981),f822(x6983,x6984,x6982))
% 81.29/80.93 [699]~E(x6991,x6992)+E(f725(x6991,x6993,x6994),f725(x6992,x6993,x6994))
% 81.29/80.93 [700]~E(x7001,x7002)+E(f725(x7003,x7001,x7004),f725(x7003,x7002,x7004))
% 81.29/80.93 [701]~E(x7011,x7012)+E(f725(x7013,x7014,x7011),f725(x7013,x7014,x7012))
% 81.29/80.93 [702]~E(x7021,x7022)+E(f475(x7021,x7023,x7024,x7025),f475(x7022,x7023,x7024,x7025))
% 81.29/80.93 [703]~E(x7031,x7032)+E(f475(x7033,x7031,x7034,x7035),f475(x7033,x7032,x7034,x7035))
% 81.29/80.93 [704]~E(x7041,x7042)+E(f475(x7043,x7044,x7041,x7045),f475(x7043,x7044,x7042,x7045))
% 81.29/80.93 [705]~E(x7051,x7052)+E(f475(x7053,x7054,x7055,x7051),f475(x7053,x7054,x7055,x7052))
% 81.29/80.93 [706]~E(x7061,x7062)+E(f574(x7061,x7063,x7064,x7065,x7066),f574(x7062,x7063,x7064,x7065,x7066))
% 81.29/80.93 [707]~E(x7071,x7072)+E(f574(x7073,x7071,x7074,x7075,x7076),f574(x7073,x7072,x7074,x7075,x7076))
% 81.29/80.93 [708]~E(x7081,x7082)+E(f574(x7083,x7084,x7081,x7085,x7086),f574(x7083,x7084,x7082,x7085,x7086))
% 81.29/80.93 [709]~E(x7091,x7092)+E(f574(x7093,x7094,x7095,x7091,x7096),f574(x7093,x7094,x7095,x7092,x7096))
% 81.29/80.93 [710]~E(x7101,x7102)+E(f574(x7103,x7104,x7105,x7106,x7101),f574(x7103,x7104,x7105,x7106,x7102))
% 81.29/80.93 [711]~E(x7111,x7112)+E(f734(x7111,x7113,x7114,x7115,x7116),f734(x7112,x7113,x7114,x7115,x7116))
% 81.29/80.93 [712]~E(x7121,x7122)+E(f734(x7123,x7121,x7124,x7125,x7126),f734(x7123,x7122,x7124,x7125,x7126))
% 81.29/80.93 [713]~E(x7131,x7132)+E(f734(x7133,x7134,x7131,x7135,x7136),f734(x7133,x7134,x7132,x7135,x7136))
% 81.29/80.93 [714]~E(x7141,x7142)+E(f734(x7143,x7144,x7145,x7141,x7146),f734(x7143,x7144,x7145,x7142,x7146))
% 81.29/80.93 [715]~E(x7151,x7152)+E(f734(x7153,x7154,x7155,x7156,x7151),f734(x7153,x7154,x7155,x7156,x7152))
% 81.29/80.93 [716]~E(x7161,x7162)+E(f706(x7161,x7163,x7164,x7165,x7166,x7167),f706(x7162,x7163,x7164,x7165,x7166,x7167))
% 81.29/80.93 [717]~E(x7171,x7172)+E(f706(x7173,x7171,x7174,x7175,x7176,x7177),f706(x7173,x7172,x7174,x7175,x7176,x7177))
% 81.29/80.93 [718]~E(x7181,x7182)+E(f706(x7183,x7184,x7181,x7185,x7186,x7187),f706(x7183,x7184,x7182,x7185,x7186,x7187))
% 81.29/80.93 [719]~E(x7191,x7192)+E(f706(x7193,x7194,x7195,x7191,x7196,x7197),f706(x7193,x7194,x7195,x7192,x7196,x7197))
% 81.29/80.93 [720]~E(x7201,x7202)+E(f706(x7203,x7204,x7205,x7206,x7201,x7207),f706(x7203,x7204,x7205,x7206,x7202,x7207))
% 81.29/80.93 [721]~E(x7211,x7212)+E(f706(x7213,x7214,x7215,x7216,x7217,x7211),f706(x7213,x7214,x7215,x7216,x7217,x7212))
% 81.29/80.93 [722]~E(x7221,x7222)+E(f479(x7221,x7223,x7224,x7225),f479(x7222,x7223,x7224,x7225))
% 81.29/80.93 [723]~E(x7231,x7232)+E(f479(x7233,x7231,x7234,x7235),f479(x7233,x7232,x7234,x7235))
% 81.29/80.93 [724]~E(x7241,x7242)+E(f479(x7243,x7244,x7241,x7245),f479(x7243,x7244,x7242,x7245))
% 81.29/80.93 [725]~E(x7251,x7252)+E(f479(x7253,x7254,x7255,x7251),f479(x7253,x7254,x7255,x7252))
% 81.29/80.93 [726]~E(x7261,x7262)+E(f849(x7261,x7263,x7264,x7265,x7266,x7267,x7268),f849(x7262,x7263,x7264,x7265,x7266,x7267,x7268))
% 81.29/80.93 [727]~E(x7271,x7272)+E(f849(x7273,x7271,x7274,x7275,x7276,x7277,x7278),f849(x7273,x7272,x7274,x7275,x7276,x7277,x7278))
% 81.29/80.93 [728]~E(x7281,x7282)+E(f849(x7283,x7284,x7281,x7285,x7286,x7287,x7288),f849(x7283,x7284,x7282,x7285,x7286,x7287,x7288))
% 81.29/80.93 [729]~E(x7291,x7292)+E(f849(x7293,x7294,x7295,x7291,x7296,x7297,x7298),f849(x7293,x7294,x7295,x7292,x7296,x7297,x7298))
% 81.29/80.93 [730]~E(x7301,x7302)+E(f849(x7303,x7304,x7305,x7306,x7301,x7307,x7308),f849(x7303,x7304,x7305,x7306,x7302,x7307,x7308))
% 81.29/80.93 [731]~E(x7311,x7312)+E(f849(x7313,x7314,x7315,x7316,x7317,x7311,x7318),f849(x7313,x7314,x7315,x7316,x7317,x7312,x7318))
% 81.29/80.93 [732]~E(x7321,x7322)+E(f849(x7323,x7324,x7325,x7326,x7327,x7328,x7321),f849(x7323,x7324,x7325,x7326,x7327,x7328,x7322))
% 81.29/80.93 [733]~E(x7331,x7332)+E(f662(x7331,x7333,x7334),f662(x7332,x7333,x7334))
% 81.29/80.93 [734]~E(x7341,x7342)+E(f662(x7343,x7341,x7344),f662(x7343,x7342,x7344))
% 81.29/80.93 [735]~E(x7351,x7352)+E(f662(x7353,x7354,x7351),f662(x7353,x7354,x7352))
% 81.29/80.93 [736]~E(x7361,x7362)+E(f336(x7361,x7363,x7364,x7365),f336(x7362,x7363,x7364,x7365))
% 81.29/80.93 [737]~E(x7371,x7372)+E(f336(x7373,x7371,x7374,x7375),f336(x7373,x7372,x7374,x7375))
% 81.29/80.93 [738]~E(x7381,x7382)+E(f336(x7383,x7384,x7381,x7385),f336(x7383,x7384,x7382,x7385))
% 81.29/80.93 [739]~E(x7391,x7392)+E(f336(x7393,x7394,x7395,x7391),f336(x7393,x7394,x7395,x7392))
% 81.29/80.93 [740]~E(x7401,x7402)+E(f441(x7401,x7403,x7404,x7405),f441(x7402,x7403,x7404,x7405))
% 81.29/80.93 [741]~E(x7411,x7412)+E(f441(x7413,x7411,x7414,x7415),f441(x7413,x7412,x7414,x7415))
% 81.29/80.93 [742]~E(x7421,x7422)+E(f441(x7423,x7424,x7421,x7425),f441(x7423,x7424,x7422,x7425))
% 81.29/80.93 [743]~E(x7431,x7432)+E(f441(x7433,x7434,x7435,x7431),f441(x7433,x7434,x7435,x7432))
% 81.29/80.93 [744]~E(x7441,x7442)+E(f605(x7441,x7443,x7444),f605(x7442,x7443,x7444))
% 81.29/80.93 [745]~E(x7451,x7452)+E(f605(x7453,x7451,x7454),f605(x7453,x7452,x7454))
% 81.29/80.93 [746]~E(x7461,x7462)+E(f605(x7463,x7464,x7461),f605(x7463,x7464,x7462))
% 81.29/80.93 [747]~E(x7471,x7472)+E(f639(x7471,x7473),f639(x7472,x7473))
% 81.29/80.93 [748]~E(x7481,x7482)+E(f639(x7483,x7481),f639(x7483,x7482))
% 81.29/80.93 [749]~E(x7491,x7492)+E(f703(x7491,x7493,x7494,x7495,x7496,x7497),f703(x7492,x7493,x7494,x7495,x7496,x7497))
% 81.29/80.93 [750]~E(x7501,x7502)+E(f703(x7503,x7501,x7504,x7505,x7506,x7507),f703(x7503,x7502,x7504,x7505,x7506,x7507))
% 81.29/80.93 [751]~E(x7511,x7512)+E(f703(x7513,x7514,x7511,x7515,x7516,x7517),f703(x7513,x7514,x7512,x7515,x7516,x7517))
% 81.29/80.93 [752]~E(x7521,x7522)+E(f703(x7523,x7524,x7525,x7521,x7526,x7527),f703(x7523,x7524,x7525,x7522,x7526,x7527))
% 81.29/80.93 [753]~E(x7531,x7532)+E(f703(x7533,x7534,x7535,x7536,x7531,x7537),f703(x7533,x7534,x7535,x7536,x7532,x7537))
% 81.29/80.93 [754]~E(x7541,x7542)+E(f703(x7543,x7544,x7545,x7546,x7547,x7541),f703(x7543,x7544,x7545,x7546,x7547,x7542))
% 81.29/80.93 [755]~E(x7551,x7552)+E(f485(x7551,x7553,x7554),f485(x7552,x7553,x7554))
% 81.29/80.93 [756]~E(x7561,x7562)+E(f485(x7563,x7561,x7564),f485(x7563,x7562,x7564))
% 81.29/80.93 [757]~E(x7571,x7572)+E(f485(x7573,x7574,x7571),f485(x7573,x7574,x7572))
% 81.29/80.93 [758]~E(x7581,x7582)+E(f102(x7581),f102(x7582))
% 81.29/80.93 [759]~E(x7591,x7592)+E(f186(x7591,x7593,x7594,x7595,x7596),f186(x7592,x7593,x7594,x7595,x7596))
% 81.29/80.93 [760]~E(x7601,x7602)+E(f186(x7603,x7601,x7604,x7605,x7606),f186(x7603,x7602,x7604,x7605,x7606))
% 81.29/80.93 [761]~E(x7611,x7612)+E(f186(x7613,x7614,x7611,x7615,x7616),f186(x7613,x7614,x7612,x7615,x7616))
% 81.29/80.93 [762]~E(x7621,x7622)+E(f186(x7623,x7624,x7625,x7621,x7626),f186(x7623,x7624,x7625,x7622,x7626))
% 81.29/80.93 [763]~E(x7631,x7632)+E(f186(x7633,x7634,x7635,x7636,x7631),f186(x7633,x7634,x7635,x7636,x7632))
% 81.29/80.93 [764]~E(x7641,x7642)+E(f320(x7641,x7643,x7644,x7645),f320(x7642,x7643,x7644,x7645))
% 81.29/80.93 [765]~E(x7651,x7652)+E(f320(x7653,x7651,x7654,x7655),f320(x7653,x7652,x7654,x7655))
% 81.29/80.93 [766]~E(x7661,x7662)+E(f320(x7663,x7664,x7661,x7665),f320(x7663,x7664,x7662,x7665))
% 81.29/80.93 [767]~E(x7671,x7672)+E(f320(x7673,x7674,x7675,x7671),f320(x7673,x7674,x7675,x7672))
% 81.29/80.93 [768]~E(x7681,x7682)+E(f484(x7681,x7683),f484(x7682,x7683))
% 81.29/80.93 [769]~E(x7691,x7692)+E(f484(x7693,x7691),f484(x7693,x7692))
% 81.29/80.93 [770]~E(x7701,x7702)+E(f190(x7701,x7703,x7704,x7705),f190(x7702,x7703,x7704,x7705))
% 81.29/80.93 [771]~E(x7711,x7712)+E(f190(x7713,x7711,x7714,x7715),f190(x7713,x7712,x7714,x7715))
% 81.29/80.93 [772]~E(x7721,x7722)+E(f190(x7723,x7724,x7721,x7725),f190(x7723,x7724,x7722,x7725))
% 81.29/80.93 [773]~E(x7731,x7732)+E(f190(x7733,x7734,x7735,x7731),f190(x7733,x7734,x7735,x7732))
% 81.29/80.93 [774]~E(x7741,x7742)+E(f224(x7741,x7743),f224(x7742,x7743))
% 81.29/80.93 [775]~E(x7751,x7752)+E(f224(x7753,x7751),f224(x7753,x7752))
% 81.29/80.93 [776]~E(x7761,x7762)+E(f476(x7761,x7763,x7764,x7765,x7766,x7767,x7768,x7769),f476(x7762,x7763,x7764,x7765,x7766,x7767,x7768,x7769))
% 81.29/80.93 [777]~E(x7771,x7772)+E(f476(x7773,x7771,x7774,x7775,x7776,x7777,x7778,x7779),f476(x7773,x7772,x7774,x7775,x7776,x7777,x7778,x7779))
% 81.29/80.93 [778]~E(x7781,x7782)+E(f476(x7783,x7784,x7781,x7785,x7786,x7787,x7788,x7789),f476(x7783,x7784,x7782,x7785,x7786,x7787,x7788,x7789))
% 81.29/80.93 [779]~E(x7791,x7792)+E(f476(x7793,x7794,x7795,x7791,x7796,x7797,x7798,x7799),f476(x7793,x7794,x7795,x7792,x7796,x7797,x7798,x7799))
% 81.29/80.93 [780]~E(x7801,x7802)+E(f476(x7803,x7804,x7805,x7806,x7801,x7807,x7808,x7809),f476(x7803,x7804,x7805,x7806,x7802,x7807,x7808,x7809))
% 81.29/80.93 [781]~E(x7811,x7812)+E(f476(x7813,x7814,x7815,x7816,x7817,x7811,x7818,x7819),f476(x7813,x7814,x7815,x7816,x7817,x7812,x7818,x7819))
% 81.29/80.93 [782]~E(x7821,x7822)+E(f476(x7823,x7824,x7825,x7826,x7827,x7828,x7821,x7829),f476(x7823,x7824,x7825,x7826,x7827,x7828,x7822,x7829))
% 81.29/80.93 [783]~E(x7831,x7832)+E(f476(x7833,x7834,x7835,x7836,x7837,x7838,x7839,x7831),f476(x7833,x7834,x7835,x7836,x7837,x7838,x7839,x7832))
% 81.29/80.93 [784]~E(x7841,x7842)+E(f813(x7841,x7843),f813(x7842,x7843))
% 81.29/80.93 [785]~E(x7851,x7852)+E(f813(x7853,x7851),f813(x7853,x7852))
% 81.29/80.93 [786]~E(x7861,x7862)+E(f264(x7861,x7863,x7864),f264(x7862,x7863,x7864))
% 81.29/80.93 [787]~E(x7871,x7872)+E(f264(x7873,x7871,x7874),f264(x7873,x7872,x7874))
% 81.29/80.93 [788]~E(x7881,x7882)+E(f264(x7883,x7884,x7881),f264(x7883,x7884,x7882))
% 81.29/80.93 [789]~E(x7891,x7892)+E(f698(x7891,x7893,x7894),f698(x7892,x7893,x7894))
% 81.29/80.93 [790]~E(x7901,x7902)+E(f698(x7903,x7901,x7904),f698(x7903,x7902,x7904))
% 81.29/80.93 [791]~E(x7911,x7912)+E(f698(x7913,x7914,x7911),f698(x7913,x7914,x7912))
% 81.29/80.93 [792]~E(x7921,x7922)+E(f469(x7921,x7923),f469(x7922,x7923))
% 81.29/80.93 [793]~E(x7931,x7932)+E(f469(x7933,x7931),f469(x7933,x7932))
% 81.29/80.93 [794]~E(x7941,x7942)+E(f796(x7941,x7943,x7944),f796(x7942,x7943,x7944))
% 81.29/80.93 [795]~E(x7951,x7952)+E(f796(x7953,x7951,x7954),f796(x7953,x7952,x7954))
% 81.29/80.93 [796]~E(x7961,x7962)+E(f796(x7963,x7964,x7961),f796(x7963,x7964,x7962))
% 81.29/80.93 [797]~E(x7971,x7972)+E(f747(x7971,x7973,x7974,x7975,x7976),f747(x7972,x7973,x7974,x7975,x7976))
% 81.29/80.93 [798]~E(x7981,x7982)+E(f747(x7983,x7981,x7984,x7985,x7986),f747(x7983,x7982,x7984,x7985,x7986))
% 81.29/80.93 [799]~E(x7991,x7992)+E(f747(x7993,x7994,x7991,x7995,x7996),f747(x7993,x7994,x7992,x7995,x7996))
% 81.29/80.93 [800]~E(x8001,x8002)+E(f747(x8003,x8004,x8005,x8001,x8006),f747(x8003,x8004,x8005,x8002,x8006))
% 81.29/80.93 [801]~E(x8011,x8012)+E(f747(x8013,x8014,x8015,x8016,x8011),f747(x8013,x8014,x8015,x8016,x8012))
% 81.29/80.93 [802]~E(x8021,x8022)+E(f134(x8021),f134(x8022))
% 81.29/80.93 [803]~E(x8031,x8032)+E(f663(x8031,x8033,x8034,x8035),f663(x8032,x8033,x8034,x8035))
% 81.29/80.93 [804]~E(x8041,x8042)+E(f663(x8043,x8041,x8044,x8045),f663(x8043,x8042,x8044,x8045))
% 81.29/80.93 [805]~E(x8051,x8052)+E(f663(x8053,x8054,x8051,x8055),f663(x8053,x8054,x8052,x8055))
% 81.29/80.93 [806]~E(x8061,x8062)+E(f663(x8063,x8064,x8065,x8061),f663(x8063,x8064,x8065,x8062))
% 81.29/80.93 [807]~E(x8071,x8072)+E(f616(x8071,x8073,x8074,x8075,x8076),f616(x8072,x8073,x8074,x8075,x8076))
% 81.29/80.93 [808]~E(x8081,x8082)+E(f616(x8083,x8081,x8084,x8085,x8086),f616(x8083,x8082,x8084,x8085,x8086))
% 81.29/80.93 [809]~E(x8091,x8092)+E(f616(x8093,x8094,x8091,x8095,x8096),f616(x8093,x8094,x8092,x8095,x8096))
% 81.29/80.93 [810]~E(x8101,x8102)+E(f616(x8103,x8104,x8105,x8101,x8106),f616(x8103,x8104,x8105,x8102,x8106))
% 81.29/80.93 [811]~E(x8111,x8112)+E(f616(x8113,x8114,x8115,x8116,x8111),f616(x8113,x8114,x8115,x8116,x8112))
% 81.29/80.93 [812]~E(x8121,x8122)+E(f493(x8121,x8123,x8124,x8125),f493(x8122,x8123,x8124,x8125))
% 81.29/80.93 [813]~E(x8131,x8132)+E(f493(x8133,x8131,x8134,x8135),f493(x8133,x8132,x8134,x8135))
% 81.29/80.93 [814]~E(x8141,x8142)+E(f493(x8143,x8144,x8141,x8145),f493(x8143,x8144,x8142,x8145))
% 81.29/80.93 [815]~E(x8151,x8152)+E(f493(x8153,x8154,x8155,x8151),f493(x8153,x8154,x8155,x8152))
% 81.29/80.93 [816]~E(x8161,x8162)+E(f339(x8161,x8163,x8164),f339(x8162,x8163,x8164))
% 81.29/80.93 [817]~E(x8171,x8172)+E(f339(x8173,x8171,x8174),f339(x8173,x8172,x8174))
% 81.29/80.93 [818]~E(x8181,x8182)+E(f339(x8183,x8184,x8181),f339(x8183,x8184,x8182))
% 81.29/80.93 [819]~E(x8191,x8192)+E(f332(x8191,x8193,x8194,x8195),f332(x8192,x8193,x8194,x8195))
% 81.29/80.93 [820]~E(x8201,x8202)+E(f332(x8203,x8201,x8204,x8205),f332(x8203,x8202,x8204,x8205))
% 81.29/80.93 [821]~E(x8211,x8212)+E(f332(x8213,x8214,x8211,x8215),f332(x8213,x8214,x8212,x8215))
% 81.29/80.93 [822]~E(x8221,x8222)+E(f332(x8223,x8224,x8225,x8221),f332(x8223,x8224,x8225,x8222))
% 81.29/80.93 [823]~E(x8231,x8232)+E(f161(x8231,x8233),f161(x8232,x8233))
% 81.29/80.93 [824]~E(x8241,x8242)+E(f161(x8243,x8241),f161(x8243,x8242))
% 81.29/80.93 [825]~E(x8251,x8252)+E(f360(x8251,x8253,x8254),f360(x8252,x8253,x8254))
% 81.29/80.93 [826]~E(x8261,x8262)+E(f360(x8263,x8261,x8264),f360(x8263,x8262,x8264))
% 81.29/80.93 [827]~E(x8271,x8272)+E(f360(x8273,x8274,x8271),f360(x8273,x8274,x8272))
% 81.29/80.93 [828]~E(x8281,x8282)+E(f409(x8281,x8283),f409(x8282,x8283))
% 81.29/80.93 [829]~E(x8291,x8292)+E(f409(x8293,x8291),f409(x8293,x8292))
% 81.29/80.93 [830]~E(x8301,x8302)+E(f830(x8301,x8303,x8304,x8305,x8306,x8307),f830(x8302,x8303,x8304,x8305,x8306,x8307))
% 81.29/80.93 [831]~E(x8311,x8312)+E(f830(x8313,x8311,x8314,x8315,x8316,x8317),f830(x8313,x8312,x8314,x8315,x8316,x8317))
% 81.29/80.93 [832]~E(x8321,x8322)+E(f830(x8323,x8324,x8321,x8325,x8326,x8327),f830(x8323,x8324,x8322,x8325,x8326,x8327))
% 81.29/80.93 [833]~E(x8331,x8332)+E(f830(x8333,x8334,x8335,x8331,x8336,x8337),f830(x8333,x8334,x8335,x8332,x8336,x8337))
% 81.29/80.93 [834]~E(x8341,x8342)+E(f830(x8343,x8344,x8345,x8346,x8341,x8347),f830(x8343,x8344,x8345,x8346,x8342,x8347))
% 81.29/80.93 [835]~E(x8351,x8352)+E(f830(x8353,x8354,x8355,x8356,x8357,x8351),f830(x8353,x8354,x8355,x8356,x8357,x8352))
% 81.29/80.93 [836]~E(x8361,x8362)+E(f373(x8361,x8363,x8364),f373(x8362,x8363,x8364))
% 81.29/80.93 [837]~E(x8371,x8372)+E(f373(x8373,x8371,x8374),f373(x8373,x8372,x8374))
% 81.29/80.93 [838]~E(x8381,x8382)+E(f373(x8383,x8384,x8381),f373(x8383,x8384,x8382))
% 81.29/80.93 [839]~E(x8391,x8392)+E(f368(x8391,x8393,x8394),f368(x8392,x8393,x8394))
% 81.29/80.93 [840]~E(x8401,x8402)+E(f368(x8403,x8401,x8404),f368(x8403,x8402,x8404))
% 81.29/80.93 [841]~E(x8411,x8412)+E(f368(x8413,x8414,x8411),f368(x8413,x8414,x8412))
% 81.29/80.93 [842]~E(x8421,x8422)+E(f568(x8421,x8423,x8424),f568(x8422,x8423,x8424))
% 81.29/80.93 [843]~E(x8431,x8432)+E(f568(x8433,x8431,x8434),f568(x8433,x8432,x8434))
% 81.29/80.93 [844]~E(x8441,x8442)+E(f568(x8443,x8444,x8441),f568(x8443,x8444,x8442))
% 81.29/80.93 [845]~E(x8451,x8452)+E(f144(x8451,x8453),f144(x8452,x8453))
% 81.29/80.93 [846]~E(x8461,x8462)+E(f144(x8463,x8461),f144(x8463,x8462))
% 81.29/80.93 [847]~E(x8471,x8472)+E(f669(x8471,x8473,x8474,x8475,x8476),f669(x8472,x8473,x8474,x8475,x8476))
% 81.29/80.93 [848]~E(x8481,x8482)+E(f669(x8483,x8481,x8484,x8485,x8486),f669(x8483,x8482,x8484,x8485,x8486))
% 81.29/80.93 [849]~E(x8491,x8492)+E(f669(x8493,x8494,x8491,x8495,x8496),f669(x8493,x8494,x8492,x8495,x8496))
% 81.29/80.93 [850]~E(x8501,x8502)+E(f669(x8503,x8504,x8505,x8501,x8506),f669(x8503,x8504,x8505,x8502,x8506))
% 81.29/80.93 [851]~E(x8511,x8512)+E(f669(x8513,x8514,x8515,x8516,x8511),f669(x8513,x8514,x8515,x8516,x8512))
% 81.29/80.93 [852]~E(x8521,x8522)+E(f586(x8521,x8523,x8524),f586(x8522,x8523,x8524))
% 81.29/80.93 [853]~E(x8531,x8532)+E(f586(x8533,x8531,x8534),f586(x8533,x8532,x8534))
% 81.29/80.93 [854]~E(x8541,x8542)+E(f586(x8543,x8544,x8541),f586(x8543,x8544,x8542))
% 81.29/80.93 [855]~E(x8551,x8552)+E(f819(x8551,x8553,x8554),f819(x8552,x8553,x8554))
% 81.29/80.93 [856]~E(x8561,x8562)+E(f819(x8563,x8561,x8564),f819(x8563,x8562,x8564))
% 81.29/80.93 [857]~E(x8571,x8572)+E(f819(x8573,x8574,x8571),f819(x8573,x8574,x8572))
% 81.29/80.93 [858]~E(x8581,x8582)+E(f494(x8581,x8583,x8584),f494(x8582,x8583,x8584))
% 81.29/80.93 [859]~E(x8591,x8592)+E(f494(x8593,x8591,x8594),f494(x8593,x8592,x8594))
% 81.29/80.93 [860]~E(x8601,x8602)+E(f494(x8603,x8604,x8601),f494(x8603,x8604,x8602))
% 81.29/80.93 [861]~E(x8611,x8612)+E(f645(x8611,x8613,x8614,x8615),f645(x8612,x8613,x8614,x8615))
% 81.29/80.93 [862]~E(x8621,x8622)+E(f645(x8623,x8621,x8624,x8625),f645(x8623,x8622,x8624,x8625))
% 81.29/80.93 [863]~E(x8631,x8632)+E(f645(x8633,x8634,x8631,x8635),f645(x8633,x8634,x8632,x8635))
% 81.29/80.93 [864]~E(x8641,x8642)+E(f645(x8643,x8644,x8645,x8641),f645(x8643,x8644,x8645,x8642))
% 81.29/80.93 [865]~E(x8651,x8652)+E(f634(x8651,x8653,x8654,x8655),f634(x8652,x8653,x8654,x8655))
% 81.29/80.93 [866]~E(x8661,x8662)+E(f634(x8663,x8661,x8664,x8665),f634(x8663,x8662,x8664,x8665))
% 81.29/80.93 [867]~E(x8671,x8672)+E(f634(x8673,x8674,x8671,x8675),f634(x8673,x8674,x8672,x8675))
% 81.29/80.93 [868]~E(x8681,x8682)+E(f634(x8683,x8684,x8685,x8681),f634(x8683,x8684,x8685,x8682))
% 81.29/80.93 [869]~E(x8691,x8692)+E(f488(x8691,x8693,x8694,x8695),f488(x8692,x8693,x8694,x8695))
% 81.29/80.93 [870]~E(x8701,x8702)+E(f488(x8703,x8701,x8704,x8705),f488(x8703,x8702,x8704,x8705))
% 81.29/80.93 [871]~E(x8711,x8712)+E(f488(x8713,x8714,x8711,x8715),f488(x8713,x8714,x8712,x8715))
% 81.29/80.93 [872]~E(x8721,x8722)+E(f488(x8723,x8724,x8725,x8721),f488(x8723,x8724,x8725,x8722))
% 81.29/80.93 [873]~E(x8731,x8732)+E(f77(x8731,x8733,x8734,x8735,x8736),f77(x8732,x8733,x8734,x8735,x8736))
% 81.29/80.93 [874]~E(x8741,x8742)+E(f77(x8743,x8741,x8744,x8745,x8746),f77(x8743,x8742,x8744,x8745,x8746))
% 81.29/80.93 [875]~E(x8751,x8752)+E(f77(x8753,x8754,x8751,x8755,x8756),f77(x8753,x8754,x8752,x8755,x8756))
% 81.29/80.93 [876]~E(x8761,x8762)+E(f77(x8763,x8764,x8765,x8761,x8766),f77(x8763,x8764,x8765,x8762,x8766))
% 81.29/80.93 [877]~E(x8771,x8772)+E(f77(x8773,x8774,x8775,x8776,x8771),f77(x8773,x8774,x8775,x8776,x8772))
% 81.29/80.93 [878]~E(x8781,x8782)+E(f561(x8781,x8783,x8784,x8785,x8786),f561(x8782,x8783,x8784,x8785,x8786))
% 81.29/80.93 [879]~E(x8791,x8792)+E(f561(x8793,x8791,x8794,x8795,x8796),f561(x8793,x8792,x8794,x8795,x8796))
% 81.29/80.93 [880]~E(x8801,x8802)+E(f561(x8803,x8804,x8801,x8805,x8806),f561(x8803,x8804,x8802,x8805,x8806))
% 81.29/80.93 [881]~E(x8811,x8812)+E(f561(x8813,x8814,x8815,x8811,x8816),f561(x8813,x8814,x8815,x8812,x8816))
% 81.29/80.93 [882]~E(x8821,x8822)+E(f561(x8823,x8824,x8825,x8826,x8821),f561(x8823,x8824,x8825,x8826,x8822))
% 81.29/80.93 [883]~E(x8831,x8832)+E(f837(x8831),f837(x8832))
% 81.29/80.93 [884]~E(x8841,x8842)+E(f567(x8841,x8843,x8844,x8845,x8846),f567(x8842,x8843,x8844,x8845,x8846))
% 81.29/80.93 [885]~E(x8851,x8852)+E(f567(x8853,x8851,x8854,x8855,x8856),f567(x8853,x8852,x8854,x8855,x8856))
% 81.29/80.93 [886]~E(x8861,x8862)+E(f567(x8863,x8864,x8861,x8865,x8866),f567(x8863,x8864,x8862,x8865,x8866))
% 81.29/80.93 [887]~E(x8871,x8872)+E(f567(x8873,x8874,x8875,x8871,x8876),f567(x8873,x8874,x8875,x8872,x8876))
% 81.29/80.93 [888]~E(x8881,x8882)+E(f567(x8883,x8884,x8885,x8886,x8881),f567(x8883,x8884,x8885,x8886,x8882))
% 81.29/80.93 [889]~E(x8891,x8892)+E(f155(x8891,x8893,x8894,x8895),f155(x8892,x8893,x8894,x8895))
% 81.29/80.93 [890]~E(x8901,x8902)+E(f155(x8903,x8901,x8904,x8905),f155(x8903,x8902,x8904,x8905))
% 81.29/80.93 [891]~E(x8911,x8912)+E(f155(x8913,x8914,x8911,x8915),f155(x8913,x8914,x8912,x8915))
% 81.29/80.93 [892]~E(x8921,x8922)+E(f155(x8923,x8924,x8925,x8921),f155(x8923,x8924,x8925,x8922))
% 81.29/80.93 [893]~E(x8931,x8932)+E(f198(x8931,x8933),f198(x8932,x8933))
% 81.29/80.94 [894]~E(x8941,x8942)+E(f198(x8943,x8941),f198(x8943,x8942))
% 81.29/80.94 [895]~E(x8951,x8952)+E(f495(x8951,x8953,x8954),f495(x8952,x8953,x8954))
% 81.29/80.94 [896]~E(x8961,x8962)+E(f495(x8963,x8961,x8964),f495(x8963,x8962,x8964))
% 81.29/80.94 [897]~E(x8971,x8972)+E(f495(x8973,x8974,x8971),f495(x8973,x8974,x8972))
% 81.29/80.94 [898]~E(x8981,x8982)+E(f124(x8981,x8983),f124(x8982,x8983))
% 81.29/80.94 [899]~E(x8991,x8992)+E(f124(x8993,x8991),f124(x8993,x8992))
% 81.29/80.94 [900]~E(x9001,x9002)+E(f766(x9001,x9003),f766(x9002,x9003))
% 81.29/80.94 [901]~E(x9011,x9012)+E(f766(x9013,x9011),f766(x9013,x9012))
% 81.29/80.94 [902]~E(x9021,x9022)+E(f804(x9021,x9023,x9024),f804(x9022,x9023,x9024))
% 81.29/80.94 [903]~E(x9031,x9032)+E(f804(x9033,x9031,x9034),f804(x9033,x9032,x9034))
% 81.29/80.94 [904]~E(x9041,x9042)+E(f804(x9043,x9044,x9041),f804(x9043,x9044,x9042))
% 81.29/80.94 [905]~E(x9051,x9052)+E(f595(x9051,x9053,x9054,x9055,x9056),f595(x9052,x9053,x9054,x9055,x9056))
% 81.29/80.94 [906]~E(x9061,x9062)+E(f595(x9063,x9061,x9064,x9065,x9066),f595(x9063,x9062,x9064,x9065,x9066))
% 81.29/80.94 [907]~E(x9071,x9072)+E(f595(x9073,x9074,x9071,x9075,x9076),f595(x9073,x9074,x9072,x9075,x9076))
% 81.29/80.94 [908]~E(x9081,x9082)+E(f595(x9083,x9084,x9085,x9081,x9086),f595(x9083,x9084,x9085,x9082,x9086))
% 81.29/80.94 [909]~E(x9091,x9092)+E(f595(x9093,x9094,x9095,x9096,x9091),f595(x9093,x9094,x9095,x9096,x9092))
% 81.29/80.94 [910]~E(x9101,x9102)+E(f827(x9101,x9103,x9104,x9105),f827(x9102,x9103,x9104,x9105))
% 81.29/80.94 [911]~E(x9111,x9112)+E(f827(x9113,x9111,x9114,x9115),f827(x9113,x9112,x9114,x9115))
% 81.29/80.94 [912]~E(x9121,x9122)+E(f827(x9123,x9124,x9121,x9125),f827(x9123,x9124,x9122,x9125))
% 81.29/80.94 [913]~E(x9131,x9132)+E(f827(x9133,x9134,x9135,x9131),f827(x9133,x9134,x9135,x9132))
% 81.29/80.94 [914]~E(x9141,x9142)+E(f631(x9141,x9143,x9144,x9145),f631(x9142,x9143,x9144,x9145))
% 81.29/80.94 [915]~E(x9151,x9152)+E(f631(x9153,x9151,x9154,x9155),f631(x9153,x9152,x9154,x9155))
% 81.29/80.94 [916]~E(x9161,x9162)+E(f631(x9163,x9164,x9161,x9165),f631(x9163,x9164,x9162,x9165))
% 81.29/80.94 [917]~E(x9171,x9172)+E(f631(x9173,x9174,x9175,x9171),f631(x9173,x9174,x9175,x9172))
% 81.29/80.94 [918]~E(x9181,x9182)+E(f410(x9181,x9183,x9184,x9185),f410(x9182,x9183,x9184,x9185))
% 81.29/80.94 [919]~E(x9191,x9192)+E(f410(x9193,x9191,x9194,x9195),f410(x9193,x9192,x9194,x9195))
% 81.29/80.94 [920]~E(x9201,x9202)+E(f410(x9203,x9204,x9201,x9205),f410(x9203,x9204,x9202,x9205))
% 81.29/80.94 [921]~E(x9211,x9212)+E(f410(x9213,x9214,x9215,x9211),f410(x9213,x9214,x9215,x9212))
% 81.29/80.94 [922]~E(x9221,x9222)+E(f652(x9221,x9223,x9224),f652(x9222,x9223,x9224))
% 81.29/80.94 [923]~E(x9231,x9232)+E(f652(x9233,x9231,x9234),f652(x9233,x9232,x9234))
% 81.29/80.94 [924]~E(x9241,x9242)+E(f652(x9243,x9244,x9241),f652(x9243,x9244,x9242))
% 81.29/80.94 [925]~E(x9251,x9252)+E(f296(x9251,x9253,x9254,x9255,x9256),f296(x9252,x9253,x9254,x9255,x9256))
% 81.29/80.94 [926]~E(x9261,x9262)+E(f296(x9263,x9261,x9264,x9265,x9266),f296(x9263,x9262,x9264,x9265,x9266))
% 81.29/80.94 [927]~E(x9271,x9272)+E(f296(x9273,x9274,x9271,x9275,x9276),f296(x9273,x9274,x9272,x9275,x9276))
% 81.29/80.94 [928]~E(x9281,x9282)+E(f296(x9283,x9284,x9285,x9281,x9286),f296(x9283,x9284,x9285,x9282,x9286))
% 81.29/80.94 [929]~E(x9291,x9292)+E(f296(x9293,x9294,x9295,x9296,x9291),f296(x9293,x9294,x9295,x9296,x9292))
% 81.29/80.94 [930]~E(x9301,x9302)+E(f690(x9301,x9303,x9304,x9305),f690(x9302,x9303,x9304,x9305))
% 81.29/80.94 [931]~E(x9311,x9312)+E(f690(x9313,x9311,x9314,x9315),f690(x9313,x9312,x9314,x9315))
% 81.29/80.94 [932]~E(x9321,x9322)+E(f690(x9323,x9324,x9321,x9325),f690(x9323,x9324,x9322,x9325))
% 81.29/80.94 [933]~E(x9331,x9332)+E(f690(x9333,x9334,x9335,x9331),f690(x9333,x9334,x9335,x9332))
% 81.29/80.94 [934]~E(x9341,x9342)+E(f675(x9341,x9343,x9344,x9345),f675(x9342,x9343,x9344,x9345))
% 81.29/80.94 [935]~E(x9351,x9352)+E(f675(x9353,x9351,x9354,x9355),f675(x9353,x9352,x9354,x9355))
% 81.29/80.94 [936]~E(x9361,x9362)+E(f675(x9363,x9364,x9361,x9365),f675(x9363,x9364,x9362,x9365))
% 81.29/80.94 [937]~E(x9371,x9372)+E(f675(x9373,x9374,x9375,x9371),f675(x9373,x9374,x9375,x9372))
% 81.29/80.94 [938]~E(x9381,x9382)+E(f513(x9381,x9383,x9384,x9385),f513(x9382,x9383,x9384,x9385))
% 81.29/80.94 [939]~E(x9391,x9392)+E(f513(x9393,x9391,x9394,x9395),f513(x9393,x9392,x9394,x9395))
% 81.29/80.94 [940]~E(x9401,x9402)+E(f513(x9403,x9404,x9401,x9405),f513(x9403,x9404,x9402,x9405))
% 81.29/80.94 [941]~E(x9411,x9412)+E(f513(x9413,x9414,x9415,x9411),f513(x9413,x9414,x9415,x9412))
% 81.29/80.94 [942]~E(x9421,x9422)+E(f210(x9421),f210(x9422))
% 81.29/80.94 [943]~E(x9431,x9432)+E(f259(x9431,x9433,x9434),f259(x9432,x9433,x9434))
% 81.29/80.94 [944]~E(x9441,x9442)+E(f259(x9443,x9441,x9444),f259(x9443,x9442,x9444))
% 81.29/80.94 [945]~E(x9451,x9452)+E(f259(x9453,x9454,x9451),f259(x9453,x9454,x9452))
% 81.29/80.94 [946]~E(x9461,x9462)+E(f335(x9461,x9463,x9464),f335(x9462,x9463,x9464))
% 81.29/80.94 [947]~E(x9471,x9472)+E(f335(x9473,x9471,x9474),f335(x9473,x9472,x9474))
% 81.29/80.94 [948]~E(x9481,x9482)+E(f335(x9483,x9484,x9481),f335(x9483,x9484,x9482))
% 81.29/80.94 [949]~E(x9491,x9492)+E(f646(x9491,x9493),f646(x9492,x9493))
% 81.29/80.94 [950]~E(x9501,x9502)+E(f646(x9503,x9501),f646(x9503,x9502))
% 81.29/80.94 [951]~E(x9511,x9512)+E(f842(x9511,x9513,x9514,x9515),f842(x9512,x9513,x9514,x9515))
% 81.29/80.94 [952]~E(x9521,x9522)+E(f842(x9523,x9521,x9524,x9525),f842(x9523,x9522,x9524,x9525))
% 81.29/80.94 [953]~E(x9531,x9532)+E(f842(x9533,x9534,x9531,x9535),f842(x9533,x9534,x9532,x9535))
% 81.29/80.94 [954]~E(x9541,x9542)+E(f842(x9543,x9544,x9545,x9541),f842(x9543,x9544,x9545,x9542))
% 81.29/80.94 [955]~E(x9551,x9552)+E(f826(x9551,x9553,x9554),f826(x9552,x9553,x9554))
% 81.29/80.94 [956]~E(x9561,x9562)+E(f826(x9563,x9561,x9564),f826(x9563,x9562,x9564))
% 81.29/80.94 [957]~E(x9571,x9572)+E(f826(x9573,x9574,x9571),f826(x9573,x9574,x9572))
% 81.29/80.94 [958]~E(x9581,x9582)+E(f799(x9581,x9583),f799(x9582,x9583))
% 81.29/80.94 [959]~E(x9591,x9592)+E(f799(x9593,x9591),f799(x9593,x9592))
% 81.29/80.94 [960]~E(x9601,x9602)+E(f53(x9601,x9603),f53(x9602,x9603))
% 81.29/80.94 [961]~E(x9611,x9612)+E(f53(x9613,x9611),f53(x9613,x9612))
% 81.29/80.94 [962]~E(x9621,x9622)+E(f854(x9621,x9623,x9624,x9625,x9626),f854(x9622,x9623,x9624,x9625,x9626))
% 81.29/80.94 [963]~E(x9631,x9632)+E(f854(x9633,x9631,x9634,x9635,x9636),f854(x9633,x9632,x9634,x9635,x9636))
% 81.29/80.94 [964]~E(x9641,x9642)+E(f854(x9643,x9644,x9641,x9645,x9646),f854(x9643,x9644,x9642,x9645,x9646))
% 81.29/80.94 [965]~E(x9651,x9652)+E(f854(x9653,x9654,x9655,x9651,x9656),f854(x9653,x9654,x9655,x9652,x9656))
% 81.29/80.94 [966]~E(x9661,x9662)+E(f854(x9663,x9664,x9665,x9666,x9661),f854(x9663,x9664,x9665,x9666,x9662))
% 81.29/80.94 [967]~E(x9671,x9672)+E(f666(x9671,x9673,x9674,x9675),f666(x9672,x9673,x9674,x9675))
% 81.29/80.94 [968]~E(x9681,x9682)+E(f666(x9683,x9681,x9684,x9685),f666(x9683,x9682,x9684,x9685))
% 81.29/80.94 [969]~E(x9691,x9692)+E(f666(x9693,x9694,x9691,x9695),f666(x9693,x9694,x9692,x9695))
% 81.29/80.94 [970]~E(x9701,x9702)+E(f666(x9703,x9704,x9705,x9701),f666(x9703,x9704,x9705,x9702))
% 81.29/80.94 [971]~E(x9711,x9712)+E(f123(x9711,x9713,x9714),f123(x9712,x9713,x9714))
% 81.29/80.94 [972]~E(x9721,x9722)+E(f123(x9723,x9721,x9724),f123(x9723,x9722,x9724))
% 81.29/80.94 [973]~E(x9731,x9732)+E(f123(x9733,x9734,x9731),f123(x9733,x9734,x9732))
% 81.29/80.94 [974]~E(x9741,x9742)+E(f781(x9741,x9743),f781(x9742,x9743))
% 81.29/80.94 [975]~E(x9751,x9752)+E(f781(x9753,x9751),f781(x9753,x9752))
% 81.29/80.94 [976]~E(x9761,x9762)+E(f716(x9761,x9763,x9764,x9765,x9766,x9767),f716(x9762,x9763,x9764,x9765,x9766,x9767))
% 81.29/80.94 [977]~E(x9771,x9772)+E(f716(x9773,x9771,x9774,x9775,x9776,x9777),f716(x9773,x9772,x9774,x9775,x9776,x9777))
% 81.29/80.94 [978]~E(x9781,x9782)+E(f716(x9783,x9784,x9781,x9785,x9786,x9787),f716(x9783,x9784,x9782,x9785,x9786,x9787))
% 81.29/80.94 [979]~E(x9791,x9792)+E(f716(x9793,x9794,x9795,x9791,x9796,x9797),f716(x9793,x9794,x9795,x9792,x9796,x9797))
% 81.29/80.94 [980]~E(x9801,x9802)+E(f716(x9803,x9804,x9805,x9806,x9801,x9807),f716(x9803,x9804,x9805,x9806,x9802,x9807))
% 81.29/80.94 [981]~E(x9811,x9812)+E(f716(x9813,x9814,x9815,x9816,x9817,x9811),f716(x9813,x9814,x9815,x9816,x9817,x9812))
% 81.29/80.94 [982]~E(x9821,x9822)+E(f421(x9821,x9823,x9824),f421(x9822,x9823,x9824))
% 81.29/80.94 [983]~E(x9831,x9832)+E(f421(x9833,x9831,x9834),f421(x9833,x9832,x9834))
% 81.29/80.94 [984]~E(x9841,x9842)+E(f421(x9843,x9844,x9841),f421(x9843,x9844,x9842))
% 81.29/80.94 [985]~E(x9851,x9852)+E(f593(x9851,x9853,x9854,x9855,x9856),f593(x9852,x9853,x9854,x9855,x9856))
% 81.29/80.94 [986]~E(x9861,x9862)+E(f593(x9863,x9861,x9864,x9865,x9866),f593(x9863,x9862,x9864,x9865,x9866))
% 81.29/80.94 [987]~E(x9871,x9872)+E(f593(x9873,x9874,x9871,x9875,x9876),f593(x9873,x9874,x9872,x9875,x9876))
% 81.29/80.94 [988]~E(x9881,x9882)+E(f593(x9883,x9884,x9885,x9881,x9886),f593(x9883,x9884,x9885,x9882,x9886))
% 81.29/80.94 [989]~E(x9891,x9892)+E(f593(x9893,x9894,x9895,x9896,x9891),f593(x9893,x9894,x9895,x9896,x9892))
% 81.29/80.94 [990]~E(x9901,x9902)+E(f58(x9901),f58(x9902))
% 81.29/80.94 [991]~E(x9911,x9912)+E(f473(x9911,x9913,x9914),f473(x9912,x9913,x9914))
% 81.29/80.94 [992]~E(x9921,x9922)+E(f473(x9923,x9921,x9924),f473(x9923,x9922,x9924))
% 81.29/80.94 [993]~E(x9931,x9932)+E(f473(x9933,x9934,x9931),f473(x9933,x9934,x9932))
% 81.29/80.94 [994]~E(x9941,x9942)+E(f468(x9941,x9943,x9944,x9945),f468(x9942,x9943,x9944,x9945))
% 81.29/80.94 [995]~E(x9951,x9952)+E(f468(x9953,x9951,x9954,x9955),f468(x9953,x9952,x9954,x9955))
% 81.29/80.94 [996]~E(x9961,x9962)+E(f468(x9963,x9964,x9961,x9965),f468(x9963,x9964,x9962,x9965))
% 81.29/80.94 [997]~E(x9971,x9972)+E(f468(x9973,x9974,x9975,x9971),f468(x9973,x9974,x9975,x9972))
% 81.29/80.94 [998]~E(x9981,x9982)+E(f629(x9981,x9983,x9984,x9985),f629(x9982,x9983,x9984,x9985))
% 81.29/80.94 [999]~E(x9991,x9992)+E(f629(x9993,x9991,x9994,x9995),f629(x9993,x9992,x9994,x9995))
% 81.29/80.94 [1000]~E(x10001,x10002)+E(f629(x10003,x10004,x10001,x10005),f629(x10003,x10004,x10002,x10005))
% 81.29/80.94 [1001]~E(x10011,x10012)+E(f629(x10013,x10014,x10015,x10011),f629(x10013,x10014,x10015,x10012))
% 81.29/80.94 [1002]~E(x10021,x10022)+E(f776(x10021,x10023,x10024,x10025,x10026),f776(x10022,x10023,x10024,x10025,x10026))
% 81.29/80.94 [1003]~E(x10031,x10032)+E(f776(x10033,x10031,x10034,x10035,x10036),f776(x10033,x10032,x10034,x10035,x10036))
% 81.29/80.94 [1004]~E(x10041,x10042)+E(f776(x10043,x10044,x10041,x10045,x10046),f776(x10043,x10044,x10042,x10045,x10046))
% 81.29/80.94 [1005]~E(x10051,x10052)+E(f776(x10053,x10054,x10055,x10051,x10056),f776(x10053,x10054,x10055,x10052,x10056))
% 81.29/80.94 [1006]~E(x10061,x10062)+E(f776(x10063,x10064,x10065,x10066,x10061),f776(x10063,x10064,x10065,x10066,x10062))
% 81.29/80.94 [1007]~E(x10071,x10072)+E(f442(x10071,x10073,x10074,x10075),f442(x10072,x10073,x10074,x10075))
% 81.29/80.94 [1008]~E(x10081,x10082)+E(f442(x10083,x10081,x10084,x10085),f442(x10083,x10082,x10084,x10085))
% 81.29/80.94 [1009]~E(x10091,x10092)+E(f442(x10093,x10094,x10091,x10095),f442(x10093,x10094,x10092,x10095))
% 81.29/80.94 [1010]~E(x10101,x10102)+E(f442(x10103,x10104,x10105,x10101),f442(x10103,x10104,x10105,x10102))
% 81.29/80.94 [1011]~E(x10111,x10112)+E(f375(x10111,x10113,x10114),f375(x10112,x10113,x10114))
% 81.29/80.94 [1012]~E(x10121,x10122)+E(f375(x10123,x10121,x10124),f375(x10123,x10122,x10124))
% 81.29/80.94 [1013]~E(x10131,x10132)+E(f375(x10133,x10134,x10131),f375(x10133,x10134,x10132))
% 81.29/80.94 [1014]~E(x10141,x10142)+E(f374(x10141,x10143,x10144),f374(x10142,x10143,x10144))
% 81.29/80.94 [1015]~E(x10151,x10152)+E(f374(x10153,x10151,x10154),f374(x10153,x10152,x10154))
% 81.29/80.94 [1016]~E(x10161,x10162)+E(f374(x10163,x10164,x10161),f374(x10163,x10164,x10162))
% 81.29/80.94 [1017]~E(x10171,x10172)+E(f555(x10171,x10173,x10174,x10175,x10176),f555(x10172,x10173,x10174,x10175,x10176))
% 81.29/80.94 [1018]~E(x10181,x10182)+E(f555(x10183,x10181,x10184,x10185,x10186),f555(x10183,x10182,x10184,x10185,x10186))
% 81.29/80.94 [1019]~E(x10191,x10192)+E(f555(x10193,x10194,x10191,x10195,x10196),f555(x10193,x10194,x10192,x10195,x10196))
% 81.29/80.94 [1020]~E(x10201,x10202)+E(f555(x10203,x10204,x10205,x10201,x10206),f555(x10203,x10204,x10205,x10202,x10206))
% 81.29/80.94 [1021]~E(x10211,x10212)+E(f555(x10213,x10214,x10215,x10216,x10211),f555(x10213,x10214,x10215,x10216,x10212))
% 81.29/80.94 [1022]~E(x10221,x10222)+E(f207(x10221,x10223),f207(x10222,x10223))
% 81.29/80.94 [1023]~E(x10231,x10232)+E(f207(x10233,x10231),f207(x10233,x10232))
% 81.29/80.94 [1024]~E(x10241,x10242)+E(f226(x10241,x10243),f226(x10242,x10243))
% 81.29/80.94 [1025]~E(x10251,x10252)+E(f226(x10253,x10251),f226(x10253,x10252))
% 81.29/80.94 [1026]~E(x10261,x10262)+E(f640(x10261,x10263),f640(x10262,x10263))
% 81.29/80.94 [1027]~E(x10271,x10272)+E(f640(x10273,x10271),f640(x10273,x10272))
% 81.29/80.94 [1028]~E(x10281,x10282)+E(f618(x10281,x10283,x10284,x10285),f618(x10282,x10283,x10284,x10285))
% 81.29/80.94 [1029]~E(x10291,x10292)+E(f618(x10293,x10291,x10294,x10295),f618(x10293,x10292,x10294,x10295))
% 81.29/80.94 [1030]~E(x10301,x10302)+E(f618(x10303,x10304,x10301,x10305),f618(x10303,x10304,x10302,x10305))
% 81.29/80.94 [1031]~E(x10311,x10312)+E(f618(x10313,x10314,x10315,x10311),f618(x10313,x10314,x10315,x10312))
% 81.29/80.94 [1032]~E(x10321,x10322)+E(f173(x10321,x10323,x10324),f173(x10322,x10323,x10324))
% 81.29/80.94 [1033]~E(x10331,x10332)+E(f173(x10333,x10331,x10334),f173(x10333,x10332,x10334))
% 81.29/80.94 [1034]~E(x10341,x10342)+E(f173(x10343,x10344,x10341),f173(x10343,x10344,x10342))
% 81.29/80.94 [1035]~E(x10351,x10352)+E(f185(x10351,x10353,x10354),f185(x10352,x10353,x10354))
% 81.29/80.94 [1036]~E(x10361,x10362)+E(f185(x10363,x10361,x10364),f185(x10363,x10362,x10364))
% 81.29/80.94 [1037]~E(x10371,x10372)+E(f185(x10373,x10374,x10371),f185(x10373,x10374,x10372))
% 81.29/80.94 [1038]~E(x10381,x10382)+E(f460(x10381,x10383,x10384),f460(x10382,x10383,x10384))
% 81.29/80.94 [1039]~E(x10391,x10392)+E(f460(x10393,x10391,x10394),f460(x10393,x10392,x10394))
% 81.29/80.94 [1040]~E(x10401,x10402)+E(f460(x10403,x10404,x10401),f460(x10403,x10404,x10402))
% 81.29/80.94 [1041]~E(x10411,x10412)+E(f379(x10411,x10413,x10414),f379(x10412,x10413,x10414))
% 81.29/80.94 [1042]~E(x10421,x10422)+E(f379(x10423,x10421,x10424),f379(x10423,x10422,x10424))
% 81.29/80.94 [1043]~E(x10431,x10432)+E(f379(x10433,x10434,x10431),f379(x10433,x10434,x10432))
% 81.29/80.94 [1044]~E(x10441,x10442)+E(f172(x10441,x10443,x10444),f172(x10442,x10443,x10444))
% 81.29/80.94 [1045]~E(x10451,x10452)+E(f172(x10453,x10451,x10454),f172(x10453,x10452,x10454))
% 81.29/80.94 [1046]~E(x10461,x10462)+E(f172(x10463,x10464,x10461),f172(x10463,x10464,x10462))
% 81.29/80.94 [1047]~E(x10471,x10472)+E(f274(x10471,x10473),f274(x10472,x10473))
% 81.29/80.94 [1048]~E(x10481,x10482)+E(f274(x10483,x10481),f274(x10483,x10482))
% 81.29/80.94 [1049]~E(x10491,x10492)+E(f60(x10491,x10493,x10494,x10495),f60(x10492,x10493,x10494,x10495))
% 81.29/80.94 [1050]~E(x10501,x10502)+E(f60(x10503,x10501,x10504,x10505),f60(x10503,x10502,x10504,x10505))
% 81.29/80.94 [1051]~E(x10511,x10512)+E(f60(x10513,x10514,x10511,x10515),f60(x10513,x10514,x10512,x10515))
% 81.29/80.94 [1052]~E(x10521,x10522)+E(f60(x10523,x10524,x10525,x10521),f60(x10523,x10524,x10525,x10522))
% 81.29/80.94 [1053]~E(x10531,x10532)+E(f743(x10531,x10533,x10534,x10535,x10536),f743(x10532,x10533,x10534,x10535,x10536))
% 81.29/80.94 [1054]~E(x10541,x10542)+E(f743(x10543,x10541,x10544,x10545,x10546),f743(x10543,x10542,x10544,x10545,x10546))
% 81.29/80.94 [1055]~E(x10551,x10552)+E(f743(x10553,x10554,x10551,x10555,x10556),f743(x10553,x10554,x10552,x10555,x10556))
% 81.29/80.94 [1056]~E(x10561,x10562)+E(f743(x10563,x10564,x10565,x10561,x10566),f743(x10563,x10564,x10565,x10562,x10566))
% 81.29/80.94 [1057]~E(x10571,x10572)+E(f743(x10573,x10574,x10575,x10576,x10571),f743(x10573,x10574,x10575,x10576,x10572))
% 81.29/80.94 [1058]~E(x10581,x10582)+E(f710(x10581,x10583,x10584,x10585,x10586,x10587,x10588,x10589),f710(x10582,x10583,x10584,x10585,x10586,x10587,x10588,x10589))
% 81.29/80.94 [1059]~E(x10591,x10592)+E(f710(x10593,x10591,x10594,x10595,x10596,x10597,x10598,x10599),f710(x10593,x10592,x10594,x10595,x10596,x10597,x10598,x10599))
% 81.29/80.94 [1060]~E(x10601,x10602)+E(f710(x10603,x10604,x10601,x10605,x10606,x10607,x10608,x10609),f710(x10603,x10604,x10602,x10605,x10606,x10607,x10608,x10609))
% 81.29/80.94 [1061]~E(x10611,x10612)+E(f710(x10613,x10614,x10615,x10611,x10616,x10617,x10618,x10619),f710(x10613,x10614,x10615,x10612,x10616,x10617,x10618,x10619))
% 81.29/80.94 [1062]~E(x10621,x10622)+E(f710(x10623,x10624,x10625,x10626,x10621,x10627,x10628,x10629),f710(x10623,x10624,x10625,x10626,x10622,x10627,x10628,x10629))
% 81.29/80.94 [1063]~E(x10631,x10632)+E(f710(x10633,x10634,x10635,x10636,x10637,x10631,x10638,x10639),f710(x10633,x10634,x10635,x10636,x10637,x10632,x10638,x10639))
% 81.29/80.94 [1064]~E(x10641,x10642)+E(f710(x10643,x10644,x10645,x10646,x10647,x10648,x10641,x10649),f710(x10643,x10644,x10645,x10646,x10647,x10648,x10642,x10649))
% 81.29/80.94 [1065]~E(x10651,x10652)+E(f710(x10653,x10654,x10655,x10656,x10657,x10658,x10659,x10651),f710(x10653,x10654,x10655,x10656,x10657,x10658,x10659,x10652))
% 81.29/80.94 [1066]~E(x10661,x10662)+E(f798(x10661,x10663,x10664,x10665),f798(x10662,x10663,x10664,x10665))
% 81.29/80.94 [1067]~E(x10671,x10672)+E(f798(x10673,x10671,x10674,x10675),f798(x10673,x10672,x10674,x10675))
% 81.29/80.94 [1068]~E(x10681,x10682)+E(f798(x10683,x10684,x10681,x10685),f798(x10683,x10684,x10682,x10685))
% 81.29/80.94 [1069]~E(x10691,x10692)+E(f798(x10693,x10694,x10695,x10691),f798(x10693,x10694,x10695,x10692))
% 81.29/80.94 [1070]~E(x10701,x10702)+E(f220(x10701),f220(x10702))
% 81.29/80.94 [1071]~E(x10711,x10712)+E(f681(x10711,x10713),f681(x10712,x10713))
% 81.29/80.94 [1072]~E(x10721,x10722)+E(f681(x10723,x10721),f681(x10723,x10722))
% 81.29/80.94 [1073]~E(x10731,x10732)+E(f650(x10731,x10733),f650(x10732,x10733))
% 81.29/80.94 [1074]~E(x10741,x10742)+E(f650(x10743,x10741),f650(x10743,x10742))
% 81.29/80.94 [1075]~E(x10751,x10752)+E(f130(x10751),f130(x10752))
% 81.29/80.94 [1076]~E(x10761,x10762)+E(f277(x10761,x10763,x10764,x10765),f277(x10762,x10763,x10764,x10765))
% 81.29/80.94 [1077]~E(x10771,x10772)+E(f277(x10773,x10771,x10774,x10775),f277(x10773,x10772,x10774,x10775))
% 81.29/80.94 [1078]~E(x10781,x10782)+E(f277(x10783,x10784,x10781,x10785),f277(x10783,x10784,x10782,x10785))
% 81.29/80.94 [1079]~E(x10791,x10792)+E(f277(x10793,x10794,x10795,x10791),f277(x10793,x10794,x10795,x10792))
% 81.29/80.94 [1080]~E(x10801,x10802)+E(f714(x10801,x10803,x10804,x10805),f714(x10802,x10803,x10804,x10805))
% 81.29/80.94 [1081]~E(x10811,x10812)+E(f714(x10813,x10811,x10814,x10815),f714(x10813,x10812,x10814,x10815))
% 81.29/80.94 [1082]~E(x10821,x10822)+E(f714(x10823,x10824,x10821,x10825),f714(x10823,x10824,x10822,x10825))
% 81.29/80.94 [1083]~E(x10831,x10832)+E(f714(x10833,x10834,x10835,x10831),f714(x10833,x10834,x10835,x10832))
% 81.29/80.94 [1084]~E(x10841,x10842)+E(f435(x10841,x10843,x10844,x10845),f435(x10842,x10843,x10844,x10845))
% 81.29/80.94 [1085]~E(x10851,x10852)+E(f435(x10853,x10851,x10854,x10855),f435(x10853,x10852,x10854,x10855))
% 81.29/80.94 [1086]~E(x10861,x10862)+E(f435(x10863,x10864,x10861,x10865),f435(x10863,x10864,x10862,x10865))
% 81.29/80.94 [1087]~E(x10871,x10872)+E(f435(x10873,x10874,x10875,x10871),f435(x10873,x10874,x10875,x10872))
% 81.29/80.94 [1088]~E(x10881,x10882)+E(f501(x10881,x10883,x10884,x10885,x10886,x10887),f501(x10882,x10883,x10884,x10885,x10886,x10887))
% 81.29/80.94 [1089]~E(x10891,x10892)+E(f501(x10893,x10891,x10894,x10895,x10896,x10897),f501(x10893,x10892,x10894,x10895,x10896,x10897))
% 81.29/80.94 [1090]~E(x10901,x10902)+E(f501(x10903,x10904,x10901,x10905,x10906,x10907),f501(x10903,x10904,x10902,x10905,x10906,x10907))
% 81.29/80.94 [1091]~E(x10911,x10912)+E(f501(x10913,x10914,x10915,x10911,x10916,x10917),f501(x10913,x10914,x10915,x10912,x10916,x10917))
% 81.29/80.94 [1092]~E(x10921,x10922)+E(f501(x10923,x10924,x10925,x10926,x10921,x10927),f501(x10923,x10924,x10925,x10926,x10922,x10927))
% 81.29/80.94 [1093]~E(x10931,x10932)+E(f501(x10933,x10934,x10935,x10936,x10937,x10931),f501(x10933,x10934,x10935,x10936,x10937,x10932))
% 81.29/80.94 [1094]~E(x10941,x10942)+E(f559(x10941,x10943,x10944),f559(x10942,x10943,x10944))
% 81.29/80.94 [1095]~E(x10951,x10952)+E(f559(x10953,x10951,x10954),f559(x10953,x10952,x10954))
% 81.29/80.94 [1096]~E(x10961,x10962)+E(f559(x10963,x10964,x10961),f559(x10963,x10964,x10962))
% 81.29/80.94 [1097]~E(x10971,x10972)+E(f641(x10971,x10973,x10974),f641(x10972,x10973,x10974))
% 81.29/80.94 [1098]~E(x10981,x10982)+E(f641(x10983,x10981,x10984),f641(x10983,x10982,x10984))
% 81.29/80.94 [1099]~E(x10991,x10992)+E(f641(x10993,x10994,x10991),f641(x10993,x10994,x10992))
% 81.29/80.94 [1100]~E(x11001,x11002)+E(f811(x11001,x11003),f811(x11002,x11003))
% 81.29/80.94 [1101]~E(x11011,x11012)+E(f811(x11013,x11011),f811(x11013,x11012))
% 81.29/80.94 [1102]~E(x11021,x11022)+E(f722(x11021,x11023,x11024),f722(x11022,x11023,x11024))
% 81.29/80.94 [1103]~E(x11031,x11032)+E(f722(x11033,x11031,x11034),f722(x11033,x11032,x11034))
% 81.29/80.94 [1104]~E(x11041,x11042)+E(f722(x11043,x11044,x11041),f722(x11043,x11044,x11042))
% 81.29/80.94 [1105]~E(x11051,x11052)+E(f89(x11051),f89(x11052))
% 81.29/80.94 [1106]~E(x11061,x11062)+E(f383(x11061,x11063,x11064),f383(x11062,x11063,x11064))
% 81.29/80.94 [1107]~E(x11071,x11072)+E(f383(x11073,x11071,x11074),f383(x11073,x11072,x11074))
% 81.29/80.94 [1108]~E(x11081,x11082)+E(f383(x11083,x11084,x11081),f383(x11083,x11084,x11082))
% 81.29/80.94 [1109]~E(x11091,x11092)+E(f786(x11091,x11093,x11094,x11095,x11096),f786(x11092,x11093,x11094,x11095,x11096))
% 81.29/80.94 [1110]~E(x11101,x11102)+E(f786(x11103,x11101,x11104,x11105,x11106),f786(x11103,x11102,x11104,x11105,x11106))
% 81.29/80.94 [1111]~E(x11111,x11112)+E(f786(x11113,x11114,x11111,x11115,x11116),f786(x11113,x11114,x11112,x11115,x11116))
% 81.29/80.94 [1112]~E(x11121,x11122)+E(f786(x11123,x11124,x11125,x11121,x11126),f786(x11123,x11124,x11125,x11122,x11126))
% 81.29/80.94 [1113]~E(x11131,x11132)+E(f786(x11133,x11134,x11135,x11136,x11131),f786(x11133,x11134,x11135,x11136,x11132))
% 81.29/80.94 [1114]~E(x11141,x11142)+E(f841(x11141,x11143),f841(x11142,x11143))
% 81.29/80.94 [1115]~E(x11151,x11152)+E(f841(x11153,x11151),f841(x11153,x11152))
% 81.29/80.94 [1116]~E(x11161,x11162)+E(f201(x11161,x11163),f201(x11162,x11163))
% 81.29/80.94 [1117]~E(x11171,x11172)+E(f201(x11173,x11171),f201(x11173,x11172))
% 81.29/80.94 [1118]~E(x11181,x11182)+E(f384(x11181,x11183,x11184,x11185),f384(x11182,x11183,x11184,x11185))
% 81.29/80.94 [1119]~E(x11191,x11192)+E(f384(x11193,x11191,x11194,x11195),f384(x11193,x11192,x11194,x11195))
% 81.29/80.94 [1120]~E(x11201,x11202)+E(f384(x11203,x11204,x11201,x11205),f384(x11203,x11204,x11202,x11205))
% 81.29/80.94 [1121]~E(x11211,x11212)+E(f384(x11213,x11214,x11215,x11211),f384(x11213,x11214,x11215,x11212))
% 81.29/80.94 [1122]~E(x11221,x11222)+E(f655(x11221,x11223),f655(x11222,x11223))
% 81.29/80.94 [1123]~E(x11231,x11232)+E(f655(x11233,x11231),f655(x11233,x11232))
% 81.29/80.94 [1124]~E(x11241,x11242)+E(f353(x11241,x11243,x11244,x11245,x11246),f353(x11242,x11243,x11244,x11245,x11246))
% 81.29/80.94 [1125]~E(x11251,x11252)+E(f353(x11253,x11251,x11254,x11255,x11256),f353(x11253,x11252,x11254,x11255,x11256))
% 81.29/80.94 [1126]~E(x11261,x11262)+E(f353(x11263,x11264,x11261,x11265,x11266),f353(x11263,x11264,x11262,x11265,x11266))
% 81.29/80.94 [1127]~E(x11271,x11272)+E(f353(x11273,x11274,x11275,x11271,x11276),f353(x11273,x11274,x11275,x11272,x11276))
% 81.29/80.94 [1128]~E(x11281,x11282)+E(f353(x11283,x11284,x11285,x11286,x11281),f353(x11283,x11284,x11285,x11286,x11282))
% 81.29/80.94 [1129]~E(x11291,x11292)+E(f162(x11291,x11293,x11294,x11295),f162(x11292,x11293,x11294,x11295))
% 81.29/80.94 [1130]~E(x11301,x11302)+E(f162(x11303,x11301,x11304,x11305),f162(x11303,x11302,x11304,x11305))
% 81.29/80.94 [1131]~E(x11311,x11312)+E(f162(x11313,x11314,x11311,x11315),f162(x11313,x11314,x11312,x11315))
% 81.29/80.94 [1132]~E(x11321,x11322)+E(f162(x11323,x11324,x11325,x11321),f162(x11323,x11324,x11325,x11322))
% 81.29/80.94 [1133]~E(x11331,x11332)+E(f523(x11331,x11333,x11334,x11335,x11336),f523(x11332,x11333,x11334,x11335,x11336))
% 81.29/80.94 [1134]~E(x11341,x11342)+E(f523(x11343,x11341,x11344,x11345,x11346),f523(x11343,x11342,x11344,x11345,x11346))
% 81.29/80.94 [1135]~E(x11351,x11352)+E(f523(x11353,x11354,x11351,x11355,x11356),f523(x11353,x11354,x11352,x11355,x11356))
% 81.29/80.94 [1136]~E(x11361,x11362)+E(f523(x11363,x11364,x11365,x11361,x11366),f523(x11363,x11364,x11365,x11362,x11366))
% 81.29/80.94 [1137]~E(x11371,x11372)+E(f523(x11373,x11374,x11375,x11376,x11371),f523(x11373,x11374,x11375,x11376,x11372))
% 81.29/80.94 [1138]~E(x11381,x11382)+E(f733(x11381,x11383,x11384,x11385),f733(x11382,x11383,x11384,x11385))
% 81.29/80.94 [1139]~E(x11391,x11392)+E(f733(x11393,x11391,x11394,x11395),f733(x11393,x11392,x11394,x11395))
% 81.29/80.94 [1140]~E(x11401,x11402)+E(f733(x11403,x11404,x11401,x11405),f733(x11403,x11404,x11402,x11405))
% 81.29/80.94 [1141]~E(x11411,x11412)+E(f733(x11413,x11414,x11415,x11411),f733(x11413,x11414,x11415,x11412))
% 81.29/80.94 [1142]~E(x11421,x11422)+E(f341(x11421,x11423,x11424),f341(x11422,x11423,x11424))
% 81.29/80.94 [1143]~E(x11431,x11432)+E(f341(x11433,x11431,x11434),f341(x11433,x11432,x11434))
% 81.29/80.94 [1144]~E(x11441,x11442)+E(f341(x11443,x11444,x11441),f341(x11443,x11444,x11442))
% 81.29/80.94 [1145]~E(x11451,x11452)+E(f648(x11451,x11453),f648(x11452,x11453))
% 81.29/80.94 [1146]~E(x11461,x11462)+E(f648(x11463,x11461),f648(x11463,x11462))
% 81.29/80.94 [1147]~E(x11471,x11472)+E(f445(x11471,x11473),f445(x11472,x11473))
% 81.29/80.94 [1148]~E(x11481,x11482)+E(f445(x11483,x11481),f445(x11483,x11482))
% 81.29/80.94 [1149]~E(x11491,x11492)+E(f763(x11491,x11493,x11494),f763(x11492,x11493,x11494))
% 81.29/80.94 [1150]~E(x11501,x11502)+E(f763(x11503,x11501,x11504),f763(x11503,x11502,x11504))
% 81.29/80.94 [1151]~E(x11511,x11512)+E(f763(x11513,x11514,x11511),f763(x11513,x11514,x11512))
% 81.29/80.94 [1152]~E(x11521,x11522)+E(f520(x11521,x11523,x11524,x11525),f520(x11522,x11523,x11524,x11525))
% 81.29/80.94 [1153]~E(x11531,x11532)+E(f520(x11533,x11531,x11534,x11535),f520(x11533,x11532,x11534,x11535))
% 81.29/80.94 [1154]~E(x11541,x11542)+E(f520(x11543,x11544,x11541,x11545),f520(x11543,x11544,x11542,x11545))
% 81.29/80.94 [1155]~E(x11551,x11552)+E(f520(x11553,x11554,x11555,x11551),f520(x11553,x11554,x11555,x11552))
% 81.29/80.94 [1156]~E(x11561,x11562)+E(f291(x11561,x11563,x11564),f291(x11562,x11563,x11564))
% 81.29/80.94 [1157]~E(x11571,x11572)+E(f291(x11573,x11571,x11574),f291(x11573,x11572,x11574))
% 81.29/80.94 [1158]~E(x11581,x11582)+E(f291(x11583,x11584,x11581),f291(x11583,x11584,x11582))
% 81.29/80.94 [1159]~E(x11591,x11592)+E(f654(x11591,x11593,x11594,x11595,x11596),f654(x11592,x11593,x11594,x11595,x11596))
% 81.29/80.94 [1160]~E(x11601,x11602)+E(f654(x11603,x11601,x11604,x11605,x11606),f654(x11603,x11602,x11604,x11605,x11606))
% 81.29/80.94 [1161]~E(x11611,x11612)+E(f654(x11613,x11614,x11611,x11615,x11616),f654(x11613,x11614,x11612,x11615,x11616))
% 81.29/80.94 [1162]~E(x11621,x11622)+E(f654(x11623,x11624,x11625,x11621,x11626),f654(x11623,x11624,x11625,x11622,x11626))
% 81.29/80.94 [1163]~E(x11631,x11632)+E(f654(x11633,x11634,x11635,x11636,x11631),f654(x11633,x11634,x11635,x11636,x11632))
% 81.29/80.94 [1164]~E(x11641,x11642)+E(f592(x11641,x11643,x11644,x11645,x11646),f592(x11642,x11643,x11644,x11645,x11646))
% 81.29/80.94 [1165]~E(x11651,x11652)+E(f592(x11653,x11651,x11654,x11655,x11656),f592(x11653,x11652,x11654,x11655,x11656))
% 81.29/80.94 [1166]~E(x11661,x11662)+E(f592(x11663,x11664,x11661,x11665,x11666),f592(x11663,x11664,x11662,x11665,x11666))
% 81.29/80.94 [1167]~E(x11671,x11672)+E(f592(x11673,x11674,x11675,x11671,x11676),f592(x11673,x11674,x11675,x11672,x11676))
% 81.29/80.94 [1168]~E(x11681,x11682)+E(f592(x11683,x11684,x11685,x11686,x11681),f592(x11683,x11684,x11685,x11686,x11682))
% 81.29/80.94 [1169]~E(x11691,x11692)+E(f825(x11691,x11693,x11694),f825(x11692,x11693,x11694))
% 81.29/80.94 [1170]~E(x11701,x11702)+E(f825(x11703,x11701,x11704),f825(x11703,x11702,x11704))
% 81.29/80.94 [1171]~E(x11711,x11712)+E(f825(x11713,x11714,x11711),f825(x11713,x11714,x11712))
% 81.29/80.94 [1172]~E(x11721,x11722)+E(f688(x11721,x11723,x11724,x11725,x11726),f688(x11722,x11723,x11724,x11725,x11726))
% 81.29/80.94 [1173]~E(x11731,x11732)+E(f688(x11733,x11731,x11734,x11735,x11736),f688(x11733,x11732,x11734,x11735,x11736))
% 81.29/80.94 [1174]~E(x11741,x11742)+E(f688(x11743,x11744,x11741,x11745,x11746),f688(x11743,x11744,x11742,x11745,x11746))
% 81.29/80.94 [1175]~E(x11751,x11752)+E(f688(x11753,x11754,x11755,x11751,x11756),f688(x11753,x11754,x11755,x11752,x11756))
% 81.29/80.94 [1176]~E(x11761,x11762)+E(f688(x11763,x11764,x11765,x11766,x11761),f688(x11763,x11764,x11765,x11766,x11762))
% 81.29/80.94 [1177]~E(x11771,x11772)+E(f455(x11771,x11773,x11774,x11775),f455(x11772,x11773,x11774,x11775))
% 81.29/80.94 [1178]~E(x11781,x11782)+E(f455(x11783,x11781,x11784,x11785),f455(x11783,x11782,x11784,x11785))
% 81.29/80.94 [1179]~E(x11791,x11792)+E(f455(x11793,x11794,x11791,x11795),f455(x11793,x11794,x11792,x11795))
% 81.29/80.94 [1180]~E(x11801,x11802)+E(f455(x11803,x11804,x11805,x11801),f455(x11803,x11804,x11805,x11802))
% 81.29/80.94 [1181]~E(x11811,x11812)+E(f541(x11811,x11813,x11814,x11815),f541(x11812,x11813,x11814,x11815))
% 81.29/80.94 [1182]~E(x11821,x11822)+E(f541(x11823,x11821,x11824,x11825),f541(x11823,x11822,x11824,x11825))
% 81.29/80.94 [1183]~E(x11831,x11832)+E(f541(x11833,x11834,x11831,x11835),f541(x11833,x11834,x11832,x11835))
% 81.29/80.94 [1184]~E(x11841,x11842)+E(f541(x11843,x11844,x11845,x11841),f541(x11843,x11844,x11845,x11842))
% 81.29/80.94 [1185]~E(x11851,x11852)+E(f667(x11851,x11853),f667(x11852,x11853))
% 81.29/80.94 [1186]~E(x11861,x11862)+E(f667(x11863,x11861),f667(x11863,x11862))
% 81.29/80.94 [1187]~E(x11871,x11872)+E(f778(x11871,x11873,x11874,x11875,x11876),f778(x11872,x11873,x11874,x11875,x11876))
% 81.29/80.94 [1188]~E(x11881,x11882)+E(f778(x11883,x11881,x11884,x11885,x11886),f778(x11883,x11882,x11884,x11885,x11886))
% 81.29/80.94 [1189]~E(x11891,x11892)+E(f778(x11893,x11894,x11891,x11895,x11896),f778(x11893,x11894,x11892,x11895,x11896))
% 81.29/80.94 [1190]~E(x11901,x11902)+E(f778(x11903,x11904,x11905,x11901,x11906),f778(x11903,x11904,x11905,x11902,x11906))
% 81.29/80.94 [1191]~E(x11911,x11912)+E(f778(x11913,x11914,x11915,x11916,x11911),f778(x11913,x11914,x11915,x11916,x11912))
% 81.29/80.94 [1192]~E(x11921,x11922)+E(f628(x11921,x11923,x11924),f628(x11922,x11923,x11924))
% 81.29/80.94 [1193]~E(x11931,x11932)+E(f628(x11933,x11931,x11934),f628(x11933,x11932,x11934))
% 81.29/80.94 [1194]~E(x11941,x11942)+E(f628(x11943,x11944,x11941),f628(x11943,x11944,x11942))
% 81.29/80.94 [1195]~E(x11951,x11952)+E(f208(x11951,x11953),f208(x11952,x11953))
% 81.29/80.94 [1196]~E(x11961,x11962)+E(f208(x11963,x11961),f208(x11963,x11962))
% 81.29/80.94 [1197]~E(x11971,x11972)+E(f783(x11971,x11973,x11974,x11975),f783(x11972,x11973,x11974,x11975))
% 81.29/80.94 [1198]~E(x11981,x11982)+E(f783(x11983,x11981,x11984,x11985),f783(x11983,x11982,x11984,x11985))
% 81.29/80.94 [1199]~E(x11991,x11992)+E(f783(x11993,x11994,x11991,x11995),f783(x11993,x11994,x11992,x11995))
% 81.29/80.94 [1200]~E(x12001,x12002)+E(f783(x12003,x12004,x12005,x12001),f783(x12003,x12004,x12005,x12002))
% 81.29/80.94 [1201]~E(x12011,x12012)+E(f128(x12011),f128(x12012))
% 81.29/80.94 [1202]~E(x12021,x12022)+E(f759(x12021,x12023,x12024),f759(x12022,x12023,x12024))
% 81.29/80.94 [1203]~E(x12031,x12032)+E(f759(x12033,x12031,x12034),f759(x12033,x12032,x12034))
% 81.29/80.94 [1204]~E(x12041,x12042)+E(f759(x12043,x12044,x12041),f759(x12043,x12044,x12042))
% 81.29/80.94 [1205]~E(x12051,x12052)+E(f637(x12051,x12053),f637(x12052,x12053))
% 81.29/80.94 [1206]~E(x12061,x12062)+E(f637(x12063,x12061),f637(x12063,x12062))
% 81.29/80.94 [1207]~E(x12071,x12072)+E(f860(x12071,x12073),f860(x12072,x12073))
% 81.29/80.94 [1208]~E(x12081,x12082)+E(f860(x12083,x12081),f860(x12083,x12082))
% 81.29/80.94 [1209]~E(x12091,x12092)+E(f870(x12091,x12093,x12094),f870(x12092,x12093,x12094))
% 81.29/80.94 [1210]~E(x12101,x12102)+E(f870(x12103,x12101,x12104),f870(x12103,x12102,x12104))
% 81.29/80.94 [1211]~E(x12111,x12112)+E(f870(x12113,x12114,x12111),f870(x12113,x12114,x12112))
% 81.29/80.94 [1212]~E(x12121,x12122)+E(f853(x12121,x12123,x12124,x12125,x12126),f853(x12122,x12123,x12124,x12125,x12126))
% 81.29/80.94 [1213]~E(x12131,x12132)+E(f853(x12133,x12131,x12134,x12135,x12136),f853(x12133,x12132,x12134,x12135,x12136))
% 81.29/80.94 [1214]~E(x12141,x12142)+E(f853(x12143,x12144,x12141,x12145,x12146),f853(x12143,x12144,x12142,x12145,x12146))
% 81.29/80.94 [1215]~E(x12151,x12152)+E(f853(x12153,x12154,x12155,x12151,x12156),f853(x12153,x12154,x12155,x12152,x12156))
% 81.29/80.94 [1216]~E(x12161,x12162)+E(f853(x12163,x12164,x12165,x12166,x12161),f853(x12163,x12164,x12165,x12166,x12162))
% 81.29/80.94 [1217]~E(x12171,x12172)+E(f422(x12171,x12173,x12174,x12175),f422(x12172,x12173,x12174,x12175))
% 81.29/80.94 [1218]~E(x12181,x12182)+E(f422(x12183,x12181,x12184,x12185),f422(x12183,x12182,x12184,x12185))
% 81.29/80.94 [1219]~E(x12191,x12192)+E(f422(x12193,x12194,x12191,x12195),f422(x12193,x12194,x12192,x12195))
% 81.29/80.94 [1220]~E(x12201,x12202)+E(f422(x12203,x12204,x12205,x12201),f422(x12203,x12204,x12205,x12202))
% 81.29/80.94 [1221]~E(x12211,x12212)+E(f125(x12211,x12213,x12214,x12215),f125(x12212,x12213,x12214,x12215))
% 81.29/80.94 [1222]~E(x12221,x12222)+E(f125(x12223,x12221,x12224,x12225),f125(x12223,x12222,x12224,x12225))
% 81.29/80.94 [1223]~E(x12231,x12232)+E(f125(x12233,x12234,x12231,x12235),f125(x12233,x12234,x12232,x12235))
% 81.29/80.94 [1224]~E(x12241,x12242)+E(f125(x12243,x12244,x12245,x12241),f125(x12243,x12244,x12245,x12242))
% 81.29/80.94 [1225]~E(x12251,x12252)+E(f397(x12251,x12253),f397(x12252,x12253))
% 81.29/80.94 [1226]~E(x12261,x12262)+E(f397(x12263,x12261),f397(x12263,x12262))
% 81.29/80.94 [1227]~E(x12271,x12272)+E(f447(x12271,x12273),f447(x12272,x12273))
% 81.29/80.94 [1228]~E(x12281,x12282)+E(f447(x12283,x12281),f447(x12283,x12282))
% 81.29/80.94 [1229]~E(x12291,x12292)+E(f459(x12291,x12293,x12294,x12295),f459(x12292,x12293,x12294,x12295))
% 81.29/80.94 [1230]~E(x12301,x12302)+E(f459(x12303,x12301,x12304,x12305),f459(x12303,x12302,x12304,x12305))
% 81.29/80.94 [1231]~E(x12311,x12312)+E(f459(x12313,x12314,x12311,x12315),f459(x12313,x12314,x12312,x12315))
% 81.29/80.94 [1232]~E(x12321,x12322)+E(f459(x12323,x12324,x12325,x12321),f459(x12323,x12324,x12325,x12322))
% 81.29/80.94 [1233]~E(x12331,x12332)+E(f580(x12331,x12333),f580(x12332,x12333))
% 81.29/80.94 [1234]~E(x12341,x12342)+E(f580(x12343,x12341),f580(x12343,x12342))
% 81.29/80.94 [1235]~E(x12351,x12352)+E(f704(x12351,x12353,x12354,x12355),f704(x12352,x12353,x12354,x12355))
% 81.29/80.94 [1236]~E(x12361,x12362)+E(f704(x12363,x12361,x12364,x12365),f704(x12363,x12362,x12364,x12365))
% 81.29/80.94 [1237]~E(x12371,x12372)+E(f704(x12373,x12374,x12371,x12375),f704(x12373,x12374,x12372,x12375))
% 81.29/80.94 [1238]~E(x12381,x12382)+E(f704(x12383,x12384,x12385,x12381),f704(x12383,x12384,x12385,x12382))
% 81.29/80.94 [1239]~E(x12391,x12392)+E(f612(x12391,x12393,x12394),f612(x12392,x12393,x12394))
% 81.29/80.94 [1240]~E(x12401,x12402)+E(f612(x12403,x12401,x12404),f612(x12403,x12402,x12404))
% 81.29/80.94 [1241]~E(x12411,x12412)+E(f612(x12413,x12414,x12411),f612(x12413,x12414,x12412))
% 81.29/80.94 [1242]~E(x12421,x12422)+E(f760(x12421,x12423),f760(x12422,x12423))
% 81.29/80.94 [1243]~E(x12431,x12432)+E(f760(x12433,x12431),f760(x12433,x12432))
% 81.29/80.94 [1244]~E(x12441,x12442)+E(f345(x12441),f345(x12442))
% 81.29/80.94 [1245]~E(x12451,x12452)+E(f68(x12451,x12453,x12454),f68(x12452,x12453,x12454))
% 81.29/80.94 [1246]~E(x12461,x12462)+E(f68(x12463,x12461,x12464),f68(x12463,x12462,x12464))
% 81.29/80.94 [1247]~E(x12471,x12472)+E(f68(x12473,x12474,x12471),f68(x12473,x12474,x12472))
% 81.29/80.94 [1248]~E(x12481,x12482)+E(f346(x12481),f346(x12482))
% 81.29/80.94 [1249]~E(x12491,x12492)+E(f222(x12491,x12493),f222(x12492,x12493))
% 81.29/80.94 [1250]~E(x12501,x12502)+E(f222(x12503,x12501),f222(x12503,x12502))
% 81.29/80.94 [1251]~E(x12511,x12512)+E(f483(x12511,x12513,x12514,x12515,x12516,x12517,x12518,x12519,x125110),f483(x12512,x12513,x12514,x12515,x12516,x12517,x12518,x12519,x125110))
% 81.29/80.94 [1252]~E(x12521,x12522)+E(f483(x12523,x12521,x12524,x12525,x12526,x12527,x12528,x12529,x125210),f483(x12523,x12522,x12524,x12525,x12526,x12527,x12528,x12529,x125210))
% 81.29/80.94 [1253]~E(x12531,x12532)+E(f483(x12533,x12534,x12531,x12535,x12536,x12537,x12538,x12539,x125310),f483(x12533,x12534,x12532,x12535,x12536,x12537,x12538,x12539,x125310))
% 81.29/80.94 [1254]~E(x12541,x12542)+E(f483(x12543,x12544,x12545,x12541,x12546,x12547,x12548,x12549,x125410),f483(x12543,x12544,x12545,x12542,x12546,x12547,x12548,x12549,x125410))
% 81.29/80.94 [1255]~E(x12551,x12552)+E(f483(x12553,x12554,x12555,x12556,x12551,x12557,x12558,x12559,x125510),f483(x12553,x12554,x12555,x12556,x12552,x12557,x12558,x12559,x125510))
% 81.29/80.94 [1256]~E(x12561,x12562)+E(f483(x12563,x12564,x12565,x12566,x12567,x12561,x12568,x12569,x125610),f483(x12563,x12564,x12565,x12566,x12567,x12562,x12568,x12569,x125610))
% 81.29/80.94 [1257]~E(x12571,x12572)+E(f483(x12573,x12574,x12575,x12576,x12577,x12578,x12571,x12579,x125710),f483(x12573,x12574,x12575,x12576,x12577,x12578,x12572,x12579,x125710))
% 81.29/80.94 [1258]~E(x12581,x12582)+E(f483(x12583,x12584,x12585,x12586,x12587,x12588,x12589,x12581,x125810),f483(x12583,x12584,x12585,x12586,x12587,x12588,x12589,x12582,x125810))
% 81.29/80.94 [1259]~E(x12591,x12592)+E(f483(x12593,x12594,x12595,x12596,x12597,x12598,x12599,x125910,x12591),f483(x12593,x12594,x12595,x12596,x12597,x12598,x12599,x125910,x12592))
% 81.29/80.94 [1260]~E(x12601,x12602)+E(f404(x12601,x12603),f404(x12602,x12603))
% 81.29/80.94 [1261]~E(x12611,x12612)+E(f404(x12613,x12611),f404(x12613,x12612))
% 81.29/80.94 [1262]~E(x12621,x12622)+E(f695(x12621,x12623,x12624,x12625),f695(x12622,x12623,x12624,x12625))
% 81.29/80.94 [1263]~E(x12631,x12632)+E(f695(x12633,x12631,x12634,x12635),f695(x12633,x12632,x12634,x12635))
% 81.29/80.94 [1264]~E(x12641,x12642)+E(f695(x12643,x12644,x12641,x12645),f695(x12643,x12644,x12642,x12645))
% 81.29/80.94 [1265]~E(x12651,x12652)+E(f695(x12653,x12654,x12655,x12651),f695(x12653,x12654,x12655,x12652))
% 81.29/80.94 [1266]~E(x12661,x12662)+E(f558(x12661,x12663,x12664,x12665,x12666),f558(x12662,x12663,x12664,x12665,x12666))
% 81.29/80.94 [1267]~E(x12671,x12672)+E(f558(x12673,x12671,x12674,x12675,x12676),f558(x12673,x12672,x12674,x12675,x12676))
% 81.29/80.94 [1268]~E(x12681,x12682)+E(f558(x12683,x12684,x12681,x12685,x12686),f558(x12683,x12684,x12682,x12685,x12686))
% 81.29/80.94 [1269]~E(x12691,x12692)+E(f558(x12693,x12694,x12695,x12691,x12696),f558(x12693,x12694,x12695,x12692,x12696))
% 81.29/80.94 [1270]~E(x12701,x12702)+E(f558(x12703,x12704,x12705,x12706,x12701),f558(x12703,x12704,x12705,x12706,x12702))
% 81.29/80.94 [1271]~E(x12711,x12712)+E(f862(x12711,x12713),f862(x12712,x12713))
% 81.29/80.94 [1272]~E(x12721,x12722)+E(f862(x12723,x12721),f862(x12723,x12722))
% 81.29/80.94 [1273]~E(x12731,x12732)+E(f516(x12731,x12733,x12734,x12735),f516(x12732,x12733,x12734,x12735))
% 81.29/80.94 [1274]~E(x12741,x12742)+E(f516(x12743,x12741,x12744,x12745),f516(x12743,x12742,x12744,x12745))
% 81.29/80.94 [1275]~E(x12751,x12752)+E(f516(x12753,x12754,x12751,x12755),f516(x12753,x12754,x12752,x12755))
% 81.29/80.94 [1276]~E(x12761,x12762)+E(f516(x12763,x12764,x12765,x12761),f516(x12763,x12764,x12765,x12762))
% 81.29/80.94 [1277]~E(x12771,x12772)+E(f615(x12771,x12773,x12774,x12775),f615(x12772,x12773,x12774,x12775))
% 81.29/80.94 [1278]~E(x12781,x12782)+E(f615(x12783,x12781,x12784,x12785),f615(x12783,x12782,x12784,x12785))
% 81.29/80.94 [1279]~E(x12791,x12792)+E(f615(x12793,x12794,x12791,x12795),f615(x12793,x12794,x12792,x12795))
% 81.29/80.94 [1280]~E(x12801,x12802)+E(f615(x12803,x12804,x12805,x12801),f615(x12803,x12804,x12805,x12802))
% 81.29/80.94 [1281]~E(x12811,x12812)+E(f700(x12811,x12813),f700(x12812,x12813))
% 81.29/80.94 [1282]~E(x12821,x12822)+E(f700(x12823,x12821),f700(x12823,x12822))
% 81.29/80.94 [1283]~E(x12831,x12832)+E(f411(x12831,x12833,x12834),f411(x12832,x12833,x12834))
% 81.29/80.94 [1284]~E(x12841,x12842)+E(f411(x12843,x12841,x12844),f411(x12843,x12842,x12844))
% 81.29/80.94 [1285]~E(x12851,x12852)+E(f411(x12853,x12854,x12851),f411(x12853,x12854,x12852))
% 81.29/80.94 [1286]~E(x12861,x12862)+E(f677(x12861,x12863,x12864,x12865,x12866),f677(x12862,x12863,x12864,x12865,x12866))
% 81.29/80.94 [1287]~E(x12871,x12872)+E(f677(x12873,x12871,x12874,x12875,x12876),f677(x12873,x12872,x12874,x12875,x12876))
% 81.29/80.94 [1288]~E(x12881,x12882)+E(f677(x12883,x12884,x12881,x12885,x12886),f677(x12883,x12884,x12882,x12885,x12886))
% 81.29/80.94 [1289]~E(x12891,x12892)+E(f677(x12893,x12894,x12895,x12891,x12896),f677(x12893,x12894,x12895,x12892,x12896))
% 81.29/80.94 [1290]~E(x12901,x12902)+E(f677(x12903,x12904,x12905,x12906,x12901),f677(x12903,x12904,x12905,x12906,x12902))
% 81.29/80.94 [1291]~E(x12911,x12912)+E(f702(x12911,x12913,x12914),f702(x12912,x12913,x12914))
% 81.29/80.94 [1292]~E(x12921,x12922)+E(f702(x12923,x12921,x12924),f702(x12923,x12922,x12924))
% 81.29/80.94 [1293]~E(x12931,x12932)+E(f702(x12933,x12934,x12931),f702(x12933,x12934,x12932))
% 81.29/80.94 [1294]~E(x12941,x12942)+E(f412(x12941,x12943,x12944),f412(x12942,x12943,x12944))
% 81.29/80.94 [1295]~E(x12951,x12952)+E(f412(x12953,x12951,x12954),f412(x12953,x12952,x12954))
% 81.29/80.94 [1296]~E(x12961,x12962)+E(f412(x12963,x12964,x12961),f412(x12963,x12964,x12962))
% 81.29/80.94 [1297]~E(x12971,x12972)+E(f132(x12971,x12973,x12974,x12975,x12976),f132(x12972,x12973,x12974,x12975,x12976))
% 81.29/80.94 [1298]~E(x12981,x12982)+E(f132(x12983,x12981,x12984,x12985,x12986),f132(x12983,x12982,x12984,x12985,x12986))
% 81.29/80.94 [1299]~E(x12991,x12992)+E(f132(x12993,x12994,x12991,x12995,x12996),f132(x12993,x12994,x12992,x12995,x12996))
% 81.29/80.94 [1300]~E(x13001,x13002)+E(f132(x13003,x13004,x13005,x13001,x13006),f132(x13003,x13004,x13005,x13002,x13006))
% 81.29/80.94 [1301]~E(x13011,x13012)+E(f132(x13013,x13014,x13015,x13016,x13011),f132(x13013,x13014,x13015,x13016,x13012))
% 81.29/80.94 [1302]~E(x13021,x13022)+E(f452(x13021,x13023,x13024,x13025),f452(x13022,x13023,x13024,x13025))
% 81.29/80.94 [1303]~E(x13031,x13032)+E(f452(x13033,x13031,x13034,x13035),f452(x13033,x13032,x13034,x13035))
% 81.29/80.94 [1304]~E(x13041,x13042)+E(f452(x13043,x13044,x13041,x13045),f452(x13043,x13044,x13042,x13045))
% 81.29/80.94 [1305]~E(x13051,x13052)+E(f452(x13053,x13054,x13055,x13051),f452(x13053,x13054,x13055,x13052))
% 81.29/80.94 [1306]~E(x13061,x13062)+E(f344(x13061,x13063,x13064,x13065,x13066,x13067),f344(x13062,x13063,x13064,x13065,x13066,x13067))
% 81.29/80.94 [1307]~E(x13071,x13072)+E(f344(x13073,x13071,x13074,x13075,x13076,x13077),f344(x13073,x13072,x13074,x13075,x13076,x13077))
% 81.29/80.94 [1308]~E(x13081,x13082)+E(f344(x13083,x13084,x13081,x13085,x13086,x13087),f344(x13083,x13084,x13082,x13085,x13086,x13087))
% 81.29/80.94 [1309]~E(x13091,x13092)+E(f344(x13093,x13094,x13095,x13091,x13096,x13097),f344(x13093,x13094,x13095,x13092,x13096,x13097))
% 81.29/80.94 [1310]~E(x13101,x13102)+E(f344(x13103,x13104,x13105,x13106,x13101,x13107),f344(x13103,x13104,x13105,x13106,x13102,x13107))
% 81.29/80.94 [1311]~E(x13111,x13112)+E(f344(x13113,x13114,x13115,x13116,x13117,x13111),f344(x13113,x13114,x13115,x13116,x13117,x13112))
% 81.29/80.94 [1312]~E(x13121,x13122)+E(f709(x13121,x13123,x13124,x13125,x13126),f709(x13122,x13123,x13124,x13125,x13126))
% 81.29/80.94 [1313]~E(x13131,x13132)+E(f709(x13133,x13131,x13134,x13135,x13136),f709(x13133,x13132,x13134,x13135,x13136))
% 81.29/80.94 [1314]~E(x13141,x13142)+E(f709(x13143,x13144,x13141,x13145,x13146),f709(x13143,x13144,x13142,x13145,x13146))
% 81.29/80.94 [1315]~E(x13151,x13152)+E(f709(x13153,x13154,x13155,x13151,x13156),f709(x13153,x13154,x13155,x13152,x13156))
% 81.29/80.94 [1316]~E(x13161,x13162)+E(f709(x13163,x13164,x13165,x13166,x13161),f709(x13163,x13164,x13165,x13166,x13162))
% 81.29/80.94 [1317]~E(x13171,x13172)+E(f231(x13171,x13173,x13174),f231(x13172,x13173,x13174))
% 81.29/80.94 [1318]~E(x13181,x13182)+E(f231(x13183,x13181,x13184),f231(x13183,x13182,x13184))
% 81.29/80.94 [1319]~E(x13191,x13192)+E(f231(x13193,x13194,x13191),f231(x13193,x13194,x13192))
% 81.29/80.94 [1320]~E(x13201,x13202)+E(f550(x13201,x13203,x13204,x13205),f550(x13202,x13203,x13204,x13205))
% 81.29/80.94 [1321]~E(x13211,x13212)+E(f550(x13213,x13211,x13214,x13215),f550(x13213,x13212,x13214,x13215))
% 81.29/80.94 [1322]~E(x13221,x13222)+E(f550(x13223,x13224,x13221,x13225),f550(x13223,x13224,x13222,x13225))
% 81.29/80.94 [1323]~E(x13231,x13232)+E(f550(x13233,x13234,x13235,x13231),f550(x13233,x13234,x13235,x13232))
% 81.29/80.94 [1324]~E(x13241,x13242)+E(f272(x13241,x13243),f272(x13242,x13243))
% 81.29/80.94 [1325]~E(x13251,x13252)+E(f272(x13253,x13251),f272(x13253,x13252))
% 81.29/80.94 [1326]~E(x13261,x13262)+E(f718(x13261,x13263),f718(x13262,x13263))
% 81.29/80.94 [1327]~E(x13271,x13272)+E(f718(x13273,x13271),f718(x13273,x13272))
% 81.29/80.94 [1328]~E(x13281,x13282)+E(f772(x13281,x13283),f772(x13282,x13283))
% 81.29/80.94 [1329]~E(x13291,x13292)+E(f772(x13293,x13291),f772(x13293,x13292))
% 81.29/80.94 [1330]~E(x13301,x13302)+E(f246(x13301,x13303),f246(x13302,x13303))
% 81.29/80.94 [1331]~E(x13311,x13312)+E(f246(x13313,x13311),f246(x13313,x13312))
% 81.29/80.94 [1332]~E(x13321,x13322)+E(f500(x13321,x13323,x13324,x13325,x13326),f500(x13322,x13323,x13324,x13325,x13326))
% 81.29/80.94 [1333]~E(x13331,x13332)+E(f500(x13333,x13331,x13334,x13335,x13336),f500(x13333,x13332,x13334,x13335,x13336))
% 81.29/80.94 [1334]~E(x13341,x13342)+E(f500(x13343,x13344,x13341,x13345,x13346),f500(x13343,x13344,x13342,x13345,x13346))
% 81.29/80.94 [1335]~E(x13351,x13352)+E(f500(x13353,x13354,x13355,x13351,x13356),f500(x13353,x13354,x13355,x13352,x13356))
% 81.29/80.94 [1336]~E(x13361,x13362)+E(f500(x13363,x13364,x13365,x13366,x13361),f500(x13363,x13364,x13365,x13366,x13362))
% 81.29/80.94 [1337]~E(x13371,x13372)+E(f544(x13371,x13373,x13374,x13375,x13376,x13377,x13378),f544(x13372,x13373,x13374,x13375,x13376,x13377,x13378))
% 81.29/80.94 [1338]~E(x13381,x13382)+E(f544(x13383,x13381,x13384,x13385,x13386,x13387,x13388),f544(x13383,x13382,x13384,x13385,x13386,x13387,x13388))
% 81.29/80.94 [1339]~E(x13391,x13392)+E(f544(x13393,x13394,x13391,x13395,x13396,x13397,x13398),f544(x13393,x13394,x13392,x13395,x13396,x13397,x13398))
% 81.29/80.94 [1340]~E(x13401,x13402)+E(f544(x13403,x13404,x13405,x13401,x13406,x13407,x13408),f544(x13403,x13404,x13405,x13402,x13406,x13407,x13408))
% 81.29/80.94 [1341]~E(x13411,x13412)+E(f544(x13413,x13414,x13415,x13416,x13411,x13417,x13418),f544(x13413,x13414,x13415,x13416,x13412,x13417,x13418))
% 81.29/80.94 [1342]~E(x13421,x13422)+E(f544(x13423,x13424,x13425,x13426,x13427,x13421,x13428),f544(x13423,x13424,x13425,x13426,x13427,x13422,x13428))
% 81.29/80.94 [1343]~E(x13431,x13432)+E(f544(x13433,x13434,x13435,x13436,x13437,x13438,x13431),f544(x13433,x13434,x13435,x13436,x13437,x13438,x13432))
% 81.29/80.94 [1344]~E(x13441,x13442)+E(f271(x13441,x13443,x13444,x13445,x13446),f271(x13442,x13443,x13444,x13445,x13446))
% 81.29/80.94 [1345]~E(x13451,x13452)+E(f271(x13453,x13451,x13454,x13455,x13456),f271(x13453,x13452,x13454,x13455,x13456))
% 81.29/80.94 [1346]~E(x13461,x13462)+E(f271(x13463,x13464,x13461,x13465,x13466),f271(x13463,x13464,x13462,x13465,x13466))
% 81.29/80.94 [1347]~E(x13471,x13472)+E(f271(x13473,x13474,x13475,x13471,x13476),f271(x13473,x13474,x13475,x13472,x13476))
% 81.29/80.94 [1348]~E(x13481,x13482)+E(f271(x13483,x13484,x13485,x13486,x13481),f271(x13483,x13484,x13485,x13486,x13482))
% 81.29/80.94 [1349]~E(x13491,x13492)+E(f768(x13491,x13493,x13494),f768(x13492,x13493,x13494))
% 81.29/80.94 [1350]~E(x13501,x13502)+E(f768(x13503,x13501,x13504),f768(x13503,x13502,x13504))
% 81.29/80.94 [1351]~E(x13511,x13512)+E(f768(x13513,x13514,x13511),f768(x13513,x13514,x13512))
% 81.29/80.94 [1352]~E(x13521,x13522)+E(f542(x13521,x13523,x13524,x13525,x13526),f542(x13522,x13523,x13524,x13525,x13526))
% 81.29/80.94 [1353]~E(x13531,x13532)+E(f542(x13533,x13531,x13534,x13535,x13536),f542(x13533,x13532,x13534,x13535,x13536))
% 81.29/80.94 [1354]~E(x13541,x13542)+E(f542(x13543,x13544,x13541,x13545,x13546),f542(x13543,x13544,x13542,x13545,x13546))
% 81.29/80.94 [1355]~E(x13551,x13552)+E(f542(x13553,x13554,x13555,x13551,x13556),f542(x13553,x13554,x13555,x13552,x13556))
% 81.29/80.94 [1356]~E(x13561,x13562)+E(f542(x13563,x13564,x13565,x13566,x13561),f542(x13563,x13564,x13565,x13566,x13562))
% 81.29/80.94 [1357]~E(x13571,x13572)+E(f571(x13571,x13573,x13574,x13575,x13576,x13577),f571(x13572,x13573,x13574,x13575,x13576,x13577))
% 81.29/80.94 [1358]~E(x13581,x13582)+E(f571(x13583,x13581,x13584,x13585,x13586,x13587),f571(x13583,x13582,x13584,x13585,x13586,x13587))
% 81.29/80.94 [1359]~E(x13591,x13592)+E(f571(x13593,x13594,x13591,x13595,x13596,x13597),f571(x13593,x13594,x13592,x13595,x13596,x13597))
% 81.29/80.94 [1360]~E(x13601,x13602)+E(f571(x13603,x13604,x13605,x13601,x13606,x13607),f571(x13603,x13604,x13605,x13602,x13606,x13607))
% 81.29/80.94 [1361]~E(x13611,x13612)+E(f571(x13613,x13614,x13615,x13616,x13611,x13617),f571(x13613,x13614,x13615,x13616,x13612,x13617))
% 81.29/80.94 [1362]~E(x13621,x13622)+E(f571(x13623,x13624,x13625,x13626,x13627,x13621),f571(x13623,x13624,x13625,x13626,x13627,x13622))
% 81.29/80.94 [1363]~E(x13631,x13632)+E(f548(x13631,x13633,x13634,x13635),f548(x13632,x13633,x13634,x13635))
% 81.29/80.94 [1364]~E(x13641,x13642)+E(f548(x13643,x13641,x13644,x13645),f548(x13643,x13642,x13644,x13645))
% 81.29/80.94 [1365]~E(x13651,x13652)+E(f548(x13653,x13654,x13651,x13655),f548(x13653,x13654,x13652,x13655))
% 81.29/80.94 [1366]~E(x13661,x13662)+E(f548(x13663,x13664,x13665,x13661),f548(x13663,x13664,x13665,x13662))
% 81.29/80.94 [1367]~E(x13671,x13672)+E(f499(x13671,x13673,x13674),f499(x13672,x13673,x13674))
% 81.29/80.94 [1368]~E(x13681,x13682)+E(f499(x13683,x13681,x13684),f499(x13683,x13682,x13684))
% 81.29/80.94 [1369]~E(x13691,x13692)+E(f499(x13693,x13694,x13691),f499(x13693,x13694,x13692))
% 81.29/80.94 [1370]~E(x13701,x13702)+E(f536(x13701,x13703,x13704,x13705),f536(x13702,x13703,x13704,x13705))
% 81.29/80.94 [1371]~E(x13711,x13712)+E(f536(x13713,x13711,x13714,x13715),f536(x13713,x13712,x13714,x13715))
% 81.29/80.94 [1372]~E(x13721,x13722)+E(f536(x13723,x13724,x13721,x13725),f536(x13723,x13724,x13722,x13725))
% 81.29/80.94 [1373]~E(x13731,x13732)+E(f536(x13733,x13734,x13735,x13731),f536(x13733,x13734,x13735,x13732))
% 81.29/80.94 [1374]~E(x13741,x13742)+E(f515(x13741,x13743,x13744,x13745,x13746),f515(x13742,x13743,x13744,x13745,x13746))
% 81.29/80.94 [1375]~E(x13751,x13752)+E(f515(x13753,x13751,x13754,x13755,x13756),f515(x13753,x13752,x13754,x13755,x13756))
% 81.29/80.94 [1376]~E(x13761,x13762)+E(f515(x13763,x13764,x13761,x13765,x13766),f515(x13763,x13764,x13762,x13765,x13766))
% 81.29/80.94 [1377]~E(x13771,x13772)+E(f515(x13773,x13774,x13775,x13771,x13776),f515(x13773,x13774,x13775,x13772,x13776))
% 81.29/80.94 [1378]~E(x13781,x13782)+E(f515(x13783,x13784,x13785,x13786,x13781),f515(x13783,x13784,x13785,x13786,x13782))
% 81.29/80.94 [1379]~E(x13791,x13792)+E(f489(x13791,x13793,x13794,x13795),f489(x13792,x13793,x13794,x13795))
% 81.29/80.94 [1380]~E(x13801,x13802)+E(f489(x13803,x13801,x13804,x13805),f489(x13803,x13802,x13804,x13805))
% 81.29/80.94 [1381]~E(x13811,x13812)+E(f489(x13813,x13814,x13811,x13815),f489(x13813,x13814,x13812,x13815))
% 81.29/80.94 [1382]~E(x13821,x13822)+E(f489(x13823,x13824,x13825,x13821),f489(x13823,x13824,x13825,x13822))
% 81.29/80.94 [1383]~E(x13831,x13832)+E(f433(x13831,x13833,x13834),f433(x13832,x13833,x13834))
% 81.29/80.94 [1384]~E(x13841,x13842)+E(f433(x13843,x13841,x13844),f433(x13843,x13842,x13844))
% 81.29/80.94 [1385]~E(x13851,x13852)+E(f433(x13853,x13854,x13851),f433(x13853,x13854,x13852))
% 81.29/80.94 [1386]~E(x13861,x13862)+E(f697(x13861,x13863),f697(x13862,x13863))
% 81.29/80.94 [1387]~E(x13871,x13872)+E(f697(x13873,x13871),f697(x13873,x13872))
% 81.29/80.94 [1388]~E(x13881,x13882)+E(f509(x13881,x13883,x13884,x13885,x13886),f509(x13882,x13883,x13884,x13885,x13886))
% 81.29/80.94 [1389]~E(x13891,x13892)+E(f509(x13893,x13891,x13894,x13895,x13896),f509(x13893,x13892,x13894,x13895,x13896))
% 81.29/80.94 [1390]~E(x13901,x13902)+E(f509(x13903,x13904,x13901,x13905,x13906),f509(x13903,x13904,x13902,x13905,x13906))
% 81.29/80.94 [1391]~E(x13911,x13912)+E(f509(x13913,x13914,x13915,x13911,x13916),f509(x13913,x13914,x13915,x13912,x13916))
% 81.29/80.94 [1392]~E(x13921,x13922)+E(f509(x13923,x13924,x13925,x13926,x13921),f509(x13923,x13924,x13925,x13926,x13922))
% 81.29/80.94 [1393]~E(x13931,x13932)+E(f613(x13931,x13933,x13934),f613(x13932,x13933,x13934))
% 81.29/80.94 [1394]~E(x13941,x13942)+E(f613(x13943,x13941,x13944),f613(x13943,x13942,x13944))
% 81.29/80.94 [1395]~E(x13951,x13952)+E(f613(x13953,x13954,x13951),f613(x13953,x13954,x13952))
% 81.29/80.94 [1396]~E(x13961,x13962)+E(f739(x13961,x13963,x13964),f739(x13962,x13963,x13964))
% 81.29/80.94 [1397]~E(x13971,x13972)+E(f739(x13973,x13971,x13974),f739(x13973,x13972,x13974))
% 81.29/80.94 [1398]~E(x13981,x13982)+E(f739(x13983,x13984,x13981),f739(x13983,x13984,x13982))
% 81.29/80.94 [1399]~E(x13991,x13992)+E(f148(x13991,x13993,x13994,x13995,x13996),f148(x13992,x13993,x13994,x13995,x13996))
% 81.29/80.94 [1400]~E(x14001,x14002)+E(f148(x14003,x14001,x14004,x14005,x14006),f148(x14003,x14002,x14004,x14005,x14006))
% 81.29/80.94 [1401]~E(x14011,x14012)+E(f148(x14013,x14014,x14011,x14015,x14016),f148(x14013,x14014,x14012,x14015,x14016))
% 81.29/80.94 [1402]~E(x14021,x14022)+E(f148(x14023,x14024,x14025,x14021,x14026),f148(x14023,x14024,x14025,x14022,x14026))
% 81.29/80.94 [1403]~E(x14031,x14032)+E(f148(x14033,x14034,x14035,x14036,x14031),f148(x14033,x14034,x14035,x14036,x14032))
% 81.29/80.94 [1404]~E(x14041,x14042)+E(f237(x14041,x14043,x14044),f237(x14042,x14043,x14044))
% 81.29/80.94 [1405]~E(x14051,x14052)+E(f237(x14053,x14051,x14054),f237(x14053,x14052,x14054))
% 81.29/80.94 [1406]~E(x14061,x14062)+E(f237(x14063,x14064,x14061),f237(x14063,x14064,x14062))
% 81.29/80.94 [1407]~E(x14071,x14072)+E(f573(x14071,x14073,x14074,x14075,x14076,x14077),f573(x14072,x14073,x14074,x14075,x14076,x14077))
% 81.29/80.94 [1408]~E(x14081,x14082)+E(f573(x14083,x14081,x14084,x14085,x14086,x14087),f573(x14083,x14082,x14084,x14085,x14086,x14087))
% 81.29/80.94 [1409]~E(x14091,x14092)+E(f573(x14093,x14094,x14091,x14095,x14096,x14097),f573(x14093,x14094,x14092,x14095,x14096,x14097))
% 81.29/80.94 [1410]~E(x14101,x14102)+E(f573(x14103,x14104,x14105,x14101,x14106,x14107),f573(x14103,x14104,x14105,x14102,x14106,x14107))
% 81.29/80.94 [1411]~E(x14111,x14112)+E(f573(x14113,x14114,x14115,x14116,x14111,x14117),f573(x14113,x14114,x14115,x14116,x14112,x14117))
% 81.29/80.94 [1412]~E(x14121,x14122)+E(f573(x14123,x14124,x14125,x14126,x14127,x14121),f573(x14123,x14124,x14125,x14126,x14127,x14122))
% 81.29/80.94 [1413]~E(x14131,x14132)+E(f851(x14131),f851(x14132))
% 81.29/80.94 [1414]~E(x14141,x14142)+E(f381(x14141,x14143,x14144),f381(x14142,x14143,x14144))
% 81.29/80.94 [1415]~E(x14151,x14152)+E(f381(x14153,x14151,x14154),f381(x14153,x14152,x14154))
% 81.29/80.94 [1416]~E(x14161,x14162)+E(f381(x14163,x14164,x14161),f381(x14163,x14164,x14162))
% 81.29/80.94 [1417]~E(x14171,x14172)+E(f461(x14171,x14173,x14174),f461(x14172,x14173,x14174))
% 81.29/80.94 [1418]~E(x14181,x14182)+E(f461(x14183,x14181,x14184),f461(x14183,x14182,x14184))
% 81.29/80.94 [1419]~E(x14191,x14192)+E(f461(x14193,x14194,x14191),f461(x14193,x14194,x14192))
% 81.29/80.94 [1420]~E(x14201,x14202)+E(f377(x14201,x14203,x14204),f377(x14202,x14203,x14204))
% 81.29/80.94 [1421]~E(x14211,x14212)+E(f377(x14213,x14211,x14214),f377(x14213,x14212,x14214))
% 81.29/80.94 [1422]~E(x14221,x14222)+E(f377(x14223,x14224,x14221),f377(x14223,x14224,x14222))
% 81.29/80.94 [1423]~E(x14231,x14232)+E(f491(x14231,x14233,x14234),f491(x14232,x14233,x14234))
% 81.29/80.94 [1424]~E(x14241,x14242)+E(f491(x14243,x14241,x14244),f491(x14243,x14242,x14244))
% 81.29/80.94 [1425]~E(x14251,x14252)+E(f491(x14253,x14254,x14251),f491(x14253,x14254,x14252))
% 81.29/80.94 [1426]~E(x14261,x14262)+E(f565(x14261,x14263,x14264,x14265),f565(x14262,x14263,x14264,x14265))
% 81.29/80.94 [1427]~E(x14271,x14272)+E(f565(x14273,x14271,x14274,x14275),f565(x14273,x14272,x14274,x14275))
% 81.29/80.94 [1428]~E(x14281,x14282)+E(f565(x14283,x14284,x14281,x14285),f565(x14283,x14284,x14282,x14285))
% 81.29/80.94 [1429]~E(x14291,x14292)+E(f565(x14293,x14294,x14295,x14291),f565(x14293,x14294,x14295,x14292))
% 81.29/80.94 [1430]~E(x14301,x14302)+E(f596(x14301,x14303,x14304,x14305,x14306),f596(x14302,x14303,x14304,x14305,x14306))
% 81.29/80.94 [1431]~E(x14311,x14312)+E(f596(x14313,x14311,x14314,x14315,x14316),f596(x14313,x14312,x14314,x14315,x14316))
% 81.29/80.94 [1432]~E(x14321,x14322)+E(f596(x14323,x14324,x14321,x14325,x14326),f596(x14323,x14324,x14322,x14325,x14326))
% 81.29/80.94 [1433]~E(x14331,x14332)+E(f596(x14333,x14334,x14335,x14331,x14336),f596(x14333,x14334,x14335,x14332,x14336))
% 81.29/80.94 [1434]~E(x14341,x14342)+E(f596(x14343,x14344,x14345,x14346,x14341),f596(x14343,x14344,x14345,x14346,x14342))
% 81.29/80.94 [1435]~E(x14351,x14352)+E(f517(x14351,x14353,x14354,x14355,x14356),f517(x14352,x14353,x14354,x14355,x14356))
% 81.29/80.94 [1436]~E(x14361,x14362)+E(f517(x14363,x14361,x14364,x14365,x14366),f517(x14363,x14362,x14364,x14365,x14366))
% 81.29/80.94 [1437]~E(x14371,x14372)+E(f517(x14373,x14374,x14371,x14375,x14376),f517(x14373,x14374,x14372,x14375,x14376))
% 81.29/80.94 [1438]~E(x14381,x14382)+E(f517(x14383,x14384,x14385,x14381,x14386),f517(x14383,x14384,x14385,x14382,x14386))
% 81.29/80.94 [1439]~E(x14391,x14392)+E(f517(x14393,x14394,x14395,x14396,x14391),f517(x14393,x14394,x14395,x14396,x14392))
% 81.29/80.94 [1440]~E(x14401,x14402)+E(f756(x14401,x14403,x14404,x14405,x14406,x14407,x14408,x14409),f756(x14402,x14403,x14404,x14405,x14406,x14407,x14408,x14409))
% 81.29/80.94 [1441]~E(x14411,x14412)+E(f756(x14413,x14411,x14414,x14415,x14416,x14417,x14418,x14419),f756(x14413,x14412,x14414,x14415,x14416,x14417,x14418,x14419))
% 81.29/80.94 [1442]~E(x14421,x14422)+E(f756(x14423,x14424,x14421,x14425,x14426,x14427,x14428,x14429),f756(x14423,x14424,x14422,x14425,x14426,x14427,x14428,x14429))
% 81.29/80.94 [1443]~E(x14431,x14432)+E(f756(x14433,x14434,x14435,x14431,x14436,x14437,x14438,x14439),f756(x14433,x14434,x14435,x14432,x14436,x14437,x14438,x14439))
% 81.29/80.94 [1444]~E(x14441,x14442)+E(f756(x14443,x14444,x14445,x14446,x14441,x14447,x14448,x14449),f756(x14443,x14444,x14445,x14446,x14442,x14447,x14448,x14449))
% 81.29/80.94 [1445]~E(x14451,x14452)+E(f756(x14453,x14454,x14455,x14456,x14457,x14451,x14458,x14459),f756(x14453,x14454,x14455,x14456,x14457,x14452,x14458,x14459))
% 81.29/80.94 [1446]~E(x14461,x14462)+E(f756(x14463,x14464,x14465,x14466,x14467,x14468,x14461,x14469),f756(x14463,x14464,x14465,x14466,x14467,x14468,x14462,x14469))
% 81.29/80.94 [1447]~E(x14471,x14472)+E(f756(x14473,x14474,x14475,x14476,x14477,x14478,x14479,x14471),f756(x14473,x14474,x14475,x14476,x14477,x14478,x14479,x14472))
% 81.29/80.94 [1448]~E(x14481,x14482)+E(f673(x14481,x14483),f673(x14482,x14483))
% 81.29/80.94 [1449]~E(x14491,x14492)+E(f673(x14493,x14491),f673(x14493,x14492))
% 81.29/80.94 [1450]~E(x14501,x14502)+E(f263(x14501,x14503,x14504),f263(x14502,x14503,x14504))
% 81.29/80.94 [1451]~E(x14511,x14512)+E(f263(x14513,x14511,x14514),f263(x14513,x14512,x14514))
% 81.29/80.94 [1452]~E(x14521,x14522)+E(f263(x14523,x14524,x14521),f263(x14523,x14524,x14522))
% 81.29/80.94 [1453]~E(x14531,x14532)+E(f457(x14531,x14533),f457(x14532,x14533))
% 81.29/80.94 [1454]~E(x14541,x14542)+E(f457(x14543,x14541),f457(x14543,x14542))
% 81.29/80.94 [1455]~E(x14551,x14552)+E(f727(x14551,x14553,x14554,x14555),f727(x14552,x14553,x14554,x14555))
% 81.29/80.94 [1456]~E(x14561,x14562)+E(f727(x14563,x14561,x14564,x14565),f727(x14563,x14562,x14564,x14565))
% 81.29/80.94 [1457]~E(x14571,x14572)+E(f727(x14573,x14574,x14571,x14575),f727(x14573,x14574,x14572,x14575))
% 81.29/80.94 [1458]~E(x14581,x14582)+E(f727(x14583,x14584,x14585,x14581),f727(x14583,x14584,x14585,x14582))
% 81.29/80.94 [1459]~E(x14591,x14592)+E(f538(x14591),f538(x14592))
% 81.29/80.94 [1460]~E(x14601,x14602)+E(f848(x14601,x14603,x14604,x14605,x14606),f848(x14602,x14603,x14604,x14605,x14606))
% 81.29/80.94 [1461]~E(x14611,x14612)+E(f848(x14613,x14611,x14614,x14615,x14616),f848(x14613,x14612,x14614,x14615,x14616))
% 81.29/80.94 [1462]~E(x14621,x14622)+E(f848(x14623,x14624,x14621,x14625,x14626),f848(x14623,x14624,x14622,x14625,x14626))
% 81.29/80.94 [1463]~E(x14631,x14632)+E(f848(x14633,x14634,x14635,x14631,x14636),f848(x14633,x14634,x14635,x14632,x14636))
% 81.29/80.94 [1464]~E(x14641,x14642)+E(f848(x14643,x14644,x14645,x14646,x14641),f848(x14643,x14644,x14645,x14646,x14642))
% 81.29/80.94 [1465]~E(x14651,x14652)+E(f471(x14651,x14653),f471(x14652,x14653))
% 81.29/80.94 [1466]~E(x14661,x14662)+E(f471(x14663,x14661),f471(x14663,x14662))
% 81.29/80.94 [1467]~E(x14671,x14672)+E(f795(x14671,x14673,x14674),f795(x14672,x14673,x14674))
% 81.29/80.94 [1468]~E(x14681,x14682)+E(f795(x14683,x14681,x14684),f795(x14683,x14682,x14684))
% 81.29/80.94 [1469]~E(x14691,x14692)+E(f795(x14693,x14694,x14691),f795(x14693,x14694,x14692))
% 81.29/80.94 [1470]~E(x14701,x14702)+E(f462(x14701,x14703,x14704),f462(x14702,x14703,x14704))
% 81.29/80.94 [1471]~E(x14711,x14712)+E(f462(x14713,x14711,x14714),f462(x14713,x14712,x14714))
% 81.29/80.94 [1472]~E(x14721,x14722)+E(f462(x14723,x14724,x14721),f462(x14723,x14724,x14722))
% 81.29/80.94 [1473]~E(x14731,x14732)+E(f429(x14731,x14733),f429(x14732,x14733))
% 81.29/80.94 [1474]~E(x14741,x14742)+E(f429(x14743,x14741),f429(x14743,x14742))
% 81.29/80.94 [1475]~E(x14751,x14752)+E(f342(x14751,x14753,x14754),f342(x14752,x14753,x14754))
% 81.29/80.94 [1476]~E(x14761,x14762)+E(f342(x14763,x14761,x14764),f342(x14763,x14762,x14764))
% 81.29/80.94 [1477]~E(x14771,x14772)+E(f342(x14773,x14774,x14771),f342(x14773,x14774,x14772))
% 81.29/80.94 [1478]~E(x14781,x14782)+E(f511(x14781,x14783,x14784,x14785,x14786,x14787,x14788),f511(x14782,x14783,x14784,x14785,x14786,x14787,x14788))
% 81.29/80.94 [1479]~E(x14791,x14792)+E(f511(x14793,x14791,x14794,x14795,x14796,x14797,x14798),f511(x14793,x14792,x14794,x14795,x14796,x14797,x14798))
% 81.29/80.94 [1480]~E(x14801,x14802)+E(f511(x14803,x14804,x14801,x14805,x14806,x14807,x14808),f511(x14803,x14804,x14802,x14805,x14806,x14807,x14808))
% 81.29/80.94 [1481]~E(x14811,x14812)+E(f511(x14813,x14814,x14815,x14811,x14816,x14817,x14818),f511(x14813,x14814,x14815,x14812,x14816,x14817,x14818))
% 81.29/80.94 [1482]~E(x14821,x14822)+E(f511(x14823,x14824,x14825,x14826,x14821,x14827,x14828),f511(x14823,x14824,x14825,x14826,x14822,x14827,x14828))
% 81.29/80.94 [1483]~E(x14831,x14832)+E(f511(x14833,x14834,x14835,x14836,x14837,x14831,x14838),f511(x14833,x14834,x14835,x14836,x14837,x14832,x14838))
% 81.29/80.94 [1484]~E(x14841,x14842)+E(f511(x14843,x14844,x14845,x14846,x14847,x14848,x14841),f511(x14843,x14844,x14845,x14846,x14847,x14848,x14842))
% 81.29/80.94 [1485]~E(x14851,x14852)+E(f569(x14851,x14853,x14854,x14855,x14856),f569(x14852,x14853,x14854,x14855,x14856))
% 81.29/80.94 [1486]~E(x14861,x14862)+E(f569(x14863,x14861,x14864,x14865,x14866),f569(x14863,x14862,x14864,x14865,x14866))
% 81.29/80.94 [1487]~E(x14871,x14872)+E(f569(x14873,x14874,x14871,x14875,x14876),f569(x14873,x14874,x14872,x14875,x14876))
% 81.29/80.94 [1488]~E(x14881,x14882)+E(f569(x14883,x14884,x14885,x14881,x14886),f569(x14883,x14884,x14885,x14882,x14886))
% 81.29/80.94 [1489]~E(x14891,x14892)+E(f569(x14893,x14894,x14895,x14896,x14891),f569(x14893,x14894,x14895,x14896,x14892))
% 81.29/80.94 [1490]~E(x14901,x14902)+E(f800(x14901,x14903,x14904,x14905,x14906),f800(x14902,x14903,x14904,x14905,x14906))
% 81.29/80.94 [1491]~E(x14911,x14912)+E(f800(x14913,x14911,x14914,x14915,x14916),f800(x14913,x14912,x14914,x14915,x14916))
% 81.29/80.94 [1492]~E(x14921,x14922)+E(f800(x14923,x14924,x14921,x14925,x14926),f800(x14923,x14924,x14922,x14925,x14926))
% 81.29/80.94 [1493]~E(x14931,x14932)+E(f800(x14933,x14934,x14935,x14931,x14936),f800(x14933,x14934,x14935,x14932,x14936))
% 81.29/80.94 [1494]~E(x14941,x14942)+E(f800(x14943,x14944,x14945,x14946,x14941),f800(x14943,x14944,x14945,x14946,x14942))
% 81.29/80.94 [1495]~E(x14951,x14952)+E(f262(x14951,x14953),f262(x14952,x14953))
% 81.29/80.94 [1496]~E(x14961,x14962)+E(f262(x14963,x14961),f262(x14963,x14962))
% 81.29/80.94 [1497]~E(x14971,x14972)+E(f525(x14971,x14973,x14974,x14975,x14976),f525(x14972,x14973,x14974,x14975,x14976))
% 81.29/80.94 [1498]~E(x14981,x14982)+E(f525(x14983,x14981,x14984,x14985,x14986),f525(x14983,x14982,x14984,x14985,x14986))
% 81.29/80.94 [1499]~E(x14991,x14992)+E(f525(x14993,x14994,x14991,x14995,x14996),f525(x14993,x14994,x14992,x14995,x14996))
% 81.29/80.94 [1500]~E(x15001,x15002)+E(f525(x15003,x15004,x15005,x15001,x15006),f525(x15003,x15004,x15005,x15002,x15006))
% 81.29/80.94 [1501]~E(x15011,x15012)+E(f525(x15013,x15014,x15015,x15016,x15011),f525(x15013,x15014,x15015,x15016,x15012))
% 81.29/80.94 [1502]~E(x15021,x15022)+E(f713(x15021,x15023),f713(x15022,x15023))
% 81.29/80.94 [1503]~E(x15031,x15032)+E(f713(x15033,x15031),f713(x15033,x15032))
% 81.29/80.94 [1504]~E(x15041,x15042)+E(f97(x15041,x15043,x15044,x15045),f97(x15042,x15043,x15044,x15045))
% 81.29/80.94 [1505]~E(x15051,x15052)+E(f97(x15053,x15051,x15054,x15055),f97(x15053,x15052,x15054,x15055))
% 81.29/80.94 [1506]~E(x15061,x15062)+E(f97(x15063,x15064,x15061,x15065),f97(x15063,x15064,x15062,x15065))
% 81.29/80.94 [1507]~E(x15071,x15072)+E(f97(x15073,x15074,x15075,x15071),f97(x15073,x15074,x15075,x15072))
% 81.29/80.94 [1508]~E(x15081,x15082)+E(f385(x15081,x15083,x15084,x15085),f385(x15082,x15083,x15084,x15085))
% 81.29/80.94 [1509]~E(x15091,x15092)+E(f385(x15093,x15091,x15094,x15095),f385(x15093,x15092,x15094,x15095))
% 81.29/80.94 [1510]~E(x15101,x15102)+E(f385(x15103,x15104,x15101,x15105),f385(x15103,x15104,x15102,x15105))
% 81.29/80.94 [1511]~E(x15111,x15112)+E(f385(x15113,x15114,x15115,x15111),f385(x15113,x15114,x15115,x15112))
% 81.29/80.94 [1512]~E(x15121,x15122)+E(f570(x15121,x15123,x15124,x15125,x15126,x15127),f570(x15122,x15123,x15124,x15125,x15126,x15127))
% 81.29/80.94 [1513]~E(x15131,x15132)+E(f570(x15133,x15131,x15134,x15135,x15136,x15137),f570(x15133,x15132,x15134,x15135,x15136,x15137))
% 81.29/80.94 [1514]~E(x15141,x15142)+E(f570(x15143,x15144,x15141,x15145,x15146,x15147),f570(x15143,x15144,x15142,x15145,x15146,x15147))
% 81.29/80.94 [1515]~E(x15151,x15152)+E(f570(x15153,x15154,x15155,x15151,x15156,x15157),f570(x15153,x15154,x15155,x15152,x15156,x15157))
% 81.29/80.94 [1516]~E(x15161,x15162)+E(f570(x15163,x15164,x15165,x15166,x15161,x15167),f570(x15163,x15164,x15165,x15166,x15162,x15167))
% 81.29/80.94 [1517]~E(x15171,x15172)+E(f570(x15173,x15174,x15175,x15176,x15177,x15171),f570(x15173,x15174,x15175,x15176,x15177,x15172))
% 81.29/80.94 [1518]~E(x15181,x15182)+E(f731(x15181,x15183,x15184,x15185,x15186,x15187),f731(x15182,x15183,x15184,x15185,x15186,x15187))
% 81.29/80.94 [1519]~E(x15191,x15192)+E(f731(x15193,x15191,x15194,x15195,x15196,x15197),f731(x15193,x15192,x15194,x15195,x15196,x15197))
% 81.29/80.94 [1520]~E(x15201,x15202)+E(f731(x15203,x15204,x15201,x15205,x15206,x15207),f731(x15203,x15204,x15202,x15205,x15206,x15207))
% 81.29/80.94 [1521]~E(x15211,x15212)+E(f731(x15213,x15214,x15215,x15211,x15216,x15217),f731(x15213,x15214,x15215,x15212,x15216,x15217))
% 81.29/80.94 [1522]~E(x15221,x15222)+E(f731(x15223,x15224,x15225,x15226,x15221,x15227),f731(x15223,x15224,x15225,x15226,x15222,x15227))
% 81.29/80.94 [1523]~E(x15231,x15232)+E(f731(x15233,x15234,x15235,x15236,x15237,x15231),f731(x15233,x15234,x15235,x15236,x15237,x15232))
% 81.29/80.94 [1524]~E(x15241,x15242)+E(f761(x15241,x15243,x15244),f761(x15242,x15243,x15244))
% 81.29/80.94 [1525]~E(x15251,x15252)+E(f761(x15253,x15251,x15254),f761(x15253,x15252,x15254))
% 81.29/80.94 [1526]~E(x15261,x15262)+E(f761(x15263,x15264,x15261),f761(x15263,x15264,x15262))
% 81.29/80.94 [1527]~E(x15271,x15272)+E(f844(x15271,x15273,x15274,x15275,x15276),f844(x15272,x15273,x15274,x15275,x15276))
% 81.29/80.94 [1528]~E(x15281,x15282)+E(f844(x15283,x15281,x15284,x15285,x15286),f844(x15283,x15282,x15284,x15285,x15286))
% 81.29/80.94 [1529]~E(x15291,x15292)+E(f844(x15293,x15294,x15291,x15295,x15296),f844(x15293,x15294,x15292,x15295,x15296))
% 81.29/80.94 [1530]~E(x15301,x15302)+E(f844(x15303,x15304,x15305,x15301,x15306),f844(x15303,x15304,x15305,x15302,x15306))
% 81.29/80.94 [1531]~E(x15311,x15312)+E(f844(x15313,x15314,x15315,x15316,x15311),f844(x15313,x15314,x15315,x15316,x15312))
% 81.29/80.94 [1532]~E(x15321,x15322)+E(f129(x15321,x15323,x15324),f129(x15322,x15323,x15324))
% 81.29/80.94 [1533]~E(x15331,x15332)+E(f129(x15333,x15331,x15334),f129(x15333,x15332,x15334))
% 81.29/80.94 [1534]~E(x15341,x15342)+E(f129(x15343,x15344,x15341),f129(x15343,x15344,x15342))
% 81.29/80.94 [1535]~E(x15351,x15352)+E(f292(x15351,x15353,x15354,x15355),f292(x15352,x15353,x15354,x15355))
% 81.29/80.94 [1536]~E(x15361,x15362)+E(f292(x15363,x15361,x15364,x15365),f292(x15363,x15362,x15364,x15365))
% 81.29/80.94 [1537]~E(x15371,x15372)+E(f292(x15373,x15374,x15371,x15375),f292(x15373,x15374,x15372,x15375))
% 81.29/80.94 [1538]~E(x15381,x15382)+E(f292(x15383,x15384,x15385,x15381),f292(x15383,x15384,x15385,x15382))
% 81.29/80.94 [1539]~E(x15391,x15392)+E(f101(x15391,x15393,x15394,x15395),f101(x15392,x15393,x15394,x15395))
% 81.29/80.94 [1540]~E(x15401,x15402)+E(f101(x15403,x15401,x15404,x15405),f101(x15403,x15402,x15404,x15405))
% 81.29/80.94 [1541]~E(x15411,x15412)+E(f101(x15413,x15414,x15411,x15415),f101(x15413,x15414,x15412,x15415))
% 81.29/80.94 [1542]~E(x15421,x15422)+E(f101(x15423,x15424,x15425,x15421),f101(x15423,x15424,x15425,x15422))
% 81.29/80.94 [1543]~E(x15431,x15432)+E(f858(x15431),f858(x15432))
% 81.29/80.94 [1544]~E(x15441,x15442)+E(f551(x15441,x15443,x15444,x15445,x15446),f551(x15442,x15443,x15444,x15445,x15446))
% 81.29/80.94 [1545]~E(x15451,x15452)+E(f551(x15453,x15451,x15454,x15455,x15456),f551(x15453,x15452,x15454,x15455,x15456))
% 81.29/80.94 [1546]~E(x15461,x15462)+E(f551(x15463,x15464,x15461,x15465,x15466),f551(x15463,x15464,x15462,x15465,x15466))
% 81.29/80.94 [1547]~E(x15471,x15472)+E(f551(x15473,x15474,x15475,x15471,x15476),f551(x15473,x15474,x15475,x15472,x15476))
% 81.29/80.94 [1548]~E(x15481,x15482)+E(f551(x15483,x15484,x15485,x15486,x15481),f551(x15483,x15484,x15485,x15486,x15482))
% 81.29/80.94 [1549]~E(x15491,x15492)+E(f369(x15491,x15493,x15494,x15495,x15496,x15497,x15498),f369(x15492,x15493,x15494,x15495,x15496,x15497,x15498))
% 81.29/80.94 [1550]~E(x15501,x15502)+E(f369(x15503,x15501,x15504,x15505,x15506,x15507,x15508),f369(x15503,x15502,x15504,x15505,x15506,x15507,x15508))
% 81.29/80.94 [1551]~E(x15511,x15512)+E(f369(x15513,x15514,x15511,x15515,x15516,x15517,x15518),f369(x15513,x15514,x15512,x15515,x15516,x15517,x15518))
% 81.29/80.94 [1552]~E(x15521,x15522)+E(f369(x15523,x15524,x15525,x15521,x15526,x15527,x15528),f369(x15523,x15524,x15525,x15522,x15526,x15527,x15528))
% 81.29/80.94 [1553]~E(x15531,x15532)+E(f369(x15533,x15534,x15535,x15536,x15531,x15537,x15538),f369(x15533,x15534,x15535,x15536,x15532,x15537,x15538))
% 81.29/80.94 [1554]~E(x15541,x15542)+E(f369(x15543,x15544,x15545,x15546,x15547,x15541,x15548),f369(x15543,x15544,x15545,x15546,x15547,x15542,x15548))
% 81.29/80.94 [1555]~E(x15551,x15552)+E(f369(x15553,x15554,x15555,x15556,x15557,x15558,x15551),f369(x15553,x15554,x15555,x15556,x15557,x15558,x15552))
% 81.29/80.94 [1556]~E(x15561,x15562)+E(f540(x15561,x15563,x15564,x15565),f540(x15562,x15563,x15564,x15565))
% 81.29/80.94 [1557]~E(x15571,x15572)+E(f540(x15573,x15571,x15574,x15575),f540(x15573,x15572,x15574,x15575))
% 81.29/80.94 [1558]~E(x15581,x15582)+E(f540(x15583,x15584,x15581,x15585),f540(x15583,x15584,x15582,x15585))
% 81.29/80.94 [1559]~E(x15591,x15592)+E(f540(x15593,x15594,x15595,x15591),f540(x15593,x15594,x15595,x15592))
% 81.29/80.94 [1560]~E(x15601,x15602)+E(f812(x15601,x15603,x15604),f812(x15602,x15603,x15604))
% 81.29/80.94 [1561]~E(x15611,x15612)+E(f812(x15613,x15611,x15614),f812(x15613,x15612,x15614))
% 81.29/80.94 [1562]~E(x15621,x15622)+E(f812(x15623,x15624,x15621),f812(x15623,x15624,x15622))
% 81.29/80.94 [1563]~E(x15631,x15632)+E(f563(x15631,x15633,x15634),f563(x15632,x15633,x15634))
% 81.29/80.94 [1564]~E(x15641,x15642)+E(f563(x15643,x15641,x15644),f563(x15643,x15642,x15644))
% 81.29/80.94 [1565]~E(x15651,x15652)+E(f563(x15653,x15654,x15651),f563(x15653,x15654,x15652))
% 81.29/80.94 [1566]~E(x15661,x15662)+E(f145(x15661,x15663),f145(x15662,x15663))
% 81.29/80.94 [1567]~E(x15671,x15672)+E(f145(x15673,x15671),f145(x15673,x15672))
% 81.29/80.94 [1568]~E(x15681,x15682)+E(f213(x15681,x15683,x15684,x15685),f213(x15682,x15683,x15684,x15685))
% 81.29/80.94 [1569]~E(x15691,x15692)+E(f213(x15693,x15691,x15694,x15695),f213(x15693,x15692,x15694,x15695))
% 81.29/80.94 [1570]~E(x15701,x15702)+E(f213(x15703,x15704,x15701,x15705),f213(x15703,x15704,x15702,x15705))
% 81.29/80.94 [1571]~E(x15711,x15712)+E(f213(x15713,x15714,x15715,x15711),f213(x15713,x15714,x15715,x15712))
% 81.29/80.94 [1572]~E(x15721,x15722)+E(f602(x15721,x15723,x15724),f602(x15722,x15723,x15724))
% 81.29/80.94 [1573]~E(x15731,x15732)+E(f602(x15733,x15731,x15734),f602(x15733,x15732,x15734))
% 81.29/80.94 [1574]~E(x15741,x15742)+E(f602(x15743,x15744,x15741),f602(x15743,x15744,x15742))
% 81.29/80.94 [1575]~E(x15751,x15752)+E(f869(x15751,x15753,x15754),f869(x15752,x15753,x15754))
% 81.29/80.94 [1576]~E(x15761,x15762)+E(f869(x15763,x15761,x15764),f869(x15763,x15762,x15764))
% 81.29/80.94 [1577]~E(x15771,x15772)+E(f869(x15773,x15774,x15771),f869(x15773,x15774,x15772))
% 81.29/80.94 [1578]~E(x15781,x15782)+E(f635(x15781,x15783,x15784,x15785),f635(x15782,x15783,x15784,x15785))
% 81.29/80.94 [1579]~E(x15791,x15792)+E(f635(x15793,x15791,x15794,x15795),f635(x15793,x15792,x15794,x15795))
% 81.29/80.94 [1580]~E(x15801,x15802)+E(f635(x15803,x15804,x15801,x15805),f635(x15803,x15804,x15802,x15805))
% 81.29/80.94 [1581]~E(x15811,x15812)+E(f635(x15813,x15814,x15815,x15811),f635(x15813,x15814,x15815,x15812))
% 81.29/80.94 [1582]~E(x15821,x15822)+E(f632(x15821,x15823,x15824),f632(x15822,x15823,x15824))
% 81.29/80.94 [1583]~E(x15831,x15832)+E(f632(x15833,x15831,x15834),f632(x15833,x15832,x15834))
% 81.29/80.94 [1584]~E(x15841,x15842)+E(f632(x15843,x15844,x15841),f632(x15843,x15844,x15842))
% 81.29/80.94 [1585]~E(x15851,x15852)+E(f846(x15851,x15853,x15854,x15855),f846(x15852,x15853,x15854,x15855))
% 81.29/80.94 [1586]~E(x15861,x15862)+E(f846(x15863,x15861,x15864,x15865),f846(x15863,x15862,x15864,x15865))
% 81.29/80.94 [1587]~E(x15871,x15872)+E(f846(x15873,x15874,x15871,x15875),f846(x15873,x15874,x15872,x15875))
% 81.29/80.94 [1588]~E(x15881,x15882)+E(f846(x15883,x15884,x15885,x15881),f846(x15883,x15884,x15885,x15882))
% 81.29/80.94 [1589]~E(x15891,x15892)+E(f752(x15891,x15893,x15894,x15895),f752(x15892,x15893,x15894,x15895))
% 81.29/80.94 [1590]~E(x15901,x15902)+E(f752(x15903,x15901,x15904,x15905),f752(x15903,x15902,x15904,x15905))
% 81.29/80.94 [1591]~E(x15911,x15912)+E(f752(x15913,x15914,x15911,x15915),f752(x15913,x15914,x15912,x15915))
% 81.29/80.94 [1592]~E(x15921,x15922)+E(f752(x15923,x15924,x15925,x15921),f752(x15923,x15924,x15925,x15922))
% 81.29/80.94 [1593]~E(x15931,x15932)+E(f340(x15931,x15933,x15934),f340(x15932,x15933,x15934))
% 81.29/80.94 [1594]~E(x15941,x15942)+E(f340(x15943,x15941,x15944),f340(x15943,x15942,x15944))
% 81.29/80.94 [1595]~E(x15951,x15952)+E(f340(x15953,x15954,x15951),f340(x15953,x15954,x15952))
% 81.29/80.94 [1596]~E(x15961,x15962)+E(f396(x15961,x15963),f396(x15962,x15963))
% 81.29/80.94 [1597]~E(x15971,x15972)+E(f396(x15973,x15971),f396(x15973,x15972))
% 81.29/80.94 [1598]~E(x15981,x15982)+E(f212(x15981),f212(x15982))
% 81.29/80.94 [1599]~E(x15991,x15992)+E(f386(x15991,x15993,x15994),f386(x15992,x15993,x15994))
% 81.29/80.94 [1600]~E(x16001,x16002)+E(f386(x16003,x16001,x16004),f386(x16003,x16002,x16004))
% 81.29/80.94 [1601]~E(x16011,x16012)+E(f386(x16013,x16014,x16011),f386(x16013,x16014,x16012))
% 81.29/80.94 [1602]~E(x16021,x16022)+E(f17(x16021,x16023,x16024,x16025),f17(x16022,x16023,x16024,x16025))
% 81.29/80.94 [1603]~E(x16031,x16032)+E(f17(x16033,x16031,x16034,x16035),f17(x16033,x16032,x16034,x16035))
% 81.29/80.94 [1604]~E(x16041,x16042)+E(f17(x16043,x16044,x16041,x16045),f17(x16043,x16044,x16042,x16045))
% 81.29/80.94 [1605]~E(x16051,x16052)+E(f17(x16053,x16054,x16055,x16051),f17(x16053,x16054,x16055,x16052))
% 81.29/80.94 [1606]~E(x16061,x16062)+E(f621(x16061,x16063,x16064,x16065,x16066),f621(x16062,x16063,x16064,x16065,x16066))
% 81.29/80.94 [1607]~E(x16071,x16072)+E(f621(x16073,x16071,x16074,x16075,x16076),f621(x16073,x16072,x16074,x16075,x16076))
% 81.29/80.94 [1608]~E(x16081,x16082)+E(f621(x16083,x16084,x16081,x16085,x16086),f621(x16083,x16084,x16082,x16085,x16086))
% 81.29/80.94 [1609]~E(x16091,x16092)+E(f621(x16093,x16094,x16095,x16091,x16096),f621(x16093,x16094,x16095,x16092,x16096))
% 81.29/80.94 [1610]~E(x16101,x16102)+E(f621(x16103,x16104,x16105,x16106,x16101),f621(x16103,x16104,x16105,x16106,x16102))
% 81.29/80.94 [1611]~E(x16111,x16112)+E(f560(x16111,x16113,x16114,x16115,x16116),f560(x16112,x16113,x16114,x16115,x16116))
% 81.29/80.94 [1612]~E(x16121,x16122)+E(f560(x16123,x16121,x16124,x16125,x16126),f560(x16123,x16122,x16124,x16125,x16126))
% 81.29/80.94 [1613]~E(x16131,x16132)+E(f560(x16133,x16134,x16131,x16135,x16136),f560(x16133,x16134,x16132,x16135,x16136))
% 81.29/80.94 [1614]~E(x16141,x16142)+E(f560(x16143,x16144,x16145,x16141,x16146),f560(x16143,x16144,x16145,x16142,x16146))
% 81.29/80.94 [1615]~E(x16151,x16152)+E(f560(x16153,x16154,x16155,x16156,x16151),f560(x16153,x16154,x16155,x16156,x16152))
% 81.29/80.94 [1616]~E(x16161,x16162)+E(f21(x16161,x16163),f21(x16162,x16163))
% 81.29/80.94 [1617]~E(x16171,x16172)+E(f21(x16173,x16171),f21(x16173,x16172))
% 81.29/80.94 [1618]~E(x16181,x16182)+E(f366(x16181,x16183),f366(x16182,x16183))
% 81.29/80.94 [1619]~E(x16191,x16192)+E(f366(x16193,x16191),f366(x16193,x16192))
% 81.29/80.94 [1620]~E(x16201,x16202)+E(f294(x16201,x16203,x16204),f294(x16202,x16203,x16204))
% 81.29/80.94 [1621]~E(x16211,x16212)+E(f294(x16213,x16211,x16214),f294(x16213,x16212,x16214))
% 81.29/80.94 [1622]~E(x16221,x16222)+E(f294(x16223,x16224,x16221),f294(x16223,x16224,x16222))
% 81.29/80.94 [1623]~E(x16231,x16232)+E(f630(x16231,x16233,x16234,x16235,x16236),f630(x16232,x16233,x16234,x16235,x16236))
% 81.29/80.94 [1624]~E(x16241,x16242)+E(f630(x16243,x16241,x16244,x16245,x16246),f630(x16243,x16242,x16244,x16245,x16246))
% 81.29/80.94 [1625]~E(x16251,x16252)+E(f630(x16253,x16254,x16251,x16255,x16256),f630(x16253,x16254,x16252,x16255,x16256))
% 81.29/80.94 [1626]~E(x16261,x16262)+E(f630(x16263,x16264,x16265,x16261,x16266),f630(x16263,x16264,x16265,x16262,x16266))
% 81.29/80.94 [1627]~E(x16271,x16272)+E(f630(x16273,x16274,x16275,x16276,x16271),f630(x16273,x16274,x16275,x16276,x16272))
% 81.29/80.94 [1628]~E(x16281,x16282)+E(f456(x16281,x16283),f456(x16282,x16283))
% 81.29/80.94 [1629]~E(x16291,x16292)+E(f456(x16293,x16291),f456(x16293,x16292))
% 81.29/80.94 [1630]~E(x16301,x16302)+E(f834(x16301,x16303),f834(x16302,x16303))
% 81.29/80.94 [1631]~E(x16311,x16312)+E(f834(x16313,x16311),f834(x16313,x16312))
% 81.29/80.94 [1632]~E(x16321,x16322)+E(f539(x16321,x16323),f539(x16322,x16323))
% 81.29/80.94 [1633]~E(x16331,x16332)+E(f539(x16333,x16331),f539(x16333,x16332))
% 81.29/80.94 [1634]~E(x16341,x16342)+E(f611(x16341,x16343),f611(x16342,x16343))
% 81.29/80.94 [1635]~E(x16351,x16352)+E(f611(x16353,x16351),f611(x16353,x16352))
% 81.29/80.94 [1636]~E(x16361,x16362)+E(f831(x16361,x16363,x16364),f831(x16362,x16363,x16364))
% 81.29/80.94 [1637]~E(x16371,x16372)+E(f831(x16373,x16371,x16374),f831(x16373,x16372,x16374))
% 81.29/80.94 [1638]~E(x16381,x16382)+E(f831(x16383,x16384,x16381),f831(x16383,x16384,x16382))
% 81.29/80.94 [1639]~E(x16391,x16392)+E(f549(x16391,x16393,x16394,x16395),f549(x16392,x16393,x16394,x16395))
% 81.29/80.94 [1640]~E(x16401,x16402)+E(f549(x16403,x16401,x16404,x16405),f549(x16403,x16402,x16404,x16405))
% 81.29/80.94 [1641]~E(x16411,x16412)+E(f549(x16413,x16414,x16411,x16415),f549(x16413,x16414,x16412,x16415))
% 81.29/80.94 [1642]~E(x16421,x16422)+E(f549(x16423,x16424,x16425,x16421),f549(x16423,x16424,x16425,x16422))
% 81.29/80.94 [1643]~E(x16431,x16432)+E(f793(x16431,x16433,x16434),f793(x16432,x16433,x16434))
% 81.29/80.94 [1644]~E(x16441,x16442)+E(f793(x16443,x16441,x16444),f793(x16443,x16442,x16444))
% 81.29/80.94 [1645]~E(x16451,x16452)+E(f793(x16453,x16454,x16451),f793(x16453,x16454,x16452))
% 81.29/80.94 [1646]~E(x16461,x16462)+E(f556(x16461,x16463,x16464,x16465,x16466),f556(x16462,x16463,x16464,x16465,x16466))
% 81.29/80.94 [1647]~E(x16471,x16472)+E(f556(x16473,x16471,x16474,x16475,x16476),f556(x16473,x16472,x16474,x16475,x16476))
% 81.29/80.94 [1648]~E(x16481,x16482)+E(f556(x16483,x16484,x16481,x16485,x16486),f556(x16483,x16484,x16482,x16485,x16486))
% 81.29/80.94 [1649]~E(x16491,x16492)+E(f556(x16493,x16494,x16495,x16491,x16496),f556(x16493,x16494,x16495,x16492,x16496))
% 81.29/80.94 [1650]~E(x16501,x16502)+E(f556(x16503,x16504,x16505,x16506,x16501),f556(x16503,x16504,x16505,x16506,x16502))
% 81.29/80.94 [1651]~E(x16511,x16512)+E(f392(x16511,x16513,x16514,x16515),f392(x16512,x16513,x16514,x16515))
% 81.29/80.94 [1652]~E(x16521,x16522)+E(f392(x16523,x16521,x16524,x16525),f392(x16523,x16522,x16524,x16525))
% 81.29/80.94 [1653]~E(x16531,x16532)+E(f392(x16533,x16534,x16531,x16535),f392(x16533,x16534,x16532,x16535))
% 81.29/80.94 [1654]~E(x16541,x16542)+E(f392(x16543,x16544,x16545,x16541),f392(x16543,x16544,x16545,x16542))
% 81.29/80.94 [1655]~E(x16551,x16552)+E(f219(x16551,x16553,x16554,x16555,x16556,x16557,x16558),f219(x16552,x16553,x16554,x16555,x16556,x16557,x16558))
% 81.29/80.94 [1656]~E(x16561,x16562)+E(f219(x16563,x16561,x16564,x16565,x16566,x16567,x16568),f219(x16563,x16562,x16564,x16565,x16566,x16567,x16568))
% 81.29/80.94 [1657]~E(x16571,x16572)+E(f219(x16573,x16574,x16571,x16575,x16576,x16577,x16578),f219(x16573,x16574,x16572,x16575,x16576,x16577,x16578))
% 81.29/80.94 [1658]~E(x16581,x16582)+E(f219(x16583,x16584,x16585,x16581,x16586,x16587,x16588),f219(x16583,x16584,x16585,x16582,x16586,x16587,x16588))
% 81.29/80.94 [1659]~E(x16591,x16592)+E(f219(x16593,x16594,x16595,x16596,x16591,x16597,x16598),f219(x16593,x16594,x16595,x16596,x16592,x16597,x16598))
% 81.29/80.94 [1660]~E(x16601,x16602)+E(f219(x16603,x16604,x16605,x16606,x16607,x16601,x16608),f219(x16603,x16604,x16605,x16606,x16607,x16602,x16608))
% 81.29/80.94 [1661]~E(x16611,x16612)+E(f219(x16613,x16614,x16615,x16616,x16617,x16618,x16611),f219(x16613,x16614,x16615,x16616,x16617,x16618,x16612))
% 81.29/80.94 [1662]~E(x16621,x16622)+E(f581(x16621,x16623,x16624),f581(x16622,x16623,x16624))
% 81.29/80.94 [1663]~E(x16631,x16632)+E(f581(x16633,x16631,x16634),f581(x16633,x16632,x16634))
% 81.29/80.94 [1664]~E(x16641,x16642)+E(f581(x16643,x16644,x16641),f581(x16643,x16644,x16642))
% 81.29/80.94 [1665]~E(x16651,x16652)+E(f418(x16651,x16653,x16654,x16655),f418(x16652,x16653,x16654,x16655))
% 81.29/80.94 [1666]~E(x16661,x16662)+E(f418(x16663,x16661,x16664,x16665),f418(x16663,x16662,x16664,x16665))
% 81.29/80.94 [1667]~E(x16671,x16672)+E(f418(x16673,x16674,x16671,x16675),f418(x16673,x16674,x16672,x16675))
% 81.29/80.94 [1668]~E(x16681,x16682)+E(f418(x16683,x16684,x16685,x16681),f418(x16683,x16684,x16685,x16682))
% 81.29/80.94 [1669]~E(x16691,x16692)+E(f371(x16691,x16693,x16694),f371(x16692,x16693,x16694))
% 81.29/80.94 [1670]~E(x16701,x16702)+E(f371(x16703,x16701,x16704),f371(x16703,x16702,x16704))
% 81.29/80.94 [1671]~E(x16711,x16712)+E(f371(x16713,x16714,x16711),f371(x16713,x16714,x16712))
% 81.29/80.94 [1672]~E(x16721,x16722)+E(f750(x16721,x16723,x16724),f750(x16722,x16723,x16724))
% 81.29/80.94 [1673]~E(x16731,x16732)+E(f750(x16733,x16731,x16734),f750(x16733,x16732,x16734))
% 81.29/80.94 [1674]~E(x16741,x16742)+E(f750(x16743,x16744,x16741),f750(x16743,x16744,x16742))
% 81.29/80.94 [1675]~E(x16751,x16752)+E(f715(x16751,x16753,x16754,x16755),f715(x16752,x16753,x16754,x16755))
% 81.29/80.94 [1676]~E(x16761,x16762)+E(f715(x16763,x16761,x16764,x16765),f715(x16763,x16762,x16764,x16765))
% 81.29/80.94 [1677]~E(x16771,x16772)+E(f715(x16773,x16774,x16771,x16775),f715(x16773,x16774,x16772,x16775))
% 81.29/80.94 [1678]~E(x16781,x16782)+E(f715(x16783,x16784,x16785,x16781),f715(x16783,x16784,x16785,x16782))
% 81.29/80.94 [1679]~E(x16791,x16792)+E(f280(x16791,x16793,x16794,x16795),f280(x16792,x16793,x16794,x16795))
% 81.29/80.94 [1680]~E(x16801,x16802)+E(f280(x16803,x16801,x16804,x16805),f280(x16803,x16802,x16804,x16805))
% 81.29/80.94 [1681]~E(x16811,x16812)+E(f280(x16813,x16814,x16811,x16815),f280(x16813,x16814,x16812,x16815))
% 81.29/80.94 [1682]~E(x16821,x16822)+E(f280(x16823,x16824,x16825,x16821),f280(x16823,x16824,x16825,x16822))
% 81.29/80.94 [1683]~E(x16831,x16832)+E(f847(x16831,x16833,x16834,x16835),f847(x16832,x16833,x16834,x16835))
% 81.29/80.94 [1684]~E(x16841,x16842)+E(f847(x16843,x16841,x16844,x16845),f847(x16843,x16842,x16844,x16845))
% 81.29/80.94 [1685]~E(x16851,x16852)+E(f847(x16853,x16854,x16851,x16855),f847(x16853,x16854,x16852,x16855))
% 81.29/80.94 [1686]~E(x16861,x16862)+E(f847(x16863,x16864,x16865,x16861),f847(x16863,x16864,x16865,x16862))
% 81.29/80.94 [1687]~E(x16871,x16872)+E(f737(x16871,x16873,x16874),f737(x16872,x16873,x16874))
% 81.29/80.94 [1688]~E(x16881,x16882)+E(f737(x16883,x16881,x16884),f737(x16883,x16882,x16884))
% 81.29/80.94 [1689]~E(x16891,x16892)+E(f737(x16893,x16894,x16891),f737(x16893,x16894,x16892))
% 81.29/80.94 [1690]~E(x16901,x16902)+E(f510(x16901,x16903,x16904,x16905,x16906),f510(x16902,x16903,x16904,x16905,x16906))
% 81.29/80.94 [1691]~E(x16911,x16912)+E(f510(x16913,x16911,x16914,x16915,x16916),f510(x16913,x16912,x16914,x16915,x16916))
% 81.29/80.94 [1692]~E(x16921,x16922)+E(f510(x16923,x16924,x16921,x16925,x16926),f510(x16923,x16924,x16922,x16925,x16926))
% 81.29/80.94 [1693]~E(x16931,x16932)+E(f510(x16933,x16934,x16935,x16931,x16936),f510(x16933,x16934,x16935,x16932,x16936))
% 81.29/80.94 [1694]~E(x16941,x16942)+E(f510(x16943,x16944,x16945,x16946,x16941),f510(x16943,x16944,x16945,x16946,x16942))
% 81.29/80.94 [1695]~E(x16951,x16952)+E(f217(x16951,x16953,x16954,x16955),f217(x16952,x16953,x16954,x16955))
% 81.29/80.94 [1696]~E(x16961,x16962)+E(f217(x16963,x16961,x16964,x16965),f217(x16963,x16962,x16964,x16965))
% 81.29/80.94 [1697]~E(x16971,x16972)+E(f217(x16973,x16974,x16971,x16975),f217(x16973,x16974,x16972,x16975))
% 81.29/80.94 [1698]~E(x16981,x16982)+E(f217(x16983,x16984,x16985,x16981),f217(x16983,x16984,x16985,x16982))
% 81.29/80.94 [1699]~E(x16991,x16992)+E(f139(x16991,x16993,x16994),f139(x16992,x16993,x16994))
% 81.29/80.94 [1700]~E(x17001,x17002)+E(f139(x17003,x17001,x17004),f139(x17003,x17002,x17004))
% 81.29/80.94 [1701]~E(x17011,x17012)+E(f139(x17013,x17014,x17011),f139(x17013,x17014,x17012))
% 81.29/80.94 [1702]~E(x17021,x17022)+E(f443(x17021,x17023,x17024,x17025),f443(x17022,x17023,x17024,x17025))
% 81.29/80.94 [1703]~E(x17031,x17032)+E(f443(x17033,x17031,x17034,x17035),f443(x17033,x17032,x17034,x17035))
% 81.29/80.94 [1704]~E(x17041,x17042)+E(f443(x17043,x17044,x17041,x17045),f443(x17043,x17044,x17042,x17045))
% 81.29/80.94 [1705]~E(x17051,x17052)+E(f443(x17053,x17054,x17055,x17051),f443(x17053,x17054,x17055,x17052))
% 81.29/80.94 [1706]~E(x17061,x17062)+E(f189(x17061,x17063,x17064),f189(x17062,x17063,x17064))
% 81.29/80.94 [1707]~E(x17071,x17072)+E(f189(x17073,x17071,x17074),f189(x17073,x17072,x17074))
% 81.29/80.94 [1708]~E(x17081,x17082)+E(f189(x17083,x17084,x17081),f189(x17083,x17084,x17082))
% 81.29/80.94 [1709]~E(x17091,x17092)+E(f526(x17091,x17093,x17094,x17095,x17096),f526(x17092,x17093,x17094,x17095,x17096))
% 81.29/80.94 [1710]~E(x17101,x17102)+E(f526(x17103,x17101,x17104,x17105,x17106),f526(x17103,x17102,x17104,x17105,x17106))
% 81.29/80.94 [1711]~E(x17111,x17112)+E(f526(x17113,x17114,x17111,x17115,x17116),f526(x17113,x17114,x17112,x17115,x17116))
% 81.29/80.94 [1712]~E(x17121,x17122)+E(f526(x17123,x17124,x17125,x17121,x17126),f526(x17123,x17124,x17125,x17122,x17126))
% 81.29/80.94 [1713]~E(x17131,x17132)+E(f526(x17133,x17134,x17135,x17136,x17131),f526(x17133,x17134,x17135,x17136,x17132))
% 81.29/80.94 [1714]~E(x17141,x17142)+E(f347(x17141),f347(x17142))
% 81.29/80.94 [1715]~E(x17151,x17152)+E(f684(x17151,x17153,x17154),f684(x17152,x17153,x17154))
% 81.29/80.94 [1716]~E(x17161,x17162)+E(f684(x17163,x17161,x17164),f684(x17163,x17162,x17164))
% 81.29/80.94 [1717]~E(x17171,x17172)+E(f684(x17173,x17174,x17171),f684(x17173,x17174,x17172))
% 81.29/80.94 [1718]~E(x17181,x17182)+E(f617(x17181,x17183,x17184,x17185),f617(x17182,x17183,x17184,x17185))
% 81.29/80.94 [1719]~E(x17191,x17192)+E(f617(x17193,x17191,x17194,x17195),f617(x17193,x17192,x17194,x17195))
% 81.29/80.94 [1720]~E(x17201,x17202)+E(f617(x17203,x17204,x17201,x17205),f617(x17203,x17204,x17202,x17205))
% 81.29/80.94 [1721]~E(x17211,x17212)+E(f617(x17213,x17214,x17215,x17211),f617(x17213,x17214,x17215,x17212))
% 81.29/80.94 [1722]~E(x17221,x17222)+E(f398(x17221,x17223,x17224,x17225,x17226,x17227,x17228),f398(x17222,x17223,x17224,x17225,x17226,x17227,x17228))
% 81.29/80.94 [1723]~E(x17231,x17232)+E(f398(x17233,x17231,x17234,x17235,x17236,x17237,x17238),f398(x17233,x17232,x17234,x17235,x17236,x17237,x17238))
% 81.29/80.94 [1724]~E(x17241,x17242)+E(f398(x17243,x17244,x17241,x17245,x17246,x17247,x17248),f398(x17243,x17244,x17242,x17245,x17246,x17247,x17248))
% 81.29/80.94 [1725]~E(x17251,x17252)+E(f398(x17253,x17254,x17255,x17251,x17256,x17257,x17258),f398(x17253,x17254,x17255,x17252,x17256,x17257,x17258))
% 81.29/80.94 [1726]~E(x17261,x17262)+E(f398(x17263,x17264,x17265,x17266,x17261,x17267,x17268),f398(x17263,x17264,x17265,x17266,x17262,x17267,x17268))
% 81.29/80.94 [1727]~E(x17271,x17272)+E(f398(x17273,x17274,x17275,x17276,x17277,x17271,x17278),f398(x17273,x17274,x17275,x17276,x17277,x17272,x17278))
% 81.29/80.94 [1728]~E(x17281,x17282)+E(f398(x17283,x17284,x17285,x17286,x17287,x17288,x17281),f398(x17283,x17284,x17285,x17286,x17287,x17288,x17282))
% 81.29/80.94 [1729]~E(x17291,x17292)+E(f472(x17291,x17293),f472(x17292,x17293))
% 81.29/80.94 [1730]~E(x17301,x17302)+E(f472(x17303,x17301),f472(x17303,x17302))
% 81.29/80.94 [1731]~E(x17311,x17312)+E(f757(x17311,x17313,x17314),f757(x17312,x17313,x17314))
% 81.29/80.94 [1732]~E(x17321,x17322)+E(f757(x17323,x17321,x17324),f757(x17323,x17322,x17324))
% 81.29/80.94 [1733]~E(x17331,x17332)+E(f757(x17333,x17334,x17331),f757(x17333,x17334,x17332))
% 81.29/80.94 [1734]~E(x17341,x17342)+E(f824(x17341,x17343,x17344),f824(x17342,x17343,x17344))
% 81.29/80.94 [1735]~E(x17351,x17352)+E(f824(x17353,x17351,x17354),f824(x17353,x17352,x17354))
% 81.29/80.94 [1736]~E(x17361,x17362)+E(f824(x17363,x17364,x17361),f824(x17363,x17364,x17362))
% 81.29/80.94 [1737]~E(x17371,x17372)+E(f437(x17371,x17373,x17374,x17375),f437(x17372,x17373,x17374,x17375))
% 81.29/80.94 [1738]~E(x17381,x17382)+E(f437(x17383,x17381,x17384,x17385),f437(x17383,x17382,x17384,x17385))
% 81.29/80.94 [1739]~E(x17391,x17392)+E(f437(x17393,x17394,x17391,x17395),f437(x17393,x17394,x17392,x17395))
% 81.29/80.94 [1740]~E(x17401,x17402)+E(f437(x17403,x17404,x17405,x17401),f437(x17403,x17404,x17405,x17402))
% 81.29/80.94 [1741]~E(x17411,x17412)+E(f537(x17411,x17413,x17414,x17415),f537(x17412,x17413,x17414,x17415))
% 81.29/80.94 [1742]~E(x17421,x17422)+E(f537(x17423,x17421,x17424,x17425),f537(x17423,x17422,x17424,x17425))
% 81.29/80.94 [1743]~E(x17431,x17432)+E(f537(x17433,x17434,x17431,x17435),f537(x17433,x17434,x17432,x17435))
% 81.29/80.94 [1744]~E(x17441,x17442)+E(f537(x17443,x17444,x17445,x17441),f537(x17443,x17444,x17445,x17442))
% 81.29/80.94 [1745]~E(x17451,x17452)+E(f436(x17451,x17453,x17454,x17455),f436(x17452,x17453,x17454,x17455))
% 81.29/80.94 [1746]~E(x17461,x17462)+E(f436(x17463,x17461,x17464,x17465),f436(x17463,x17462,x17464,x17465))
% 81.29/80.94 [1747]~E(x17471,x17472)+E(f436(x17473,x17474,x17471,x17475),f436(x17473,x17474,x17472,x17475))
% 81.29/80.94 [1748]~E(x17481,x17482)+E(f436(x17483,x17484,x17485,x17481),f436(x17483,x17484,x17485,x17482))
% 81.29/80.94 [1749]~E(x17491,x17492)+E(f367(x17491,x17493,x17494),f367(x17492,x17493,x17494))
% 81.29/80.94 [1750]~E(x17501,x17502)+E(f367(x17503,x17501,x17504),f367(x17503,x17502,x17504))
% 81.29/80.94 [1751]~E(x17511,x17512)+E(f367(x17513,x17514,x17511),f367(x17513,x17514,x17512))
% 81.29/80.94 [1752]~E(x17521,x17522)+E(f497(x17521,x17523,x17524),f497(x17522,x17523,x17524))
% 81.29/80.94 [1753]~E(x17531,x17532)+E(f497(x17533,x17531,x17534),f497(x17533,x17532,x17534))
% 81.29/80.94 [1754]~E(x17541,x17542)+E(f497(x17543,x17544,x17541),f497(x17543,x17544,x17542))
% 81.29/80.94 [1755]~E(x17551,x17552)+E(f773(x17551,x17553,x17554),f773(x17552,x17553,x17554))
% 81.29/80.94 [1756]~E(x17561,x17562)+E(f773(x17563,x17561,x17564),f773(x17563,x17562,x17564))
% 81.29/80.94 [1757]~E(x17571,x17572)+E(f773(x17573,x17574,x17571),f773(x17573,x17574,x17572))
% 81.29/80.94 [1758]~E(x17581,x17582)+E(f659(x17581,x17583),f659(x17582,x17583))
% 81.29/80.94 [1759]~E(x17591,x17592)+E(f659(x17593,x17591),f659(x17593,x17592))
% 81.29/80.94 [1760]~E(x17601,x17602)+E(f503(x17601,x17603,x17604,x17605,x17606),f503(x17602,x17603,x17604,x17605,x17606))
% 81.29/80.94 [1761]~E(x17611,x17612)+E(f503(x17613,x17611,x17614,x17615,x17616),f503(x17613,x17612,x17614,x17615,x17616))
% 81.29/80.94 [1762]~E(x17621,x17622)+E(f503(x17623,x17624,x17621,x17625,x17626),f503(x17623,x17624,x17622,x17625,x17626))
% 81.29/80.94 [1763]~E(x17631,x17632)+E(f503(x17633,x17634,x17635,x17631,x17636),f503(x17633,x17634,x17635,x17632,x17636))
% 81.29/80.94 [1764]~E(x17641,x17642)+E(f503(x17643,x17644,x17645,x17646,x17641),f503(x17643,x17644,x17645,x17646,x17642))
% 81.29/80.94 [1765]~E(x17651,x17652)+E(f214(x17651,x17653,x17654,x17655),f214(x17652,x17653,x17654,x17655))
% 81.29/80.94 [1766]~E(x17661,x17662)+E(f214(x17663,x17661,x17664,x17665),f214(x17663,x17662,x17664,x17665))
% 81.29/80.94 [1767]~E(x17671,x17672)+E(f214(x17673,x17674,x17671,x17675),f214(x17673,x17674,x17672,x17675))
% 81.29/80.94 [1768]~E(x17681,x17682)+E(f214(x17683,x17684,x17685,x17681),f214(x17683,x17684,x17685,x17682))
% 81.29/80.94 [1769]~E(x17691,x17692)+E(f448(x17691,x17693),f448(x17692,x17693))
% 81.29/80.94 [1770]~E(x17701,x17702)+E(f448(x17703,x17701),f448(x17703,x17702))
% 81.29/80.94 [1771]~E(x17711,x17712)+E(f423(x17711,x17713,x17714,x17715),f423(x17712,x17713,x17714,x17715))
% 81.29/80.94 [1772]~E(x17721,x17722)+E(f423(x17723,x17721,x17724,x17725),f423(x17723,x17722,x17724,x17725))
% 81.29/80.94 [1773]~E(x17731,x17732)+E(f423(x17733,x17734,x17731,x17735),f423(x17733,x17734,x17732,x17735))
% 81.29/80.94 [1774]~E(x17741,x17742)+E(f423(x17743,x17744,x17745,x17741),f423(x17743,x17744,x17745,x17742))
% 81.29/80.94 [1775]~E(x17751,x17752)+E(f401(x17751,x17753),f401(x17752,x17753))
% 81.29/80.94 [1776]~E(x17761,x17762)+E(f401(x17763,x17761),f401(x17763,x17762))
% 81.29/80.94 [1777]~E(x17771,x17772)+E(f649(x17771,x17773,x17774),f649(x17772,x17773,x17774))
% 81.29/80.94 [1778]~E(x17781,x17782)+E(f649(x17783,x17781,x17784),f649(x17783,x17782,x17784))
% 81.29/80.94 [1779]~E(x17791,x17792)+E(f649(x17793,x17794,x17791),f649(x17793,x17794,x17792))
% 81.29/80.94 [1780]~E(x17801,x17802)+E(f821(x17801,x17803,x17804),f821(x17802,x17803,x17804))
% 81.29/80.94 [1781]~E(x17811,x17812)+E(f821(x17813,x17811,x17814),f821(x17813,x17812,x17814))
% 81.29/80.94 [1782]~E(x17821,x17822)+E(f821(x17823,x17824,x17821),f821(x17823,x17824,x17822))
% 81.29/80.94 [1783]~E(x17831,x17832)+E(f600(x17831),f600(x17832))
% 81.29/80.94 [1784]~E(x17841,x17842)+E(f506(x17841,x17843,x17844,x17845),f506(x17842,x17843,x17844,x17845))
% 81.29/80.94 [1785]~E(x17851,x17852)+E(f506(x17853,x17851,x17854,x17855),f506(x17853,x17852,x17854,x17855))
% 81.29/80.94 [1786]~E(x17861,x17862)+E(f506(x17863,x17864,x17861,x17865),f506(x17863,x17864,x17862,x17865))
% 81.29/80.94 [1787]~E(x17871,x17872)+E(f506(x17873,x17874,x17875,x17871),f506(x17873,x17874,x17875,x17872))
% 81.29/80.94 [1788]~E(x17881,x17882)+E(f738(x17881,x17883,x17884),f738(x17882,x17883,x17884))
% 81.29/80.94 [1789]~E(x17891,x17892)+E(f738(x17893,x17891,x17894),f738(x17893,x17892,x17894))
% 81.29/80.94 [1790]~E(x17901,x17902)+E(f738(x17903,x17904,x17901),f738(x17903,x17904,x17902))
% 81.29/80.94 [1791]~E(x17911,x17912)+E(f521(x17911,x17913,x17914,x17915,x17916,x17917,x17918),f521(x17912,x17913,x17914,x17915,x17916,x17917,x17918))
% 81.29/80.94 [1792]~E(x17921,x17922)+E(f521(x17923,x17921,x17924,x17925,x17926,x17927,x17928),f521(x17923,x17922,x17924,x17925,x17926,x17927,x17928))
% 81.29/80.94 [1793]~E(x17931,x17932)+E(f521(x17933,x17934,x17931,x17935,x17936,x17937,x17938),f521(x17933,x17934,x17932,x17935,x17936,x17937,x17938))
% 81.29/80.94 [1794]~E(x17941,x17942)+E(f521(x17943,x17944,x17945,x17941,x17946,x17947,x17948),f521(x17943,x17944,x17945,x17942,x17946,x17947,x17948))
% 81.29/80.94 [1795]~E(x17951,x17952)+E(f521(x17953,x17954,x17955,x17956,x17951,x17957,x17958),f521(x17953,x17954,x17955,x17956,x17952,x17957,x17958))
% 81.29/80.94 [1796]~E(x17961,x17962)+E(f521(x17963,x17964,x17965,x17966,x17967,x17961,x17968),f521(x17963,x17964,x17965,x17966,x17967,x17962,x17968))
% 81.29/80.94 [1797]~E(x17971,x17972)+E(f521(x17973,x17974,x17975,x17976,x17977,x17978,x17971),f521(x17973,x17974,x17975,x17976,x17977,x17978,x17972))
% 81.29/80.94 [1798]~E(x17981,x17982)+E(f575(x17981,x17983,x17984,x17985,x17986),f575(x17982,x17983,x17984,x17985,x17986))
% 81.29/80.94 [1799]~E(x17991,x17992)+E(f575(x17993,x17991,x17994,x17995,x17996),f575(x17993,x17992,x17994,x17995,x17996))
% 81.29/80.94 [1800]~E(x18001,x18002)+E(f575(x18003,x18004,x18001,x18005,x18006),f575(x18003,x18004,x18002,x18005,x18006))
% 81.29/80.94 [1801]~E(x18011,x18012)+E(f575(x18013,x18014,x18015,x18011,x18016),f575(x18013,x18014,x18015,x18012,x18016))
% 81.29/80.94 [1802]~E(x18021,x18022)+E(f575(x18023,x18024,x18025,x18026,x18021),f575(x18023,x18024,x18025,x18026,x18022))
% 81.29/80.94 [1803]~E(x18031,x18032)+E(f651(x18031,x18033,x18034),f651(x18032,x18033,x18034))
% 81.29/80.94 [1804]~E(x18041,x18042)+E(f651(x18043,x18041,x18044),f651(x18043,x18042,x18044))
% 81.29/80.94 [1805]~E(x18051,x18052)+E(f651(x18053,x18054,x18051),f651(x18053,x18054,x18052))
% 81.29/80.94 [1806]~E(x18061,x18062)+E(f99(x18061,x18063,x18064),f99(x18062,x18063,x18064))
% 81.29/80.94 [1807]~E(x18071,x18072)+E(f99(x18073,x18071,x18074),f99(x18073,x18072,x18074))
% 81.29/80.94 [1808]~E(x18081,x18082)+E(f99(x18083,x18084,x18081),f99(x18083,x18084,x18082))
% 81.29/80.94 [1809]~E(x18091,x18092)+E(f584(x18091,x18093),f584(x18092,x18093))
% 81.29/80.94 [1810]~E(x18101,x18102)+E(f584(x18103,x18101),f584(x18103,x18102))
% 81.29/80.94 [1811]~E(x18111,x18112)+E(f543(x18111,x18113,x18114,x18115,x18116,x18117,x18118),f543(x18112,x18113,x18114,x18115,x18116,x18117,x18118))
% 81.29/80.94 [1812]~E(x18121,x18122)+E(f543(x18123,x18121,x18124,x18125,x18126,x18127,x18128),f543(x18123,x18122,x18124,x18125,x18126,x18127,x18128))
% 81.29/80.94 [1813]~E(x18131,x18132)+E(f543(x18133,x18134,x18131,x18135,x18136,x18137,x18138),f543(x18133,x18134,x18132,x18135,x18136,x18137,x18138))
% 81.29/80.94 [1814]~E(x18141,x18142)+E(f543(x18143,x18144,x18145,x18141,x18146,x18147,x18148),f543(x18143,x18144,x18145,x18142,x18146,x18147,x18148))
% 81.29/80.94 [1815]~E(x18151,x18152)+E(f543(x18153,x18154,x18155,x18156,x18151,x18157,x18158),f543(x18153,x18154,x18155,x18156,x18152,x18157,x18158))
% 81.29/80.94 [1816]~E(x18161,x18162)+E(f543(x18163,x18164,x18165,x18166,x18167,x18161,x18168),f543(x18163,x18164,x18165,x18166,x18167,x18162,x18168))
% 81.29/80.94 [1817]~E(x18171,x18172)+E(f543(x18173,x18174,x18175,x18176,x18177,x18178,x18171),f543(x18173,x18174,x18175,x18176,x18177,x18178,x18172))
% 81.29/80.94 [1818]~E(x18181,x18182)+E(f832(x18181,x18183),f832(x18182,x18183))
% 81.29/80.94 [1819]~E(x18191,x18192)+E(f832(x18193,x18191),f832(x18193,x18192))
% 81.29/80.94 [1820]~E(x18201,x18202)+E(f764(x18201,x18203,x18204),f764(x18202,x18203,x18204))
% 81.29/80.94 [1821]~E(x18211,x18212)+E(f764(x18213,x18211,x18214),f764(x18213,x18212,x18214))
% 81.29/80.94 [1822]~E(x18221,x18222)+E(f764(x18223,x18224,x18221),f764(x18223,x18224,x18222))
% 81.29/80.94 [1823]~E(x18231,x18232)+E(f624(x18231,x18233,x18234,x18235,x18236,x18237,x18238,x18239),f624(x18232,x18233,x18234,x18235,x18236,x18237,x18238,x18239))
% 81.29/80.94 [1824]~E(x18241,x18242)+E(f624(x18243,x18241,x18244,x18245,x18246,x18247,x18248,x18249),f624(x18243,x18242,x18244,x18245,x18246,x18247,x18248,x18249))
% 81.29/80.94 [1825]~E(x18251,x18252)+E(f624(x18253,x18254,x18251,x18255,x18256,x18257,x18258,x18259),f624(x18253,x18254,x18252,x18255,x18256,x18257,x18258,x18259))
% 81.29/80.94 [1826]~E(x18261,x18262)+E(f624(x18263,x18264,x18265,x18261,x18266,x18267,x18268,x18269),f624(x18263,x18264,x18265,x18262,x18266,x18267,x18268,x18269))
% 81.29/80.94 [1827]~E(x18271,x18272)+E(f624(x18273,x18274,x18275,x18276,x18271,x18277,x18278,x18279),f624(x18273,x18274,x18275,x18276,x18272,x18277,x18278,x18279))
% 81.29/80.94 [1828]~E(x18281,x18282)+E(f624(x18283,x18284,x18285,x18286,x18287,x18281,x18288,x18289),f624(x18283,x18284,x18285,x18286,x18287,x18282,x18288,x18289))
% 81.29/80.94 [1829]~E(x18291,x18292)+E(f624(x18293,x18294,x18295,x18296,x18297,x18298,x18291,x18299),f624(x18293,x18294,x18295,x18296,x18297,x18298,x18292,x18299))
% 81.29/80.94 [1830]~E(x18301,x18302)+E(f624(x18303,x18304,x18305,x18306,x18307,x18308,x18309,x18301),f624(x18303,x18304,x18305,x18306,x18307,x18308,x18309,x18302))
% 81.29/80.94 [1831]~E(x18311,x18312)+E(f576(x18311,x18313,x18314,x18315,x18316,x18317,x18318,x18319),f576(x18312,x18313,x18314,x18315,x18316,x18317,x18318,x18319))
% 81.29/80.94 [1832]~E(x18321,x18322)+E(f576(x18323,x18321,x18324,x18325,x18326,x18327,x18328,x18329),f576(x18323,x18322,x18324,x18325,x18326,x18327,x18328,x18329))
% 81.29/80.94 [1833]~E(x18331,x18332)+E(f576(x18333,x18334,x18331,x18335,x18336,x18337,x18338,x18339),f576(x18333,x18334,x18332,x18335,x18336,x18337,x18338,x18339))
% 81.29/80.94 [1834]~E(x18341,x18342)+E(f576(x18343,x18344,x18345,x18341,x18346,x18347,x18348,x18349),f576(x18343,x18344,x18345,x18342,x18346,x18347,x18348,x18349))
% 81.29/80.94 [1835]~E(x18351,x18352)+E(f576(x18353,x18354,x18355,x18356,x18351,x18357,x18358,x18359),f576(x18353,x18354,x18355,x18356,x18352,x18357,x18358,x18359))
% 81.29/80.94 [1836]~E(x18361,x18362)+E(f576(x18363,x18364,x18365,x18366,x18367,x18361,x18368,x18369),f576(x18363,x18364,x18365,x18366,x18367,x18362,x18368,x18369))
% 81.29/80.94 [1837]~E(x18371,x18372)+E(f576(x18373,x18374,x18375,x18376,x18377,x18378,x18371,x18379),f576(x18373,x18374,x18375,x18376,x18377,x18378,x18372,x18379))
% 81.29/80.94 [1838]~E(x18381,x18382)+E(f576(x18383,x18384,x18385,x18386,x18387,x18388,x18389,x18381),f576(x18383,x18384,x18385,x18386,x18387,x18388,x18389,x18382))
% 81.29/80.94 [1839]~E(x18391,x18392)+E(f686(x18391,x18393,x18394),f686(x18392,x18393,x18394))
% 81.29/80.94 [1840]~E(x18401,x18402)+E(f686(x18403,x18401,x18404),f686(x18403,x18402,x18404))
% 81.29/80.94 [1841]~E(x18411,x18412)+E(f686(x18413,x18414,x18411),f686(x18413,x18414,x18412))
% 81.29/80.94 [1842]~E(x18421,x18422)+E(f785(x18421,x18423,x18424,x18425,x18426,x18427),f785(x18422,x18423,x18424,x18425,x18426,x18427))
% 81.29/80.94 [1843]~E(x18431,x18432)+E(f785(x18433,x18431,x18434,x18435,x18436,x18437),f785(x18433,x18432,x18434,x18435,x18436,x18437))
% 81.29/80.94 [1844]~E(x18441,x18442)+E(f785(x18443,x18444,x18441,x18445,x18446,x18447),f785(x18443,x18444,x18442,x18445,x18446,x18447))
% 81.29/80.94 [1845]~E(x18451,x18452)+E(f785(x18453,x18454,x18455,x18451,x18456,x18457),f785(x18453,x18454,x18455,x18452,x18456,x18457))
% 81.29/80.94 [1846]~E(x18461,x18462)+E(f785(x18463,x18464,x18465,x18466,x18461,x18467),f785(x18463,x18464,x18465,x18466,x18462,x18467))
% 81.29/80.94 [1847]~E(x18471,x18472)+E(f785(x18473,x18474,x18475,x18476,x18477,x18471),f785(x18473,x18474,x18475,x18476,x18477,x18472))
% 81.29/80.94 [1848]~E(x18481,x18482)+E(f530(x18481),f530(x18482))
% 81.29/80.94 [1849]~E(x18491,x18492)+E(f350(x18491,x18493,x18494),f350(x18492,x18493,x18494))
% 81.29/80.94 [1850]~E(x18501,x18502)+E(f350(x18503,x18501,x18504),f350(x18503,x18502,x18504))
% 81.29/80.94 [1851]~E(x18511,x18512)+E(f350(x18513,x18514,x18511),f350(x18513,x18514,x18512))
% 81.29/80.94 [1852]~E(x18521,x18522)+E(f865(x18521,x18523),f865(x18522,x18523))
% 81.29/80.94 [1853]~E(x18531,x18532)+E(f865(x18533,x18531),f865(x18533,x18532))
% 81.29/80.94 [1854]~E(x18541,x18542)+E(f625(x18541,x18543,x18544),f625(x18542,x18543,x18544))
% 81.29/80.94 [1855]~E(x18551,x18552)+E(f625(x18553,x18551,x18554),f625(x18553,x18552,x18554))
% 81.29/80.94 [1856]~E(x18561,x18562)+E(f625(x18563,x18564,x18561),f625(x18563,x18564,x18562))
% 81.29/80.94 [1857]~E(x18571,x18572)+E(f372(x18571,x18573,x18574),f372(x18572,x18573,x18574))
% 81.29/80.94 [1858]~E(x18581,x18582)+E(f372(x18583,x18581,x18584),f372(x18583,x18582,x18584))
% 81.29/80.94 [1859]~E(x18591,x18592)+E(f372(x18593,x18594,x18591),f372(x18593,x18594,x18592))
% 81.29/80.94 [1860]~E(x18601,x18602)+E(f850(x18601),f850(x18602))
% 81.29/80.94 [1861]~E(x18611,x18612)+E(f562(x18611,x18613,x18614),f562(x18612,x18613,x18614))
% 81.29/80.94 [1862]~E(x18621,x18622)+E(f562(x18623,x18621,x18624),f562(x18623,x18622,x18624))
% 81.29/80.94 [1863]~E(x18631,x18632)+E(f562(x18633,x18634,x18631),f562(x18633,x18634,x18632))
% 81.29/80.94 [1864]~E(x18641,x18642)+E(f585(x18641,x18643,x18644,x18645),f585(x18642,x18643,x18644,x18645))
% 81.29/80.94 [1865]~E(x18651,x18652)+E(f585(x18653,x18651,x18654,x18655),f585(x18653,x18652,x18654,x18655))
% 81.29/80.94 [1866]~E(x18661,x18662)+E(f585(x18663,x18664,x18661,x18665),f585(x18663,x18664,x18662,x18665))
% 81.29/80.94 [1867]~E(x18671,x18672)+E(f585(x18673,x18674,x18675,x18671),f585(x18673,x18674,x18675,x18672))
% 81.29/80.94 [1868]~E(x18681,x18682)+E(f707(x18681,x18683,x18684,x18685),f707(x18682,x18683,x18684,x18685))
% 81.29/80.94 [1869]~E(x18691,x18692)+E(f707(x18693,x18691,x18694,x18695),f707(x18693,x18692,x18694,x18695))
% 81.29/80.94 [1870]~E(x18701,x18702)+E(f707(x18703,x18704,x18701,x18705),f707(x18703,x18704,x18702,x18705))
% 81.29/80.94 [1871]~E(x18711,x18712)+E(f707(x18713,x18714,x18715,x18711),f707(x18713,x18714,x18715,x18712))
% 81.29/80.94 [1872]~E(x18721,x18722)+E(f774(x18721,x18723,x18724,x18725,x18726),f774(x18722,x18723,x18724,x18725,x18726))
% 81.29/80.94 [1873]~E(x18731,x18732)+E(f774(x18733,x18731,x18734,x18735,x18736),f774(x18733,x18732,x18734,x18735,x18736))
% 81.29/80.94 [1874]~E(x18741,x18742)+E(f774(x18743,x18744,x18741,x18745,x18746),f774(x18743,x18744,x18742,x18745,x18746))
% 81.29/80.94 [1875]~E(x18751,x18752)+E(f774(x18753,x18754,x18755,x18751,x18756),f774(x18753,x18754,x18755,x18752,x18756))
% 81.29/80.94 [1876]~E(x18761,x18762)+E(f774(x18763,x18764,x18765,x18766,x18761),f774(x18763,x18764,x18765,x18766,x18762))
% 81.29/80.94 [1877]~E(x18771,x18772)+E(f424(x18771,x18773,x18774,x18775),f424(x18772,x18773,x18774,x18775))
% 81.29/80.94 [1878]~E(x18781,x18782)+E(f424(x18783,x18781,x18784,x18785),f424(x18783,x18782,x18784,x18785))
% 81.29/80.94 [1879]~E(x18791,x18792)+E(f424(x18793,x18794,x18791,x18795),f424(x18793,x18794,x18792,x18795))
% 81.29/80.94 [1880]~E(x18801,x18802)+E(f424(x18803,x18804,x18805,x18801),f424(x18803,x18804,x18805,x18802))
% 81.29/80.94 [1881]~E(x18811,x18812)+E(f693(x18811,x18813,x18814,x18815),f693(x18812,x18813,x18814,x18815))
% 81.29/80.94 [1882]~E(x18821,x18822)+E(f693(x18823,x18821,x18824,x18825),f693(x18823,x18822,x18824,x18825))
% 81.29/80.94 [1883]~E(x18831,x18832)+E(f693(x18833,x18834,x18831,x18835),f693(x18833,x18834,x18832,x18835))
% 81.29/80.94 [1884]~E(x18841,x18842)+E(f693(x18843,x18844,x18845,x18841),f693(x18843,x18844,x18845,x18842))
% 81.29/80.94 [1885]~E(x18851,x18852)+E(f689(x18851,x18853,x18854,x18855),f689(x18852,x18853,x18854,x18855))
% 81.29/80.94 [1886]~E(x18861,x18862)+E(f689(x18863,x18861,x18864,x18865),f689(x18863,x18862,x18864,x18865))
% 81.29/80.94 [1887]~E(x18871,x18872)+E(f689(x18873,x18874,x18871,x18875),f689(x18873,x18874,x18872,x18875))
% 81.29/80.94 [1888]~E(x18881,x18882)+E(f689(x18883,x18884,x18885,x18881),f689(x18883,x18884,x18885,x18882))
% 81.29/80.94 [1889]~E(x18891,x18892)+E(f453(x18891,x18893,x18894,x18895),f453(x18892,x18893,x18894,x18895))
% 81.29/80.94 [1890]~E(x18901,x18902)+E(f453(x18903,x18901,x18904,x18905),f453(x18903,x18902,x18904,x18905))
% 81.29/80.94 [1891]~E(x18911,x18912)+E(f453(x18913,x18914,x18911,x18915),f453(x18913,x18914,x18912,x18915))
% 81.29/80.94 [1892]~E(x18921,x18922)+E(f453(x18923,x18924,x18925,x18921),f453(x18923,x18924,x18925,x18922))
% 81.29/80.94 [1893]~E(x18931,x18932)+E(f364(x18931,x18933),f364(x18932,x18933))
% 81.29/80.94 [1894]~E(x18941,x18942)+E(f364(x18943,x18941),f364(x18943,x18942))
% 81.29/80.94 [1895]~E(x18951,x18952)+E(f545(x18951,x18953,x18954,x18955,x18956,x18957,x18958),f545(x18952,x18953,x18954,x18955,x18956,x18957,x18958))
% 81.29/80.94 [1896]~E(x18961,x18962)+E(f545(x18963,x18961,x18964,x18965,x18966,x18967,x18968),f545(x18963,x18962,x18964,x18965,x18966,x18967,x18968))
% 81.29/80.94 [1897]~E(x18971,x18972)+E(f545(x18973,x18974,x18971,x18975,x18976,x18977,x18978),f545(x18973,x18974,x18972,x18975,x18976,x18977,x18978))
% 81.29/80.94 [1898]~E(x18981,x18982)+E(f545(x18983,x18984,x18985,x18981,x18986,x18987,x18988),f545(x18983,x18984,x18985,x18982,x18986,x18987,x18988))
% 81.29/80.94 [1899]~E(x18991,x18992)+E(f545(x18993,x18994,x18995,x18996,x18991,x18997,x18998),f545(x18993,x18994,x18995,x18996,x18992,x18997,x18998))
% 81.29/80.94 [1900]~E(x19001,x19002)+E(f545(x19003,x19004,x19005,x19006,x19007,x19001,x19008),f545(x19003,x19004,x19005,x19006,x19007,x19002,x19008))
% 81.29/80.94 [1901]~E(x19011,x19012)+E(f545(x19013,x19014,x19015,x19016,x19017,x19018,x19011),f545(x19013,x19014,x19015,x19016,x19017,x19018,x19012))
% 81.29/80.94 [1902]~E(x19021,x19022)+E(f721(x19021,x19023,x19024,x19025),f721(x19022,x19023,x19024,x19025))
% 81.29/80.94 [1903]~E(x19031,x19032)+E(f721(x19033,x19031,x19034,x19035),f721(x19033,x19032,x19034,x19035))
% 81.29/80.94 [1904]~E(x19041,x19042)+E(f721(x19043,x19044,x19041,x19045),f721(x19043,x19044,x19042,x19045))
% 81.29/80.94 [1905]~E(x19051,x19052)+E(f721(x19053,x19054,x19055,x19051),f721(x19053,x19054,x19055,x19052))
% 81.29/80.94 [1906]~E(x19061,x19062)+E(f643(x19061,x19063,x19064),f643(x19062,x19063,x19064))
% 81.29/80.94 [1907]~E(x19071,x19072)+E(f643(x19073,x19071,x19074),f643(x19073,x19072,x19074))
% 81.29/80.94 [1908]~E(x19081,x19082)+E(f643(x19083,x19084,x19081),f643(x19083,x19084,x19082))
% 81.29/80.94 [1909]~E(x19091,x19092)+E(f343(x19091,x19093,x19094,x19095),f343(x19092,x19093,x19094,x19095))
% 81.29/80.94 [1910]~E(x19101,x19102)+E(f343(x19103,x19101,x19104,x19105),f343(x19103,x19102,x19104,x19105))
% 81.29/80.94 [1911]~E(x19111,x19112)+E(f343(x19113,x19114,x19111,x19115),f343(x19113,x19114,x19112,x19115))
% 81.29/80.94 [1912]~E(x19121,x19122)+E(f343(x19123,x19124,x19125,x19121),f343(x19123,x19124,x19125,x19122))
% 81.29/80.94 [1913]~E(x19131,x19132)+E(f239(x19131,x19133,x19134,x19135,x19136),f239(x19132,x19133,x19134,x19135,x19136))
% 81.29/80.94 [1914]~E(x19141,x19142)+E(f239(x19143,x19141,x19144,x19145,x19146),f239(x19143,x19142,x19144,x19145,x19146))
% 81.29/80.94 [1915]~E(x19151,x19152)+E(f239(x19153,x19154,x19151,x19155,x19156),f239(x19153,x19154,x19152,x19155,x19156))
% 81.29/80.94 [1916]~E(x19161,x19162)+E(f239(x19163,x19164,x19165,x19161,x19166),f239(x19163,x19164,x19165,x19162,x19166))
% 81.29/80.94 [1917]~E(x19171,x19172)+E(f239(x19173,x19174,x19175,x19176,x19171),f239(x19173,x19174,x19175,x19176,x19172))
% 81.29/80.94 [1918]~E(x19181,x19182)+E(f403(x19181,x19183,x19184),f403(x19182,x19183,x19184))
% 81.29/80.94 [1919]~E(x19191,x19192)+E(f403(x19193,x19191,x19194),f403(x19193,x19192,x19194))
% 81.29/80.94 [1920]~E(x19201,x19202)+E(f403(x19203,x19204,x19201),f403(x19203,x19204,x19202))
% 81.29/80.94 [1921]~E(x19211,x19212)+E(f582(x19211,x19213),f582(x19212,x19213))
% 81.29/80.94 [1922]~E(x19221,x19222)+E(f582(x19223,x19221),f582(x19223,x19222))
% 81.29/80.94 [1923]~E(x19231,x19232)+E(f682(x19231,x19233),f682(x19232,x19233))
% 81.29/80.94 [1924]~E(x19241,x19242)+E(f682(x19243,x19241),f682(x19243,x19242))
% 81.29/80.94 [1925]~E(x19251,x19252)+E(f482(x19251,x19253,x19254),f482(x19252,x19253,x19254))
% 81.29/80.94 [1926]~E(x19261,x19262)+E(f482(x19263,x19261,x19264),f482(x19263,x19262,x19264))
% 81.29/80.94 [1927]~E(x19271,x19272)+E(f482(x19273,x19274,x19271),f482(x19273,x19274,x19272))
% 81.29/80.94 [1928]~E(x19281,x19282)+E(f312(x19281,x19283,x19284),f312(x19282,x19283,x19284))
% 81.29/80.94 [1929]~E(x19291,x19292)+E(f312(x19293,x19291,x19294),f312(x19293,x19292,x19294))
% 81.29/80.94 [1930]~E(x19301,x19302)+E(f312(x19303,x19304,x19301),f312(x19303,x19304,x19302))
% 81.29/80.94 [1931]~E(x19311,x19312)+E(f578(x19311,x19313,x19314),f578(x19312,x19313,x19314))
% 81.29/80.94 [1932]~E(x19321,x19322)+E(f578(x19323,x19321,x19324),f578(x19323,x19322,x19324))
% 81.29/80.94 [1933]~E(x19331,x19332)+E(f578(x19333,x19334,x19331),f578(x19333,x19334,x19332))
% 81.29/80.94 [1934]~E(x19341,x19342)+E(f535(x19341,x19343,x19344),f535(x19342,x19343,x19344))
% 81.29/80.94 [1935]~E(x19351,x19352)+E(f535(x19353,x19351,x19354),f535(x19353,x19352,x19354))
% 81.29/80.94 [1936]~E(x19361,x19362)+E(f535(x19363,x19364,x19361),f535(x19363,x19364,x19362))
% 81.29/80.94 [1937]~E(x19371,x19372)+E(f514(x19371,x19373,x19374,x19375,x19376),f514(x19372,x19373,x19374,x19375,x19376))
% 81.29/80.94 [1938]~E(x19381,x19382)+E(f514(x19383,x19381,x19384,x19385,x19386),f514(x19383,x19382,x19384,x19385,x19386))
% 81.29/80.94 [1939]~E(x19391,x19392)+E(f514(x19393,x19394,x19391,x19395,x19396),f514(x19393,x19394,x19392,x19395,x19396))
% 81.29/80.94 [1940]~E(x19401,x19402)+E(f514(x19403,x19404,x19405,x19401,x19406),f514(x19403,x19404,x19405,x19402,x19406))
% 81.29/80.94 [1941]~E(x19411,x19412)+E(f514(x19413,x19414,x19415,x19416,x19411),f514(x19413,x19414,x19415,x19416,x19412))
% 81.29/80.94 [1942]~E(x19421,x19422)+E(f868(x19421,x19423,x19424,x19425,x19426),f868(x19422,x19423,x19424,x19425,x19426))
% 81.29/80.94 [1943]~E(x19431,x19432)+E(f868(x19433,x19431,x19434,x19435,x19436),f868(x19433,x19432,x19434,x19435,x19436))
% 81.29/80.94 [1944]~E(x19441,x19442)+E(f868(x19443,x19444,x19441,x19445,x19446),f868(x19443,x19444,x19442,x19445,x19446))
% 81.29/80.94 [1945]~E(x19451,x19452)+E(f868(x19453,x19454,x19455,x19451,x19456),f868(x19453,x19454,x19455,x19452,x19456))
% 81.29/80.94 [1946]~E(x19461,x19462)+E(f868(x19463,x19464,x19465,x19466,x19461),f868(x19463,x19464,x19465,x19466,x19462))
% 81.29/80.94 [1947]~E(x19471,x19472)+E(f712(x19471),f712(x19472))
% 81.29/80.94 [1948]~E(x19481,x19482)+E(f466(x19481,x19483,x19484),f466(x19482,x19483,x19484))
% 81.29/80.94 [1949]~E(x19491,x19492)+E(f466(x19493,x19491,x19494),f466(x19493,x19492,x19494))
% 81.29/80.94 [1950]~E(x19501,x19502)+E(f466(x19503,x19504,x19501),f466(x19503,x19504,x19502))
% 81.29/80.94 [1951]~E(x19511,x19512)+E(f534(x19511),f534(x19512))
% 81.29/80.94 [1952]~E(x19521,x19522)+E(f370(x19521,x19523),f370(x19522,x19523))
% 81.29/80.94 [1953]~E(x19531,x19532)+E(f370(x19533,x19531),f370(x19533,x19532))
% 81.29/80.94 [1954]~E(x19541,x19542)+E(f619(x19541,x19543,x19544,x19545),f619(x19542,x19543,x19544,x19545))
% 81.29/80.94 [1955]~E(x19551,x19552)+E(f619(x19553,x19551,x19554,x19555),f619(x19553,x19552,x19554,x19555))
% 81.29/80.94 [1956]~E(x19561,x19562)+E(f619(x19563,x19564,x19561,x19565),f619(x19563,x19564,x19562,x19565))
% 81.29/80.94 [1957]~E(x19571,x19572)+E(f619(x19573,x19574,x19575,x19571),f619(x19573,x19574,x19575,x19572))
% 81.29/80.94 [1958]~E(x19581,x19582)+E(f601(x19581,x19583,x19584),f601(x19582,x19583,x19584))
% 81.29/80.94 [1959]~E(x19591,x19592)+E(f601(x19593,x19591,x19594),f601(x19593,x19592,x19594))
% 81.29/80.94 [1960]~E(x19601,x19602)+E(f601(x19603,x19604,x19601),f601(x19603,x19604,x19602))
% 81.29/80.94 [1961]~E(x19611,x19612)+E(f434(x19611,x19613,x19614),f434(x19612,x19613,x19614))
% 81.29/80.94 [1962]~E(x19621,x19622)+E(f434(x19623,x19621,x19624),f434(x19623,x19622,x19624))
% 81.29/80.94 [1963]~E(x19631,x19632)+E(f434(x19633,x19634,x19631),f434(x19633,x19634,x19632))
% 81.29/80.94 [1964]~E(x19641,x19642)+E(f439(x19641,x19643,x19644,x19645),f439(x19642,x19643,x19644,x19645))
% 81.29/80.94 [1965]~E(x19651,x19652)+E(f439(x19653,x19651,x19654,x19655),f439(x19653,x19652,x19654,x19655))
% 81.29/80.94 [1966]~E(x19661,x19662)+E(f439(x19663,x19664,x19661,x19665),f439(x19663,x19664,x19662,x19665))
% 81.29/80.94 [1967]~E(x19671,x19672)+E(f439(x19673,x19674,x19675,x19671),f439(x19673,x19674,x19675,x19672))
% 81.29/80.94 [1968]~E(x19681,x19682)+E(f719(x19681,x19683),f719(x19682,x19683))
% 81.29/80.94 [1969]~E(x19691,x19692)+E(f719(x19693,x19691),f719(x19693,x19692))
% 81.29/80.94 [1970]~E(x19701,x19702)+E(f687(x19701,x19703,x19704,x19705),f687(x19702,x19703,x19704,x19705))
% 81.29/80.94 [1971]~E(x19711,x19712)+E(f687(x19713,x19711,x19714,x19715),f687(x19713,x19712,x19714,x19715))
% 81.29/80.94 [1972]~E(x19721,x19722)+E(f687(x19723,x19724,x19721,x19725),f687(x19723,x19724,x19722,x19725))
% 81.29/80.94 [1973]~E(x19731,x19732)+E(f687(x19733,x19734,x19735,x19731),f687(x19733,x19734,x19735,x19732))
% 81.29/80.94 [1974]~E(x19741,x19742)+E(f408(x19741),f408(x19742))
% 81.29/80.94 [1975]~E(x19751,x19752)+E(f363(x19751,x19753,x19754),f363(x19752,x19753,x19754))
% 81.29/80.94 [1976]~E(x19761,x19762)+E(f363(x19763,x19761,x19764),f363(x19763,x19762,x19764))
% 81.29/80.94 [1977]~E(x19771,x19772)+E(f363(x19773,x19774,x19771),f363(x19773,x19774,x19772))
% 81.29/80.94 [1978]~E(x19781,x19782)+E(f835(x19781,x19783,x19784,x19785,x19786),f835(x19782,x19783,x19784,x19785,x19786))
% 81.29/80.94 [1979]~E(x19791,x19792)+E(f835(x19793,x19791,x19794,x19795,x19796),f835(x19793,x19792,x19794,x19795,x19796))
% 81.29/80.94 [1980]~E(x19801,x19802)+E(f835(x19803,x19804,x19801,x19805,x19806),f835(x19803,x19804,x19802,x19805,x19806))
% 81.29/80.94 [1981]~E(x19811,x19812)+E(f835(x19813,x19814,x19815,x19811,x19816),f835(x19813,x19814,x19815,x19812,x19816))
% 81.29/80.94 [1982]~E(x19821,x19822)+E(f835(x19823,x19824,x19825,x19826,x19821),f835(x19823,x19824,x19825,x19826,x19822))
% 81.29/80.94 [1983]~E(x19831,x19832)+E(f354(x19831,x19833,x19834,x19835,x19836),f354(x19832,x19833,x19834,x19835,x19836))
% 81.29/80.94 [1984]~E(x19841,x19842)+E(f354(x19843,x19841,x19844,x19845,x19846),f354(x19843,x19842,x19844,x19845,x19846))
% 81.29/80.94 [1985]~E(x19851,x19852)+E(f354(x19853,x19854,x19851,x19855,x19856),f354(x19853,x19854,x19852,x19855,x19856))
% 81.29/80.94 [1986]~E(x19861,x19862)+E(f354(x19863,x19864,x19865,x19861,x19866),f354(x19863,x19864,x19865,x19862,x19866))
% 81.29/80.94 [1987]~E(x19871,x19872)+E(f354(x19873,x19874,x19875,x19876,x19871),f354(x19873,x19874,x19875,x19876,x19872))
% 81.29/80.94 [1988]~E(x19881,x19882)+E(f728(x19881,x19883,x19884,x19885,x19886),f728(x19882,x19883,x19884,x19885,x19886))
% 81.29/80.94 [1989]~E(x19891,x19892)+E(f728(x19893,x19891,x19894,x19895,x19896),f728(x19893,x19892,x19894,x19895,x19896))
% 81.29/80.94 [1990]~E(x19901,x19902)+E(f728(x19903,x19904,x19901,x19905,x19906),f728(x19903,x19904,x19902,x19905,x19906))
% 81.29/80.94 [1991]~E(x19911,x19912)+E(f728(x19913,x19914,x19915,x19911,x19916),f728(x19913,x19914,x19915,x19912,x19916))
% 81.29/80.94 [1992]~E(x19921,x19922)+E(f728(x19923,x19924,x19925,x19926,x19921),f728(x19923,x19924,x19925,x19926,x19922))
% 81.29/80.94 [1993]~E(x19931,x19932)+E(f784(x19931,x19933,x19934,x19935,x19936),f784(x19932,x19933,x19934,x19935,x19936))
% 81.29/80.94 [1994]~E(x19941,x19942)+E(f784(x19943,x19941,x19944,x19945,x19946),f784(x19943,x19942,x19944,x19945,x19946))
% 81.29/80.94 [1995]~E(x19951,x19952)+E(f784(x19953,x19954,x19951,x19955,x19956),f784(x19953,x19954,x19952,x19955,x19956))
% 81.29/80.94 [1996]~E(x19961,x19962)+E(f784(x19963,x19964,x19965,x19961,x19966),f784(x19963,x19964,x19965,x19962,x19966))
% 81.29/80.94 [1997]~E(x19971,x19972)+E(f784(x19973,x19974,x19975,x19976,x19971),f784(x19973,x19974,x19975,x19976,x19972))
% 81.29/80.94 [1998]~E(x19981,x19982)+E(f209(x19981),f209(x19982))
% 81.29/80.94 [1999]~E(x19991,x19992)+E(f685(x19991,x19993),f685(x19992,x19993))
% 81.29/80.94 [2000]~E(x20001,x20002)+E(f685(x20003,x20001),f685(x20003,x20002))
% 81.29/80.94 [2001]~E(x20011,x20012)+E(f792(x20011,x20013,x20014),f792(x20012,x20013,x20014))
% 81.29/80.94 [2002]~E(x20021,x20022)+E(f792(x20023,x20021,x20024),f792(x20023,x20022,x20024))
% 81.29/80.94 [2003]~E(x20031,x20032)+E(f792(x20033,x20034,x20031),f792(x20033,x20034,x20032))
% 81.29/80.94 [2004]~E(x20041,x20042)+E(f742(x20041,x20043,x20044,x20045,x20046),f742(x20042,x20043,x20044,x20045,x20046))
% 81.29/80.94 [2005]~E(x20051,x20052)+E(f742(x20053,x20051,x20054,x20055,x20056),f742(x20053,x20052,x20054,x20055,x20056))
% 81.29/80.94 [2006]~E(x20061,x20062)+E(f742(x20063,x20064,x20061,x20065,x20066),f742(x20063,x20064,x20062,x20065,x20066))
% 81.29/80.94 [2007]~E(x20071,x20072)+E(f742(x20073,x20074,x20075,x20071,x20076),f742(x20073,x20074,x20075,x20072,x20076))
% 81.29/80.94 [2008]~E(x20081,x20082)+E(f742(x20083,x20084,x20085,x20086,x20081),f742(x20083,x20084,x20085,x20086,x20082))
% 81.29/80.94 [2009]~E(x20091,x20092)+E(f708(x20091,x20093,x20094,x20095,x20096),f708(x20092,x20093,x20094,x20095,x20096))
% 81.29/80.94 [2010]~E(x20101,x20102)+E(f708(x20103,x20101,x20104,x20105,x20106),f708(x20103,x20102,x20104,x20105,x20106))
% 81.29/80.94 [2011]~E(x20111,x20112)+E(f708(x20113,x20114,x20111,x20115,x20116),f708(x20113,x20114,x20112,x20115,x20116))
% 81.29/80.94 [2012]~E(x20121,x20122)+E(f708(x20123,x20124,x20125,x20121,x20126),f708(x20123,x20124,x20125,x20122,x20126))
% 81.29/80.94 [2013]~E(x20131,x20132)+E(f708(x20133,x20134,x20135,x20136,x20131),f708(x20133,x20134,x20135,x20136,x20132))
% 81.29/80.94 [2014]~E(x20141,x20142)+E(f794(x20141,x20143,x20144),f794(x20142,x20143,x20144))
% 81.29/80.94 [2015]~E(x20151,x20152)+E(f794(x20153,x20151,x20154),f794(x20153,x20152,x20154))
% 81.29/80.94 [2016]~E(x20161,x20162)+E(f794(x20163,x20164,x20161),f794(x20163,x20164,x20162))
% 81.29/80.94 [2017]~E(x20171,x20172)+E(f839(x20171,x20173,x20174,x20175,x20176),f839(x20172,x20173,x20174,x20175,x20176))
% 81.29/80.94 [2018]~E(x20181,x20182)+E(f839(x20183,x20181,x20184,x20185,x20186),f839(x20183,x20182,x20184,x20185,x20186))
% 81.29/80.94 [2019]~E(x20191,x20192)+E(f839(x20193,x20194,x20191,x20195,x20196),f839(x20193,x20194,x20192,x20195,x20196))
% 81.29/80.94 [2020]~E(x20201,x20202)+E(f839(x20203,x20204,x20205,x20201,x20206),f839(x20203,x20204,x20205,x20202,x20206))
% 81.29/80.94 [2021]~E(x20211,x20212)+E(f839(x20213,x20214,x20215,x20216,x20211),f839(x20213,x20214,x20215,x20216,x20212))
% 81.29/80.94 [2022]~E(x20221,x20222)+E(f765(x20221,x20223),f765(x20222,x20223))
% 81.29/80.94 [2023]~E(x20231,x20232)+E(f765(x20233,x20231),f765(x20233,x20232))
% 81.29/80.94 [2024]~E(x20241,x20242)+E(f735(x20241,x20243),f735(x20242,x20243))
% 81.29/80.94 [2025]~E(x20251,x20252)+E(f735(x20253,x20251),f735(x20253,x20252))
% 81.29/80.94 [2026]~E(x20261,x20262)+E(f438(x20261,x20263,x20264,x20265),f438(x20262,x20263,x20264,x20265))
% 81.29/80.94 [2027]~E(x20271,x20272)+E(f438(x20273,x20271,x20274,x20275),f438(x20273,x20272,x20274,x20275))
% 81.29/80.94 [2028]~E(x20281,x20282)+E(f438(x20283,x20284,x20281,x20285),f438(x20283,x20284,x20282,x20285))
% 81.29/80.94 [2029]~E(x20291,x20292)+E(f438(x20293,x20294,x20295,x20291),f438(x20293,x20294,x20295,x20292))
% 81.29/80.94 [2030]~E(x20301,x20302)+E(f840(x20301,x20303,x20304,x20305,x20306,x20307),f840(x20302,x20303,x20304,x20305,x20306,x20307))
% 81.29/80.94 [2031]~E(x20311,x20312)+E(f840(x20313,x20311,x20314,x20315,x20316,x20317),f840(x20313,x20312,x20314,x20315,x20316,x20317))
% 81.29/80.94 [2032]~E(x20321,x20322)+E(f840(x20323,x20324,x20321,x20325,x20326,x20327),f840(x20323,x20324,x20322,x20325,x20326,x20327))
% 81.29/80.94 [2033]~E(x20331,x20332)+E(f840(x20333,x20334,x20335,x20331,x20336,x20337),f840(x20333,x20334,x20335,x20332,x20336,x20337))
% 81.29/80.94 [2034]~E(x20341,x20342)+E(f840(x20343,x20344,x20345,x20346,x20341,x20347),f840(x20343,x20344,x20345,x20346,x20342,x20347))
% 81.29/80.94 [2035]~E(x20351,x20352)+E(f840(x20353,x20354,x20355,x20356,x20357,x20351),f840(x20353,x20354,x20355,x20356,x20357,x20352))
% 81.29/80.94 [2036]~E(x20361,x20362)+E(f75(x20361,x20363),f75(x20362,x20363))
% 81.29/80.94 [2037]~E(x20371,x20372)+E(f75(x20373,x20371),f75(x20373,x20372))
% 81.29/80.94 [2038]~E(x20381,x20382)+E(f610(x20381,x20383,x20384),f610(x20382,x20383,x20384))
% 81.29/80.94 [2039]~E(x20391,x20392)+E(f610(x20393,x20391,x20394),f610(x20393,x20392,x20394))
% 81.29/80.94 [2040]~E(x20401,x20402)+E(f610(x20403,x20404,x20401),f610(x20403,x20404,x20402))
% 81.29/80.94 [2041]~E(x20411,x20412)+E(f597(x20411,x20413,x20414,x20415,x20416),f597(x20412,x20413,x20414,x20415,x20416))
% 81.29/80.94 [2042]~E(x20421,x20422)+E(f597(x20423,x20421,x20424,x20425,x20426),f597(x20423,x20422,x20424,x20425,x20426))
% 81.29/80.94 [2043]~E(x20431,x20432)+E(f597(x20433,x20434,x20431,x20435,x20436),f597(x20433,x20434,x20432,x20435,x20436))
% 81.29/80.94 [2044]~E(x20441,x20442)+E(f597(x20443,x20444,x20445,x20441,x20446),f597(x20443,x20444,x20445,x20442,x20446))
% 81.29/80.94 [2045]~E(x20451,x20452)+E(f597(x20453,x20454,x20455,x20456,x20451),f597(x20453,x20454,x20455,x20456,x20452))
% 81.29/80.94 [2046]~E(x20461,x20462)+E(f664(x20461,x20463,x20464),f664(x20462,x20463,x20464))
% 81.29/80.94 [2047]~E(x20471,x20472)+E(f664(x20473,x20471,x20474),f664(x20473,x20472,x20474))
% 81.29/80.94 [2048]~E(x20481,x20482)+E(f664(x20483,x20484,x20481),f664(x20483,x20484,x20482))
% 81.29/80.94 [2049]~E(x20491,x20492)+E(f732(x20491,x20493,x20494,x20495,x20496,x20497),f732(x20492,x20493,x20494,x20495,x20496,x20497))
% 81.29/80.94 [2050]~E(x20501,x20502)+E(f732(x20503,x20501,x20504,x20505,x20506,x20507),f732(x20503,x20502,x20504,x20505,x20506,x20507))
% 81.29/80.94 [2051]~E(x20511,x20512)+E(f732(x20513,x20514,x20511,x20515,x20516,x20517),f732(x20513,x20514,x20512,x20515,x20516,x20517))
% 81.29/80.94 [2052]~E(x20521,x20522)+E(f732(x20523,x20524,x20525,x20521,x20526,x20527),f732(x20523,x20524,x20525,x20522,x20526,x20527))
% 81.29/80.94 [2053]~E(x20531,x20532)+E(f732(x20533,x20534,x20535,x20536,x20531,x20537),f732(x20533,x20534,x20535,x20536,x20532,x20537))
% 81.29/80.94 [2054]~E(x20541,x20542)+E(f732(x20543,x20544,x20545,x20546,x20547,x20541),f732(x20543,x20544,x20545,x20546,x20547,x20542))
% 81.29/80.94 [2055]~E(x20551,x20552)+E(f564(x20551,x20553,x20554,x20555,x20556,x20557),f564(x20552,x20553,x20554,x20555,x20556,x20557))
% 81.29/80.94 [2056]~E(x20561,x20562)+E(f564(x20563,x20561,x20564,x20565,x20566,x20567),f564(x20563,x20562,x20564,x20565,x20566,x20567))
% 81.29/80.94 [2057]~E(x20571,x20572)+E(f564(x20573,x20574,x20571,x20575,x20576,x20577),f564(x20573,x20574,x20572,x20575,x20576,x20577))
% 81.29/80.94 [2058]~E(x20581,x20582)+E(f564(x20583,x20584,x20585,x20581,x20586,x20587),f564(x20583,x20584,x20585,x20582,x20586,x20587))
% 81.29/80.94 [2059]~E(x20591,x20592)+E(f564(x20593,x20594,x20595,x20596,x20591,x20597),f564(x20593,x20594,x20595,x20596,x20592,x20597))
% 81.29/80.94 [2060]~E(x20601,x20602)+E(f564(x20603,x20604,x20605,x20606,x20607,x20601),f564(x20603,x20604,x20605,x20606,x20607,x20602))
% 81.29/80.94 [2061]~E(x20611,x20612)+E(f599(x20611,x20613,x20614),f599(x20612,x20613,x20614))
% 81.29/80.94 [2062]~E(x20621,x20622)+E(f599(x20623,x20621,x20624),f599(x20623,x20622,x20624))
% 81.29/80.94 [2063]~E(x20631,x20632)+E(f599(x20633,x20634,x20631),f599(x20633,x20634,x20632))
% 81.29/80.94 [2064]~E(x20641,x20642)+E(f694(x20641,x20643,x20644,x20645),f694(x20642,x20643,x20644,x20645))
% 81.29/80.94 [2065]~E(x20651,x20652)+E(f694(x20653,x20651,x20654,x20655),f694(x20653,x20652,x20654,x20655))
% 81.29/80.94 [2066]~E(x20661,x20662)+E(f694(x20663,x20664,x20661,x20665),f694(x20663,x20664,x20662,x20665))
% 81.29/80.94 [2067]~E(x20671,x20672)+E(f694(x20673,x20674,x20675,x20671),f694(x20673,x20674,x20675,x20672))
% 81.29/80.94 [2068]~E(x20681,x20682)+E(f748(x20681,x20683,x20684,x20685,x20686,x20687,x20688),f748(x20682,x20683,x20684,x20685,x20686,x20687,x20688))
% 81.29/80.94 [2069]~E(x20691,x20692)+E(f748(x20693,x20691,x20694,x20695,x20696,x20697,x20698),f748(x20693,x20692,x20694,x20695,x20696,x20697,x20698))
% 81.29/80.94 [2070]~E(x20701,x20702)+E(f748(x20703,x20704,x20701,x20705,x20706,x20707,x20708),f748(x20703,x20704,x20702,x20705,x20706,x20707,x20708))
% 81.29/80.94 [2071]~E(x20711,x20712)+E(f748(x20713,x20714,x20715,x20711,x20716,x20717,x20718),f748(x20713,x20714,x20715,x20712,x20716,x20717,x20718))
% 81.29/80.94 [2072]~E(x20721,x20722)+E(f748(x20723,x20724,x20725,x20726,x20721,x20727,x20728),f748(x20723,x20724,x20725,x20726,x20722,x20727,x20728))
% 81.29/80.94 [2073]~E(x20731,x20732)+E(f748(x20733,x20734,x20735,x20736,x20737,x20731,x20738),f748(x20733,x20734,x20735,x20736,x20737,x20732,x20738))
% 81.29/80.94 [2074]~E(x20741,x20742)+E(f748(x20743,x20744,x20745,x20746,x20747,x20748,x20741),f748(x20743,x20744,x20745,x20746,x20747,x20748,x20742))
% 81.29/80.94 [2075]~E(x20751,x20752)+E(f278(x20751,x20753,x20754),f278(x20752,x20753,x20754))
% 81.29/80.94 [2076]~E(x20761,x20762)+E(f278(x20763,x20761,x20764),f278(x20763,x20762,x20764))
% 81.29/80.94 [2077]~E(x20771,x20772)+E(f278(x20773,x20774,x20771),f278(x20773,x20774,x20772))
% 81.29/80.94 [2078]~E(x20781,x20782)+E(f233(x20781,x20783,x20784),f233(x20782,x20783,x20784))
% 81.29/80.94 [2079]~E(x20791,x20792)+E(f233(x20793,x20791,x20794),f233(x20793,x20792,x20794))
% 81.29/80.94 [2080]~E(x20801,x20802)+E(f233(x20803,x20804,x20801),f233(x20803,x20804,x20802))
% 81.29/80.94 [2081]~E(x20811,x20812)+E(f508(x20811,x20813,x20814,x20815,x20816),f508(x20812,x20813,x20814,x20815,x20816))
% 81.29/80.94 [2082]~E(x20821,x20822)+E(f508(x20823,x20821,x20824,x20825,x20826),f508(x20823,x20822,x20824,x20825,x20826))
% 81.29/80.94 [2083]~E(x20831,x20832)+E(f508(x20833,x20834,x20831,x20835,x20836),f508(x20833,x20834,x20832,x20835,x20836))
% 81.29/80.94 [2084]~E(x20841,x20842)+E(f508(x20843,x20844,x20845,x20841,x20846),f508(x20843,x20844,x20845,x20842,x20846))
% 81.29/80.94 [2085]~E(x20851,x20852)+E(f508(x20853,x20854,x20855,x20856,x20851),f508(x20853,x20854,x20855,x20856,x20852))
% 81.29/80.94 [2086]~E(x20861,x20862)+E(f572(x20861,x20863,x20864,x20865),f572(x20862,x20863,x20864,x20865))
% 81.29/80.94 [2087]~E(x20871,x20872)+E(f572(x20873,x20871,x20874,x20875),f572(x20873,x20872,x20874,x20875))
% 81.29/80.94 [2088]~E(x20881,x20882)+E(f572(x20883,x20884,x20881,x20885),f572(x20883,x20884,x20882,x20885))
% 81.29/80.94 [2089]~E(x20891,x20892)+E(f572(x20893,x20894,x20895,x20891),f572(x20893,x20894,x20895,x20892))
% 81.29/80.94 [2090]~E(x20901,x20902)+E(f855(x20901,x20903,x20904,x20905,x20906),f855(x20902,x20903,x20904,x20905,x20906))
% 81.29/80.94 [2091]~E(x20911,x20912)+E(f855(x20913,x20911,x20914,x20915,x20916),f855(x20913,x20912,x20914,x20915,x20916))
% 81.29/80.94 [2092]~E(x20921,x20922)+E(f855(x20923,x20924,x20921,x20925,x20926),f855(x20923,x20924,x20922,x20925,x20926))
% 81.29/80.94 [2093]~E(x20931,x20932)+E(f855(x20933,x20934,x20935,x20931,x20936),f855(x20933,x20934,x20935,x20932,x20936))
% 81.29/80.94 [2094]~E(x20941,x20942)+E(f855(x20943,x20944,x20945,x20946,x20941),f855(x20943,x20944,x20945,x20946,x20942))
% 81.29/80.94 [2095]~E(x20951,x20952)+E(f577(x20951,x20953,x20954),f577(x20952,x20953,x20954))
% 81.29/80.94 [2096]~E(x20961,x20962)+E(f577(x20963,x20961,x20964),f577(x20963,x20962,x20964))
% 81.29/80.94 [2097]~E(x20971,x20972)+E(f577(x20973,x20974,x20971),f577(x20973,x20974,x20972))
% 81.29/80.94 [2098]~E(x20981,x20982)+E(f528(x20981,x20983,x20984,x20985),f528(x20982,x20983,x20984,x20985))
% 81.29/80.94 [2099]~E(x20991,x20992)+E(f528(x20993,x20991,x20994,x20995),f528(x20993,x20992,x20994,x20995))
% 81.29/80.94 [2100]~E(x21001,x21002)+E(f528(x21003,x21004,x21001,x21005),f528(x21003,x21004,x21002,x21005))
% 81.29/80.94 [2101]~E(x21011,x21012)+E(f528(x21013,x21014,x21015,x21011),f528(x21013,x21014,x21015,x21012))
% 81.29/80.94 [2102]~E(x21021,x21022)+E(f478(x21021,x21023,x21024),f478(x21022,x21023,x21024))
% 81.29/80.94 [2103]~E(x21031,x21032)+E(f478(x21033,x21031,x21034),f478(x21033,x21032,x21034))
% 81.29/80.94 [2104]~E(x21041,x21042)+E(f478(x21043,x21044,x21041),f478(x21043,x21044,x21042))
% 81.29/80.94 [2105]~E(x21051,x21052)+E(f474(x21051,x21053,x21054),f474(x21052,x21053,x21054))
% 81.29/80.94 [2106]~E(x21061,x21062)+E(f474(x21063,x21061,x21064),f474(x21063,x21062,x21064))
% 81.29/80.94 [2107]~E(x21071,x21072)+E(f474(x21073,x21074,x21071),f474(x21073,x21074,x21072))
% 81.29/80.94 [2108]~E(x21081,x21082)+E(f419(x21081,x21083,x21084,x21085),f419(x21082,x21083,x21084,x21085))
% 81.29/80.94 [2109]~E(x21091,x21092)+E(f419(x21093,x21091,x21094,x21095),f419(x21093,x21092,x21094,x21095))
% 81.29/80.94 [2110]~E(x21101,x21102)+E(f419(x21103,x21104,x21101,x21105),f419(x21103,x21104,x21102,x21105))
% 81.29/80.94 [2111]~E(x21111,x21112)+E(f419(x21113,x21114,x21115,x21111),f419(x21113,x21114,x21115,x21112))
% 81.29/80.94 [2112]~E(x21121,x21122)+E(f333(x21121),f333(x21122))
% 81.29/80.94 [2113]~E(x21131,x21132)+E(f431(x21131,x21133,x21134),f431(x21132,x21133,x21134))
% 81.29/80.94 [2114]~E(x21141,x21142)+E(f431(x21143,x21141,x21144),f431(x21143,x21142,x21144))
% 81.29/80.94 [2115]~E(x21151,x21152)+E(f431(x21153,x21154,x21151),f431(x21153,x21154,x21152))
% 81.29/80.94 [2116]~E(x21161,x21162)+E(f806(x21161),f806(x21162))
% 81.29/80.94 [2117]~E(x21171,x21172)+E(f519(x21171,x21173,x21174,x21175,x21176),f519(x21172,x21173,x21174,x21175,x21176))
% 81.29/80.94 [2118]~E(x21181,x21182)+E(f519(x21183,x21181,x21184,x21185,x21186),f519(x21183,x21182,x21184,x21185,x21186))
% 81.29/80.94 [2119]~E(x21191,x21192)+E(f519(x21193,x21194,x21191,x21195,x21196),f519(x21193,x21194,x21192,x21195,x21196))
% 81.29/80.94 [2120]~E(x21201,x21202)+E(f519(x21203,x21204,x21205,x21201,x21206),f519(x21203,x21204,x21205,x21202,x21206))
% 81.29/80.94 [2121]~E(x21211,x21212)+E(f519(x21213,x21214,x21215,x21216,x21211),f519(x21213,x21214,x21215,x21216,x21212))
% 81.29/80.94 [2122]~E(x21221,x21222)+E(f388(x21221,x21223,x21224,x21225),f388(x21222,x21223,x21224,x21225))
% 81.29/80.94 [2123]~E(x21231,x21232)+E(f388(x21233,x21231,x21234,x21235),f388(x21233,x21232,x21234,x21235))
% 81.29/80.94 [2124]~E(x21241,x21242)+E(f388(x21243,x21244,x21241,x21245),f388(x21243,x21244,x21242,x21245))
% 81.29/80.94 [2125]~E(x21251,x21252)+E(f388(x21253,x21254,x21255,x21251),f388(x21253,x21254,x21255,x21252))
% 81.29/80.94 [2126]~E(x21261,x21262)+E(f400(x21261,x21263),f400(x21262,x21263))
% 81.29/80.94 [2127]~E(x21271,x21272)+E(f400(x21273,x21271),f400(x21273,x21272))
% 81.29/80.94 [2128]~E(x21281,x21282)+E(f365(x21281),f365(x21282))
% 81.29/80.94 [2129]~E(x21291,x21292)+E(f234(x21291,x21293,x21294,x21295),f234(x21292,x21293,x21294,x21295))
% 81.29/80.94 [2130]~E(x21301,x21302)+E(f234(x21303,x21301,x21304,x21305),f234(x21303,x21302,x21304,x21305))
% 81.29/80.94 [2131]~E(x21311,x21312)+E(f234(x21313,x21314,x21311,x21315),f234(x21313,x21314,x21312,x21315))
% 81.29/80.94 [2132]~E(x21321,x21322)+E(f234(x21323,x21324,x21325,x21321),f234(x21323,x21324,x21325,x21322))
% 81.29/80.94 [2133]~E(x21331,x21332)+E(f726(x21331,x21333,x21334),f726(x21332,x21333,x21334))
% 81.29/80.94 [2134]~E(x21341,x21342)+E(f726(x21343,x21341,x21344),f726(x21343,x21342,x21344))
% 81.29/80.94 [2135]~E(x21351,x21352)+E(f726(x21353,x21354,x21351),f726(x21353,x21354,x21352))
% 81.29/80.94 [2136]~E(x21361,x21362)+E(f247(x21361,x21363),f247(x21362,x21363))
% 81.29/80.94 [2137]~E(x21371,x21372)+E(f247(x21373,x21371),f247(x21373,x21372))
% 81.29/80.94 [2138]~E(x21381,x21382)+E(f507(x21381,x21383,x21384,x21385,x21386),f507(x21382,x21383,x21384,x21385,x21386))
% 81.29/80.94 [2139]~E(x21391,x21392)+E(f507(x21393,x21391,x21394,x21395,x21396),f507(x21393,x21392,x21394,x21395,x21396))
% 81.29/80.94 [2140]~E(x21401,x21402)+E(f507(x21403,x21404,x21401,x21405,x21406),f507(x21403,x21404,x21402,x21405,x21406))
% 81.29/80.94 [2141]~E(x21411,x21412)+E(f507(x21413,x21414,x21415,x21411,x21416),f507(x21413,x21414,x21415,x21412,x21416))
% 81.29/80.94 [2142]~E(x21421,x21422)+E(f507(x21423,x21424,x21425,x21426,x21421),f507(x21423,x21424,x21425,x21426,x21422))
% 81.29/80.94 [2143]~E(x21431,x21432)+E(f724(x21431,x21433,x21434),f724(x21432,x21433,x21434))
% 81.29/80.94 [2144]~E(x21441,x21442)+E(f724(x21443,x21441,x21444),f724(x21443,x21442,x21444))
% 81.29/80.94 [2145]~E(x21451,x21452)+E(f724(x21453,x21454,x21451),f724(x21453,x21454,x21452))
% 81.29/80.94 [2146]~E(x21461,x21462)+E(f440(x21461,x21463,x21464,x21465),f440(x21462,x21463,x21464,x21465))
% 81.29/80.94 [2147]~E(x21471,x21472)+E(f440(x21473,x21471,x21474,x21475),f440(x21473,x21472,x21474,x21475))
% 81.29/80.94 [2148]~E(x21481,x21482)+E(f440(x21483,x21484,x21481,x21485),f440(x21483,x21484,x21482,x21485))
% 81.29/80.94 [2149]~E(x21491,x21492)+E(f440(x21493,x21494,x21495,x21491),f440(x21493,x21494,x21495,x21492))
% 81.29/80.94 [2150]~E(x21501,x21502)+E(f741(x21501,x21503,x21504),f741(x21502,x21503,x21504))
% 81.29/80.94 [2151]~E(x21511,x21512)+E(f741(x21513,x21511,x21514),f741(x21513,x21512,x21514))
% 81.29/80.94 [2152]~E(x21521,x21522)+E(f741(x21523,x21524,x21521),f741(x21523,x21524,x21522))
% 81.29/80.94 [2153]~E(x21531,x21532)+E(f487(x21531,x21533,x21534),f487(x21532,x21533,x21534))
% 81.29/80.94 [2154]~E(x21541,x21542)+E(f487(x21543,x21541,x21544),f487(x21543,x21542,x21544))
% 81.29/80.94 [2155]~E(x21551,x21552)+E(f487(x21553,x21554,x21551),f487(x21553,x21554,x21552))
% 81.29/80.94 [2156]~E(x21561,x21562)+E(f389(x21561,x21563,x21564,x21565,x21566),f389(x21562,x21563,x21564,x21565,x21566))
% 81.29/80.94 [2157]~E(x21571,x21572)+E(f389(x21573,x21571,x21574,x21575,x21576),f389(x21573,x21572,x21574,x21575,x21576))
% 81.29/80.94 [2158]~E(x21581,x21582)+E(f389(x21583,x21584,x21581,x21585,x21586),f389(x21583,x21584,x21582,x21585,x21586))
% 81.29/80.94 [2159]~E(x21591,x21592)+E(f389(x21593,x21594,x21595,x21591,x21596),f389(x21593,x21594,x21595,x21592,x21596))
% 81.29/80.94 [2160]~E(x21601,x21602)+E(f389(x21603,x21604,x21605,x21606,x21601),f389(x21603,x21604,x21605,x21606,x21602))
% 81.29/80.94 [2161]~E(x21611,x21612)+E(f467(x21611,x21613,x21614),f467(x21612,x21613,x21614))
% 81.29/80.94 [2162]~E(x21621,x21622)+E(f467(x21623,x21621,x21624),f467(x21623,x21622,x21624))
% 81.29/80.94 [2163]~E(x21631,x21632)+E(f467(x21633,x21634,x21631),f467(x21633,x21634,x21632))
% 81.29/80.94 [2164]~E(x21641,x21642)+E(f754(x21641,x21643,x21644),f754(x21642,x21643,x21644))
% 81.29/80.94 [2165]~E(x21651,x21652)+E(f754(x21653,x21651,x21654),f754(x21653,x21652,x21654))
% 81.29/80.94 [2166]~E(x21661,x21662)+E(f754(x21663,x21664,x21661),f754(x21663,x21664,x21662))
% 81.29/80.94 [2167]~E(x21671,x21672)+E(f351(x21671,x21673,x21674,x21675,x21676),f351(x21672,x21673,x21674,x21675,x21676))
% 81.29/80.94 [2168]~E(x21681,x21682)+E(f351(x21683,x21681,x21684,x21685,x21686),f351(x21683,x21682,x21684,x21685,x21686))
% 81.29/80.94 [2169]~E(x21691,x21692)+E(f351(x21693,x21694,x21691,x21695,x21696),f351(x21693,x21694,x21692,x21695,x21696))
% 81.29/80.94 [2170]~E(x21701,x21702)+E(f351(x21703,x21704,x21705,x21701,x21706),f351(x21703,x21704,x21705,x21702,x21706))
% 81.29/80.94 [2171]~E(x21711,x21712)+E(f351(x21713,x21714,x21715,x21716,x21711),f351(x21713,x21714,x21715,x21716,x21712))
% 81.29/80.94 [2172]~E(x21721,x21722)+E(f557(x21721,x21723,x21724,x21725,x21726,x21727,x21728,x21729),f557(x21722,x21723,x21724,x21725,x21726,x21727,x21728,x21729))
% 81.29/80.94 [2173]~E(x21731,x21732)+E(f557(x21733,x21731,x21734,x21735,x21736,x21737,x21738,x21739),f557(x21733,x21732,x21734,x21735,x21736,x21737,x21738,x21739))
% 81.29/80.94 [2174]~E(x21741,x21742)+E(f557(x21743,x21744,x21741,x21745,x21746,x21747,x21748,x21749),f557(x21743,x21744,x21742,x21745,x21746,x21747,x21748,x21749))
% 81.29/80.94 [2175]~E(x21751,x21752)+E(f557(x21753,x21754,x21755,x21751,x21756,x21757,x21758,x21759),f557(x21753,x21754,x21755,x21752,x21756,x21757,x21758,x21759))
% 81.29/80.94 [2176]~E(x21761,x21762)+E(f557(x21763,x21764,x21765,x21766,x21761,x21767,x21768,x21769),f557(x21763,x21764,x21765,x21766,x21762,x21767,x21768,x21769))
% 81.29/80.94 [2177]~E(x21771,x21772)+E(f557(x21773,x21774,x21775,x21776,x21777,x21771,x21778,x21779),f557(x21773,x21774,x21775,x21776,x21777,x21772,x21778,x21779))
% 81.29/80.94 [2178]~E(x21781,x21782)+E(f557(x21783,x21784,x21785,x21786,x21787,x21788,x21781,x21789),f557(x21783,x21784,x21785,x21786,x21787,x21788,x21782,x21789))
% 81.29/80.94 [2179]~E(x21791,x21792)+E(f557(x21793,x21794,x21795,x21796,x21797,x21798,x21799,x21791),f557(x21793,x21794,x21795,x21796,x21797,x21798,x21799,x21792))
% 81.29/80.94 [2180]~E(x21801,x21802)+E(f531(x21801,x21803),f531(x21802,x21803))
% 81.29/80.94 [2181]~E(x21811,x21812)+E(f531(x21813,x21811),f531(x21813,x21812))
% 81.29/80.94 [2182]~E(x21821,x21822)+E(f620(x21821,x21823,x21824,x21825),f620(x21822,x21823,x21824,x21825))
% 81.29/80.94 [2183]~E(x21831,x21832)+E(f620(x21833,x21831,x21834,x21835),f620(x21833,x21832,x21834,x21835))
% 81.29/80.94 [2184]~E(x21841,x21842)+E(f620(x21843,x21844,x21841,x21845),f620(x21843,x21844,x21842,x21845))
% 81.29/80.94 [2185]~E(x21851,x21852)+E(f620(x21853,x21854,x21855,x21851),f620(x21853,x21854,x21855,x21852))
% 81.29/80.94 [2186]~E(x21861,x21862)+E(f746(x21861,x21863,x21864,x21865,x21866,x21867,x21868),f746(x21862,x21863,x21864,x21865,x21866,x21867,x21868))
% 81.29/80.94 [2187]~E(x21871,x21872)+E(f746(x21873,x21871,x21874,x21875,x21876,x21877,x21878),f746(x21873,x21872,x21874,x21875,x21876,x21877,x21878))
% 81.29/80.94 [2188]~E(x21881,x21882)+E(f746(x21883,x21884,x21881,x21885,x21886,x21887,x21888),f746(x21883,x21884,x21882,x21885,x21886,x21887,x21888))
% 81.29/80.94 [2189]~E(x21891,x21892)+E(f746(x21893,x21894,x21895,x21891,x21896,x21897,x21898),f746(x21893,x21894,x21895,x21892,x21896,x21897,x21898))
% 81.29/80.94 [2190]~E(x21901,x21902)+E(f746(x21903,x21904,x21905,x21906,x21901,x21907,x21908),f746(x21903,x21904,x21905,x21906,x21902,x21907,x21908))
% 81.29/80.94 [2191]~E(x21911,x21912)+E(f746(x21913,x21914,x21915,x21916,x21917,x21911,x21918),f746(x21913,x21914,x21915,x21916,x21917,x21912,x21918))
% 81.29/80.94 [2192]~E(x21921,x21922)+E(f746(x21923,x21924,x21925,x21926,x21927,x21928,x21921),f746(x21923,x21924,x21925,x21926,x21927,x21928,x21922))
% 81.29/80.94 [2193]~E(x21931,x21932)+E(f417(x21931,x21933,x21934),f417(x21932,x21933,x21934))
% 81.29/80.94 [2194]~E(x21941,x21942)+E(f417(x21943,x21941,x21944),f417(x21943,x21942,x21944))
% 81.29/80.94 [2195]~E(x21951,x21952)+E(f417(x21953,x21954,x21951),f417(x21953,x21954,x21952))
% 81.29/80.94 [2196]~E(x21961,x21962)+E(f678(x21961,x21963),f678(x21962,x21963))
% 81.29/80.94 [2197]~E(x21971,x21972)+E(f678(x21973,x21971),f678(x21973,x21972))
% 81.29/80.94 [2198]~E(x21981,x21982)+E(f856(x21981,x21983,x21984,x21985,x21986,x21987,x21988),f856(x21982,x21983,x21984,x21985,x21986,x21987,x21988))
% 81.29/80.94 [2199]~E(x21991,x21992)+E(f856(x21993,x21991,x21994,x21995,x21996,x21997,x21998),f856(x21993,x21992,x21994,x21995,x21996,x21997,x21998))
% 81.29/80.94 [2200]~E(x22001,x22002)+E(f856(x22003,x22004,x22001,x22005,x22006,x22007,x22008),f856(x22003,x22004,x22002,x22005,x22006,x22007,x22008))
% 81.29/80.94 [2201]~E(x22011,x22012)+E(f856(x22013,x22014,x22015,x22011,x22016,x22017,x22018),f856(x22013,x22014,x22015,x22012,x22016,x22017,x22018))
% 81.29/80.94 [2202]~E(x22021,x22022)+E(f856(x22023,x22024,x22025,x22026,x22021,x22027,x22028),f856(x22023,x22024,x22025,x22026,x22022,x22027,x22028))
% 81.29/80.94 [2203]~E(x22031,x22032)+E(f856(x22033,x22034,x22035,x22036,x22037,x22031,x22038),f856(x22033,x22034,x22035,x22036,x22037,x22032,x22038))
% 81.29/80.94 [2204]~E(x22041,x22042)+E(f856(x22043,x22044,x22045,x22046,x22047,x22048,x22041),f856(x22043,x22044,x22045,x22046,x22047,x22048,x22042))
% 81.29/80.94 [2205]~E(x22051,x22052)+E(f355(x22051,x22053,x22054,x22055,x22056),f355(x22052,x22053,x22054,x22055,x22056))
% 81.29/80.94 [2206]~E(x22061,x22062)+E(f355(x22063,x22061,x22064,x22065,x22066),f355(x22063,x22062,x22064,x22065,x22066))
% 81.29/80.94 [2207]~E(x22071,x22072)+E(f355(x22073,x22074,x22071,x22075,x22076),f355(x22073,x22074,x22072,x22075,x22076))
% 81.29/80.94 [2208]~E(x22081,x22082)+E(f355(x22083,x22084,x22085,x22081,x22086),f355(x22083,x22084,x22085,x22082,x22086))
% 81.29/80.94 [2209]~E(x22091,x22092)+E(f355(x22093,x22094,x22095,x22096,x22091),f355(x22093,x22094,x22095,x22096,x22092))
% 81.29/80.94 [2210]~E(x22101,x22102)+E(f399(x22101,x22103,x22104,x22105,x22106,x22107,x22108),f399(x22102,x22103,x22104,x22105,x22106,x22107,x22108))
% 81.29/80.94 [2211]~E(x22111,x22112)+E(f399(x22113,x22111,x22114,x22115,x22116,x22117,x22118),f399(x22113,x22112,x22114,x22115,x22116,x22117,x22118))
% 81.29/80.94 [2212]~E(x22121,x22122)+E(f399(x22123,x22124,x22121,x22125,x22126,x22127,x22128),f399(x22123,x22124,x22122,x22125,x22126,x22127,x22128))
% 81.29/80.94 [2213]~E(x22131,x22132)+E(f399(x22133,x22134,x22135,x22131,x22136,x22137,x22138),f399(x22133,x22134,x22135,x22132,x22136,x22137,x22138))
% 81.29/80.94 [2214]~E(x22141,x22142)+E(f399(x22143,x22144,x22145,x22146,x22141,x22147,x22148),f399(x22143,x22144,x22145,x22146,x22142,x22147,x22148))
% 81.29/80.94 [2215]~E(x22151,x22152)+E(f399(x22153,x22154,x22155,x22156,x22157,x22151,x22158),f399(x22153,x22154,x22155,x22156,x22157,x22152,x22158))
% 81.29/80.94 [2216]~E(x22161,x22162)+E(f399(x22163,x22164,x22165,x22166,x22167,x22168,x22161),f399(x22163,x22164,x22165,x22166,x22167,x22168,x22162))
% 81.29/80.94 [2217]~E(x22171,x22172)+E(f775(x22171,x22173,x22174,x22175,x22176),f775(x22172,x22173,x22174,x22175,x22176))
% 81.29/80.94 [2218]~E(x22181,x22182)+E(f775(x22183,x22181,x22184,x22185,x22186),f775(x22183,x22182,x22184,x22185,x22186))
% 81.29/80.94 [2219]~E(x22191,x22192)+E(f775(x22193,x22194,x22191,x22195,x22196),f775(x22193,x22194,x22192,x22195,x22196))
% 81.29/80.94 [2220]~E(x22201,x22202)+E(f775(x22203,x22204,x22205,x22201,x22206),f775(x22203,x22204,x22205,x22202,x22206))
% 81.29/80.94 [2221]~E(x22211,x22212)+E(f775(x22213,x22214,x22215,x22216,x22211),f775(x22213,x22214,x22215,x22216,x22212))
% 81.29/80.94 [2222]~E(x22221,x22222)+E(f293(x22221,x22223,x22224,x22225,x22226),f293(x22222,x22223,x22224,x22225,x22226))
% 81.29/80.94 [2223]~E(x22231,x22232)+E(f293(x22233,x22231,x22234,x22235,x22236),f293(x22233,x22232,x22234,x22235,x22236))
% 81.29/80.94 [2224]~E(x22241,x22242)+E(f293(x22243,x22244,x22241,x22245,x22246),f293(x22243,x22244,x22242,x22245,x22246))
% 81.29/80.94 [2225]~E(x22251,x22252)+E(f293(x22253,x22254,x22255,x22251,x22256),f293(x22253,x22254,x22255,x22252,x22256))
% 81.29/80.94 [2226]~E(x22261,x22262)+E(f293(x22263,x22264,x22265,x22266,x22261),f293(x22263,x22264,x22265,x22266,x22262))
% 81.29/80.94 [2227]~E(x22271,x22272)+E(f356(x22271,x22273,x22274),f356(x22272,x22273,x22274))
% 81.29/80.94 [2228]~E(x22281,x22282)+E(f356(x22283,x22281,x22284),f356(x22283,x22282,x22284))
% 81.29/80.94 [2229]~E(x22291,x22292)+E(f356(x22293,x22294,x22291),f356(x22293,x22294,x22292))
% 81.29/80.94 [2230]~E(x22301,x22302)+E(f658(x22301,x22303,x22304),f658(x22302,x22303,x22304))
% 81.29/80.94 [2231]~E(x22311,x22312)+E(f658(x22313,x22311,x22314),f658(x22313,x22312,x22314))
% 81.29/80.94 [2232]~E(x22321,x22322)+E(f658(x22323,x22324,x22321),f658(x22323,x22324,x22322))
% 81.29/80.94 [2233]~E(x22331,x22332)+E(f674(x22331,x22333,x22334,x22335),f674(x22332,x22333,x22334,x22335))
% 81.29/80.94 [2234]~E(x22341,x22342)+E(f674(x22343,x22341,x22344,x22345),f674(x22343,x22342,x22344,x22345))
% 81.29/80.94 [2235]~E(x22351,x22352)+E(f674(x22353,x22354,x22351,x22355),f674(x22353,x22354,x22352,x22355))
% 81.29/80.94 [2236]~E(x22361,x22362)+E(f674(x22363,x22364,x22365,x22361),f674(x22363,x22364,x22365,x22362))
% 81.29/80.94 [2237]~E(x22371,x22372)+E(f430(x22371,x22373),f430(x22372,x22373))
% 81.29/80.94 [2238]~E(x22381,x22382)+E(f430(x22383,x22381),f430(x22383,x22382))
% 81.29/80.94 [2239]~E(x22391,x22392)+E(f287(x22391,x22393),f287(x22392,x22393))
% 81.29/80.94 [2240]~E(x22401,x22402)+E(f287(x22403,x22401),f287(x22403,x22402))
% 81.29/80.94 [2241]~E(x22411,x22412)+E(f490(x22411,x22413,x22414),f490(x22412,x22413,x22414))
% 81.29/80.94 [2242]~E(x22421,x22422)+E(f490(x22423,x22421,x22424),f490(x22423,x22422,x22424))
% 81.29/80.94 [2243]~E(x22431,x22432)+E(f490(x22433,x22434,x22431),f490(x22433,x22434,x22432))
% 81.29/80.94 [2244]~E(x22441,x22442)+E(f590(x22441,x22443,x22444,x22445,x22446),f590(x22442,x22443,x22444,x22445,x22446))
% 81.29/80.94 [2245]~E(x22451,x22452)+E(f590(x22453,x22451,x22454,x22455,x22456),f590(x22453,x22452,x22454,x22455,x22456))
% 81.29/80.94 [2246]~E(x22461,x22462)+E(f590(x22463,x22464,x22461,x22465,x22466),f590(x22463,x22464,x22462,x22465,x22466))
% 81.29/80.94 [2247]~E(x22471,x22472)+E(f590(x22473,x22474,x22475,x22471,x22476),f590(x22473,x22474,x22475,x22472,x22476))
% 81.29/80.94 [2248]~E(x22481,x22482)+E(f590(x22483,x22484,x22485,x22486,x22481),f590(x22483,x22484,x22485,x22486,x22482))
% 81.29/80.94 [2249]~E(x22491,x22492)+E(f512(x22491,x22493,x22494,x22495),f512(x22492,x22493,x22494,x22495))
% 81.29/80.94 [2250]~E(x22501,x22502)+E(f512(x22503,x22501,x22504,x22505),f512(x22503,x22502,x22504,x22505))
% 81.29/80.94 [2251]~E(x22511,x22512)+E(f512(x22513,x22514,x22511,x22515),f512(x22513,x22514,x22512,x22515))
% 81.29/80.94 [2252]~E(x22521,x22522)+E(f512(x22523,x22524,x22525,x22521),f512(x22523,x22524,x22525,x22522))
% 81.29/80.94 [2253]~E(x22531,x22532)+E(f498(x22531,x22533,x22534),f498(x22532,x22533,x22534))
% 81.29/80.94 [2254]~E(x22541,x22542)+E(f498(x22543,x22541,x22544),f498(x22543,x22542,x22544))
% 81.29/80.94 [2255]~E(x22551,x22552)+E(f498(x22553,x22554,x22551),f498(x22553,x22554,x22552))
% 81.29/80.94 [2256]~E(x22561,x22562)+E(f828(x22561,x22563,x22564),f828(x22562,x22563,x22564))
% 81.29/80.94 [2257]~E(x22571,x22572)+E(f828(x22573,x22571,x22574),f828(x22573,x22572,x22574))
% 81.29/80.94 [2258]~E(x22581,x22582)+E(f828(x22583,x22584,x22581),f828(x22583,x22584,x22582))
% 81.29/80.94 [2259]~E(x22591,x22592)+E(f311(x22591,x22593,x22594),f311(x22592,x22593,x22594))
% 81.29/80.94 [2260]~E(x22601,x22602)+E(f311(x22603,x22601,x22604),f311(x22603,x22602,x22604))
% 81.29/80.94 [2261]~E(x22611,x22612)+E(f311(x22613,x22614,x22611),f311(x22613,x22614,x22612))
% 81.29/80.94 [2262]~E(x22621,x22622)+E(f745(x22621,x22623,x22624,x22625,x22626),f745(x22622,x22623,x22624,x22625,x22626))
% 81.29/80.94 [2263]~E(x22631,x22632)+E(f745(x22633,x22631,x22634,x22635,x22636),f745(x22633,x22632,x22634,x22635,x22636))
% 81.29/80.94 [2264]~E(x22641,x22642)+E(f745(x22643,x22644,x22641,x22645,x22646),f745(x22643,x22644,x22642,x22645,x22646))
% 81.29/80.94 [2265]~E(x22651,x22652)+E(f745(x22653,x22654,x22655,x22651,x22656),f745(x22653,x22654,x22655,x22652,x22656))
% 81.29/80.94 [2266]~E(x22661,x22662)+E(f745(x22663,x22664,x22665,x22666,x22661),f745(x22663,x22664,x22665,x22666,x22662))
% 81.29/80.94 [2267]~E(x22671,x22672)+E(f753(x22671,x22673,x22674,x22675,x22676),f753(x22672,x22673,x22674,x22675,x22676))
% 81.29/80.94 [2268]~E(x22681,x22682)+E(f753(x22683,x22681,x22684,x22685,x22686),f753(x22683,x22682,x22684,x22685,x22686))
% 81.29/80.94 [2269]~E(x22691,x22692)+E(f753(x22693,x22694,x22691,x22695,x22696),f753(x22693,x22694,x22692,x22695,x22696))
% 81.29/80.94 [2270]~E(x22701,x22702)+E(f753(x22703,x22704,x22705,x22701,x22706),f753(x22703,x22704,x22705,x22702,x22706))
% 81.29/80.94 [2271]~E(x22711,x22712)+E(f753(x22713,x22714,x22715,x22716,x22711),f753(x22713,x22714,x22715,x22716,x22712))
% 81.29/80.94 [2272]~E(x22721,x22722)+E(f589(x22721,x22723,x22724,x22725,x22726),f589(x22722,x22723,x22724,x22725,x22726))
% 81.29/80.94 [2273]~E(x22731,x22732)+E(f589(x22733,x22731,x22734,x22735,x22736),f589(x22733,x22732,x22734,x22735,x22736))
% 81.29/80.94 [2274]~E(x22741,x22742)+E(f589(x22743,x22744,x22741,x22745,x22746),f589(x22743,x22744,x22742,x22745,x22746))
% 81.29/80.94 [2275]~E(x22751,x22752)+E(f589(x22753,x22754,x22755,x22751,x22756),f589(x22753,x22754,x22755,x22752,x22756))
% 81.29/80.94 [2276]~E(x22761,x22762)+E(f589(x22763,x22764,x22765,x22766,x22761),f589(x22763,x22764,x22765,x22766,x22762))
% 81.29/80.94 [2277]~E(x22771,x22772)+E(f857(x22771),f857(x22772))
% 81.29/80.94 [2278]~E(x22781,x22782)+E(f380(x22781,x22783,x22784),f380(x22782,x22783,x22784))
% 81.29/80.94 [2279]~E(x22791,x22792)+E(f380(x22793,x22791,x22794),f380(x22793,x22792,x22794))
% 81.29/80.94 [2280]~E(x22801,x22802)+E(f380(x22803,x22804,x22801),f380(x22803,x22804,x22802))
% 81.29/80.94 [2281]~E(x22811,x22812)+E(f295(x22811,x22813,x22814,x22815),f295(x22812,x22813,x22814,x22815))
% 81.29/80.94 [2282]~E(x22821,x22822)+E(f295(x22823,x22821,x22824,x22825),f295(x22823,x22822,x22824,x22825))
% 81.29/80.94 [2283]~E(x22831,x22832)+E(f295(x22833,x22834,x22831,x22835),f295(x22833,x22834,x22832,x22835))
% 81.29/80.94 [2284]~E(x22841,x22842)+E(f295(x22843,x22844,x22845,x22841),f295(x22843,x22844,x22845,x22842))
% 81.29/80.94 [2285]~E(x22851,x22852)+E(f779(x22851,x22853,x22854,x22855,x22856),f779(x22852,x22853,x22854,x22855,x22856))
% 81.29/80.94 [2286]~E(x22861,x22862)+E(f779(x22863,x22861,x22864,x22865,x22866),f779(x22863,x22862,x22864,x22865,x22866))
% 81.29/80.94 [2287]~E(x22871,x22872)+E(f779(x22873,x22874,x22871,x22875,x22876),f779(x22873,x22874,x22872,x22875,x22876))
% 81.29/80.94 [2288]~E(x22881,x22882)+E(f779(x22883,x22884,x22885,x22881,x22886),f779(x22883,x22884,x22885,x22882,x22886))
% 81.29/80.94 [2289]~E(x22891,x22892)+E(f779(x22893,x22894,x22895,x22896,x22891),f779(x22893,x22894,x22895,x22896,x22892))
% 81.29/80.94 [2290]~E(x22901,x22902)+E(f691(x22901,x22903,x22904,x22905),f691(x22902,x22903,x22904,x22905))
% 81.29/80.94 [2291]~E(x22911,x22912)+E(f691(x22913,x22911,x22914,x22915),f691(x22913,x22912,x22914,x22915))
% 81.29/80.94 [2292]~E(x22921,x22922)+E(f691(x22923,x22924,x22921,x22925),f691(x22923,x22924,x22922,x22925))
% 81.29/80.94 [2293]~E(x22931,x22932)+E(f691(x22933,x22934,x22935,x22931),f691(x22933,x22934,x22935,x22932))
% 81.29/80.94 [2294]~E(x22941,x22942)+E(f782(x22941,x22943,x22944,x22945),f782(x22942,x22943,x22944,x22945))
% 81.29/80.94 [2295]~E(x22951,x22952)+E(f782(x22953,x22951,x22954,x22955),f782(x22953,x22952,x22954,x22955))
% 81.29/80.94 [2296]~E(x22961,x22962)+E(f782(x22963,x22964,x22961,x22965),f782(x22963,x22964,x22962,x22965))
% 81.29/80.94 [2297]~E(x22971,x22972)+E(f782(x22973,x22974,x22975,x22971),f782(x22973,x22974,x22975,x22972))
% 81.29/80.94 [2298]~E(x22981,x22982)+E(f603(x22981,x22983,x22984),f603(x22982,x22983,x22984))
% 81.29/80.94 [2299]~E(x22991,x22992)+E(f603(x22993,x22991,x22994),f603(x22993,x22992,x22994))
% 81.29/80.94 [2300]~E(x23001,x23002)+E(f603(x23003,x23004,x23001),f603(x23003,x23004,x23002))
% 81.29/80.94 [2301]~E(x23011,x23012)+E(f670(x23011,x23013),f670(x23012,x23013))
% 81.29/80.94 [2302]~E(x23021,x23022)+E(f670(x23023,x23021),f670(x23023,x23022))
% 81.29/80.94 [2303]~E(x23031,x23032)+E(f273(x23031),f273(x23032))
% 81.29/80.94 [2304]~E(x23041,x23042)+E(f465(x23041,x23043,x23044,x23045,x23046),f465(x23042,x23043,x23044,x23045,x23046))
% 81.29/80.94 [2305]~E(x23051,x23052)+E(f465(x23053,x23051,x23054,x23055,x23056),f465(x23053,x23052,x23054,x23055,x23056))
% 81.29/80.94 [2306]~E(x23061,x23062)+E(f465(x23063,x23064,x23061,x23065,x23066),f465(x23063,x23064,x23062,x23065,x23066))
% 81.29/80.94 [2307]~E(x23071,x23072)+E(f465(x23073,x23074,x23075,x23071,x23076),f465(x23073,x23074,x23075,x23072,x23076))
% 81.29/80.94 [2308]~E(x23081,x23082)+E(f465(x23083,x23084,x23085,x23086,x23081),f465(x23083,x23084,x23085,x23086,x23082))
% 81.29/80.94 [2309]~E(x23091,x23092)+E(f656(x23091,x23093,x23094,x23095),f656(x23092,x23093,x23094,x23095))
% 81.29/80.94 [2310]~E(x23101,x23102)+E(f656(x23103,x23101,x23104,x23105),f656(x23103,x23102,x23104,x23105))
% 81.29/80.94 [2311]~E(x23111,x23112)+E(f656(x23113,x23114,x23111,x23115),f656(x23113,x23114,x23112,x23115))
% 81.29/80.94 [2312]~E(x23121,x23122)+E(f656(x23123,x23124,x23125,x23121),f656(x23123,x23124,x23125,x23122))
% 81.29/80.94 [2313]~E(x23131,x23132)+E(f692(x23131,x23133,x23134,x23135),f692(x23132,x23133,x23134,x23135))
% 81.29/80.94 [2314]~E(x23141,x23142)+E(f692(x23143,x23141,x23144,x23145),f692(x23143,x23142,x23144,x23145))
% 81.29/80.94 [2315]~E(x23151,x23152)+E(f692(x23153,x23154,x23151,x23155),f692(x23153,x23154,x23152,x23155))
% 81.29/80.94 [2316]~E(x23161,x23162)+E(f692(x23163,x23164,x23165,x23161),f692(x23163,x23164,x23165,x23162))
% 81.29/80.94 [2317]~E(x23171,x23172)+E(f446(x23171,x23173),f446(x23172,x23173))
% 81.29/80.94 [2318]~E(x23181,x23182)+E(f446(x23183,x23181),f446(x23183,x23182))
% 81.29/80.94 [2319]~E(x23191,x23192)+E(f867(x23191,x23193),f867(x23192,x23193))
% 81.29/80.94 [2320]~E(x23201,x23202)+E(f867(x23203,x23201),f867(x23203,x23202))
% 81.29/80.94 [2321]~E(x23211,x23212)+E(f387(x23211,x23213,x23214,x23215),f387(x23212,x23213,x23214,x23215))
% 81.29/80.94 [2322]~E(x23221,x23222)+E(f387(x23223,x23221,x23224,x23225),f387(x23223,x23222,x23224,x23225))
% 81.29/80.94 [2323]~E(x23231,x23232)+E(f387(x23233,x23234,x23231,x23235),f387(x23233,x23234,x23232,x23235))
% 81.29/80.94 [2324]~E(x23241,x23242)+E(f387(x23243,x23244,x23245,x23241),f387(x23243,x23244,x23245,x23242))
% 81.29/80.94 [2325]~E(x23251,x23252)+E(f428(x23251,x23253),f428(x23252,x23253))
% 81.29/80.94 [2326]~E(x23261,x23262)+E(f428(x23263,x23261),f428(x23263,x23262))
% 81.29/80.94 [2327]~E(x23271,x23272)+E(f668(x23271,x23273,x23274,x23275,x23276,x23277),f668(x23272,x23273,x23274,x23275,x23276,x23277))
% 81.29/80.94 [2328]~E(x23281,x23282)+E(f668(x23283,x23281,x23284,x23285,x23286,x23287),f668(x23283,x23282,x23284,x23285,x23286,x23287))
% 81.29/80.94 [2329]~E(x23291,x23292)+E(f668(x23293,x23294,x23291,x23295,x23296,x23297),f668(x23293,x23294,x23292,x23295,x23296,x23297))
% 81.29/80.94 [2330]~E(x23301,x23302)+E(f668(x23303,x23304,x23305,x23301,x23306,x23307),f668(x23303,x23304,x23305,x23302,x23306,x23307))
% 81.29/80.94 [2331]~E(x23311,x23312)+E(f668(x23313,x23314,x23315,x23316,x23311,x23317),f668(x23313,x23314,x23315,x23316,x23312,x23317))
% 81.29/80.94 [2332]~E(x23321,x23322)+E(f668(x23323,x23324,x23325,x23326,x23327,x23321),f668(x23323,x23324,x23325,x23326,x23327,x23322))
% 81.29/80.94 [2333]~E(x23331,x23332)+E(f680(x23331,x23333),f680(x23332,x23333))
% 81.29/80.94 [2334]~E(x23341,x23342)+E(f680(x23343,x23341),f680(x23343,x23342))
% 81.29/80.94 [2335]~E(x23351,x23352)+E(f229(x23351,x23353,x23354),f229(x23352,x23353,x23354))
% 81.29/80.94 [2336]~E(x23361,x23362)+E(f229(x23363,x23361,x23364),f229(x23363,x23362,x23364))
% 81.29/80.94 [2337]~E(x23371,x23372)+E(f229(x23373,x23374,x23371),f229(x23373,x23374,x23372))
% 81.29/80.94 [2338]~E(x23381,x23382)+E(f420(x23381,x23383,x23384),f420(x23382,x23383,x23384))
% 81.29/80.94 [2339]~E(x23391,x23392)+E(f420(x23393,x23391,x23394),f420(x23393,x23392,x23394))
% 81.29/80.94 [2340]~E(x23401,x23402)+E(f420(x23403,x23404,x23401),f420(x23403,x23404,x23402))
% 81.29/80.94 [2341]~E(x23411,x23412)+E(f740(x23411,x23413,x23414),f740(x23412,x23413,x23414))
% 81.29/80.94 [2342]~E(x23421,x23422)+E(f740(x23423,x23421,x23424),f740(x23423,x23422,x23424))
% 81.29/80.94 [2343]~E(x23431,x23432)+E(f740(x23433,x23434,x23431),f740(x23433,x23434,x23432))
% 81.29/80.94 [2344]~E(x23441,x23442)+E(f458(x23441,x23443),f458(x23442,x23443))
% 81.29/80.94 [2345]~E(x23451,x23452)+E(f458(x23453,x23451),f458(x23453,x23452))
% 81.29/80.94 [2346]~E(x23461,x23462)+E(f522(x23461,x23463),f522(x23462,x23463))
% 81.29/80.94 [2347]~E(x23471,x23472)+E(f522(x23473,x23471),f522(x23473,x23472))
% 81.29/80.94 [2348]~E(x23481,x23482)+E(f390(x23481,x23483),f390(x23482,x23483))
% 81.29/80.94 [2349]~E(x23491,x23492)+E(f390(x23493,x23491),f390(x23493,x23492))
% 81.29/80.94 [2350]~E(x23501,x23502)+E(f797(x23501,x23503,x23504,x23505),f797(x23502,x23503,x23504,x23505))
% 81.29/80.94 [2351]~E(x23511,x23512)+E(f797(x23513,x23511,x23514,x23515),f797(x23513,x23512,x23514,x23515))
% 81.29/80.94 [2352]~E(x23521,x23522)+E(f797(x23523,x23524,x23521,x23525),f797(x23523,x23524,x23522,x23525))
% 81.29/80.94 [2353]~E(x23531,x23532)+E(f797(x23533,x23534,x23535,x23531),f797(x23533,x23534,x23535,x23532))
% 81.29/80.94 [2354]~E(x23541,x23542)+E(f95(x23541,x23543,x23544),f95(x23542,x23543,x23544))
% 81.29/80.94 [2355]~E(x23551,x23552)+E(f95(x23553,x23551,x23554),f95(x23553,x23552,x23554))
% 81.29/80.94 [2356]~E(x23561,x23562)+E(f95(x23563,x23564,x23561),f95(x23563,x23564,x23562))
% 81.29/80.94 [2357]~E(x23571,x23572)+E(f100(x23571,x23573,x23574,x23575),f100(x23572,x23573,x23574,x23575))
% 81.29/80.94 [2358]~E(x23581,x23582)+E(f100(x23583,x23581,x23584,x23585),f100(x23583,x23582,x23584,x23585))
% 81.29/80.94 [2359]~E(x23591,x23592)+E(f100(x23593,x23594,x23591,x23595),f100(x23593,x23594,x23592,x23595))
% 81.29/80.94 [2360]~E(x23601,x23602)+E(f100(x23603,x23604,x23605,x23601),f100(x23603,x23604,x23605,x23602))
% 81.29/80.94 [2361]~E(x23611,x23612)+E(f627(x23611,x23613,x23614),f627(x23612,x23613,x23614))
% 81.29/80.94 [2362]~E(x23621,x23622)+E(f627(x23623,x23621,x23624),f627(x23623,x23622,x23624))
% 81.29/80.94 [2363]~E(x23631,x23632)+E(f627(x23633,x23634,x23631),f627(x23633,x23634,x23632))
% 81.29/80.94 [2364]~E(x23641,x23642)+E(f720(x23641,x23643),f720(x23642,x23643))
% 81.29/80.94 [2365]~E(x23651,x23652)+E(f720(x23653,x23651),f720(x23653,x23652))
% 81.29/80.94 [2366]~E(x23661,x23662)+E(f622(x23661,x23663,x23664,x23665),f622(x23662,x23663,x23664,x23665))
% 81.29/80.94 [2367]~E(x23671,x23672)+E(f622(x23673,x23671,x23674,x23675),f622(x23673,x23672,x23674,x23675))
% 81.29/80.94 [2368]~E(x23681,x23682)+E(f622(x23683,x23684,x23681,x23685),f622(x23683,x23684,x23682,x23685))
% 81.29/80.94 [2369]~E(x23691,x23692)+E(f622(x23693,x23694,x23695,x23691),f622(x23693,x23694,x23695,x23692))
% 81.29/80.94 [2370]~E(x23701,x23702)+E(f626(x23701,x23703,x23704),f626(x23702,x23703,x23704))
% 81.29/80.94 [2371]~E(x23711,x23712)+E(f626(x23713,x23711,x23714),f626(x23713,x23712,x23714))
% 81.29/80.94 [2372]~E(x23721,x23722)+E(f626(x23723,x23724,x23721),f626(x23723,x23724,x23722))
% 81.29/80.94 [2373]~E(x23731,x23732)+E(f425(x23731,x23733,x23734,x23735),f425(x23732,x23733,x23734,x23735))
% 81.29/80.94 [2374]~E(x23741,x23742)+E(f425(x23743,x23741,x23744,x23745),f425(x23743,x23742,x23744,x23745))
% 81.29/80.94 [2375]~E(x23751,x23752)+E(f425(x23753,x23754,x23751,x23755),f425(x23753,x23754,x23752,x23755))
% 81.29/80.94 [2376]~E(x23761,x23762)+E(f425(x23763,x23764,x23765,x23761),f425(x23763,x23764,x23765,x23762))
% 81.29/80.94 [2377]~E(x23771,x23772)+E(f730(x23771,x23773,x23774,x23775,x23776,x23777),f730(x23772,x23773,x23774,x23775,x23776,x23777))
% 81.29/80.94 [2378]~E(x23781,x23782)+E(f730(x23783,x23781,x23784,x23785,x23786,x23787),f730(x23783,x23782,x23784,x23785,x23786,x23787))
% 81.29/80.94 [2379]~E(x23791,x23792)+E(f730(x23793,x23794,x23791,x23795,x23796,x23797),f730(x23793,x23794,x23792,x23795,x23796,x23797))
% 81.29/80.94 [2380]~E(x23801,x23802)+E(f730(x23803,x23804,x23805,x23801,x23806,x23807),f730(x23803,x23804,x23805,x23802,x23806,x23807))
% 81.29/80.94 [2381]~E(x23811,x23812)+E(f730(x23813,x23814,x23815,x23816,x23811,x23817),f730(x23813,x23814,x23815,x23816,x23812,x23817))
% 81.29/80.94 [2382]~E(x23821,x23822)+E(f730(x23823,x23824,x23825,x23826,x23827,x23821),f730(x23823,x23824,x23825,x23826,x23827,x23822))
% 81.29/80.94 [2383]~E(x23831,x23832)+E(f405(x23831,x23833,x23834),f405(x23832,x23833,x23834))
% 81.29/80.94 [2384]~E(x23841,x23842)+E(f405(x23843,x23841,x23844),f405(x23843,x23842,x23844))
% 81.29/80.94 [2385]~E(x23851,x23852)+E(f405(x23853,x23854,x23851),f405(x23853,x23854,x23852))
% 81.29/80.94 [2386]~E(x23861,x23862)+E(f647(x23861,x23863,x23864),f647(x23862,x23863,x23864))
% 81.29/80.94 [2387]~E(x23871,x23872)+E(f647(x23873,x23871,x23874),f647(x23873,x23872,x23874))
% 81.29/80.94 [2388]~E(x23881,x23882)+E(f647(x23883,x23884,x23881),f647(x23883,x23884,x23882))
% 81.29/80.94 [2389]~E(x23891,x23892)+E(f524(x23891,x23893,x23894,x23895,x23896),f524(x23892,x23893,x23894,x23895,x23896))
% 81.29/80.94 [2390]~E(x23901,x23902)+E(f524(x23903,x23901,x23904,x23905,x23906),f524(x23903,x23902,x23904,x23905,x23906))
% 81.29/80.94 [2391]~E(x23911,x23912)+E(f524(x23913,x23914,x23911,x23915,x23916),f524(x23913,x23914,x23912,x23915,x23916))
% 81.29/80.94 [2392]~E(x23921,x23922)+E(f524(x23923,x23924,x23925,x23921,x23926),f524(x23923,x23924,x23925,x23922,x23926))
% 81.29/80.94 [2393]~E(x23931,x23932)+E(f524(x23933,x23934,x23935,x23936,x23931),f524(x23933,x23934,x23935,x23936,x23932))
% 81.29/80.94 [2394]~E(x23941,x23942)+E(f376(x23941,x23943,x23944),f376(x23942,x23943,x23944))
% 81.29/80.94 [2395]~E(x23951,x23952)+E(f376(x23953,x23951,x23954),f376(x23953,x23952,x23954))
% 81.29/80.94 [2396]~E(x23961,x23962)+E(f376(x23963,x23964,x23961),f376(x23963,x23964,x23962))
% 81.29/80.94 [2397]~E(x23971,x23972)+E(f427(x23971,x23973,x23974,x23975),f427(x23972,x23973,x23974,x23975))
% 81.29/80.94 [2398]~E(x23981,x23982)+E(f427(x23983,x23981,x23984,x23985),f427(x23983,x23982,x23984,x23985))
% 81.29/80.94 [2399]~E(x23991,x23992)+E(f427(x23993,x23994,x23991,x23995),f427(x23993,x23994,x23992,x23995))
% 81.29/80.94 [2400]~E(x24001,x24002)+E(f427(x24003,x24004,x24005,x24001),f427(x24003,x24004,x24005,x24002))
% 81.29/80.94 [2401]~E(x24011,x24012)+E(f790(x24011,x24013,x24014),f790(x24012,x24013,x24014))
% 81.29/80.94 [2402]~E(x24021,x24022)+E(f790(x24023,x24021,x24024),f790(x24023,x24022,x24024))
% 81.29/80.94 [2403]~E(x24031,x24032)+E(f790(x24033,x24034,x24031),f790(x24033,x24034,x24032))
% 81.29/80.94 [2404]~E(x24041,x24042)+E(f758(x24041,x24043,x24044),f758(x24042,x24043,x24044))
% 81.29/80.94 [2405]~E(x24051,x24052)+E(f758(x24053,x24051,x24054),f758(x24053,x24052,x24054))
% 81.29/80.94 [2406]~E(x24061,x24062)+E(f758(x24063,x24064,x24061),f758(x24063,x24064,x24062))
% 81.29/80.94 [2407]~E(x24071,x24072)+E(f864(x24071,x24073,x24074),f864(x24072,x24073,x24074))
% 81.29/80.94 [2408]~E(x24081,x24082)+E(f864(x24083,x24081,x24084),f864(x24083,x24082,x24084))
% 81.29/80.94 [2409]~E(x24091,x24092)+E(f864(x24093,x24094,x24091),f864(x24093,x24094,x24092))
% 81.29/80.94 [2410]~E(x24101,x24102)+E(f393(x24101,x24103,x24104),f393(x24102,x24103,x24104))
% 81.29/80.94 [2411]~E(x24111,x24112)+E(f393(x24113,x24111,x24114),f393(x24113,x24112,x24114))
% 81.29/80.94 [2412]~E(x24121,x24122)+E(f393(x24123,x24124,x24121),f393(x24123,x24124,x24122))
% 81.29/80.94 [2413]~E(x24131,x24132)+E(f382(x24131,x24133,x24134),f382(x24132,x24133,x24134))
% 81.29/80.94 [2414]~E(x24141,x24142)+E(f382(x24143,x24141,x24144),f382(x24143,x24142,x24144))
% 81.29/80.94 [2415]~E(x24151,x24152)+E(f382(x24153,x24154,x24151),f382(x24153,x24154,x24152))
% 81.29/80.94 [2416]~E(x24161,x24162)+E(f633(x24161,x24163,x24164),f633(x24162,x24163,x24164))
% 81.29/80.94 [2417]~E(x24171,x24172)+E(f633(x24173,x24171,x24174),f633(x24173,x24172,x24174))
% 81.29/80.94 [2418]~E(x24181,x24182)+E(f633(x24183,x24184,x24181),f633(x24183,x24184,x24182))
% 81.29/80.94 [2419]~E(x24191,x24192)+E(f808(x24191,x24193,x24194,x24195),f808(x24192,x24193,x24194,x24195))
% 81.29/80.94 [2420]~E(x24201,x24202)+E(f808(x24203,x24201,x24204,x24205),f808(x24203,x24202,x24204,x24205))
% 81.29/80.94 [2421]~E(x24211,x24212)+E(f808(x24213,x24214,x24211,x24215),f808(x24213,x24214,x24212,x24215))
% 81.29/80.94 [2422]~E(x24221,x24222)+E(f808(x24223,x24224,x24225,x24221),f808(x24223,x24224,x24225,x24222))
% 81.29/80.94 [2423]~E(x24231,x24232)+E(f583(x24231,x24233),f583(x24232,x24233))
% 81.29/80.94 [2424]~E(x24241,x24242)+E(f583(x24243,x24241),f583(x24243,x24242))
% 81.29/80.94 [2425]~E(x24251,x24252)+E(f671(x24251,x24253),f671(x24252,x24253))
% 81.29/80.94 [2426]~E(x24261,x24262)+E(f671(x24263,x24261),f671(x24263,x24262))
% 81.29/80.94 [2427]~E(x24271,x24272)+E(f810(x24271,x24273),f810(x24272,x24273))
% 81.29/80.94 [2428]~E(x24281,x24282)+E(f810(x24283,x24281),f810(x24283,x24282))
% 81.29/80.94 [2429]~E(x24291,x24292)+E(f791(x24291,x24293,x24294),f791(x24292,x24293,x24294))
% 81.29/80.94 [2430]~E(x24301,x24302)+E(f791(x24303,x24301,x24304),f791(x24303,x24302,x24304))
% 81.29/80.94 [2431]~E(x24311,x24312)+E(f791(x24313,x24314,x24311),f791(x24313,x24314,x24312))
% 81.29/80.94 [2432]~E(x24321,x24322)+E(f270(x24321,x24323,x24324,x24325,x24326),f270(x24322,x24323,x24324,x24325,x24326))
% 81.29/80.94 [2433]~E(x24331,x24332)+E(f270(x24333,x24331,x24334,x24335,x24336),f270(x24333,x24332,x24334,x24335,x24336))
% 81.29/80.94 [2434]~E(x24341,x24342)+E(f270(x24343,x24344,x24341,x24345,x24346),f270(x24343,x24344,x24342,x24345,x24346))
% 81.29/80.94 [2435]~E(x24351,x24352)+E(f270(x24353,x24354,x24355,x24351,x24356),f270(x24353,x24354,x24355,x24352,x24356))
% 81.29/80.94 [2436]~E(x24361,x24362)+E(f270(x24363,x24364,x24365,x24366,x24361),f270(x24363,x24364,x24365,x24366,x24362))
% 81.29/80.94 [2437]~E(x24371,x24372)+E(f579(x24371,x24373,x24374,x24375),f579(x24372,x24373,x24374,x24375))
% 81.29/80.94 [2438]~E(x24381,x24382)+E(f579(x24383,x24381,x24384,x24385),f579(x24383,x24382,x24384,x24385))
% 81.29/80.94 [2439]~E(x24391,x24392)+E(f579(x24393,x24394,x24391,x24395),f579(x24393,x24394,x24392,x24395))
% 81.29/80.94 [2440]~E(x24401,x24402)+E(f579(x24403,x24404,x24405,x24401),f579(x24403,x24404,x24405,x24402))
% 81.29/80.94 [2441]~E(x24411,x24412)+E(f454(x24411,x24413,x24414,x24415),f454(x24412,x24413,x24414,x24415))
% 81.29/80.94 [2442]~E(x24421,x24422)+E(f454(x24423,x24421,x24424,x24425),f454(x24423,x24422,x24424,x24425))
% 81.29/80.94 [2443]~E(x24431,x24432)+E(f454(x24433,x24434,x24431,x24435),f454(x24433,x24434,x24432,x24435))
% 81.29/80.94 [2444]~E(x24441,x24442)+E(f454(x24443,x24444,x24445,x24441),f454(x24443,x24444,x24445,x24442))
% 81.29/80.94 [2445]~E(x24451,x24452)+E(f642(x24451,x24453,x24454),f642(x24452,x24453,x24454))
% 81.29/80.94 [2446]~E(x24461,x24462)+E(f642(x24463,x24461,x24464),f642(x24463,x24462,x24464))
% 81.29/80.94 [2447]~E(x24471,x24472)+E(f642(x24473,x24474,x24471),f642(x24473,x24474,x24472))
% 81.29/80.94 [2448]~E(x24481,x24482)+E(f833(x24481,x24483,x24484,x24485,x24486),f833(x24482,x24483,x24484,x24485,x24486))
% 81.29/80.94 [2449]~E(x24491,x24492)+E(f833(x24493,x24491,x24494,x24495,x24496),f833(x24493,x24492,x24494,x24495,x24496))
% 81.29/80.94 [2450]~E(x24501,x24502)+E(f833(x24503,x24504,x24501,x24505,x24506),f833(x24503,x24504,x24502,x24505,x24506))
% 81.29/80.94 [2451]~E(x24511,x24512)+E(f833(x24513,x24514,x24515,x24511,x24516),f833(x24513,x24514,x24515,x24512,x24516))
% 81.29/80.94 [2452]~E(x24521,x24522)+E(f833(x24523,x24524,x24525,x24526,x24521),f833(x24523,x24524,x24525,x24526,x24522))
% 81.29/80.94 [2453]~E(x24531,x24532)+E(f290(x24531,x24533,x24534),f290(x24532,x24533,x24534))
% 81.29/80.94 [2454]~E(x24541,x24542)+E(f290(x24543,x24541,x24544),f290(x24543,x24542,x24544))
% 81.29/80.94 [2455]~E(x24551,x24552)+E(f290(x24553,x24554,x24551),f290(x24553,x24554,x24552))
% 81.29/80.94 [2456]~E(x24561,x24562)+E(f357(x24561,x24563,x24564),f357(x24562,x24563,x24564))
% 81.29/80.94 [2457]~E(x24571,x24572)+E(f357(x24573,x24571,x24574),f357(x24573,x24572,x24574))
% 81.29/80.94 [2458]~E(x24581,x24582)+E(f357(x24583,x24584,x24581),f357(x24583,x24584,x24582))
% 81.29/80.94 [2459]~E(x24591,x24592)+E(f322(x24591,x24593,x24594),f322(x24592,x24593,x24594))
% 81.29/80.94 [2460]~E(x24601,x24602)+E(f322(x24603,x24601,x24604),f322(x24603,x24602,x24604))
% 81.29/80.94 [2461]~E(x24611,x24612)+E(f322(x24613,x24614,x24611),f322(x24613,x24614,x24612))
% 81.29/80.94 [2462]~E(x24621,x24622)+E(f771(x24621,x24623,x24624),f771(x24622,x24623,x24624))
% 81.29/80.94 [2463]~E(x24631,x24632)+E(f771(x24633,x24631,x24634),f771(x24633,x24632,x24634))
% 81.29/80.94 [2464]~E(x24641,x24642)+E(f771(x24643,x24644,x24641),f771(x24643,x24644,x24642))
% 81.29/80.94 [2465]~E(x24651,x24652)+E(f767(x24651,x24653,x24654),f767(x24652,x24653,x24654))
% 81.29/80.94 [2466]~E(x24661,x24662)+E(f767(x24663,x24661,x24664),f767(x24663,x24662,x24664))
% 81.29/80.94 [2467]~E(x24671,x24672)+E(f767(x24673,x24674,x24671),f767(x24673,x24674,x24672))
% 81.29/80.94 [2468]~E(x24681,x24682)+E(f863(x24681,x24683,x24684),f863(x24682,x24683,x24684))
% 81.29/80.94 [2469]~E(x24691,x24692)+E(f863(x24693,x24691,x24694),f863(x24693,x24692,x24694))
% 81.29/80.94 [2470]~E(x24701,x24702)+E(f863(x24703,x24704,x24701),f863(x24703,x24704,x24702))
% 81.29/80.94 [2471]~E(x24711,x24712)+E(f744(x24711,x24713,x24714,x24715,x24716),f744(x24712,x24713,x24714,x24715,x24716))
% 81.29/80.94 [2472]~E(x24721,x24722)+E(f744(x24723,x24721,x24724,x24725,x24726),f744(x24723,x24722,x24724,x24725,x24726))
% 81.29/80.94 [2473]~E(x24731,x24732)+E(f744(x24733,x24734,x24731,x24735,x24736),f744(x24733,x24734,x24732,x24735,x24736))
% 81.29/80.94 [2474]~E(x24741,x24742)+E(f744(x24743,x24744,x24745,x24741,x24746),f744(x24743,x24744,x24745,x24742,x24746))
% 81.29/80.94 [2475]~E(x24751,x24752)+E(f744(x24753,x24754,x24755,x24756,x24751),f744(x24753,x24754,x24755,x24756,x24752))
% 81.29/80.94 [2476]~E(x24761,x24762)+E(f230(x24761,x24763,x24764,x24765),f230(x24762,x24763,x24764,x24765))
% 81.29/80.94 [2477]~E(x24771,x24772)+E(f230(x24773,x24771,x24774,x24775),f230(x24773,x24772,x24774,x24775))
% 81.29/80.94 [2478]~E(x24781,x24782)+E(f230(x24783,x24784,x24781,x24785),f230(x24783,x24784,x24782,x24785))
% 81.29/80.94 [2479]~E(x24791,x24792)+E(f230(x24793,x24794,x24795,x24791),f230(x24793,x24794,x24795,x24792))
% 81.29/80.94 [2480]~E(x24801,x24802)+E(f591(x24801,x24803,x24804,x24805),f591(x24802,x24803,x24804,x24805))
% 81.29/80.94 [2481]~E(x24811,x24812)+E(f591(x24813,x24811,x24814,x24815),f591(x24813,x24812,x24814,x24815))
% 81.29/80.94 [2482]~E(x24821,x24822)+E(f591(x24823,x24824,x24821,x24825),f591(x24823,x24824,x24822,x24825))
% 81.29/80.94 [2483]~E(x24831,x24832)+E(f591(x24833,x24834,x24835,x24831),f591(x24833,x24834,x24835,x24832))
% 81.29/80.94 [2484]~E(x24841,x24842)+E(f395(x24841,x24843,x24844),f395(x24842,x24843,x24844))
% 81.29/80.94 [2485]~E(x24851,x24852)+E(f395(x24853,x24851,x24854),f395(x24853,x24852,x24854))
% 81.29/80.94 [2486]~E(x24861,x24862)+E(f395(x24863,x24864,x24861),f395(x24863,x24864,x24862))
% 81.29/80.94 [2487]~E(x24871,x24872)+E(f770(x24871,x24873,x24874),f770(x24872,x24873,x24874))
% 81.29/80.94 [2488]~E(x24881,x24882)+E(f770(x24883,x24881,x24884),f770(x24883,x24882,x24884))
% 81.29/80.94 [2489]~E(x24891,x24892)+E(f770(x24893,x24894,x24891),f770(x24893,x24894,x24892))
% 81.29/80.94 [2490]~E(x24901,x24902)+E(f518(x24901,x24903,x24904,x24905,x24906),f518(x24902,x24903,x24904,x24905,x24906))
% 81.29/80.94 [2491]~E(x24911,x24912)+E(f518(x24913,x24911,x24914,x24915,x24916),f518(x24913,x24912,x24914,x24915,x24916))
% 81.29/80.94 [2492]~E(x24921,x24922)+E(f518(x24923,x24924,x24921,x24925,x24926),f518(x24923,x24924,x24922,x24925,x24926))
% 81.29/80.94 [2493]~E(x24931,x24932)+E(f518(x24933,x24934,x24935,x24931,x24936),f518(x24933,x24934,x24935,x24932,x24936))
% 81.29/80.94 [2494]~E(x24941,x24942)+E(f518(x24943,x24944,x24945,x24946,x24941),f518(x24943,x24944,x24945,x24946,x24942))
% 81.29/80.94 [2495]~E(x24951,x24952)+E(f787(x24951,x24953,x24954,x24955,x24956),f787(x24952,x24953,x24954,x24955,x24956))
% 81.29/80.94 [2496]~E(x24961,x24962)+E(f787(x24963,x24961,x24964,x24965,x24966),f787(x24963,x24962,x24964,x24965,x24966))
% 81.29/80.94 [2497]~E(x24971,x24972)+E(f787(x24973,x24974,x24971,x24975,x24976),f787(x24973,x24974,x24972,x24975,x24976))
% 81.29/80.94 [2498]~E(x24981,x24982)+E(f787(x24983,x24984,x24985,x24981,x24986),f787(x24983,x24984,x24985,x24982,x24986))
% 81.29/80.94 [2499]~E(x24991,x24992)+E(f787(x24993,x24994,x24995,x24996,x24991),f787(x24993,x24994,x24995,x24996,x24992))
% 81.29/80.94 [2500]~E(x25001,x25002)+E(f660(x25001,x25003),f660(x25002,x25003))
% 81.29/80.94 [2501]~E(x25011,x25012)+E(f660(x25013,x25011),f660(x25013,x25012))
% 81.29/80.94 [2502]~E(x25021,x25022)+E(f749(x25021,x25023,x25024,x25025,x25026,x25027),f749(x25022,x25023,x25024,x25025,x25026,x25027))
% 81.29/80.94 [2503]~E(x25031,x25032)+E(f749(x25033,x25031,x25034,x25035,x25036,x25037),f749(x25033,x25032,x25034,x25035,x25036,x25037))
% 81.29/80.94 [2504]~E(x25041,x25042)+E(f749(x25043,x25044,x25041,x25045,x25046,x25047),f749(x25043,x25044,x25042,x25045,x25046,x25047))
% 81.29/80.94 [2505]~E(x25051,x25052)+E(f749(x25053,x25054,x25055,x25051,x25056,x25057),f749(x25053,x25054,x25055,x25052,x25056,x25057))
% 81.29/80.94 [2506]~E(x25061,x25062)+E(f749(x25063,x25064,x25065,x25066,x25061,x25067),f749(x25063,x25064,x25065,x25066,x25062,x25067))
% 81.29/80.94 [2507]~E(x25071,x25072)+E(f749(x25073,x25074,x25075,x25076,x25077,x25071),f749(x25073,x25074,x25075,x25076,x25077,x25072))
% 81.29/80.94 [2508]~E(x25081,x25082)+E(f349(x25081),f349(x25082))
% 81.29/80.94 [2509]~E(x25091,x25092)+E(f729(x25091,x25093,x25094,x25095,x25096,x25097),f729(x25092,x25093,x25094,x25095,x25096,x25097))
% 81.29/80.94 [2510]~E(x25101,x25102)+E(f729(x25103,x25101,x25104,x25105,x25106,x25107),f729(x25103,x25102,x25104,x25105,x25106,x25107))
% 81.29/80.94 [2511]~E(x25111,x25112)+E(f729(x25113,x25114,x25111,x25115,x25116,x25117),f729(x25113,x25114,x25112,x25115,x25116,x25117))
% 81.29/80.94 [2512]~E(x25121,x25122)+E(f729(x25123,x25124,x25125,x25121,x25126,x25127),f729(x25123,x25124,x25125,x25122,x25126,x25127))
% 81.29/80.94 [2513]~E(x25131,x25132)+E(f729(x25133,x25134,x25135,x25136,x25131,x25137),f729(x25133,x25134,x25135,x25136,x25132,x25137))
% 81.29/80.94 [2514]~E(x25141,x25142)+E(f729(x25143,x25144,x25145,x25146,x25147,x25141),f729(x25143,x25144,x25145,x25146,x25147,x25142))
% 81.29/80.94 [2515]~E(x25151,x25152)+E(f464(x25151,x25153,x25154,x25155,x25156),f464(x25152,x25153,x25154,x25155,x25156))
% 81.29/80.94 [2516]~E(x25161,x25162)+E(f464(x25163,x25161,x25164,x25165,x25166),f464(x25163,x25162,x25164,x25165,x25166))
% 81.29/80.94 [2517]~E(x25171,x25172)+E(f464(x25173,x25174,x25171,x25175,x25176),f464(x25173,x25174,x25172,x25175,x25176))
% 81.29/80.94 [2518]~E(x25181,x25182)+E(f464(x25183,x25184,x25185,x25181,x25186),f464(x25183,x25184,x25185,x25182,x25186))
% 81.29/80.94 [2519]~E(x25191,x25192)+E(f464(x25193,x25194,x25195,x25196,x25191),f464(x25193,x25194,x25195,x25196,x25192))
% 81.29/80.94 [2520]~E(x25201,x25202)+E(f215(x25201,x25203,x25204,x25205,x25206,x25207,x25208),f215(x25202,x25203,x25204,x25205,x25206,x25207,x25208))
% 81.29/80.94 [2521]~E(x25211,x25212)+E(f215(x25213,x25211,x25214,x25215,x25216,x25217,x25218),f215(x25213,x25212,x25214,x25215,x25216,x25217,x25218))
% 81.29/80.94 [2522]~E(x25221,x25222)+E(f215(x25223,x25224,x25221,x25225,x25226,x25227,x25228),f215(x25223,x25224,x25222,x25225,x25226,x25227,x25228))
% 81.29/80.94 [2523]~E(x25231,x25232)+E(f215(x25233,x25234,x25235,x25231,x25236,x25237,x25238),f215(x25233,x25234,x25235,x25232,x25236,x25237,x25238))
% 81.29/80.94 [2524]~E(x25241,x25242)+E(f215(x25243,x25244,x25245,x25246,x25241,x25247,x25248),f215(x25243,x25244,x25245,x25246,x25242,x25247,x25248))
% 81.29/80.94 [2525]~E(x25251,x25252)+E(f215(x25253,x25254,x25255,x25256,x25257,x25251,x25258),f215(x25253,x25254,x25255,x25256,x25257,x25252,x25258))
% 81.29/80.94 [2526]~E(x25261,x25262)+E(f215(x25263,x25264,x25265,x25266,x25267,x25268,x25261),f215(x25263,x25264,x25265,x25266,x25267,x25268,x25262))
% 81.29/80.94 [2527]~E(x25271,x25272)+E(f711(x25271,x25273),f711(x25272,x25273))
% 81.29/80.94 [2528]~E(x25281,x25282)+E(f711(x25283,x25281),f711(x25283,x25282))
% 81.29/80.94 [2529]~E(x25291,x25292)+E(f789(x25291,x25293,x25294),f789(x25292,x25293,x25294))
% 81.29/80.94 [2530]~E(x25301,x25302)+E(f789(x25303,x25301,x25304),f789(x25303,x25302,x25304))
% 81.29/80.94 [2531]~E(x25311,x25312)+E(f789(x25313,x25314,x25311),f789(x25313,x25314,x25312))
% 81.29/80.94 [2532]~E(x25321,x25322)+E(f529(x25321),f529(x25322))
% 81.29/80.94 [2533]~E(x25331,x25332)+E(f205(x25331,x25333,x25334,x25335),f205(x25332,x25333,x25334,x25335))
% 81.29/80.94 [2534]~E(x25341,x25342)+E(f205(x25343,x25341,x25344,x25345),f205(x25343,x25342,x25344,x25345))
% 81.29/80.94 [2535]~E(x25351,x25352)+E(f205(x25353,x25354,x25351,x25355),f205(x25353,x25354,x25352,x25355))
% 81.29/80.94 [2536]~E(x25361,x25362)+E(f205(x25363,x25364,x25365,x25361),f205(x25363,x25364,x25365,x25362))
% 81.29/80.94 [2537]~E(x25371,x25372)+E(f769(x25371,x25373,x25374),f769(x25372,x25373,x25374))
% 81.29/80.94 [2538]~E(x25381,x25382)+E(f769(x25383,x25381,x25384),f769(x25383,x25382,x25384))
% 81.29/80.94 [2539]~E(x25391,x25392)+E(f769(x25393,x25394,x25391),f769(x25393,x25394,x25392))
% 81.29/80.94 [2540]~E(x25401,x25402)+E(f348(x25401,x25403),f348(x25402,x25403))
% 81.29/80.94 [2541]~E(x25411,x25412)+E(f348(x25413,x25411),f348(x25413,x25412))
% 81.29/80.94 [2542]~E(x25421,x25422)+E(f260(x25421,x25423,x25424),f260(x25422,x25423,x25424))
% 81.29/80.94 [2543]~E(x25431,x25432)+E(f260(x25433,x25431,x25434),f260(x25433,x25432,x25434))
% 81.29/80.94 [2544]~E(x25441,x25442)+E(f260(x25443,x25444,x25441),f260(x25443,x25444,x25442))
% 81.29/80.94 [2545]~E(x25451,x25452)+E(f334(x25451,x25453),f334(x25452,x25453))
% 81.29/80.94 [2546]~E(x25461,x25462)+E(f334(x25463,x25461),f334(x25463,x25462))
% 81.29/80.94 [2547]~E(x25471,x25472)+E(f402(x25471),f402(x25472))
% 81.29/80.94 [2548]~E(x25481,x25482)+E(f696(x25481,x25483,x25484,x25485),f696(x25482,x25483,x25484,x25485))
% 81.29/80.94 [2549]~E(x25491,x25492)+E(f696(x25493,x25491,x25494,x25495),f696(x25493,x25492,x25494,x25495))
% 81.29/80.94 [2550]~E(x25501,x25502)+E(f696(x25503,x25504,x25501,x25505),f696(x25503,x25504,x25502,x25505))
% 81.29/80.94 [2551]~E(x25511,x25512)+E(f696(x25513,x25514,x25515,x25511),f696(x25513,x25514,x25515,x25512))
% 81.29/80.94 [2552]~E(x25521,x25522)+E(f843(x25521,x25523,x25524,x25525,x25526),f843(x25522,x25523,x25524,x25525,x25526))
% 81.29/80.94 [2553]~E(x25531,x25532)+E(f843(x25533,x25531,x25534,x25535,x25536),f843(x25533,x25532,x25534,x25535,x25536))
% 81.29/80.94 [2554]~E(x25541,x25542)+E(f843(x25543,x25544,x25541,x25545,x25546),f843(x25543,x25544,x25542,x25545,x25546))
% 81.29/80.94 [2555]~E(x25551,x25552)+E(f843(x25553,x25554,x25555,x25551,x25556),f843(x25553,x25554,x25555,x25552,x25556))
% 81.29/80.94 [2556]~E(x25561,x25562)+E(f843(x25563,x25564,x25565,x25566,x25561),f843(x25563,x25564,x25565,x25566,x25562))
% 81.29/80.94 [2557]~E(x25571,x25572)+E(f699(x25571,x25573),f699(x25572,x25573))
% 81.29/80.94 [2558]~E(x25581,x25582)+E(f699(x25583,x25581),f699(x25583,x25582))
% 81.29/80.94 [2559]~E(x25591,x25592)+E(f480(x25591,x25593,x25594,x25595),f480(x25592,x25593,x25594,x25595))
% 81.29/80.94 [2560]~E(x25601,x25602)+E(f480(x25603,x25601,x25604,x25605),f480(x25603,x25602,x25604,x25605))
% 81.29/80.94 [2561]~E(x25611,x25612)+E(f480(x25613,x25614,x25611,x25615),f480(x25613,x25614,x25612,x25615))
% 81.29/80.94 [2562]~E(x25621,x25622)+E(f480(x25623,x25624,x25625,x25621),f480(x25623,x25624,x25625,x25622))
% 81.29/80.94 [2563]~E(x25631,x25632)+E(f594(x25631,x25633,x25634,x25635,x25636),f594(x25632,x25633,x25634,x25635,x25636))
% 81.29/80.94 [2564]~E(x25641,x25642)+E(f594(x25643,x25641,x25644,x25645,x25646),f594(x25643,x25642,x25644,x25645,x25646))
% 81.29/80.94 [2565]~E(x25651,x25652)+E(f594(x25653,x25654,x25651,x25655,x25656),f594(x25653,x25654,x25652,x25655,x25656))
% 81.29/80.94 [2566]~E(x25661,x25662)+E(f594(x25663,x25664,x25665,x25661,x25666),f594(x25663,x25664,x25665,x25662,x25666))
% 81.29/80.94 [2567]~E(x25671,x25672)+E(f594(x25673,x25674,x25675,x25676,x25671),f594(x25673,x25674,x25675,x25676,x25672))
% 81.29/80.94 [2568]~E(x25681,x25682)+E(f866(x25681,x25683,x25684,x25685,x25686),f866(x25682,x25683,x25684,x25685,x25686))
% 81.29/80.94 [2569]~E(x25691,x25692)+E(f866(x25693,x25691,x25694,x25695,x25696),f866(x25693,x25692,x25694,x25695,x25696))
% 81.29/80.94 [2570]~E(x25701,x25702)+E(f866(x25703,x25704,x25701,x25705,x25706),f866(x25703,x25704,x25702,x25705,x25706))
% 81.29/80.94 [2571]~E(x25711,x25712)+E(f866(x25713,x25714,x25715,x25711,x25716),f866(x25713,x25714,x25715,x25712,x25716))
% 81.29/80.94 [2572]~E(x25721,x25722)+E(f866(x25723,x25724,x25725,x25726,x25721),f866(x25723,x25724,x25725,x25726,x25722))
% 81.29/80.94 [2573]~E(x25731,x25732)+E(f861(x25731),f861(x25732))
% 81.29/80.94 [2574]~E(x25741,x25742)+E(f275(x25741,x25743),f275(x25742,x25743))
% 81.29/80.94 [2575]~E(x25751,x25752)+E(f275(x25753,x25751),f275(x25753,x25752))
% 81.29/80.94 [2576]~E(x25761,x25762)+E(f852(x25761,x25763,x25764,x25765,x25766),f852(x25762,x25763,x25764,x25765,x25766))
% 81.29/80.94 [2577]~E(x25771,x25772)+E(f852(x25773,x25771,x25774,x25775,x25776),f852(x25773,x25772,x25774,x25775,x25776))
% 81.29/80.94 [2578]~E(x25781,x25782)+E(f852(x25783,x25784,x25781,x25785,x25786),f852(x25783,x25784,x25782,x25785,x25786))
% 81.29/80.94 [2579]~E(x25791,x25792)+E(f852(x25793,x25794,x25795,x25791,x25796),f852(x25793,x25794,x25795,x25792,x25796))
% 81.29/80.94 [2580]~E(x25801,x25802)+E(f852(x25803,x25804,x25805,x25806,x25801),f852(x25803,x25804,x25805,x25806,x25802))
% 81.29/80.94 [2581]~E(x25811,x25812)+E(f527(x25811,x25813,x25814),f527(x25812,x25813,x25814))
% 81.29/80.94 [2582]~E(x25821,x25822)+E(f527(x25823,x25821,x25824),f527(x25823,x25822,x25824))
% 81.29/80.94 [2583]~E(x25831,x25832)+E(f527(x25833,x25834,x25831),f527(x25833,x25834,x25832))
% 81.29/80.94 [2584]~E(x25841,x25842)+E(f533(x25841),f533(x25842))
% 81.29/80.94 [2585]~E(x25851,x25852)+E(f358(x25851),f358(x25852))
% 81.29/80.94 [2586]~E(x25861,x25862)+E(f126(x25861),f126(x25862))
% 81.29/80.94 [2587]~E(x25871,x25872)+E(f609(x25871,x25873,x25874,x25875),f609(x25872,x25873,x25874,x25875))
% 81.29/80.94 [2588]~E(x25881,x25882)+E(f609(x25883,x25881,x25884,x25885),f609(x25883,x25882,x25884,x25885))
% 81.29/80.94 [2589]~E(x25891,x25892)+E(f609(x25893,x25894,x25891,x25895),f609(x25893,x25894,x25892,x25895))
% 81.29/80.94 [2590]~E(x25901,x25902)+E(f609(x25903,x25904,x25905,x25901),f609(x25903,x25904,x25905,x25902))
% 81.29/80.94 [2591]~E(x25911,x25912)+E(f552(x25911,x25913,x25914,x25915),f552(x25912,x25913,x25914,x25915))
% 81.29/80.94 [2592]~E(x25921,x25922)+E(f552(x25923,x25921,x25924,x25925),f552(x25923,x25922,x25924,x25925))
% 81.29/80.94 [2593]~E(x25931,x25932)+E(f552(x25933,x25934,x25931,x25935),f552(x25933,x25934,x25932,x25935))
% 81.29/80.94 [2594]~E(x25941,x25942)+E(f552(x25943,x25944,x25945,x25941),f552(x25943,x25944,x25945,x25942))
% 81.29/80.94 [2595]~E(x25951,x25952)+E(f426(x25951,x25953,x25954,x25955),f426(x25952,x25953,x25954,x25955))
% 81.29/80.94 [2596]~E(x25961,x25962)+E(f426(x25963,x25961,x25964,x25965),f426(x25963,x25962,x25964,x25965))
% 81.29/80.94 [2597]~E(x25971,x25972)+E(f426(x25973,x25974,x25971,x25975),f426(x25973,x25974,x25972,x25975))
% 81.29/80.94 [2598]~E(x25981,x25982)+E(f426(x25983,x25984,x25985,x25981),f426(x25983,x25984,x25985,x25982))
% 81.29/80.94 [2599]~E(x25991,x25992)+E(f133(x25991,x25993,x25994,x25995),f133(x25992,x25993,x25994,x25995))
% 81.29/80.94 [2600]~E(x26001,x26002)+E(f133(x26003,x26001,x26004,x26005),f133(x26003,x26002,x26004,x26005))
% 81.29/80.94 [2601]~E(x26011,x26012)+E(f133(x26013,x26014,x26011,x26015),f133(x26013,x26014,x26012,x26015))
% 81.29/80.94 [2602]~E(x26021,x26022)+E(f133(x26023,x26024,x26025,x26021),f133(x26023,x26024,x26025,x26022))
% 81.29/80.94 [2603]~E(x26031,x26032)+E(f683(x26031,x26033),f683(x26032,x26033))
% 81.29/80.94 [2604]~E(x26041,x26042)+E(f683(x26043,x26041),f683(x26043,x26042))
% 81.29/80.94 [2605]~E(x26051,x26052)+E(f378(x26051,x26053,x26054),f378(x26052,x26053,x26054))
% 81.29/80.94 [2606]~E(x26061,x26062)+E(f378(x26063,x26061,x26064),f378(x26063,x26062,x26064))
% 81.29/80.94 [2607]~E(x26071,x26072)+E(f378(x26073,x26074,x26071),f378(x26073,x26074,x26072))
% 81.29/80.94 [2608]~P1(x26081)+P1(x26082)+~E(x26081,x26082)
% 81.29/80.94 [2609]~P2(x26091)+P2(x26092)+~E(x26091,x26092)
% 81.29/80.94 [2610]~P24(x26101)+P24(x26102)+~E(x26101,x26102)
% 81.29/80.94 [2611]~P25(x26111)+P25(x26112)+~E(x26111,x26112)
% 81.29/80.94 [2612]~P106(x26121)+P106(x26122)+~E(x26121,x26122)
% 81.29/80.94 [2613]~P26(x26131)+P26(x26132)+~E(x26131,x26132)
% 81.29/80.94 [2614]P29(x26142,x26143)+~E(x26141,x26142)+~P29(x26141,x26143)
% 81.29/80.94 [2615]P29(x26153,x26152)+~E(x26151,x26152)+~P29(x26153,x26151)
% 81.29/80.94 [2616]~P105(x26161)+P105(x26162)+~E(x26161,x26162)
% 81.29/80.94 [2617]~P87(x26171)+P87(x26172)+~E(x26171,x26172)
% 81.29/80.94 [2618]~P110(x26181)+P110(x26182)+~E(x26181,x26182)
% 81.29/80.94 [2619]~P123(x26191)+P123(x26192)+~E(x26191,x26192)
% 81.29/80.94 [2620]~P89(x26201)+P89(x26202)+~E(x26201,x26202)
% 81.29/80.94 [2621]P146(x26212,x26213,x26214)+~E(x26211,x26212)+~P146(x26211,x26213,x26214)
% 81.29/80.94 [2622]P146(x26223,x26222,x26224)+~E(x26221,x26222)+~P146(x26223,x26221,x26224)
% 81.29/80.94 [2623]P146(x26233,x26234,x26232)+~E(x26231,x26232)+~P146(x26233,x26234,x26231)
% 81.29/80.94 [2624]~P27(x26241)+P27(x26242)+~E(x26241,x26242)
% 81.29/80.94 [2625]~P107(x26251)+P107(x26252)+~E(x26251,x26252)
% 81.29/80.94 [2626]~P80(x26261)+P80(x26262)+~E(x26261,x26262)
% 81.29/80.94 [2627]P145(x26272,x26273,x26274)+~E(x26271,x26272)+~P145(x26271,x26273,x26274)
% 81.29/80.94 [2628]P145(x26283,x26282,x26284)+~E(x26281,x26282)+~P145(x26283,x26281,x26284)
% 81.29/80.94 [2629]P145(x26293,x26294,x26292)+~E(x26291,x26292)+~P145(x26293,x26294,x26291)
% 81.29/80.94 [2630]P12(x26302,x26303,x26304)+~E(x26301,x26302)+~P12(x26301,x26303,x26304)
% 81.29/80.94 [2631]P12(x26313,x26312,x26314)+~E(x26311,x26312)+~P12(x26313,x26311,x26314)
% 81.29/80.94 [2632]P12(x26323,x26324,x26322)+~E(x26321,x26322)+~P12(x26323,x26324,x26321)
% 81.29/80.94 [2633]~P108(x26331)+P108(x26332)+~E(x26331,x26332)
% 81.29/80.94 [2634]~P63(x26341)+P63(x26342)+~E(x26341,x26342)
% 81.29/80.94 [2635]P35(x26352,x26353,x26354,x26355,x26356)+~E(x26351,x26352)+~P35(x26351,x26353,x26354,x26355,x26356)
% 81.29/80.94 [2636]P35(x26363,x26362,x26364,x26365,x26366)+~E(x26361,x26362)+~P35(x26363,x26361,x26364,x26365,x26366)
% 81.29/80.94 [2637]P35(x26373,x26374,x26372,x26375,x26376)+~E(x26371,x26372)+~P35(x26373,x26374,x26371,x26375,x26376)
% 81.29/80.94 [2638]P35(x26383,x26384,x26385,x26382,x26386)+~E(x26381,x26382)+~P35(x26383,x26384,x26385,x26381,x26386)
% 81.29/80.94 [2639]P35(x26393,x26394,x26395,x26396,x26392)+~E(x26391,x26392)+~P35(x26393,x26394,x26395,x26396,x26391)
% 81.29/80.94 [2640]~P127(x26401)+P127(x26402)+~E(x26401,x26402)
% 81.29/80.94 [2641]~P65(x26411)+P65(x26412)+~E(x26411,x26412)
% 81.29/80.94 [2642]~P64(x26421)+P64(x26422)+~E(x26421,x26422)
% 81.29/80.94 [2643]~P94(x26431)+P94(x26432)+~E(x26431,x26432)
% 81.29/80.94 [2644]~P66(x26441)+P66(x26442)+~E(x26441,x26442)
% 81.29/80.94 [2645]P32(x26452,x26453,x26454)+~E(x26451,x26452)+~P32(x26451,x26453,x26454)
% 81.29/80.94 [2646]P32(x26463,x26462,x26464)+~E(x26461,x26462)+~P32(x26463,x26461,x26464)
% 81.29/80.94 [2647]P32(x26473,x26474,x26472)+~E(x26471,x26472)+~P32(x26473,x26474,x26471)
% 81.29/80.94 [2648]P15(x26482,x26483,x26484,x26485)+~E(x26481,x26482)+~P15(x26481,x26483,x26484,x26485)
% 81.29/80.94 [2649]P15(x26493,x26492,x26494,x26495)+~E(x26491,x26492)+~P15(x26493,x26491,x26494,x26495)
% 81.29/80.94 [2650]P15(x26503,x26504,x26502,x26505)+~E(x26501,x26502)+~P15(x26503,x26504,x26501,x26505)
% 81.29/80.94 [2651]P15(x26513,x26514,x26515,x26512)+~E(x26511,x26512)+~P15(x26513,x26514,x26515,x26511)
% 81.29/80.94 [2652]P38(x26522,x26523)+~E(x26521,x26522)+~P38(x26521,x26523)
% 81.29/80.94 [2653]P38(x26533,x26532)+~E(x26531,x26532)+~P38(x26533,x26531)
% 81.29/80.94 [2654]~P78(x26541)+P78(x26542)+~E(x26541,x26542)
% 81.29/80.94 [2655]~P133(x26551)+P133(x26552)+~E(x26551,x26552)
% 81.29/80.94 [2656]~P62(x26561)+P62(x26562)+~E(x26561,x26562)
% 81.29/80.94 [2657]~P79(x26571)+P79(x26572)+~E(x26571,x26572)
% 81.29/80.94 [2658]~P140(x26581)+P140(x26582)+~E(x26581,x26582)
% 81.29/80.94 [2659]P21(x26592,x26593,x26594,x26595)+~E(x26591,x26592)+~P21(x26591,x26593,x26594,x26595)
% 81.29/80.94 [2660]P21(x26603,x26602,x26604,x26605)+~E(x26601,x26602)+~P21(x26603,x26601,x26604,x26605)
% 81.29/80.94 [2661]P21(x26613,x26614,x26612,x26615)+~E(x26611,x26612)+~P21(x26613,x26614,x26611,x26615)
% 81.29/80.94 [2662]P21(x26623,x26624,x26625,x26622)+~E(x26621,x26622)+~P21(x26623,x26624,x26625,x26621)
% 81.29/80.94 [2663]~P67(x26631)+P67(x26632)+~E(x26631,x26632)
% 81.29/80.94 [2664]~P81(x26641)+P81(x26642)+~E(x26641,x26642)
% 81.29/80.94 [2665]~P40(x26651)+P40(x26652)+~E(x26651,x26652)
% 81.29/80.94 [2666]~P74(x26661)+P74(x26662)+~E(x26661,x26662)
% 81.29/80.94 [2667]~P109(x26671)+P109(x26672)+~E(x26671,x26672)
% 81.29/80.94 [2668]~P84(x26681)+P84(x26682)+~E(x26681,x26682)
% 81.29/80.94 [2669]~P111(x26691)+P111(x26692)+~E(x26691,x26692)
% 81.29/80.94 [2670]~P124(x26701)+P124(x26702)+~E(x26701,x26702)
% 81.29/80.94 [2671]~P68(x26711)+P68(x26712)+~E(x26711,x26712)
% 81.29/80.94 [2672]P9(x26722,x26723,x26724,x26725)+~E(x26721,x26722)+~P9(x26721,x26723,x26724,x26725)
% 81.29/80.94 [2673]P9(x26733,x26732,x26734,x26735)+~E(x26731,x26732)+~P9(x26733,x26731,x26734,x26735)
% 81.29/80.94 [2674]P9(x26743,x26744,x26742,x26745)+~E(x26741,x26742)+~P9(x26743,x26744,x26741,x26745)
% 81.29/80.94 [2675]P9(x26753,x26754,x26755,x26752)+~E(x26751,x26752)+~P9(x26753,x26754,x26755,x26751)
% 81.29/80.94 [2676]~P96(x26761)+P96(x26762)+~E(x26761,x26762)
% 81.29/80.94 [2677]~P69(x26771)+P69(x26772)+~E(x26771,x26772)
% 81.29/80.94 [2678]P48(x26782,x26783,x26784)+~E(x26781,x26782)+~P48(x26781,x26783,x26784)
% 81.29/80.94 [2679]P48(x26793,x26792,x26794)+~E(x26791,x26792)+~P48(x26793,x26791,x26794)
% 81.29/80.94 [2680]P48(x26803,x26804,x26802)+~E(x26801,x26802)+~P48(x26803,x26804,x26801)
% 81.29/80.94 [2681]P55(x26812,x26813)+~E(x26811,x26812)+~P55(x26811,x26813)
% 81.29/80.94 [2682]P55(x26823,x26822)+~E(x26821,x26822)+~P55(x26823,x26821)
% 81.29/80.94 [2683]~P85(x26831)+P85(x26832)+~E(x26831,x26832)
% 81.29/80.94 [2684]~P60(x26841)+P60(x26842)+~E(x26841,x26842)
% 81.29/80.94 [2685]~P112(x26851)+P112(x26852)+~E(x26851,x26852)
% 81.29/80.94 [2686]~P70(x26861)+P70(x26862)+~E(x26861,x26862)
% 81.29/80.94 [2687]P6(x26872,x26873,x26874)+~E(x26871,x26872)+~P6(x26871,x26873,x26874)
% 81.29/80.94 [2688]P6(x26883,x26882,x26884)+~E(x26881,x26882)+~P6(x26883,x26881,x26884)
% 81.29/80.94 [2689]P6(x26893,x26894,x26892)+~E(x26891,x26892)+~P6(x26893,x26894,x26891)
% 81.29/80.94 [2690]~P141(x26901)+P141(x26902)+~E(x26901,x26902)
% 81.29/80.94 [2691]~P86(x26911)+P86(x26912)+~E(x26911,x26912)
% 81.29/80.94 [2692]~P143(x26921)+P143(x26922)+~E(x26921,x26922)
% 81.29/80.94 [2693]~P98(x26931)+P98(x26932)+~E(x26931,x26932)
% 81.29/80.94 [2694]~P73(x26941)+P73(x26942)+~E(x26941,x26942)
% 81.29/80.94 [2695]~P61(x26951)+P61(x26952)+~E(x26951,x26952)
% 81.29/80.94 [2696]~P75(x26961)+P75(x26962)+~E(x26961,x26962)
% 81.29/80.94 [2697]~P120(x26971)+P120(x26972)+~E(x26971,x26972)
% 81.29/80.94 [2698]~P82(x26981)+P82(x26982)+~E(x26981,x26982)
% 81.29/80.94 [2699]~P44(x26991)+P44(x26992)+~E(x26991,x26992)
% 81.29/80.94 [2700]P20(x27002,x27003,x27004)+~E(x27001,x27002)+~P20(x27001,x27003,x27004)
% 81.29/80.94 [2701]P20(x27013,x27012,x27014)+~E(x27011,x27012)+~P20(x27013,x27011,x27014)
% 81.29/80.94 [2702]P20(x27023,x27024,x27022)+~E(x27021,x27022)+~P20(x27023,x27024,x27021)
% 81.29/80.94 [2703]~P102(x27031)+P102(x27032)+~E(x27031,x27032)
% 81.29/80.94 [2704]~P76(x27041)+P76(x27042)+~E(x27041,x27042)
% 81.29/80.94 [2705]~P71(x27051)+P71(x27052)+~E(x27051,x27052)
% 81.29/80.94 [2706]~P100(x27061)+P100(x27062)+~E(x27061,x27062)
% 81.29/80.94 [2707]P14(x27072,x27073,x27074)+~E(x27071,x27072)+~P14(x27071,x27073,x27074)
% 81.29/80.94 [2708]P14(x27083,x27082,x27084)+~E(x27081,x27082)+~P14(x27083,x27081,x27084)
% 81.29/80.94 [2709]P14(x27093,x27094,x27092)+~E(x27091,x27092)+~P14(x27093,x27094,x27091)
% 81.29/80.94 [2710]P13(x27102,x27103,x27104)+~E(x27101,x27102)+~P13(x27101,x27103,x27104)
% 81.29/80.94 [2711]P13(x27113,x27112,x27114)+~E(x27111,x27112)+~P13(x27113,x27111,x27114)
% 81.29/80.94 [2712]P13(x27123,x27124,x27122)+~E(x27121,x27122)+~P13(x27123,x27124,x27121)
% 81.29/80.94 [2713]~P137(x27131)+P137(x27132)+~E(x27131,x27132)
% 81.29/80.94 [2714]~P88(x27141)+P88(x27142)+~E(x27141,x27142)
% 81.29/80.94 [2715]P36(x27152,x27153,x27154)+~E(x27151,x27152)+~P36(x27151,x27153,x27154)
% 81.29/80.94 [2716]P36(x27163,x27162,x27164)+~E(x27161,x27162)+~P36(x27163,x27161,x27164)
% 81.29/80.94 [2717]P36(x27173,x27174,x27172)+~E(x27171,x27172)+~P36(x27173,x27174,x27171)
% 81.29/80.94 [2718]~P93(x27181)+P93(x27182)+~E(x27181,x27182)
% 81.29/80.94 [2719]~P58(x27191)+P58(x27192)+~E(x27191,x27192)
% 81.29/80.94 [2720]P34(x27202,x27203,x27204)+~E(x27201,x27202)+~P34(x27201,x27203,x27204)
% 81.29/80.94 [2721]P34(x27213,x27212,x27214)+~E(x27211,x27212)+~P34(x27213,x27211,x27214)
% 81.29/80.94 [2722]P34(x27223,x27224,x27222)+~E(x27221,x27222)+~P34(x27223,x27224,x27221)
% 81.29/80.94 [2723]~P97(x27231)+P97(x27232)+~E(x27231,x27232)
% 81.29/80.94 [2724]~P138(x27241)+P138(x27242)+~E(x27241,x27242)
% 81.29/80.94 [2725]~P136(x27251)+P136(x27252)+~E(x27251,x27252)
% 81.29/80.94 [2726]P57(x27262,x27263)+~E(x27261,x27262)+~P57(x27261,x27263)
% 81.29/80.94 [2727]P57(x27273,x27272)+~E(x27271,x27272)+~P57(x27273,x27271)
% 81.29/80.94 [2728]~P83(x27281)+P83(x27282)+~E(x27281,x27282)
% 81.29/80.94 [2729]P31(x27292,x27293)+~E(x27291,x27292)+~P31(x27291,x27293)
% 81.29/80.94 [2730]P31(x27303,x27302)+~E(x27301,x27302)+~P31(x27303,x27301)
% 81.29/80.94 [2731]P50(x27312,x27313)+~E(x27311,x27312)+~P50(x27311,x27313)
% 81.29/80.94 [2732]P50(x27323,x27322)+~E(x27321,x27322)+~P50(x27323,x27321)
% 81.29/80.94 [2733]~P128(x27331)+P128(x27332)+~E(x27331,x27332)
% 81.29/80.94 [2734]P52(x27342,x27343,x27344)+~E(x27341,x27342)+~P52(x27341,x27343,x27344)
% 81.29/80.94 [2735]P52(x27353,x27352,x27354)+~E(x27351,x27352)+~P52(x27353,x27351,x27354)
% 81.29/80.94 [2736]P52(x27363,x27364,x27362)+~E(x27361,x27362)+~P52(x27363,x27364,x27361)
% 81.29/80.94 [2737]~P130(x27371)+P130(x27372)+~E(x27371,x27372)
% 81.29/80.94 [2738]~P132(x27381)+P132(x27382)+~E(x27381,x27382)
% 81.29/80.94 [2739]~P142(x27391)+P142(x27392)+~E(x27391,x27392)
% 81.29/80.94 [2740]P53(x27402,x27403,x27404)+~E(x27401,x27402)+~P53(x27401,x27403,x27404)
% 81.29/80.94 [2741]P53(x27413,x27412,x27414)+~E(x27411,x27412)+~P53(x27413,x27411,x27414)
% 81.29/80.94 [2742]P53(x27423,x27424,x27422)+~E(x27421,x27422)+~P53(x27423,x27424,x27421)
% 81.29/80.94 [2743]~P116(x27431)+P116(x27432)+~E(x27431,x27432)
% 81.29/80.94 [2744]~P28(x27441)+P28(x27442)+~E(x27441,x27442)
% 81.29/80.94 [2745]P16(x27452,x27453,x27454,x27455)+~E(x27451,x27452)+~P16(x27451,x27453,x27454,x27455)
% 81.29/80.94 [2746]P16(x27463,x27462,x27464,x27465)+~E(x27461,x27462)+~P16(x27463,x27461,x27464,x27465)
% 81.29/80.94 [2747]P16(x27473,x27474,x27472,x27475)+~E(x27471,x27472)+~P16(x27473,x27474,x27471,x27475)
% 81.29/80.94 [2748]P16(x27483,x27484,x27485,x27482)+~E(x27481,x27482)+~P16(x27483,x27484,x27485,x27481)
% 81.29/80.94 [2749]P33(x27492,x27493,x27494,x27495)+~E(x27491,x27492)+~P33(x27491,x27493,x27494,x27495)
% 81.29/80.94 [2750]P33(x27503,x27502,x27504,x27505)+~E(x27501,x27502)+~P33(x27503,x27501,x27504,x27505)
% 81.29/80.94 [2751]P33(x27513,x27514,x27512,x27515)+~E(x27511,x27512)+~P33(x27513,x27514,x27511,x27515)
% 81.29/80.94 [2752]P33(x27523,x27524,x27525,x27522)+~E(x27521,x27522)+~P33(x27523,x27524,x27525,x27521)
% 81.29/80.94 [2753]~P131(x27531)+P131(x27532)+~E(x27531,x27532)
% 81.29/80.94 [2754]~P135(x27541)+P135(x27542)+~E(x27541,x27542)
% 81.29/80.94 [2755]~P95(x27551)+P95(x27552)+~E(x27551,x27552)
% 81.29/80.94 [2756]~P126(x27561)+P126(x27562)+~E(x27561,x27562)
% 81.29/80.94 [2757]~P139(x27571)+P139(x27572)+~E(x27571,x27572)
% 81.29/80.94 [2758]~P125(x27581)+P125(x27582)+~E(x27581,x27582)
% 81.29/80.94 [2759]~P115(x27591)+P115(x27592)+~E(x27591,x27592)
% 81.29/80.94 [2760]P19(x27602,x27603,x27604,x27605,x27606,x27607)+~E(x27601,x27602)+~P19(x27601,x27603,x27604,x27605,x27606,x27607)
% 81.29/80.94 [2761]P19(x27613,x27612,x27614,x27615,x27616,x27617)+~E(x27611,x27612)+~P19(x27613,x27611,x27614,x27615,x27616,x27617)
% 81.29/80.94 [2762]P19(x27623,x27624,x27622,x27625,x27626,x27627)+~E(x27621,x27622)+~P19(x27623,x27624,x27621,x27625,x27626,x27627)
% 81.29/80.94 [2763]P19(x27633,x27634,x27635,x27632,x27636,x27637)+~E(x27631,x27632)+~P19(x27633,x27634,x27635,x27631,x27636,x27637)
% 81.29/80.94 [2764]P19(x27643,x27644,x27645,x27646,x27642,x27647)+~E(x27641,x27642)+~P19(x27643,x27644,x27645,x27646,x27641,x27647)
% 81.29/80.94 [2765]P19(x27653,x27654,x27655,x27656,x27657,x27652)+~E(x27651,x27652)+~P19(x27653,x27654,x27655,x27656,x27657,x27651)
% 81.29/80.94 [2766]~P101(x27661)+P101(x27662)+~E(x27661,x27662)
% 81.29/80.94 [2767]P30(x27672,x27673,x27674)+~E(x27671,x27672)+~P30(x27671,x27673,x27674)
% 81.29/80.94 [2768]P30(x27683,x27682,x27684)+~E(x27681,x27682)+~P30(x27683,x27681,x27684)
% 81.29/80.94 [2769]P30(x27693,x27694,x27692)+~E(x27691,x27692)+~P30(x27693,x27694,x27691)
% 81.29/80.94 [2770]P46(x27702,x27703,x27704)+~E(x27701,x27702)+~P46(x27701,x27703,x27704)
% 81.29/80.94 [2771]P46(x27713,x27712,x27714)+~E(x27711,x27712)+~P46(x27713,x27711,x27714)
% 81.29/80.94 [2772]P46(x27723,x27724,x27722)+~E(x27721,x27722)+~P46(x27723,x27724,x27721)
% 81.29/80.94 [2773]P22(x27732,x27733)+~E(x27731,x27732)+~P22(x27731,x27733)
% 81.29/80.94 [2774]P22(x27743,x27742)+~E(x27741,x27742)+~P22(x27743,x27741)
% 81.29/80.94 [2775]~P113(x27751)+P113(x27752)+~E(x27751,x27752)
% 81.29/80.94 [2776]P5(x27762,x27763)+~E(x27761,x27762)+~P5(x27761,x27763)
% 81.29/80.94 [2777]P5(x27773,x27772)+~E(x27771,x27772)+~P5(x27773,x27771)
% 81.29/80.94 [2778]~P90(x27781)+P90(x27782)+~E(x27781,x27782)
% 81.29/80.94 [2779]P56(x27792,x27793,x27794,x27795)+~E(x27791,x27792)+~P56(x27791,x27793,x27794,x27795)
% 81.29/80.94 [2780]P56(x27803,x27802,x27804,x27805)+~E(x27801,x27802)+~P56(x27803,x27801,x27804,x27805)
% 81.29/80.94 [2781]P56(x27813,x27814,x27812,x27815)+~E(x27811,x27812)+~P56(x27813,x27814,x27811,x27815)
% 81.29/80.94 [2782]P56(x27823,x27824,x27825,x27822)+~E(x27821,x27822)+~P56(x27823,x27824,x27825,x27821)
% 81.29/80.94 [2783]~P144(x27831)+P144(x27832)+~E(x27831,x27832)
% 81.29/80.94 [2784]P10(x27842,x27843,x27844,x27845,x27846,x27847)+~E(x27841,x27842)+~P10(x27841,x27843,x27844,x27845,x27846,x27847)
% 81.29/80.94 [2785]P10(x27853,x27852,x27854,x27855,x27856,x27857)+~E(x27851,x27852)+~P10(x27853,x27851,x27854,x27855,x27856,x27857)
% 81.29/80.94 [2786]P10(x27863,x27864,x27862,x27865,x27866,x27867)+~E(x27861,x27862)+~P10(x27863,x27864,x27861,x27865,x27866,x27867)
% 81.29/80.94 [2787]P10(x27873,x27874,x27875,x27872,x27876,x27877)+~E(x27871,x27872)+~P10(x27873,x27874,x27875,x27871,x27876,x27877)
% 81.29/80.94 [2788]P10(x27883,x27884,x27885,x27886,x27882,x27887)+~E(x27881,x27882)+~P10(x27883,x27884,x27885,x27886,x27881,x27887)
% 81.29/80.94 [2789]P10(x27893,x27894,x27895,x27896,x27897,x27892)+~E(x27891,x27892)+~P10(x27893,x27894,x27895,x27896,x27897,x27891)
% 81.29/80.94 [2790]~P99(x27901)+P99(x27902)+~E(x27901,x27902)
% 81.29/80.94 [2791]P51(x27912,x27913,x27914,x27915,x27916,x27917,x27918)+~E(x27911,x27912)+~P51(x27911,x27913,x27914,x27915,x27916,x27917,x27918)
% 81.29/80.94 [2792]P51(x27923,x27922,x27924,x27925,x27926,x27927,x27928)+~E(x27921,x27922)+~P51(x27923,x27921,x27924,x27925,x27926,x27927,x27928)
% 81.29/80.94 [2793]P51(x27933,x27934,x27932,x27935,x27936,x27937,x27938)+~E(x27931,x27932)+~P51(x27933,x27934,x27931,x27935,x27936,x27937,x27938)
% 81.29/80.94 [2794]P51(x27943,x27944,x27945,x27942,x27946,x27947,x27948)+~E(x27941,x27942)+~P51(x27943,x27944,x27945,x27941,x27946,x27947,x27948)
% 81.29/80.94 [2795]P51(x27953,x27954,x27955,x27956,x27952,x27957,x27958)+~E(x27951,x27952)+~P51(x27953,x27954,x27955,x27956,x27951,x27957,x27958)
% 81.29/80.94 [2796]P51(x27963,x27964,x27965,x27966,x27967,x27962,x27968)+~E(x27961,x27962)+~P51(x27963,x27964,x27965,x27966,x27967,x27961,x27968)
% 81.29/80.94 [2797]P51(x27973,x27974,x27975,x27976,x27977,x27978,x27972)+~E(x27971,x27972)+~P51(x27973,x27974,x27975,x27976,x27977,x27978,x27971)
% 81.29/80.94 [2798]~P114(x27981)+P114(x27982)+~E(x27981,x27982)
% 81.29/80.94 [2799]P23(x27992,x27993,x27994)+~E(x27991,x27992)+~P23(x27991,x27993,x27994)
% 81.29/80.94 [2800]P23(x28003,x28002,x28004)+~E(x28001,x28002)+~P23(x28003,x28001,x28004)
% 81.29/80.94 [2801]P23(x28013,x28014,x28012)+~E(x28011,x28012)+~P23(x28013,x28014,x28011)
% 81.29/80.94 [2802]P43(x28022,x28023)+~E(x28021,x28022)+~P43(x28021,x28023)
% 81.29/80.94 [2803]P43(x28033,x28032)+~E(x28031,x28032)+~P43(x28033,x28031)
% 81.29/80.94 [2804]P54(x28042,x28043,x28044,x28045,x28046)+~E(x28041,x28042)+~P54(x28041,x28043,x28044,x28045,x28046)
% 81.29/80.94 [2805]P54(x28053,x28052,x28054,x28055,x28056)+~E(x28051,x28052)+~P54(x28053,x28051,x28054,x28055,x28056)
% 81.29/80.94 [2806]P54(x28063,x28064,x28062,x28065,x28066)+~E(x28061,x28062)+~P54(x28063,x28064,x28061,x28065,x28066)
% 81.29/80.94 [2807]P54(x28073,x28074,x28075,x28072,x28076)+~E(x28071,x28072)+~P54(x28073,x28074,x28075,x28071,x28076)
% 81.29/80.94 [2808]P54(x28083,x28084,x28085,x28086,x28082)+~E(x28081,x28082)+~P54(x28083,x28084,x28085,x28086,x28081)
% 81.29/80.94 [2809]P42(x28092,x28093,x28094,x28095,x28096,x28097)+~E(x28091,x28092)+~P42(x28091,x28093,x28094,x28095,x28096,x28097)
% 81.29/80.94 [2810]P42(x28103,x28102,x28104,x28105,x28106,x28107)+~E(x28101,x28102)+~P42(x28103,x28101,x28104,x28105,x28106,x28107)
% 81.29/80.94 [2811]P42(x28113,x28114,x28112,x28115,x28116,x28117)+~E(x28111,x28112)+~P42(x28113,x28114,x28111,x28115,x28116,x28117)
% 81.29/80.94 [2812]P42(x28123,x28124,x28125,x28122,x28126,x28127)+~E(x28121,x28122)+~P42(x28123,x28124,x28125,x28121,x28126,x28127)
% 81.29/80.94 [2813]P42(x28133,x28134,x28135,x28136,x28132,x28137)+~E(x28131,x28132)+~P42(x28133,x28134,x28135,x28136,x28131,x28137)
% 81.29/80.94 [2814]P42(x28143,x28144,x28145,x28146,x28147,x28142)+~E(x28141,x28142)+~P42(x28143,x28144,x28145,x28146,x28147,x28141)
% 81.29/80.94 [2815]P8(x28152,x28153,x28154)+~E(x28151,x28152)+~P8(x28151,x28153,x28154)
% 81.29/80.94 [2816]P8(x28163,x28162,x28164)+~E(x28161,x28162)+~P8(x28163,x28161,x28164)
% 81.29/80.94 [2817]P8(x28173,x28174,x28172)+~E(x28171,x28172)+~P8(x28173,x28174,x28171)
% 81.29/80.94 [2818]~P59(x28181)+P59(x28182)+~E(x28181,x28182)
% 81.29/80.94 [2819]P7(x28192,x28193,x28194)+~E(x28191,x28192)+~P7(x28191,x28193,x28194)
% 81.29/80.94 [2820]P7(x28203,x28202,x28204)+~E(x28201,x28202)+~P7(x28203,x28201,x28204)
% 81.29/80.94 [2821]P7(x28213,x28214,x28212)+~E(x28211,x28212)+~P7(x28213,x28214,x28211)
% 81.29/80.94 [2822]~P134(x28221)+P134(x28222)+~E(x28221,x28222)
% 81.29/80.94 [2823]~P91(x28231)+P91(x28232)+~E(x28231,x28232)
% 81.29/80.94 [2824]~P104(x28241)+P104(x28242)+~E(x28241,x28242)
% 81.29/80.94 [2825]P17(x28252,x28253,x28254,x28255,x28256)+~E(x28251,x28252)+~P17(x28251,x28253,x28254,x28255,x28256)
% 81.29/80.94 [2826]P17(x28263,x28262,x28264,x28265,x28266)+~E(x28261,x28262)+~P17(x28263,x28261,x28264,x28265,x28266)
% 81.29/80.94 [2827]P17(x28273,x28274,x28272,x28275,x28276)+~E(x28271,x28272)+~P17(x28273,x28274,x28271,x28275,x28276)
% 81.29/80.94 [2828]P17(x28283,x28284,x28285,x28282,x28286)+~E(x28281,x28282)+~P17(x28283,x28284,x28285,x28281,x28286)
% 81.29/80.94 [2829]P17(x28293,x28294,x28295,x28296,x28292)+~E(x28291,x28292)+~P17(x28293,x28294,x28295,x28296,x28291)
% 81.29/80.94 [2830]P11(x28302,x28303,x28304)+~E(x28301,x28302)+~P11(x28301,x28303,x28304)
% 81.29/80.94 [2831]P11(x28313,x28312,x28314)+~E(x28311,x28312)+~P11(x28313,x28311,x28314)
% 81.29/80.94 [2832]P11(x28323,x28324,x28322)+~E(x28321,x28322)+~P11(x28323,x28324,x28321)
% 81.29/80.94 [2833]P45(x28332,x28333)+~E(x28331,x28332)+~P45(x28331,x28333)
% 81.29/80.94 [2834]P45(x28343,x28342)+~E(x28341,x28342)+~P45(x28343,x28341)
% 81.29/80.94 [2835]~P77(x28351)+P77(x28352)+~E(x28351,x28352)
% 81.29/80.94 [2836]~P103(x28361)+P103(x28362)+~E(x28361,x28362)
% 81.29/80.94 [2837]~P129(x28371)+P129(x28372)+~E(x28371,x28372)
% 81.29/80.94 [2838]~P72(x28381)+P72(x28382)+~E(x28381,x28382)
% 81.29/80.94 [2839]~P92(x28391)+P92(x28392)+~E(x28391,x28392)
% 81.29/80.94 [2840]~P118(x28401)+P118(x28402)+~E(x28401,x28402)
% 81.29/80.94 [2841]~P121(x28411)+P121(x28412)+~E(x28411,x28412)
% 81.29/80.94 [2842]P4(x28422,x28423,x28424,x28425,x28426)+~E(x28421,x28422)+~P4(x28421,x28423,x28424,x28425,x28426)
% 81.29/80.94 [2843]P4(x28433,x28432,x28434,x28435,x28436)+~E(x28431,x28432)+~P4(x28433,x28431,x28434,x28435,x28436)
% 81.29/80.94 [2844]P4(x28443,x28444,x28442,x28445,x28446)+~E(x28441,x28442)+~P4(x28443,x28444,x28441,x28445,x28446)
% 81.29/80.94 [2845]P4(x28453,x28454,x28455,x28452,x28456)+~E(x28451,x28452)+~P4(x28453,x28454,x28455,x28451,x28456)
% 81.29/80.94 [2846]P4(x28463,x28464,x28465,x28466,x28462)+~E(x28461,x28462)+~P4(x28463,x28464,x28465,x28466,x28461)
% 81.29/80.94 [2847]P3(x28472,x28473,x28474)+~E(x28471,x28472)+~P3(x28471,x28473,x28474)
% 81.29/80.94 [2848]P3(x28483,x28482,x28484)+~E(x28481,x28482)+~P3(x28483,x28481,x28484)
% 81.29/80.94 [2849]P3(x28493,x28494,x28492)+~E(x28491,x28492)+~P3(x28493,x28494,x28491)
% 81.29/80.94 [2850]~P37(x28501)+P37(x28502)+~E(x28501,x28502)
% 81.29/80.94 [2851]P47(x28512,x28513,x28514)+~E(x28511,x28512)+~P47(x28511,x28513,x28514)
% 81.29/80.94 [2852]P47(x28523,x28522,x28524)+~E(x28521,x28522)+~P47(x28523,x28521,x28524)
% 81.29/80.94 [2853]P47(x28533,x28534,x28532)+~E(x28531,x28532)+~P47(x28533,x28534,x28531)
% 81.29/80.94 [2854]P39(x28542,x28543)+~E(x28541,x28542)+~P39(x28541,x28543)
% 81.29/80.94 [2855]P39(x28553,x28552)+~E(x28551,x28552)+~P39(x28553,x28551)
% 81.29/80.94 [2856]P18(x28562,x28563,x28564,x28565,x28566,x28567)+~E(x28561,x28562)+~P18(x28561,x28563,x28564,x28565,x28566,x28567)
% 81.29/80.94 [2857]P18(x28573,x28572,x28574,x28575,x28576,x28577)+~E(x28571,x28572)+~P18(x28573,x28571,x28574,x28575,x28576,x28577)
% 81.29/80.94 [2858]P18(x28583,x28584,x28582,x28585,x28586,x28587)+~E(x28581,x28582)+~P18(x28583,x28584,x28581,x28585,x28586,x28587)
% 81.29/80.94 [2859]P18(x28593,x28594,x28595,x28592,x28596,x28597)+~E(x28591,x28592)+~P18(x28593,x28594,x28595,x28591,x28596,x28597)
% 81.29/80.94 [2860]P18(x28603,x28604,x28605,x28606,x28602,x28607)+~E(x28601,x28602)+~P18(x28603,x28604,x28605,x28606,x28601,x28607)
% 81.29/80.94 [2861]P18(x28613,x28614,x28615,x28616,x28617,x28612)+~E(x28611,x28612)+~P18(x28613,x28614,x28615,x28616,x28617,x28611)
% 81.29/80.94 [2862]P41(x28622,x28623,x28624,x28625)+~E(x28621,x28622)+~P41(x28621,x28623,x28624,x28625)
% 81.29/80.94 [2863]P41(x28633,x28632,x28634,x28635)+~E(x28631,x28632)+~P41(x28633,x28631,x28634,x28635)
% 81.29/80.94 [2864]P41(x28643,x28644,x28642,x28645)+~E(x28641,x28642)+~P41(x28643,x28644,x28641,x28645)
% 81.29/80.94 [2865]P41(x28653,x28654,x28655,x28652)+~E(x28651,x28652)+~P41(x28653,x28654,x28655,x28651)
% 81.29/80.94 [2866]~P119(x28661)+P119(x28662)+~E(x28661,x28662)
% 81.29/80.94 [2867]P49(x28672,x28673)+~E(x28671,x28672)+~P49(x28671,x28673)
% 81.29/80.94 [2868]P49(x28683,x28682)+~E(x28681,x28682)+~P49(x28683,x28681)
% 81.29/80.94 [2869]~P122(x28691)+P122(x28692)+~E(x28691,x28692)
% 81.29/80.94 [2870]~P117(x28701)+P117(x28702)+~E(x28701,x28702)
% 81.29/80.94
% 81.29/80.94 %-------------------------------------------
% 81.39/80.98 cnf(10208,plain,
% 81.39/80.98 (E(f328(f253(x102081,x102081),f254(x102081,x102082)),x102082)),
% 81.39/80.98 inference(rename_variables,[],[3241])).
% 81.39/80.98 cnf(10211,plain,
% 81.39/80.98 (~E(f328(a118,x102111),x102111)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(10214,plain,
% 81.39/80.98 (~E(f328(a118,x102141),x102141)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(10217,plain,
% 81.39/80.98 (E(f328(f253(x102171,x102171),f254(x102171,x102172)),x102172)),
% 81.39/80.98 inference(rename_variables,[],[3241])).
% 81.39/80.98 cnf(10224,plain,
% 81.39/80.98 (~E(f328(a118,x102241),x102241)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(10235,plain,
% 81.39/80.98 (~E(f328(a118,x102351),x102351)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(10240,plain,
% 81.39/80.98 (~P24(f328(f63(x102401,x102402,f193(f885(x102401,a871))),x102403))),
% 81.39/80.98 inference(rename_variables,[],[4556])).
% 81.39/80.98 cnf(10243,plain,
% 81.39/80.98 (~P24(f328(f63(x102431,x102432,f193(f885(x102431,a871))),x102433))),
% 81.39/80.98 inference(rename_variables,[],[4556])).
% 81.39/80.98 cnf(10246,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x102461),f2(a877)))),
% 81.39/80.98 inference(rename_variables,[],[4532])).
% 81.39/80.98 cnf(10249,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x102491),f2(a877)))),
% 81.39/80.98 inference(rename_variables,[],[4532])).
% 81.39/80.98 cnf(10266,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a877),f328(a118,x102661)),x102661))),
% 81.39/80.98 inference(rename_variables,[],[4541])).
% 81.39/80.98 cnf(10269,plain,
% 81.39/80.98 (~E(f328(f328(f150(x102691),x102692),x102693),x102693)),
% 81.39/80.98 inference(rename_variables,[],[4484])).
% 81.39/80.98 cnf(10275,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x102751),f2(a877)))),
% 81.39/80.98 inference(rename_variables,[],[4532])).
% 81.39/80.98 cnf(10278,plain,
% 81.39/80.98 (E(f328(f253(x102781,x102781),f254(x102781,x102782)),x102782)),
% 81.39/80.98 inference(rename_variables,[],[3241])).
% 81.39/80.98 cnf(10281,plain,
% 81.39/80.98 (E(f328(f253(x102811,x102811),f254(x102811,x102812)),x102812)),
% 81.39/80.98 inference(rename_variables,[],[3241])).
% 81.39/80.98 cnf(10288,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),f328(f328(f81(a877),x102881),x102882)),x102882))),
% 81.39/80.98 inference(rename_variables,[],[4558])).
% 81.39/80.98 cnf(10291,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),f328(f328(f81(a877),x102911),x102912)),x102912))),
% 81.39/80.98 inference(rename_variables,[],[4558])).
% 81.39/80.98 cnf(10312,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x103121),x103121))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(10315,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),f45(a877,x103151,x103152)),x103151))),
% 81.39/80.98 inference(rename_variables,[],[3743])).
% 81.39/80.98 cnf(10336,plain,
% 81.39/80.98 (E(f328(f38(a877),f328(f250(a877),x103361)),x103361)),
% 81.39/80.98 inference(rename_variables,[],[3175])).
% 81.39/80.98 cnf(10344,plain,
% 81.39/80.98 (~E(f328(a118,x103441),x103441)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(10347,plain,
% 81.39/80.98 (~E(f328(a118,x103471),x103471)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(10350,plain,
% 81.39/80.98 (~E(f328(a118,x103501),x103501)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(10355,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x103551),f328(a118,x103551)))),
% 81.39/80.98 inference(rename_variables,[],[3356])).
% 81.39/80.98 cnf(10364,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x103641),x103641))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(10371,plain,
% 81.39/80.98 (E(f328(f253(x103711,x103711),f254(x103711,x103712)),x103712)),
% 81.39/80.98 inference(rename_variables,[],[3241])).
% 81.39/80.98 cnf(10374,plain,
% 81.39/80.98 (E(f328(f253(x103741,x103741),f254(x103741,x103742)),x103742)),
% 81.39/80.98 inference(rename_variables,[],[3241])).
% 81.39/80.98 cnf(10393,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x103931),x103931))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(10402,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x104021),x104021))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(10407,plain,
% 81.39/80.98 (~E(f328(f328(f328(f73(x104071,f881(x104072)),x104073),x104074),f328(f236(x104072),x104075)),f328(f16(f881(x104072),x104071),f196(x104072)))),
% 81.39/80.98 inference(rename_variables,[],[4553])).
% 81.39/80.98 cnf(10434,plain,
% 81.39/80.98 (~E(f328(f328(f150(x104341),x104342),x104343),x104343)),
% 81.39/80.98 inference(rename_variables,[],[4484])).
% 81.39/80.98 cnf(10437,plain,
% 81.39/80.98 (~E(f328(a26,x104371),f34(x104372,x104373))),
% 81.39/80.98 inference(rename_variables,[],[4473])).
% 81.39/80.98 cnf(10448,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x104481),x104481))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(10453,plain,
% 81.39/80.98 (~E(f328(a118,x104531),x104531)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(10460,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x104601),x104601))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(10473,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x104731),f328(a118,x104731)))),
% 81.39/80.98 inference(rename_variables,[],[3356])).
% 81.39/80.98 cnf(10478,plain,
% 81.39/80.98 (E(f328(f328(f127(x104781),f119(x104781)),x104782),x104782)),
% 81.39/80.98 inference(rename_variables,[],[3236])).
% 81.39/80.98 cnf(10496,plain,
% 81.39/80.98 (~P24(f328(f63(x104961,x104962,f193(f885(x104961,a871))),x104963))),
% 81.39/80.98 inference(rename_variables,[],[4556])).
% 81.39/80.98 cnf(10515,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x105151),x105151))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(10530,plain,
% 81.39/80.98 (~E(f328(a26,x105301),f34(x105302,x105303))),
% 81.39/80.98 inference(rename_variables,[],[4473])).
% 81.39/80.98 cnf(10539,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x105391),x105391))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(10544,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x105441),f328(a118,x105441)))),
% 81.39/80.98 inference(rename_variables,[],[3356])).
% 81.39/80.98 cnf(10547,plain,
% 81.39/80.98 (~P24(f328(f63(x105471,x105472,f193(f885(x105471,a871))),x105473))),
% 81.39/80.98 inference(rename_variables,[],[4556])).
% 81.39/80.98 cnf(10550,plain,
% 81.39/80.98 (~P24(f328(f63(x105501,x105502,f193(f885(x105501,a871))),x105503))),
% 81.39/80.98 inference(rename_variables,[],[4556])).
% 81.39/80.98 cnf(10555,plain,
% 81.39/80.98 (~P24(f328(f63(x105551,x105552,f193(f885(x105551,a871))),x105553))),
% 81.39/80.98 inference(rename_variables,[],[4556])).
% 81.39/80.98 cnf(10566,plain,
% 81.39/80.98 (~E(f328(a118,x105661),x105661)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(10591,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x105911),x105911))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(10594,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x105941),f328(f328(f82(a877),x105941),x105941)))),
% 81.39/80.98 inference(rename_variables,[],[3555])).
% 81.39/80.98 cnf(10597,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x105971),f328(f328(f82(a877),x105971),x105971)))),
% 81.39/80.98 inference(rename_variables,[],[3555])).
% 81.39/80.98 cnf(10600,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x106001),f328(a118,f328(f328(f81(a877),x106002),x106001))))),
% 81.39/80.98 inference(rename_variables,[],[3736])).
% 81.39/80.98 cnf(10605,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x106051),f328(a118,x106051)))),
% 81.39/80.98 inference(rename_variables,[],[3356])).
% 81.39/80.98 cnf(10608,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x106081),f328(a118,x106081)))),
% 81.39/80.98 inference(rename_variables,[],[3356])).
% 81.39/80.98 cnf(10611,plain,
% 81.39/80.98 (P24(f328(f328(f330(x106111),x106112),f252(f885(x106111,a871))))),
% 81.39/80.98 inference(rename_variables,[],[3444])).
% 81.39/80.98 cnf(10626,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a877),f328(a118,x106261)),x106261))),
% 81.39/80.98 inference(rename_variables,[],[4541])).
% 81.39/80.98 cnf(10629,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a877),f328(a118,x106291)),x106291))),
% 81.39/80.98 inference(rename_variables,[],[4541])).
% 81.39/80.98 cnf(10632,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),f328(f328(f81(a877),x106321),x106322)),x106322))),
% 81.39/80.98 inference(rename_variables,[],[4558])).
% 81.39/80.98 cnf(10635,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),f328(f328(f81(a877),x106351),x106352)),x106352))),
% 81.39/80.98 inference(rename_variables,[],[4558])).
% 81.39/80.98 cnf(10638,plain,
% 81.39/80.98 (P24(f328(f252(f885(x106381,a871)),x106382))),
% 81.39/80.98 inference(rename_variables,[],[3350])).
% 81.39/80.98 cnf(10641,plain,
% 81.39/80.98 (E(f328(f38(a877),f328(f250(a877),x106411)),x106411)),
% 81.39/80.98 inference(rename_variables,[],[3175])).
% 81.39/80.98 cnf(10644,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x106441),f328(a118,x106441)))),
% 81.39/80.98 inference(rename_variables,[],[3356])).
% 81.39/80.98 cnf(10651,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x106511),x106511))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(10656,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x106561),x106561))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(10665,plain,
% 81.39/80.98 (E(f328(f253(x106651,x106651),f254(x106651,x106652)),x106652)),
% 81.39/80.98 inference(rename_variables,[],[3241])).
% 81.39/80.98 cnf(10668,plain,
% 81.39/80.98 (P24(f328(f252(f885(x106681,a871)),x106682))),
% 81.39/80.98 inference(rename_variables,[],[3350])).
% 81.39/80.98 cnf(10671,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),f2(a877)),x106711))),
% 81.39/80.98 inference(rename_variables,[],[3307])).
% 81.39/80.98 cnf(10674,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x106741,a871)),f193(f885(x106741,a871))),x106742))),
% 81.39/80.98 inference(rename_variables,[],[3734])).
% 81.39/80.98 cnf(10677,plain,
% 81.39/80.98 (P24(f328(f252(f885(x106771,a871)),x106772))),
% 81.39/80.98 inference(rename_variables,[],[3350])).
% 81.39/80.98 cnf(10680,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x106801),f328(f328(f82(a877),x106801),x106801)))),
% 81.39/80.98 inference(rename_variables,[],[3555])).
% 81.39/80.98 cnf(10685,plain,
% 81.39/80.98 (E(f172(x106851,x106852,f119(x106851)),x106852)),
% 81.39/80.98 inference(rename_variables,[],[3219])).
% 81.39/80.98 cnf(10720,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x107201),x107201))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(10731,plain,
% 81.39/80.98 (~P24(f328(f328(f193(f885(x107311,f885(x107312,a871))),x107313),x107314))),
% 81.39/80.98 inference(rename_variables,[],[4562])).
% 81.39/80.98 cnf(10738,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x107381),f328(a118,x107381)))),
% 81.39/80.98 inference(rename_variables,[],[3356])).
% 81.39/80.98 cnf(10743,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x107431),x107431))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(10748,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x107481),f2(a877)))),
% 81.39/80.98 inference(rename_variables,[],[4532])).
% 81.39/80.98 cnf(10761,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x107611),f2(a877)))),
% 81.39/80.98 inference(rename_variables,[],[4532])).
% 81.39/80.98 cnf(10764,plain,
% 81.39/80.98 (~P24(f328(f328(f245(f885(x107641,a871)),x107642),f193(f885(x107641,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4554])).
% 81.39/80.98 cnf(10767,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x107671),x107671))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(10770,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x107701),x107701))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(10785,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x107851),x107851))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(10794,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x107941),x107942),f193(f885(x107941,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(10803,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x108031),x108031))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(10806,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x108061),x108062),f193(f885(x108061,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(10809,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x108091,a871)),f328(f307(x108092,x108091,x108093),f328(f308(x108092,x108091,x108093),x108094))),x108094))),
% 81.39/80.98 inference(rename_variables,[],[4171])).
% 81.39/80.98 cnf(10816,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x108161,a871)),f328(f171(x108161),f328(f135(x108161,x108162),x108163))),f328(f171(x108161),x108163)))),
% 81.39/80.98 inference(rename_variables,[],[3932])).
% 81.39/80.98 cnf(10819,plain,
% 81.39/80.98 (E(f328(f307(x108191,x108191,f5(x108191)),x108192),x108192)),
% 81.39/80.98 inference(rename_variables,[],[3346])).
% 81.39/80.98 cnf(10826,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),f2(a877)),x108261))),
% 81.39/80.98 inference(rename_variables,[],[3307])).
% 81.39/80.98 cnf(10829,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x108291),x108291))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(10832,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x108321),x108321))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(10835,plain,
% 81.39/80.98 (~P24(f328(f328(f193(f885(x108351,f885(x108352,a871))),x108353),x108354))),
% 81.39/80.98 inference(rename_variables,[],[4562])).
% 81.39/80.98 cnf(10842,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x108421),x108421))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(10853,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x108531),f328(f328(f82(a877),x108531),x108531)))),
% 81.39/80.98 inference(rename_variables,[],[3555])).
% 81.39/80.98 cnf(10859,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x108591),f328(a118,f328(f328(f81(a877),x108592),x108591))))),
% 81.39/80.98 inference(rename_variables,[],[3736])).
% 81.39/80.98 cnf(10866,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x108661),x108661))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(10869,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x108691),x108691))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(10872,plain,
% 81.39/80.98 (~E(f328(a118,x108721),x108721)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(10877,plain,
% 81.39/80.98 (P24(f328(f328(f330(x108771),x108772),f252(f885(x108771,a871))))),
% 81.39/80.98 inference(rename_variables,[],[3444])).
% 81.39/80.98 cnf(10882,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x108821),f2(a877)))),
% 81.39/80.98 inference(rename_variables,[],[4532])).
% 81.39/80.98 cnf(10897,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),f2(a877)),x108971))),
% 81.39/80.98 inference(rename_variables,[],[3307])).
% 81.39/80.98 cnf(10904,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x109041),x109041))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(10915,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x109151),x109152),f193(f885(x109151,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(10923,plain,
% 81.39/80.98 (P24(f328(f328(f330(x109231),x109232),f252(f885(x109231,a871))))),
% 81.39/80.98 inference(rename_variables,[],[3444])).
% 81.39/80.98 cnf(10926,plain,
% 81.39/80.98 (~P24(f328(f328(f330(f884(f878(x109261),f878(x109261))),f328(f328(f257(f878(x109261),f878(x109261)),x109262),f119(x109261))),f144(x109261,x109263)))),
% 81.39/80.98 inference(rename_variables,[],[4566])).
% 81.39/80.98 cnf(10933,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x109331),x109332),f193(f885(x109331,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(10936,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x109361),x109362),f193(f885(x109361,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(10939,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x109391,a871)),x109392),f328(f328(f306(x109391),x109393),x109392)))),
% 81.39/80.98 inference(rename_variables,[],[3732])).
% 81.39/80.98 cnf(10942,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x109421),x109421))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(10945,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x109451,a871)),x109452),f328(f328(f306(x109451),x109453),x109452)))),
% 81.39/80.98 inference(rename_variables,[],[3732])).
% 81.39/80.98 cnf(10960,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x109601,a871)),x109602),f328(f328(f306(x109601),x109603),x109602)))),
% 81.39/80.98 inference(rename_variables,[],[3732])).
% 81.39/80.98 cnf(10965,plain,
% 81.39/80.98 (~P24(f328(f63(x109651,x109652,f193(f885(x109651,a871))),x109653))),
% 81.39/80.98 inference(rename_variables,[],[4556])).
% 81.39/80.98 cnf(10978,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x109781),f328(a118,x109781)))),
% 81.39/80.98 inference(rename_variables,[],[3356])).
% 81.39/80.98 cnf(10988,plain,
% 81.39/80.98 (~E(f328(f307(x109881,f885(x109881,a871),x109882),x109883),f328(f305(x109881),x109883))),
% 81.39/80.98 inference(rename_variables,[],[4542])).
% 81.39/80.98 cnf(10991,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x109911),x109912),f193(f885(x109911,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(10994,plain,
% 81.39/80.98 (P24(f328(f328(f330(f884(x109941,x109941)),f328(f328(f257(x109941,x109941),x109942),x109942)),f304(x109941,x109943)))),
% 81.39/80.98 inference(rename_variables,[],[3922])).
% 81.39/80.98 cnf(10997,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x109971,a871)),x109972),f252(f885(x109971,a871))))),
% 81.39/80.98 inference(rename_variables,[],[3668])).
% 81.39/80.98 cnf(11000,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x110001,a871)),f328(f171(x110001),f169(x110001,x110002,x110003))),f328(f171(x110001),x110003)))),
% 81.39/80.98 inference(rename_variables,[],[3983])).
% 81.39/80.98 cnf(11016,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x110161,a871)),f193(f885(x110161,a871))),x110162))),
% 81.39/80.98 inference(rename_variables,[],[3734])).
% 81.39/80.98 cnf(11027,plain,
% 81.39/80.98 (~P24(f328(f328(f330(f884(f878(x110271),f878(x110271))),f328(f328(f257(f878(x110271),f878(x110271)),x110272),f119(x110271))),f146(x110271,x110273)))),
% 81.39/80.98 inference(rename_variables,[],[4567])).
% 81.39/80.98 cnf(11038,plain,
% 81.39/80.98 (~E(f328(a118,x110381),x110381)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(11041,plain,
% 81.39/80.98 (~E(f328(a118,x110411),x110411)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(11053,plain,
% 81.39/80.98 (P21(x110531,x110531,f5(x110531),x110532)),
% 81.39/80.98 inference(rename_variables,[],[3527])).
% 81.39/80.98 cnf(11058,plain,
% 81.39/80.98 (~E(f328(f307(x110581,f885(x110581,a871),x110582),x110583),f328(f305(x110581),x110583))),
% 81.39/80.98 inference(rename_variables,[],[4542])).
% 81.39/80.98 cnf(11063,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x110631,a871)),x110632),f252(f885(x110631,a871))))),
% 81.39/80.98 inference(rename_variables,[],[3668])).
% 81.39/80.98 cnf(11077,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x110771),x110772),f193(f885(x110771,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11080,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a877),f328(a118,x110801)),x110801))),
% 81.39/80.98 inference(rename_variables,[],[4541])).
% 81.39/80.98 cnf(11085,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x110851),x110852),f193(f885(x110851,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11098,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a877),f328(a118,x110981)),x110981))),
% 81.39/80.98 inference(rename_variables,[],[4541])).
% 81.39/80.98 cnf(11101,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x111011),x111012),f193(f885(x111011,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11120,plain,
% 81.39/80.98 (P24(f328(f328(f330(f884(x111201,x111201)),f328(f328(f257(x111201,x111201),x111202),x111202)),f304(x111201,x111203)))),
% 81.39/80.98 inference(rename_variables,[],[3922])).
% 81.39/80.98 cnf(11125,plain,
% 81.39/80.98 (~P24(f328(f328(f330(f884(f878(x111251),f878(x111251))),f328(f328(f257(f878(x111251),f878(x111251)),x111252),f119(x111251))),f144(x111251,x111253)))),
% 81.39/80.98 inference(rename_variables,[],[4566])).
% 81.39/80.98 cnf(11128,plain,
% 81.39/80.98 (~P24(f328(f328(f330(f884(f878(x111281),f878(x111281))),f328(f328(f257(f878(x111281),f878(x111281)),x111282),f119(x111281))),f146(x111281,x111283)))),
% 81.39/80.98 inference(rename_variables,[],[4567])).
% 81.39/80.98 cnf(11131,plain,
% 81.39/80.98 (~P24(f328(f328(f330(f884(f878(x111311),f878(x111311))),f328(f328(f257(f878(x111311),f878(x111311)),x111312),f119(x111311))),f156(x111311,x111313)))),
% 81.39/80.98 inference(rename_variables,[],[4568])).
% 81.39/80.98 cnf(11136,plain,
% 81.39/80.98 (~P24(f328(f328(f245(f885(x111361,a871)),x111362),f193(f885(x111361,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4554])).
% 81.39/80.98 cnf(11139,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x111391),x111392),f193(f885(x111391,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11144,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x111441,a871)),x111442),f252(f885(x111441,a871))))),
% 81.39/80.98 inference(rename_variables,[],[3668])).
% 81.39/80.98 cnf(11147,plain,
% 81.39/80.98 (~P24(f328(f328(f193(f885(x111471,f885(x111472,a871))),x111473),x111474))),
% 81.39/80.98 inference(rename_variables,[],[4562])).
% 81.39/80.98 cnf(11156,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x111561),x111562),f193(f885(x111561,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11159,plain,
% 81.39/80.98 (~P24(f328(f328(f330(f884(x111591,x111591)),f328(f328(f257(x111591,x111591),x111592),x111593)),f152(x111591,f119(f885(x111591,a877)))))),
% 81.39/80.98 inference(rename_variables,[],[4564])).
% 81.39/80.98 cnf(11162,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x111621,a871)),x111622),x111622))),
% 81.39/80.98 inference(rename_variables,[],[3586])).
% 81.39/80.98 cnf(11165,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x111651),x111652),f193(f885(x111651,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11168,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x111681,a871)),f193(f885(x111681,a871))),x111682))),
% 81.39/80.98 inference(rename_variables,[],[3734])).
% 81.39/80.98 cnf(11171,plain,
% 81.39/80.98 (P24(f328(f328(f330(f884(x111711,x111711)),f328(f328(f257(x111711,x111711),x111712),x111712)),f304(x111711,x111713)))),
% 81.39/80.98 inference(rename_variables,[],[3922])).
% 81.39/80.98 cnf(11182,plain,
% 81.39/80.98 (~P24(f328(f328(f330(f884(f878(x111821),f878(x111821))),f328(f328(f257(f878(x111821),f878(x111821)),x111822),f119(x111821))),f156(x111821,x111823)))),
% 81.39/80.98 inference(rename_variables,[],[4568])).
% 81.39/80.98 cnf(11185,plain,
% 81.39/80.98 (~P24(f328(f328(f330(f884(f878(x111851),f878(x111851))),f328(f328(f257(f878(x111851),f878(x111851)),f119(x111851)),x111852)),f144(x111851,x111853)))),
% 81.39/80.98 inference(rename_variables,[],[4569])).
% 81.39/80.98 cnf(11193,plain,
% 81.39/80.98 (P24(f328(f328(f330(x111931),x111932),f252(f885(x111931,a871))))),
% 81.39/80.98 inference(rename_variables,[],[3444])).
% 81.39/80.98 cnf(11198,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x111981,a871)),f193(f885(x111981,a871))),x111982))),
% 81.39/80.98 inference(rename_variables,[],[3734])).
% 81.39/80.98 cnf(11201,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x112011),x112012),f193(f885(x112011,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11204,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x112041,a871)),x112042),f252(f885(x112041,a871))))),
% 81.39/80.98 inference(rename_variables,[],[3668])).
% 81.39/80.98 cnf(11209,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x112091,a871)),f193(f885(x112091,a871))),x112092))),
% 81.39/80.98 inference(rename_variables,[],[3734])).
% 81.39/80.98 cnf(11222,plain,
% 81.39/80.98 (P24(f328(f252(f885(x112221,a871)),x112222))),
% 81.39/80.98 inference(rename_variables,[],[3350])).
% 81.39/80.98 cnf(11230,plain,
% 81.39/80.98 (~P24(f328(f328(f330(f884(f878(x112301),f878(x112301))),f328(f328(f257(f878(x112301),f878(x112301)),x112302),f119(x112301))),f144(x112301,x112303)))),
% 81.39/80.98 inference(rename_variables,[],[4566])).
% 81.39/80.98 cnf(11233,plain,
% 81.39/80.98 (~P24(f328(f328(f330(f884(f878(x112331),f878(x112331))),f328(f328(f257(f878(x112331),f878(x112331)),x112332),f119(x112331))),f146(x112331,x112333)))),
% 81.39/80.98 inference(rename_variables,[],[4567])).
% 81.39/80.98 cnf(11236,plain,
% 81.39/80.98 (~E(f328(f328(f150(x112361),x112362),x112363),x112363)),
% 81.39/80.98 inference(rename_variables,[],[4484])).
% 81.39/80.98 cnf(11239,plain,
% 81.39/80.98 (~E(f328(a118,x112391),x112391)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(11242,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x112421),x112422),f193(f885(x112421,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11247,plain,
% 81.39/80.98 (P24(f328(f328(f330(f884(f878(x112471),f878(x112471))),f328(f328(f257(f878(x112471),f878(x112471)),x112472),x112472)),f157(x112471,f304(x112471,x112473))))),
% 81.39/80.98 inference(rename_variables,[],[4061])).
% 81.39/80.98 cnf(11252,plain,
% 81.39/80.98 (~P24(f328(f328(f330(f884(f878(x112521),f878(x112521))),f328(f328(f257(f878(x112521),f878(x112521)),x112522),f119(x112521))),f144(x112521,x112523)))),
% 81.39/80.98 inference(rename_variables,[],[4566])).
% 81.39/80.98 cnf(11262,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x112621),x112622),f193(f885(x112621,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11265,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x112651),x112652),f193(f885(x112651,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11268,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x112681),x112682),f193(f885(x112681,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11271,plain,
% 81.39/80.98 (P24(f328(f328(f330(x112711),x112712),f252(f885(x112711,a871))))),
% 81.39/80.98 inference(rename_variables,[],[3444])).
% 81.39/80.98 cnf(11276,plain,
% 81.39/80.98 (~P24(f328(f328(f330(f884(x112761,x112761)),f328(f328(f257(x112761,x112761),x112762),x112763)),f152(x112761,f119(f885(x112761,a877)))))),
% 81.39/80.98 inference(rename_variables,[],[4564])).
% 81.39/80.98 cnf(11279,plain,
% 81.39/80.98 (~E(f328(f307(x112791,f885(x112791,a871),x112792),x112793),f328(f305(x112791),x112793))),
% 81.39/80.98 inference(rename_variables,[],[4542])).
% 81.39/80.98 cnf(11282,plain,
% 81.39/80.98 (~E(f328(f307(x112821,f885(x112821,a871),x112822),x112823),f328(f305(x112821),x112823))),
% 81.39/80.98 inference(rename_variables,[],[4542])).
% 81.39/80.98 cnf(11287,plain,
% 81.39/80.98 (~P24(f328(f328(f330(f884(f878(x112871),f878(x112871))),f328(f328(f257(f878(x112871),f878(x112871)),x112872),f119(x112871))),f144(x112871,x112873)))),
% 81.39/80.98 inference(rename_variables,[],[4566])).
% 81.39/80.98 cnf(11293,plain,
% 81.39/80.98 (~P24(f328(f328(f330(f884(f878(x112931),f878(x112931))),f328(f328(f257(f878(x112931),f878(x112931)),x112932),f119(x112931))),f144(x112931,x112933)))),
% 81.39/80.98 inference(rename_variables,[],[4566])).
% 81.39/80.98 cnf(11296,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x112961),x112962),f193(f885(x112961,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11299,plain,
% 81.39/80.98 (~P24(f328(f328(f193(f885(x112991,f885(x112992,a871))),x112993),x112994))),
% 81.39/80.98 inference(rename_variables,[],[4562])).
% 81.39/80.98 cnf(11302,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x113021),f2(a877)))),
% 81.39/80.98 inference(rename_variables,[],[4532])).
% 81.39/80.98 cnf(11309,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x113091),x113092),f193(f885(x113091,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11312,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x113121),x113122),f193(f885(x113121,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11315,plain,
% 81.39/80.98 (P24(f328(f328(f330(x113151),f328(x113152,x113153)),f328(f307(x113154,x113151,x113152),f252(f885(x113154,a871)))))),
% 81.39/80.98 inference(rename_variables,[],[3888])).
% 81.39/80.98 cnf(11318,plain,
% 81.39/80.98 (~P24(f328(f328(f330(f884(x113181,x113181)),f328(f328(f257(x113181,x113181),x113182),x113183)),f152(x113181,f119(f885(x113181,a877)))))),
% 81.39/80.98 inference(rename_variables,[],[4564])).
% 81.39/80.98 cnf(11326,plain,
% 81.39/80.98 (E(f120(x113261,f119(x113261)),f119(x113261))),
% 81.39/80.98 inference(rename_variables,[],[3126])).
% 81.39/80.98 cnf(11329,plain,
% 81.39/80.98 (~E(f328(a118,x113291),x113291)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(11336,plain,
% 81.39/80.98 (~E(f328(a118,x113361),x113361)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(11341,plain,
% 81.39/80.98 (E(f328(f253(x113411,x113411),f254(x113411,x113412)),x113412)),
% 81.39/80.98 inference(rename_variables,[],[3241])).
% 81.39/80.98 cnf(11344,plain,
% 81.39/80.98 (E(f328(f253(x113441,x113441),f254(x113441,x113442)),x113442)),
% 81.39/80.98 inference(rename_variables,[],[3241])).
% 81.39/80.98 cnf(11350,plain,
% 81.39/80.98 (~E(f328(a118,x113501),x113501)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(11357,plain,
% 81.39/80.98 (~E(f328(f328(f81(a1),x113571),x113571),a103)),
% 81.39/80.98 inference(rename_variables,[],[4481])).
% 81.39/80.98 cnf(11366,plain,
% 81.39/80.98 (E(f328(f328(f22(a877),f2(a877)),x113661),f2(a877))),
% 81.39/80.98 inference(rename_variables,[],[3196])).
% 81.39/80.98 cnf(11369,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x113691),f2(a877)))),
% 81.39/80.98 inference(rename_variables,[],[4532])).
% 81.39/80.98 cnf(11376,plain,
% 81.39/80.98 (E(f328(f328(f81(a1),f328(f328(f82(a1),x113761),f328(f328(f39(a1),x113762),x113761))),f45(a1,x113762,x113761)),x113762)),
% 81.39/80.98 inference(rename_variables,[],[3836])).
% 81.39/80.98 cnf(11402,plain,
% 81.39/80.98 (~E(f328(a118,x114021),x114021)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(11405,plain,
% 81.39/80.98 (~E(f328(a118,x114051),x114051)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(11431,plain,
% 81.39/80.98 (~P24(f328(f63(x114311,x114312,f193(f885(x114311,a871))),x114313))),
% 81.39/80.98 inference(rename_variables,[],[4556])).
% 81.39/80.98 cnf(11434,plain,
% 81.39/80.98 (~P24(f328(f328(f193(f885(x114341,f885(x114342,a871))),x114343),x114344))),
% 81.39/80.98 inference(rename_variables,[],[4562])).
% 81.39/80.98 cnf(11437,plain,
% 81.39/80.98 (P24(f328(f328(f330(x114371),x114372),f252(f885(x114371,a871))))),
% 81.39/80.98 inference(rename_variables,[],[3444])).
% 81.39/80.98 cnf(11449,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x114491),x114491))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(11456,plain,
% 81.39/80.98 (P24(f328(f67(x114561,x114562,x114563,x114564,f193(f885(x114561,a871))),x114564))),
% 81.39/80.98 inference(rename_variables,[],[4209])).
% 81.39/80.98 cnf(11457,plain,
% 81.39/80.98 (E(f328(f253(x114571,x114571),f254(x114571,x114572)),x114572)),
% 81.39/80.98 inference(rename_variables,[],[3241])).
% 81.39/80.98 cnf(11462,plain,
% 81.39/80.98 (~P24(f328(f328(f193(f885(x114621,f885(x114622,a871))),x114623),x114624))),
% 81.39/80.98 inference(rename_variables,[],[4562])).
% 81.39/80.98 cnf(11473,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),f328(f328(f81(a877),x114731),x114732)),x114732))),
% 81.39/80.98 inference(rename_variables,[],[4558])).
% 81.39/80.98 cnf(11476,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a1),f328(f106(a1),x114761)),f2(a1)))),
% 81.39/80.98 inference(rename_variables,[],[4548])).
% 81.39/80.98 cnf(11501,plain,
% 81.39/80.98 (E(f328(f253(x115011,x115011),f254(x115011,x115012)),x115012)),
% 81.39/80.98 inference(rename_variables,[],[3241])).
% 81.39/80.98 cnf(11506,plain,
% 81.39/80.98 (E(f328(f253(x115061,x115061),f254(x115061,x115062)),x115062)),
% 81.39/80.98 inference(rename_variables,[],[3241])).
% 81.39/80.98 cnf(11509,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a1),f328(f106(a1),x115091)),f2(a1)))),
% 81.39/80.98 inference(rename_variables,[],[4548])).
% 81.39/80.98 cnf(11514,plain,
% 81.39/80.98 (~E(f328(a118,x115141),x115141)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(11523,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x115231),x115231))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(11546,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a1),f328(f106(a1),x115461)),f2(a1)))),
% 81.39/80.98 inference(rename_variables,[],[4548])).
% 81.39/80.98 cnf(11561,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a877),f328(a118,x115611)),x115611))),
% 81.39/80.98 inference(rename_variables,[],[4541])).
% 81.39/80.98 cnf(11562,plain,
% 81.39/80.98 (~E(f328(a118,x115621),x115621)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(11572,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),f328(f328(f81(a877),x115721),x115722)),x115721))),
% 81.39/80.98 inference(rename_variables,[],[4559])).
% 81.39/80.98 cnf(11575,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a1),f328(f106(a1),x115751)),f2(a1)))),
% 81.39/80.98 inference(rename_variables,[],[4548])).
% 81.39/80.98 cnf(11578,plain,
% 81.39/80.98 (~E(f328(a118,x115781),x115781)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(11591,plain,
% 81.39/80.98 (P24(f328(f328(f330(x115911),x115912),f328(f328(f306(x115911),x115912),x115913)))),
% 81.39/80.98 inference(rename_variables,[],[3599])).
% 81.39/80.98 cnf(11592,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a1),f2(a1)),f328(f80(a1),f328(f106(a1),f328(a118,x115921)))))),
% 81.39/80.98 inference(rename_variables,[],[4560])).
% 81.39/80.98 cnf(11595,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),f328(f328(f22(a877),x115951),x115952)),f328(a118,x115951)))),
% 81.39/80.98 inference(rename_variables,[],[3738])).
% 81.39/80.98 cnf(11598,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),f45(a877,x115981,x115982)),x115981))),
% 81.39/80.98 inference(rename_variables,[],[3743])).
% 81.39/80.98 cnf(11604,plain,
% 81.39/80.98 (E(f328(f328(f127(x116041),x116042),f119(x116041)),x116042)),
% 81.39/80.98 inference(rename_variables,[],[3213])).
% 81.39/80.98 cnf(11607,plain,
% 81.39/80.98 (E(f328(f253(x116071,x116071),f254(x116071,x116072)),x116072)),
% 81.39/80.98 inference(rename_variables,[],[3241])).
% 81.39/80.98 cnf(11610,plain,
% 81.39/80.98 (E(f172(x116101,x116102,f119(x116101)),x116102)),
% 81.39/80.98 inference(rename_variables,[],[3219])).
% 81.39/80.98 cnf(11616,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a877),f328(a118,x116161)),x116161))),
% 81.39/80.98 inference(rename_variables,[],[4541])).
% 81.39/80.98 cnf(11625,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x116251),x116251))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(11628,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),f45(a877,x116281,x116282)),x116281))),
% 81.39/80.98 inference(rename_variables,[],[3743])).
% 81.39/80.98 cnf(11629,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),f2(a877)),x116291))),
% 81.39/80.98 inference(rename_variables,[],[3307])).
% 81.39/80.98 cnf(11646,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x116461),x116461))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(11649,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x116491),x116491))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(11652,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x116521),x116521))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(11655,plain,
% 81.39/80.98 (P24(f328(f328(f330(x116551),f328(x116552,x116553)),f328(f307(x116554,x116551,x116552),f252(f885(x116554,a871)))))),
% 81.39/80.98 inference(rename_variables,[],[3888])).
% 81.39/80.98 cnf(11656,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a877),f328(a118,x116561)),x116561))),
% 81.39/80.98 inference(rename_variables,[],[4541])).
% 81.39/80.98 cnf(11659,plain,
% 81.39/80.98 (P24(f328(f328(f330(x116591),f328(x116592,x116593)),f328(f307(x116594,x116591,x116592),f252(f885(x116594,a871)))))),
% 81.39/80.98 inference(rename_variables,[],[3888])).
% 81.39/80.98 cnf(11660,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),f328(f328(f81(a877),x116601),x116602)),x116602))),
% 81.39/80.98 inference(rename_variables,[],[4558])).
% 81.39/80.98 cnf(11665,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),f328(f328(f81(a877),x116651),x116652)),x116651))),
% 81.39/80.98 inference(rename_variables,[],[4559])).
% 81.39/80.98 cnf(11668,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x116681),x116681))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(11671,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x116711),x116711))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(11677,plain,
% 81.39/80.98 (~P36(x116771,x116772,f119(x116771))),
% 81.39/80.98 inference(rename_variables,[],[4495])).
% 81.39/80.98 cnf(11680,plain,
% 81.39/80.98 (P24(f328(f328(f330(x116801),x116802),f252(f885(x116801,a871))))),
% 81.39/80.98 inference(rename_variables,[],[3444])).
% 81.39/80.98 cnf(11681,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a877),f328(a118,x116811)),x116811))),
% 81.39/80.98 inference(rename_variables,[],[4541])).
% 81.39/80.98 cnf(11684,plain,
% 81.39/80.98 (~P24(f328(f63(x116841,x116842,f193(f885(x116841,a871))),x116843))),
% 81.39/80.98 inference(rename_variables,[],[4556])).
% 81.39/80.98 cnf(11697,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x116971),x116972),f193(f885(x116971,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11700,plain,
% 81.39/80.98 (E(f328(f328(f16(x117001,x117002),x117003),x117004),x117003)),
% 81.39/80.98 inference(rename_variables,[],[3274])).
% 81.39/80.98 cnf(11703,plain,
% 81.39/80.98 (E(f328(f328(f16(x117031,x117032),x117033),x117034),x117033)),
% 81.39/80.98 inference(rename_variables,[],[3274])).
% 81.39/80.98 cnf(11715,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),f2(a877)),f328(a118,x117151)))),
% 81.39/80.98 inference(rename_variables,[],[3368])).
% 81.39/80.98 cnf(11718,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x117181),x117181))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(11723,plain,
% 81.39/80.98 (P24(f328(f62(x117231),f328(f171(x117231),x117232)))),
% 81.39/80.98 inference(rename_variables,[],[3328])).
% 81.39/80.98 cnf(11726,plain,
% 81.39/80.98 (P24(f328(f62(x117261),f328(f171(x117261),x117262)))),
% 81.39/80.98 inference(rename_variables,[],[3328])).
% 81.39/80.98 cnf(11729,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),f328(f80(a1),f328(f106(a1),x117291))),f328(f106(a1),x117292)))),
% 81.39/80.98 inference(rename_variables,[],[3765])).
% 81.39/80.98 cnf(11732,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x117321),x117322),f193(f885(x117321,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(11751,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x117511),x117511))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(11754,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x117541),x117541))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(11763,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x117631),x117631))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(11766,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x117661),f2(a877)))),
% 81.39/80.98 inference(rename_variables,[],[4532])).
% 81.39/80.98 cnf(11771,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x117711),f2(a877)))),
% 81.39/80.98 inference(rename_variables,[],[4532])).
% 81.39/80.98 cnf(11778,plain,
% 81.39/80.98 (P24(f328(f252(f885(x117781,a871)),x117782))),
% 81.39/80.98 inference(rename_variables,[],[3350])).
% 81.39/80.98 cnf(11783,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),f2(a877)),x117831))),
% 81.39/80.98 inference(rename_variables,[],[3307])).
% 81.39/80.98 cnf(11784,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a877),f328(a118,x117841)),x117841))),
% 81.39/80.98 inference(rename_variables,[],[4541])).
% 81.39/80.98 cnf(11787,plain,
% 81.39/80.98 (~P24(f328(f63(x117871,x117872,f193(f885(x117871,a871))),x117873))),
% 81.39/80.98 inference(rename_variables,[],[4556])).
% 81.39/80.98 cnf(11809,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a877),f328(a118,x118091)),x118091))),
% 81.39/80.98 inference(rename_variables,[],[4541])).
% 81.39/80.98 cnf(11812,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a877),f328(a118,x118121)),x118121))),
% 81.39/80.98 inference(rename_variables,[],[4541])).
% 81.39/80.98 cnf(11815,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a877),f328(a118,x118151)),x118151))),
% 81.39/80.98 inference(rename_variables,[],[4541])).
% 81.39/80.98 cnf(11818,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a877),f328(a118,x118181)),x118181))),
% 81.39/80.98 inference(rename_variables,[],[4541])).
% 81.39/80.98 cnf(11821,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x118211),x118211))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(11824,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x118241),x118241))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(11827,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x118271),x118271))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(11830,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x118301),x118301))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(11847,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x118471),x118471))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(11853,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x118531),x118531))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(11864,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x118641),x118641))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(11867,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x118671,a871)),x118672),f328(f328(f306(x118671),x118673),x118672)))),
% 81.39/80.98 inference(rename_variables,[],[3732])).
% 81.39/80.98 cnf(11874,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x118741),f328(a118,x118741)))),
% 81.39/80.98 inference(rename_variables,[],[3356])).
% 81.39/80.98 cnf(11877,plain,
% 81.39/80.98 (P24(f328(f328(f330(f885(x118771,a871)),x118772),f328(f305(x118771),x118772)))),
% 81.39/80.98 inference(rename_variables,[],[3650])).
% 81.39/80.98 cnf(11878,plain,
% 81.39/80.98 (~E(f328(a118,x118781),x118781)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(11883,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x118831),x118831))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(11888,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x118881),x118881))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(11895,plain,
% 81.39/80.98 (P24(f328(f62(a877),f301(a877,x118951,x118952)))),
% 81.39/80.98 inference(rename_variables,[],[3498])).
% 81.39/80.98 cnf(11902,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x119021,a871)),x119022),f328(f328(f306(x119021),x119023),x119022)))),
% 81.39/80.98 inference(rename_variables,[],[3732])).
% 81.39/80.98 cnf(11905,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x119051),x119051))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(11906,plain,
% 81.39/80.98 (~E(f328(a118,x119061),x119061)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(11917,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x119171),x119171))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(11918,plain,
% 81.39/80.98 (~E(f328(a118,x119181),x119181)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(11921,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x119211),x119211))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(11924,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x119241),x119241))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(11927,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x119271),x119271))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(11930,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x119301),x119301))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(11933,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x119331),x119331))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(11936,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x119361),x119361))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(11939,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x119391),x119391))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(11940,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x119401),f328(a118,x119401)))),
% 81.39/80.98 inference(rename_variables,[],[3356])).
% 81.39/80.98 cnf(11949,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x119491),x119491))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(11950,plain,
% 81.39/80.98 (~E(f328(a118,x119501),x119501)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(11953,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x119531),x119531))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(11970,plain,
% 81.39/80.98 (P24(f328(f328(f244(a1),x119701),x119701))),
% 81.39/80.98 inference(rename_variables,[],[3284])).
% 81.39/80.98 cnf(11975,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),f2(a877)),x119751))),
% 81.39/80.98 inference(rename_variables,[],[3307])).
% 81.39/80.98 cnf(11992,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x119921),f2(a877)))),
% 81.39/80.98 inference(rename_variables,[],[4532])).
% 81.39/80.98 cnf(11995,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x119951),f2(a877)))),
% 81.39/80.98 inference(rename_variables,[],[4532])).
% 81.39/80.98 cnf(11998,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x119981),x119982),f193(f885(x119981,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(12001,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x120011),x120012),f193(f885(x120011,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(12004,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x120041),x120041))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(12007,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x120071),x120071))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(12010,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x120101),x120101))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(12013,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x120131),x120131))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(12016,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x120161),f328(a118,x120161)))),
% 81.39/80.98 inference(rename_variables,[],[3356])).
% 81.39/80.98 cnf(12023,plain,
% 81.39/80.98 (P24(f328(f328(f330(f885(x120231,a871)),x120232),f328(f305(x120231),x120232)))),
% 81.39/80.98 inference(rename_variables,[],[3650])).
% 81.39/80.98 cnf(12028,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x120281,a871)),f328(f171(x120281),f328(f135(x120281,x120282),x120283))),f328(f171(x120281),x120283)))),
% 81.39/80.98 inference(rename_variables,[],[3932])).
% 81.39/80.98 cnf(12035,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x120351),x120352),f193(f885(x120351,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(12040,plain,
% 81.39/80.98 (E(f328(f194(f878(x120401)),f328(f167(x120401),x120402)),f328(f194(f878(x120401)),x120402))),
% 81.39/80.98 inference(rename_variables,[],[3298])).
% 81.39/80.98 cnf(12047,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x120471,a871)),x120472),f252(f885(x120471,a871))))),
% 81.39/80.98 inference(rename_variables,[],[3668])).
% 81.39/80.98 cnf(12048,plain,
% 81.39/80.98 (~E(f328(a118,x120481),x120481)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(12051,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x120511,a871)),f328(f307(x120512,x120511,x120513),f328(f308(x120512,x120511,x120513),x120514))),x120514))),
% 81.39/80.98 inference(rename_variables,[],[4171])).
% 81.39/80.98 cnf(12054,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x120541,a871)),f328(f171(x120541),f328(f135(x120541,x120542),x120543))),f328(f171(x120541),x120543)))),
% 81.39/80.98 inference(rename_variables,[],[3932])).
% 81.39/80.98 cnf(12060,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x120601),f328(a118,x120601)))),
% 81.39/80.98 inference(rename_variables,[],[3356])).
% 81.39/80.98 cnf(12069,plain,
% 81.39/80.98 (E(f328(f253(x120691,x120691),f254(x120691,x120692)),x120692)),
% 81.39/80.98 inference(rename_variables,[],[3241])).
% 81.39/80.98 cnf(12080,plain,
% 81.39/80.98 (~P24(f328(f328(f244(a877),f328(a118,x120801)),x120801))),
% 81.39/80.98 inference(rename_variables,[],[4541])).
% 81.39/80.98 cnf(12081,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x120811),f2(a877)))),
% 81.39/80.98 inference(rename_variables,[],[4532])).
% 81.39/80.98 cnf(12084,plain,
% 81.39/80.98 (P24(f328(f62(x120841),f193(f885(x120841,a871))))),
% 81.39/80.98 inference(rename_variables,[],[3364])).
% 81.39/80.98 cnf(12085,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x120851),x120852),f193(f885(x120851,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(12090,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x120901),f2(a877)))),
% 81.39/80.98 inference(rename_variables,[],[4532])).
% 81.39/80.98 cnf(12091,plain,
% 81.39/80.98 (~P24(f328(f328(f245(a877),x120911),x120911))),
% 81.39/80.98 inference(rename_variables,[],[4528])).
% 81.39/80.98 cnf(12096,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x120961,a871)),f328(f171(x120961),f169(x120961,x120962,x120963))),f328(f171(x120961),x120963)))),
% 81.39/80.98 inference(rename_variables,[],[3983])).
% 81.39/80.98 cnf(12099,plain,
% 81.39/80.98 (P21(x120991,x120991,f5(x120991),x120992)),
% 81.39/80.98 inference(rename_variables,[],[3527])).
% 81.39/80.98 cnf(12104,plain,
% 81.39/80.98 (P24(f328(f328(f330(f885(x121041,a871)),x121042),f328(f305(x121041),x121042)))),
% 81.39/80.98 inference(rename_variables,[],[3650])).
% 81.39/80.98 cnf(12111,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x121111),x121111))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(12114,plain,
% 81.39/80.98 (~P24(f328(f328(f330(x121141),x121142),f193(f885(x121141,a871))))),
% 81.39/80.98 inference(rename_variables,[],[4544])).
% 81.39/80.98 cnf(12117,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x121171,a871)),x121172),f328(f328(f306(x121171),x121173),x121172)))),
% 81.39/80.98 inference(rename_variables,[],[3732])).
% 81.39/80.98 cnf(12118,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x121181,a871)),x121182),f252(f885(x121181,a871))))),
% 81.39/80.98 inference(rename_variables,[],[3668])).
% 81.39/80.98 cnf(12125,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x121251),x121251))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(12128,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x121281),x121281))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(12131,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x121311),x121311))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(12134,plain,
% 81.39/80.98 (P24(f328(f328(f244(a877),x121341),x121341))),
% 81.39/80.98 inference(rename_variables,[],[3283])).
% 81.39/80.98 cnf(12137,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x121371),f328(a118,x121371)))),
% 81.39/80.98 inference(rename_variables,[],[3356])).
% 81.39/80.98 cnf(12140,plain,
% 81.39/80.98 (P24(f328(f328(f245(a877),x121401),f328(a118,x121401)))),
% 81.39/80.98 inference(rename_variables,[],[3356])).
% 81.39/80.98 cnf(12143,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x121431,a871)),x121432),x121432))),
% 81.39/80.98 inference(rename_variables,[],[3586])).
% 81.39/80.98 cnf(12150,plain,
% 81.39/80.98 (P24(f328(f328(f330(f885(x121501,a871)),x121502),f328(f305(x121501),x121502)))),
% 81.39/80.98 inference(rename_variables,[],[3650])).
% 81.39/80.98 cnf(12159,plain,
% 81.39/80.98 (~E(f328(a118,x121591),x121591)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(12160,plain,
% 81.39/80.98 (E(f328(f307(x121601,x121601,f5(x121601)),x121602),x121602)),
% 81.39/80.98 inference(rename_variables,[],[3346])).
% 81.39/80.98 cnf(12163,plain,
% 81.39/80.98 (P33(x121631,x121632,f119(x121631),f119(x121631))),
% 81.39/80.98 inference(rename_variables,[],[3536])).
% 81.39/80.98 cnf(12166,plain,
% 81.39/80.98 (~E(f328(a118,x121661),x121661)),
% 81.39/80.98 inference(rename_variables,[],[4458])).
% 81.39/80.98 cnf(12169,plain,
% 81.39/80.98 (P24(f328(f328(f244(f885(x121691,a871)),f328(f171(x121691),f169(x121691,x121692,x121693))),f328(f171(x121691),x121693)))),
% 81.39/80.98 inference(rename_variables,[],[3983])).
% 81.39/80.98 cnf(12170,plain,
% 81.39/80.99 (P24(f328(f62(x121701),f328(f171(x121701),x121702)))),
% 81.39/80.99 inference(rename_variables,[],[3328])).
% 81.39/80.99 cnf(12181,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x121811),x121811))),
% 81.39/80.99 inference(rename_variables,[],[4528])).
% 81.39/80.99 cnf(12184,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x121841),x121841))),
% 81.39/80.99 inference(rename_variables,[],[4528])).
% 81.39/80.99 cnf(12189,plain,
% 81.39/80.99 (E(f328(f194(f878(x121891)),f328(f167(x121891),x121892)),f328(f194(f878(x121891)),x121892))),
% 81.39/80.99 inference(rename_variables,[],[3298])).
% 81.39/80.99 cnf(12192,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),f2(a877)),x121921))),
% 81.39/80.99 inference(rename_variables,[],[3307])).
% 81.39/80.99 cnf(12201,plain,
% 81.39/80.99 (P29(a877,f328(f168(a877),f328(f328(f153(f878(x122011),a877),f194(f878(x122011))),f179(x122011,x122012))))),
% 81.39/80.99 inference(rename_variables,[],[3846])).
% 81.39/80.99 cnf(12204,plain,
% 81.39/80.99 (P21(x122041,x122041,f5(x122041),x122042)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(12207,plain,
% 81.39/80.99 (P24(f328(f328(f330(f878(x122071)),f119(x122071)),f160(x122071,x122072)))),
% 81.39/80.99 inference(rename_variables,[],[3489])).
% 81.39/80.99 cnf(12210,plain,
% 81.39/80.99 (~P24(f328(f328(f193(f885(x122101,f885(x122102,a871))),x122103),x122104))),
% 81.39/80.99 inference(rename_variables,[],[4562])).
% 81.39/80.99 cnf(12215,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x122151),x122151))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12216,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),f2(a877)),x122161))),
% 81.39/80.99 inference(rename_variables,[],[3307])).
% 81.39/80.99 cnf(12219,plain,
% 81.39/80.99 (~P24(f328(f328(f193(f885(x122191,f885(x122192,a871))),x122193),x122194))),
% 81.39/80.99 inference(rename_variables,[],[4562])).
% 81.39/80.99 cnf(12222,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(f884(f878(x122221),f878(x122221)),a871)),f157(x122221,x122222)),f304(f878(x122221),f156(x122221,x122222))))),
% 81.39/80.99 inference(rename_variables,[],[3988])).
% 81.39/80.99 cnf(12228,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x122281,a871)),f328(f171(x122281),f169(x122281,x122282,x122283))),f328(f171(x122281),x122283)))),
% 81.39/80.99 inference(rename_variables,[],[3983])).
% 81.39/80.99 cnf(12229,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x122291,a871)),f328(f171(x122291),f328(f135(x122291,x122292),x122293))),f328(f171(x122291),x122293)))),
% 81.39/80.99 inference(rename_variables,[],[3932])).
% 81.39/80.99 cnf(12232,plain,
% 81.39/80.99 (~P24(f328(f328(f245(f885(x122321,a871)),x122322),f193(f885(x122321,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4554])).
% 81.39/80.99 cnf(12235,plain,
% 81.39/80.99 (P21(x122351,f881(x122351),f236(x122351),x122352)),
% 81.39/80.99 inference(rename_variables,[],[3537])).
% 81.39/80.99 cnf(12240,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x122401,a871)),f328(f307(x122402,x122401,x122403),f328(f308(x122402,x122401,x122403),x122404))),x122404))),
% 81.39/80.99 inference(rename_variables,[],[4171])).
% 81.39/80.99 cnf(12248,plain,
% 81.39/80.99 (P24(f328(f328(f330(f878(x122481)),f119(x122481)),f160(x122481,x122482)))),
% 81.39/80.99 inference(rename_variables,[],[3489])).
% 81.39/80.99 cnf(12251,plain,
% 81.39/80.99 (~P24(f328(f328(f330(f884(f878(x122511),f878(x122511))),f328(f328(f257(f878(x122511),f878(x122511)),x122512),f119(x122511))),f144(x122511,x122513)))),
% 81.39/80.99 inference(rename_variables,[],[4566])).
% 81.39/80.99 cnf(12254,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x122541),f2(a877)))),
% 81.39/80.99 inference(rename_variables,[],[4532])).
% 81.39/80.99 cnf(12257,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x122571,a871)),x122572),x122572))),
% 81.39/80.99 inference(rename_variables,[],[3586])).
% 81.39/80.99 cnf(12260,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x122601),x122602),f193(f885(x122601,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12263,plain,
% 81.39/80.99 (~P24(f328(f328(f193(f885(x122631,f885(x122632,a871))),x122633),x122634))),
% 81.39/80.99 inference(rename_variables,[],[4562])).
% 81.39/80.99 cnf(12266,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x122661,a871)),f328(f307(x122662,x122661,x122663),f328(f308(x122662,x122661,x122663),x122664))),x122664))),
% 81.39/80.99 inference(rename_variables,[],[4171])).
% 81.39/80.99 cnf(12267,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x122671,a871)),x122672),x122672))),
% 81.39/80.99 inference(rename_variables,[],[3586])).
% 81.39/80.99 cnf(12272,plain,
% 81.39/80.99 (E(f328(f253(x122721,x122721),f254(x122721,x122722)),x122722)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(12275,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x122751,a871)),f328(f171(x122751),f169(x122751,x122752,x122753))),f328(f171(x122751),x122753)))),
% 81.39/80.99 inference(rename_variables,[],[3983])).
% 81.39/80.99 cnf(12276,plain,
% 81.39/80.99 (P24(f328(f62(x122761),f328(f171(x122761),x122762)))),
% 81.39/80.99 inference(rename_variables,[],[3328])).
% 81.39/80.99 cnf(12279,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x122791),x122791))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12282,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x122821),x122821))),
% 81.39/80.99 inference(rename_variables,[],[4528])).
% 81.39/80.99 cnf(12285,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x122851),x122851))),
% 81.39/80.99 inference(rename_variables,[],[4528])).
% 81.39/80.99 cnf(12296,plain,
% 81.39/80.99 (P21(x122961,x122961,f5(x122961),x122962)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(12303,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x123031),x123032),f193(f885(x123031,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12306,plain,
% 81.39/80.99 (P24(f328(f328(f330(f884(x123061,x123061)),f328(f328(f257(x123061,x123061),x123062),x123062)),f304(x123061,x123063)))),
% 81.39/80.99 inference(rename_variables,[],[3922])).
% 81.39/80.99 cnf(12309,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x123091),x123092),f193(f885(x123091,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12312,plain,
% 81.39/80.99 (P24(f328(f328(f330(f884(x123121,x123121)),f328(f328(f257(x123121,x123121),x123122),x123122)),f304(x123121,x123123)))),
% 81.39/80.99 inference(rename_variables,[],[3922])).
% 81.39/80.99 cnf(12322,plain,
% 81.39/80.99 (~E(f328(f328(f150(x123221),x123222),x123223),x123223)),
% 81.39/80.99 inference(rename_variables,[],[4484])).
% 81.39/80.99 cnf(12325,plain,
% 81.39/80.99 (P24(f328(f328(f330(x123251),x123252),f252(f885(x123251,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3444])).
% 81.39/80.99 cnf(12326,plain,
% 81.39/80.99 (~E(f328(a118,x123261),x123261)),
% 81.39/80.99 inference(rename_variables,[],[4458])).
% 81.39/80.99 cnf(12333,plain,
% 81.39/80.99 (P24(f328(f328(f330(x123331),f328(x123332,x123333)),f328(f307(x123334,x123331,x123332),f252(f885(x123334,a871)))))),
% 81.39/80.99 inference(rename_variables,[],[3888])).
% 81.39/80.99 cnf(12334,plain,
% 81.39/80.99 (P21(x123341,x123341,f5(x123341),x123342)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(12337,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x123371,a871)),f193(f885(x123371,a871))),x123372))),
% 81.39/80.99 inference(rename_variables,[],[3734])).
% 81.39/80.99 cnf(12338,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x123381,a871)),x123382),x123382))),
% 81.39/80.99 inference(rename_variables,[],[3586])).
% 81.39/80.99 cnf(12341,plain,
% 81.39/80.99 (P24(f328(f328(f330(x123411),f328(x123412,x123413)),f328(f307(x123414,x123411,x123412),f252(f885(x123414,a871)))))),
% 81.39/80.99 inference(rename_variables,[],[3888])).
% 81.39/80.99 cnf(12342,plain,
% 81.39/80.99 (P21(x123421,x123421,f5(x123421),x123422)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(12345,plain,
% 81.39/80.99 (P24(f328(f328(f330(f884(f878(x123451),f878(x123451))),f328(f328(f257(f878(x123451),f878(x123451)),f119(x123451)),f119(x123451))),f157(x123451,x123452)))),
% 81.39/80.99 inference(rename_variables,[],[4067])).
% 81.39/80.99 cnf(12348,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x123481),x123481))),
% 81.39/80.99 inference(rename_variables,[],[4528])).
% 81.39/80.99 cnf(12349,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x123491),f2(a877)))),
% 81.39/80.99 inference(rename_variables,[],[4532])).
% 81.39/80.99 cnf(12355,plain,
% 81.39/80.99 (E(f328(f328(f127(x123551),x123552),f119(x123551)),x123552)),
% 81.39/80.99 inference(rename_variables,[],[3213])).
% 81.39/80.99 cnf(12356,plain,
% 81.39/80.99 (~E(f328(f328(f150(x123561),x123562),x123563),x123563)),
% 81.39/80.99 inference(rename_variables,[],[4484])).
% 81.39/80.99 cnf(12359,plain,
% 81.39/80.99 (E(f328(f328(f127(x123591),x123592),f119(x123591)),x123592)),
% 81.39/80.99 inference(rename_variables,[],[3213])).
% 81.39/80.99 cnf(12360,plain,
% 81.39/80.99 (~E(f328(f328(f150(x123601),x123602),x123603),x123603)),
% 81.39/80.99 inference(rename_variables,[],[4484])).
% 81.39/80.99 cnf(12363,plain,
% 81.39/80.99 (E(f328(f328(f127(x123631),x123632),f119(x123631)),x123632)),
% 81.39/80.99 inference(rename_variables,[],[3213])).
% 81.39/80.99 cnf(12372,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x123721,a871)),x123722),f252(f885(x123721,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3668])).
% 81.39/80.99 cnf(12376,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x123761),x123761))),
% 81.39/80.99 inference(rename_variables,[],[4528])).
% 81.39/80.99 cnf(12377,plain,
% 81.39/80.99 (~E(f328(a118,x123771),x123771)),
% 81.39/80.99 inference(rename_variables,[],[4458])).
% 81.39/80.99 cnf(12380,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x123801,a871)),f193(f885(x123801,a871))),x123802))),
% 81.39/80.99 inference(rename_variables,[],[3734])).
% 81.39/80.99 cnf(12383,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x123831),x123831))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12386,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x123861,a871)),x123862),x123862))),
% 81.39/80.99 inference(rename_variables,[],[3586])).
% 81.39/80.99 cnf(12391,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x123911,a871)),x123912),f328(f328(f306(x123911),x123913),x123912)))),
% 81.39/80.99 inference(rename_variables,[],[3732])).
% 81.39/80.99 cnf(12394,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x123941,a871)),x123942),x123942))),
% 81.39/80.99 inference(rename_variables,[],[3586])).
% 81.39/80.99 cnf(12395,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x123951),x123952),f193(f885(x123951,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12398,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x123981),x123982),f193(f885(x123981,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12407,plain,
% 81.39/80.99 (P21(x124071,x124071,f5(x124071),x124072)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(12410,plain,
% 81.39/80.99 (E(f328(f194(f878(x124101)),f328(f167(x124101),x124102)),f328(f194(f878(x124101)),x124102))),
% 81.39/80.99 inference(rename_variables,[],[3298])).
% 81.39/80.99 cnf(12413,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x124131),x124131))),
% 81.39/80.99 inference(rename_variables,[],[4528])).
% 81.39/80.99 cnf(12414,plain,
% 81.39/80.99 (P24(f328(f252(f885(x124141,a871)),x124142))),
% 81.39/80.99 inference(rename_variables,[],[3350])).
% 81.39/80.99 cnf(12417,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x124171),x124172),f193(f885(x124171,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12420,plain,
% 81.39/80.99 (P24(f328(f328(f330(x124201),f328(x124202,x124203)),f328(f307(x124204,x124201,x124202),f252(f885(x124204,a871)))))),
% 81.39/80.99 inference(rename_variables,[],[3888])).
% 81.39/80.99 cnf(12421,plain,
% 81.39/80.99 (P24(f328(f328(f330(f884(x124211,x124211)),f328(f328(f257(x124211,x124211),x124212),x124212)),f304(x124211,x124213)))),
% 81.39/80.99 inference(rename_variables,[],[3922])).
% 81.39/80.99 cnf(12424,plain,
% 81.39/80.99 (P24(f328(f328(f330(f884(x124241,x124241)),f328(f328(f257(x124241,x124241),x124242),x124242)),f304(x124241,x124243)))),
% 81.39/80.99 inference(rename_variables,[],[3922])).
% 81.39/80.99 cnf(12427,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x124271),x124271))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12428,plain,
% 81.39/80.99 (P24(f328(f252(f885(x124281,a871)),x124282))),
% 81.39/80.99 inference(rename_variables,[],[3350])).
% 81.39/80.99 cnf(12431,plain,
% 81.39/80.99 (P24(f328(f62(x124311),f328(f171(x124311),x124312)))),
% 81.39/80.99 inference(rename_variables,[],[3328])).
% 81.39/80.99 cnf(12441,plain,
% 81.39/80.99 (~P24(f328(f328(f193(f885(x124411,f885(x124412,a871))),x124413),x124414))),
% 81.39/80.99 inference(rename_variables,[],[4562])).
% 81.39/80.99 cnf(12444,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x124441,a871)),x124442),f252(f885(x124441,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3668])).
% 81.39/80.99 cnf(12447,plain,
% 81.39/80.99 (P24(f328(f328(f330(f884(x124471,x124471)),f328(f328(f257(x124471,x124471),x124472),x124472)),f304(x124471,x124473)))),
% 81.39/80.99 inference(rename_variables,[],[3922])).
% 81.39/80.99 cnf(12450,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),f328(f328(f81(a877),x124501),x124502)),x124502))),
% 81.39/80.99 inference(rename_variables,[],[4558])).
% 81.39/80.99 cnf(12451,plain,
% 81.39/80.99 (P24(f328(f328(f245(a877),x124511),f328(a118,x124511)))),
% 81.39/80.99 inference(rename_variables,[],[3356])).
% 81.39/80.99 cnf(12454,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x124541,a871)),f328(f171(x124541),f328(f135(x124541,x124542),x124543))),f328(f171(x124541),x124543)))),
% 81.39/80.99 inference(rename_variables,[],[3932])).
% 81.39/80.99 cnf(12457,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x124571,a871)),x124572),f252(f885(x124571,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3668])).
% 81.39/80.99 cnf(12460,plain,
% 81.39/80.99 (E(f328(f253(x124601,x124601),f254(x124601,x124602)),x124602)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(12471,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x124711),x124712),f193(f885(x124711,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12472,plain,
% 81.39/80.99 (P24(f328(f328(f330(f884(f878(x124721),f878(x124721))),f328(f328(f257(f878(x124721),f878(x124721)),f119(x124721)),f119(x124721))),f157(x124721,x124722)))),
% 81.39/80.99 inference(rename_variables,[],[4067])).
% 81.39/80.99 cnf(12477,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x124771),x124772),f193(f885(x124771,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12480,plain,
% 81.39/80.99 (P32(x124801,x124802,f119(x124801))),
% 81.39/80.99 inference(rename_variables,[],[3218])).
% 81.39/80.99 cnf(12483,plain,
% 81.39/80.99 (E(f328(f194(f878(x124831)),f328(f167(x124831),x124832)),f328(f194(f878(x124831)),x124832))),
% 81.39/80.99 inference(rename_variables,[],[3298])).
% 81.39/80.99 cnf(12486,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x124861),x124862),f193(f885(x124861,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12489,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x124891),x124892),f193(f885(x124891,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12494,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x124941),x124942),f193(f885(x124941,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12497,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x124971),x124971))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12501,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x125011),x125011))),
% 81.39/80.99 inference(rename_variables,[],[4528])).
% 81.39/80.99 cnf(12504,plain,
% 81.39/80.99 (P24(f328(f328(f330(x125041),x125042),f252(f885(x125041,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3444])).
% 81.39/80.99 cnf(12511,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x125111,a871)),x125112),x125112))),
% 81.39/80.99 inference(rename_variables,[],[3586])).
% 81.39/80.99 cnf(12514,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x125141),x125142),f193(f885(x125141,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12517,plain,
% 81.39/80.99 (P24(f328(f328(f244(a1),f2(a1)),f328(f328(f258(a1),f328(f76(a1),x125171)),x125172)))),
% 81.39/80.99 inference(rename_variables,[],[3764])).
% 81.39/80.99 cnf(12520,plain,
% 81.39/80.99 (~E(f328(a118,x125201),x125201)),
% 81.39/80.99 inference(rename_variables,[],[4458])).
% 81.39/80.99 cnf(12522,plain,
% 81.39/80.99 (E(f328(f253(x125221,x125221),f254(x125221,x125222)),x125222)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(12524,plain,
% 81.39/80.99 (E(f328(f253(x125241,x125241),f254(x125241,x125242)),x125242)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(12531,plain,
% 81.39/80.99 (E(f328(f253(x125311,x125311),f254(x125311,x125312)),x125312)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(12533,plain,
% 81.39/80.99 (E(f328(f253(x125331,x125331),f254(x125331,x125332)),x125332)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(12546,plain,
% 81.39/80.99 (P38(x125461,f152(x125461,x125462))),
% 81.39/80.99 inference(rename_variables,[],[3154])).
% 81.39/80.99 cnf(12550,plain,
% 81.39/80.99 (P21(x125501,x125501,f5(x125501),x125502)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(12552,plain,
% 81.39/80.99 (P21(x125521,x125521,f5(x125521),x125522)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(12558,plain,
% 81.39/80.99 (E(f328(f253(x125581,x125581),f254(x125581,x125582)),x125582)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(12560,plain,
% 81.39/80.99 (E(f328(f253(x125601,x125601),f254(x125601,x125602)),x125602)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(12562,plain,
% 81.39/80.99 (E(f328(f253(x125621,x125621),f254(x125621,x125622)),x125622)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(12566,plain,
% 81.39/80.99 (P48(x125661,x125662,f254(x125661,x125662))),
% 81.39/80.99 inference(rename_variables,[],[3251])).
% 81.39/80.99 cnf(12568,plain,
% 81.39/80.99 (P48(x125681,x125682,f254(x125681,x125682))),
% 81.39/80.99 inference(rename_variables,[],[3251])).
% 81.39/80.99 cnf(12574,plain,
% 81.39/80.99 (E(f193(f885(f884(x125741,x125741),a871)),f254(x125741,f193(f885(x125741,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3359])).
% 81.39/80.99 cnf(12576,plain,
% 81.39/80.99 (E(f328(f253(x125761,x125761),f254(x125761,x125762)),x125762)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(12578,plain,
% 81.39/80.99 (P20(x125781,x125782,f193(f885(f876(x125781),a871)))),
% 81.39/80.99 inference(rename_variables,[],[3344])).
% 81.39/80.99 cnf(12591,plain,
% 81.39/80.99 (P52(x125911,x125911,f254(x125911,x125912))),
% 81.39/80.99 inference(rename_variables,[],[3252])).
% 81.39/80.99 cnf(12597,plain,
% 81.39/80.99 (P53(x125971,f193(f885(x125971,a871)),x125972)),
% 81.39/80.99 inference(rename_variables,[],[3305])).
% 81.39/80.99 cnf(12601,plain,
% 81.39/80.99 (E(f328(f253(x126011,x126011),f254(x126011,x126012)),x126012)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(12603,plain,
% 81.39/80.99 (P33(x126031,x126032,f119(x126031),f119(x126031))),
% 81.39/80.99 inference(rename_variables,[],[3536])).
% 81.39/80.99 cnf(12605,plain,
% 81.39/80.99 (P33(x126051,x126052,f119(x126051),f119(x126051))),
% 81.39/80.99 inference(rename_variables,[],[3536])).
% 81.39/80.99 cnf(12609,plain,
% 81.39/80.99 (E(f328(f253(x126091,x126091),f254(x126091,x126092)),x126092)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(12611,plain,
% 81.39/80.99 (P30(x126111,f2(a877),f328(f328(f328(f93(x126111),x126112),f328(a26,x126113)),x126114))),
% 81.39/80.99 inference(rename_variables,[],[3661])).
% 81.39/80.99 cnf(12623,plain,
% 81.39/80.99 (P42(x126231,x126232,x126233,x126234,f193(f885(x126231,a871)),x126234)),
% 81.39/80.99 inference(rename_variables,[],[4233])).
% 81.39/80.99 cnf(12626,plain,
% 81.39/80.99 (P42(x126261,x126262,x126263,x126264,f193(f885(x126261,a871)),x126264)),
% 81.39/80.99 inference(rename_variables,[],[4233])).
% 81.39/80.99 cnf(12630,plain,
% 81.39/80.99 (P11(x126301,f885(x126301,a871),f306(x126301))),
% 81.39/80.99 inference(rename_variables,[],[3255])).
% 81.39/80.99 cnf(12635,plain,
% 81.39/80.99 (P39(x126351,f196(x126351))),
% 81.39/80.99 inference(rename_variables,[],[3113])).
% 81.39/80.99 cnf(12642,plain,
% 81.39/80.99 (P24(f328(f328(f245(a877),f2(a877)),f328(a118,x126421)))),
% 81.39/80.99 inference(rename_variables,[],[3368])).
% 81.39/80.99 cnf(12643,plain,
% 81.39/80.99 (~E(f328(a118,x126431),x126431)),
% 81.39/80.99 inference(rename_variables,[],[4458])).
% 81.39/80.99 cnf(12649,plain,
% 81.39/80.99 (P24(f328(f328(f245(a877),x126491),f328(a118,x126491)))),
% 81.39/80.99 inference(rename_variables,[],[3356])).
% 81.39/80.99 cnf(12654,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x126541),f2(a877)))),
% 81.39/80.99 inference(rename_variables,[],[4532])).
% 81.39/80.99 cnf(12663,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a1),f328(f106(a1),x126631)),f328(f80(a1),f328(f106(a1),x126632))))),
% 81.39/80.99 inference(rename_variables,[],[4555])).
% 81.39/80.99 cnf(12673,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x126731),f2(a877)))),
% 81.39/80.99 inference(rename_variables,[],[4532])).
% 81.39/80.99 cnf(12676,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x126761),f2(a877)))),
% 81.39/80.99 inference(rename_variables,[],[4532])).
% 81.39/80.99 cnf(12679,plain,
% 81.39/80.99 (P24(f328(f62(a877),f301(a877,x126791,x126792)))),
% 81.39/80.99 inference(rename_variables,[],[3498])).
% 81.39/80.99 cnf(12682,plain,
% 81.39/80.99 (P24(f328(f62(a877),f301(a877,x126821,x126822)))),
% 81.39/80.99 inference(rename_variables,[],[3498])).
% 81.39/80.99 cnf(12685,plain,
% 81.39/80.99 (P24(f328(f62(a877),f301(a877,x126851,x126852)))),
% 81.39/80.99 inference(rename_variables,[],[3498])).
% 81.39/80.99 cnf(12688,plain,
% 81.39/80.99 (P24(f328(f62(a877),f301(a877,x126881,x126882)))),
% 81.39/80.99 inference(rename_variables,[],[3498])).
% 81.39/80.99 cnf(12695,plain,
% 81.39/80.99 (P24(f328(f328(f244(a1),f328(f80(a1),f328(f106(a1),x126951))),f328(f106(a1),x126952)))),
% 81.39/80.99 inference(rename_variables,[],[3765])).
% 81.39/80.99 cnf(12700,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x127001),f2(a877)))),
% 81.39/80.99 inference(rename_variables,[],[4532])).
% 81.39/80.99 cnf(12701,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x127011),x127011))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12708,plain,
% 81.39/80.99 (P24(f328(f328(f245(a877),x127081),f328(a118,x127081)))),
% 81.39/80.99 inference(rename_variables,[],[3356])).
% 81.39/80.99 cnf(12713,plain,
% 81.39/80.99 (~E(f328(a118,x127131),f2(a877))),
% 81.39/80.99 inference(rename_variables,[],[4468])).
% 81.39/80.99 cnf(12718,plain,
% 81.39/80.99 (P24(f328(f328(f244(a1),x127181),x127181))),
% 81.39/80.99 inference(rename_variables,[],[3284])).
% 81.39/80.99 cnf(12721,plain,
% 81.39/80.99 (P24(f328(f62(a877),f301(a877,x127211,x127212)))),
% 81.39/80.99 inference(rename_variables,[],[3498])).
% 81.39/80.99 cnf(12724,plain,
% 81.39/80.99 (P24(f328(f62(a877),f301(a877,x127241,x127242)))),
% 81.39/80.99 inference(rename_variables,[],[3498])).
% 81.39/80.99 cnf(12727,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x127271),x127271))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12728,plain,
% 81.39/80.99 (~E(f328(a118,x127281),f2(a877))),
% 81.39/80.99 inference(rename_variables,[],[4468])).
% 81.39/80.99 cnf(12745,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),f45(a877,x127451,x127452)),x127451))),
% 81.39/80.99 inference(rename_variables,[],[3743])).
% 81.39/80.99 cnf(12750,plain,
% 81.39/80.99 (P24(f328(f328(f245(a877),x127501),f328(a118,x127501)))),
% 81.39/80.99 inference(rename_variables,[],[3356])).
% 81.39/80.99 cnf(12753,plain,
% 81.39/80.99 (P24(f328(f328(f245(a877),x127531),f328(a118,x127531)))),
% 81.39/80.99 inference(rename_variables,[],[3356])).
% 81.39/80.99 cnf(12754,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x127541),f2(a877)))),
% 81.39/80.99 inference(rename_variables,[],[4532])).
% 81.39/80.99 cnf(12765,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a1),f328(f106(a1),x127651)),f2(a1)))),
% 81.39/80.99 inference(rename_variables,[],[4548])).
% 81.39/80.99 cnf(12766,plain,
% 81.39/80.99 (P24(f328(f252(f885(x127661,a871)),x127662))),
% 81.39/80.99 inference(rename_variables,[],[3350])).
% 81.39/80.99 cnf(12769,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a1),f328(f106(a1),x127691)),f2(a1)))),
% 81.39/80.99 inference(rename_variables,[],[4548])).
% 81.39/80.99 cnf(12770,plain,
% 81.39/80.99 (P24(f328(f252(f885(x127701,a871)),x127702))),
% 81.39/80.99 inference(rename_variables,[],[3350])).
% 81.39/80.99 cnf(12773,plain,
% 81.39/80.99 (P24(f328(f252(f885(x127731,a871)),x127732))),
% 81.39/80.99 inference(rename_variables,[],[3350])).
% 81.39/80.99 cnf(12784,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x127841),x127842),f193(f885(x127841,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12785,plain,
% 81.39/80.99 (P24(f328(f62(x127851),f193(f885(x127851,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3364])).
% 81.39/80.99 cnf(12794,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),f2(a877)),x127941))),
% 81.39/80.99 inference(rename_variables,[],[3307])).
% 81.39/80.99 cnf(12797,plain,
% 81.39/80.99 (P24(f328(f328(f245(a877),x127971),f328(a118,x127971)))),
% 81.39/80.99 inference(rename_variables,[],[3356])).
% 81.39/80.99 cnf(12798,plain,
% 81.39/80.99 (~E(f328(a118,x127981),x127981)),
% 81.39/80.99 inference(rename_variables,[],[4458])).
% 81.39/80.99 cnf(12801,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x128011),x128012),f193(f885(x128011,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12804,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x128041),x128042),f193(f885(x128041,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12807,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x128071),x128071))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12815,plain,
% 81.39/80.99 (P24(f328(f328(f245(a877),x128151),f328(a118,x128151)))),
% 81.39/80.99 inference(rename_variables,[],[3356])).
% 81.39/80.99 cnf(12818,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x128181),x128181))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12823,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x128231),x128231))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12826,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x128261),x128261))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12829,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x128291),x128291))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12832,plain,
% 81.39/80.99 (E(f328(f328(f22(f885(x128321,a871)),f193(f885(x128321,a871))),x128322),f193(f885(x128321,a871)))),
% 81.39/80.99 inference(rename_variables,[],[3557])).
% 81.39/80.99 cnf(12833,plain,
% 81.39/80.99 (P24(f328(f62(x128331),f193(f885(x128331,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3364])).
% 81.39/80.99 cnf(12836,plain,
% 81.39/80.99 (E(f328(f328(f22(f885(x128361,a871)),f193(f885(x128361,a871))),x128362),f193(f885(x128361,a871)))),
% 81.39/80.99 inference(rename_variables,[],[3557])).
% 81.39/80.99 cnf(12837,plain,
% 81.39/80.99 (P24(f328(f62(x128371),f193(f885(x128371,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3364])).
% 81.39/80.99 cnf(12840,plain,
% 81.39/80.99 (E(f328(f328(f22(f885(x128401,a871)),f193(f885(x128401,a871))),x128402),f193(f885(x128401,a871)))),
% 81.39/80.99 inference(rename_variables,[],[3557])).
% 81.39/80.99 cnf(12841,plain,
% 81.39/80.99 (P24(f328(f62(x128411),f193(f885(x128411,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3364])).
% 81.39/80.99 cnf(12844,plain,
% 81.39/80.99 (E(f328(f328(f22(f885(x128441,a871)),f193(f885(x128441,a871))),x128442),f193(f885(x128441,a871)))),
% 81.39/80.99 inference(rename_variables,[],[3557])).
% 81.39/80.99 cnf(12845,plain,
% 81.39/80.99 (P24(f328(f62(x128451),f193(f885(x128451,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3364])).
% 81.39/80.99 cnf(12849,plain,
% 81.39/80.99 (E(f328(f253(x128491,x128491),f254(x128491,x128492)),x128492)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(12854,plain,
% 81.39/80.99 (E(f328(f328(f22(f885(x128541,a871)),f193(f885(x128541,a871))),x128542),f193(f885(x128541,a871)))),
% 81.39/80.99 inference(rename_variables,[],[3557])).
% 81.39/80.99 cnf(12855,plain,
% 81.39/80.99 (P24(f328(f62(x128551),f193(f885(x128551,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3364])).
% 81.39/80.99 cnf(12859,plain,
% 81.39/80.99 (P24(f328(f62(x128591),f193(f885(x128591,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3364])).
% 81.39/80.99 cnf(12862,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x128621),x128621))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12866,plain,
% 81.39/80.99 (P24(f328(f328(f244(a1),x128661),x128661))),
% 81.39/80.99 inference(rename_variables,[],[3284])).
% 81.39/80.99 cnf(12873,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x128731),x128731))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12886,plain,
% 81.39/80.99 (P24(f328(f328(f244(a1),x128861),x128861))),
% 81.39/80.99 inference(rename_variables,[],[3284])).
% 81.39/80.99 cnf(12895,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x128951),x128952),f193(f885(x128951,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12908,plain,
% 81.39/80.99 (P24(f328(f328(f330(x129081),x129082),f252(f885(x129081,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3444])).
% 81.39/80.99 cnf(12912,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x129121,a871)),x129122),f252(f885(x129121,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3668])).
% 81.39/80.99 cnf(12915,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x129151,a871)),f328(f171(x129151),f328(f135(x129151,x129152),x129153))),f328(f171(x129151),x129153)))),
% 81.39/80.99 inference(rename_variables,[],[3932])).
% 81.39/80.99 cnf(12921,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x129211),f2(a877)))),
% 81.39/80.99 inference(rename_variables,[],[4532])).
% 81.39/80.99 cnf(12922,plain,
% 81.39/80.99 (P24(f328(f328(f244(a1),x129221),x129221))),
% 81.39/80.99 inference(rename_variables,[],[3284])).
% 81.39/80.99 cnf(12926,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x129261),f2(a877)))),
% 81.39/80.99 inference(rename_variables,[],[4532])).
% 81.39/80.99 cnf(12927,plain,
% 81.39/80.99 (P24(f328(f328(f244(a1),x129271),x129271))),
% 81.39/80.99 inference(rename_variables,[],[3284])).
% 81.39/80.99 cnf(12931,plain,
% 81.39/80.99 (P24(f328(f328(f328(f328(a202,a24),x129311),x129312),x129311))),
% 81.39/80.99 inference(rename_variables,[],[3622])).
% 81.39/80.99 cnf(12936,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x129361),x129361))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12943,plain,
% 81.39/80.99 (E(f328(f328(f16(x129431,x129432),x129433),x129434),x129433)),
% 81.39/80.99 inference(rename_variables,[],[3274])).
% 81.39/80.99 cnf(12948,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x129481,a871)),f328(f171(x129481),f169(x129481,x129482,x129483))),f328(f171(x129481),x129483)))),
% 81.39/80.99 inference(rename_variables,[],[3983])).
% 81.39/80.99 cnf(12952,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x129521),f2(a877)))),
% 81.39/80.99 inference(rename_variables,[],[4532])).
% 81.39/80.99 cnf(12953,plain,
% 81.39/80.99 (P24(f328(f328(f244(a1),x129531),x129531))),
% 81.39/80.99 inference(rename_variables,[],[3284])).
% 81.39/80.99 cnf(12957,plain,
% 81.39/80.99 (~P24(f328(f328(f245(a877),x129571),f2(a877)))),
% 81.39/80.99 inference(rename_variables,[],[4532])).
% 81.39/80.99 cnf(12958,plain,
% 81.39/80.99 (P24(f328(f328(f244(a1),x129581),x129581))),
% 81.39/80.99 inference(rename_variables,[],[3284])).
% 81.39/80.99 cnf(12963,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x129631),x129631))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12966,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),x129661),x129661))),
% 81.39/80.99 inference(rename_variables,[],[3283])).
% 81.39/80.99 cnf(12969,plain,
% 81.39/80.99 (~P24(f328(f328(f244(a877),f328(a118,x129691)),x129691))),
% 81.39/80.99 inference(rename_variables,[],[4541])).
% 81.39/80.99 cnf(12975,plain,
% 81.39/80.99 (P24(f328(f328(f330(x129751),f328(x129752,x129753)),f328(f307(x129754,x129751,x129752),f252(f885(x129754,a871)))))),
% 81.39/80.99 inference(rename_variables,[],[3888])).
% 81.39/80.99 cnf(12976,plain,
% 81.39/80.99 (P21(x129761,x129761,f5(x129761),x129762)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(12980,plain,
% 81.39/80.99 (P24(f328(f328(f330(x129801),x129802),f252(f885(x129801,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3444])).
% 81.39/80.99 cnf(12981,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x129811),x129812),f193(f885(x129811,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(12985,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x129851,a871)),x129852),f252(f885(x129851,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3668])).
% 81.39/80.99 cnf(12986,plain,
% 81.39/80.99 (P21(x129861,x129861,f5(x129861),x129862)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(12990,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x129901,a871)),x129902),f252(f885(x129901,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3668])).
% 81.39/80.99 cnf(12991,plain,
% 81.39/80.99 (P21(x129911,x129911,f5(x129911),x129912)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(12995,plain,
% 81.39/80.99 (P21(x129951,x129951,f5(x129951),x129952)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(12998,plain,
% 81.39/80.99 (~P24(f328(f328(f245(f885(x129981,a871)),x129982),f193(f885(x129981,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4554])).
% 81.39/80.99 cnf(13001,plain,
% 81.39/80.99 (P21(x130011,x130011,f5(x130011),x130012)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(13004,plain,
% 81.39/80.99 (P21(x130041,x130041,f5(x130041),x130042)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(13007,plain,
% 81.39/80.99 (P24(f328(f328(f330(x130071),f328(x130072,x130073)),f328(f307(x130074,x130071,x130072),f252(f885(x130074,a871)))))),
% 81.39/80.99 inference(rename_variables,[],[3888])).
% 81.39/80.99 cnf(13013,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x130131,a871)),x130132),f252(f885(x130131,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3668])).
% 81.39/80.99 cnf(13018,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x130181,a871)),f193(f885(x130181,a871))),x130182))),
% 81.39/80.99 inference(rename_variables,[],[3734])).
% 81.39/80.99 cnf(13022,plain,
% 81.39/80.99 (E(f328(f253(x130221,x130221),f254(x130221,x130222)),x130222)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(13026,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x130261),x130262),f193(f885(x130261,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(13031,plain,
% 81.39/80.99 (P21(x130311,x130311,f5(x130311),x130312)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(13034,plain,
% 81.39/80.99 (P24(f328(f328(f330(x130341),x130342),f252(f885(x130341,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3444])).
% 81.39/80.99 cnf(13038,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x130381,a871)),x130382),x130382))),
% 81.39/80.99 inference(rename_variables,[],[3586])).
% 81.39/80.99 cnf(13044,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x130441),x130442),f193(f885(x130441,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(13047,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x130471),x130472),f193(f885(x130471,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(13051,plain,
% 81.39/80.99 (P21(x130511,x130511,f5(x130511),x130512)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(13054,plain,
% 81.39/80.99 (E(f328(f328(f16(x130541,x130542),x130543),x130544),x130543)),
% 81.39/80.99 inference(rename_variables,[],[3274])).
% 81.39/80.99 cnf(13057,plain,
% 81.39/80.99 (P24(f328(f328(f245(a877),x130571),f328(a118,x130571)))),
% 81.39/80.99 inference(rename_variables,[],[3356])).
% 81.39/80.99 cnf(13058,plain,
% 81.39/80.99 (~E(f328(a118,x130581),x130581)),
% 81.39/80.99 inference(rename_variables,[],[4458])).
% 81.39/80.99 cnf(13061,plain,
% 81.39/80.99 (P24(f328(f328(f245(a877),x130611),f328(a118,f328(f328(f81(a877),x130612),x130611))))),
% 81.39/80.99 inference(rename_variables,[],[3736])).
% 81.39/80.99 cnf(13062,plain,
% 81.39/80.99 (P24(f328(f328(f245(a877),x130621),f328(a118,x130621)))),
% 81.39/80.99 inference(rename_variables,[],[3356])).
% 81.39/80.99 cnf(13071,plain,
% 81.39/80.99 (P24(f328(f328(f244(a1),f2(a1)),f328(f106(a1),x130711)))),
% 81.39/80.99 inference(rename_variables,[],[3387])).
% 81.39/80.99 cnf(13074,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),f2(a877)),x130741))),
% 81.39/80.99 inference(rename_variables,[],[3307])).
% 81.39/80.99 cnf(13078,plain,
% 81.39/80.99 (~E(f328(a118,x130781),f2(a877))),
% 81.39/80.99 inference(rename_variables,[],[4468])).
% 81.39/80.99 cnf(13083,plain,
% 81.39/80.99 (P24(f328(f328(f330(x130831),x130832),f252(f885(x130831,a871))))),
% 81.39/80.99 inference(rename_variables,[],[3444])).
% 81.39/80.99 cnf(13087,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x130871),x130872),f193(f885(x130871,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(13090,plain,
% 81.39/80.99 (P24(f328(f62(a877),f301(a877,x130901,x130902)))),
% 81.39/80.99 inference(rename_variables,[],[3498])).
% 81.39/80.99 cnf(13091,plain,
% 81.39/80.99 (E(f328(f328(f242(a877),f328(a118,x130911)),f328(a118,x130912)),f328(a118,f328(f328(f242(a877),x130911),x130912)))),
% 81.39/80.99 inference(rename_variables,[],[3461])).
% 81.39/80.99 cnf(13094,plain,
% 81.39/80.99 (P24(f328(f62(a877),f301(a877,x130941,x130942)))),
% 81.39/80.99 inference(rename_variables,[],[3498])).
% 81.39/80.99 cnf(13095,plain,
% 81.39/80.99 (E(f328(f328(f243(a877),f328(a118,x130951)),f328(a118,x130952)),f328(a118,f328(f328(f243(a877),x130951),x130952)))),
% 81.39/80.99 inference(rename_variables,[],[3462])).
% 81.39/80.99 cnf(13098,plain,
% 81.39/80.99 (P24(f328(f62(a877),f301(a877,x130981,x130982)))),
% 81.39/80.99 inference(rename_variables,[],[3498])).
% 81.39/80.99 cnf(13106,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x131061,a871)),f328(f171(x131061),f328(f135(x131061,x131062),x131063))),f328(f171(x131061),x131063)))),
% 81.39/80.99 inference(rename_variables,[],[3932])).
% 81.39/80.99 cnf(13107,plain,
% 81.39/80.99 (E(f328(f328(f16(x131071,x131072),x131073),x131074),x131073)),
% 81.39/80.99 inference(rename_variables,[],[3274])).
% 81.39/80.99 cnf(13110,plain,
% 81.39/80.99 (P24(f328(f328(f244(f885(x131101,a871)),f328(f171(x131101),f328(f328(f174(x131101),x131102),x131103))),f328(f171(x131101),x131103)))),
% 81.39/80.99 inference(rename_variables,[],[3977])).
% 81.39/80.99 cnf(13111,plain,
% 81.39/80.99 (E(f328(f328(f16(x131111,x131112),x131113),x131114),x131113)),
% 81.39/80.99 inference(rename_variables,[],[3274])).
% 81.39/80.99 cnf(13115,plain,
% 81.39/80.99 (E(f328(f328(f16(x131151,x131152),x131153),x131154),x131153)),
% 81.39/80.99 inference(rename_variables,[],[3274])).
% 81.39/80.99 cnf(13128,plain,
% 81.39/80.99 (P24(f328(f328(f244(a1),f2(a1)),f328(f106(a1),x131281)))),
% 81.39/80.99 inference(rename_variables,[],[3387])).
% 81.39/80.99 cnf(13131,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x131311),x131312),f193(f885(x131311,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(13134,plain,
% 81.39/80.99 (~P24(f328(f328(f330(x131341),x131342),f193(f885(x131341,a871))))),
% 81.39/80.99 inference(rename_variables,[],[4544])).
% 81.39/80.99 cnf(13135,plain,
% 81.39/80.99 (E(f328(f253(x131351,x131351),f254(x131351,x131352)),x131352)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(13136,plain,
% 81.39/80.99 (P21(x131361,x131361,f5(x131361),x131362)),
% 81.39/80.99 inference(rename_variables,[],[3527])).
% 81.39/80.99 cnf(13140,plain,
% 81.39/80.99 (E(f328(f253(x131401,x131401),f254(x131401,x131402)),x131402)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(13154,plain,
% 81.39/80.99 (P24(f328(f328(f244(a877),f2(a877)),x131541))),
% 81.39/80.99 inference(rename_variables,[],[3307])).
% 81.39/80.99 cnf(13155,plain,
% 81.39/80.99 (P24(f328(f328(f245(a877),f2(a877)),f328(a118,x131551)))),
% 81.39/80.99 inference(rename_variables,[],[3368])).
% 81.39/80.99 cnf(13156,plain,
% 81.39/80.99 (E(f328(f253(x131561,x131561),f254(x131561,x131562)),x131562)),
% 81.39/80.99 inference(rename_variables,[],[3241])).
% 81.39/80.99 cnf(13202,plain,
% 81.39/80.99 ($false),
% 81.39/80.99 inference(scs_inference,[],[3567,3527,11053,12099,12204,12296,12334,12342,12407,12550,12552,12976,12986,12991,12995,13001,13004,13031,13051,13136,3536,12163,12603,12605,3537,12235,3251,12566,12568,3252,12591,3218,12480,4494,4495,11677,4233,12623,12626,3255,12630,3093,3113,12635,3154,12546,4476,3588,4458,10211,10214,10224,10235,10344,10347,10350,10453,10566,10872,11038,11041,11239,11329,11336,11350,11402,11405,11514,11562,11578,11878,11906,11918,11950,12048,12159,12166,12326,12377,12520,12643,12798,13058,4473,10437,10530,3345,3305,12597,3496,3200,4468,12713,12728,13078,2871,2872,2882,2883,2885,2886,2888,2889,2892,2893,2894,2897,2898,2903,2904,2907,2908,2909,2913,2914,2920,2923,2930,2932,2933,2934,2936,2940,2941,2945,2952,2956,2957,2959,2962,2963,2964,2966,2969,2970,2973,2986,2993,3002,3005,3015,3018,3019,3021,3022,3029,3030,3051,3057,4453,3072,3153,4454,3624,3126,11326,3265,3329,3238,3241,10208,10217,10278,10281,10371,10374,10665,11341,11344,11457,11501,11506,11607,12069,12272,12460,12522,12524,12531,12533,12558,12560,12562,12576,12601,12609,12849,13022,13135,13140,13156,3611,3862,3213,11604,12355,12359,12363,3219,10685,11610,3226,3746,3980,3115,3116,4470,4482,3836,11376,3344,12578,3180,3145,3321,3661,12611,3140,3954,3161,3666,4437,3123,3124,3103,3160,3298,12040,12189,12410,12483,3346,10819,12160,3211,3212,3236,10478,3391,4553,10407,3920,4484,10269,10434,11236,12322,12356,12360,4493,3274,11700,11703,12943,13054,13107,13111,13115,4542,10988,11058,11279,11282,3269,3392,3610,3384,3359,12574,3175,10336,10641,3176,4526,3449,3168,3094,3279,4561,3196,11366,4067,12345,12472,3922,10994,11120,11171,12306,12312,12421,12424,12447,4566,10926,11125,11230,11252,11287,11293,12251,4567,11027,11128,11233,4568,11131,11182,4569,11185,4570,3195,3489,12207,12248,3649,4349,4350,3472,4481,11357,3590,3627,3800,3557,12832,12836,12840,12844,12854,3846,12201,3475,3727,3356,10355,10473,10544,10605,10608,10644,10738,10978,11874,11940,12016,12060,12137,12140,12451,12649,12708,12750,12753,12797,12815,13057,13062,3738,11595,3267,3368,11715,12642,13155,3552,4532,10246,10249,10275,10748,10761,10882,11302,11369,11766,11771,11992,11995,12081,12090,12254,12349,12654,12673,12676,12700,12754,12921,12926,12952,12957,4548,11476,11509,11546,11575,12765,12769,3725,3497,3498,11895,12679,12682,12685,12688,12721,12724,13090,13094,13098,3871,3461,13091,3462,13095,3313,3315,3288,4529,3174,3488,4478,3677,4203,3989,3481,4549,4061,11247,3609,3328,11723,11726,12170,12276,12431,4031,3988,12222,3932,10816,12028,12054,12229,12454,12915,13106,3977,13110,3983,11000,12096,12169,12228,12275,12948,3984,3650,11877,12023,12104,12150,4020,3668,10997,11063,11144,11204,12047,12118,12372,12444,12457,12912,12985,12990,13013,4554,10764,11136,12232,12998,3283,10364,10460,10591,10651,10720,10767,10770,10803,10829,10866,10904,10942,11671,11718,11847,11905,11921,11924,11927,11930,12111,12125,12128,12131,12134,12215,12279,12383,12427,12497,12701,12727,12807,12818,12823,12826,12829,12862,12873,12936,12963,12966,3284,10393,10448,10656,10743,10869,11449,11751,11754,11763,11853,11864,11883,11888,11933,11953,11970,12718,12866,12886,12922,12927,12953,12958,3287,3364,12084,12785,12833,12837,12841,12845,12855,12859,4528,10312,10402,10515,10539,10785,10832,10842,11523,11625,11646,11649,11652,11668,11821,11824,11827,11830,11917,11936,11939,11949,12004,12007,12010,12013,12091,12181,12184,12282,12285,12348,12376,12413,12501,3444,10611,10877,10923,11193,11271,11437,11680,12325,12504,12908,12980,13034,13083,4544,10794,10806,10915,10933,10936,10991,11077,11085,11101,11139,11156,11165,11201,11242,11262,11265,11268,11296,11309,11312,11697,11732,11998,12001,12035,12085,12114,12260,12303,12309,12395,12398,12417,12471,12477,12486,12489,12494,12514,12784,12801,12804,12895,12981,13026,13044,13047,13087,13131,13134,3350,10638,10668,10677,11222,11778,12414,12428,12766,12770,12773,3387,13071,13128,3381,3804,3743,10315,11598,11628,12745,4541,10266,10626,10629,11080,11098,11561,11616,11656,11681,11784,11809,11812,11815,11818,12080,12969,3307,10671,10826,10897,11629,11783,11975,12192,12216,12794,13074,13154,3765,11729,12695,4111,3503,4539,3776,3812,4518,4521,4522,3258,3262,4520,4519,4523,4286,3783,3599,11591,4209,11456,4556,10240,10243,10496,10547,10550,10555,10965,11431,11684,11787,4564,11159,11276,11318,3997,3888,11315,11655,11659,12333,12341,12420,12975,13007,3732,10939,10945,10960,11867,11902,12117,12391,3586,11162,12143,12257,12267,12338,12386,12394,12511,13038,3622,12931,4065,3734,10674,11016,11168,11198,11209,12337,12380,13018,3555,10594,10597,10680,10853,3554,4560,11592,4550,4555,12663,4562,10731,10835,11147,11299,11434,11462,12210,12219,12263,12441,4171,10809,12051,12240,12266,4072,3764,12517,3712,3713,4558,10288,10291,10632,10635,11473,11660,12450,4559,11572,11665,3736,10600,10859,13061,4004,4580,4585,4592,4608,4657,4659,4689,4706,4713,4714,4753,4783,4789,4874,4900,4901,4961,4962,4984,4985,4998,5002,5024,5031,5048,5051,5052,5053,5058,5059,5080,5105,5106,5116,5121,5127,5172,5173,5181,5191,5195,5197,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55,6794,6809,6881,6882,6886,6908,6931,6939,6941,6988,7013,7014,7032,7033,7068,7112,7113,7210,7271,7272,7273,7274,7288,7321,7377,7378,7387,7395,7396,7408,7440,7441,7442,7443,7585,7587,7588,7589,7595,7596,7805,7811,7812,7818,7821,7860,7939,7981,8039,8060,8061,8076,8135,8238,8307,8308,8310,8313,8345,8407,8408,8481,8502,8503,8504,8505,8648,8861,8885,8886,8965,8980,9035,9036,9150,9152,9188,9211,9245,9287,9478,9736,9867,9931,9989,9991,10187,6033,6406,6407,6494,6515,6516,6930,7148,8573,8606,8802,8991,8992,9063,9064,9335,9336,9337,9338,9537,9806,10113,10164,10165,6476,8398,8399,8851,8869,9248,9807,9814,10031,10163,4618,4649,4651,4652,4707,4715,4852,4868,4869,4891,4894]),
% 81.39/80.99 ['proof']).
% 81.39/80.99 % SZS output end Proof
% 81.39/80.99 % Total time :66.990000s
%------------------------------------------------------------------------------