TSTP Solution File: SWW378+1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW378+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 : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:08:50 EDT 2024
% Result : Theorem 160.93s 160.64s
% Output : CNFRefutation 161.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW378+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
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jun 19 09:49:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.46/0.58 start to proof:theBenchmark
% 160.44/160.47 %-------------------------------------------
% 160.44/160.47 % File :CSE---1.7
% 160.44/160.47 % Problem :theBenchmark
% 160.44/160.47 % Transform :cnf
% 160.44/160.47 % Format :tptp:raw
% 160.44/160.47 % Command :java -jar mcs_scs.jar %d %s
% 160.44/160.47
% 160.44/160.47 % Result :Theorem 146.580000s
% 160.44/160.47 % Output :CNFRefutation 146.580000s
% 160.44/160.47 %-------------------------------------------
% 160.44/160.48 %------------------------------------------------------------------------------
% 160.44/160.48 % File : SWW378+1 : TPTP v8.2.0. Released v5.2.0.
% 160.44/160.48 % Domain : Software Verification
% 160.44/160.48 % Problem : Hoare's Logic with Procedures 435570, 5000 axioms selected
% 160.44/160.48 % Version : Especial.
% 160.44/160.48 % English :
% 160.44/160.48
% 160.44/160.48 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 160.44/160.48 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 160.44/160.48 % Source : [Bla11]
% 160.44/160.48 % Names : hoare_435570.5000.p [Bla11]
% 160.44/160.48
% 160.44/160.48 % Status : ContradictoryAxioms
% 160.44/160.48 % Rating : 0.83 v8.2.0, 0.78 v8.1.0, 0.83 v7.5.0, 0.84 v7.4.0, 0.93 v7.3.0, 0.90 v7.1.0, 0.87 v7.0.0, 0.90 v6.4.0, 0.88 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.96 v5.3.0, 1.00 v5.2.0
% 160.44/160.48 % Syntax : Number of formulae : 5243 (1729 unt; 0 def)
% 160.44/160.48 % Number of atoms : 12616 (4511 equ)
% 160.44/160.48 % Maximal formula atoms : 13 ( 2 avg)
% 160.44/160.48 % Number of connectives : 8384 (1011 ~; 154 |; 717 &)
% 160.44/160.48 % ( 894 <=>;5608 =>; 0 <=; 0 <~>)
% 160.44/160.48 % Maximal formula depth : 22 ( 6 avg)
% 160.44/160.48 % Maximal term depth : 19 ( 2 avg)
% 160.44/160.48 % Number of predicates : 146 ( 145 usr; 2 prp; 0-6 aty)
% 160.44/160.48 % Number of functors : 395 ( 395 usr; 58 con; 0-7 aty)
% 160.44/160.48 % Number of variables : 16660 (16517 !; 143 ?)
% 160.44/160.48 % SPC : FOF_CAX_RFO_SEQ
% 160.44/160.48
% 160.44/160.48 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 160.44/160.48 % 2011-03-01 12:52:03
% 160.44/160.48 %------------------------------------------------------------------------------
% 160.44/160.48 %----Relevant facts (4986)
% 160.44/160.48 fof(fact_ext,axiom,
% 160.44/160.48 ! [V_g_2,V_f_2] :
% 160.44/160.48 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 160.44/160.48 => V_f_2 = V_g_2 ) ).
% 160.44/160.48
% 160.44/160.48 fof(fact_triple_Oinject,axiom,
% 160.44/160.48 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] :
% 160.44/160.48 ( 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)
% 160.44/160.48 <=> ( V_fun1_2 = V_fun1_H_2
% 160.44/160.48 & V_com_2 = V_com_H_2
% 160.44/160.48 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 160.44/160.48
% 160.44/160.48 fof(fact_cut,axiom,
% 160.44/160.48 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] :
% 160.44/160.48 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2)
% 160.44/160.48 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_G_H_2)
% 160.44/160.48 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ).
% 160.44/160.48
% 160.44/160.48 fof(fact_hoare__derivs_OBody,axiom,
% 160.44/160.48 ! [V_Procsa_2,V_Q_2,V_P_2,V_Ga_2,T_a] :
% 160.44/160.48 ( 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_Ga_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_Procsa_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_Procsa_2))
% 160.44/160.48 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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_Procsa_2)) ) ).
% 160.44/160.48
% 160.44/160.48 fof(fact_evalc__elim__cases_I6_J,axiom,
% 160.44/160.48 ! [V_s1,V_s,V_P] :
% 160.44/160.48 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1))
% 160.44/160.48 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ).
% 160.44/160.48
% 160.44/160.48 fof(fact_evalc_OBody,axiom,
% 160.44/160.48 ! [V_s1,V_s0,V_pn] :
% 160.44/160.48 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1))
% 160.44/160.48 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ).
% 160.44/160.48
% 160.44/160.48 fof(fact_Body__sound__lemma,axiom,
% 160.44/160.48 ! [V_Procsa_2,V_Q_2,V_P_2,V_Ga_2,T_a] :
% 160.44/160.49 ( 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_Ga_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_Procsa_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_Procsa_2))
% 160.44/160.49 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_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_Procsa_2)) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_evalc_Oequations_I9_J,axiom,
% 160.44/160.49 ! [V_a3_2,V_a2_2,V_a1_2] :
% 160.44/160.49 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
% 160.44/160.49 <=> hBOOL(hAPP(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)) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup1E,axiom,
% 160.44/160.49 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 160.44/160.49 ( 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))
% 160.44/160.49 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 160.44/160.49 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup1CI,axiom,
% 160.44/160.49 ! [T_a,V_A_2,V_x_2,V_B_2] :
% 160.44/160.49 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 160.44/160.49 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 160.44/160.49 => 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)) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup__fun__def,axiom,
% 160.44/160.49 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 160.44/160.49 ( class_Lattices_Olattice(T_a)
% 160.44/160.49 => 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)) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_triple_Orecs,axiom,
% 160.44/160.49 ! [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) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_triple_Osimps_I2_J,axiom,
% 160.44/160.49 ! [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) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_image__Un,axiom,
% 160.44/160.49 ! [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)) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup__apply,axiom,
% 160.44/160.49 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 160.44/160.49 ( class_Lattices_Olattice(T_a)
% 160.44/160.49 => 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)) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_MGT__def,axiom,
% 160.44/160.49 ! [V_c_2] : c_Hoare__Mirabelle_OMGT(V_c_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_c_2),hAPP(c_Natural_Oevalc,V_c_2)) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_hoare__sound,axiom,
% 160.44/160.49 ! [V_ts_2,V_Ga_2,T_a] :
% 160.44/160.49 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
% 160.44/160.49 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup__assoc,axiom,
% 160.44/160.49 ! [V_z,V_y,V_x,T_a] :
% 160.44/160.49 ( class_Lattices_Osemilattice__sup(T_a)
% 160.44/160.49 => 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)) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_inf__sup__aci_I6_J,axiom,
% 160.44/160.49 ! [V_z,V_y,V_x,T_a] :
% 160.44/160.49 ( class_Lattices_Olattice(T_a)
% 160.44/160.49 => 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)) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup_Oassoc,axiom,
% 160.44/160.49 ! [V_c,V_b,V_a,T_a] :
% 160.44/160.49 ( class_Lattices_Osemilattice__sup(T_a)
% 160.44/160.49 => 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)) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup__left__commute,axiom,
% 160.44/160.49 ! [V_z,V_y,V_x,T_a] :
% 160.44/160.49 ( class_Lattices_Osemilattice__sup(T_a)
% 160.44/160.49 => 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)) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_inf__sup__aci_I7_J,axiom,
% 160.44/160.49 ! [V_z,V_y,V_x,T_a] :
% 160.44/160.49 ( class_Lattices_Olattice(T_a)
% 160.44/160.49 => 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)) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup_Oleft__commute,axiom,
% 160.44/160.49 ! [V_c,V_a,V_b,T_a] :
% 160.44/160.49 ( class_Lattices_Osemilattice__sup(T_a)
% 160.44/160.49 => 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)) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup__left__idem,axiom,
% 160.44/160.49 ! [V_y,V_x,T_a] :
% 160.44/160.49 ( class_Lattices_Osemilattice__sup(T_a)
% 160.44/160.49 => 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) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_inf__sup__aci_I8_J,axiom,
% 160.44/160.49 ! [V_y,V_x,T_a] :
% 160.44/160.49 ( class_Lattices_Olattice(T_a)
% 160.44/160.49 => 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) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup_Oleft__idem,axiom,
% 160.44/160.49 ! [V_b,V_a,T_a] :
% 160.44/160.49 ( class_Lattices_Osemilattice__sup(T_a)
% 160.44/160.49 => 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) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup__commute,axiom,
% 160.44/160.49 ! [V_y,V_x,T_a] :
% 160.44/160.49 ( class_Lattices_Osemilattice__sup(T_a)
% 160.44/160.49 => 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) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_inf__sup__aci_I5_J,axiom,
% 160.44/160.49 ! [V_y,V_x,T_a] :
% 160.44/160.49 ( class_Lattices_Olattice(T_a)
% 160.44/160.49 => 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) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup_Ocommute,axiom,
% 160.44/160.49 ! [V_b,V_a,T_a] :
% 160.44/160.49 ( class_Lattices_Osemilattice__sup(T_a)
% 160.44/160.49 => 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) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup__idem,axiom,
% 160.44/160.49 ! [V_x,T_a] :
% 160.44/160.49 ( class_Lattices_Osemilattice__sup(T_a)
% 160.44/160.49 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup_Oidem,axiom,
% 160.44/160.49 ! [V_a,T_a] :
% 160.44/160.49 ( class_Lattices_Osemilattice__sup(T_a)
% 160.44/160.49 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup1I2,axiom,
% 160.44/160.49 ! [V_A_2,T_a,V_x_2,V_B_2] :
% 160.44/160.49 ( hBOOL(hAPP(V_B_2,V_x_2))
% 160.44/160.49 => 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)) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_sup1I1,axiom,
% 160.44/160.49 ! [V_B_2,T_a,V_x_2,V_A_2] :
% 160.44/160.49 ( hBOOL(hAPP(V_A_2,V_x_2))
% 160.44/160.49 => 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)) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_ball__Un,axiom,
% 160.44/160.49 ! [V_P_2,V_B_2,V_A_2,T_a] :
% 160.44/160.49 ( ! [B_x] :
% 160.44/160.49 ( 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)))
% 160.44/160.49 => hBOOL(hAPP(V_P_2,B_x)) )
% 160.44/160.49 <=> ( ! [B_x] :
% 160.44/160.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.44/160.49 => hBOOL(hAPP(V_P_2,B_x)) )
% 160.44/160.49 & ! [B_x] :
% 160.44/160.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 160.44/160.49 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_bex__Un,axiom,
% 160.44/160.49 ! [V_P_2,V_B_2,V_A_2,T_a] :
% 160.44/160.49 ( ? [B_x] :
% 160.44/160.49 ( 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)))
% 160.44/160.49 & hBOOL(hAPP(V_P_2,B_x)) )
% 160.44/160.49 <=> ( ? [B_x] :
% 160.44/160.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.44/160.49 & hBOOL(hAPP(V_P_2,B_x)) )
% 160.44/160.49 | ? [B_x] :
% 160.44/160.49 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 160.44/160.49 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_Un__assoc,axiom,
% 160.44/160.49 ! [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)) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_Un__left__commute,axiom,
% 160.44/160.49 ! [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)) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_Un__left__absorb,axiom,
% 160.44/160.49 ! [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) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_Un__commute,axiom,
% 160.44/160.49 ! [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) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_Un__absorb,axiom,
% 160.44/160.49 ! [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 ).
% 160.44/160.49
% 160.44/160.49 fof(fact_com__det,axiom,
% 160.44/160.49 ! [V_u,V_t,V_s,V_c] :
% 160.44/160.49 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c),V_s),V_t))
% 160.44/160.49 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c),V_s),V_u))
% 160.44/160.49 => V_u = V_t ) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_image__image,axiom,
% 160.44/160.49 ! [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) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_image__ident,axiom,
% 160.44/160.49 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ).
% 160.44/160.49
% 160.44/160.49 fof(fact_com_Osimps_I6_J,axiom,
% 160.44/160.49 ! [V_pname_H_2,V_pname_2] :
% 160.44/160.49 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2)
% 160.44/160.49 <=> V_pname_2 = V_pname_H_2 ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_Sup__fin_Oidem,axiom,
% 160.44/160.49 ! [V_x,T_a] :
% 160.44/160.49 ( class_Lattices_Olattice(T_a)
% 160.44/160.49 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_MGT__BodyN,axiom,
% 160.44/160.49 ! [V_Ga_2,V_pn_2] :
% 160.44/160.49 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,V_pn_2))),V_Ga_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),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))))
% 160.44/160.49 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),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)))) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_Body1,axiom,
% 160.44/160.49 ! [V_pn_2,V_Procsa_2,V_Q_2,V_P_2,V_Ga_2,T_a] :
% 160.44/160.49 ( 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_Ga_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_Procsa_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_Procsa_2))
% 160.44/160.49 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procsa_2))
% 160.44/160.49 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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)))) ) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_Body__triple__valid__Suc,axiom,
% 160.44/160.49 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] :
% 160.44/160.49 ( 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))
% 160.44/160.49 <=> 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)) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_BodyN,axiom,
% 160.44/160.49 ! [V_Ga_2,V_Q_2,V_pn_2,V_P_2,T_a] :
% 160.44/160.49 ( 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_Ga_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))))
% 160.44/160.49 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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)))) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_weak__Body,axiom,
% 160.44/160.49 ! [V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_a] :
% 160.44/160.49 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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))))
% 160.44/160.49 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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)))) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_inv__imagep__def,axiom,
% 160.44/160.49 ! [V_y_2,V_x_2,V_f_2,V_r_2,T_b,T_a] :
% 160.44/160.49 ( c_Predicate_Oinv__imagep(T_a,T_b,V_r_2,V_f_2,V_x_2,V_y_2)
% 160.44/160.49 <=> hBOOL(hAPP(hAPP(V_r_2,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ).
% 160.44/160.49
% 160.44/160.49 fof(fact_MGF__complete,axiom,
% 160.44/160.49 ! [V_Q_2,V_P_2,V_c_2] :
% 160.44/160.49 ( 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)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
% 160.44/160.49 => ( 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_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
% 160.44/160.50 => 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_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ).
% 160.44/160.50
% 160.44/160.50 fof(fact_evalc__elim__cases_I1_J,axiom,
% 160.44/160.50 ! [V_t,V_s] :
% 160.44/160.50 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),V_s),V_t))
% 160.44/160.50 => V_t = V_s ) ).
% 160.44/160.50
% 160.44/160.50 fof(fact_evalc_OSkip,axiom,
% 160.44/160.50 ! [V_s] : hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),V_s),V_s)) ).
% 160.44/160.50
% 160.44/160.50 fof(fact_equalityCE,axiom,
% 160.44/160.50 ! [V_c_2,T_a,V_B_2,V_A_2] :
% 160.44/160.50 ( V_A_2 = V_B_2
% 160.44/160.50 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.44/160.50 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) )
% 160.44/160.50 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.44/160.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ) ).
% 160.44/160.50
% 160.44/160.50 fof(fact_emptyE,axiom,
% 160.44/160.50 ! [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)))) ).
% 160.44/160.50
% 160.44/160.50 fof(fact_insertE,axiom,
% 160.44/160.50 ! [V_A_2,V_b_2,V_a_2,T_a] :
% 160.44/160.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)))
% 160.44/160.50 => ( V_a_2 != V_b_2
% 160.44/160.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 160.44/160.50
% 160.44/160.50 fof(fact_insertCI,axiom,
% 160.44/160.50 ! [V_b_2,V_B_2,V_a_2,T_a] :
% 160.44/160.50 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 160.44/160.50 => V_a_2 = V_b_2 )
% 160.44/160.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ).
% 160.44/160.50
% 160.44/160.50 fof(fact_image__eqI,axiom,
% 160.44/160.50 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] :
% 160.44/160.50 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 160.44/160.50 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 160.44/160.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ).
% 160.44/160.50
% 160.44/160.50 fof(fact_UnE,axiom,
% 160.44/160.50 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 160.44/160.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 160.44/160.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.44/160.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 160.44/160.50
% 160.44/160.50 fof(fact_UnCI,axiom,
% 160.44/160.50 ! [V_A_2,V_B_2,V_c_2,T_a] :
% 160.44/160.50 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
% 160.44/160.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) )
% 160.44/160.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 160.44/160.50
% 160.44/160.50 fof(fact_empty__not__insert,axiom,
% 160.44/160.50 ! [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) ).
% 160.44/160.50
% 160.44/160.50 fof(fact_insert__not__empty,axiom,
% 160.44/160.50 ! [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)) ).
% 160.44/160.50
% 160.44/160.50 fof(fact_bot__empty__eq,axiom,
% 160.44/160.50 ! [V_x_2,T_a] :
% 160.44/160.50 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2))
% 160.44/160.50 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 160.44/160.50
% 160.44/160.50 fof(fact_insertI1,axiom,
% 160.44/160.50 ! [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))) ).
% 160.44/160.50
% 160.44/160.50 fof(fact_all__not__in__conv,axiom,
% 160.44/160.50 ! [V_A_2,T_a] :
% 160.44/160.50 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.55/160.50 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_ex__in__conv,axiom,
% 160.55/160.50 ! [V_A_2,T_a] :
% 160.55/160.50 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.55/160.50 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_empty__iff,axiom,
% 160.55/160.50 ! [V_c_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_mem__def,axiom,
% 160.55/160.50 ! [V_A_2,V_x_2,T_a] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.55/160.50 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_eq__mem,axiom,
% 160.55/160.50 ! [V_y_2,V_x_2,T_a] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2)))
% 160.55/160.50 <=> V_x_2 = V_y_2 ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_singleton__iff,axiom,
% 160.55/160.50 ! [V_a_2,V_b_2,T_a] :
% 160.55/160.50 ( 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)))))
% 160.55/160.50 <=> V_b_2 = V_a_2 ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_insert__absorb2,axiom,
% 160.55/160.50 ! [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) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_insert__commute,axiom,
% 160.55/160.50 ! [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)) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_insert__iff,axiom,
% 160.55/160.50 ! [V_A_2,V_b_2,V_a_2,T_a] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)))
% 160.55/160.50 <=> ( V_a_2 = V_b_2
% 160.55/160.50 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_doubleton__eq__iff,axiom,
% 160.55/160.50 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 160.55/160.50 ( 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_c_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 160.55/160.50 <=> ( ( V_a_2 = V_c_2
% 160.55/160.50 & V_b_2 = V_d_2 )
% 160.55/160.50 | ( V_a_2 = V_d_2
% 160.55/160.50 & V_b_2 = V_c_2 ) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_insert__code,axiom,
% 160.55/160.50 ! [V_x_2,V_A_2,V_y_2,T_a] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2))
% 160.55/160.50 <=> ( V_y_2 = V_x_2
% 160.55/160.50 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_insert__ident,axiom,
% 160.55/160.50 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 160.55/160.50 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.55/160.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 160.55/160.50 => ( 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)
% 160.55/160.50 <=> V_A_2 = V_B_2 ) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_equals0D,axiom,
% 160.55/160.50 ! [V_a_2,T_a,V_A_2] :
% 160.55/160.50 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.55/160.50 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_insertI2,axiom,
% 160.55/160.50 ! [V_b_2,V_B_2,V_a_2,T_a] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 160.55/160.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_insert__absorb,axiom,
% 160.55/160.50 ! [V_A_2,V_a_2,T_a] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.55/160.50 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_eqset__imp__iff,axiom,
% 160.55/160.50 ! [V_x_2,T_a,V_B_2,V_A_2] :
% 160.55/160.50 ( V_A_2 = V_B_2
% 160.55/160.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.55/160.50 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_eqelem__imp__iff,axiom,
% 160.55/160.50 ! [V_A_2,T_a,V_y_2,V_x_2] :
% 160.55/160.50 ( V_x_2 = V_y_2
% 160.55/160.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.55/160.50 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_eq__mem__trans,axiom,
% 160.55/160.50 ! [V_A_2,T_a,V_b_2,V_a_2] :
% 160.55/160.50 ( V_a_2 = V_b_2
% 160.55/160.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 160.55/160.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_singletonE,axiom,
% 160.55/160.50 ! [V_a_2,V_b_2,T_a] :
% 160.55/160.50 ( 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)))))
% 160.55/160.50 => V_b_2 = V_a_2 ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_singleton__inject,axiom,
% 160.55/160.50 ! [V_b_2,V_a_2,T_a] :
% 160.55/160.50 ( 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)))
% 160.55/160.50 => V_a_2 = V_b_2 ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_triple__valid__Suc,axiom,
% 160.55/160.50 ! [V_t,V_n,T_a] :
% 160.55/160.50 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
% 160.55/160.50 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_image__constant,axiom,
% 160.55/160.50 ! [V_c_2,T_b,V_A_2,V_x_2,T_a] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.55/160.50 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_insert__image,axiom,
% 160.55/160.50 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.55/160.50 => 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) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_insert__is__Un,axiom,
% 160.55/160.50 ! [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) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_hoare__derivs_Oinsert,axiom,
% 160.55/160.50 ! [V_ts_2,V_t_2,V_Ga_2,T_a] :
% 160.55/160.50 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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))))
% 160.55/160.50 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
% 160.55/160.50 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_derivs__insertD,axiom,
% 160.55/160.50 ! [V_ts_2,V_t_2,V_Ga_2,T_a] :
% 160.55/160.50 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2))
% 160.55/160.50 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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))))
% 160.55/160.50 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_pred__equals__eq,axiom,
% 160.55/160.50 ! [V_S_2,V_R_2,T_a] :
% 160.55/160.50 ( 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)
% 160.55/160.50 <=> V_R_2 = V_S_2 ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_image__constant__conv,axiom,
% 160.55/160.50 ! [V_c_2,T_b,T_a,V_A_2] :
% 160.55/160.50 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.55/160.50 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 160.55/160.50 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.55/160.50 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_hoare__derivs_OSkip,axiom,
% 160.55/160.50 ! [V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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)))) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 160.55/160.50 ! [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)))) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_com_Osimps_I18_J,axiom,
% 160.55/160.50 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_com_Osimps_I19_J,axiom,
% 160.55/160.50 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ).
% 160.55/160.50
% 160.55/160.50 fof(fact_image__insert,axiom,
% 160.55/160.50 ! [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)) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_Un__insert__right,axiom,
% 160.55/160.50 ! [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)) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_Un__insert__left,axiom,
% 160.55/160.50 ! [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)) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_in__inv__imagep,axiom,
% 160.55/160.50 ! [V_y_2,V_x_2,V_f_2,V_r_2,T_b,T_a] :
% 160.55/160.50 ( c_Predicate_Oinv__imagep(T_a,T_b,V_r_2,V_f_2,V_x_2,V_y_2)
% 160.55/160.50 <=> hBOOL(hAPP(hAPP(V_r_2,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_image__iff,axiom,
% 160.55/160.50 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 160.55/160.50 <=> ? [B_x] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 160.55/160.50 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_imageI,axiom,
% 160.55/160.50 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.55/160.50 => 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))) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_rev__image__eqI,axiom,
% 160.55/160.50 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.55/160.50 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 160.55/160.50 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_Un__iff,axiom,
% 160.55/160.50 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 160.55/160.50 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.55/160.50 | hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_UnI1,axiom,
% 160.55/160.50 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.55/160.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_UnI2,axiom,
% 160.55/160.50 ! [V_A_2,V_B_2,V_c_2,T_a] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
% 160.55/160.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_empty__is__image,axiom,
% 160.55/160.50 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.55/160.50 ( 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)
% 160.55/160.50 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_image__empty,axiom,
% 160.55/160.50 ! [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)) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_image__is__empty,axiom,
% 160.55/160.50 ! [V_A_2,V_f_2,T_a,T_b] :
% 160.55/160.50 ( 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))
% 160.55/160.50 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_Un__empty__left,axiom,
% 160.55/160.50 ! [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 ).
% 160.55/160.50
% 160.55/160.50 fof(fact_Un__empty__right,axiom,
% 160.55/160.50 ! [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 ).
% 160.55/160.50
% 160.55/160.50 fof(fact_Un__empty,axiom,
% 160.55/160.50 ! [V_B_2,V_A_2,T_a] :
% 160.55/160.50 ( 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))
% 160.55/160.50 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.55/160.50 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_empty,axiom,
% 160.55/160.50 ! [V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 160.55/160.50 ! [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))) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_sup__Un__eq,axiom,
% 160.55/160.50 ! [V_x_2,V_S_2,V_R_2,T_a] :
% 160.55/160.50 ( 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))
% 160.55/160.50 <=> 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))) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_evalc_Oequations_I1_J,axiom,
% 160.55/160.50 ! [V_a] : hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSKIP),V_a),V_a)) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_sup__bot__left,axiom,
% 160.55/160.50 ! [V_x,T_a] :
% 160.55/160.50 ( class_Lattices_Obounded__lattice__bot(T_a)
% 160.55/160.50 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_sup__bot__right,axiom,
% 160.55/160.50 ! [V_x,T_a] :
% 160.55/160.50 ( class_Lattices_Obounded__lattice__bot(T_a)
% 160.55/160.50 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_sup__eq__bot__iff,axiom,
% 160.55/160.50 ! [V_y_2,V_x_2,T_a] :
% 160.55/160.50 ( class_Lattices_Obounded__lattice__bot(T_a)
% 160.55/160.50 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a)
% 160.55/160.50 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a)
% 160.55/160.50 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_the__elem__eq,axiom,
% 160.55/160.50 ! [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 ).
% 160.55/160.50
% 160.55/160.50 fof(fact_MGT__alternI,axiom,
% 160.55/160.50 ! [V_c_2,V_Ga_2] :
% 160.55/160.50 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
% 160.55/160.50 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_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)),hAPP(c_Natural_Oevalc,V_c_2))))),c_fequal))),V_c_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_bot__fun__def,axiom,
% 160.55/160.50 ! [V_x_2,T_b,T_a] :
% 160.55/160.50 ( class_Orderings_Obot(T_a)
% 160.55/160.50 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_bot__apply,axiom,
% 160.55/160.50 ! [V_x_2,T_b,T_a] :
% 160.55/160.50 ( class_Orderings_Obot(T_a)
% 160.55/160.50 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_escape,axiom,
% 160.55/160.50 ! [V_Q_2,V_c_2,V_Ga_2,T_a,V_P_2] :
% 160.55/160.50 ( ! [B_Z,B_s] :
% 160.55/160.50 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 160.55/160.50 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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_c_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)))) )
% 160.55/160.50 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_MGT__alternD,axiom,
% 160.55/160.50 ! [V_c_2,V_Ga_2] :
% 160.55/160.50 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 160.55/160.50 => ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_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)),hAPP(c_Natural_Oevalc,V_c_2))))),c_fequal))),V_c_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
% 160.55/160.50 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ).
% 160.55/160.50
% 160.55/160.50 fof(fact_conseq2,axiom,
% 160.55/160.51 ! [V_Q_2,V_Q_H_2,V_c_2,V_P_2,V_Ga_2,T_a] :
% 160.55/160.51 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 160.55/160.51 => ( ! [B_Z,B_s] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
% 160.55/160.51 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) )
% 160.55/160.51 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_conseq1,axiom,
% 160.55/160.51 ! [V_P_2,V_Q_2,V_c_2,V_P_H_2,V_Ga_2,T_a] :
% 160.55/160.51 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 160.55/160.51 => ( ! [B_Z,B_s] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 160.55/160.51 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 160.55/160.51 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evaln_OBody,axiom,
% 160.55/160.51 ! [V_s1,V_n,V_s0,V_pn] :
% 160.55/160.51 ( 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))
% 160.55/160.51 => 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)) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_Comp,axiom,
% 160.55/160.51 ! [V_R_2,V_d_2,V_Q_2,V_c_2,V_P_2,V_Ga_2,T_a] :
% 160.55/160.51 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 160.55/160.51 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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))))
% 160.55/160.51 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_LoopF,axiom,
% 160.55/160.51 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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_c_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evaln_OWhileTrue,axiom,
% 160.55/160.51 ! [V_s2_2,V_s1_2,V_n_2,V_c_2,V_s0_2,V_b_2] :
% 160.55/160.51 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 160.55/160.51 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),V_s0_2),V_n_2),V_s1_2))
% 160.55/160.51 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_n_2),V_s2_2))
% 160.55/160.51 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_n_2),V_s2_2)) ) ) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evaln_OWhileFalse,axiom,
% 160.55/160.51 ! [V_n_2,V_c_2,V_s_2,V_b_2] :
% 160.55/160.51 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 160.55/160.51 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_n_2),V_s_2)) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evalc_OWhileTrue,axiom,
% 160.55/160.51 ! [V_s2_2,V_s1_2,V_c_2,V_s0_2,V_b_2] :
% 160.55/160.51 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 160.55/160.51 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c_2),V_s0_2),V_s1_2))
% 160.55/160.51 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_s2_2))
% 160.55/160.51 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_s2_2)) ) ) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evalc_OWhileFalse,axiom,
% 160.55/160.51 ! [V_c_2,V_s_2,V_b_2] :
% 160.55/160.51 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 160.55/160.51 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_s_2)) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evaln_OSemi,axiom,
% 160.55/160.51 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1))
% 160.55/160.51 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2))
% 160.55/160.51 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2)) ) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evaln__elim__cases_I1_J,axiom,
% 160.55/160.51 ! [V_t,V_n,V_s] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_t))
% 160.55/160.51 => V_t = V_s ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evaln_OSkip,axiom,
% 160.55/160.51 ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evalc_OSemi,axiom,
% 160.55/160.51 ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c0),V_s0),V_s1))
% 160.55/160.51 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c1),V_s1),V_s2))
% 160.55/160.51 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_com_Osimps_I5_J,axiom,
% 160.55/160.51 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 160.55/160.51 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 160.55/160.51 <=> ( V_fun_2 = V_fun_H_2
% 160.55/160.51 & V_com_2 = V_com_H_2 ) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_com_Osimps_I3_J,axiom,
% 160.55/160.51 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 160.55/160.51 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 160.55/160.51 <=> ( V_com1_2 = V_com1_H_2
% 160.55/160.51 & V_com2_2 = V_com2_H_2 ) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_com_Osimps_I47_J,axiom,
% 160.55/160.51 ! [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) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_com_Osimps_I46_J,axiom,
% 160.55/160.51 ! [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) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evaln_Oequations_I8_J,axiom,
% 160.55/160.51 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 160.55/160.51 ( 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))
% 160.55/160.51 <=> ( ( V_a6_2 = V_a2_2
% 160.55/160.51 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 160.55/160.51 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 160.55/160.51 & ? [B_s1] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1))
% 160.55/160.51 & 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)) ) ) ) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evaln_Oequations_I7_J,axiom,
% 160.55/160.51 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 160.55/160.51 ( 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))
% 160.55/160.51 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 160.55/160.51 => ? [B_s1] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1))
% 160.55/160.51 & 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)) ) ) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evaln_Oequations_I4_J,axiom,
% 160.55/160.51 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] :
% 160.55/160.51 ( 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))
% 160.55/160.51 <=> ? [B_s1] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1))
% 160.55/160.51 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2)) ) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_triple__valid__def,axiom,
% 160.55/160.51 ! [V_t_2,V_n_2,T_a] :
% 160.55/160.51 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2)
% 160.55/160.51 <=> 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)) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evaln__Suc,axiom,
% 160.55/160.51 ! [V_s_H,V_n,V_s,V_c] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H))
% 160.55/160.51 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H)) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evaln__evalc,axiom,
% 160.55/160.51 ! [V_t,V_n,V_s,V_c] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t))
% 160.55/160.51 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c),V_s),V_t)) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_eval__eq,axiom,
% 160.55/160.51 ! [V_t_2,V_s_2,V_c_2] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c_2),V_s_2),V_t_2))
% 160.55/160.51 <=> ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),V_s_2),B_n),V_t_2)) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evaln_Oequations_I1_J,axiom,
% 160.55/160.51 ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_a1),V_a2),V_a1)) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evalc_Oequations_I8_J,axiom,
% 160.55/160.51 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2))
% 160.55/160.51 <=> ( ( V_a5_2 = V_a2_2
% 160.55/160.51 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 160.55/160.51 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 160.55/160.51 & ? [B_s1] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),B_s1))
% 160.55/160.51 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evalc_Oequations_I7_J,axiom,
% 160.55/160.51 ! [V_a2_2,V_a3_2,V_a1_2] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2))
% 160.55/160.51 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 160.55/160.51 => ? [B_s1] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),B_s1))
% 160.55/160.51 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_com_Osimps_I58_J,axiom,
% 160.55/160.51 ! [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) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_com_Osimps_I59_J,axiom,
% 160.55/160.51 ! [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) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_com_Osimps_I16_J,axiom,
% 160.55/160.51 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_com_Osimps_I17_J,axiom,
% 160.55/160.51 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 160.55/160.51
% 160.55/160.51 fof(fact_evalc_Oequations_I4_J,axiom,
% 160.55/160.51 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2))
% 160.55/160.51 <=> ? [B_s1] :
% 160.55/160.51 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a1_2),V_a2_2),B_s1))
% 160.55/160.51 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a4_2),B_s1),V_a5_2)) ) ) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_com_Osimps_I48_J,axiom,
% 160.55/160.51 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 160.55/160.51
% 160.55/160.51 fof(fact_com_Osimps_I49_J,axiom,
% 160.55/160.51 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
% 160.55/160.51
% 160.59/160.51 fof(fact_com_Osimps_I12_J,axiom,
% 160.59/160.51 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_com_Osimps_I13_J,axiom,
% 160.59/160.51 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 160.59/160.51
% 160.59/160.51 fof(fact_triple__valid__def2,axiom,
% 160.59/160.51 ! [V_Q_2,V_c_2,V_P_2,V_n_2,T_a] :
% 160.59/160.51 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2))
% 160.59/160.51 <=> ! [B_Z,B_s] :
% 160.59/160.51 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 160.59/160.51 => ! [B_s_H] :
% 160.59/160.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),B_s),V_n_2),B_s_H))
% 160.59/160.51 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_evaln_Oequations_I9_J,axiom,
% 160.59/160.51 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
% 160.59/160.51 ( 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))
% 160.59/160.51 <=> 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)) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_evaln__elim__cases_I6_J,axiom,
% 160.59/160.51 ! [V_s1,V_n,V_s,V_P] :
% 160.59/160.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_n),V_s1))
% 160.59/160.51 => ~ ! [B_n] :
% 160.59/160.51 ( V_n = hAPP(c_Nat_OSuc,B_n)
% 160.59/160.51 => ~ 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)) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_the__elem__def,axiom,
% 160.59/160.51 ! [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))))) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_MGF,axiom,
% 160.59/160.51 ! [V_c_2] :
% 160.59/160.51 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 160.59/160.51 => ( c_Com_OWT__bodies
% 160.59/160.51 => ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 160.59/160.51 => 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)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_Body__triple__valid__0,axiom,
% 160.59/160.51 ! [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)) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_override__on__def,axiom,
% 160.59/160.51 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 160.59/160.51 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.51 => 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) )
% 160.59/160.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.51 => 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) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_imageE,axiom,
% 160.59/160.51 ! [V_A_2,V_f_2,T_b,V_b_2,T_a] :
% 160.59/160.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 160.59/160.51 => ~ ! [B_x] :
% 160.59/160.51 ( V_b_2 = hAPP(V_f_2,B_x)
% 160.59/160.51 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_evalc__elim__cases_I4_J,axiom,
% 160.59/160.51 ! [V_t,V_s,V_c2,V_c1] :
% 160.59/160.51 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t))
% 160.59/160.51 => ~ ! [B_s1] :
% 160.59/160.51 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c1),V_s),B_s1))
% 160.59/160.51 => ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c2),B_s1),V_t)) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_evaln__elim__cases_I4_J,axiom,
% 160.59/160.51 ! [V_t,V_n,V_s,V_c2,V_c1] :
% 160.59/160.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_n),V_t))
% 160.59/160.51 => ~ ! [B_s1] :
% 160.59/160.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s),V_n),B_s1))
% 160.59/160.51 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2),B_s1),V_n),V_t)) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_Loop__sound__lemma,axiom,
% 160.59/160.51 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] :
% 160.59/160.51 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_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_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 160.59/160.51 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_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_c_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)))) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_Loop,axiom,
% 160.59/160.51 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] :
% 160.59/160.51 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 160.59/160.51 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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_c_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)))) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_finite__pointwise,axiom,
% 160.59/160.51 ! [V_Q_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_b,V_U_2,T_a] :
% 160.59/160.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2))
% 160.59/160.51 => ( ! [B_p] :
% 160.59/160.51 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_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))))
% 160.59/160.51 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_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)))) )
% 160.59/160.51 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_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))
% 160.59/160.51 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_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)) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_WTs__elim__cases_I6_J,axiom,
% 160.59/160.51 ! [V_c_2,V_b_2] :
% 160.59/160.51 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2)))
% 160.59/160.51 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_WTs__elim__cases_I4_J,axiom,
% 160.59/160.51 ! [V_c2,V_c1] :
% 160.59/160.51 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2)))
% 160.59/160.51 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 160.59/160.51 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_o__assoc,axiom,
% 160.59/160.51 ! [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) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_o__apply,axiom,
% 160.59/160.51 ! [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)) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_o__eq__dest,axiom,
% 160.59/160.51 ! [V_v_2,V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
% 160.59/160.51 ( 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_c_2),V_d_2)
% 160.59/160.51 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_o__eq__elim,axiom,
% 160.59/160.51 ! [V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
% 160.59/160.51 ( 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_c_2),V_d_2)
% 160.59/160.51 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_o__def,axiom,
% 160.59/160.51 ! [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)) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_image__compose,axiom,
% 160.59/160.51 ! [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)) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_peek__and__def,axiom,
% 160.59/160.51 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] :
% 160.59/160.51 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2))
% 160.59/160.51 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2))
% 160.59/160.51 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_WT_Oequations_I6_J,axiom,
% 160.59/160.51 ! [V_a1_2,V_a2_2] :
% 160.59/160.51 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2)))
% 160.59/160.51 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_While,axiom,
% 160.59/160.51 ! [V_b_2,V_c_2] :
% 160.59/160.51 ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 160.59/160.51 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_WT_Oequations_I4_J,axiom,
% 160.59/160.51 ! [V_a2_2,V_a1_2] :
% 160.59/160.51 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2)))
% 160.59/160.51 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 160.59/160.51 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_WT_OSemi,axiom,
% 160.59/160.51 ! [V_c1,V_c0] :
% 160.59/160.51 ( hBOOL(hAPP(c_Com_OWT,V_c0))
% 160.59/160.51 => ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 160.59/160.51 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_WT_Oequations_I1_J,axiom,
% 160.59/160.51 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_WT_OSkip,axiom,
% 160.59/160.51 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_override__on__apply__in,axiom,
% 160.59/160.51 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 160.59/160.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.51 => 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) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_override__on__apply__notin,axiom,
% 160.59/160.51 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] :
% 160.59/160.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.51 => 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) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_override__on__emptyset,axiom,
% 160.59/160.51 ! [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 ).
% 160.59/160.51
% 160.59/160.51 fof(fact_finite__imageI,axiom,
% 160.59/160.51 ! [V_h_2,T_b,V_F_2,T_a] :
% 160.59/160.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 160.59/160.51 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_finite_OinsertI,axiom,
% 160.59/160.51 ! [V_a_2,V_A_2,T_a] :
% 160.59/160.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.51 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_finite_OemptyI,axiom,
% 160.59/160.51 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_triple_Osize_I1_J,axiom,
% 160.59/160.51 ! [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) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_hoare__derivs_OIf,axiom,
% 160.59/160.51 ! [V_d_2,V_Q_2,V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] :
% 160.59/160.51 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))))
% 160.59/160.51 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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))))
% 160.59/160.51 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_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_c_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_triple_Osize_I2_J,axiom,
% 160.59/160.51 ! [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) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_finite__Un,axiom,
% 160.59/160.51 ! [V_Ga_2,V_F_2,T_a] :
% 160.59/160.51 ( 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_Ga_2)))
% 160.59/160.51 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 160.59/160.51 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_finite__UnI,axiom,
% 160.59/160.51 ! [V_Ga_2,V_F_2,T_a] :
% 160.59/160.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 160.59/160.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2))
% 160.59/160.51 => 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_Ga_2))) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_Suc__neq__Zero,axiom,
% 160.59/160.51 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_Zero__neq__Suc,axiom,
% 160.59/160.51 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_nat_Osimps_I3_J,axiom,
% 160.59/160.51 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_evaln__elim__cases_I5_J,axiom,
% 160.59/160.51 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 160.59/160.51 ( 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))
% 160.59/160.51 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 160.59/160.51 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) )
% 160.59/160.51 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 160.59/160.51 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2)) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_evaln_OIfTrue,axiom,
% 160.59/160.51 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] :
% 160.59/160.51 ( hBOOL(hAPP(V_b_2,V_s_2))
% 160.59/160.51 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2))
% 160.59/160.51 => 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)) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_evaln_OIfFalse,axiom,
% 160.59/160.51 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] :
% 160.59/160.51 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 160.59/160.51 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2))
% 160.59/160.51 => 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)) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_evalc__elim__cases_I5_J,axiom,
% 160.59/160.51 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 160.59/160.51 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)),V_s_2),V_t_2))
% 160.59/160.51 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 160.59/160.51 => ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c1_2),V_s_2),V_t_2)) )
% 160.59/160.51 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 160.59/160.51 => ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c2_2),V_s_2),V_t_2)) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_evalc_OIfTrue,axiom,
% 160.59/160.51 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] :
% 160.59/160.51 ( hBOOL(hAPP(V_b_2,V_s_2))
% 160.59/160.51 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c0_2),V_s_2),V_s1_2))
% 160.59/160.51 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_evalc_OIfFalse,axiom,
% 160.59/160.51 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] :
% 160.59/160.51 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 160.59/160.51 => ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_c1_2),V_s_2),V_s1_2))
% 160.59/160.51 => hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_WTs__elim__cases_I5_J,axiom,
% 160.59/160.51 ! [V_c2_2,V_c1_2,V_b_2] :
% 160.59/160.51 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)))
% 160.59/160.51 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 160.59/160.51 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_com_Osimps_I4_J,axiom,
% 160.59/160.51 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 160.59/160.51 ( 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)
% 160.59/160.51 <=> ( V_fun_2 = V_fun_H_2
% 160.59/160.51 & V_com1_2 = V_com1_H_2
% 160.59/160.51 & V_com2_2 = V_com2_H_2 ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_evaln_Oequations_I6_J,axiom,
% 160.59/160.51 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] :
% 160.59/160.51 ( 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))
% 160.59/160.51 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 160.59/160.51 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) )
% 160.59/160.51 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 160.59/160.51 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_evaln_Oequations_I5_J,axiom,
% 160.59/160.51 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] :
% 160.59/160.51 ( 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))
% 160.59/160.51 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 160.59/160.51 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) )
% 160.59/160.51 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 160.59/160.51 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_evalc_Oequations_I6_J,axiom,
% 160.59/160.51 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] :
% 160.59/160.51 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(V_a1_2,V_a5_2,V_a3_2)),V_a2_2),V_a4_2))
% 160.59/160.51 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 160.59/160.51 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a5_2),V_a2_2),V_a4_2)) )
% 160.59/160.51 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 160.59/160.51 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),V_a4_2)) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_evalc_Oequations_I5_J,axiom,
% 160.59/160.51 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
% 160.59/160.51 ( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a5_2)),V_a2_2),V_a4_2))
% 160.59/160.51 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 160.59/160.51 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a3_2),V_a2_2),V_a4_2)) )
% 160.59/160.51 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 160.59/160.51 & hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,V_a5_2),V_a2_2),V_a4_2)) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_WT_OIf,axiom,
% 160.59/160.51 ! [V_b_2,V_c1_2,V_c0_2] :
% 160.59/160.51 ( hBOOL(hAPP(c_Com_OWT,V_c0_2))
% 160.59/160.51 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 160.59/160.51 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_WT_Oequations_I5_J,axiom,
% 160.59/160.51 ! [V_a2_2,V_a1_2,V_a3_2] :
% 160.59/160.51 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2)))
% 160.59/160.51 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 160.59/160.51 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_com_Osimps_I54_J,axiom,
% 160.59/160.51 ! [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) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_com_Osimps_I55_J,axiom,
% 160.59/160.51 ! [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) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_com_Osimps_I52_J,axiom,
% 160.59/160.51 ! [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) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_com_Osimps_I53_J,axiom,
% 160.59/160.51 ! [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) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_com_Osimps_I45_J,axiom,
% 160.59/160.51 ! [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) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_com_Osimps_I44_J,axiom,
% 160.59/160.51 ! [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) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_com_Osimps_I14_J,axiom,
% 160.59/160.51 ! [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) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_com_Osimps_I15_J,axiom,
% 160.59/160.51 ! [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 ).
% 160.59/160.51
% 160.59/160.51 fof(fact_finite,axiom,
% 160.59/160.51 ! [V_A_2,T_a] :
% 160.59/160.51 ( class_Finite__Set_Ofinite(T_a)
% 160.59/160.51 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_finite__code,axiom,
% 160.59/160.51 ! [V_A_2,T_a] :
% 160.59/160.51 ( class_Finite__Set_Ofinite(T_a)
% 160.59/160.51 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_bot__nat__def,axiom,
% 160.59/160.51 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_n__not__Suc__n,axiom,
% 160.59/160.51 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_Suc__n__not__n,axiom,
% 160.59/160.51 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 160.59/160.51
% 160.59/160.51 fof(fact_nat_Oinject,axiom,
% 160.59/160.51 ! [V_nat_H_2,V_nat_2] :
% 160.59/160.51 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 160.59/160.51 <=> V_nat_2 = V_nat_H_2 ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_Suc__inject,axiom,
% 160.59/160.51 ! [V_y,V_x] :
% 160.59/160.51 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 160.59/160.51 => V_x = V_y ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_finite_Oequations_I1_J,axiom,
% 160.59/160.51 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_finite__insert,axiom,
% 160.59/160.51 ! [V_A_2,V_a_2,T_a] :
% 160.59/160.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)))
% 160.59/160.51 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_Zero__not__Suc,axiom,
% 160.59/160.51 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_nat_Osimps_I2_J,axiom,
% 160.59/160.51 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_Suc__not__Zero,axiom,
% 160.59/160.51 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_folding__one_Oinsert,axiom,
% 160.59/160.51 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 160.59/160.51 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 160.59/160.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.51 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.51 => 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)) ) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_folding__idem_Ounion__idem,axiom,
% 160.59/160.51 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.51 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.51 => 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)) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_folding__idem_Oinsert__idem,axiom,
% 160.59/160.51 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.51 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.51 => 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)) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 160.59/160.51 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.51 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.51 => 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) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 160.59/160.51 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 160.59/160.51 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 160.59/160.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.51 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.51 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.51 => 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)) ) ) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 160.59/160.51 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 160.59/160.51 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 160.59/160.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.51 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.51 => 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)) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_folding_Oinsert,axiom,
% 160.59/160.51 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.51 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.51 => 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)) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_image__eq__fold__image,axiom,
% 160.59/160.51 ! [V_f_2,T_b,V_A_2,T_a] :
% 160.59/160.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.51 => 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) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_Sup__fin_Oinsert,axiom,
% 160.59/160.51 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.51 ( class_Lattices_Olattice(T_a)
% 160.59/160.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.51 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.51 => 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)) ) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_MGF__lemma1,axiom,
% 160.59/160.51 ! [V_c_2,V_Ga_2] :
% 160.59/160.51 ( c_Hoare__Mirabelle_Ostate__not__singleton
% 160.59/160.51 => ( ! [B_x] :
% 160.59/160.51 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))
% 160.59/160.51 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),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)))) )
% 160.59/160.51 => ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 160.59/160.51 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_folding__image__simple_Oinsert,axiom,
% 160.59/160.51 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.51 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 160.59/160.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 160.59/160.51 => 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)) ) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_folding__one__idem_Oidem,axiom,
% 160.59/160.51 ! [V_x_2,V_F_2,V_f_2,T_a] :
% 160.59/160.51 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 160.59/160.51 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 160.59/160.51 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.51 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 160.59/160.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.51 => 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) ) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_fold__image__empty,axiom,
% 160.59/160.51 ! [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 ).
% 160.59/160.51
% 160.59/160.51 fof(fact_finite__dom__body,axiom,
% 160.59/160.51 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_folding_Ocommute__left__comp,axiom,
% 160.59/160.51 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.51 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.51 => 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)) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_folding_Ocommute__comp,axiom,
% 160.59/160.51 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.51 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.51 => 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)) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 160.59/160.51 ! [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] :
% 160.59/160.51 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2)
% 160.59/160.51 => 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) ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_folding__image__simple_Oempty,axiom,
% 160.59/160.51 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.51 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 160.59/160.51 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_Sup__fin_Osingleton,axiom,
% 160.59/160.51 ! [V_x_2,T_a] :
% 160.59/160.51 ( class_Lattices_Olattice(T_a)
% 160.59/160.51 => 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 ) ).
% 160.59/160.51
% 160.59/160.51 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 160.59/160.51 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__idem_Oidem__comp,axiom,
% 160.59/160.52 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 160.59/160.52 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.52 => 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)) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.52 => 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)) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 160.59/160.52 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => 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)) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding_Ocommute__comp_H,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => 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)) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Sup__fin_Oin__idem,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.52 => 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) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__one_Osingleton,axiom,
% 160.59/160.52 ! [V_x_2,V_F_2,V_f_2,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 160.59/160.52 => 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 ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__one__idem_Oin__idem,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.52 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => 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)) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Sup__fin_Ounion__idem,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.52 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => 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)) ) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_comm__monoid__big_OF__eq,axiom,
% 160.59/160.52 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 160.59/160.52 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.52 => 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) )
% 160.59/160.52 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.52 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Sup__fin_Oclosed,axiom,
% 160.59/160.52 ! [V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => ( ! [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))))))
% 160.59/160.52 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__one_Oclosed,axiom,
% 160.59/160.52 ! [V_A_2,V_F_2,V_f_2,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => ( ! [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))))))
% 160.59/160.52 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Sup__fin_Ohom__commute,axiom,
% 160.59/160.52 ! [V_N_2,V_h_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( ! [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))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 160.59/160.52 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => 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)) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding_Oremove,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.52 => 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)) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Sup__fin_Oremove,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.52 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.52 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 )
% 160.59/160.52 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.52 => 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)))))) ) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 160.59/160.52 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 160.59/160.52 => ( ! [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))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 160.59/160.52 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => 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)) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_the__eq__trivial,axiom,
% 160.59/160.52 ! [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 ).
% 160.59/160.52
% 160.59/160.52 fof(fact_the__sym__eq__trivial,axiom,
% 160.59/160.52 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding_Ounion,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.52 => ( 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))
% 160.59/160.52 => 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)) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__image__simple_Oremove,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 160.59/160.52 => 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)))))) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf1E,axiom,
% 160.59/160.52 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 160.59/160.52 ( 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))
% 160.59/160.52 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 160.59/160.52 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf1I,axiom,
% 160.59/160.52 ! [T_a,V_B_2,V_x_2,V_A_2] :
% 160.59/160.52 ( hBOOL(hAPP(V_A_2,V_x_2))
% 160.59/160.52 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 160.59/160.52 => 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)) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_IntE,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 160.59/160.52 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.59/160.52 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_IntI,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
% 160.59/160.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_DiffE,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 160.59/160.52 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.59/160.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_DiffI,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.59/160.52 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2))
% 160.59/160.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_finite__Int,axiom,
% 160.59/160.52 ! [V_Ga_2,V_F_2,T_a] :
% 160.59/160.52 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 160.59/160.52 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) )
% 160.59/160.52 => 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_Ga_2))) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_finite__Diff,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => 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))) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__diff__def,axiom,
% 160.59/160.52 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.52 ( class_Groups_Ominus(T_a)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__fun__def,axiom,
% 160.59/160.52 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Inf__fin_Oidem,axiom,
% 160.59/160.52 ! [V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf1D2,axiom,
% 160.59/160.52 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 160.59/160.52 ( 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))
% 160.59/160.52 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf1D1,axiom,
% 160.59/160.52 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 160.59/160.52 ( 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))
% 160.59/160.52 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__apply,axiom,
% 160.59/160.52 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_minus__apply,axiom,
% 160.59/160.52 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.52 ( class_Groups_Ominus(T_a)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Diff__Int2,axiom,
% 160.59/160.52 ! [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) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Diff__Int__distrib2,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__assoc,axiom,
% 160.59/160.52 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__sup__aci_I2_J,axiom,
% 160.59/160.52 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf_Oassoc,axiom,
% 160.59/160.52 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.52 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__assoc,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__Diff,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Diff__idemp,axiom,
% 160.59/160.52 ! [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) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Diff__Int__distrib,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__left__commute,axiom,
% 160.59/160.52 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__sup__aci_I3_J,axiom,
% 160.59/160.52 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf_Oleft__commute,axiom,
% 160.59/160.52 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.52 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__left__commute,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__left__idem,axiom,
% 160.59/160.52 ! [V_y,V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__sup__aci_I4_J,axiom,
% 160.59/160.52 ! [V_y,V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf_Oleft__idem,axiom,
% 160.59/160.52 ! [V_b,V_a,T_a] :
% 160.59/160.52 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__left__absorb,axiom,
% 160.59/160.52 ! [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) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__commute,axiom,
% 160.59/160.52 ! [V_y,V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__sup__aci_I1_J,axiom,
% 160.59/160.52 ! [V_y,V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf_Ocommute,axiom,
% 160.59/160.52 ! [V_b,V_a,T_a] :
% 160.59/160.52 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__commute,axiom,
% 160.59/160.52 ! [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) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__idem,axiom,
% 160.59/160.52 ! [V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf_Oidem,axiom,
% 160.59/160.52 ! [V_a,T_a] :
% 160.59/160.52 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.52 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__absorb,axiom,
% 160.59/160.52 ! [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 ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Diff__triv,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.52 ( 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))
% 160.59/160.52 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Diff__disjoint,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Diff__Int,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Diff__Un,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Un__Diff__Int,axiom,
% 160.59/160.52 ! [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 ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__bot__right,axiom,
% 160.59/160.52 ! [V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Obounded__lattice__bot(T_a)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__bot__left,axiom,
% 160.59/160.52 ! [V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Obounded__lattice__bot(T_a)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_sup__inf__distrib2,axiom,
% 160.59/160.52 ! [V_x,V_z,V_y,T_a] :
% 160.59/160.52 ( class_Lattices_Odistrib__lattice(T_a)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__sup__distrib2,axiom,
% 160.59/160.52 ! [V_x,V_z,V_y,T_a] :
% 160.59/160.52 ( class_Lattices_Odistrib__lattice(T_a)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_sup__inf__distrib1,axiom,
% 160.59/160.52 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Odistrib__lattice(T_a)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__sup__distrib1,axiom,
% 160.59/160.52 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Odistrib__lattice(T_a)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_sup__inf__absorb,axiom,
% 160.59/160.52 ! [V_y,V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => 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 ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__sup__absorb,axiom,
% 160.59/160.52 ! [V_y,V_x,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => 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 ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_DiffD2,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 160.59/160.52 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_DiffD1,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 160.59/160.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Diff__iff,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 160.59/160.52 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.59/160.52 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_IntD2,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 160.59/160.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_IntD1,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 160.59/160.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__iff,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_c_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))
% 160.59/160.52 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.59/160.52 & hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Diff__cancel,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Diff__empty,axiom,
% 160.59/160.52 ! [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 ).
% 160.59/160.52
% 160.59/160.52 fof(fact_empty__Diff,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_finite__Diff2,axiom,
% 160.59/160.52 ! [V_A_2,V_B_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.52 => ( 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)))
% 160.59/160.52 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_disjoint__iff__not__equal,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.52 ( 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))
% 160.59/160.52 <=> ! [B_x] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.52 => ! [B_xa] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2))
% 160.59/160.52 => B_x != B_xa ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__empty__right,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__empty__left,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_insert__inter__insert,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Un__Diff,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Un__Diff__cancel2,axiom,
% 160.59/160.52 ! [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) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Un__Diff__cancel,axiom,
% 160.59/160.52 ! [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) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Un__Int__crazy,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Un__Int__distrib2,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__Un__distrib2,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Un__Int__distrib,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__Un__distrib,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__Int__eq,axiom,
% 160.59/160.52 ! [V_x_2,V_S_2,V_R_2,T_a] :
% 160.59/160.52 ( 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))
% 160.59/160.52 <=> 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))) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_insert__Diff1,axiom,
% 160.59/160.52 ! [V_A_2,V_B_2,V_x_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_insert__Diff__if,axiom,
% 160.59/160.52 ! [V_A_2,V_B_2,V_x_2,T_a] :
% 160.59/160.52 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 160.59/160.52 => 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) )
% 160.59/160.52 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 160.59/160.52 => 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)) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_insert__Diff__single,axiom,
% 160.59/160.52 ! [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) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Diff__insert2,axiom,
% 160.59/160.52 ! [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) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Diff__insert,axiom,
% 160.59/160.52 ! [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)))) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_finite__Diff__insert,axiom,
% 160.59/160.52 ! [V_B_2,V_a_2,V_A_2,T_a] :
% 160.59/160.52 ( 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))))
% 160.59/160.52 <=> 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))) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__insert__left__if1,axiom,
% 160.59/160.52 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__insert__right__if1,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__insert__left__if0,axiom,
% 160.59/160.52 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 160.59/160.52 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__insert__right__if0,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 160.59/160.52 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__insert__left,axiom,
% 160.59/160.52 ! [V_B_2,V_C_2,V_a_2,T_a] :
% 160.59/160.52 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 160.59/160.52 => 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)) )
% 160.59/160.52 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2))
% 160.59/160.52 => 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) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Int__insert__right,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_a_2,T_a] :
% 160.59/160.52 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.52 => 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)) )
% 160.59/160.52 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.52 => 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) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_insert__Diff,axiom,
% 160.59/160.52 ! [V_A_2,V_a_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.52 => 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 ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Diff__insert__absorb,axiom,
% 160.59/160.52 ! [V_A_2,V_x_2,T_a] :
% 160.59/160.52 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.52 => 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 ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_inf__Sup__absorb,axiom,
% 160.59/160.52 ! [V_a_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.52 => 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 ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 160.59/160.52 => 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)) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__one_Oinsert__remove,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.52 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 160.59/160.52 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.52 => 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)))))) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.52 => 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)))))) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding_Ounion__inter,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.52 => 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)) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 160.59/160.52 => ( 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))
% 160.59/160.52 => 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)) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__one_Ounion__disjoint,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.52 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => ( 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))
% 160.59/160.52 => 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)) ) ) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__one_Ounion__inter,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.52 => ( 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))
% 160.59/160.52 => 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)) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 160.59/160.52 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 160.59/160.52 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.52 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.52 => 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 )
% 160.59/160.52 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.52 => 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)))))) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.52 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => ( 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))
% 160.59/160.52 => 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)) ) ) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Sup__fin_Ounion__inter,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.52 => ( 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))
% 160.59/160.52 => 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)) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding_Oinsert__remove,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => 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)) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__one_Oremove,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.52 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.52 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 160.59/160.52 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.52 => 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)))))) ) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Inf__fin_Oremove,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.52 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.52 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 )
% 160.59/160.52 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.52 => 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)))))) ) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_diff__0__right,axiom,
% 160.59/160.52 ! [V_a,T_a] :
% 160.59/160.52 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.52 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_diff__self,axiom,
% 160.59/160.52 ! [V_a,T_a] :
% 160.59/160.52 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.52 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_eq__iff__diff__eq__0,axiom,
% 160.59/160.52 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.52 ( class_Groups_Oab__group__add(T_a)
% 160.59/160.52 => ( V_a_2 = V_b_2
% 160.59/160.52 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_right__minus__eq,axiom,
% 160.59/160.52 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.52 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.52 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.52 <=> V_a_2 = V_b_2 ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__upd__image,axiom,
% 160.59/160.52 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 160.59/160.52 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.52 => 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)))))) )
% 160.59/160.52 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.52 => 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) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_finite__empty__induct,axiom,
% 160.59/160.52 ! [V_P_2,V_A_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 160.59/160.52 => ( ! [B_a,B_A] :
% 160.59/160.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A))
% 160.59/160.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A))
% 160.59/160.52 => ( hBOOL(hAPP(V_P_2,B_A))
% 160.59/160.52 => 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)))))) ) ) )
% 160.59/160.52 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Inf__fin_Ounion__inter,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.52 => ( 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))
% 160.59/160.52 => 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)) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.52 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => ( 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))
% 160.59/160.52 => 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)) ) ) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.52 => 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 )
% 160.59/160.52 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.52 => 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)))))) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__upd__triv,axiom,
% 160.59/160.52 ! [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 ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__upd__idem__iff,axiom,
% 160.59/160.52 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2
% 160.59/160.52 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__upd__upd,axiom,
% 160.59/160.52 ! [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) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__upd__same,axiom,
% 160.59/160.52 ! [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 ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__upd__apply,axiom,
% 160.59/160.52 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
% 160.59/160.52 ( ( V_z_2 = V_x_2
% 160.59/160.52 => 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 )
% 160.59/160.52 & ( V_z_2 != V_x_2
% 160.59/160.52 => 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) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__upd__twist,axiom,
% 160.59/160.52 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_c_2,V_a_2] :
% 160.59/160.52 ( V_a_2 != V_c_2
% 160.59/160.52 => 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_c_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_c_2),V_d_2)),V_a_2),V_b_2) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__upd__other,axiom,
% 160.59/160.52 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] :
% 160.59/160.52 ( V_z_2 != V_x_2
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__upd__idem,axiom,
% 160.59/160.52 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] :
% 160.59/160.52 ( hAPP(V_f_2,V_x_2) = V_y_2
% 160.59/160.52 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__upd__def,axiom,
% 160.59/160.52 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] :
% 160.59/160.52 ( ( V_x_2 = V_a_2
% 160.59/160.52 => 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 )
% 160.59/160.52 & ( V_x_2 != V_a_2
% 160.59/160.52 => 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) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_diffs0__imp__equal,axiom,
% 160.59/160.52 ! [V_n,V_m] :
% 160.59/160.52 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.52 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.52 => V_m = V_n ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_diff__self__eq__0,axiom,
% 160.59/160.52 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_minus__nat_Odiff__0,axiom,
% 160.59/160.52 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 160.59/160.52
% 160.59/160.52 fof(fact_diff__0__eq__0,axiom,
% 160.59/160.52 ! [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) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Suc__diff__diff,axiom,
% 160.59/160.52 ! [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) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_diff__Suc__Suc,axiom,
% 160.59/160.52 ! [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) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__upd__comp,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Inf__fin_Osingleton,axiom,
% 160.59/160.52 ! [V_x_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => 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 ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_zero__reorient,axiom,
% 160.59/160.52 ! [V_x_2,T_a] :
% 160.59/160.52 ( class_Groups_Ozero(T_a)
% 160.59/160.52 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 160.59/160.52 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_diff__eq__diff__eq,axiom,
% 160.59/160.52 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.52 ( class_Groups_Oab__group__add(T_a)
% 160.59/160.52 => ( 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_c_2),V_d_2)
% 160.59/160.52 => ( V_a_2 = V_b_2
% 160.59/160.52 <=> V_c_2 = V_d_2 ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_sup__Inf__absorb,axiom,
% 160.59/160.52 ! [V_a_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.52 => 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 ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Inf__fin_Oin__idem,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.52 => 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) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => 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)) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Inf__fin_Ounion__idem,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.52 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => 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)) ) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Inf__fin_Oinsert,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.52 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => 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)) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Inf__fin_Oclosed,axiom,
% 160.59/160.52 ! [V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => ( ! [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))))))
% 160.59/160.52 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Inf__fin_Ohom__commute,axiom,
% 160.59/160.52 ! [V_N_2,V_h_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( ! [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))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 160.59/160.52 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 => 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)) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_card__Suc__Diff1,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.52 => 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) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 160.59/160.52 => ( ! [B_x] :
% 160.59/160.52 ( 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)))
% 160.59/160.52 => hAPP(V_g_2,B_x) = V_z_2 )
% 160.59/160.52 => 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)) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__left__comm__idem__remove,axiom,
% 160.59/160.52 ! [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))))) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_setsum__diff1__ring,axiom,
% 160.59/160.52 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 160.59/160.52 ( class_Rings_Oring(T_b)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.52 => 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)) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_setsum__diff1,axiom,
% 160.59/160.52 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 160.59/160.52 ( class_Groups_Oab__group__add(T_b)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.52 => 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)) )
% 160.59/160.52 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.52 => 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) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 160.59/160.52 => 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)) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.52 => 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) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 160.59/160.52 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Olattice(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.52 => 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) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_diff__commute,axiom,
% 160.59/160.52 ! [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) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_setsum__commute,axiom,
% 160.59/160.52 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 160.59/160.52 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 160.59/160.52 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 160.59/160.52 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 160.59/160.52 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 160.59/160.52 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fold__empty,axiom,
% 160.59/160.52 ! [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 ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 160.59/160.52 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => 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)) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 160.59/160.52 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => 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) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_setsum__0,axiom,
% 160.59/160.52 ! [V_A_2,T_b,T_a] :
% 160.59/160.52 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_setsum__subtractf,axiom,
% 160.59/160.52 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( class_Groups_Oab__group__add(T_a)
% 160.59/160.52 => 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)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fold__image__def,axiom,
% 160.59/160.52 ! [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)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_setsum__empty,axiom,
% 160.59/160.52 ! [V_f_2,T_b,T_a] :
% 160.59/160.52 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_setsum_Oempty,axiom,
% 160.59/160.52 ! [V_g_2,T_b,T_a] :
% 160.59/160.52 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_setsum_Oinfinite,axiom,
% 160.59/160.52 ! [V_g_2,V_A_2,T_a,T_b] :
% 160.59/160.52 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.52 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => 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) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_setsum__infinite,axiom,
% 160.59/160.52 ! [V_f_2,V_A_2,T_a,T_b] :
% 160.59/160.52 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.52 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => 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) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_setsum__eq__0__iff,axiom,
% 160.59/160.52 ! [V_f_2,V_F_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 160.59/160.52 => ( 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)
% 160.59/160.52 <=> ! [B_x] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2))
% 160.59/160.52 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__left__comm__idem__insert,axiom,
% 160.59/160.52 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_card_Oempty,axiom,
% 160.59/160.52 ! [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) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_card__infinite,axiom,
% 160.59/160.52 ! [V_A_2,T_a] :
% 160.59/160.52 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__left__comm__idem__sup,axiom,
% 160.59/160.52 ! [T_a] :
% 160.59/160.52 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.52 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__left__comm__idem__inf,axiom,
% 160.59/160.52 ! [T_a] :
% 160.59/160.52 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.52 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 160.59/160.52 ! [V_x_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_folding_Oeq__fold,axiom,
% 160.59/160.52 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.52 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => 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) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_setsum__eq__Suc0__iff,axiom,
% 160.59/160.52 ! [V_f_2,V_A_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => ( 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))
% 160.59/160.52 <=> ? [B_x] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.52 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 160.59/160.52 & ! [B_xa] :
% 160.59/160.52 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 160.59/160.52 => ( B_x != B_xa
% 160.59/160.52 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_card__eq__0__iff,axiom,
% 160.59/160.52 ! [V_A_2,T_a] :
% 160.59/160.52 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.52 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.52 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_card__Diff__subset__Int,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.52 ( 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)))
% 160.59/160.52 => 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))) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_union__fold__insert,axiom,
% 160.59/160.52 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.52 => 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) ) ).
% 160.59/160.52
% 160.59/160.52 fof(fact_fold__sup__insert,axiom,
% 160.59/160.52 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 160.59/160.52 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => 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)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_fold__inf__insert,axiom,
% 160.59/160.53 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 160.59/160.53 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => 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)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_setsum__delta_H,axiom,
% 160.59/160.53 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 160.59/160.53 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.53 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 160.59/160.53 => 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) )
% 160.59/160.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 160.59/160.53 => 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) ) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_setsum__delta,axiom,
% 160.59/160.53 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 160.59/160.53 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.53 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 160.59/160.53 => 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) )
% 160.59/160.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 160.59/160.53 => 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) ) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 160.59/160.53 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] :
% 160.59/160.53 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => 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) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_setsum__diff1__nat,axiom,
% 160.59/160.53 ! [V_f_2,V_A_2,V_a_2,T_a] :
% 160.59/160.53 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.53 => 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)) )
% 160.59/160.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.53 => 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) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_card__insert__if,axiom,
% 160.59/160.53 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.53 => 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) )
% 160.59/160.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.53 => 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)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_card__insert__disjoint,axiom,
% 160.59/160.53 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.53 => 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)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_setsum__restrict__set,axiom,
% 160.59/160.53 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
% 160.59/160.53 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => 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) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 160.59/160.53 ! [V_a_2,V_A_2,T_a] :
% 160.59/160.53 ( class_Lattices_Olattice(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => 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) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 160.59/160.53 ! [V_a_2,V_A_2,T_a] :
% 160.59/160.53 ( class_Lattices_Olattice(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => 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) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_minus__fold__remove,axiom,
% 160.59/160.53 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => 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) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_folding__one_Oeq__fold_H,axiom,
% 160.59/160.53 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] :
% 160.59/160.53 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.53 => 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) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_card__insert,axiom,
% 160.59/160.53 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => 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)))))) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 160.59/160.53 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.53 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 160.59/160.53 => 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) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 160.59/160.53 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.53 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.53 => 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)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 160.59/160.53 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.53 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.53 => 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)))))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 160.59/160.53 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.53 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => 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)))))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_card__Suc__eq,axiom,
% 160.59/160.53 ! [V_k_2,V_A_2,T_a] :
% 160.59/160.53 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 160.59/160.53 <=> ? [B_b,B_B] :
% 160.59/160.53 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B)
% 160.59/160.53 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B))
% 160.59/160.53 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2
% 160.59/160.53 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.53 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_setsum__reindex__nonzero,axiom,
% 160.59/160.53 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] :
% 160.59/160.53 ( class_Groups_Ocomm__monoid__add(T_c)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.53 => ( ! [B_x] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 160.59/160.53 => ! [B_y] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2))
% 160.59/160.53 => ( B_x != B_y
% 160.59/160.53 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 160.59/160.53 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) )
% 160.59/160.53 => 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) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_card__Diff__singleton__if,axiom,
% 160.59/160.53 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.53 => 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)) )
% 160.59/160.53 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.53 => 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) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_card__Diff__singleton,axiom,
% 160.59/160.53 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.53 => 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)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_SUPR__fold__sup,axiom,
% 160.59/160.53 ! [V_f_2,V_A_2,T_a,T_b] :
% 160.59/160.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => 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) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 160.59/160.53 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.53 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.53 => 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)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 160.59/160.53 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.53 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.53 => 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) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_card__Diff__insert,axiom,
% 160.59/160.53 ! [V_B_2,V_a_2,V_A_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.53 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
% 160.59/160.53 => 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)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_SUP1__I,axiom,
% 160.59/160.53 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 160.59/160.53 => 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)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_SUP2__I,axiom,
% 160.59/160.53 ! [T_c,T_b,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 160.59/160.53 => 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_c_2)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 160.59/160.53 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 160.59/160.53 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 160.59/160.53 => 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)) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_one__reorient,axiom,
% 160.59/160.53 ! [V_x_2,T_a] :
% 160.59/160.53 ( class_Groups_Oone(T_a)
% 160.59/160.53 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 160.59/160.53 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 160.59/160.53 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 160.59/160.53 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 160.59/160.53 => 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)) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_finite__UN,axiom,
% 160.59/160.53 ! [V_B_2,T_b,V_A_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( 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)))
% 160.59/160.53 <=> ! [B_x] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.53 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__o,axiom,
% 160.59/160.53 ! [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) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_card__eq__setsum,axiom,
% 160.59/160.53 ! [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) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 160.59/160.53 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 160.59/160.53 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 160.59/160.53 => 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)) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_setsum__eq__1__iff,axiom,
% 160.59/160.53 ! [V_f_2,V_A_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( 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)
% 160.59/160.53 <=> ? [B_x] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.53 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 160.59/160.53 & ! [B_xa] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 160.59/160.53 => ( B_x != B_xa
% 160.59/160.53 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_One__nat__def,axiom,
% 160.59/160.53 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 160.59/160.53 ! [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) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_diff__Suc__1,axiom,
% 160.59/160.53 ! [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 ).
% 160.59/160.53
% 160.59/160.53 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 160.59/160.53 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.53 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => 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) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_sup__SUPR__fold__sup,axiom,
% 160.59/160.53 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => 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) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_image__eq__UN,axiom,
% 160.59/160.53 ! [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)))) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__I,axiom,
% 160.59/160.53 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 160.59/160.53 => 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))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_SUP__const,axiom,
% 160.59/160.53 ! [V_M_2,T_a,V_A_2,T_b] :
% 160.59/160.53 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 160.59/160.53 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.53 => 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 ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__insert,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__simps_I3_J,axiom,
% 160.59/160.53 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 160.59/160.53 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.53 => 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)) )
% 160.59/160.53 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.53 => 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)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__simps_I2_J,axiom,
% 160.59/160.53 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 160.59/160.53 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.53 => 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)) )
% 160.59/160.53 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.53 => 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) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__extend__simps_I3_J,axiom,
% 160.59/160.53 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 160.59/160.53 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.53 => 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 )
% 160.59/160.53 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.53 => 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)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__extend__simps_I2_J,axiom,
% 160.59/160.53 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 160.59/160.53 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.53 => 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 )
% 160.59/160.53 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.53 => 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)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__extend__simps_I1_J,axiom,
% 160.59/160.53 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] :
% 160.59/160.53 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.53 => 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))) )
% 160.59/160.53 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.53 => 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)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__singleton,axiom,
% 160.59/160.53 ! [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 ).
% 160.59/160.53
% 160.59/160.53 fof(fact_ball__UN,axiom,
% 160.59/160.53 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.53 ( ! [B_x] :
% 160.59/160.53 ( 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)))
% 160.59/160.53 => hBOOL(hAPP(V_P_2,B_x)) )
% 160.59/160.53 <=> ! [B_x] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 160.59/160.53 => ! [B_xa] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x)))
% 160.59/160.53 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__extend__simps_I9_J,axiom,
% 160.59/160.53 ! [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) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__simps_I9_J,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__UN__flatten,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_SUP1__iff,axiom,
% 160.59/160.53 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.53 ( 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))
% 160.59/160.53 <=> ? [B_x] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.53 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_SUP2__iff,axiom,
% 160.59/160.53 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 160.59/160.53 ( 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_c_2))
% 160.59/160.53 <=> ? [B_x] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.53 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__iff,axiom,
% 160.59/160.53 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 160.59/160.53 ( 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)))
% 160.59/160.53 <=> ? [B_x] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 160.59/160.53 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UNION__empty__conv_I1_J,axiom,
% 160.59/160.53 ! [V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.53 ( 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)
% 160.59/160.53 <=> ! [B_x] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 160.59/160.53 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__empty2,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__constant,axiom,
% 160.59/160.53 ! [V_c_2,T_b,T_a,V_A_2] :
% 160.59/160.53 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.53 => 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_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 160.59/160.53 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.53 => 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_c_2)) = V_c_2 ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UNION__empty__conv_I2_J,axiom,
% 160.59/160.53 ! [V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.53 ( 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))
% 160.59/160.53 <=> ! [B_x] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 160.59/160.53 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__simps_I10_J,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_image__UN,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__extend__simps_I10_J,axiom,
% 160.59/160.53 ! [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) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__Un,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__Un__distrib,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_Int__UN__distrib2,axiom,
% 160.59/160.53 ! [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))) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__extend__simps_I4_J,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_Int__UN__distrib,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__extend__simps_I5_J,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__simps_I4_J,axiom,
% 160.59/160.53 ! [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) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__simps_I5_J,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_SUPR__apply,axiom,
% 160.59/160.53 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
% 160.59/160.53 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.53 => 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)) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_SUP__commute,axiom,
% 160.59/160.53 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
% 160.59/160.53 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.53 => 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))) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__extend__simps_I6_J,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__simps_I6_J,axiom,
% 160.59/160.53 ! [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) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__insert__distrib,axiom,
% 160.59/160.53 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2))
% 160.59/160.53 => 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)) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__absorb,axiom,
% 160.59/160.53 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2))
% 160.59/160.53 => 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) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_UN__simps_I1_J,axiom,
% 160.59/160.53 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] :
% 160.59/160.53 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.53 => 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)) )
% 160.59/160.53 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.53 => 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)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_card_Oremove,axiom,
% 160.59/160.53 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.53 => 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)))))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_one__neq__zero,axiom,
% 160.59/160.53 ! [T_a] :
% 160.59/160.53 ( class_Rings_Ozero__neq__one(T_a)
% 160.59/160.53 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_zero__neq__one,axiom,
% 160.59/160.53 ! [T_a] :
% 160.59/160.53 ( class_Rings_Ozero__neq__one(T_a)
% 160.59/160.53 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_card_Oinsert__remove,axiom,
% 160.59/160.53 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => 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)))))) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_fold__Un__disjoint,axiom,
% 160.59/160.53 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.53 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.53 => ( 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))
% 160.59/160.53 => 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)) ) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_card__Diff1__less,axiom,
% 160.59/160.53 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.53 => 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))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_card__Diff2__less,axiom,
% 160.59/160.53 ! [V_y_2,V_x_2,V_A_2,T_a] :
% 160.59/160.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_setsum__diff1_H,axiom,
% 160.59/160.53 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 160.59/160.53 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.53 => 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)))))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_setsum_Oremove,axiom,
% 160.59/160.53 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 160.59/160.53 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.53 => 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)))))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__zeroE,axiom,
% 160.59/160.53 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_Suc__mono,axiom,
% 160.59/160.53 ! [V_n,V_m] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_lessI,axiom,
% 160.59/160.53 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_zero__less__Suc,axiom,
% 160.59/160.53 ! [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))) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__1__mult,axiom,
% 160.59/160.53 ! [V_n,V_m,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__add__one,axiom,
% 160.59/160.53 ! [V_a,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.53 => 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)))) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_eq__add__iff2,axiom,
% 160.59/160.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 160.59/160.53 ( class_Rings_Oring(T_a)
% 160.59/160.53 => ( 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_c_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)
% 160.59/160.53 <=> V_c_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) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__add__iff2,axiom,
% 160.59/160.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 160.59/160.53 ( class_Rings_Oordered__ring(T_a)
% 160.59/160.53 => ( 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_c_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)))
% 160.59/160.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_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))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_eq__add__iff1,axiom,
% 160.59/160.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 160.59/160.53 ( class_Rings_Oring(T_a)
% 160.59/160.53 => ( 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_c_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)
% 160.59/160.53 <=> 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_c_2) = V_d_2 ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__add__iff1,axiom,
% 160.59/160.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 160.59/160.53 ( class_Rings_Oordered__ring(T_a)
% 160.59/160.53 => ( 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_c_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)))
% 160.59/160.53 <=> 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_c_2)),V_d_2)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__not__refl,axiom,
% 160.59/160.53 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_not__add__less1,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_not__add__less2,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_nat__neq__iff,axiom,
% 160.59/160.53 ! [V_n_2,V_m_2] :
% 160.59/160.53 ( V_m_2 != V_n_2
% 160.59/160.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_nat__add__commute,axiom,
% 160.59/160.53 ! [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) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_nat__add__left__commute,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__mult__distrib2,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_nat__add__assoc,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__mult__distrib,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_nat__add__left__cancel,axiom,
% 160.59/160.53 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.53 ( 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)
% 160.59/160.53 <=> V_m_2 = V_n_2 ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_nat__add__right__cancel,axiom,
% 160.59/160.53 ! [V_n_2,V_k_2,V_m_2] :
% 160.59/160.53 ( 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)
% 160.59/160.53 <=> V_m_2 = V_n_2 ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_nat__add__left__cancel__less,axiom,
% 160.59/160.53 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.53 ( 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)))
% 160.59/160.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_linorder__neqE__nat,axiom,
% 160.59/160.53 ! [V_y,V_x] :
% 160.59/160.53 ( V_x != V_y
% 160.59/160.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__irrefl__nat,axiom,
% 160.59/160.53 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__not__refl2,axiom,
% 160.59/160.53 ! [V_m,V_n] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 160.59/160.53 => V_m != V_n ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__not__refl3,axiom,
% 160.59/160.53 ! [V_t,V_s] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 160.59/160.53 => V_s != V_t ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_trans__less__add1,axiom,
% 160.59/160.53 ! [V_m,V_j,V_i] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 160.59/160.53 => 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))) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_trans__less__add2,axiom,
% 160.59/160.53 ! [V_m,V_j,V_i] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 160.59/160.53 => 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))) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__less__mono1,axiom,
% 160.59/160.53 ! [V_k,V_j,V_i] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 160.59/160.53 => 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))) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__less__mono,axiom,
% 160.59/160.53 ! [V_l,V_k,V_j,V_i] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 160.59/160.53 => 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))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__add__eq__less,axiom,
% 160.59/160.53 ! [V_n,V_m,V_l,V_k] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 160.59/160.53 => ( 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)
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__lessD1,axiom,
% 160.59/160.53 ! [V_k,V_j,V_i] :
% 160.59/160.53 ( 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))
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_nat__less__cases,axiom,
% 160.59/160.53 ! [V_P_2,V_n_2,V_m_2] :
% 160.59/160.53 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.53 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 160.59/160.53 => ( ( V_m_2 = V_n_2
% 160.59/160.53 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 160.59/160.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 160.59/160.53 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 160.59/160.53 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_order__less__irrefl,axiom,
% 160.59/160.53 ! [V_x,T_a] :
% 160.59/160.53 ( class_Orderings_Opreorder(T_a)
% 160.59/160.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_linorder__neq__iff,axiom,
% 160.59/160.53 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.53 ( class_Orderings_Olinorder(T_a)
% 160.59/160.53 => ( V_x_2 != V_y_2
% 160.59/160.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 160.59/160.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_not__less__iff__gr__or__eq,axiom,
% 160.59/160.53 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.53 ( class_Orderings_Olinorder(T_a)
% 160.59/160.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 160.59/160.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 160.59/160.53 | V_x_2 = V_y_2 ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_linorder__less__linear,axiom,
% 160.59/160.53 ! [V_y,V_x,T_a] :
% 160.59/160.53 ( class_Orderings_Olinorder(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.53 | V_x = V_y
% 160.59/160.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_linorder__antisym__conv3,axiom,
% 160.59/160.53 ! [V_x_2,V_y_2,T_a] :
% 160.59/160.53 ( class_Orderings_Olinorder(T_a)
% 160.59/160.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 160.59/160.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 160.59/160.53 <=> V_x_2 = V_y_2 ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_linorder__neqE,axiom,
% 160.59/160.53 ! [V_y,V_x,T_a] :
% 160.59/160.53 ( class_Orderings_Olinorder(T_a)
% 160.59/160.53 => ( V_x != V_y
% 160.59/160.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__imp__neq,axiom,
% 160.59/160.53 ! [V_y,V_x,T_a] :
% 160.59/160.53 ( class_Orderings_Oorder(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.53 => V_x != V_y ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_order__less__not__sym,axiom,
% 160.59/160.53 ! [V_y,V_x,T_a] :
% 160.59/160.53 ( class_Orderings_Opreorder(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_order__less__imp__not__less,axiom,
% 160.59/160.53 ! [V_y,V_x,T_a] :
% 160.59/160.53 ( class_Orderings_Opreorder(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_order__less__imp__not__eq,axiom,
% 160.59/160.53 ! [V_y,V_x,T_a] :
% 160.59/160.53 ( class_Orderings_Oorder(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.53 => V_x != V_y ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_order__less__imp__not__eq2,axiom,
% 160.59/160.53 ! [V_y,V_x,T_a] :
% 160.59/160.53 ( class_Orderings_Oorder(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.53 => V_y != V_x ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_order__less__asym_H,axiom,
% 160.59/160.53 ! [V_b,V_a,T_a] :
% 160.59/160.53 ( class_Orderings_Opreorder(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_xt1_I9_J,axiom,
% 160.59/160.53 ! [V_a,V_b,T_a] :
% 160.59/160.53 ( class_Orderings_Oorder(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 160.59/160.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_ord__eq__less__trans,axiom,
% 160.59/160.53 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.53 ( class_Orderings_Oord(T_a)
% 160.59/160.53 => ( V_a = V_b
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_xt1_I1_J,axiom,
% 160.59/160.53 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.53 ( class_Orderings_Oorder(T_a)
% 160.59/160.53 => ( V_a = V_b
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_ord__less__eq__trans,axiom,
% 160.59/160.53 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.53 ( class_Orderings_Oord(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.53 => ( V_b = V_c
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_xt1_I2_J,axiom,
% 160.59/160.53 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.53 ( class_Orderings_Oorder(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 160.59/160.53 => ( V_b = V_c
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_order__less__trans,axiom,
% 160.59/160.53 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.53 ( class_Orderings_Opreorder(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_xt1_I10_J,axiom,
% 160.59/160.53 ! [V_z,V_x,V_y,T_a] :
% 160.59/160.53 ( class_Orderings_Oorder(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_order__less__asym,axiom,
% 160.59/160.53 ! [V_y,V_x,T_a] :
% 160.59/160.53 ( class_Orderings_Opreorder(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.53 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_linorder__cases,axiom,
% 160.59/160.53 ! [V_y,V_x,T_a] :
% 160.59/160.53 ( class_Orderings_Olinorder(T_a)
% 160.59/160.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.53 => ( V_x != V_y
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_times_Oidem,axiom,
% 160.59/160.53 ! [V_a,T_a] :
% 160.59/160.53 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 160.59/160.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__idem,axiom,
% 160.59/160.53 ! [V_x,T_a] :
% 160.59/160.53 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 160.59/160.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__left__idem,axiom,
% 160.59/160.53 ! [V_b,V_a,T_a] :
% 160.59/160.53 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 160.59/160.53 => 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) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_linorder__neqE__linordered__idom,axiom,
% 160.59/160.53 ! [V_y,V_x,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.53 => ( V_x != V_y
% 160.59/160.53 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_combine__common__factor,axiom,
% 160.59/160.53 ! [V_c,V_b,V_e,V_a,T_a] :
% 160.59/160.53 ( class_Rings_Osemiring(T_a)
% 160.59/160.53 => 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) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_comm__semiring__class_Odistrib,axiom,
% 160.59/160.53 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.53 ( class_Rings_Ocomm__semiring(T_a)
% 160.59/160.53 => 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)) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_Suc__mult__less__cancel1,axiom,
% 160.59/160.53 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.53 ( 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)))
% 160.59/160.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__iff__Suc__add,axiom,
% 160.59/160.53 ! [V_n_2,V_m_2] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.53 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__add__Suc2,axiom,
% 160.59/160.53 ! [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)))) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__add__Suc1,axiom,
% 160.59/160.53 ! [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)))) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__less__mono2,axiom,
% 160.59/160.53 ! [V_k,V_j,V_i] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 160.59/160.53 => 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))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__less__mono1,axiom,
% 160.59/160.53 ! [V_k,V_j,V_i] :
% 160.59/160.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 160.59/160.53 => 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))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__less__cancel2,axiom,
% 160.59/160.53 ! [V_n_2,V_k_2,V_m_2] :
% 160.59/160.53 ( 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)))
% 160.59/160.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 160.59/160.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__less__cancel1,axiom,
% 160.59/160.53 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.53 ( 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)))
% 160.59/160.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 160.59/160.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_nat__0__less__mult__iff,axiom,
% 160.59/160.53 ! [V_n_2,V_m_2] :
% 160.59/160.53 ( 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)))
% 160.59/160.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 160.59/160.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__gr__0,axiom,
% 160.59/160.53 ! [V_n_2,V_m_2] :
% 160.59/160.53 ( 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)))
% 160.59/160.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 160.59/160.53 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__Suc,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__Suc__right,axiom,
% 160.59/160.53 ! [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)) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_not__sum__squares__lt__zero,axiom,
% 160.59/160.53 ! [V_y,V_x,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__ring(T_a)
% 160.59/160.53 => ~ 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))) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_sum__squares__gt__zero__iff,axiom,
% 160.59/160.53 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__ring__strict(T_a)
% 160.59/160.53 => ( 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))))
% 160.59/160.53 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.53 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__strict__left__mono__neg,axiom,
% 160.59/160.53 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__ring__strict(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__strict__right__mono__neg,axiom,
% 160.59/160.53 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__ring__strict(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_comm__mult__strict__left__mono,axiom,
% 160.59/160.53 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__strict__left__mono,axiom,
% 160.59/160.53 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__strict__right__mono,axiom,
% 160.59/160.53 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__neg__neg,axiom,
% 160.59/160.53 ! [V_b,V_a,T_a] :
% 160.59/160.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__neg__neg,axiom,
% 160.59/160.53 ! [V_b,V_a,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__ring__strict(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__neg__pos,axiom,
% 160.59/160.53 ! [V_b,V_a,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__less__cancel__left__neg,axiom,
% 160.59/160.53 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__ring__strict(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 160.59/160.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_zero__less__mult__pos2,axiom,
% 160.59/160.53 ! [V_a,V_b,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.53 => ( 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)))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_zero__less__mult__pos,axiom,
% 160.59/160.53 ! [V_b,V_a,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.53 => ( 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)))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_pos__add__strict,axiom,
% 160.59/160.53 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__pos__neg2,axiom,
% 160.59/160.53 ! [V_b,V_a,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__pos__neg,axiom,
% 160.59/160.53 ! [V_b,V_a,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__pos__pos,axiom,
% 160.59/160.53 ! [V_b,V_a,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__pos__pos,axiom,
% 160.59/160.53 ! [V_b,V_a,T_a] :
% 160.59/160.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__less__cancel__left__pos,axiom,
% 160.59/160.53 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__ring__strict(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 160.59/160.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__less__cancel__left__disj,axiom,
% 160.59/160.53 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__ring__strict(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 160.59/160.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
% 160.59/160.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__less__cancel__right__disj,axiom,
% 160.59/160.53 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__ring__strict(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))
% 160.59/160.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) )
% 160.59/160.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 160.59/160.53 ! [V_a_2,T_a] :
% 160.59/160.53 ( class_Groups_Olinordered__ab__group__add(T_a)
% 160.59/160.53 => ( 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)))
% 160.59/160.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 160.59/160.53 ! [V_a_2,T_a] :
% 160.59/160.53 ( class_Groups_Olinordered__ab__group__add(T_a)
% 160.59/160.53 => ( 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)))
% 160.59/160.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_not__square__less__zero,axiom,
% 160.59/160.53 ! [V_a,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__ring(T_a)
% 160.59/160.53 => ~ 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))) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 160.59/160.53 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.53 ( class_Groups_Oab__semigroup__add(T_a)
% 160.59/160.53 => 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)) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 160.59/160.53 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.53 ( class_Groups_Oab__semigroup__mult(T_a)
% 160.59/160.53 => 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)) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__left__cancel,axiom,
% 160.59/160.53 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.53 ( class_Groups_Ocancel__semigroup__add(T_a)
% 160.59/160.53 => ( 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_c_2)
% 160.59/160.53 <=> V_b_2 = V_c_2 ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__right__cancel,axiom,
% 160.59/160.53 ! [V_c_2,V_a_2,V_b_2,T_a] :
% 160.59/160.53 ( class_Groups_Ocancel__semigroup__add(T_a)
% 160.59/160.53 => ( 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_c_2),V_a_2)
% 160.59/160.53 <=> V_b_2 = V_c_2 ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__less__cancel__right,axiom,
% 160.59/160.53 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 160.59/160.53 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
% 160.59/160.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__less__cancel__left,axiom,
% 160.59/160.53 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 160.59/160.53 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
% 160.59/160.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__strict__right__mono,axiom,
% 160.59/160.53 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.53 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.53 => 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))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__strict__left__mono,axiom,
% 160.59/160.53 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.53 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.53 => 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))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__strict__mono,axiom,
% 160.59/160.53 ! [V_d,V_c,V_b,V_a,T_a] :
% 160.59/160.53 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 160.59/160.53 => 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))) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__left__imp__eq,axiom,
% 160.59/160.53 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.53 ( class_Groups_Ocancel__semigroup__add(T_a)
% 160.59/160.53 => ( 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)
% 160.59/160.53 => V_b = V_c ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__imp__eq,axiom,
% 160.59/160.53 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.53 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 160.59/160.53 => ( 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)
% 160.59/160.53 => V_b = V_c ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__right__imp__eq,axiom,
% 160.59/160.53 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.53 ( class_Groups_Ocancel__semigroup__add(T_a)
% 160.59/160.53 => ( 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)
% 160.59/160.53 => V_b = V_c ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__less__imp__less__right,axiom,
% 160.59/160.53 ! [V_b,V_c,V_a,T_a] :
% 160.59/160.53 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 160.59/160.53 => ( 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)))
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__less__imp__less__left,axiom,
% 160.59/160.53 ! [V_b,V_a,V_c,T_a] :
% 160.59/160.53 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 160.59/160.53 => ( 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)))
% 160.59/160.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_sum__squares__eq__zero__iff,axiom,
% 160.59/160.53 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__ring__strict(T_a)
% 160.59/160.53 => ( 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)
% 160.59/160.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__diff__inverse,axiom,
% 160.59/160.53 ! [V_n,V_m] :
% 160.59/160.53 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.53 => 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 ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__diff__conv,axiom,
% 160.59/160.53 ! [V_k_2,V_j_2,V_i_2] :
% 160.59/160.53 ( 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)))
% 160.59/160.53 <=> 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)) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_divisors__zero,axiom,
% 160.59/160.53 ! [V_b,V_a,T_a] :
% 160.59/160.53 ( class_Rings_Ono__zero__divisors(T_a)
% 160.59/160.53 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.53 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.53 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_no__zero__divisors,axiom,
% 160.59/160.53 ! [V_b,V_a,T_a] :
% 160.59/160.53 ( class_Rings_Ono__zero__divisors(T_a)
% 160.59/160.53 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__eq__0__iff,axiom,
% 160.59/160.53 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.53 ( class_Rings_Oring__no__zero__divisors(T_a)
% 160.59/160.53 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.53 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.53 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__zero__right,axiom,
% 160.59/160.53 ! [V_a,T_a] :
% 160.59/160.53 ( class_Rings_Omult__zero(T_a)
% 160.59/160.53 => 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) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__zero__left,axiom,
% 160.59/160.53 ! [V_a,T_a] :
% 160.59/160.53 ( class_Rings_Omult__zero(T_a)
% 160.59/160.53 => 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) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_zero__less__two,axiom,
% 160.59/160.53 ! [T_a] :
% 160.59/160.53 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.53 => 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)))) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_n__less__m__mult__n,axiom,
% 160.59/160.53 ! [V_m,V_n] :
% 160.59/160.53 ( 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))
% 160.59/160.53 => ( 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))
% 160.59/160.53 => 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))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_n__less__n__mult__m,axiom,
% 160.59/160.53 ! [V_m,V_n] :
% 160.59/160.53 ( 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))
% 160.59/160.53 => ( 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))
% 160.59/160.53 => 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))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_one__less__mult,axiom,
% 160.59/160.53 ! [V_m,V_n] :
% 160.59/160.53 ( 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))
% 160.59/160.53 => ( 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))
% 160.59/160.53 => 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))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_nat__diff__split,axiom,
% 160.59/160.53 ! [V_b_2,V_a_2,V_P_2] :
% 160.59/160.53 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 160.59/160.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 160.59/160.53 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 160.59/160.53 & ! [B_d] :
% 160.59/160.53 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 160.59/160.53 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_nat__diff__split__asm,axiom,
% 160.59/160.53 ! [V_b_2,V_a_2,V_P_2] :
% 160.59/160.53 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 160.59/160.53 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 160.59/160.53 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 160.59/160.53 | ? [B_d] :
% 160.59/160.53 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 160.59/160.53 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add_Ocomm__neutral,axiom,
% 160.59/160.53 ! [V_a,T_a] :
% 160.59/160.53 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.53 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__0__right,axiom,
% 160.59/160.53 ! [V_a,T_a] :
% 160.59/160.53 ( class_Groups_Omonoid__add(T_a)
% 160.59/160.53 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_double__zero__sym,axiom,
% 160.59/160.53 ! [V_a_2,T_a] :
% 160.59/160.53 ( class_Groups_Olinordered__ab__group__add(T_a)
% 160.59/160.53 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)
% 160.59/160.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__0,axiom,
% 160.59/160.53 ! [V_a,T_a] :
% 160.59/160.53 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.53 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__0__left,axiom,
% 160.59/160.53 ! [V_a,T_a] :
% 160.59/160.53 ( class_Groups_Omonoid__add(T_a)
% 160.59/160.53 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__diff__cancel,axiom,
% 160.59/160.53 ! [V_b,V_a,T_a] :
% 160.59/160.53 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.53 => 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 ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_diff__add__cancel,axiom,
% 160.59/160.53 ! [V_b,V_a,T_a] :
% 160.59/160.53 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.53 => 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 ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_diff__eq__diff__less,axiom,
% 160.59/160.53 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.53 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.53 => ( 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_c_2),V_d_2)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 160.59/160.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) ) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__1__left,axiom,
% 160.59/160.53 ! [V_a,T_a] :
% 160.59/160.53 ( class_Groups_Omonoid__mult(T_a)
% 160.59/160.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__1,axiom,
% 160.59/160.53 ! [V_a,T_a] :
% 160.59/160.53 ( class_Groups_Ocomm__monoid__mult(T_a)
% 160.59/160.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__1__right,axiom,
% 160.59/160.53 ! [V_a,T_a] :
% 160.59/160.53 ( class_Groups_Omonoid__mult(T_a)
% 160.59/160.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult_Ocomm__neutral,axiom,
% 160.59/160.53 ! [V_a,T_a] :
% 160.59/160.53 ( class_Groups_Ocomm__monoid__mult(T_a)
% 160.59/160.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__eq__self__zero,axiom,
% 160.59/160.53 ! [V_n,V_m] :
% 160.59/160.53 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 160.59/160.53 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_add__is__0,axiom,
% 160.59/160.53 ! [V_n_2,V_m_2] :
% 160.59/160.53 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.53 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.53 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_Nat_Oadd__0__right,axiom,
% 160.59/160.53 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 160.59/160.53
% 160.59/160.53 fof(fact_plus__nat_Oadd__0,axiom,
% 160.59/160.53 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__supI1,axiom,
% 160.59/160.53 ! [V_b,V_a,V_x,T_a] :
% 160.59/160.53 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 160.59/160.53 => 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))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_less__supI2,axiom,
% 160.59/160.53 ! [V_a,V_b,V_x,T_a] :
% 160.59/160.53 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 160.59/160.53 => 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))) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__cancel2,axiom,
% 160.59/160.53 ! [V_n_2,V_k_2,V_m_2] :
% 160.59/160.53 ( 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)
% 160.59/160.53 <=> ( V_m_2 = V_n_2
% 160.59/160.53 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__cancel1,axiom,
% 160.59/160.53 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.53 ( 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)
% 160.59/160.53 <=> ( V_m_2 = V_n_2
% 160.59/160.53 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__is__0,axiom,
% 160.59/160.53 ! [V_n_2,V_m_2] :
% 160.59/160.53 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.53 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.53 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 160.59/160.53
% 160.59/160.53 fof(fact_mult__0__right,axiom,
% 160.59/160.54 ! [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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_mult__0,axiom,
% 160.59/160.54 ! [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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_less__infI1,axiom,
% 160.59/160.54 ! [V_b,V_x,V_a,T_a] :
% 160.59/160.54 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 160.59/160.54 => 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)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_less__infI2,axiom,
% 160.59/160.54 ! [V_a,V_x,V_b,T_a] :
% 160.59/160.54 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 160.59/160.54 => 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)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_add__Suc__shift,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_add__Suc,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_add__Suc__right,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Suc__mult__cancel1,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.54 ( 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)
% 160.59/160.54 <=> V_m_2 = V_n_2 ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_gr0I,axiom,
% 160.59/160.54 ! [V_n] :
% 160.59/160.54 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_gr__implies__not0,axiom,
% 160.59/160.54 ! [V_n,V_m] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.54 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_less__nat__zero__code,axiom,
% 160.59/160.54 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_neq0__conv,axiom,
% 160.59/160.54 ! [V_n_2] :
% 160.59/160.54 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_not__less0,axiom,
% 160.59/160.54 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Suc__less__SucD,axiom,
% 160.59/160.54 ! [V_n,V_m] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 160.59/160.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Suc__lessD,axiom,
% 160.59/160.54 ! [V_n,V_m] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 160.59/160.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_less__SucE,axiom,
% 160.59/160.54 ! [V_n,V_m] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 160.59/160.54 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.54 => V_m = V_n ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_less__trans__Suc,axiom,
% 160.59/160.54 ! [V_k,V_j,V_i] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 160.59/160.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Suc__lessI,axiom,
% 160.59/160.54 ! [V_n,V_m] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.54 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 160.59/160.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_less__SucI,axiom,
% 160.59/160.54 ! [V_n,V_m] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_less__antisym,axiom,
% 160.59/160.54 ! [V_m,V_n] :
% 160.59/160.54 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 160.59/160.54 => V_m = V_n ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_not__less__less__Suc__eq,axiom,
% 160.59/160.54 ! [V_m_2,V_n_2] :
% 160.59/160.54 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 160.59/160.54 <=> V_n_2 = V_m_2 ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Suc__less__eq,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_less__Suc__eq,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 160.59/160.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.54 | V_m_2 = V_n_2 ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_not__less__eq,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2] :
% 160.59/160.54 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_diff__add__inverse2,axiom,
% 160.59/160.54 ! [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 ).
% 160.59/160.54
% 160.59/160.54 fof(fact_diff__add__inverse,axiom,
% 160.59/160.54 ! [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 ).
% 160.59/160.54
% 160.59/160.54 fof(fact_diff__diff__left,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_diff__cancel,axiom,
% 160.59/160.54 ! [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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_diff__cancel2,axiom,
% 160.59/160.54 ! [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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_diff__mult__distrib2,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_diff__mult__distrib,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_less__imp__diff__less,axiom,
% 160.59/160.54 ! [V_n,V_k,V_j] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_diff__less__mono2,axiom,
% 160.59/160.54 ! [V_l,V_n,V_m] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 160.59/160.54 => 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))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_nat__mult__1,axiom,
% 160.59/160.54 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 160.59/160.54
% 160.59/160.54 fof(fact_nat__1__eq__mult__iff,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2] :
% 160.59/160.54 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 160.59/160.54 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 160.59/160.54 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_nat__mult__1__right,axiom,
% 160.59/160.54 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 160.59/160.54
% 160.59/160.54 fof(fact_nat__mult__eq__1__iff,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2] :
% 160.59/160.54 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 160.59/160.54 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 160.59/160.54 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_zero__less__one,axiom,
% 160.59/160.54 ! [T_a] :
% 160.59/160.54 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_not__one__less__zero,axiom,
% 160.59/160.54 ! [T_a] :
% 160.59/160.54 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.54 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fun__left__comm,axiom,
% 160.59/160.54 ! [T_a] :
% 160.59/160.54 ( class_Groups_Oab__semigroup__mult(T_a)
% 160.59/160.54 => c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fun__left__comm__idem,axiom,
% 160.59/160.54 ! [T_a] :
% 160.59/160.54 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 160.59/160.54 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum__addf,axiom,
% 160.59/160.54 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 160.59/160.54 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_mult__eq__if,axiom,
% 160.59/160.54 ! [V_n,V_m] :
% 160.59/160.54 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.54 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 160.59/160.54 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.54 => 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)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum__product,axiom,
% 160.59/160.54 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.54 ( class_Rings_Osemiring__0(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum__left__distrib,axiom,
% 160.59/160.54 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.54 ( class_Rings_Osemiring__0(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum__right__distrib,axiom,
% 160.59/160.54 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] :
% 160.59/160.54 ( class_Rings_Osemiring__0(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_less__SUP__iff,axiom,
% 160.59/160.54 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] :
% 160.59/160.54 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.54 & class_Orderings_Olinorder(T_a) )
% 160.59/160.54 => ( 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)))
% 160.59/160.54 <=> ? [B_x] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 160.59/160.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_less__iff__diff__less__0,axiom,
% 160.59/160.54 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.54 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 160.59/160.54 <=> 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))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_one__is__add,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2] :
% 160.59/160.54 ( 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)
% 160.59/160.54 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 160.59/160.54 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 160.59/160.54 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.54 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_add__is__1,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2] :
% 160.59/160.54 ( 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))
% 160.59/160.54 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 160.59/160.54 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 160.59/160.54 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.54 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_mult__eq__1__iff,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2] :
% 160.59/160.54 ( 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))
% 160.59/160.54 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 160.59/160.54 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_gr0__conv__Suc,axiom,
% 160.59/160.54 ! [V_n_2] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 160.59/160.54 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_less__Suc0,axiom,
% 160.59/160.54 ! [V_n_2] :
% 160.59/160.54 ( 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))))
% 160.59/160.54 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_less__Suc__eq__0__disj,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 160.59/160.54 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.54 | ? [B_j] :
% 160.59/160.54 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 160.59/160.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_diff__add__0,axiom,
% 160.59/160.54 ! [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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_zero__less__diff,axiom,
% 160.59/160.54 ! [V_m_2,V_n_2] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_diff__less,axiom,
% 160.59/160.54 ! [V_m,V_n] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 160.59/160.54 => 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)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_diff__less__Suc,axiom,
% 160.59/160.54 ! [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))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Suc__eq__plus1,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Suc__eq__plus1__left,axiom,
% 160.59/160.54 ! [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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_mult__eq__self__implies__10,axiom,
% 160.59/160.54 ! [V_n,V_m] :
% 160.59/160.54 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 160.59/160.54 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 160.59/160.54 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum_Odistrib,axiom,
% 160.59/160.54 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 160.59/160.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => 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)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_card__ge__0__finite,axiom,
% 160.59/160.54 ! [V_A_2,T_a] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Suc__pred,axiom,
% 160.59/160.54 ! [V_n] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.54 => 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 ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_diff__Suc__less,axiom,
% 160.59/160.54 ! [V_i,V_n] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold__image__distrib,axiom,
% 160.59/160.54 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 160.59/160.54 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => 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)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum__insert,axiom,
% 160.59/160.54 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] :
% 160.59/160.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 160.59/160.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2))
% 160.59/160.54 => 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)) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum_Oinsert,axiom,
% 160.59/160.54 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 160.59/160.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.54 => 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)) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum__Un__Int,axiom,
% 160.59/160.54 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.54 => 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)) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum_OF__eq,axiom,
% 160.59/160.54 ! [V_g_2,V_A_2,T_a,T_b] :
% 160.59/160.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.54 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => 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) )
% 160.59/160.54 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => 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) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum_Oeq__fold,axiom,
% 160.59/160.54 ! [V_g_2,V_A_2,T_a,T_b] :
% 160.59/160.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => 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) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold__image__insert,axiom,
% 160.59/160.54 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] :
% 160.59/160.54 ( class_Groups_Oab__semigroup__mult(T_b)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.54 => 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)) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_card_Ounion__inter,axiom,
% 160.59/160.54 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.54 => 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)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_card__Un__Int,axiom,
% 160.59/160.54 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.54 => 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))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_card__gt__0__iff,axiom,
% 160.59/160.54 ! [V_A_2,T_a] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.54 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_add__eq__if,axiom,
% 160.59/160.54 ! [V_n,V_m] :
% 160.59/160.54 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.54 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 160.59/160.54 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.54 => 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)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Suc__pred_H,axiom,
% 160.59/160.54 ! [V_n] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.54 => 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))) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Suc__diff__1,axiom,
% 160.59/160.54 ! [V_n] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.54 => 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 ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_card__def,axiom,
% 160.59/160.54 ! [V_A_2,T_a] :
% 160.59/160.54 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => 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) )
% 160.59/160.54 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_card_Oeq__fold__g,axiom,
% 160.59/160.54 ! [V_A_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum_Oinsert__remove,axiom,
% 160.59/160.54 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
% 160.59/160.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => 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)))))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum__Un__disjoint,axiom,
% 160.59/160.54 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.54 => ( 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))
% 160.59/160.54 => 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)) ) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum__Un,axiom,
% 160.59/160.54 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.54 ( class_Groups_Oab__group__add(T_b)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.54 => 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))) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_card__Un__disjoint,axiom,
% 160.59/160.54 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.54 => ( 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))
% 160.59/160.54 => 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)) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_card_Oinsert,axiom,
% 160.59/160.54 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.54 => 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)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold__image__Un__Int,axiom,
% 160.59/160.54 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.54 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.54 => 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))) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum__Un__nat,axiom,
% 160.59/160.54 ! [V_f_2,V_B_2,V_A_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.54 => 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))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 160.59/160.54 ! [V_m,V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 160.59/160.54 ! [V_a,V_m,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 160.59/160.54 ! [V_m,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_add__scale__eq__noteq,axiom,
% 160.59/160.54 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 160.59/160.54 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 160.59/160.54 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.54 => ( ( V_a = V_b
% 160.59/160.54 & V_c != V_d )
% 160.59/160.54 => 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)) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_even__less__0__iff,axiom,
% 160.59/160.54 ! [V_a_2,T_a] :
% 160.59/160.54 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.54 => ( 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)))
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_card_Ounion__inter__neutral,axiom,
% 160.59/160.54 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.54 => ( ( ? [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)))
% 160.59/160.54 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 160.59/160.54 => 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)) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold__image__Un__one,axiom,
% 160.59/160.54 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 160.59/160.54 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 160.59/160.54 => ( ! [B_x] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 160.59/160.54 => 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)) ) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum__Un__zero,axiom,
% 160.59/160.54 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 160.59/160.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 160.59/160.54 => ( ! [B_x] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 160.59/160.54 => 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)) ) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 160.59/160.54 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.54 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.54 => ( ! [B_x] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 160.59/160.54 => 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)) ) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_nat__mult__commute,axiom,
% 160.59/160.54 ! [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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_nat__mult__assoc,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_psubsetD,axiom,
% 160.59/160.54 ! [V_c_2,V_B_2,V_A_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.59/160.54 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_not__psubset__empty,axiom,
% 160.59/160.54 ! [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)))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_psubset__card__mono,axiom,
% 160.59/160.54 ! [V_A_2,V_B_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.54 => 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))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 160.59/160.54 ! [V_c,V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 160.59/160.54 ! [V_d,V_c,V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 160.59/160.54 ! [V_d,V_c,V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 160.59/160.54 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 160.59/160.54 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 160.59/160.54 ! [V_d,V_c,V_b,V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 160.59/160.54 ! [V_b,V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 160.59/160.54 ! [V_ry,V_rx,V_lx,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 160.59/160.54 ! [V_ry,V_rx,V_lx,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 160.59/160.54 ! [V_rx,V_ly,V_lx,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 160.59/160.54 ! [V_rx,V_ly,V_lx,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 160.59/160.54 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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))) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 160.59/160.54 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 160.59/160.54 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_double__eq__0__iff,axiom,
% 160.59/160.54 ! [V_a_2,T_a] :
% 160.59/160.54 ( class_Groups_Olinordered__ab__group__add(T_a)
% 160.59/160.54 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.54 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_add__0__iff,axiom,
% 160.59/160.54 ! [V_a_2,V_b_2,T_a] :
% 160.59/160.54 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 160.59/160.54 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)
% 160.59/160.54 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 160.59/160.54 ! [V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 160.59/160.54 ! [V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 160.59/160.54 ! [V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 160.59/160.54 ! [V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 160.59/160.54 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_crossproduct__noteq,axiom,
% 160.59/160.54 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.54 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 160.59/160.54 => ( ( V_a_2 != V_b_2
% 160.59/160.54 & V_c_2 != V_d_2 )
% 160.59/160.54 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_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_c_2)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 160.59/160.54 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 160.59/160.54 ! [V_b,V_m,V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_crossproduct__eq,axiom,
% 160.59/160.54 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
% 160.59/160.54 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 160.59/160.54 => ( 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))
% 160.59/160.54 <=> ( V_w_2 = V_x_2
% 160.59/160.54 | V_y_2 = V_z_2 ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 160.59/160.54 ! [V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 160.59/160.54 ! [V_a,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_nat__mult__eq__cancel1,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 160.59/160.54 => ( 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)
% 160.59/160.54 <=> V_m_2 = V_n_2 ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_nat__mult__less__cancel1,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 160.59/160.54 => ( 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)))
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_left__add__mult__distrib,axiom,
% 160.59/160.54 ! [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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.54 ( 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)
% 160.59/160.54 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.54 | V_m_2 = V_n_2 ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_termination__basic__simps_I1_J,axiom,
% 160.59/160.54 ! [V_z,V_y,V_x] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 160.59/160.54 => 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))) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_termination__basic__simps_I2_J,axiom,
% 160.59/160.54 ! [V_y,V_z,V_x] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 160.59/160.54 => 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))) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Ints__odd__less__0,axiom,
% 160.59/160.54 ! [V_a_2,T_a] :
% 160.59/160.54 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 160.59/160.54 => ( 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)))
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_com_Osize_I4_J,axiom,
% 160.59/160.54 ! [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))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_psubset__trans,axiom,
% 160.59/160.54 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 160.59/160.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Ints__0,axiom,
% 160.59/160.54 ! [T_a] :
% 160.59/160.54 ( class_Rings_Oring__1(T_a)
% 160.59/160.54 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Ints__add,axiom,
% 160.59/160.54 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.54 ( class_Rings_Oring__1(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 160.59/160.54 => 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))) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Ints__mult,axiom,
% 160.59/160.54 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.54 ( class_Rings_Oring__1(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 160.59/160.54 => 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))) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Ints__diff,axiom,
% 160.59/160.54 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.54 ( class_Rings_Oring__1(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a)))
% 160.59/160.54 => 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))) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Ints__1,axiom,
% 160.59/160.54 ! [T_a] :
% 160.59/160.54 ( class_Rings_Oring__1(T_a)
% 160.59/160.54 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_comp__cong,axiom,
% 160.59/160.54 ! [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] :
% 160.59/160.54 ( 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))
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_com_Osize_I7_J,axiom,
% 160.59/160.54 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_com_Osize_I1_J,axiom,
% 160.59/160.54 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Ints__double__eq__0__iff,axiom,
% 160.59/160.54 ! [V_a_2,T_a] :
% 160.59/160.54 ( class_Int_Oring__char__0(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 160.59/160.54 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.54 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Ints__odd__nonzero,axiom,
% 160.59/160.54 ! [V_a_2,T_a] :
% 160.59/160.54 ( class_Int_Oring__char__0(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 160.59/160.54 => 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) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_com_Osize_I6_J,axiom,
% 160.59/160.54 ! [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))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_com_Osize_I5_J,axiom,
% 160.59/160.54 ! [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))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_card__Plus__conv__if,axiom,
% 160.59/160.54 ! [V_B_2,T_b,V_A_2,T_a] :
% 160.59/160.54 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) )
% 160.59/160.54 => 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)) )
% 160.59/160.54 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) )
% 160.59/160.54 => 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) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_com_Osize_I12_J,axiom,
% 160.59/160.54 ! [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))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_com_Osize_I13_J,axiom,
% 160.59/160.54 ! [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))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_com_Osize_I14_J,axiom,
% 160.59/160.54 ! [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))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum__strict__mono,axiom,
% 160.59/160.54 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
% 160.59/160.54 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.54 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) )
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.54 => ( ! [B_x] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 160.59/160.54 => 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))) ) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold__graph__permute__diff,axiom,
% 160.59/160.54 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] :
% 160.59/160.54 ( class_Groups_Oab__semigroup__mult(T_a)
% 160.59/160.54 => ( 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))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 160.59/160.54 => 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)) ) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_diff__Suc,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Sup__fold__sup,axiom,
% 160.59/160.54 ! [V_A_2,T_a] :
% 160.59/160.54 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => 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) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_UnionI,axiom,
% 160.59/160.54 ! [V_A_2,V_C_2,V_X_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2))
% 160.59/160.54 => 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))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Union__empty,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_finite__UnionD,axiom,
% 160.59/160.54 ! [V_A_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))
% 160.59/160.54 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Union__insert,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Un__eq__Union,axiom,
% 160.59/160.54 ! [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))))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Union__Un__distrib,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold__graph_OemptyI,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_empty__fold__graphE,axiom,
% 160.59/160.54 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.54 ( 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))
% 160.59/160.54 => V_x_2 = V_z_2 ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold__graph__imp__finite,axiom,
% 160.59/160.54 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2))
% 160.59/160.54 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_image__Union,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Int__Union2,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Int__Union,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_UN__extend__simps_I8_J,axiom,
% 160.59/160.54 ! [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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_UN__simps_I8_J,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_UNION__eq__Union__image,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Union__image__eq,axiom,
% 160.59/160.54 ! [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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_less__Sup__iff,axiom,
% 160.59/160.54 ! [V_S_2,V_a_2,T_a] :
% 160.59/160.54 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.54 & class_Orderings_Olinorder(T_a) )
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2)))
% 160.59/160.54 <=> ? [B_x] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 160.59/160.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 160.59/160.54 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.54 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 160.59/160.54 => V_y_2 = V_x_2 ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_finite__Plus__iff,axiom,
% 160.59/160.54 ! [V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_finite__Plus,axiom,
% 160.59/160.54 ! [V_B_2,T_b,V_A_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 160.59/160.54 => 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))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_finite__PlusD_I1_J,axiom,
% 160.59/160.54 ! [V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_finite__PlusD_I2_J,axiom,
% 160.59/160.54 ! [V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Union__disjoint,axiom,
% 160.59/160.54 ! [V_A_2,V_C_2,T_a] :
% 160.59/160.54 ( 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))
% 160.59/160.54 <=> ! [B_x] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2))
% 160.59/160.54 => 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)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold__graph_OinsertI,axiom,
% 160.59/160.54 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 160.59/160.54 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 160.59/160.54 => 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))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Un__Union__image,axiom,
% 160.59/160.54 ! [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))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_nat__case__0,axiom,
% 160.59/160.54 ! [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 ).
% 160.59/160.54
% 160.59/160.54 fof(fact_nat__case__Suc,axiom,
% 160.59/160.54 ! [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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Sup__empty,axiom,
% 160.59/160.54 ! [T_a] :
% 160.59/160.54 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Sup__singleton,axiom,
% 160.59/160.54 ! [V_a_2,T_a] :
% 160.59/160.54 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.54 => 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 ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Sup__insert,axiom,
% 160.59/160.54 ! [V_A_2,V_a_2,T_a] :
% 160.59/160.54 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 160.59/160.54 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.54 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 160.59/160.54 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold__def,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_com_Osize_I15_J,axiom,
% 160.59/160.54 ! [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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold__graph__insert__swap,axiom,
% 160.59/160.54 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] :
% 160.59/160.54 ( class_Groups_Oab__semigroup__mult(T_a)
% 160.59/160.54 => ( 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))
% 160.59/160.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 160.59/160.54 => 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))) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_com_Osize_I9_J,axiom,
% 160.59/160.54 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 160.59/160.54 ! [V_z_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.54 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => 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))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Sup__binary,axiom,
% 160.59/160.54 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.54 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_sup__Sup__fold__sup,axiom,
% 160.59/160.54 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.54 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => 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) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Sup__fin__Sup,axiom,
% 160.59/160.54 ! [V_A_2,T_a] :
% 160.59/160.54 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.54 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Diff1__fold__graph,axiom,
% 160.59/160.54 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.54 ( 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))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.54 => 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))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_card__Plus,axiom,
% 160.59/160.54 ! [V_B_2,T_b,V_A_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 160.59/160.54 => 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)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold1Set_Ointros,axiom,
% 160.59/160.54 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2))
% 160.59/160.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.54 => 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)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Plus__eq__empty__conv,axiom,
% 160.59/160.54 ! [V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.54 ( 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))
% 160.59/160.54 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.54 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 160.59/160.54 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.54 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.54 => ? [B_y_H] :
% 160.59/160.54 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 160.59/160.54 & 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)) ) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold1__eq__fold,axiom,
% 160.59/160.54 ! [V_a_2,V_A_2,T_a] :
% 160.59/160.54 ( class_Groups_Oab__semigroup__mult(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.54 => 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) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold1__Un,axiom,
% 160.59/160.54 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.54 ( class_Groups_Oab__semigroup__mult(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.54 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.54 => ( 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))
% 160.59/160.54 => 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)) ) ) ) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold1__insert,axiom,
% 160.59/160.54 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.54 ( class_Groups_Oab__semigroup__mult(T_a)
% 160.59/160.54 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.54 => 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)) ) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 160.59/160.54 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.54 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 160.59/160.54 => ( 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))
% 160.59/160.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.54 => ~ ! [B_y] :
% 160.59/160.54 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 160.59/160.54 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_finite__UN__I,axiom,
% 160.59/160.54 ! [V_B_2,T_b,V_A_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( ! [B_a] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 160.59/160.54 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) )
% 160.59/160.54 => 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))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Union__def,axiom,
% 160.59/160.54 ! [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))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold1__def,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold1Set__nonempty,axiom,
% 160.59/160.54 ! [V_x_2,V_A_2,V_f_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2))
% 160.59/160.54 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_empty__fold1SetE,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold1__singleton__def,axiom,
% 160.59/160.54 ! [V_a_2,V_f_2,T_a,V_g_2] :
% 160.59/160.54 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2)
% 160.59/160.54 => 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 ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold1__singleton,axiom,
% 160.59/160.54 ! [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 ).
% 160.59/160.54
% 160.59/160.54 fof(fact_folding__one_Oeq__fold,axiom,
% 160.59/160.54 ! [V_A_2,V_F_2,V_f_2,T_a] :
% 160.59/160.54 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Sup__fin_OF__eq,axiom,
% 160.59/160.54 ! [V_A_2,T_a] :
% 160.59/160.54 ( class_Lattices_Olattice(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => 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) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Inf__fin_OF__eq,axiom,
% 160.59/160.54 ! [V_A_2,T_a] :
% 160.59/160.54 ( class_Lattices_Olattice(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => 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) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold1Set__sing,axiom,
% 160.59/160.54 ! [V_b_2,V_a_2,V_f_2,T_a] :
% 160.59/160.54 ( 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))
% 160.59/160.54 <=> V_a_2 = V_b_2 ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold1__insert__idem,axiom,
% 160.59/160.54 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.54 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 160.59/160.54 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => 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)) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold1__Un2,axiom,
% 160.59/160.54 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.54 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.54 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.54 => 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)) ) ) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold1__eq__fold__idem,axiom,
% 160.59/160.54 ! [V_a_2,V_A_2,T_a] :
% 160.59/160.54 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => 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) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_semilattice__big_OF__eq,axiom,
% 160.59/160.54 ! [V_A_2,V_F_2,V_f_2,T_a] :
% 160.59/160.54 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold1__in,axiom,
% 160.59/160.54 ! [V_A_2,T_a] :
% 160.59/160.54 ( class_Groups_Oab__semigroup__mult(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.54 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.54 => ( ! [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))))))
% 160.59/160.54 => 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)) ) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_finite__Union,axiom,
% 160.59/160.54 ! [V_A_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2))
% 160.59/160.54 => ( ! [B_M] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2))
% 160.59/160.54 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) )
% 160.59/160.54 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_insert__partition,axiom,
% 160.59/160.54 ! [V_F_2,V_x_2,T_a] :
% 160.59/160.54 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))
% 160.59/160.54 => ( ! [B_x] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 => ! [B_xa] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 => ( B_x != B_xa
% 160.59/160.54 => 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)) ) ) )
% 160.59/160.54 => 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)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_hom__fold1__commute,axiom,
% 160.59/160.54 ! [V_N_2,V_h_2,T_a] :
% 160.59/160.54 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 160.59/160.54 => ( ! [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))
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 160.59/160.54 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.54 => 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)) ) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_insert__fold1SetE,axiom,
% 160.59/160.54 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] :
% 160.59/160.54 ( 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))
% 160.59/160.54 => ~ ! [B_a,B_A] :
% 160.59/160.54 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A)
% 160.59/160.54 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2))
% 160.59/160.54 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_fold1Set_Oequations,axiom,
% 160.59/160.54 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] :
% 160.59/160.54 ( 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))
% 160.59/160.54 <=> ? [B_a,B_A] :
% 160.59/160.54 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A)
% 160.59/160.54 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2))
% 160.59/160.54 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_arith__series__nat,axiom,
% 160.59/160.54 ! [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)))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_finite__lessThan,axiom,
% 160.59/160.54 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_lessThan__Suc,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_lessThan__0,axiom,
% 160.59/160.54 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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_lessThan__eq__iff,axiom,
% 160.59/160.54 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.54 ( class_Orderings_Olinorder(T_a)
% 160.59/160.54 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2)
% 160.59/160.54 <=> V_x_2 = V_y_2 ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_card__lessThan,axiom,
% 160.59/160.54 ! [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 ).
% 160.59/160.54
% 160.59/160.54 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 160.59/160.54 ! [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))) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_lessThan__iff,axiom,
% 160.59/160.54 ! [V_k_2,V_i_2,T_a] :
% 160.59/160.54 ( class_Orderings_Oord(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)))
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_setsum__lessThan__Suc,axiom,
% 160.59/160.54 ! [V_n_2,V_f_2,T_a] :
% 160.59/160.54 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_lessThan__strict__subset__iff,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2,T_a] :
% 160.59/160.54 ( class_Orderings_Olinorder(T_a)
% 160.59/160.54 => ( 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)))
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_single__Diff__lessThan,axiom,
% 160.59/160.54 ! [V_k_2,T_a] :
% 160.59/160.54 ( class_Orderings_Oorder(T_a)
% 160.59/160.54 => 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))) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_finite__nat__set__iff__bounded,axiom,
% 160.59/160.54 ! [V_N_2] :
% 160.59/160.54 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 160.59/160.54 <=> ? [B_m] :
% 160.59/160.54 ! [B_x] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 160.59/160.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_arith__series__general,axiom,
% 160.59/160.54 ! [V_n_2,V_d_2,V_a_2,T_a] :
% 160.59/160.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.54 => 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)))) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_ord_OatMost__iff,axiom,
% 160.59/160.54 ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2)))
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_ord_OatLeast__iff,axiom,
% 160.59/160.54 ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2)))
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_ord_OlessThan__iff,axiom,
% 160.59/160.54 ! [V_k_2,V_less_2,V_i_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2)))
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_ord_OgreaterThan__iff,axiom,
% 160.59/160.54 ! [V_k_2,V_less_2,V_i_2,T_a] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2)))
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 160.59/160.54 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 160.59/160.54 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 160.59/160.54 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 160.59/160.54 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 160.59/160.54 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 160.59/160.54 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_of__nat__eq__iff,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2,T_a] :
% 160.59/160.54 ( class_Nat_Osemiring__char__0(T_a)
% 160.59/160.54 => ( 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)
% 160.59/160.54 <=> V_m_2 = V_n_2 ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_int__eq__0__conv,axiom,
% 160.59/160.54 ! [V_n_2] :
% 160.59/160.54 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.54 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_int__0,axiom,
% 160.59/160.54 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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_int__Suc,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_zless__iff__Suc__zadd,axiom,
% 160.59/160.54 ! [V_z_2,V_w_2] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 160.59/160.54 <=> ? [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))) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_zless__int,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_zadd__int__left,axiom,
% 160.59/160.54 ! [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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_zadd__int,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_int__mult,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_zmult__int,axiom,
% 160.59/160.54 ! [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)) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_int__1,axiom,
% 160.59/160.54 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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_int__setsum,axiom,
% 160.59/160.54 ! [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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_int__Suc0__eq__1,axiom,
% 160.59/160.54 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) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_zmult__zless__mono2__lemma,axiom,
% 160.59/160.54 ! [V_k,V_j,V_i] :
% 160.59/160.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 160.59/160.54 => 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))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_zero__less__int__conv,axiom,
% 160.59/160.54 ! [V_n_2] :
% 160.59/160.54 ( 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)))
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_of__nat__less__0__iff,axiom,
% 160.59/160.54 ! [V_m,T_a] :
% 160.59/160.54 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.54 => ~ 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))) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_of__nat__0,axiom,
% 160.59/160.54 ! [T_a] :
% 160.59/160.54 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_of__nat__less__iff,axiom,
% 160.59/160.54 ! [V_n_2,V_m_2,T_a] :
% 160.59/160.54 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.54 => ( 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)))
% 160.59/160.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_less__imp__of__nat__less,axiom,
% 160.59/160.54 ! [V_n,V_m,T_a] :
% 160.59/160.54 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.54 => 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))) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_of__nat__less__imp__less,axiom,
% 160.59/160.54 ! [V_n,V_m,T_a] :
% 160.59/160.54 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.54 => ( 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)))
% 160.59/160.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_of__nat__add,axiom,
% 160.59/160.54 ! [V_n,V_m,T_a] :
% 160.59/160.54 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_of__nat__mult,axiom,
% 160.59/160.54 ! [V_n,V_m,T_a] :
% 160.59/160.54 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.54 => 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)) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_of__nat__1,axiom,
% 160.59/160.54 ! [T_a] :
% 160.59/160.54 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.54 => 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) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_Ints__of__nat,axiom,
% 160.59/160.54 ! [V_n_2,T_a] :
% 160.59/160.54 ( class_Rings_Oring__1(T_a)
% 160.59/160.54 => 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))) ) ).
% 160.59/160.54
% 160.59/160.54 fof(fact_of__nat__setsum,axiom,
% 160.59/160.55 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.55 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.55 => 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) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_of__nat__Suc,axiom,
% 160.59/160.55 ! [V_m,T_a] :
% 160.59/160.55 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.55 => 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)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setsum__constant,axiom,
% 160.59/160.55 ! [V_A_2,V_y_2,T_b,T_a] :
% 160.59/160.55 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.55 => 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) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_of__nat__0__less__iff,axiom,
% 160.59/160.55 ! [V_n_2,T_a] :
% 160.59/160.55 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.55 => ( 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)))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 160.59/160.55 ! [V_n_2,T_a] :
% 160.59/160.55 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.55 => 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)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 160.59/160.55 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
% 160.59/160.55 ( 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)))
% 160.59/160.55 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 160.59/160.55 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 160.59/160.55 ! [V_x_2,V_y_2,V_c_2] :
% 160.59/160.55 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 160.59/160.55 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) )
% 160.59/160.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 160.59/160.55 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 160.59/160.55 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
% 160.59/160.55 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 160.59/160.55 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_gauss__sum,axiom,
% 160.59/160.55 ! [V_n_2,T_a] :
% 160.59/160.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_ivl__disj__un_I2_J,axiom,
% 160.59/160.55 ! [V_u_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => 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) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_psubset__insert__iff,axiom,
% 160.59/160.55 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 160.59/160.55 ( 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)))
% 160.59/160.55 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 160.59/160.55 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 160.59/160.55 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.55 => 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)) )
% 160.59/160.55 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setsum__SucD,axiom,
% 160.59/160.55 ! [V_n_2,V_A_2,V_f_2,T_a] :
% 160.59/160.55 ( 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)
% 160.59/160.55 => ? [B_x] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.55 & 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setprod_Oremove,axiom,
% 160.59/160.55 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 160.59/160.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.55 => 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)))))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_order__refl,axiom,
% 160.59/160.55 ! [V_x,T_a] :
% 160.59/160.55 ( class_Orderings_Opreorder(T_a)
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_equalityI,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.55 => V_A_2 = V_B_2 ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_finite__atMost,axiom,
% 160.59/160.55 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_subsetD,axiom,
% 160.59/160.55 ! [V_c_2,V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_empty__subsetI,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_finite__atLeastLessThan,axiom,
% 160.59/160.55 ! [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))) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_finite__atLeastAtMost,axiom,
% 160.59/160.55 ! [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))) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastatMost__empty__iff2,axiom,
% 160.59/160.55 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( 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)
% 160.59/160.55 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastatMost__empty__iff,axiom,
% 160.59/160.55 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( 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))
% 160.59/160.55 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastLessThan__empty,axiom,
% 160.59/160.55 ! [V_a_2,V_b_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
% 160.59/160.55 => 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)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_lessThan__subset__iff,axiom,
% 160.59/160.55 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( 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)))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_int__setprod,axiom,
% 160.59/160.55 ! [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) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_of__nat__setprod,axiom,
% 160.59/160.55 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.55 ( ( class_Groups_Ocomm__monoid__mult(T_a)
% 160.59/160.55 & class_Rings_Osemiring__1(T_a) )
% 160.59/160.55 => 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) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_int__int__eq,axiom,
% 160.59/160.55 ! [V_n_2,V_m_2] :
% 160.59/160.55 ( 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)
% 160.59/160.55 <=> V_m_2 = V_n_2 ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_of__nat__le__iff,axiom,
% 160.59/160.55 ! [V_n_2,V_m_2,T_a] :
% 160.59/160.55 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.55 => ( 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)))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_int__less__0__conv,axiom,
% 160.59/160.55 ! [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))) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Union__mono,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( 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))
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_SUP__subset,axiom,
% 160.59/160.55 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zless__add1__eq,axiom,
% 160.59/160.55 ! [V_z_2,V_w_2] :
% 160.59/160.55 ( 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))))
% 160.59/160.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 160.59/160.55 | V_w_2 = V_z_2 ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_pos__zmult__eq__1__iff,axiom,
% 160.59/160.55 ! [V_n_2,V_m_2] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 160.59/160.55 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 160.59/160.55 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 160.59/160.55 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_odd__less__0,axiom,
% 160.59/160.55 ! [V_z_2] :
% 160.59/160.55 ( 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)))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_int__0__less__1,axiom,
% 160.59/160.55 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))) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_less__bin__lemma,axiom,
% 160.59/160.55 ! [V_l_2,V_k_2] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 160.59/160.55 <=> 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zadd__strict__right__mono,axiom,
% 160.59/160.55 ! [V_k,V_j,V_i] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zless__linear,axiom,
% 160.59/160.55 ! [V_y,V_x] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 160.59/160.55 | V_x = V_y
% 160.59/160.55 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zmult__zless__mono2,axiom,
% 160.59/160.55 ! [V_k,V_j,V_i] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_equalityE,axiom,
% 160.59/160.55 ! [T_a,V_B_2,V_A_2] :
% 160.59/160.55 ( V_A_2 = V_B_2
% 160.59/160.55 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_subset__trans,axiom,
% 160.59/160.55 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_predicate1D,axiom,
% 160.59/160.55 ! [V_x_2,V_Q_2,V_P_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2))
% 160.59/160.55 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 160.59/160.55 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_equalityD2,axiom,
% 160.59/160.55 ! [T_a,V_B_2,V_A_2] :
% 160.59/160.55 ( V_A_2 = V_B_2
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_equalityD1,axiom,
% 160.59/160.55 ! [T_a,V_B_2,V_A_2] :
% 160.59/160.55 ( V_A_2 = V_B_2
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_rev__predicate1D,axiom,
% 160.59/160.55 ! [V_Q_2,T_a,V_x_2,V_P_2] :
% 160.59/160.55 ( hBOOL(hAPP(V_P_2,V_x_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2))
% 160.59/160.55 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_set__eq__subset,axiom,
% 160.59/160.55 ! [T_a,V_B_2,V_A_2] :
% 160.59/160.55 ( V_A_2 = V_B_2
% 160.59/160.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_subset__refl,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_linorder__le__cases,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__funE,axiom,
% 160.59/160.55 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 160.59/160.55 ( class_Orderings_Oord(T_b)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_xt1_I6_J,axiom,
% 160.59/160.55 ! [V_z,V_x,V_y,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_xt1_I5_J,axiom,
% 160.59/160.55 ! [V_x,V_y,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.55 => V_x = V_y ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_order__trans,axiom,
% 160.59/160.55 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.55 ( class_Orderings_Opreorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_order__antisym,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 160.59/160.55 => V_x = V_y ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_xt1_I4_J,axiom,
% 160.59/160.55 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 160.59/160.55 => ( V_b = V_c
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_ord__le__eq__trans,axiom,
% 160.59/160.55 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.55 ( class_Orderings_Oord(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.55 => ( V_b = V_c
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_xt1_I3_J,axiom,
% 160.59/160.55 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( V_a = V_b
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_ord__eq__le__trans,axiom,
% 160.59/160.55 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.55 ( class_Orderings_Oord(T_a)
% 160.59/160.55 => ( V_a = V_b
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_order__antisym__conv,axiom,
% 160.59/160.55 ! [V_x_2,V_y_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 160.59/160.55 <=> V_x_2 = V_y_2 ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__funD,axiom,
% 160.59/160.55 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 160.59/160.55 ( class_Orderings_Oord(T_b)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_order__eq__refl,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Orderings_Opreorder(T_a)
% 160.59/160.55 => ( V_x = V_y
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_order__eq__iff,axiom,
% 160.59/160.55 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( V_x_2 = V_y_2
% 160.59/160.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_linorder__linear,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.55 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__fun__def,axiom,
% 160.59/160.55 ! [V_g_2,V_f_2,T_a,T_b] :
% 160.59/160.55 ( class_Orderings_Oord(T_b)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 160.59/160.55 <=> ! [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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_int__0__neq__1,axiom,
% 160.59/160.55 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zadd__0,axiom,
% 160.59/160.55 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zadd__0__right,axiom,
% 160.59/160.55 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zadd__commute,axiom,
% 160.59/160.55 ! [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) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zmult__commute,axiom,
% 160.59/160.55 ! [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) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zadd__left__commute,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zadd__zmult__distrib2,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zadd__assoc,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zmult__assoc,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zadd__zmult__distrib,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zdiff__zmult__distrib,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zdiff__zmult__distrib2,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_odd__nonzero,axiom,
% 160.59/160.55 ! [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) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zmult__1,axiom,
% 160.59/160.55 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zmult__1__right,axiom,
% 160.59/160.55 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 160.59/160.55
% 160.59/160.55 fof(fact_ivl__diff,axiom,
% 160.59/160.55 ! [V_m_2,V_n_2,V_i_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2))
% 160.59/160.55 => 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) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastLessThan__subset__iff,axiom,
% 160.59/160.55 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( 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_c_2),V_d_2)))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2))
% 160.59/160.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastatMost__subset__iff,axiom,
% 160.59/160.55 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( 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_c_2,V_d_2)))
% 160.59/160.55 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 160.59/160.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atMost__subset__iff,axiom,
% 160.59/160.55 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( 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)))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atMost__eq__iff,axiom,
% 160.59/160.55 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2)
% 160.59/160.55 <=> V_x_2 = V_y_2 ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 160.59/160.55 ! [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) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeast0AtMost,axiom,
% 160.59/160.55 ! [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) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_ivl__disj__un_I17_J,axiom,
% 160.59/160.55 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 160.59/160.55 => 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) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_ivl__disj__un_I21_J,axiom,
% 160.59/160.55 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 160.59/160.55 => 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) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atMost__iff,axiom,
% 160.59/160.55 ! [V_k_2,V_i_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oord(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_UN__le__add__shift,axiom,
% 160.59/160.55 ! [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) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_ivl__disj__un_I10_J,axiom,
% 160.59/160.55 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 160.59/160.55 => 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) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_ivl__disj__un_I6_J,axiom,
% 160.59/160.55 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 160.59/160.55 => 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) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_subset__card__intvl__is__intvl,axiom,
% 160.59/160.55 ! [V_k_2,V_A_2] :
% 160.59/160.55 ( 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)))))
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_xt1_I8_J,axiom,
% 160.59/160.55 ! [V_z,V_x,V_y,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_order__le__less__trans,axiom,
% 160.59/160.55 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.55 ( class_Orderings_Opreorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_xt1_I7_J,axiom,
% 160.59/160.55 ! [V_z,V_x,V_y,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_order__less__le__trans,axiom,
% 160.59/160.55 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.55 ( class_Orderings_Opreorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_xt1_I11_J,axiom,
% 160.59/160.55 ! [V_a,V_b,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 160.59/160.55 => ( V_a != V_b
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_order__le__neq__trans,axiom,
% 160.59/160.55 ! [V_b,V_a,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.55 => ( V_a != V_b
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_order__le__imp__less__or__eq,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.55 | V_x = V_y ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_linorder__antisym__conv2,axiom,
% 160.59/160.55 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 160.59/160.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 160.59/160.55 <=> V_x_2 = V_y_2 ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_order__less__imp__le,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Orderings_Opreorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_leD,axiom,
% 160.59/160.55 ! [V_x,V_y,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 160.59/160.55 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_xt1_I12_J,axiom,
% 160.59/160.55 ! [V_b,V_a,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( V_a != V_b
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_order__neq__le__trans,axiom,
% 160.59/160.55 ! [V_b,V_a,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( V_a != V_b
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_linorder__antisym__conv1,axiom,
% 160.59/160.55 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 160.59/160.55 <=> V_x_2 = V_y_2 ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_not__leE,axiom,
% 160.59/160.55 ! [V_x,V_y,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_leI,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_order__le__less,axiom,
% 160.59/160.55 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 160.59/160.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 160.59/160.55 | V_x_2 = V_y_2 ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_less__le__not__le,axiom,
% 160.59/160.55 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Orderings_Opreorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 160.59/160.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 160.59/160.55 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_order__less__le,axiom,
% 160.59/160.55 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 160.59/160.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 160.59/160.55 & V_x_2 != V_y_2 ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_linorder__le__less__linear,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.55 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_linorder__not__le,axiom,
% 160.59/160.55 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_linorder__not__less,axiom,
% 160.59/160.55 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastatMost__psubset__iff,axiom,
% 160.59/160.55 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( 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_c_2,V_d_2)))
% 160.59/160.55 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 160.59/160.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2))
% 160.59/160.55 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_a_2))
% 160.59/160.55 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) )
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_set__mp,axiom,
% 160.59/160.55 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_set__rev__mp,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_in__mono,axiom,
% 160.59/160.55 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_add__le__imp__le__left,axiom,
% 160.59/160.55 ! [V_b,V_a,V_c,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 160.59/160.55 => ( 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)))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_add__le__imp__le__right,axiom,
% 160.59/160.55 ! [V_b,V_c,V_a,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 160.59/160.55 => ( 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)))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_add__mono,axiom,
% 160.59/160.55 ! [V_d,V_c,V_b,V_a,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_add__left__mono,axiom,
% 160.59/160.55 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_add__right__mono,axiom,
% 160.59/160.55 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_add__le__cancel__left,axiom,
% 160.59/160.55 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_add__le__cancel__right,axiom,
% 160.59/160.55 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_ivl__disj__int_I15_J,axiom,
% 160.59/160.55 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => 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)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_bot__least,axiom,
% 160.59/160.55 ! [V_x,T_a] :
% 160.59/160.55 ( class_Orderings_Obot(T_a)
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_diff__eq__diff__less__eq,axiom,
% 160.59/160.55 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.55 => ( 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_c_2),V_d_2)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_ivl__disj__un_I8_J,axiom,
% 160.59/160.55 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 160.59/160.55 => 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) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_subset__empty,axiom,
% 160.59/160.55 ! [V_A_2,T_a] :
% 160.59/160.55 ( 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))))
% 160.59/160.55 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__supE,axiom,
% 160.59/160.55 ! [V_x,V_b,V_a,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.55 => ( 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))
% 160.59/160.55 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 160.59/160.55 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_sup__mono,axiom,
% 160.59/160.55 ! [V_d,V_b,V_c,V_a,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_sup__least,axiom,
% 160.59/160.55 ! [V_z,V_x,V_y,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 160.59/160.55 => 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)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__supI,axiom,
% 160.59/160.55 ! [V_b,V_x,V_a,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 160.59/160.55 => 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)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_sup__absorb1,axiom,
% 160.59/160.55 ! [V_x,V_y,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 160.59/160.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_sup__absorb2,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__supI2,axiom,
% 160.59/160.55 ! [V_a,V_b,V_x,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__supI1,axiom,
% 160.59/160.55 ! [V_b,V_a,V_x,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__sup__iff,axiom,
% 160.59/160.55 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.55 => ( 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))
% 160.59/160.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__iff__sup,axiom,
% 160.59/160.55 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 160.59/160.55 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_sup__ge2,axiom,
% 160.59/160.55 ! [V_x,V_y,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_inf__sup__ord_I4_J,axiom,
% 160.59/160.55 ! [V_x,V_y,T_a] :
% 160.59/160.55 ( class_Lattices_Olattice(T_a)
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_sup__ge1,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_inf__sup__ord_I3_J,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Lattices_Olattice(T_a)
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_rev__finite__subset,axiom,
% 160.59/160.55 ! [V_A_2,V_B_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_finite__subset,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__infE,axiom,
% 160.59/160.55 ! [V_b,V_a,V_x,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.55 => ( 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)))
% 160.59/160.55 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 160.59/160.55 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_inf__mono,axiom,
% 160.59/160.55 ! [V_d,V_b,V_c,V_a,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_inf__greatest,axiom,
% 160.59/160.55 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__infI,axiom,
% 160.59/160.55 ! [V_b,V_a,V_x,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_inf__absorb2,axiom,
% 160.59/160.55 ! [V_x,V_y,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 160.59/160.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_inf__absorb1,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__infI2,axiom,
% 160.59/160.55 ! [V_a,V_x,V_b,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 160.59/160.55 => 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)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__infI1,axiom,
% 160.59/160.55 ! [V_b,V_x,V_a,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 160.59/160.55 => 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)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__inf__iff,axiom,
% 160.59/160.55 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.55 => ( 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)))
% 160.59/160.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__iff__inf,axiom,
% 160.59/160.55 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 160.59/160.55 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_inf__le2,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.55 => 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)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_inf__sup__ord_I2_J,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Lattices_Olattice(T_a)
% 160.59/160.55 => 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)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_inf__le1,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.55 => 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)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_inf__sup__ord_I1_J,axiom,
% 160.59/160.55 ! [V_y,V_x,T_a] :
% 160.59/160.55 ( class_Lattices_Olattice(T_a)
% 160.59/160.55 => 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)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_insert__mono,axiom,
% 160.59/160.55 ! [V_a_2,V_D_2,V_C_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_subset__insertI2,axiom,
% 160.59/160.55 ! [V_b_2,V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_subset__insertI,axiom,
% 160.59/160.55 ! [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))) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_image__mono,axiom,
% 160.59/160.55 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_subset__image__iff,axiom,
% 160.59/160.55 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] :
% 160.59/160.55 ( 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)))
% 160.59/160.55 <=> ? [B_AA] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2))
% 160.59/160.55 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Un__mono,axiom,
% 160.59/160.55 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Un__least,axiom,
% 160.59/160.55 ! [V_B_2,V_C_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 160.59/160.55 => 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)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Un__absorb2,axiom,
% 160.59/160.55 ! [V_A_2,V_B_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Un__absorb1,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_subset__Un__eq,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Un__upper2,axiom,
% 160.59/160.55 ! [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))) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Un__upper1,axiom,
% 160.59/160.55 ! [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))) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Int__mono,axiom,
% 160.59/160.55 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Int__greatest,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,V_C_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2))
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Int__absorb1,axiom,
% 160.59/160.55 ! [V_A_2,V_B_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Int__absorb2,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Int__lower2,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Int__lower1,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_double__diff,axiom,
% 160.59/160.55 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 160.59/160.55 => 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 ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Diff__mono,axiom,
% 160.59/160.55 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2))
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Diff__subset,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Sup__le__iff,axiom,
% 160.59/160.55 ! [V_b_2,V_A_2,T_a] :
% 160.59/160.55 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.55 => ( 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))
% 160.59/160.55 <=> ! [B_x] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_less__fun__def,axiom,
% 160.59/160.55 ! [V_g_2,V_f_2,T_a,T_b] :
% 160.59/160.55 ( class_Orderings_Oord(T_b)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 160.59/160.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 160.59/160.55 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setprod__timesf,axiom,
% 160.59/160.55 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] :
% 160.59/160.55 ( class_Groups_Ocomm__monoid__mult(T_a)
% 160.59/160.55 => 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)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_thin,axiom,
% 160.59/160.55 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] :
% 160.59/160.55 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2)
% 160.59/160.55 => ( 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_Ga_2))
% 160.59/160.55 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_weaken,axiom,
% 160.59/160.55 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_a] :
% 160.59/160.55 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_H_2)
% 160.59/160.55 => ( 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))
% 160.59/160.55 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_asm,axiom,
% 160.59/160.55 ! [V_Ga_2,V_ts_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_Ga_2))
% 160.59/160.55 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setprod__1,axiom,
% 160.59/160.55 ! [V_A_2,T_b,T_a] :
% 160.59/160.55 ( class_Groups_Ocomm__monoid__mult(T_a)
% 160.59/160.55 => 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) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastLessThan__eq__iff,axiom,
% 160.59/160.55 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2))
% 160.59/160.55 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)
% 160.59/160.55 <=> ( V_a_2 = V_c_2
% 160.59/160.55 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 160.59/160.55 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2))
% 160.59/160.55 => V_a_2 = V_c_2 ) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 160.59/160.55 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Orderings_Olinorder(T_a)
% 160.59/160.55 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2))
% 160.59/160.55 => V_b_2 = V_d_2 ) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_subset__psubset__trans,axiom,
% 160.59/160.55 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_psubset__subset__trans,axiom,
% 160.59/160.55 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_psubset__imp__subset,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_subset__iff__psubset__eq,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 | V_A_2 = V_B_2 ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_psubset__eq,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 & V_A_2 != V_B_2 ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_pred__subset__eq,axiom,
% 160.59/160.55 ! [V_S_2,V_R_2,T_a] :
% 160.59/160.55 ( 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)))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_SUP__le__iff,axiom,
% 160.59/160.55 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] :
% 160.59/160.55 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.55 => ( 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))
% 160.59/160.55 <=> ! [B_x] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 160.59/160.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_UN__subset__iff,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] :
% 160.59/160.55 ( 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))
% 160.59/160.55 <=> ! [B_x] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 160.59/160.55 => 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)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setprod__zero,axiom,
% 160.59/160.55 ! [V_f_2,V_A_2,T_a,T_b] :
% 160.59/160.55 ( class_Rings_Ocomm__semiring__1(T_b)
% 160.59/160.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.55 => ( ? [B_x] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.55 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 160.59/160.55 => 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) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setprod__zero__iff,axiom,
% 160.59/160.55 ! [V_f_2,V_A_2,T_a,T_b] :
% 160.59/160.55 ( ( class_Rings_Ocomm__semiring__1(T_b)
% 160.59/160.55 & class_Rings_Ono__zero__divisors(T_b) )
% 160.59/160.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.55 => ( 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)
% 160.59/160.55 <=> ? [B_x] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.55 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_UN__le__eq__Un0,axiom,
% 160.59/160.55 ! [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))) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setprod_Oempty,axiom,
% 160.59/160.55 ! [V_g_2,T_b,T_a] :
% 160.59/160.55 ( class_Groups_Ocomm__monoid__mult(T_a)
% 160.59/160.55 => 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) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setprod__empty,axiom,
% 160.59/160.55 ! [V_f_2,T_b,T_a] :
% 160.59/160.55 ( class_Groups_Ocomm__monoid__mult(T_a)
% 160.59/160.55 => 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) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setprod_Oinfinite,axiom,
% 160.59/160.55 ! [V_g_2,V_A_2,T_a,T_b] :
% 160.59/160.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.55 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.55 => 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) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setprod__infinite,axiom,
% 160.59/160.55 ! [V_f_2,V_A_2,T_a,T_b] :
% 160.59/160.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.55 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.55 => 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) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setprod__eq__1__iff,axiom,
% 160.59/160.55 ! [V_f_2,V_F_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 160.59/160.55 => ( 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)
% 160.59/160.55 <=> ! [B_x] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2))
% 160.59/160.55 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 160.59/160.55 ! [V_a_2,T_a] :
% 160.59/160.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 160.59/160.55 => ( 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)))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 160.59/160.55 ! [V_a_2,T_a] :
% 160.59/160.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 160.59/160.55 => ( 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)))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_add__nonneg__nonneg,axiom,
% 160.59/160.55 ! [V_b,V_a,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_add__nonneg__eq__0__iff,axiom,
% 160.59/160.55 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2))
% 160.59/160.55 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.55 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.55 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_add__increasing,axiom,
% 160.59/160.55 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_add__increasing2,axiom,
% 160.59/160.55 ! [V_a,V_b,V_c,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_add__nonpos__nonpos,axiom,
% 160.59/160.55 ! [V_b,V_a,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zero__le__square,axiom,
% 160.59/160.55 ! [V_a,T_a] :
% 160.59/160.55 ( class_Rings_Olinordered__ring(T_a)
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zero__le__mult__iff,axiom,
% 160.59/160.55 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Rings_Olinordered__ring__strict(T_a)
% 160.59/160.55 => ( 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)))
% 160.59/160.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 160.59/160.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_mult__le__0__iff,axiom,
% 160.59/160.55 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Rings_Olinordered__ring__strict(T_a)
% 160.59/160.55 => ( 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)))
% 160.59/160.55 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 160.59/160.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_mult__nonneg__nonneg,axiom,
% 160.59/160.55 ! [V_b,V_a,T_a] :
% 160.59/160.55 ( class_Rings_Oordered__cancel__semiring(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_mult__nonneg__nonpos,axiom,
% 160.59/160.55 ! [V_b,V_a,T_a] :
% 160.59/160.55 ( class_Rings_Oordered__cancel__semiring(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_mult__nonneg__nonpos2,axiom,
% 160.59/160.55 ! [V_b,V_a,T_a] :
% 160.59/160.55 ( class_Rings_Oordered__cancel__semiring(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_mult__nonpos__nonneg,axiom,
% 160.59/160.55 ! [V_b,V_a,T_a] :
% 160.59/160.55 ( class_Rings_Oordered__cancel__semiring(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_mult__nonpos__nonpos,axiom,
% 160.59/160.55 ! [V_b,V_a,T_a] :
% 160.59/160.55 ( class_Rings_Oordered__ring(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_mult__right__mono,axiom,
% 160.59/160.55 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.55 ( class_Rings_Oordered__semiring(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_mult__left__mono,axiom,
% 160.59/160.55 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.55 ( class_Rings_Oordered__semiring(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_comm__mult__left__mono,axiom,
% 160.59/160.55 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.55 ( class_Rings_Oordered__comm__semiring(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_mult__right__mono__neg,axiom,
% 160.59/160.55 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.55 ( class_Rings_Oordered__ring(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_mult__left__mono__neg,axiom,
% 160.59/160.55 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.55 ( class_Rings_Oordered__ring(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_mult__mono_H,axiom,
% 160.59/160.55 ! [V_d,V_c,V_b,V_a,T_a] :
% 160.59/160.55 ( class_Rings_Oordered__semiring(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.55 => 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))) ) ) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_mult__mono,axiom,
% 160.59/160.55 ! [V_d,V_c,V_b,V_a,T_a] :
% 160.59/160.55 ( class_Rings_Oordered__semiring(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.55 => 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))) ) ) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_split__mult__pos__le,axiom,
% 160.59/160.55 ! [V_b,V_a,T_a] :
% 160.59/160.55 ( class_Rings_Oordered__ring(T_a)
% 160.59/160.55 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 160.59/160.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_split__mult__neg__le,axiom,
% 160.59/160.55 ! [V_b,V_a,T_a] :
% 160.59/160.55 ( class_Rings_Oordered__cancel__semiring(T_a)
% 160.59/160.55 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 160.59/160.55 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_add__le__less__mono,axiom,
% 160.59/160.55 ! [V_d,V_c,V_b,V_a,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_add__less__le__mono,axiom,
% 160.59/160.55 ! [V_d,V_c,V_b,V_a,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__iff__diff__le__0,axiom,
% 160.59/160.55 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 160.59/160.55 <=> 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_not__one__le__zero,axiom,
% 160.59/160.55 ! [T_a] :
% 160.59/160.55 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.55 => ~ 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zero__le__one,axiom,
% 160.59/160.55 ! [T_a] :
% 160.59/160.55 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_subset__insert,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 160.59/160.55 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.55 => ( 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)))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_insert__subset,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 160.59/160.55 ( 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))
% 160.59/160.55 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 160.59/160.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setprod_Odistrib,axiom,
% 160.59/160.55 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 160.59/160.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.55 => 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)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_zero__le__imp__of__nat,axiom,
% 160.59/160.55 ! [V_m,T_a] :
% 160.59/160.55 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_of__nat__0__le__iff,axiom,
% 160.59/160.55 ! [V_n,T_a] :
% 160.59/160.55 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_distrib__sup__le,axiom,
% 160.59/160.55 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.55 ( class_Lattices_Olattice(T_a)
% 160.59/160.55 => 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)))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_distrib__inf__le,axiom,
% 160.59/160.55 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.55 ( class_Lattices_Olattice(T_a)
% 160.59/160.55 => 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)))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_subset__singletonD,axiom,
% 160.59/160.55 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.55 ( 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)))))
% 160.59/160.55 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.55 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastLessThan0,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_finite__surj,axiom,
% 160.59/160.55 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.55 => ( 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)))
% 160.59/160.55 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeast0LessThan,axiom,
% 160.59/160.55 ! [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) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_image__Int__subset,axiom,
% 160.59/160.55 ! [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)))) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Sup__upper,axiom,
% 160.59/160.55 ! [V_A_2,V_x_2,T_a] :
% 160.59/160.55 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Un__Int__assoc__eq,axiom,
% 160.59/160.55 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( 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))
% 160.59/160.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_image__diff__subset,axiom,
% 160.59/160.55 ! [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)))) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Diff__subset__conv,axiom,
% 160.59/160.55 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( 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))
% 160.59/160.55 <=> 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Diff__partition,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.55 => 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 ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_card__atLeastLessThan,axiom,
% 160.59/160.55 ! [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) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Union__Int__subset,axiom,
% 160.59/160.55 ! [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)))) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_Union__upper,axiom,
% 160.59/160.55 ! [V_A_2,V_B_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastatMost__empty,axiom,
% 160.59/160.55 ! [V_a_2,V_b_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2))
% 160.59/160.55 => 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)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_image__Suc__atLeastLessThan,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastAtMost__singleton,axiom,
% 160.59/160.55 ! [V_a_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 160.59/160.55 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.55 <=> ( V_a_2 = V_b_2
% 160.59/160.55 & V_b_2 = V_c_2 ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastAtMost__singleton_H,axiom,
% 160.59/160.55 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( V_a_2 = V_b_2
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastLessThan__empty__iff,axiom,
% 160.59/160.55 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( 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))
% 160.59/160.55 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 160.59/160.55 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => ( 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)
% 160.59/160.55 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 160.59/160.55 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 160.59/160.55 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.55 => 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)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 160.59/160.55 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] :
% 160.59/160.55 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.55 => 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)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_ivl__disj__int_I11_J,axiom,
% 160.59/160.55 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.55 ( class_Orderings_Oorder(T_a)
% 160.59/160.55 => 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)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_le__SUPI,axiom,
% 160.59/160.55 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
% 160.59/160.55 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
% 160.59/160.55 => 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))) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_image__Suc__atLeastAtMost,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_UN__upper,axiom,
% 160.59/160.55 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.55 => 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))) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 160.59/160.55 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 160.59/160.55 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.55 => 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)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 160.59/160.55 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] :
% 160.59/160.55 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.55 => 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)) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setprod__pos__nat__iff,axiom,
% 160.59/160.55 ! [V_f_2,V_S_2,T_a] :
% 160.59/160.55 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.55 => ( 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)))
% 160.59/160.55 <=> ! [B_x] :
% 160.59/160.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 160.59/160.55 => 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))) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 160.59/160.55 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.55 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2)
% 160.59/160.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.55 => 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) ) ) ) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_image__add__atLeastLessThan,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_lessThan__Suc__atMost,axiom,
% 160.59/160.55 ! [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) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_card__atMost,axiom,
% 160.59/160.55 ! [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) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_image__add__atLeastAtMost,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_atMost__Suc,axiom,
% 160.59/160.55 ! [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)) ).
% 160.59/160.55
% 160.59/160.55 fof(fact_setprod__delta_H,axiom,
% 160.59/160.55 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 160.59/160.55 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 160.59/160.56 => 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) )
% 160.59/160.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 160.59/160.56 => 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) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setprod__delta,axiom,
% 160.59/160.56 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 160.59/160.56 => 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) )
% 160.59/160.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 160.59/160.56 => 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) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_add__pos__nonneg,axiom,
% 160.59/160.56 ! [V_b,V_a,T_a] :
% 160.59/160.56 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 160.59/160.56 => 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))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_add__nonneg__pos,axiom,
% 160.59/160.56 ! [V_b,V_a,T_a] :
% 160.59/160.56 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 160.59/160.56 => 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))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_add__strict__increasing,axiom,
% 160.59/160.56 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.56 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 160.59/160.56 => 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))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_add__strict__increasing2,axiom,
% 160.59/160.56 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.56 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 160.59/160.56 => 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))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_add__neg__nonpos,axiom,
% 160.59/160.56 ! [V_b,V_a,T_a] :
% 160.59/160.56 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.56 => 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))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_add__nonpos__neg,axiom,
% 160.59/160.56 ! [V_b,V_a,T_a] :
% 160.59/160.56 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.56 => 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))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__le__cancel__left__pos,axiom,
% 160.59/160.56 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__le__cancel__left__neg,axiom,
% 160.59/160.56 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__strict__mono,axiom,
% 160.59/160.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.56 => 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))) ) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__strict__mono_H,axiom,
% 160.59/160.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.56 => 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))) ) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__less__le__imp__less,axiom,
% 160.59/160.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.56 => 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))) ) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__le__less__imp__less,axiom,
% 160.59/160.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.56 => 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))) ) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__right__less__imp__less,axiom,
% 160.59/160.56 ! [V_b,V_c,V_a,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semiring(T_a)
% 160.59/160.56 => ( 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)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__less__imp__less__right,axiom,
% 160.59/160.56 ! [V_b,V_c,V_a,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.56 => ( 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)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__left__less__imp__less,axiom,
% 160.59/160.56 ! [V_b,V_a,V_c,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semiring(T_a)
% 160.59/160.56 => ( 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)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__less__imp__less__left,axiom,
% 160.59/160.56 ! [V_b,V_a,V_c,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.56 => ( 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)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__right__le__imp__le,axiom,
% 160.59/160.56 ! [V_b,V_c,V_a,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.56 => ( 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)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__left__le__imp__le,axiom,
% 160.59/160.56 ! [V_b,V_a,V_c,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 160.59/160.56 => ( 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)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_sum__squares__le__zero__iff,axiom,
% 160.59/160.56 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 160.59/160.56 => ( 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)))
% 160.59/160.56 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.56 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_sum__squares__ge__zero,axiom,
% 160.59/160.56 ! [V_y,V_x,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__ring(T_a)
% 160.59/160.56 => 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)))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__right__le__one__le,axiom,
% 160.59/160.56 ! [V_y,V_x,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 160.59/160.56 => 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)) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__left__le__one__le,axiom,
% 160.59/160.56 ! [V_y,V_x,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 160.59/160.56 => 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)) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__add__iff1,axiom,
% 160.59/160.56 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 160.59/160.56 ( class_Rings_Oordered__ring(T_a)
% 160.59/160.56 => ( 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_c_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)))
% 160.59/160.56 <=> 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_c_2)),V_d_2)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__add__iff2,axiom,
% 160.59/160.56 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 160.59/160.56 ( class_Rings_Oordered__ring(T_a)
% 160.59/160.56 => ( 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_c_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)))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 160.59/160.56 ! [V_i_2,V_inc_2,T_a] :
% 160.59/160.56 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.56 => 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 ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 160.59/160.56 ! [V_i_2,V_n_2,V_inc_2,T_a] :
% 160.59/160.56 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_card__atLeastAtMost,axiom,
% 160.59/160.56 ! [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) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_atLeastLessThan__singleton,axiom,
% 160.59/160.56 ! [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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setprod__insert,axiom,
% 160.59/160.56 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.56 => 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)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setprod_Oinsert,axiom,
% 160.59/160.56 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.56 => 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)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 160.59/160.56 ! [V_k_2,V_f_2] :
% 160.59/160.56 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setprod__Un__Int,axiom,
% 160.59/160.56 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.56 => 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)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setprod_Ounion__inter,axiom,
% 160.59/160.56 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.56 => 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)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 160.59/160.56 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] :
% 160.59/160.56 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.56 => 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) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setprod_OF__eq,axiom,
% 160.59/160.56 ! [V_g_2,V_A_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.56 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => 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) )
% 160.59/160.56 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => 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) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setprod_Oeq__fold,axiom,
% 160.59/160.56 ! [V_g_2,V_A_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => 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) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 160.59/160.56 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.56 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.56 => 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) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__int_I4_J,axiom,
% 160.59/160.56 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Oorder(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__int_I2_J,axiom,
% 160.59/160.56 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Oorder(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 160.59/160.56 ! [V_k_2,V_f_2,T_a] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.56 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.56 => 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)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__head__upt__Suc,axiom,
% 160.59/160.56 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 => 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_convex__bound__le,axiom,
% 160.59/160.56 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semiring__1(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 160.59/160.56 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 160.59/160.56 => 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)) ) ) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_diff__single__insert,axiom,
% 160.59/160.56 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 160.59/160.56 ( 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))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.56 => 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_subset__insert__iff,axiom,
% 160.59/160.56 ! [V_B_2,V_x_2,V_A_2,T_a] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.56 => 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)) )
% 160.59/160.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_sup__le__fold__sup,axiom,
% 160.59/160.56 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 160.59/160.56 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.56 => 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))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_fold__inf__le__inf,axiom,
% 160.59/160.56 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 160.59/160.56 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.56 => 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))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__diff,axiom,
% 160.59/160.56 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Oab__group__add(T_b)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.56 => 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)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_fold1__belowI,axiom,
% 160.59/160.56 ! [V_a_2,V_A_2,T_a] :
% 160.59/160.56 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.56 => 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)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_below__fold1__iff,axiom,
% 160.59/160.56 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.56 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.56 => ( 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)))
% 160.59/160.56 <=> ! [B_x] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_card__Diff__subset,axiom,
% 160.59/160.56 ! [V_A_2,V_B_2,T_a] :
% 160.59/160.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.56 => 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)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Sup__fin_Osubset__idem,axiom,
% 160.59/160.56 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.56 ( class_Lattices_Olattice(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.56 => 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) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Inf__fin_Osubset__idem,axiom,
% 160.59/160.56 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.56 ( class_Lattices_Olattice(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.56 => 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) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__atMost__Suc,axiom,
% 160.59/160.56 ! [V_n_2,V_f_2,T_a] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_atMost__0,axiom,
% 160.59/160.56 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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_card__psubset,axiom,
% 160.59/160.56 ! [V_A_2,V_B_2,T_a] :
% 160.59/160.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.56 => ( 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)))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setprod_Oinsert__remove,axiom,
% 160.59/160.56 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => 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)))))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setprod_Ounion__disjoint,axiom,
% 160.59/160.56 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.56 => ( 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))
% 160.59/160.56 => 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)) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setprod__Un__disjoint,axiom,
% 160.59/160.56 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.56 => ( 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))
% 160.59/160.56 => 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)) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__diff__nat,axiom,
% 160.59/160.56 ! [V_f_2,V_A_2,V_B_2,T_a] :
% 160.59/160.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.56 => 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)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Inf__le__Sup,axiom,
% 160.59/160.56 ! [V_A_2,T_a] :
% 160.59/160.56 ( class_Lattices_Olattice(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.56 => 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))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__op__ivl__Suc,axiom,
% 160.59/160.56 ! [V_f_2,V_m_2,V_n_2,T_a] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 160.59/160.56 => 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) )
% 160.59/160.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 160.59/160.56 => 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)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_convex__bound__lt,axiom,
% 160.59/160.56 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 160.59/160.56 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 160.59/160.56 => 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)) ) ) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__cl__ivl__Suc,axiom,
% 160.59/160.56 ! [V_f_2,V_m_2,V_n_2,T_a] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 160.59/160.56 => 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) )
% 160.59/160.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 160.59/160.56 => 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))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 160.59/160.56 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)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 160.59/160.56 ! [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)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ex__nat__less__eq,axiom,
% 160.59/160.56 ! [V_P_2,V_n_2] :
% 160.59/160.56 ( ? [B_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 160.59/160.56 & hBOOL(hAPP(V_P_2,B_m)) )
% 160.59/160.56 <=> ? [B_x] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_all__nat__less__eq,axiom,
% 160.59/160.56 ! [V_P_2,V_n_2] :
% 160.59/160.56 ( ! [B_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 160.59/160.56 => hBOOL(hAPP(V_P_2,B_m)) )
% 160.59/160.56 <=> ! [B_x] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 160.59/160.56 ! [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)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 160.59/160.56 ! [V_y_2,V_x_2] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 160.59/160.56 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)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__mono2,axiom,
% 160.59/160.56 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.56 => ( ! [B_b] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) )
% 160.59/160.56 => 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))) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le0,axiom,
% 160.59/160.56 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zle__int,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 160.59/160.56 ! [V_y_2,V_x_2] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 160.59/160.56 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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__antisym,axiom,
% 160.59/160.56 ! [V_n,V_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 160.59/160.56 => V_m = V_n ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__trans,axiom,
% 160.59/160.56 ! [V_k,V_j,V_i] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_eq__imp__le,axiom,
% 160.59/160.56 ! [V_n,V_m] :
% 160.59/160.56 ( V_m = V_n
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_nat__le__linear,axiom,
% 160.59/160.56 ! [V_n,V_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 160.59/160.56 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__refl,axiom,
% 160.59/160.56 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 160.59/160.56 ! [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) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__0__eq,axiom,
% 160.59/160.56 ! [V_n_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 160.59/160.56 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 160.59/160.56 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Suc__leD,axiom,
% 160.59/160.56 ! [V_n,V_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__SucE,axiom,
% 160.59/160.56 ! [V_n,V_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 160.59/160.56 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 160.59/160.56 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__SucI,axiom,
% 160.59/160.56 ! [V_n,V_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Suc__le__mono,axiom,
% 160.59/160.56 ! [V_m_2,V_n_2] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__Suc__eq,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 160.59/160.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_not__less__eq__eq,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2] :
% 160.59/160.56 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Suc__n__not__le__n,axiom,
% 160.59/160.56 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_termination__basic__simps_I5_J,axiom,
% 160.59/160.56 ! [V_y,V_x] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_nat__less__le,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 & V_m_2 != V_n_2 ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__eq__less__or__eq,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 | V_m_2 = V_n_2 ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_less__imp__le__nat,axiom,
% 160.59/160.56 ! [V_n,V_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__neq__implies__less,axiom,
% 160.59/160.56 ! [V_n,V_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 160.59/160.56 => ( V_m != V_n
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_less__or__eq__imp__le,axiom,
% 160.59/160.56 ! [V_n,V_m] :
% 160.59/160.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.56 | V_m = V_n )
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_termination__basic__simps_I3_J,axiom,
% 160.59/160.56 ! [V_z,V_y,V_x] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_termination__basic__simps_I4_J,axiom,
% 160.59/160.56 ! [V_y,V_z,V_x] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__add2,axiom,
% 160.59/160.56 ! [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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__add1,axiom,
% 160.59/160.56 ! [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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__iff__add,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_nat__add__left__cancel__le,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_trans__le__add1,axiom,
% 160.59/160.56 ! [V_m,V_j,V_i] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_trans__le__add2,axiom,
% 160.59/160.56 ! [V_m,V_j,V_i] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_add__le__mono1,axiom,
% 160.59/160.56 ! [V_k,V_j,V_i] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_add__le__mono,axiom,
% 160.59/160.56 ! [V_l,V_k,V_j,V_i] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 160.59/160.56 => 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_add__leD2,axiom,
% 160.59/160.56 ! [V_n,V_k,V_m] :
% 160.59/160.56 ( 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))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_add__leD1,axiom,
% 160.59/160.56 ! [V_n,V_k,V_m] :
% 160.59/160.56 ( 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))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_add__leE,axiom,
% 160.59/160.56 ! [V_n,V_k,V_m] :
% 160.59/160.56 ( 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))
% 160.59/160.56 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 160.59/160.56 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zless__le,axiom,
% 160.59/160.56 ! [V_w_2,V_z_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 160.59/160.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 160.59/160.56 & V_z_2 != V_w_2 ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zadd__left__mono,axiom,
% 160.59/160.56 ! [V_k,V_j,V_i] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_diff__le__self,axiom,
% 160.59/160.56 ! [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)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_diff__le__mono2,axiom,
% 160.59/160.56 ! [V_l,V_n,V_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_diff__le__mono,axiom,
% 160.59/160.56 ! [V_l,V_n,V_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_diff__diff__cancel,axiom,
% 160.59/160.56 ! [V_n,V_i] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 160.59/160.56 => 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 ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_eq__diff__iff,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 160.59/160.56 => ( 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)
% 160.59/160.56 <=> V_m_2 = V_n_2 ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Nat_Odiff__diff__eq,axiom,
% 160.59/160.56 ! [V_n,V_m,V_k] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 160.59/160.56 => 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) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__diff__iff,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 160.59/160.56 => ( 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)))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__le__mono,axiom,
% 160.59/160.56 ! [V_l,V_k,V_j,V_i] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 160.59/160.56 => 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__le__mono2,axiom,
% 160.59/160.56 ! [V_k,V_j,V_i] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__le__mono1,axiom,
% 160.59/160.56 ! [V_k,V_j,V_i] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__cube,axiom,
% 160.59/160.56 ! [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)))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__square,axiom,
% 160.59/160.56 ! [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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 160.59/160.56 ! [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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_evaln__nonstrict,axiom,
% 160.59/160.56 ! [V_m,V_t,V_n,V_s,V_c] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 160.59/160.56 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_m),V_t)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 160.59/160.56 ! [V_y,V_x] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 160.59/160.56 => 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 160.59/160.56 ! [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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 160.59/160.56 ! [V_P_2] :
% 160.59/160.56 ( ? [B_x] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 160.59/160.56 & hBOOL(hAPP(V_P_2,B_x)) )
% 160.59/160.56 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 160.59/160.56 ! [V_P_2] :
% 160.59/160.56 ( ! [B_x] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 160.59/160.56 => hBOOL(hAPP(V_P_2,B_x)) )
% 160.59/160.56 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 160.59/160.56 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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 160.59/160.56 ! [V_y,V_x] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 160.59/160.56 => 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 160.59/160.56 ! [V_N_2] :
% 160.59/160.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 160.59/160.56 <=> ? [B_m] :
% 160.59/160.56 ! [B_x] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_all__nat__less,axiom,
% 160.59/160.56 ! [V_P_2,V_n_2] :
% 160.59/160.56 ( ! [B_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 160.59/160.56 => hBOOL(hAPP(V_P_2,B_m)) )
% 160.59/160.56 <=> ! [B_x] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ex__nat__less,axiom,
% 160.59/160.56 ! [V_P_2,V_n_2] :
% 160.59/160.56 ( ? [B_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 160.59/160.56 & hBOOL(hAPP(V_P_2,B_m)) )
% 160.59/160.56 <=> ? [B_x] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 160.59/160.56 <=> 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Suc__le__lessD,axiom,
% 160.59/160.56 ! [V_n,V_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__less__Suc__eq,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 160.59/160.56 <=> V_n_2 = V_m_2 ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Suc__leI,axiom,
% 160.59/160.56 ! [V_n,V_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__imp__less__Suc,axiom,
% 160.59/160.56 ! [V_n,V_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Suc__le__eq,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_less__Suc__eq__le,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_less__eq__Suc__le,axiom,
% 160.59/160.56 ! [V_m_2,V_n_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_diff__is__0__eq,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2] :
% 160.59/160.56 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_diff__is__0__eq_H,axiom,
% 160.59/160.56 ! [V_n,V_m] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 160.59/160.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Suc__diff__le,axiom,
% 160.59/160.56 ! [V_m,V_n] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Suc__mult__le__cancel1,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_less__diff__iff,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 160.59/160.56 => ( 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)))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_diff__less__mono,axiom,
% 160.59/160.56 ! [V_c,V_b,V_a] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 160.59/160.56 => 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zero__zle__int,axiom,
% 160.59/160.56 ! [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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zadd__zless__mono,axiom,
% 160.59/160.56 ! [V_z,V_z_H,V_w,V_w_H] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 160.59/160.56 => 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_diff__add__assoc2,axiom,
% 160.59/160.56 ! [V_i,V_j,V_k] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 160.59/160.56 => 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) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_add__diff__assoc2,axiom,
% 160.59/160.56 ! [V_i,V_j,V_k] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 160.59/160.56 => 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) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_diff__add__assoc,axiom,
% 160.59/160.56 ! [V_i,V_j,V_k] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__imp__diff__is__add,axiom,
% 160.59/160.56 ! [V_k_2,V_j_2,V_i_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 160.59/160.56 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 160.59/160.56 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__add__diff__inverse2,axiom,
% 160.59/160.56 ! [V_m,V_n] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 160.59/160.56 => 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 ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__diff__conv2,axiom,
% 160.59/160.56 ! [V_i_2,V_j_2,V_k_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 160.59/160.56 => ( 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)))
% 160.59/160.56 <=> 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)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_add__diff__assoc,axiom,
% 160.59/160.56 ! [V_i,V_j,V_k] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 160.59/160.56 => 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) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__add__diff__inverse,axiom,
% 160.59/160.56 ! [V_m,V_n] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 160.59/160.56 => 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 ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__add__diff,axiom,
% 160.59/160.56 ! [V_m,V_n,V_k] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__diff__conv,axiom,
% 160.59/160.56 ! [V_i_2,V_k_2,V_j_2] :
% 160.59/160.56 ( 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))
% 160.59/160.56 <=> 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_diff__diff__right,axiom,
% 160.59/160.56 ! [V_i,V_j,V_k] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 160.59/160.56 => 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) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zle__diff1__eq,axiom,
% 160.59/160.56 ! [V_z_2,V_w_2] :
% 160.59/160.56 ( 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))))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zle__iff__zadd,axiom,
% 160.59/160.56 ! [V_z_2,V_w_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 160.59/160.56 <=> ? [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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zdiff__int,axiom,
% 160.59/160.56 ! [V_m,V_n] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_atLeastLessThan__add__Un,axiom,
% 160.59/160.56 ! [V_k_2,V_j_2,V_i_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_less__eq__Suc__le__raw,axiom,
% 160.59/160.56 ! [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)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_image__add__int__atLeastLessThan,axiom,
% 160.59/160.56 ! [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) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_card__insert__le,axiom,
% 160.59/160.56 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => 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)))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_one__le__mult__iff,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 <=> ( 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))
% 160.59/160.56 & 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)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_nat__mult__le__cancel1,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 160.59/160.56 => ( 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)))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__le__cancel1,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2,V_k_2] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_mult__le__cancel2,axiom,
% 160.59/160.56 ! [V_n_2,V_k_2,V_m_2] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_card__mono,axiom,
% 160.59/160.56 ! [V_A_2,V_B_2,T_a] :
% 160.59/160.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.56 => 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_card__seteq,axiom,
% 160.59/160.56 ! [V_A_2,V_B_2,T_a] :
% 160.59/160.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.56 => ( 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)))
% 160.59/160.56 => V_A_2 = V_B_2 ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_int__le__0__conv,axiom,
% 160.59/160.56 ! [V_n_2] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_card__image__le,axiom,
% 160.59/160.56 ! [V_f_2,T_b,V_A_2,T_a] :
% 160.59/160.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_diff__Suc__diff__eq2,axiom,
% 160.59/160.56 ! [V_m,V_j,V_k] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_diff__Suc__diff__eq1,axiom,
% 160.59/160.56 ! [V_m,V_j,V_k] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_of__nat__diff,axiom,
% 160.59/160.56 ! [V_m,V_n,T_a] :
% 160.59/160.56 ( class_Rings_Oring__1(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 160.59/160.56 => 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)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_int__one__le__iff__zero__less,axiom,
% 160.59/160.56 ! [V_z_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_nat__eq__add__iff2,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 160.59/160.56 => ( 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)
% 160.59/160.56 <=> 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) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_nat__diff__add__eq2,axiom,
% 160.59/160.56 ! [V_n,V_m,V_u,V_j,V_i] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_nat__le__add__iff2,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 160.59/160.56 => ( 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)))
% 160.59/160.56 <=> 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_nat__eq__add__iff1,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 160.59/160.56 => ( 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)
% 160.59/160.56 <=> 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 ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_nat__diff__add__eq1,axiom,
% 160.59/160.56 ! [V_n,V_m,V_u,V_i,V_j] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 160.59/160.56 => 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) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_nat__le__add__iff1,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 160.59/160.56 => ( 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)))
% 160.59/160.56 <=> 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)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zle__add1__eq__le,axiom,
% 160.59/160.56 ! [V_z_2,V_w_2] :
% 160.59/160.56 ( 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))))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_add1__zle__eq,axiom,
% 160.59/160.56 ! [V_z_2,V_w_2] :
% 160.59/160.56 ( 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))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zless__imp__add1__zle,axiom,
% 160.59/160.56 ! [V_z,V_w] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__add__nat__ivl,axiom,
% 160.59/160.56 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 160.59/160.56 => 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)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__diff__nat__ivl,axiom,
% 160.59/160.56 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
% 160.59/160.56 ( class_Groups_Oab__group__add(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 160.59/160.56 => 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)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 160.59/160.56 ! [V_B_2,V_A_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.56 <=> 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 160.59/160.56 ! [V_B_2,V_A_2] :
% 160.59/160.56 ( V_A_2 = V_B_2
% 160.59/160.56 <=> 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) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 160.59/160.56 ! [V_A_2,V_x_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 160.59/160.56 <=> 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 160.59/160.56 ! [V_B_2,V_A_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.56 <=> 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 160.59/160.56 ! [V_y_2,V_x_2] :
% 160.59/160.56 ( 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)
% 160.59/160.56 <=> V_x_2 = V_y_2 ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_atLeastAtMostSuc__conv,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_nat__less__add__iff2,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 160.59/160.56 => ( 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)))
% 160.59/160.56 <=> 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_nat__less__add__iff1,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 160.59/160.56 => ( 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)))
% 160.59/160.56 <=> 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)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_le__imp__0__less,axiom,
% 160.59/160.56 ! [V_z] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_diff__card__le__card__Diff,axiom,
% 160.59/160.56 ! [V_A_2,V_B_2,T_a] :
% 160.59/160.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.56 => 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)))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__head__Suc,axiom,
% 160.59/160.56 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 => 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_atLeastLessThanSuc,axiom,
% 160.59/160.56 ! [V_n_2,V_m_2] :
% 160.59/160.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 => 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)) )
% 160.59/160.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 => 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)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_card__Diff1__le,axiom,
% 160.59/160.56 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__ub__add__nat,axiom,
% 160.59/160.56 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.56 => ( 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))))
% 160.59/160.56 => 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)))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__natinterval__difff,axiom,
% 160.59/160.56 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 160.59/160.56 ( class_Groups_Oab__group__add(T_a)
% 160.59/160.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 => 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)))) )
% 160.59/160.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 => 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) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 160.59/160.56 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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 160.59/160.56 ! [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)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 160.59/160.56 ! [V_A_2] :
% 160.59/160.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 160.59/160.56 <=> 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zdiff__int__split,axiom,
% 160.59/160.56 ! [V_y_2,V_x_2,V_P_2] :
% 160.59/160.56 ( 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))))
% 160.59/160.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 160.59/160.56 => 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)))) )
% 160.59/160.56 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 160.59/160.56 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_self__quotient__aux2,axiom,
% 160.59/160.56 ! [V_q,V_r,V_a] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.56 => ( 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))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_self__quotient__aux1,axiom,
% 160.59/160.56 ! [V_q,V_r,V_a] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.56 => ( 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))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_q__pos__lemma,axiom,
% 160.59/160.56 ! [V_r_H,V_q_H,V_b_H] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_q__neg__lemma,axiom,
% 160.59/160.56 ! [V_r_H,V_q_H,V_b_H] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_unique__quotient__lemma,axiom,
% 160.59/160.56 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zdiv__mono2__lemma,axiom,
% 160.59/160.56 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 160.59/160.56 ( 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)
% 160.59/160.56 => ( 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)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_finite__atLeastAtMost__int,axiom,
% 160.59/160.56 ! [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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_finite__atLeastLessThan__int,axiom,
% 160.59/160.56 ! [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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zle__antisym,axiom,
% 160.59/160.56 ! [V_w,V_z] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 160.59/160.56 => V_z = V_w ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zle__trans,axiom,
% 160.59/160.56 ! [V_k,V_j,V_i] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zle__linear,axiom,
% 160.59/160.56 ! [V_w,V_z] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 160.59/160.56 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zle__refl,axiom,
% 160.59/160.56 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_simp__from__to,axiom,
% 160.59/160.56 ! [V_i_2,V_j_2] :
% 160.59/160.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 160.59/160.56 => 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)) )
% 160.59/160.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 160.59/160.56 => 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)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 160.59/160.56 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 160.59/160.56 ( 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)
% 160.59/160.56 => ( 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)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_unique__quotient__lemma__neg,axiom,
% 160.59/160.56 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_bset_I8_J,axiom,
% 160.59/160.56 ! [V_B_2,V_t_2,V_D_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 160.59/160.56 => ( 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))
% 160.59/160.56 => ! [B_x] :
% 160.59/160.56 ( ! [B_xa] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ! [B_xb] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 160.59/160.56 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 160.59/160.56 => 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))) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_aset_I6_J,axiom,
% 160.59/160.56 ! [V_A_2,V_t_2,V_D_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 160.59/160.56 => ( 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))
% 160.59/160.56 => ! [B_x] :
% 160.59/160.56 ( ! [B_xa] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ! [B_xb] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 160.59/160.56 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 160.59/160.56 => 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)) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_aset_I4_J,axiom,
% 160.59/160.56 ! [V_A_2,V_t_2,V_D_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 160.59/160.56 => ! [B_x] :
% 160.59/160.56 ( ! [B_xa] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ! [B_xb] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 160.59/160.56 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 160.59/160.56 => ( B_x != V_t_2
% 160.59/160.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_bset_I4_J,axiom,
% 160.59/160.56 ! [V_B_2,V_t_2,V_D_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 160.59/160.56 => ! [B_x] :
% 160.59/160.56 ( ! [B_xa] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ! [B_xb] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 160.59/160.56 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 160.59/160.56 => ( B_x != V_t_2
% 160.59/160.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_bset_I7_J,axiom,
% 160.59/160.56 ! [V_B_2,V_t_2,V_D_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 160.59/160.56 => ! [B_x] :
% 160.59/160.56 ( ! [B_xa] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ! [B_xb] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 160.59/160.56 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 160.59/160.56 => 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))) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_aset_I5_J,axiom,
% 160.59/160.56 ! [V_A_2,V_t_2,V_D_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 160.59/160.56 => ! [B_x] :
% 160.59/160.56 ( ! [B_xa] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ! [B_xb] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 160.59/160.56 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 160.59/160.56 => 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)) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_bset_I3_J,axiom,
% 160.59/160.56 ! [V_B_2,V_t_2,V_D_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 160.59/160.56 => ( 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))
% 160.59/160.56 => ( ! [B_x] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ! [B_xa] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 160.59/160.56 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 160.59/160.56 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_aset_I3_J,axiom,
% 160.59/160.56 ! [V_A_2,V_t_2,V_D_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 160.59/160.56 => ( 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))
% 160.59/160.56 => ( ! [B_x] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ! [B_xa] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 160.59/160.56 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 160.59/160.56 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_aset_I8_J,axiom,
% 160.59/160.56 ! [V_t_2,V_A_2,V_D_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 160.59/160.56 => ! [B_x] :
% 160.59/160.56 ( ! [B_xa] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ! [B_xb] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 160.59/160.56 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 160.59/160.56 => 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))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_bset_I6_J,axiom,
% 160.59/160.56 ! [V_t_2,V_B_2,V_D_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 160.59/160.56 => ! [B_x] :
% 160.59/160.56 ( ! [B_xa] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ! [B_xb] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 160.59/160.56 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 160.59/160.56 => 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)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_flat__lub__def,axiom,
% 160.59/160.56 ! [V_b_2,V_A_2,T_a] :
% 160.59/160.56 ( ( 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)))))
% 160.59/160.56 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 )
% 160.59/160.56 & ( ~ 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)))))
% 160.59/160.56 => 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)))))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_periodic__finite__ex,axiom,
% 160.59/160.56 ! [V_P_2,V_d_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 160.59/160.56 => ( ! [B_x,B_k] :
% 160.59/160.56 ( hBOOL(hAPP(V_P_2,B_x))
% 160.59/160.56 <=> 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)))) )
% 160.59/160.56 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 160.59/160.56 <=> ? [B_x] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_bset_I5_J,axiom,
% 160.59/160.56 ! [V_t_2,V_B_2,V_D_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 160.59/160.56 => ! [B_x] :
% 160.59/160.56 ( ! [B_xa] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ! [B_xb] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 160.59/160.56 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 160.59/160.56 => 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)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_aset_I7_J,axiom,
% 160.59/160.56 ! [V_t_2,V_A_2,V_D_2] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 160.59/160.56 => ! [B_x] :
% 160.59/160.56 ( ! [B_xa] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => ! [B_xb] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 160.59/160.56 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 160.59/160.56 => 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))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setprod__Un__one,axiom,
% 160.59/160.56 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 160.59/160.56 => ( ! [B_x] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 160.59/160.56 => 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)) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 160.59/160.56 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.56 => ( ! [B_x] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 160.59/160.56 => 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)) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__bounded,axiom,
% 160.59/160.56 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] :
% 160.59/160.56 ( ( class_Groups_Oordered__ab__semigroup__add(T_b)
% 160.59/160.56 & class_Rings_Osemiring__1(T_b) )
% 160.59/160.56 => ( ! [B_i] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) )
% 160.59/160.56 => 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__mono3,axiom,
% 160.59/160.56 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] :
% 160.59/160.56 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.56 & class_Groups_Oordered__ab__semigroup__add(T_b) )
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.56 => ( ! [B_x] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
% 160.59/160.56 => 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))) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setprod__gen__delta,axiom,
% 160.59/160.56 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 160.59/160.56 => 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_c_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_c_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)))) )
% 160.59/160.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2))
% 160.59/160.56 => 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_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_c_2),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_tsub__def,axiom,
% 160.59/160.56 ! [V_x,V_y] :
% 160.59/160.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 160.59/160.56 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 160.59/160.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 160.59/160.56 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__un_I18_J,axiom,
% 160.59/160.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Olinorder(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
% 160.59/160.56 => 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) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__un_I3_J,axiom,
% 160.59/160.56 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Olinorder(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 160.59/160.56 => 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) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__un_I5_J,axiom,
% 160.59/160.56 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Olinorder(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 160.59/160.56 => 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) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Powp__mono,axiom,
% 160.59/160.56 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_finite__greaterThanAtMost,axiom,
% 160.59/160.56 ! [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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_finite__greaterThanLessThan,axiom,
% 160.59/160.56 ! [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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_finite__greaterThanAtMost__int,axiom,
% 160.59/160.56 ! [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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_finite__greaterThanLessThan__int,axiom,
% 160.59/160.56 ! [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))) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 160.59/160.56 ! [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)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zpower__int,axiom,
% 160.59/160.56 ! [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)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_int__power,axiom,
% 160.59/160.56 ! [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) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 160.59/160.56 ! [V_q,V_y,V_x,T_a] :
% 160.59/160.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 160.59/160.56 ! [V_q,V_p,V_x,T_a] :
% 160.59/160.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zpower__zpower,axiom,
% 160.59/160.56 ! [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)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 160.59/160.56 ! [V_x,T_a] :
% 160.59/160.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.56 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__int_I10_J,axiom,
% 160.59/160.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Oorder(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__un_I16_J,axiom,
% 160.59/160.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Olinorder(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2))
% 160.59/160.56 => 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) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 160.59/160.56 ! [V_q,V_x,T_a] :
% 160.59/160.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 160.59/160.56 ! [V_q,V_x,T_a] :
% 160.59/160.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 160.59/160.56 ! [V_q,V_x,T_a] :
% 160.59/160.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 160.59/160.56 ! [V_x,T_a] :
% 160.59/160.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.56 => 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) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 160.59/160.56 ! [V_q,V_p,V_x,T_a] :
% 160.59/160.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 160.59/160.56 ! [V_n,V_x] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.56 => 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))) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zpower__zadd__distrib,axiom,
% 160.59/160.56 ! [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)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Ints__power,axiom,
% 160.59/160.56 ! [V_n_2,V_a_2,T_a] :
% 160.59/160.56 ( class_Rings_Oring__1(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 160.59/160.56 => 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__un_I4_J,axiom,
% 160.59/160.56 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Olinorder(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 160.59/160.56 => 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) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__un_I19_J,axiom,
% 160.59/160.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Olinorder(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 160.59/160.56 => 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) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_greaterThanAtMost__empty,axiom,
% 160.59/160.56 ! [V_k_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Oorder(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
% 160.59/160.56 => 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)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 160.59/160.56 ! [V_l_2,V_k_2,T_a] :
% 160.59/160.56 ( class_Orderings_Oorder(T_a)
% 160.59/160.56 => ( 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))
% 160.59/160.56 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 160.59/160.56 ! [V_l_2,V_k_2,T_a] :
% 160.59/160.56 ( class_Orderings_Oorder(T_a)
% 160.59/160.56 => ( 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)
% 160.59/160.56 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__un_I20_J,axiom,
% 160.59/160.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Olinorder(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 160.59/160.56 => 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) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_greaterThanLessThan__empty,axiom,
% 160.59/160.56 ! [V_k_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Oorder(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2))
% 160.59/160.56 => 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)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__int_I14_J,axiom,
% 160.59/160.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Oorder(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 160.59/160.56 ! [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) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 160.59/160.56 ! [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) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_card__greaterThanAtMost,axiom,
% 160.59/160.56 ! [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) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setprod__constant,axiom,
% 160.59/160.56 ! [V_y_2,V_A_2,T_a,T_b] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.56 => 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)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_power__eq__if,axiom,
% 160.59/160.56 ! [V_p,V_m] :
% 160.59/160.56 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.56 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 160.59/160.56 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.56 => 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)))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__un_I22_J,axiom,
% 160.59/160.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Olinorder(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 160.59/160.56 => 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) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 160.59/160.56 ! [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) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__int_I16_J,axiom,
% 160.59/160.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Oorder(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__un_I9_J,axiom,
% 160.59/160.56 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Olinorder(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 160.59/160.56 => 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) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__int_I13_J,axiom,
% 160.59/160.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Oorder(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__int_I12_J,axiom,
% 160.59/160.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Oorder(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__int_I9_J,axiom,
% 160.59/160.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Oorder(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__int_I3_J,axiom,
% 160.59/160.56 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Oorder(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_card__greaterThanLessThan,axiom,
% 160.59/160.56 ! [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)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__int_I1_J,axiom,
% 160.59/160.56 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Oorder(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 160.59/160.56 ! [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) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 160.59/160.56 ! [V_y,V_x] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 160.59/160.56 => 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_tsub__eq,axiom,
% 160.59/160.56 ! [V_x,V_y] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 160.59/160.56 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 160.59/160.56 ! [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)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__un_I15_J,axiom,
% 160.59/160.56 ! [V_u_2,V_m_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Olinorder(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2))
% 160.59/160.56 => 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) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_setsum__head,axiom,
% 160.59/160.56 ! [V_P_2,V_n_2,V_m_2,T_a] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.59/160.56 => 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_ivl__disj__un_I7_J,axiom,
% 160.59/160.56 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.56 ( class_Orderings_Olinorder(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 160.59/160.56 => 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) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_power__strict__mono,axiom,
% 160.59/160.56 ! [V_n,V_b,V_a,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.56 => 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))) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_one__less__power,axiom,
% 160.59/160.56 ! [V_n,V_a,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.56 => 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))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_power__le__imp__le__exp,axiom,
% 160.59/160.56 ! [V_n,V_m,V_a,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 160.59/160.56 => ( 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)))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_power__increasing__iff,axiom,
% 160.59/160.56 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 160.59/160.56 => ( 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)))
% 160.59/160.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_power__decreasing,axiom,
% 160.59/160.56 ! [V_a,V_N,V_n,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 160.59/160.56 => 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))) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_power__strict__decreasing,axiom,
% 160.59/160.56 ! [V_a,V_N,V_n,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 160.59/160.56 => 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))) ) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_field__power__not__zero,axiom,
% 160.59/160.56 ! [V_n,V_a,T_a] :
% 160.59/160.56 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 160.59/160.56 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.56 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_power__Suc__0,axiom,
% 160.59/160.56 ! [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)) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 160.59/160.56 ! [V_m_2,V_x_2] :
% 160.59/160.56 ( 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))
% 160.59/160.56 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.56 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_nat__power__less__imp__less,axiom,
% 160.59/160.56 ! [V_n,V_m,V_i] :
% 160.59/160.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 160.59/160.56 => ( 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)))
% 160.59/160.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_nat__zero__less__power__iff,axiom,
% 160.59/160.56 ! [V_n_2,V_x_2] :
% 160.59/160.56 ( 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)))
% 160.59/160.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 160.59/160.56 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_power__commutes,axiom,
% 160.59/160.56 ! [V_n,V_a,T_a] :
% 160.59/160.56 ( class_Groups_Omonoid__mult(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_power__mult__distrib,axiom,
% 160.59/160.56 ! [V_n,V_b,V_a,T_a] :
% 160.59/160.56 ( class_Groups_Ocomm__monoid__mult(T_a)
% 160.59/160.56 => 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)) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_power__one,axiom,
% 160.59/160.56 ! [V_n,T_a] :
% 160.59/160.56 ( class_Groups_Omonoid__mult(T_a)
% 160.59/160.56 => 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) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_of__nat__power,axiom,
% 160.59/160.56 ! [V_n,V_m,T_a] :
% 160.59/160.56 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.56 => 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) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_power__mult,axiom,
% 160.59/160.56 ! [V_n,V_m,V_a,T_a] :
% 160.59/160.56 ( class_Groups_Omonoid__mult(T_a)
% 160.59/160.56 => 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) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_power__one__right,axiom,
% 160.59/160.56 ! [V_a,T_a] :
% 160.59/160.56 ( class_Groups_Omonoid__mult(T_a)
% 160.59/160.56 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_power__mono,axiom,
% 160.59/160.56 ! [V_n,V_b,V_a,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.56 => 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))) ) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zero__le__power,axiom,
% 160.59/160.56 ! [V_n,V_a,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.56 => 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))) ) ) ).
% 160.59/160.56
% 160.59/160.56 fof(fact_zero__less__power,axiom,
% 160.59/160.56 ! [V_n,V_a,T_a] :
% 160.59/160.56 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.57 => 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__eq__0__iff,axiom,
% 160.59/160.57 ! [V_n_2,V_a_2,T_a] :
% 160.59/160.57 ( ( class_Power_Opower(T_a)
% 160.59/160.57 & class_Rings_Omult__zero(T_a)
% 160.59/160.57 & class_Rings_Ono__zero__divisors(T_a)
% 160.59/160.57 & class_Rings_Ozero__neq__one(T_a) )
% 160.59/160.57 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_one__le__power,axiom,
% 160.59/160.57 ! [V_n,V_a,T_a] :
% 160.59/160.57 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 160.59/160.57 => 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__0__Suc,axiom,
% 160.59/160.57 ! [V_n,T_a] :
% 160.59/160.57 ( ( class_Power_Opower(T_a)
% 160.59/160.57 & class_Rings_Osemiring__0(T_a) )
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__inject__exp,axiom,
% 160.59/160.57 ! [V_n_2,V_m_2,V_a_2,T_a] :
% 160.59/160.57 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2))
% 160.59/160.57 => ( 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)
% 160.59/160.57 <=> V_m_2 = V_n_2 ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__Suc,axiom,
% 160.59/160.57 ! [V_n,V_a,T_a] :
% 160.59/160.57 ( class_Power_Opower(T_a)
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__Suc2,axiom,
% 160.59/160.57 ! [V_n,V_a,T_a] :
% 160.59/160.57 ( class_Groups_Omonoid__mult(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__one__le__power,axiom,
% 160.59/160.57 ! [V_n,V_i] :
% 160.59/160.57 ( 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))
% 160.59/160.57 => 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))) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__0,axiom,
% 160.59/160.57 ! [V_a,T_a] :
% 160.59/160.57 ( class_Power_Opower(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__add,axiom,
% 160.59/160.57 ! [V_n,V_m,V_a,T_a] :
% 160.59/160.57 ( class_Groups_Omonoid__mult(T_a)
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__less__imp__less__base,axiom,
% 160.59/160.57 ! [V_b,V_n,V_a,T_a] :
% 160.59/160.57 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.57 => ( 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)))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__inject__base,axiom,
% 160.59/160.57 ! [V_b,V_n,V_a,T_a] :
% 160.59/160.57 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.57 => ( 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))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 160.59/160.57 => V_a = V_b ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__le__imp__le__base,axiom,
% 160.59/160.57 ! [V_b,V_n,V_a,T_a] :
% 160.59/160.57 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.57 => ( 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))))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__less__power__Suc,axiom,
% 160.59/160.57 ! [V_n,V_a,T_a] :
% 160.59/160.57 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 160.59/160.57 => 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)))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__gt1__lemma,axiom,
% 160.59/160.57 ! [V_n,V_a,T_a] :
% 160.59/160.57 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 160.59/160.57 => 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)))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__0__left,axiom,
% 160.59/160.57 ! [V_n,T_a] :
% 160.59/160.57 ( ( class_Power_Opower(T_a)
% 160.59/160.57 & class_Rings_Osemiring__0(T_a) )
% 160.59/160.57 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.57 => 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) )
% 160.59/160.57 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.57 => 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) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__gt1,axiom,
% 160.59/160.57 ! [V_n,V_a,T_a] :
% 160.59/160.57 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 160.59/160.57 => 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)))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__strict__increasing,axiom,
% 160.59/160.57 ! [V_a,V_N,V_n,T_a] :
% 160.59/160.57 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__less__imp__less__exp,axiom,
% 160.59/160.57 ! [V_n,V_m,V_a,T_a] :
% 160.59/160.57 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__strict__increasing__iff,axiom,
% 160.59/160.57 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 160.59/160.57 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__increasing,axiom,
% 160.59/160.57 ! [V_a,V_N,V_n,T_a] :
% 160.59/160.57 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__Suc__less,axiom,
% 160.59/160.57 ! [V_n,V_a,T_a] :
% 160.59/160.57 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__eq__imp__eq__base,axiom,
% 160.59/160.57 ! [V_b,V_n,V_a,T_a] :
% 160.59/160.57 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.57 => ( 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)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.57 => V_a = V_b ) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__Suc__less__one,axiom,
% 160.59/160.57 ! [V_n,V_a,T_a] :
% 160.59/160.57 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__power__power,axiom,
% 160.59/160.57 ! [T_a] :
% 160.59/160.57 ( class_Power_Opower(T_a)
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_int__power__div__base,axiom,
% 160.59/160.57 ! [V_k,V_m] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 160.59/160.57 => 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)))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_setprod__diff1,axiom,
% 160.59/160.57 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] :
% 160.59/160.57 ( class_Fields_Ofield(T_b)
% 160.59/160.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.57 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b)
% 160.59/160.57 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.57 => 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)) )
% 160.59/160.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.57 => 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) ) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 160.59/160.57 ! [V_u_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 160.59/160.57 => 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))) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_setsum__nonneg__leq__bound,axiom,
% 160.59/160.57 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] :
% 160.59/160.57 ( class_Groups_Oordered__ab__group__add(T_b)
% 160.59/160.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 160.59/160.57 => ( ! [B_i] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) )
% 160.59/160.57 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_setsum__nonneg__0,axiom,
% 160.59/160.57 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] :
% 160.59/160.57 ( class_Groups_Oordered__ab__group__add(T_b)
% 160.59/160.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 160.59/160.57 => ( ! [B_i] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) )
% 160.59/160.57 => ( 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)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2))
% 160.59/160.57 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__zero,axiom,
% 160.59/160.57 ! [V_a,T_a] :
% 160.59/160.57 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__zero__left,axiom,
% 160.59/160.57 ! [V_a,T_a] :
% 160.59/160.57 ( class_Rings_Odivision__ring(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_add__divide__distrib,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Rings_Odivision__ring(T_a)
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_times__divide__eq__right,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Rings_Odivision__ring(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_diff__divide__distrib,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Rings_Odivision__ring(T_a)
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__1,axiom,
% 160.59/160.57 ! [V_a,T_a] :
% 160.59/160.57 ( class_Rings_Odivision__ring(T_a)
% 160.59/160.57 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zdiv__zero,axiom,
% 160.59/160.57 ! [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) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__divide,axiom,
% 160.59/160.57 ! [V_n,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__int,axiom,
% 160.59/160.57 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__0,axiom,
% 160.59/160.57 ! [V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__by__0,axiom,
% 160.59/160.57 ! [V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__by__1,axiom,
% 160.59/160.57 ! [V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_setsum__divide__distrib,axiom,
% 160.59/160.57 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.57 ( class_Fields_Ofield(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nonzero__eq__divide__eq,axiom,
% 160.59/160.57 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 160.59/160.57 ( class_Rings_Odivision__ring(T_a)
% 160.59/160.57 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)
% 160.59/160.57 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nonzero__divide__eq__eq,axiom,
% 160.59/160.57 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 160.59/160.57 ( class_Rings_Odivision__ring(T_a)
% 160.59/160.57 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2
% 160.59/160.57 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__eq__imp,axiom,
% 160.59/160.57 ! [V_a,V_b,V_c,T_a] :
% 160.59/160.57 ( class_Rings_Odivision__ring(T_a)
% 160.59/160.57 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 160.59/160.57 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_eq__divide__imp,axiom,
% 160.59/160.57 ! [V_b,V_a,V_c,T_a] :
% 160.59/160.57 ( class_Rings_Odivision__ring(T_a)
% 160.59/160.57 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 160.59/160.57 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__self__if,axiom,
% 160.59/160.57 ! [V_a,T_a] :
% 160.59/160.57 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 160.59/160.57 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 160.59/160.57 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__self,axiom,
% 160.59/160.57 ! [V_a,T_a] :
% 160.59/160.57 ( class_Rings_Odivision__ring(T_a)
% 160.59/160.57 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_right__inverse__eq,axiom,
% 160.59/160.57 ! [V_a_2,V_b_2,T_a] :
% 160.59/160.57 ( class_Rings_Odivision__ring(T_a)
% 160.59/160.57 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a)
% 160.59/160.57 <=> V_a_2 = V_b_2 ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nonzero__power__divide,axiom,
% 160.59/160.57 ! [V_n,V_a,V_b,T_a] :
% 160.59/160.57 ( class_Fields_Ofield(T_a)
% 160.59/160.57 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__0,axiom,
% 160.59/160.57 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 160.59/160.57 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 160.59/160.57 ! [V_y,V_x] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 160.59/160.57 => 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__neg__pos__less0,axiom,
% 160.59/160.57 ! [V_b,V_a] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.57 => 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 160.59/160.57 ! [V_a_2,V_b_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 160.59/160.57 ! [V_a_2,V_b_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_eq__nat__nat__iff,axiom,
% 160.59/160.57 ! [V_z_H_2,V_z_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 160.59/160.57 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 160.59/160.57 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 160.59/160.57 ! [V_y_2,V_x_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 160.59/160.57 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 160.59/160.57 <=> V_x_2 = V_y_2 ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_all__nat,axiom,
% 160.59/160.57 ! [V_P_2] :
% 160.59/160.57 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 160.59/160.57 <=> ! [B_x] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 160.59/160.57 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_ex__nat,axiom,
% 160.59/160.57 ! [V_P_2] :
% 160.59/160.57 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 160.59/160.57 <=> ? [B_x] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 160.59/160.57 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__one__over,axiom,
% 160.59/160.57 ! [V_n,V_a,T_a] :
% 160.59/160.57 ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zdiv__self,axiom,
% 160.59/160.57 ! [V_a] :
% 160.59/160.57 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 160.59/160.57 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__mult__mult1__if,axiom,
% 160.59/160.57 ! [V_b,V_a,V_c,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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) )
% 160.59/160.57 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__mult__self2__is__id,axiom,
% 160.59/160.57 ! [V_a,V_b,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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 ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__mult__self1__is__id,axiom,
% 160.59/160.57 ! [V_a,V_b,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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 ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__mult__mult2,axiom,
% 160.59/160.57 ! [V_b,V_a,V_c,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__mult__mult1,axiom,
% 160.59/160.57 ! [V_b,V_a,V_c,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__self,axiom,
% 160.59/160.57 ! [V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 160.59/160.57 ! [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 ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 160.59/160.57 ! [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))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_setprod__dividef,axiom,
% 160.59/160.57 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
% 160.59/160.57 ( class_Fields_Ofield__inverse__zero(T_b)
% 160.59/160.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 160.59/160.57 ! [V_A_2,V_f_2,T_a] :
% 160.59/160.57 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.57 & class_Groups_Ocomm__monoid__mult(T_a) )
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 160.59/160.57 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))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__le__0,axiom,
% 160.59/160.57 ! [V_z] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__0__iff,axiom,
% 160.59/160.57 ! [V_i_2] :
% 160.59/160.57 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zdiv__eq__0__iff,axiom,
% 160.59/160.57 ! [V_k_2,V_i_2] :
% 160.59/160.57 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.57 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.57 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 160.59/160.57 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 160.59/160.57 ! [V_a_2,V_b_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 160.59/160.57 ! [V_i_2,V_k_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 160.59/160.57 ! [V_b_2,V_a_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zdiv__mono2,axiom,
% 160.59/160.57 ! [V_b,V_b_H,V_a] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__nonneg__neg__le0,axiom,
% 160.59/160.57 ! [V_b,V_a] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 => 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__pos__pos__trivial,axiom,
% 160.59/160.57 ! [V_b,V_a] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 160.59/160.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 160.59/160.57 ! [V_a_2,V_b_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__nonpos__pos__le0,axiom,
% 160.59/160.57 ! [V_b,V_a] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.57 => 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zdiv__mono2__neg,axiom,
% 160.59/160.57 ! [V_b,V_b_H,V_a] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__neg__neg__trivial,axiom,
% 160.59/160.57 ! [V_b,V_a] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 160.59/160.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zdiv__mono1,axiom,
% 160.59/160.57 ! [V_b,V_a_H,V_a] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.57 => 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zdiv__mono1__neg,axiom,
% 160.59/160.57 ! [V_b,V_a_H,V_a] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 => 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__mono__iff,axiom,
% 160.59/160.57 ! [V_w_2,V_z_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zless__nat__conj,axiom,
% 160.59/160.57 ! [V_z_2,V_w_2] :
% 160.59/160.57 ( 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)))
% 160.59/160.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 160.59/160.57 ! [V_y_2,V_x_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__1,axiom,
% 160.59/160.57 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_int__div__less__self,axiom,
% 160.59/160.57 ! [V_k,V_x] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zdiv__zmult2__eq,axiom,
% 160.59/160.57 ! [V_b,V_a,V_c] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_int__nat__eq,axiom,
% 160.59/160.57 ! [V_z] :
% 160.59/160.57 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 160.59/160.57 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 160.59/160.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 160.59/160.57 => 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) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_int__eq__iff,axiom,
% 160.59/160.57 ! [V_z_2,V_m_2] :
% 160.59/160.57 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 160.59/160.57 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__0__le,axiom,
% 160.59/160.57 ! [V_z] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 160.59/160.57 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zless__nat__eq__int__zless,axiom,
% 160.59/160.57 ! [V_z_2,V_m_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 160.59/160.57 <=> 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power_Opower_Opower__0,axiom,
% 160.59/160.57 ! [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 ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power_Opower_Opower__Suc,axiom,
% 160.59/160.57 ! [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)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__mult__self2,axiom,
% 160.59/160.57 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__mult__self1,axiom,
% 160.59/160.57 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 160.59/160.57 ! [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))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__add__self2,axiom,
% 160.59/160.57 ! [V_a,V_b,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__add__self1,axiom,
% 160.59/160.57 ! [V_a,V_b,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 160.59/160.57 ! [V_A_2,V_f_2,T_a] :
% 160.59/160.57 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.57 & class_Groups_Ocomm__monoid__mult(T_a) )
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 160.59/160.57 ! [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) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_card__atLeastLessThan__int,axiom,
% 160.59/160.57 ! [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)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zero__less__nat__eq,axiom,
% 160.59/160.57 ! [V_z_2] :
% 160.59/160.57 ( 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)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_power__diff,axiom,
% 160.59/160.57 ! [V_m,V_n,V_a,T_a] :
% 160.59/160.57 ( class_Fields_Ofield(T_a)
% 160.59/160.57 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 160.59/160.57 => 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)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__less__eq__zless,axiom,
% 160.59/160.57 ! [V_z_2,V_w_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 160.59/160.57 ! [V_y_2,V_x_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__eq__iff2,axiom,
% 160.59/160.57 ! [V_w_2,V_m_2] :
% 160.59/160.57 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 160.59/160.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 160.59/160.57 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 160.59/160.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 160.59/160.57 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__eq__iff,axiom,
% 160.59/160.57 ! [V_m_2,V_w_2] :
% 160.59/160.57 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 160.59/160.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 160.59/160.57 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 160.59/160.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 160.59/160.57 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__le__eq__zle,axiom,
% 160.59/160.57 ! [V_z_2,V_w_2] :
% 160.59/160.57 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 160.59/160.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_split__nat,axiom,
% 160.59/160.57 ! [V_i_2,V_P_2] :
% 160.59/160.57 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 160.59/160.57 <=> ( ! [B_n] :
% 160.59/160.57 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 160.59/160.57 => hBOOL(hAPP(V_P_2,B_n)) )
% 160.59/160.57 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__add__distrib,axiom,
% 160.59/160.57 ! [V_z_H,V_z] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 160.59/160.57 ! [V_y,V_x] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__mult__distrib,axiom,
% 160.59/160.57 ! [V_z_H,V_z] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 160.59/160.57 ! [V_y,V_x] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 160.59/160.57 ! [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))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__diff__distrib,axiom,
% 160.59/160.57 ! [V_z,V_z_H] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 160.59/160.57 ! [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)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_card__greaterThanAtMost__int,axiom,
% 160.59/160.57 ! [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)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 160.59/160.57 ! [V_n,V_x] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__power__eq,axiom,
% 160.59/160.57 ! [V_n,V_z] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 160.59/160.57 ! [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))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 160.59/160.57 ! [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)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 160.59/160.57 ! [V_y,V_x] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_one__less__nat__eq,axiom,
% 160.59/160.57 ! [V_z_2] :
% 160.59/160.57 ( 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)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divmod__int__rel__div__eq,axiom,
% 160.59/160.57 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 160.59/160.57 ( 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)
% 160.59/160.57 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 160.59/160.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 160.59/160.57 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_split__zdiv,axiom,
% 160.59/160.57 ! [V_k_2,V_n_2,V_P_2] :
% 160.59/160.57 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 160.59/160.57 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.57 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 160.59/160.57 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 160.59/160.57 => ! [B_i] :
% 160.59/160.57 ( ? [B_j] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 160.59/160.57 & 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) )
% 160.59/160.57 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 160.59/160.57 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 => ! [B_i] :
% 160.59/160.57 ( ? [B_j] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 & 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) )
% 160.59/160.57 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__less__iff,axiom,
% 160.59/160.57 ! [V_m_2,V_w_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 160.59/160.57 <=> 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 160.59/160.57 ! [V_z] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_card__atLeastAtMost__int,axiom,
% 160.59/160.57 ! [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))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_card__greaterThanLessThan__int,axiom,
% 160.59/160.57 ! [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)))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_geometric__sum,axiom,
% 160.59/160.57 ! [V_n_2,V_x_2,T_a] :
% 160.59/160.57 ( class_Fields_Ofield(T_a)
% 160.59/160.57 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a)
% 160.59/160.57 => 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_le__divide__eq,axiom,
% 160.59/160.57 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.57 => ( 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_c_2)))
% 160.59/160.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) )
% 160.59/160.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => 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_c_2))) )
% 160.59/160.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__le__eq,axiom,
% 160.59/160.57 ! [V_a_2,V_c_2,V_b_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
% 160.59/160.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.57 => 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_c_2))) )
% 160.59/160.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) )
% 160.59/160.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_pos__le__divide__eq,axiom,
% 160.59/160.57 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.57 => ( 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_c_2)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_pos__divide__le__eq,axiom,
% 160.59/160.57 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
% 160.59/160.57 <=> 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_c_2))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mult__imp__div__pos__le,axiom,
% 160.59/160.57 ! [V_z,V_x,V_y,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 => 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)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mult__imp__le__div__pos,axiom,
% 160.59/160.57 ! [V_x,V_z,V_y,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 160.59/160.57 => ( 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))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__le__mono,axiom,
% 160.59/160.57 ! [V_k,V_n,V_m] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 160.59/160.57 => 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))) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__le__dividend,axiom,
% 160.59/160.57 ! [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)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__mult2__eq,axiom,
% 160.59/160.57 ! [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) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__1,axiom,
% 160.59/160.57 ! [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 ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__less,axiom,
% 160.59/160.57 ! [V_n,V_m] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__mult__div__cancel__disj,axiom,
% 160.59/160.57 ! [V_n,V_m,V_k] :
% 160.59/160.57 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.57 => 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) )
% 160.59/160.57 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.57 => 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) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zdiv__int,axiom,
% 160.59/160.57 ! [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)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 160.59/160.57 ! [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)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__le__mono2,axiom,
% 160.59/160.57 ! [V_k,V_n,V_m] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 160.59/160.57 => 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__mult__div__cancel1,axiom,
% 160.59/160.57 ! [V_n,V_m,V_k] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__mult__self1__is__m,axiom,
% 160.59/160.57 ! [V_m,V_n] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.57 => 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 ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__mult__self__is__m,axiom,
% 160.59/160.57 ! [V_m,V_n] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.57 => 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 ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__less__dividend,axiom,
% 160.59/160.57 ! [V_m,V_n] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__if,axiom,
% 160.59/160.57 ! [V_m,V_n] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 160.59/160.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.57 => 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)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_div__geq,axiom,
% 160.59/160.57 ! [V_m,V_n] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.57 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_split__div,axiom,
% 160.59/160.57 ! [V_k_2,V_n_2,V_P_2] :
% 160.59/160.57 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 160.59/160.57 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.57 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 160.59/160.57 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.57 => ! [B_i,B_j] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 160.59/160.57 => ( 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)
% 160.59/160.57 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__div__distrib,axiom,
% 160.59/160.57 ! [V_y,V_x] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 160.59/160.57 ! [V_y,V_x] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_le__div__geq,axiom,
% 160.59/160.57 ! [V_m,V_n] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_split__div_H,axiom,
% 160.59/160.57 ! [V_n_2,V_m_2,V_P_2] :
% 160.59/160.57 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 160.59/160.57 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.57 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 160.59/160.57 | ? [B_q] :
% 160.59/160.57 ( 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))
% 160.59/160.57 & 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))))
% 160.59/160.57 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_split__div__lemma,axiom,
% 160.59/160.57 ! [V_m_2,V_q_2,V_n_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 160.59/160.57 => ( ( 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))
% 160.59/160.57 & 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)))) )
% 160.59/160.57 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_times__divide__times__eq,axiom,
% 160.59/160.57 ! [V_w,V_z,V_y,V_x,T_a] :
% 160.59/160.57 ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__right__mono__neg,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__right__mono,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__le__0__iff,axiom,
% 160.59/160.57 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 160.59/160.57 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zero__le__divide__iff,axiom,
% 160.59/160.57 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 160.59/160.57 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__strict__right__mono__neg,axiom,
% 160.59/160.57 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__strict__right__mono,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__neg__neg,axiom,
% 160.59/160.57 ! [V_y,V_x,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__neg__pos,axiom,
% 160.59/160.57 ! [V_y,V_x,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__pos__neg,axiom,
% 160.59/160.57 ! [V_y,V_x,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__pos__pos,axiom,
% 160.59/160.57 ! [V_y,V_x,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__less__0__iff,axiom,
% 160.59/160.57 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 160.59/160.57 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zero__less__divide__iff,axiom,
% 160.59/160.57 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 160.59/160.57 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_frac__eq__eq,axiom,
% 160.59/160.57 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] :
% 160.59/160.57 ( class_Fields_Ofield(T_a)
% 160.59/160.57 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => ( 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)
% 160.59/160.57 <=> 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) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mult__divide__mult__cancel__left,axiom,
% 160.59/160.57 ! [V_b,V_a,V_c,T_a] :
% 160.59/160.57 ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.57 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mult__divide__mult__cancel__right,axiom,
% 160.59/160.57 ! [V_b,V_a,V_c,T_a] :
% 160.59/160.57 ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.57 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__eq__eq,axiom,
% 160.59/160.57 ! [V_a_2,V_c_2,V_b_2,T_a] :
% 160.59/160.57 ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.57 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2
% 160.59/160.57 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) )
% 160.59/160.57 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_eq__divide__eq,axiom,
% 160.59/160.57 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.57 ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.57 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)
% 160.59/160.57 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 )
% 160.59/160.57 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__nonpos__neg,axiom,
% 160.59/160.57 ! [V_y,V_x,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__nonpos__pos,axiom,
% 160.59/160.57 ! [V_y,V_x,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_frac__le,axiom,
% 160.59/160.57 ! [V_z,V_w,V_y,V_x,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 160.59/160.57 => 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))) ) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_frac__less,axiom,
% 160.59/160.57 ! [V_z,V_w,V_y,V_x,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 160.59/160.57 => 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))) ) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_frac__less2,axiom,
% 160.59/160.57 ! [V_z,V_w,V_y,V_x,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 160.59/160.57 => 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))) ) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__nonneg__neg,axiom,
% 160.59/160.57 ! [V_y,V_x,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__nonneg__pos,axiom,
% 160.59/160.57 ! [V_y,V_x,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__strict__left__mono__neg,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 => 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))) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__strict__left__mono,axiom,
% 160.59/160.57 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 => 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))) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_neg__divide__less__eq,axiom,
% 160.59/160.57 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_neg__less__divide__eq,axiom,
% 160.59/160.57 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => ( 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_c_2)))
% 160.59/160.57 <=> 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_c_2))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mult__imp__less__div__pos,axiom,
% 160.59/160.57 ! [V_x,V_z,V_y,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 160.59/160.57 => ( 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))
% 160.59/160.57 => 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mult__imp__div__pos__less,axiom,
% 160.59/160.57 ! [V_z,V_x,V_y,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 => 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)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_pos__divide__less__eq,axiom,
% 160.59/160.57 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
% 160.59/160.57 <=> 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_c_2))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_pos__less__divide__eq,axiom,
% 160.59/160.57 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.57 => ( 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_c_2)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__less__eq,axiom,
% 160.59/160.57 ! [V_a_2,V_c_2,V_b_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
% 160.59/160.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.57 => 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_c_2))) )
% 160.59/160.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) )
% 160.59/160.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_less__divide__eq,axiom,
% 160.59/160.57 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.57 => ( 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_c_2)))
% 160.59/160.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) )
% 160.59/160.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => 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_c_2))) )
% 160.59/160.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_add__frac__eq,axiom,
% 160.59/160.57 ! [V_w,V_x,V_z,V_y,T_a] :
% 160.59/160.57 ( class_Fields_Ofield(T_a)
% 160.59/160.57 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__add__eq__iff,axiom,
% 160.59/160.57 ! [V_y,V_x,V_z,T_a] :
% 160.59/160.57 ( class_Fields_Ofield(T_a)
% 160.59/160.57 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_add__frac__num,axiom,
% 160.59/160.57 ! [V_z,V_x,V_y,T_a] :
% 160.59/160.57 ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.57 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_add__divide__eq__iff,axiom,
% 160.59/160.57 ! [V_y,V_x,V_z,T_a] :
% 160.59/160.57 ( class_Fields_Ofield(T_a)
% 160.59/160.57 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_add__num__frac,axiom,
% 160.59/160.57 ! [V_x,V_z,V_y,T_a] :
% 160.59/160.57 ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.57 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_diff__divide__eq__iff,axiom,
% 160.59/160.57 ! [V_y,V_x,V_z,T_a] :
% 160.59/160.57 ( class_Fields_Ofield(T_a)
% 160.59/160.57 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__diff__eq__iff,axiom,
% 160.59/160.57 ! [V_y,V_x,V_z,T_a] :
% 160.59/160.57 ( class_Fields_Ofield(T_a)
% 160.59/160.57 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_diff__frac__eq,axiom,
% 160.59/160.57 ! [V_w,V_x,V_z,V_y,T_a] :
% 160.59/160.57 ( class_Fields_Ofield(T_a)
% 160.59/160.57 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.57 => 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)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_gt__half__sum,axiom,
% 160.59/160.57 ! [V_b,V_a,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_less__half__sum,axiom,
% 160.59/160.57 ! [V_b,V_a,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 160.59/160.57 => 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))))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__left__mono__neg,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 => 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))) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_divide__left__mono,axiom,
% 160.59/160.57 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 => 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))) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_neg__divide__le__eq,axiom,
% 160.59/160.57 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_neg__le__divide__eq,axiom,
% 160.59/160.57 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.57 => ( 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_c_2)))
% 160.59/160.57 <=> 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_c_2))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__aux__def,axiom,
% 160.59/160.57 ! [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) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 160.59/160.57 ! [V_B_2,V_A_2] :
% 160.59/160.57 ( c_Nat__Transfer_Onat__set(V_A_2)
% 160.59/160.57 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 160.59/160.57 => 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 160.59/160.57 ! [V_B_2,V_A_2] :
% 160.59/160.57 ( c_Nat__Transfer_Onat__set(V_A_2)
% 160.59/160.57 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 160.59/160.57 => 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__morphism__nat__int,axiom,
% 160.59/160.57 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))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 160.59/160.57 ! [V_f_2,V_A_2,T_a] :
% 160.59/160.57 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.57 & class_Groups_Ocomm__monoid__mult(T_a) )
% 160.59/160.57 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 160.59/160.57 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 160.59/160.57 ! [V_B_2,V_A_2] :
% 160.59/160.57 ( c_Nat__Transfer_Onat__set(V_A_2)
% 160.59/160.57 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 160.59/160.57 ! [V_B_2,V_A_2] :
% 160.59/160.57 ( c_Nat__Transfer_Onat__set(V_A_2)
% 160.59/160.57 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_nat__set__def,axiom,
% 160.59/160.57 ! [V_S_2] :
% 160.59/160.57 ( c_Nat__Transfer_Onat__set(V_S_2)
% 160.59/160.57 <=> ! [B_x] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 160.59/160.57 ! [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)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 160.59/160.57 ! [V_B_2,V_A_2] :
% 160.59/160.57 ( c_Nat__Transfer_Onat__set(V_A_2)
% 160.59/160.57 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 160.59/160.57 => ( V_A_2 = V_B_2
% 160.59/160.57 <=> 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) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 160.59/160.57 ! [V_y_2,V_x_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 160.59/160.57 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 160.59/160.57 ! [V_x_2,V_A_2] :
% 160.59/160.57 ( c_Nat__Transfer_Onat__set(V_A_2)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 160.59/160.57 ! [V_A_2] :
% 160.59/160.57 ( c_Nat__Transfer_Onat__set(V_A_2)
% 160.59/160.57 => 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 ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 160.59/160.57 ! [V_A_2] :
% 160.59/160.57 ( c_Nat__Transfer_Onat__set(V_A_2)
% 160.59/160.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 160.59/160.57 <=> 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 160.59/160.57 ! [V_A_2] :
% 160.59/160.57 ( c_Nat__Transfer_Onat__set(V_A_2)
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 160.59/160.57 ! [V_B_2,V_A_2] :
% 160.59/160.57 ( c_Nat__Transfer_Onat__set(V_A_2)
% 160.59/160.57 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.57 <=> 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 160.59/160.57 ! [V_B_2,V_A_2] :
% 160.59/160.57 ( c_Nat__Transfer_Onat__set(V_A_2)
% 160.59/160.57 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.57 <=> 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 160.59/160.57 ! [V_f_2,V_A_2,T_a] :
% 160.59/160.57 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.57 & class_Groups_Ocomm__monoid__mult(T_a) )
% 160.59/160.57 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 160.59/160.57 => 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)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_setprod__Un,axiom,
% 160.59/160.57 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.57 ( class_Fields_Ofield(T_b)
% 160.59/160.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.57 => ( ! [B_x] :
% 160.59/160.57 ( 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)))
% 160.59/160.57 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) )
% 160.59/160.57 => 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))) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 160.59/160.57 ! [V_A_2,V_x_2] :
% 160.59/160.57 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 160.59/160.57 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 160.59/160.57 <=> 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))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 160.59/160.57 ! [V_n_2,V_m_2] :
% 160.59/160.57 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 160.59/160.57 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 160.59/160.57 => 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_sum__diff__distrib,axiom,
% 160.59/160.57 ! [V_n_2,V_P_2,V_Q_2] :
% 160.59/160.57 ( ! [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)))
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_decr__mult__lemma,axiom,
% 160.59/160.57 ! [V_k_2,V_P_2,V_d_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 160.59/160.57 => ( ! [B_x] :
% 160.59/160.57 ( hBOOL(hAPP(V_P_2,B_x))
% 160.59/160.57 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 160.59/160.57 => ! [B_x] :
% 160.59/160.57 ( hBOOL(hAPP(V_P_2,B_x))
% 160.59/160.57 => 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)))) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 160.59/160.57 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 160.59/160.57 ! [V_y,V_x] :
% 160.59/160.57 ( c_Nat__Transfer_Ois__nat(V_x)
% 160.59/160.57 => ( c_Nat__Transfer_Ois__nat(V_y)
% 160.59/160.57 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 160.59/160.57 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 160.59/160.57 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 160.59/160.57 ! [V_y,V_x] :
% 160.59/160.57 ( c_Nat__Transfer_Ois__nat(V_x)
% 160.59/160.57 => ( c_Nat__Transfer_Ois__nat(V_y)
% 160.59/160.57 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 160.59/160.57 ! [V_y,V_x] :
% 160.59/160.57 ( c_Nat__Transfer_Ois__nat(V_x)
% 160.59/160.57 => ( c_Nat__Transfer_Ois__nat(V_y)
% 160.59/160.57 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 160.59/160.57 ! [V_n,V_x] :
% 160.59/160.57 ( c_Nat__Transfer_Ois__nat(V_x)
% 160.59/160.57 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 160.59/160.57 ! [V_y,V_x] :
% 160.59/160.57 ( c_Nat__Transfer_Ois__nat(V_x)
% 160.59/160.57 => ( c_Nat__Transfer_Ois__nat(V_y)
% 160.59/160.57 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_is__nat__def,axiom,
% 160.59/160.57 ! [V_x_2] :
% 160.59/160.57 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 160.59/160.57 ! [V_y_2,V_x_2] :
% 160.59/160.57 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 160.59/160.57 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 160.59/160.57 ! [V_x_2,V_A_2] :
% 160.59/160.57 ( c_Nat__Transfer_Onat__set(V_A_2)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 160.59/160.57 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 160.59/160.57 ! [V_f_2,V_A_2,T_a] :
% 160.59/160.57 ( ! [B_x] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.57 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 160.59/160.57 ! [V_f_2,V_A_2,T_a] :
% 160.59/160.57 ( ! [B_x] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.57 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_incr__mult__lemma,axiom,
% 160.59/160.57 ! [V_k_2,V_P_2,V_d_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 160.59/160.57 => ( ! [B_x] :
% 160.59/160.57 ( hBOOL(hAPP(V_P_2,B_x))
% 160.59/160.57 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 160.59/160.57 => ! [B_x] :
% 160.59/160.57 ( hBOOL(hAPP(V_P_2,B_x))
% 160.59/160.57 => 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)))) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_ex__least__nat__less,axiom,
% 160.59/160.57 ! [V_n_2,V_P_2] :
% 160.59/160.57 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 160.59/160.57 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 160.59/160.57 => ? [B_k] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 160.59/160.57 & ! [B_i] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 160.59/160.57 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 160.59/160.57 & 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)))) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_setprod__mono__one__left,axiom,
% 160.59/160.57 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 160.59/160.57 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 160.59/160.57 => ( ! [B_x] :
% 160.59/160.57 ( 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)))
% 160.59/160.57 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 160.59/160.57 => 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) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_setprod__mono__one__right,axiom,
% 160.59/160.57 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 160.59/160.57 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 160.59/160.57 => ( ! [B_x] :
% 160.59/160.57 ( 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)))
% 160.59/160.57 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 160.59/160.57 => 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) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zero__less__imp__eq__int,axiom,
% 160.59/160.57 ! [V_k] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 160.59/160.57 => ? [B_n] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 160.59/160.57 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_setsum__mono__zero__left,axiom,
% 160.59/160.57 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 160.59/160.57 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 160.59/160.57 => ( ! [B_x] :
% 160.59/160.57 ( 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)))
% 160.59/160.57 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 160.59/160.57 => 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) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_setsum__mono__zero__right,axiom,
% 160.59/160.57 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] :
% 160.59/160.57 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))
% 160.59/160.57 => ( ! [B_x] :
% 160.59/160.57 ( 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)))
% 160.59/160.57 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) )
% 160.59/160.57 => 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) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_card__Pow,axiom,
% 160.59/160.57 ! [V_A_2,T_a] :
% 160.59/160.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_PowI,axiom,
% 160.59/160.57 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_image__Pow__surj,axiom,
% 160.59/160.57 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] :
% 160.59/160.57 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Pow__top,axiom,
% 160.59/160.57 ! [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))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Union__Pow__eq,axiom,
% 160.59/160.57 ! [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 ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Cantors__paradox,axiom,
% 160.59/160.57 ! [V_A_2,T_a] :
% 160.59/160.57 ~ ? [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) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Pow__not__empty,axiom,
% 160.59/160.57 ! [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)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Pow__bottom,axiom,
% 160.59/160.57 ! [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))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_PowD,axiom,
% 160.59/160.57 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Pow__iff,axiom,
% 160.59/160.57 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Pow__mono,axiom,
% 160.59/160.57 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.57 => 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))) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_finite__Pow__iff,axiom,
% 160.59/160.57 ! [V_A_2,T_a] :
% 160.59/160.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)))
% 160.59/160.57 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_subset__Pow__Union,axiom,
% 160.59/160.57 ! [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)))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Pow__insert,axiom,
% 160.59/160.57 ! [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))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_UN__Pow__subset,axiom,
% 160.59/160.57 ! [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)))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Pow__Int__eq,axiom,
% 160.59/160.57 ! [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)) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_image__Pow__mono,axiom,
% 160.59/160.57 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.57 ( 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))
% 160.59/160.57 => 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))) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Pow__empty,axiom,
% 160.59/160.57 ! [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))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Un__Pow__subset,axiom,
% 160.59/160.57 ! [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)))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Powp__Pow__eq,axiom,
% 160.59/160.57 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.57 ( 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))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_card__partition,axiom,
% 160.59/160.57 ! [V_k_2,V_C_2,T_a] :
% 160.59/160.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2))
% 160.59/160.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)))
% 160.59/160.57 => ( ! [B_c] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2))
% 160.59/160.57 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 )
% 160.59/160.57 => ( ! [B_c1] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2))
% 160.59/160.57 => ! [B_c2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2))
% 160.59/160.57 => ( B_c1 != B_c2
% 160.59/160.57 => 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)) ) ) )
% 160.59/160.57 => 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)) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_finite__subset__induct,axiom,
% 160.59/160.57 ! [V_P_2,V_A_2,V_F_2,T_a] :
% 160.59/160.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2))
% 160.59/160.57 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 160.59/160.57 => ( ! [B_a,B_F] :
% 160.59/160.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 160.59/160.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F))
% 160.59/160.57 => ( hBOOL(hAPP(V_P_2,B_F))
% 160.59/160.57 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) )
% 160.59/160.57 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_atMost__Int__atLeast,axiom,
% 160.59/160.57 ! [V_n_2,T_a] :
% 160.59/160.57 ( class_Orderings_Oorder(T_a)
% 160.59/160.57 => 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))) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_field__le__mult__one__interval,axiom,
% 160.59/160.57 ! [V_y,V_x,T_a] :
% 160.59/160.57 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.57 => ( ! [B_z] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 160.59/160.57 => 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)) ) )
% 160.59/160.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 160.59/160.57 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
% 160.59/160.57 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.57 & class_Groups_Ocomm__monoid__mult(T_a) )
% 160.59/160.57 => ( V_A_2 = V_B_2
% 160.59/160.57 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 160.59/160.57 => ( ! [B_x] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 160.59/160.57 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 160.59/160.57 => 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) ) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_atLeast__eq__iff,axiom,
% 160.59/160.57 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.57 ( class_Orderings_Olinorder(T_a)
% 160.59/160.57 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2)
% 160.59/160.57 <=> V_x_2 = V_y_2 ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_atLeast__iff,axiom,
% 160.59/160.57 ! [V_k_2,V_i_2,T_a] :
% 160.59/160.57 ( class_Orderings_Oord(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_atLeast__subset__iff,axiom,
% 160.59/160.57 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.57 ( class_Orderings_Oorder(T_a)
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_ivl__disj__un_I14_J,axiom,
% 160.59/160.57 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.57 ( class_Orderings_Olinorder(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 160.59/160.57 => 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) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_ivl__disj__int_I8_J,axiom,
% 160.59/160.57 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.57 ( class_Orderings_Oorder(T_a)
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_ivl__disj__int_I6_J,axiom,
% 160.59/160.57 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.57 ( class_Orderings_Oorder(T_a)
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_atLeast__Suc,axiom,
% 160.59/160.57 ! [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)))) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_ivl__disj__un_I12_J,axiom,
% 160.59/160.57 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.57 ( class_Orderings_Olinorder(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2))
% 160.59/160.57 => 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) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_ivl__disj__un_I13_J,axiom,
% 160.59/160.57 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.57 ( class_Orderings_Olinorder(T_a)
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 160.59/160.57 => 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) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_ivl__disj__un_I1_J,axiom,
% 160.59/160.57 ! [V_l_2,T_a] :
% 160.59/160.57 ( class_Orderings_Olinorder(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_split__neg__lemma,axiom,
% 160.59/160.57 ! [V_n_2,V_P_2,V_k_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> ! [B_i,B_j] :
% 160.59/160.57 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 & 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) )
% 160.59/160.57 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_split__pos__lemma,axiom,
% 160.59/160.57 ! [V_n_2,V_P_2,V_k_2] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 160.59/160.57 => ( 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)))
% 160.59/160.57 <=> ! [B_i,B_j] :
% 160.59/160.57 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 160.59/160.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 160.59/160.57 & 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) )
% 160.59/160.57 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__mod__trivial,axiom,
% 160.59/160.57 ! [V_b,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_greaterThan__eq__iff,axiom,
% 160.59/160.57 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.57 ( class_Orderings_Olinorder(T_a)
% 160.59/160.57 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2)
% 160.59/160.57 <=> V_x_2 = V_y_2 ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__diff__right__eq,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Oring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__diff__left__eq,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Oring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__diff__eq,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Oring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__diff__cong,axiom,
% 160.59/160.57 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Oring__div(T_a)
% 160.59/160.57 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 160.59/160.57 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 160.59/160.57 => 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) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__mult__cong,axiom,
% 160.59/160.57 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 160.59/160.57 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 160.59/160.57 => 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) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zmod__simps_I4_J,axiom,
% 160.59/160.57 ! [V_b,V_c,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__mult__mult2,axiom,
% 160.59/160.57 ! [V_b,V_c,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__mult__mult1,axiom,
% 160.59/160.57 ! [V_b,V_a,V_c,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__mult__eq,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__mult__left__eq,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__mult__right__eq,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__add__self2,axiom,
% 160.59/160.57 ! [V_b,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__add__self1,axiom,
% 160.59/160.57 ! [V_a,V_b,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__add__right__eq,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__add__left__eq,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__add__eq,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zmod__simps_I2_J,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zmod__simps_I1_J,axiom,
% 160.59/160.57 ! [V_b,V_c,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__add__cong,axiom,
% 160.59/160.57 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 160.59/160.57 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 160.59/160.57 => 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) ) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__0,axiom,
% 160.59/160.57 ! [V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__by__0,axiom,
% 160.59/160.57 ! [V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__self,axiom,
% 160.59/160.57 ! [V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zmod__self,axiom,
% 160.59/160.57 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zmod__zero,axiom,
% 160.59/160.57 ! [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) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zmod__zmult1__eq,axiom,
% 160.59/160.57 ! [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) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zmod__simps_I3_J,axiom,
% 160.59/160.57 ! [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) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zdiff__zmod__left,axiom,
% 160.59/160.57 ! [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) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zdiff__zmod__right,axiom,
% 160.59/160.57 ! [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) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 160.59/160.57 ! [V_y,V_x] :
% 160.59/160.57 ( c_Nat__Transfer_Ois__nat(V_x)
% 160.59/160.57 => ( c_Nat__Transfer_Ois__nat(V_y)
% 160.59/160.57 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zpower__zmod,axiom,
% 160.59/160.57 ! [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) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_atLeast__Suc__greaterThan,axiom,
% 160.59/160.57 ! [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) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__mult__self1__is__0,axiom,
% 160.59/160.57 ! [V_a,V_b,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__mult__self2__is__0,axiom,
% 160.59/160.57 ! [V_b,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__mult__self1,axiom,
% 160.59/160.57 ! [V_b,V_c,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__mult__self2,axiom,
% 160.59/160.57 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__by__1,axiom,
% 160.59/160.57 ! [V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_mod__div__trivial,axiom,
% 160.59/160.57 ! [V_b,V_a,T_a] :
% 160.59/160.57 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.57 => 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) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 160.59/160.57 ! [V_y,V_x] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 160.59/160.57 => 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))) ) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zmod__le__nonneg__dividend,axiom,
% 160.59/160.57 ! [V_k,V_m] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_pos__mod__bound,axiom,
% 160.59/160.57 ! [V_a,V_b] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.57 => 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)) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_neg__mod__bound,axiom,
% 160.59/160.57 ! [V_a,V_b] :
% 160.59/160.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.57 => 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))) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zmod__eq__0__iff,axiom,
% 160.59/160.57 ! [V_d_2,V_m_2] :
% 160.59/160.57 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.57 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zmod__zdiv__trivial,axiom,
% 160.59/160.57 ! [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) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_DIVISION__BY__ZERO,axiom,
% 160.59/160.57 ! [V_a] :
% 160.59/160.57 ( 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)
% 160.59/160.57 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 160.59/160.57
% 160.59/160.57 fof(fact_zdiv__zadd1__eq,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.58 => 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 ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__div__equality2,axiom,
% 160.59/160.58 ! [V_a,V_b,T_a] :
% 160.59/160.58 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.58 => 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 ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__div__equality,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.58 => 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 ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_div__mod__equality2,axiom,
% 160.59/160.58 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.58 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_div__mod__equality,axiom,
% 160.59/160.58 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.58 ( class_Divides_Osemiring__div(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__neg__neg__trivial,axiom,
% 160.59/160.58 ! [V_b,V_a] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 160.59/160.58 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_neg__mod__conj,axiom,
% 160.59/160.58 ! [V_a,V_b] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.58 => ( 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)))
% 160.59/160.58 & 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))) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_neg__mod__sign,axiom,
% 160.59/160.58 ! [V_a,V_b] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.58 => 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))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__pos__pos__trivial,axiom,
% 160.59/160.58 ! [V_b,V_a] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 160.59/160.58 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_pos__mod__conj,axiom,
% 160.59/160.58 ! [V_a,V_b] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.58 => ( 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)))
% 160.59/160.58 & 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_pos__mod__sign,axiom,
% 160.59/160.58 ! [V_a,V_b] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.58 => 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))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zdiv__zmod__equality2,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zdiv__zmod__equality,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zdiv__zmult1__eq,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zmod__zdiv__equality,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_greaterThan__iff,axiom,
% 160.59/160.58 ! [V_k_2,V_i_2,T_a] :
% 160.59/160.58 ( class_Orderings_Oord(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)))
% 160.59/160.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zmult__div__cancel,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zmod__zdiv__equality_H,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_greaterThan__subset__iff,axiom,
% 160.59/160.58 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( 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)))
% 160.59/160.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__pos__neg__trivial,axiom,
% 160.59/160.58 ! [V_b,V_a] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.58 => ( 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)))
% 160.59/160.58 => 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) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_ivl__disj__int_I7_J,axiom,
% 160.59/160.58 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.58 ( class_Orderings_Oorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_split__zmod,axiom,
% 160.59/160.58 ! [V_k_2,V_n_2,V_P_2] :
% 160.59/160.58 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 160.59/160.58 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.58 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 160.59/160.58 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 160.59/160.58 => ! [B_i,B_j] :
% 160.59/160.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 160.59/160.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 160.59/160.58 & 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) )
% 160.59/160.58 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 160.59/160.58 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.58 => ! [B_i,B_j] :
% 160.59/160.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 160.59/160.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.58 & 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) )
% 160.59/160.58 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zmult2__lemma__aux3,axiom,
% 160.59/160.58 ! [V_q,V_b,V_r,V_c] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 160.59/160.58 => 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))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zmult2__lemma__aux4,axiom,
% 160.59/160.58 ! [V_q,V_b,V_r,V_c] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 160.59/160.58 => 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))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zmult2__lemma__aux1,axiom,
% 160.59/160.58 ! [V_q,V_r,V_b,V_c] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.58 => 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))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zmult2__lemma__aux2,axiom,
% 160.59/160.58 ! [V_q,V_r,V_b,V_c] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.58 => 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))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_divmod__int__rel__mod__eq,axiom,
% 160.59/160.58 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 160.59/160.58 ( 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)
% 160.59/160.58 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 160.59/160.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 160.59/160.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 160.59/160.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 160.59/160.58 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.58 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_ivl__disj__un_I11_J,axiom,
% 160.59/160.58 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2))
% 160.59/160.58 => 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) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_ivl__disj__int_I5_J,axiom,
% 160.59/160.58 ! [V_u_2,V_l_2,T_a] :
% 160.59/160.58 ( class_Orderings_Oorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zmod__zmult2__eq,axiom,
% 160.59/160.58 ! [V_b,V_a,V_c] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_greaterThan__Suc,axiom,
% 160.59/160.58 ! [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)))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_incr__lemma,axiom,
% 160.59/160.58 ! [V_x,V_z,V_d] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 160.59/160.58 => 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)))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_decr__lemma,axiom,
% 160.59/160.58 ! [V_z,V_x,V_d] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 160.59/160.58 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.58 & class_Groups_Ocomm__monoid__mult(T_a) )
% 160.59/160.58 => ( V_A_2 = V_B_2
% 160.59/160.58 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 160.59/160.58 => ( ! [B_x] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 160.59/160.58 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 160.59/160.58 => 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) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_setprod__pos__nat,axiom,
% 160.59/160.58 ! [V_f_2,V_S_2,T_a] :
% 160.59/160.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.58 => ( ! [B_x] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 160.59/160.58 => 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))) )
% 160.59/160.58 => 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))) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_card__less__Suc2,axiom,
% 160.59/160.58 ! [V_i_2,V_M_2] :
% 160.59/160.58 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 160.59/160.58 => 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))))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_CollectI,axiom,
% 160.59/160.58 ! [T_a,V_a_2,V_P_2] :
% 160.59/160.58 ( hBOOL(hAPP(V_P_2,V_a_2))
% 160.59/160.58 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__Collect__conjI,axiom,
% 160.59/160.58 ! [V_Q_2,V_P_2,T_a] :
% 160.59/160.58 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 160.59/160.58 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) )
% 160.59/160.58 => 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)))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_setsum__abs,axiom,
% 160.59/160.58 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => 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))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__Collect__less__nat,axiom,
% 160.59/160.58 ! [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)))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__Collect__le__nat,axiom,
% 160.59/160.58 ! [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)))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_setsum__abs__ge__zero,axiom,
% 160.59/160.58 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => 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))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__minus__commute,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__less,axiom,
% 160.59/160.58 ! [V_n,V_m] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.58 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__less__eq__dividend,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__mult__distrib2,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__mult__distrib,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__divide,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__ge__self,axiom,
% 160.59/160.58 ! [V_a,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__le__D1,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 160.59/160.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__eq__0,axiom,
% 160.59/160.58 ! [V_a_2,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.58 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__zero,axiom,
% 160.59/160.58 ! [T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__add__abs,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__mult__self,axiom,
% 160.59/160.58 ! [V_a,T_a] :
% 160.59/160.58 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__mult,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__one,axiom,
% 160.59/160.58 ! [T_a] :
% 160.59/160.58 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.58 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_empty__Collect__eq,axiom,
% 160.59/160.58 ! [V_P_2,T_a] :
% 160.59/160.58 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2)
% 160.59/160.58 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Collect__empty__eq,axiom,
% 160.59/160.58 ! [V_P_2,T_a] :
% 160.59/160.58 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__idempotent,axiom,
% 160.59/160.58 ! [V_a,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Collect__def,axiom,
% 160.59/160.58 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ).
% 160.59/160.58
% 160.59/160.58 fof(fact_power__abs,axiom,
% 160.59/160.58 ! [V_n,V_a,T_a] :
% 160.59/160.58 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__of__nat,axiom,
% 160.59/160.58 ! [V_n,T_a] :
% 160.59/160.58 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__int__eq,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_CollectE,axiom,
% 160.59/160.58 ! [V_P_2,V_a_2,T_a] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 160.59/160.58 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_CollectD,axiom,
% 160.59/160.58 ! [V_P_2,V_a_2,T_a] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 160.59/160.58 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mem__Collect__eq,axiom,
% 160.59/160.58 ! [V_P_2,V_a_2,T_a] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 160.59/160.58 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Collect__mem__eq,axiom,
% 160.59/160.58 ! [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 ).
% 160.59/160.58
% 160.59/160.58 fof(fact_empty__def,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__Collect__disjI,axiom,
% 160.59/160.58 ! [V_Q_2,V_P_2,T_a] :
% 160.59/160.58 ( 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))))
% 160.59/160.58 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 160.59/160.58 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_insert__Collect,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__setsum__abs,axiom,
% 160.59/160.58 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Collect__disj__eq,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Collect__conj__eq,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__setprod,axiom,
% 160.59/160.58 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.58 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__ge__zero,axiom,
% 160.59/160.58 ! [V_a,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => 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))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__le__zero__iff,axiom,
% 160.59/160.58 ! [V_a_2,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => ( 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)))
% 160.59/160.58 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__of__nonneg,axiom,
% 160.59/160.58 ! [V_a,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.58 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__not__less__zero,axiom,
% 160.59/160.58 ! [V_a,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => ~ 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))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zero__less__abs__iff,axiom,
% 160.59/160.58 ! [V_a_2,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => ( 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)))
% 160.59/160.58 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__of__pos,axiom,
% 160.59/160.58 ! [V_a,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.58 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__triangle__ineq,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => 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)))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__mult__less,axiom,
% 160.59/160.58 ! [V_d,V_b,V_c,V_a,T_a] :
% 160.59/160.58 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 160.59/160.58 => 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))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__triangle__ineq2__sym,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => 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)))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__triangle__ineq2,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => 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)))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__triangle__ineq3,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => 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)))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_nonzero__abs__divide,axiom,
% 160.59/160.58 ! [V_a,V_b,T_a] :
% 160.59/160.58 ( class_Fields_Olinordered__field(T_a)
% 160.59/160.58 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__Suc,axiom,
% 160.59/160.58 ! [V_n,V_m] :
% 160.59/160.58 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 160.59/160.58 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 160.59/160.58 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__1,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__less__divisor,axiom,
% 160.59/160.58 ! [V_m,V_n] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__eq__0__iff,axiom,
% 160.59/160.58 ! [V_d_2,V_m_2] :
% 160.59/160.58 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.58 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__geq,axiom,
% 160.59/160.58 ! [V_n,V_m] :
% 160.59/160.58 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__if,axiom,
% 160.59/160.58 ! [V_n,V_m] :
% 160.59/160.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.58 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 160.59/160.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.58 => 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) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__mult__self3,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_le__mod__geq,axiom,
% 160.59/160.58 ! [V_m,V_n] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__zmult__eq__1,axiom,
% 160.59/160.58 ! [V_n,V_m] :
% 160.59/160.58 ( 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)
% 160.59/160.58 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zmod__int,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_div__add1__eq,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_insert__compr__raw,axiom,
% 160.59/160.58 ! [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))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_insert__compr,axiom,
% 160.59/160.58 ! [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))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Un__def,axiom,
% 160.59/160.58 ! [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))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Int__Collect,axiom,
% 160.59/160.58 ! [V_P_2,V_A_2,V_x_2,T_a] :
% 160.59/160.58 ( 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))))
% 160.59/160.58 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Int__def,axiom,
% 160.59/160.58 ! [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))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Collect__conv__if,axiom,
% 160.59/160.58 ! [T_a,V_a_2,V_P_2] :
% 160.59/160.58 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 160.59/160.58 => 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))) )
% 160.59/160.58 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Collect__conv__if2,axiom,
% 160.59/160.58 ! [T_a,V_a_2,V_P_2] :
% 160.59/160.58 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 160.59/160.58 => 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))) )
% 160.59/160.58 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_singleton__conv,axiom,
% 160.59/160.58 ! [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))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_singleton__conv2,axiom,
% 160.59/160.58 ! [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))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_set__diff__eq,axiom,
% 160.59/160.58 ! [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)))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_insert__def,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__M__bounded__by__nat,axiom,
% 160.59/160.58 ! [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))))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__mult__pos,axiom,
% 160.59/160.58 ! [V_y,V_x,T_a] :
% 160.59/160.58 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__eq__mult,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Rings_Oordered__ring__abs(T_a)
% 160.59/160.58 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.58 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 160.59/160.58 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 160.59/160.58 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__diff__triangle__ineq,axiom,
% 160.59/160.58 ! [V_d,V_c,V_b,V_a,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => 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))))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__triangle__ineq4,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.58 => 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)))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zero__le__power__abs,axiom,
% 160.59/160.58 ! [V_n,V_a,T_a] :
% 160.59/160.58 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.58 => 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))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_abs__div__pos,axiom,
% 160.59/160.58 ! [V_x,V_y,T_a] :
% 160.59/160.58 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__le__divisor,axiom,
% 160.59/160.58 ! [V_m,V_n] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zabs__less__one__iff,axiom,
% 160.59/160.58 ! [V_z_2] :
% 160.59/160.58 ( 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)))
% 160.59/160.58 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__mult__self4,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_nat__abs__mult__distrib,axiom,
% 160.59/160.58 ! [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))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_div__mult1__eq,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__mult2__eq,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zero__le__zpower__abs,axiom,
% 160.59/160.58 ! [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))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_div__mod__equality_H,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mult__div__cancel,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Divides_Omod__div__equality_H,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_setsum__setsum__restrict,axiom,
% 160.59/160.58 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] :
% 160.59/160.58 ( class_Groups_Ocomm__monoid__add(T_c)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 160.59/160.58 => 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) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_if__image__distrib,axiom,
% 160.59/160.58 ! [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))))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_nat__seg__image__imp__finite,axiom,
% 160.59/160.58 ! [V_n_2,V_f_2,T_a,V_A_2] :
% 160.59/160.58 ( 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)))
% 160.59/160.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_split__mod,axiom,
% 160.59/160.58 ! [V_k_2,V_n_2,V_P_2] :
% 160.59/160.58 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 160.59/160.58 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.58 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 160.59/160.58 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.58 => ! [B_i,B_j] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 160.59/160.58 => ( 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)
% 160.59/160.58 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_mod__lemma,axiom,
% 160.59/160.58 ! [V_q,V_b,V_r,V_c] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 160.59/160.58 => 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))) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Suc__times__mod__eq,axiom,
% 160.59/160.58 ! [V_m,V_k] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 160.59/160.58 ! [V_y,V_x] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_nat__mod__distrib,axiom,
% 160.59/160.58 ! [V_y,V_x] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_zero__less__zpower__abs__iff,axiom,
% 160.59/160.58 ! [V_n_2,V_x_2] :
% 160.59/160.58 ( 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)))
% 160.59/160.58 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.58 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_setsum__restrict__set_H,axiom,
% 160.59/160.58 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] :
% 160.59/160.58 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => 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) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_setsum__image__gen,axiom,
% 160.59/160.58 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] :
% 160.59/160.58 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_card__less__Suc,axiom,
% 160.59/160.58 ! [V_i_2,V_M_2] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 160.59/160.58 => 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))))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_card__less,axiom,
% 160.59/160.58 ! [V_i_2,V_M_2] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_dom__override__on,axiom,
% 160.59/160.58 ! [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))))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_dom__if,axiom,
% 160.59/160.58 ! [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)))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_setsum__multicount,axiom,
% 160.59/160.58 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] :
% 160.59/160.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 160.59/160.58 => ( ! [B_x] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2))
% 160.59/160.58 => 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 )
% 160.59/160.58 => 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)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_setsum__multicount__gen,axiom,
% 160.59/160.58 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] :
% 160.59/160.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2))
% 160.59/160.58 => ( ! [B_x] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2))
% 160.59/160.58 => 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) )
% 160.59/160.58 => 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) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_inf__Sup1__distrib,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Lattices_Odistrib__lattice(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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))))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__Collect__subsets,axiom,
% 160.59/160.58 ! [V_A_2,T_a] :
% 160.59/160.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => 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)))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Pow__def,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__image__set,axiom,
% 160.59/160.58 ! [V_f_2,T_b,V_P_2,T_a] :
% 160.59/160.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 160.59/160.58 => 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))))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__Collect__bounded__ex,axiom,
% 160.59/160.58 ! [V_Q_2,T_b,V_P_2,T_a] :
% 160.59/160.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 160.59/160.58 => ( 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)))))
% 160.59/160.58 <=> ! [B_y] :
% 160.59/160.58 ( hBOOL(hAPP(V_P_2,B_y))
% 160.59/160.58 => 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)))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 160.59/160.58 ! [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))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 160.59/160.58 ! [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)))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 160.59/160.58 ! [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)))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_sup__Inf1__distrib,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Lattices_Odistrib__lattice(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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))))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_sup__Inf2__distrib,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Lattices_Odistrib__lattice(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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))))))) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_inf__Sup2__distrib,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Lattices_Odistrib__lattice(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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))))))) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_add__Min__commute,axiom,
% 160.59/160.58 ! [V_k_2,V_N_2,T_a] :
% 160.59/160.58 ( class_Groups_Olinordered__ab__semigroup__add(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 160.59/160.58 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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))))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_add__Max__commute,axiom,
% 160.59/160.58 ! [V_k_2,V_N_2,T_a] :
% 160.59/160.58 ( class_Groups_Olinordered__ab__semigroup__add(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 160.59/160.58 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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))))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__conv__nat__seg__image,axiom,
% 160.59/160.58 ! [V_A_2,T_a] :
% 160.59/160.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 <=> ? [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))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_nat0__intermed__int__val,axiom,
% 160.59/160.58 ! [V_k_2,V_f_2,V_n_2] :
% 160.59/160.58 ( ! [B_i] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 160.59/160.58 => 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))) )
% 160.59/160.58 => ( 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))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 160.59/160.58 => ? [B_i] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 160.59/160.58 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_int__val__lemma,axiom,
% 160.59/160.58 ! [V_k_2,V_f_2,V_n_2] :
% 160.59/160.58 ( ! [B_i] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 160.59/160.58 => 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))) )
% 160.59/160.58 => ( 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))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 160.59/160.58 => ? [B_i] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 160.59/160.58 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max_Osingleton,axiom,
% 160.59/160.58 ! [V_x_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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 ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min_Osingleton,axiom,
% 160.59/160.58 ! [V_x_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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 ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max__ge,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => 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))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min__le,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => 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)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max__in,axiom,
% 160.59/160.58 ! [V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min__in,axiom,
% 160.59/160.58 ! [V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min__antimono,axiom,
% 160.59/160.58 ! [V_N_2,V_M_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
% 160.59/160.58 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 160.59/160.58 => 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))) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max__mono,axiom,
% 160.59/160.58 ! [V_N_2,V_M_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2))
% 160.59/160.58 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 160.59/160.58 => 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))) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min_Oremove,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 )
% 160.59/160.58 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => 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)))))) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max_Oremove,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 )
% 160.59/160.58 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => 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)))))) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_pigeonhole__infinite,axiom,
% 160.59/160.58 ! [V_f_2,T_b,V_A_2,T_a] :
% 160.59/160.58 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 160.59/160.58 => ? [B_x] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.58 & ~ 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)))))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_greaterThan__0,axiom,
% 160.59/160.58 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))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_diff__nat__eq__if,axiom,
% 160.59/160.58 ! [V_z_2,V_z_H_2] :
% 160.59/160.58 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 160.59/160.58 => 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) )
% 160.59/160.58 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_top1I,axiom,
% 160.59/160.58 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_UNIV__I,axiom,
% 160.59/160.58 ! [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)))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__diff,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__fun__UNIVD2,axiom,
% 160.59/160.58 ! [T_b,T_a] :
% 160.59/160.58 ( 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))))
% 160.59/160.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oless__supI2,axiom,
% 160.59/160.58 ! [V_a,V_b,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 160.59/160.58 => 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))) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oless__supI1,axiom,
% 160.59/160.58 ! [V_b,V_a,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 160.59/160.58 => 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))) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_max__less__iff__conj,axiom,
% 160.59/160.58 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( 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))
% 160.59/160.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2))
% 160.59/160.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_less__max__iff__disj,axiom,
% 160.59/160.58 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( 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)))
% 160.59/160.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2))
% 160.59/160.58 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oless__infI2,axiom,
% 160.59/160.58 ! [V_a,V_x,V_b,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oless__infI1,axiom,
% 160.59/160.58 ! [V_b,V_x,V_a,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__less__iff__disj,axiom,
% 160.59/160.58 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( 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))
% 160.59/160.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2))
% 160.59/160.58 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__less__iff__conj,axiom,
% 160.59/160.58 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( 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)))
% 160.59/160.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2))
% 160.59/160.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_max__add__distrib__left,axiom,
% 160.59/160.58 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__add__distrib__left,axiom,
% 160.59/160.58 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_sup__max,axiom,
% 160.59/160.58 ! [T_a] :
% 160.59/160.58 ( ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.58 & class_Orderings_Olinorder(T_a) )
% 160.59/160.58 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_max__0L,axiom,
% 160.59/160.58 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 160.59/160.58
% 160.59/160.58 fof(fact_max__0R,axiom,
% 160.59/160.58 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Odistrib__inf__le,axiom,
% 160.59/160.58 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Odistrib__sup__le,axiom,
% 160.59/160.58 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__option__UNIV,axiom,
% 160.59/160.58 ! [T_a] :
% 160.59/160.58 ( 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))))
% 160.59/160.58 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__Prod__UNIV,axiom,
% 160.59/160.58 ! [T_b,T_a] :
% 160.59/160.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 160.59/160.58 => 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)))) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_top__apply,axiom,
% 160.59/160.58 ! [V_x_2,T_b,T_a] :
% 160.59/160.58 ( class_Orderings_Otop(T_a)
% 160.59/160.58 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup_Oidem,axiom,
% 160.59/160.58 ! [V_a,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf_Oidem,axiom,
% 160.59/160.58 ! [V_a,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup_Ocommute,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup__commute,axiom,
% 160.59/160.58 ! [V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf_Ocommute,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__commute,axiom,
% 160.59/160.58 ! [V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup__inf__absorb,axiom,
% 160.59/160.58 ! [V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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 ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 160.59/160.58 ! [V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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 ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup__left__idem,axiom,
% 160.59/160.58 ! [V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 160.59/160.58 ! [V_b,V_a,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__left__idem,axiom,
% 160.59/160.58 ! [V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 160.59/160.58 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup__left__commute,axiom,
% 160.59/160.58 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 160.59/160.58 ! [V_c,V_a,V_b,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__left__commute,axiom,
% 160.59/160.58 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 160.59/160.58 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 160.59/160.58 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup_Oassoc,axiom,
% 160.59/160.58 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup__assoc,axiom,
% 160.59/160.58 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf_Oassoc,axiom,
% 160.59/160.58 ! [V_c,V_b,V_a,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__assoc,axiom,
% 160.59/160.58 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 160.59/160.58 ! [V_x,V_z,V_y,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 160.59/160.58 ! [V_x,V_z,V_y,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max_Oidem,axiom,
% 160.59/160.58 ! [V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min_Oidem,axiom,
% 160.59/160.58 ! [V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Sup__UNIV,axiom,
% 160.59/160.58 ! [T_a] :
% 160.59/160.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Union__UNIV,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_UNIV__Plus__UNIV,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ole__infE,axiom,
% 160.59/160.58 ! [V_b,V_a,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( 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)))
% 160.59/160.58 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 160.59/160.58 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__mono,axiom,
% 160.59/160.58 ! [V_d,V_b,V_c,V_a,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 160.59/160.58 => 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))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__greatest,axiom,
% 160.59/160.58 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 160.59/160.58 => 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))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ole__infI,axiom,
% 160.59/160.58 ! [V_b,V_a,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 160.59/160.58 => 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))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__absorb2,axiom,
% 160.59/160.58 ! [V_x,V_y,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 160.59/160.58 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__absorb1,axiom,
% 160.59/160.58 ! [V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.58 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ole__infI2,axiom,
% 160.59/160.58 ! [V_a,V_x,V_b,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ole__infI1,axiom,
% 160.59/160.58 ! [V_b,V_x,V_a,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ole__inf__iff,axiom,
% 160.59/160.58 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( 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)))
% 160.59/160.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 160.59/160.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ole__iff__inf,axiom,
% 160.59/160.58 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 160.59/160.58 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__le2,axiom,
% 160.59/160.58 ! [V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__le1,axiom,
% 160.59/160.58 ! [V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__le__iff__disj,axiom,
% 160.59/160.58 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( 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))
% 160.59/160.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 160.59/160.58 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ole__supE,axiom,
% 160.59/160.58 ! [V_x,V_b,V_a,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( 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))
% 160.59/160.58 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 160.59/160.58 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup__mono,axiom,
% 160.59/160.58 ! [V_d,V_b,V_c,V_a,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 160.59/160.58 => 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))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup__least,axiom,
% 160.59/160.58 ! [V_z,V_x,V_y,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 160.59/160.58 => 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)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ole__supI,axiom,
% 160.59/160.58 ! [V_b,V_x,V_a,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 160.59/160.58 => 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)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup__absorb1,axiom,
% 160.59/160.58 ! [V_x,V_y,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 160.59/160.58 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup__absorb2,axiom,
% 160.59/160.58 ! [V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.58 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ole__supI2,axiom,
% 160.59/160.58 ! [V_a,V_b,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 160.59/160.58 => 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))) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ole__supI1,axiom,
% 160.59/160.58 ! [V_b,V_a,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 160.59/160.58 => 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))) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ole__sup__iff,axiom,
% 160.59/160.58 ! [V_z_2,V_y_2,V_x_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( 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))
% 160.59/160.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2))
% 160.59/160.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ole__iff__sup,axiom,
% 160.59/160.58 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 160.59/160.58 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_le__maxI2,axiom,
% 160.59/160.58 ! [V_x,V_y,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_le__maxI1,axiom,
% 160.59/160.58 ! [V_y,V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_le__max__iff__disj,axiom,
% 160.59/160.58 ! [V_y_2,V_x_2,V_z_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( 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)))
% 160.59/160.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2))
% 160.59/160.58 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Int__greaterThanLessThan,axiom,
% 160.59/160.58 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Int__greaterThanAtMost,axiom,
% 160.59/160.58 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Int__atLeastAtMost,axiom,
% 160.59/160.58 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Int__atLeastLessThan,axiom,
% 160.59/160.58 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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_c_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_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__Suc__Suc,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_max__Suc__Suc,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__0L,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__0R,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_inf__min,axiom,
% 160.59/160.58 ! [T_a] :
% 160.59/160.58 ( ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.58 & class_Orderings_Olinorder(T_a) )
% 160.59/160.58 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Pow__UNIV,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__diff__distrib__left,axiom,
% 160.59/160.58 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_max__diff__distrib__left,axiom,
% 160.59/160.58 ! [V_z,V_y,V_x,T_a] :
% 160.59/160.58 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Int__UNIV__right,axiom,
% 160.59/160.58 ! [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 ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Int__UNIV__left,axiom,
% 160.59/160.58 ! [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 ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Un__UNIV__right,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Un__UNIV__left,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_subset__UNIV,axiom,
% 160.59/160.58 ! [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)))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__UNIV,axiom,
% 160.59/160.58 ! [T_a] :
% 160.59/160.58 ( class_Finite__Set_Ofinite(T_a)
% 160.59/160.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_UNIV__not__empty,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__Plus__UNIV__iff,axiom,
% 160.59/160.58 ! [T_b,T_a] :
% 160.59/160.58 ( 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))))
% 160.59/160.58 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 160.59/160.58 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_not__neg__0,axiom,
% 160.59/160.58 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 160.59/160.58 ! [T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 160.59/160.58 ! [T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_not__neg__int,axiom,
% 160.59/160.58 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_not__neg__1,axiom,
% 160.59/160.58 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_infinite__UNIV__nat,axiom,
% 160.59/160.58 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_UNIV__def,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_range__composition,axiom,
% 160.59/160.58 ! [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)))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_top__greatest,axiom,
% 160.59/160.58 ! [V_x,T_a] :
% 160.59/160.58 ( class_Orderings_Otop(T_a)
% 160.59/160.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_sup__top__left,axiom,
% 160.59/160.58 ! [V_x,T_a] :
% 160.59/160.58 ( class_Lattices_Obounded__lattice__top(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_sup__top__right,axiom,
% 160.59/160.58 ! [V_x,T_a] :
% 160.59/160.58 ( class_Lattices_Obounded__lattice__top(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_inf__top__left,axiom,
% 160.59/160.58 ! [V_x,T_a] :
% 160.59/160.58 ( class_Lattices_Obounded__lattice__top(T_a)
% 160.59/160.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_inf__top__right,axiom,
% 160.59/160.58 ! [V_x,T_a] :
% 160.59/160.58 ( class_Lattices_Obounded__lattice__top(T_a)
% 160.59/160.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_inf__eq__top__iff,axiom,
% 160.59/160.58 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.58 ( class_Lattices_Obounded__lattice__top(T_a)
% 160.59/160.58 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a)
% 160.59/160.58 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a)
% 160.59/160.58 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_UN__lessThan__UNIV,axiom,
% 160.59/160.58 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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_UN__atMost__UNIV,axiom,
% 160.59/160.58 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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_nat__minus__add__max,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_range__eqI,axiom,
% 160.59/160.58 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] :
% 160.59/160.58 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 160.59/160.58 => 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))))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_rangeI,axiom,
% 160.59/160.58 ! [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))))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_UN__atLeast__UNIV,axiom,
% 160.59/160.58 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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Diff__UNIV,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_comp__surj,axiom,
% 160.59/160.58 ! [V_g_2,T_c,V_f_2,T_a,T_b] :
% 160.59/160.58 ( 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))
% 160.59/160.58 => ( 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))
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 160.59/160.58 ! [V_A_2,T_a] :
% 160.59/160.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 160.59/160.58 => ( 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)))
% 160.59/160.58 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_not__neg__eq__ge__0,axiom,
% 160.59/160.58 ! [V_x_2] :
% 160.59/160.58 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 160.59/160.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_neg__def,axiom,
% 160.59/160.58 ! [V_Z_2] :
% 160.59/160.58 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 160.59/160.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_neg__nat,axiom,
% 160.59/160.58 ! [V_z] :
% 160.59/160.58 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 160.59/160.58 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_not__neg__nat,axiom,
% 160.59/160.58 ! [V_z] :
% 160.59/160.58 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 160.59/160.58 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__Collect__not,axiom,
% 160.59/160.58 ! [V_P_2,T_a] :
% 160.59/160.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2)))
% 160.59/160.58 => ( 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))))
% 160.59/160.58 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_SUP__UN__eq,axiom,
% 160.59/160.58 ! [V_x_2,V_r_2,T_b,T_a] :
% 160.59/160.58 ( 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))
% 160.59/160.58 <=> 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))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__range__imageI,axiom,
% 160.59/160.58 ! [V_f_2,T_c,V_g_2,T_b,T_a] :
% 160.59/160.58 ( 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)))))
% 160.59/160.58 => 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))))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_atLeast__0,axiom,
% 160.59/160.58 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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_max__Suc1,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_max__Suc2,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ofold__sup__insert,axiom,
% 160.59/160.58 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ofold__inf__insert,axiom,
% 160.59/160.58 ! [V_a_2,V_b_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => 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)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max_Oin__idem,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => 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) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min_Oin__idem,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => 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) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Int__atLeastAtMostR1,axiom,
% 160.59/160.58 ! [V_d_2,V_c_2,V_b_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Int__atLeastAtMostL1,axiom,
% 160.59/160.58 ! [V_d_2,V_b_2,V_a_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Int__atLeastAtMostR2,axiom,
% 160.59/160.58 ! [V_d_2,V_c_2,V_a_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),V_d_2) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Int__atLeastAtMostL2,axiom,
% 160.59/160.58 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),V_b_2) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max_OF__eq,axiom,
% 160.59/160.58 ! [V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => 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) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min_OF__eq,axiom,
% 160.59/160.58 ! [V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => 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) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__Suc2,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__Suc1,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 160.59/160.58 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.58 => 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))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 160.59/160.58 ! [V_b_2,V_a_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.58 => 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))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Ofold1__belowI,axiom,
% 160.59/160.58 ! [V_a_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.58 => 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)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_UN__UN__finite__eq,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( 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)))
% 160.59/160.58 <=> ! [B_x] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_fold1__below__iff,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( 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))
% 160.59/160.58 <=> ? [B_x] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_fold1__strict__below__iff,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( 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))
% 160.59/160.58 <=> ? [B_x] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_strict__below__fold1__iff,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( 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)))
% 160.59/160.58 <=> ! [B_x] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max__insert,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min__insert,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max_Osubset__idem,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.58 => 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) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min_Osubset__idem,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.58 => 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) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max__Un,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min__Un,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 160.59/160.58 ! [V_a_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => 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) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 160.59/160.58 ! [V_a_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => 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) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__UNIV__card__ge__0,axiom,
% 160.59/160.58 ! [T_a] :
% 160.59/160.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 160.59/160.58 => 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))))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max_Oinsert,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min_Oinsert,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_fold1__antimono,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => 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))) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max_Oinsert__remove,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 160.59/160.58 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => 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)))))) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max_Ounion__disjoint,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( 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))
% 160.59/160.58 => 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)) ) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max_Ounion__inter,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( 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))
% 160.59/160.58 => 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)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min_Oinsert__remove,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 )
% 160.59/160.58 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => 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)))))) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min_Ounion__disjoint,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( 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))
% 160.59/160.58 => 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)) ) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min_Ounion__inter,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( 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))
% 160.59/160.58 => 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)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max_Oeq__fold_H,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => 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) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min_Oeq__fold_H,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => 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) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__fun__UNIVD1,axiom,
% 160.59/160.58 ! [T_b,T_a] :
% 160.59/160.58 ( 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))))
% 160.59/160.58 => ( 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))
% 160.59/160.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_dual__min,axiom,
% 160.59/160.58 ! [T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_dual__max,axiom,
% 160.59/160.58 ! [T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_UN__finite2__subset,axiom,
% 160.59/160.58 ! [V_B_2,V_k_2,V_A_2,T_a] :
% 160.59/160.58 ( ! [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)))
% 160.59/160.58 => 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))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_max__ord__max,axiom,
% 160.59/160.58 ! [T_a] :
% 160.59/160.58 ( class_Orderings_Oord(T_a)
% 160.59/160.58 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_inf__nat__def,axiom,
% 160.59/160.58 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_sup__nat__def,axiom,
% 160.59/160.58 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_card__UNIV__unit,axiom,
% 160.59/160.58 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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_infinite__UNIV__int,axiom,
% 160.59/160.58 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__ord__min,axiom,
% 160.59/160.58 ! [T_a] :
% 160.59/160.58 ( class_Orderings_Oord(T_a)
% 160.59/160.58 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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))))))) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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))))))) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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))))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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))))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__le__Sup,axiom,
% 160.59/160.58 ! [V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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))) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => 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) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => 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) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 160.59/160.58 ! [V_x_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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 ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 160.59/160.58 ! [V_x_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => 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 ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 160.59/160.58 ! [V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => 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) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 160.59/160.58 ! [V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => 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) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.58 => 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) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.58 => 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) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 160.59/160.58 ! [V_a_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.58 => 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 ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 160.59/160.58 ! [V_a_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.58 => 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 ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 160.59/160.58 ! [V_a_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => 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) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 160.59/160.58 ! [V_a_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => 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) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => 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 )
% 160.59/160.58 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => 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)))))) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => 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 )
% 160.59/160.58 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => 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)))))) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( 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))
% 160.59/160.58 => 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)) ) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( 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))
% 160.59/160.58 => 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)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( 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))
% 160.59/160.58 => 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)) ) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2))
% 160.59/160.58 => ( 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))
% 160.59/160.58 => 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)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => 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) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => 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) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 )
% 160.59/160.58 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => 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)))))) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 160.59/160.58 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.58 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 )
% 160.59/160.58 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_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))
% 160.59/160.58 => 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)))))) ) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 160.59/160.58 ! [V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( ! [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))))))
% 160.59/160.58 => 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)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 160.59/160.58 ! [V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( ! [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))))))
% 160.59/160.58 => 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)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max_Oclosed,axiom,
% 160.59/160.58 ! [V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( ! [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))))))
% 160.59/160.58 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min_Oclosed,axiom,
% 160.59/160.58 ! [V_A_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => ( ! [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))))))
% 160.59/160.58 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_UN__finite2__eq,axiom,
% 160.59/160.58 ! [V_B_2,V_k_2,V_A_2,T_a] :
% 160.59/160.58 ( ! [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)
% 160.59/160.58 => 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) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_UN__finite__subset,axiom,
% 160.59/160.58 ! [V_C_2,V_A_2,T_a] :
% 160.59/160.58 ( ! [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))
% 160.59/160.58 => 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)) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_iso__tuple__UNIV__I,axiom,
% 160.59/160.58 ! [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)))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 160.59/160.58 ! [V_N_2,V_h_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( ! [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))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 160.59/160.58 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_o__eq__dest__lhs,axiom,
% 160.59/160.58 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_a,T_b,T_c] :
% 160.59/160.58 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_c_2
% 160.59/160.58 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_K__record__comp,axiom,
% 160.59/160.58 ! [V_x_2,V_f_2,V_c_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_c_2)),V_f_2),V_x_2) = V_c_2 ).
% 160.59/160.58
% 160.59/160.58 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 160.59/160.58 ! [V_N_2,V_h_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( ! [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))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 160.59/160.58 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Max_Ohom__commute,axiom,
% 160.59/160.58 ! [V_N_2,V_h_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( ! [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))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 160.59/160.58 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Min_Ohom__commute,axiom,
% 160.59/160.58 ! [V_N_2,V_h_2,T_a] :
% 160.59/160.58 ( class_Orderings_Olinorder(T_a)
% 160.59/160.58 => ( ! [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))
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2))
% 160.59/160.58 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.58 => 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)) ) ) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_INFI__fold__inf,axiom,
% 160.59/160.58 ! [V_f_2,V_A_2,T_a,T_b] :
% 160.59/160.58 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 160.59/160.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.58 => 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) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_INT__D,axiom,
% 160.59/160.58 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 160.59/160.58 ( 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)))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 160.59/160.58 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_INT__E,axiom,
% 160.59/160.58 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 160.59/160.58 ( 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)))
% 160.59/160.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2)))
% 160.59/160.58 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_INF1__E,axiom,
% 160.59/160.58 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.58 ( 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))
% 160.59/160.58 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 160.59/160.58 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_INF1__D,axiom,
% 160.59/160.58 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.58 ( 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))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.58 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_INF2__E,axiom,
% 160.59/160.58 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 160.59/160.58 ( 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_c_2))
% 160.59/160.58 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 160.59/160.58 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_INF2__D,axiom,
% 160.59/160.58 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 160.59/160.58 ( 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_c_2))
% 160.59/160.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.58 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_finite__INT,axiom,
% 160.59/160.58 ! [V_A_2,T_b,V_I_2,T_a] :
% 160.59/160.58 ( ? [B_x] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2))
% 160.59/160.58 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) )
% 160.59/160.58 => 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))) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.58 ( 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)
% 160.59/160.58 <=> ! [B_x] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 160.59/160.58 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 160.59/160.58 ! [V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.58 ( 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))
% 160.59/160.58 <=> ! [B_x] :
% 160.59/160.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 160.59/160.58 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Un__INT__distrib2,axiom,
% 160.59/160.58 ! [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))) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_INT__extend__simps_I6_J,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_Un__INT__distrib,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_INT__extend__simps_I7_J,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_INT__simps_I6_J,axiom,
% 160.59/160.58 ! [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) ).
% 160.59/160.58
% 160.59/160.58 fof(fact_INT__simps_I7_J,axiom,
% 160.59/160.58 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__Int__distrib,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Pow__INT__eq,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INF__commute,axiom,
% 160.59/160.59 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__extend__simps_I8_J,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__simps_I8_J,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INFI__apply,axiom,
% 160.59/160.59 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__extend__simps_I10_J,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__simps_I10_J,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__subset__iff,axiom,
% 160.59/160.59 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 <=> ! [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 160.59/160.59 => 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))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__extend__simps_I5_J,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__simps_I5_J,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__iff,axiom,
% 160.59/160.59 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 <=> ! [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__simps_I9_J,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__extend__simps_I9_J,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__INF__iff,axiom,
% 160.59/160.59 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> ! [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INF__less__iff,axiom,
% 160.59/160.59 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] :
% 160.59/160.59 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.59 & class_Orderings_Olinorder(T_a) )
% 160.59/160.59 => ( 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))
% 160.59/160.59 <=> ? [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 160.59/160.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__insert__distrib,axiom,
% 160.59/160.59 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2))
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__lower,axiom,
% 160.59/160.59 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INF__INT__eq,axiom,
% 160.59/160.59 ! [V_x_2,V_r_2,T_b,T_a] :
% 160.59/160.59 ( 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))
% 160.59/160.59 <=> 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__absorb,axiom,
% 160.59/160.59 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2))
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INF__const,axiom,
% 160.59/160.59 ! [V_M_2,T_a,V_A_2,T_b] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 160.59/160.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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 ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__empty,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__constant,axiom,
% 160.59/160.59 ! [V_c_2,T_b,T_a,V_A_2] :
% 160.59/160.59 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) )
% 160.59/160.59 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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_c_2)) = V_c_2 ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__extend__simps_I2_J,axiom,
% 160.59/160.59 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 160.59/160.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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 )
% 160.59/160.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__extend__simps_I1_J,axiom,
% 160.59/160.59 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 160.59/160.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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 )
% 160.59/160.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__insert,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__Un,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_UN__simps_I7_J,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_UN__extend__simps_I7_J,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INF__subset,axiom,
% 160.59/160.59 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.59 => 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))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__simps_I1_J,axiom,
% 160.59/160.59 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 160.59/160.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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)) )
% 160.59/160.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__simps_I2_J,axiom,
% 160.59/160.59 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 160.59/160.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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)) )
% 160.59/160.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Collect__all__eq,axiom,
% 160.59/160.59 ! [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))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__simps_I3_J,axiom,
% 160.59/160.59 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 160.59/160.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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)) )
% 160.59/160.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__extend__simps_I3_J,axiom,
% 160.59/160.59 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 160.59/160.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__extend__simps_I4_J,axiom,
% 160.59/160.59 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 160.59/160.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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 )
% 160.59/160.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INF__leI,axiom,
% 160.59/160.59 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2))
% 160.59/160.59 => 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))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__greaterThan__UNIV,axiom,
% 160.59/160.59 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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INT__simps_I4_J,axiom,
% 160.59/160.59 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] :
% 160.59/160.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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)) )
% 160.59/160.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_inf__INFI__fold__inf,axiom,
% 160.59/160.59 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.59 => 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) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inf__fold__inf,axiom,
% 160.59/160.59 ! [V_A_2,T_a] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.59 => 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) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_setsum__cases,axiom,
% 160.59/160.59 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] :
% 160.59/160.59 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.59 => 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))))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__mod__eq__lemma,axiom,
% 160.59/160.59 ! [V_y,V_n,V_x] :
% 160.59/160.59 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 160.59/160.59 => ? [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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zdiv__zminus1__eq__if,axiom,
% 160.59/160.59 ! [V_a,V_b] :
% 160.59/160.59 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.59 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.59 => 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)) )
% 160.59/160.59 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.59 => 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)) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_finite__Inter,axiom,
% 160.59/160.59 ! [V_M_2,T_a] :
% 160.59/160.59 ( ? [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2))
% 160.59/160.59 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) )
% 160.59/160.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_InterE,axiom,
% 160.59/160.59 ! [V_X_2,V_C_2,V_A_2,T_a] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_InterD,axiom,
% 160.59/160.59 ! [V_X_2,V_C_2,V_A_2,T_a] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_ComplI,axiom,
% 160.59/160.59 ! [V_A_2,V_c_2,T_a] :
% 160.59/160.59 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_negative__zle,axiom,
% 160.59/160.59 ! [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))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_negative__zless,axiom,
% 160.59/160.59 ! [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))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INF2__iff,axiom,
% 160.59/160.59 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] :
% 160.59/160.59 ( 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_c_2))
% 160.59/160.59 <=> ! [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INF1__iff,axiom,
% 160.59/160.59 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.59 ( 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))
% 160.59/160.59 <=> ! [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inter__def,axiom,
% 160.59/160.59 ! [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))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__divide__left,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Rings_Odivision__ring(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__divide__divide,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__divide__right,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zminus__zadd__distrib,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zmult__zminus,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__anti__mono,axiom,
% 160.59/160.59 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__subset__Compl__iff,axiom,
% 160.59/160.59 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zminus__0,axiom,
% 160.59/160.59 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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__less__iff__less,axiom,
% 160.59/160.59 ! [V_a_2,V_b_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__less__iff,axiom,
% 160.59/160.59 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__minus__iff,axiom,
% 160.59/160.59 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__add__cancel,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => 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 ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_add__minus__cancel,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => 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 ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__add,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__add__distrib,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Groups_Oab__group__add(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__mult__right,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Rings_Oring(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__mult__left,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Rings_Oring(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__mult__commute,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Rings_Oring(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__mult__minus,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Rings_Oring(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_square__eq__iff,axiom,
% 160.59/160.59 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.59 ( class_Rings_Oidom(T_a)
% 160.59/160.59 => ( 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)
% 160.59/160.59 <=> ( V_a_2 = V_b_2
% 160.59/160.59 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_ComplE,axiom,
% 160.59/160.59 ! [V_A_2,V_c_2,T_a] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 160.59/160.59 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_ComplD,axiom,
% 160.59/160.59 ! [V_A_2,V_c_2,T_a] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 160.59/160.59 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__iff,axiom,
% 160.59/160.59 ! [V_A_2,V_c_2,T_a] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 160.59/160.59 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zminus__zminus,axiom,
% 160.59/160.59 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 160.59/160.59
% 160.59/160.59 fof(fact_double__complement,axiom,
% 160.59/160.59 ! [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 ).
% 160.59/160.59
% 160.59/160.59 fof(fact_double__compl,axiom,
% 160.59/160.59 ! [V_x,T_a] :
% 160.59/160.59 ( class_Lattices_Oboolean__algebra(T_a)
% 160.59/160.59 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_uminus__apply,axiom,
% 160.59/160.59 ! [V_x_2,V_A_2,T_b,T_a] :
% 160.59/160.59 ( class_Groups_Ouminus(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__eq__Compl__iff,axiom,
% 160.59/160.59 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.59 ( 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)
% 160.59/160.59 <=> V_A_2 = V_B_2 ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_compl__eq__compl__iff,axiom,
% 160.59/160.59 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.59 ( class_Lattices_Oboolean__algebra(T_a)
% 160.59/160.59 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)
% 160.59/160.59 <=> V_x_2 = V_y_2 ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_fun__Compl__def,axiom,
% 160.59/160.59 ! [V_x_2,V_A_2,T_b,T_a] :
% 160.59/160.59 ( class_Groups_Ouminus(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__minus,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_equation__minus__iff,axiom,
% 160.59/160.59 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 160.59/160.59 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__equation__iff,axiom,
% 160.59/160.59 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2
% 160.59/160.59 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__equal__iff__equal,axiom,
% 160.59/160.59 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 160.59/160.59 <=> V_a_2 = V_b_2 ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__zero,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__0__equal__iff__equal,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)
% 160.59/160.59 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_equal__neg__zero,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Olinordered__ab__group__add(T_a)
% 160.59/160.59 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)
% 160.59/160.59 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__equal__0__iff__equal,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__equal__zero,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Olinordered__ab__group__add(T_a)
% 160.59/160.59 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2
% 160.59/160.59 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__imp__neg__le,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.59 => 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))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__le__iff__le,axiom,
% 160.59/160.59 ! [V_a_2,V_b_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__le__iff,axiom,
% 160.59/160.59 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => ( 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))
% 160.59/160.59 <=> 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__minus__iff,axiom,
% 160.59/160.59 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> 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))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_compl__mono,axiom,
% 160.59/160.59 ! [V_y,V_x,T_a] :
% 160.59/160.59 ( class_Lattices_Oboolean__algebra(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.59/160.59 => 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))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_compl__le__compl__iff,axiom,
% 160.59/160.59 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.59 ( class_Lattices_Oboolean__algebra(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__diff__eq,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Groups_Oab__group__add(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zdiv__zminus__zminus,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zdiv__zminus2,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zminus__zmod,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zmod__zminus__zminus,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zmod__zminus2,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_abs__minus__cancel,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_mod__minus__cong,axiom,
% 160.59/160.59 ! [V_a_H,V_b,V_a,T_a] :
% 160.59/160.59 ( class_Divides_Oring__div(T_a)
% 160.59/160.59 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 160.59/160.59 => 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) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_mod__minus__eq,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Divides_Oring__div(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_setsum__negf,axiom,
% 160.59/160.59 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.59 ( class_Groups_Oab__group__add(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Collect__neg__eq,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__INT,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__UN,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__Inf__iff,axiom,
% 160.59/160.59 ! [V_A_2,V_b_2,T_a] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> ! [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inf__less__iff,axiom,
% 160.59/160.59 ! [V_a_2,V_S_2,T_a] :
% 160.59/160.59 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.59 & class_Orderings_Olinorder(T_a) )
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2))
% 160.59/160.59 <=> ? [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 160.59/160.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Un__Inter,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_INTER__eq__Inter__image,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inter__image__eq,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__le__self__iff,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Olinordered__ab__group__add(T_a)
% 160.59/160.59 => ( 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))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__le__0__iff__le,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__minus__self__iff,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Olinordered__ab__group__add(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__0__le__iff__le,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__less__nonneg,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Olinordered__ab__group__add(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__less__0__iff__less,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__minus__self__iff,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__0__less__iff__less,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__unique,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_ab__left__minus,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Groups_Oab__group__add(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_left__minus,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 160.59/160.59 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)
% 160.59/160.59 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_right__minus,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_diff__0,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_diff__def,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_ab__diff__minus,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Groups_Oab__group__add(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_diff__minus__eq__add,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Groups_Ogroup__add(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 160.59/160.59 ! [V_y,V_x,T_a] :
% 160.59/160.59 ( class_Rings_Ocomm__ring__1(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_square__eq__1__iff,axiom,
% 160.59/160.59 ! [V_x_2,T_a] :
% 160.59/160.59 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 160.59/160.59 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 160.59/160.59 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
% 160.59/160.59 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 160.59/160.59 ! [V_x,T_a] :
% 160.59/160.59 ( class_Rings_Ocomm__ring__1(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_compl__inf__bot,axiom,
% 160.59/160.59 ! [V_x,T_a] :
% 160.59/160.59 ( class_Lattices_Oboolean__algebra(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_inf__compl__bot,axiom,
% 160.59/160.59 ! [V_x,T_a] :
% 160.59/160.59 ( class_Lattices_Oboolean__algebra(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_diff__eq,axiom,
% 160.59/160.59 ! [V_y,V_x,T_a] :
% 160.59/160.59 ( class_Lattices_Oboolean__algebra(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_compl__bot__eq,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Lattices_Oboolean__algebra(T_a)
% 160.59/160.59 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_compl__top__eq,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Lattices_Oboolean__algebra(T_a)
% 160.59/160.59 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_compl__inf,axiom,
% 160.59/160.59 ! [V_y,V_x,T_a] :
% 160.59/160.59 ( class_Lattices_Oboolean__algebra(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_compl__sup,axiom,
% 160.59/160.59 ! [V_y,V_x,T_a] :
% 160.59/160.59 ( class_Lattices_Oboolean__algebra(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_compl__sup__top,axiom,
% 160.59/160.59 ! [V_x,T_a] :
% 160.59/160.59 ( class_Lattices_Oboolean__algebra(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_sup__compl__top,axiom,
% 160.59/160.59 ! [V_x,T_a] :
% 160.59/160.59 ( class_Lattices_Oboolean__algebra(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nonzero__minus__divide__divide,axiom,
% 160.59/160.59 ! [V_a,V_b,T_a] :
% 160.59/160.59 ( class_Rings_Odivision__ring(T_a)
% 160.59/160.59 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 => 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) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nonzero__minus__divide__right,axiom,
% 160.59/160.59 ! [V_a,V_b,T_a] :
% 160.59/160.59 ( class_Rings_Odivision__ring(T_a)
% 160.59/160.59 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_abs__le__D2,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_abs__leI,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_abs__le__iff,axiom,
% 160.59/160.59 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.59 => ( 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))
% 160.59/160.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2))
% 160.59/160.59 & 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)) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_abs__ge__minus__self,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_abs__less__iff,axiom,
% 160.59/160.59 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2))
% 160.59/160.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2))
% 160.59/160.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_subset__Compl__self__eq,axiom,
% 160.59/160.59 ! [V_A_2,T_a] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__empty__eq,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__UNIV__eq,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_finite__compl,axiom,
% 160.59/160.59 ! [V_A_2,T_a] :
% 160.59/160.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)))
% 160.59/160.59 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__disjoint,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__disjoint2,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__partition2,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__partition,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__Un,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__Int,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__max__eq__min,axiom,
% 160.59/160.59 ! [V_y,V_x,T_a] :
% 160.59/160.59 ( class_Groups_Olinordered__ab__group__add(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__min__eq__max,axiom,
% 160.59/160.59 ! [V_y,V_x,T_a] :
% 160.59/160.59 ( class_Groups_Olinordered__ab__group__add(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_image__uminus__atLeastAtMost,axiom,
% 160.59/160.59 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_abs__power__minus,axiom,
% 160.59/160.59 ! [V_n,V_a,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zadd__zminus__inverse2,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__Diff__eq,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Diff__eq,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Diff__Compl,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_negative__eq__positive,axiom,
% 160.59/160.59 ! [V_m_2,V_n_2] :
% 160.59/160.59 ( 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)
% 160.59/160.59 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.59 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_not__int__zless__negative,axiom,
% 160.59/160.59 ! [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)))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zmod__zminus1__not__zero,axiom,
% 160.59/160.59 ! [V_l,V_k] :
% 160.59/160.59 ( 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)
% 160.59/160.59 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zmod__zminus2__not__zero,axiom,
% 160.59/160.59 ! [V_l,V_k] :
% 160.59/160.59 ( 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)
% 160.59/160.59 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_diff__int__def,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_diff__int__def__symmetric,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Ints__minus,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Rings_Oring__1(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a)))
% 160.59/160.59 => 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))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 160.59/160.59 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inter__lower,axiom,
% 160.59/160.59 ! [V_A_2,V_B_2,T_a] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__eq,axiom,
% 160.59/160.59 ! [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))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__lessThan,axiom,
% 160.59/160.59 ! [V_k_2,T_a] :
% 160.59/160.59 ( class_Orderings_Olinorder(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__atLeast,axiom,
% 160.59/160.59 ! [V_k_2,T_a] :
% 160.59/160.59 ( class_Orderings_Olinorder(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Collect__imp__eq,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__atMost,axiom,
% 160.59/160.59 ! [V_k_2,T_a] :
% 160.59/160.59 ( class_Orderings_Olinorder(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Compl__greaterThan,axiom,
% 160.59/160.59 ! [V_k_2,T_a] :
% 160.59/160.59 ( class_Orderings_Olinorder(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inter__anti__mono,axiom,
% 160.59/160.59 ! [V_A_2,V_B_2,T_a] :
% 160.59/160.59 ( 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))
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inter__empty,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inter__insert,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inter__UNIV,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inf__lower,axiom,
% 160.59/160.59 ! [V_A_2,V_x_2,T_a] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_abs__of__nonpos,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.59 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_abs__minus__le__zero,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_abs__of__neg,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.59 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_abs__if,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Groups_Oabs__if(T_a)
% 160.59/160.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.59 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.59 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inter__Un__distrib,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_power__minus,axiom,
% 160.59/160.59 ! [V_n,V_a,T_a] :
% 160.59/160.59 ( class_Rings_Oring__1(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Int__Inter__image,axiom,
% 160.59/160.59 ! [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))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inf__singleton,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.59 => 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 ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_disjoint__eq__subset__Compl,axiom,
% 160.59/160.59 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.59 ( 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))
% 160.59/160.59 <=> 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inf__empty,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inf__UNIV,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_surj__Compl__image__subset,axiom,
% 160.59/160.59 ! [V_A_2,V_f_2,T_a,T_b] :
% 160.59/160.59 ( 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))
% 160.59/160.59 => 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)))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inf__insert,axiom,
% 160.59/160.59 ! [V_A_2,V_a_2,T_a] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_int__zle__neg,axiom,
% 160.59/160.59 ! [V_m_2,V_n_2] :
% 160.59/160.59 ( 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))))
% 160.59/160.59 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.59 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_negative__zle__0,axiom,
% 160.59/160.59 ! [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))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__zminus__int,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zmod__zminus2__eq__if,axiom,
% 160.59/160.59 ! [V_b,V_a] :
% 160.59/160.59 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.59 => 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) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zmod__zminus1__eq__if,axiom,
% 160.59/160.59 ! [V_b,V_a] :
% 160.59/160.59 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zabs__def,axiom,
% 160.59/160.59 ! [V_i] :
% 160.59/160.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.59 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.59 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_image__uminus__atLeastLessThan,axiom,
% 160.59/160.59 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 160.59/160.59 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__zminus__int,axiom,
% 160.59/160.59 ! [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))))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_image__uminus__lessThan,axiom,
% 160.59/160.59 ! [V_x_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_image__uminus__greaterThan,axiom,
% 160.59/160.59 ! [V_x_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_image__uminus__atMost,axiom,
% 160.59/160.59 ! [V_x_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_image__uminus__atLeast,axiom,
% 160.59/160.59 ! [V_x_2,T_a] :
% 160.59/160.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Pow__Compl,axiom,
% 160.59/160.59 ! [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))))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_compl__unique,axiom,
% 160.59/160.59 ! [V_y,V_x,T_a] :
% 160.59/160.59 ( class_Lattices_Oboolean__algebra(T_a)
% 160.59/160.59 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 160.59/160.59 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 160.59/160.59 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_not__zle__0__negative,axiom,
% 160.59/160.59 ! [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))))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_negative__zless__0,axiom,
% 160.59/160.59 ! [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))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Int__eq__Inter,axiom,
% 160.59/160.59 ! [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))))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inter__Un__subset,axiom,
% 160.59/160.59 ! [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)))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inf__binary,axiom,
% 160.59/160.59 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_inf__Inf__fold__inf,axiom,
% 160.59/160.59 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.59 => 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) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inf__fin__Inf,axiom,
% 160.59/160.59 ! [V_A_2,T_a] :
% 160.59/160.59 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__mult__distrib__neg,axiom,
% 160.59/160.59 ! [V_z_H,V_z] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__Max__eq__Min,axiom,
% 160.59/160.59 ! [V_S_2,T_a] :
% 160.59/160.59 ( class_Groups_Olinordered__ab__group__add(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.59 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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)) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__Min__eq__Max,axiom,
% 160.59/160.59 ! [V_S_2,T_a] :
% 160.59/160.59 ( class_Groups_Olinordered__ab__group__add(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.59 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.59 => 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)) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zdiv__zminus2__eq__if,axiom,
% 160.59/160.59 ! [V_a,V_b] :
% 160.59/160.59 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.59 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.59 => 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)) )
% 160.59/160.59 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.59 => 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)) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_z3div__def,axiom,
% 160.59/160.59 ! [V_k,V_l] :
% 160.59/160.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 160.59/160.59 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 160.59/160.59 => 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))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_z3mod__def,axiom,
% 160.59/160.59 ! [V_k,V_l] :
% 160.59/160.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 160.59/160.59 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__of__nat,axiom,
% 160.59/160.59 ! [V_k,T_a] :
% 160.59/160.59 ( class_Rings_Oring__1(T_a)
% 160.59/160.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.59 => 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)))) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.59 => 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)) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_negD,axiom,
% 160.59/160.59 ! [V_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.59 => ? [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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__eq__iff,axiom,
% 160.59/160.59 ! [V_z_2,V_w_2,T_a] :
% 160.59/160.59 ( class_Int_Oring__char__0(T_a)
% 160.59/160.59 => ( 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)
% 160.59/160.59 <=> V_w_2 = V_z_2 ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__int__eq,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__0,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Rings_Oring__1(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__0__eq__iff,axiom,
% 160.59/160.59 ! [V_z_2,T_a] :
% 160.59/160.59 ( class_Int_Oring__char__0(T_a)
% 160.59/160.59 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)
% 160.59/160.59 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__eq__0__iff,axiom,
% 160.59/160.59 ! [V_z_2,T_a] :
% 160.59/160.59 ( class_Int_Oring__char__0(T_a)
% 160.59/160.59 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__le__iff,axiom,
% 160.59/160.59 ! [V_z_2,V_w_2,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__less__iff,axiom,
% 160.59/160.59 ! [V_z_2,V_w_2,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__add,axiom,
% 160.59/160.59 ! [V_z,V_w,T_a] :
% 160.59/160.59 ( class_Rings_Oring__1(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__mult,axiom,
% 160.59/160.59 ! [V_z,V_w,T_a] :
% 160.59/160.59 ( class_Rings_Oring__1(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__1,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Rings_Oring__1(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__diff,axiom,
% 160.59/160.59 ! [V_z,V_w,T_a] :
% 160.59/160.59 ( class_Rings_Oring__1(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__of__nat__eq,axiom,
% 160.59/160.59 ! [V_n,T_a] :
% 160.59/160.59 ( class_Rings_Oring__1(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__minus,axiom,
% 160.59/160.59 ! [V_z,T_a] :
% 160.59/160.59 ( class_Rings_Oring__1(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Ints__of__int,axiom,
% 160.59/160.59 ! [V_z_2,T_a] :
% 160.59/160.59 ( class_Rings_Oring__1(T_a)
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__power,axiom,
% 160.59/160.59 ! [V_n,V_z,T_a] :
% 160.59/160.59 ( class_Rings_Oring__1(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__setsum,axiom,
% 160.59/160.59 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.59 ( class_Rings_Oring__1(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__setprod,axiom,
% 160.59/160.59 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.59 ( ( class_Groups_Ocomm__monoid__mult(T_a)
% 160.59/160.59 & class_Rings_Oring__1(T_a) )
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__le__0__iff,axiom,
% 160.59/160.59 ! [V_z_2,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__0__le__iff,axiom,
% 160.59/160.59 ! [V_z_2,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__0__less__iff,axiom,
% 160.59/160.59 ! [V_z_2,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__less__0__iff,axiom,
% 160.59/160.59 ! [V_z_2,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__nat__nat,axiom,
% 160.59/160.59 ! [V_z,T_a] :
% 160.59/160.59 ( class_Rings_Oring__1(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 160.59/160.59 => 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) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_sgn__if,axiom,
% 160.59/160.59 ! [V_x,T_a] :
% 160.59/160.59 ( class_Groups_Osgn__if(T_a)
% 160.59/160.59 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 160.59/160.59 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 160.59/160.59 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 160.59/160.59 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_sgn__1__neg,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => ( 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))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_sgn__neg,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.59 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zsgn__def,axiom,
% 160.59/160.59 ! [V_i] :
% 160.59/160.59 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.59 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 160.59/160.59 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 160.59/160.59 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 160.59/160.59 => 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)) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_sgn__sgn,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_sgn__0__0,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_sgn0,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Groups_Osgn__if(T_a)
% 160.59/160.59 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_sgn__times,axiom,
% 160.59/160.59 ! [V_b,V_a,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_sgn__less,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_sgn__greater,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_mult__sgn__abs,axiom,
% 160.59/160.59 ! [V_x,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => 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 ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_abs__sgn,axiom,
% 160.59/160.59 ! [V_k,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_sgn__pos,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 160.59/160.59 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_sgn__1__pos,axiom,
% 160.59/160.59 ! [V_a_2,T_a] :
% 160.59/160.59 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.59 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Inter__subset,axiom,
% 160.59/160.59 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.59 ( ! [B_X] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) )
% 160.59/160.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_fold__image__1,axiom,
% 160.59/160.59 ! [V_f_2,V_S_2,T_a,T_b] :
% 160.59/160.59 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2))
% 160.59/160.59 => ( ! [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2))
% 160.59/160.59 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) )
% 160.59/160.59 => 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) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_card_Oneutral,axiom,
% 160.59/160.59 ! [V_A_2,T_a] :
% 160.59/160.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.59 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.59 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 160.59/160.59 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 160.59/160.59 ! [V_c_2,V_b_2,V_A_2,T_a] :
% 160.59/160.59 ( class_Orderings_Olinorder(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.59 => ( ! [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) )
% 160.59/160.59 => 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_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b_2),V_c_2))) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 160.59/160.59 ! [V_c_2,V_b_2,V_A_2,T_a] :
% 160.59/160.59 ( class_Orderings_Olinorder(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.59 => ( ! [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) )
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_c_2),V_A_2))) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_mod__induct__0,axiom,
% 160.59/160.59 ! [V_i_2,V_P_2,V_p_2] :
% 160.59/160.59 ( ! [B_i] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 160.59/160.59 => ( hBOOL(hAPP(V_P_2,B_i))
% 160.59/160.59 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 160.59/160.59 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 160.59/160.59 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_InterI,axiom,
% 160.59/160.59 ! [V_A_2,V_C_2,T_a] :
% 160.59/160.59 ( ! [B_X] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) )
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_fold__image__cong,axiom,
% 160.59/160.59 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] :
% 160.59/160.59 ( class_Groups_Oab__semigroup__mult(T_b)
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.59 => ( ! [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.59 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 160.59/160.59 => 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) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Min__eqI,axiom,
% 160.59/160.59 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.59 ( class_Orderings_Olinorder(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.59 => ( ! [B_y] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) )
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.59 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Max__eqI,axiom,
% 160.59/160.59 ! [V_x_2,V_A_2,T_a] :
% 160.59/160.59 ( class_Orderings_Olinorder(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.59 => ( ! [B_y] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) )
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.59 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_inf__le__fold__inf,axiom,
% 160.59/160.59 ! [V_c_2,V_b_2,V_A_2,T_a] :
% 160.59/160.59 ( class_Lattices_Osemilattice__inf(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.59 => ( ! [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) )
% 160.59/160.59 => 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_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_c_2),V_A_2))) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_fold__sup__le__sup,axiom,
% 160.59/160.59 ! [V_c_2,V_b_2,V_A_2,T_a] :
% 160.59/160.59 ( class_Lattices_Osemilattice__sup(T_a)
% 160.59/160.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.59 => ( ! [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) )
% 160.59/160.59 => 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_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b_2),V_c_2))) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_expand__Suc,axiom,
% 160.59/160.59 ! [V_v] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_com_Osize_I11_J,axiom,
% 160.59/160.59 ! [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))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_com_Osize_I3_J,axiom,
% 160.59/160.59 ! [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))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_setsum__ivl__cong,axiom,
% 160.59/160.59 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_a,T_b] :
% 160.59/160.59 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.59 & class_Orderings_Oord(T_a) )
% 160.59/160.59 => ( V_a_2 = V_c_2
% 160.59/160.59 => ( V_b_2 = V_d_2
% 160.59/160.59 => ( ! [B_x] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),B_x))
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2))
% 160.59/160.59 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 160.59/160.59 => 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_c_2),V_d_2)) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_WTs__elim__cases_I3_J,axiom,
% 160.59/160.59 ! [V_c_2,V_a_2,V_Y_2] :
% 160.59/160.59 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)))
% 160.59/160.59 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_com_Osimps_I36_J,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_com_Osimps_I37_J,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_WT_OLocal,axiom,
% 160.59/160.59 ! [V_a_2,V_Y_2,V_c_2] :
% 160.59/160.59 ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 160.59/160.59 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_WT_Oequations_I3_J,axiom,
% 160.59/160.59 ! [V_a1_2,V_a3_2,V_a2_2] :
% 160.59/160.59 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2)))
% 160.59/160.59 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_com_Osimps_I40_J,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_com_Osimps_I41_J,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_number__of__reorient,axiom,
% 160.59/160.59 ! [V_x_2,V_w_2,T_a] :
% 160.59/160.59 ( class_Int_Onumber(T_a)
% 160.59/160.59 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2
% 160.59/160.59 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_eq__number__of,axiom,
% 160.59/160.59 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.59 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 & class_Int_Oring__char__0(T_a) )
% 160.59/160.59 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 160.59/160.59 <=> V_x_2 = V_y_2 ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_com_Osimps_I2_J,axiom,
% 160.59/160.59 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 160.59/160.59 ( 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)
% 160.59/160.59 <=> ( V_loc_2 = V_loc_H_2
% 160.59/160.59 & V_fun_2 = V_fun_H_2
% 160.59/160.59 & V_com_2 = V_com_H_2 ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__nat__number__of__lemma,axiom,
% 160.59/160.59 ! [V_v,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => ( ( 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)))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => 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) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__nat__number__of__eq,axiom,
% 160.59/160.59 ! [V_v,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => 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) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_com_Osimps_I38_J,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_com_Osimps_I39_J,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_number__of__eq,axiom,
% 160.59/160.59 ! [V_k,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_of__int__number__of__eq,axiom,
% 160.59/160.59 ! [V_v,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_com_Osimps_I35_J,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_com_Osimps_I34_J,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_com_Osimps_I11_J,axiom,
% 160.59/160.59 ! [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 ).
% 160.59/160.59
% 160.59/160.59 fof(fact_com_Osimps_I10_J,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__number__of__eq__not__less,axiom,
% 160.59/160.59 ! [V_w_2,V_v_2,T_a] :
% 160.59/160.59 ( ( class_Int_Onumber(T_a)
% 160.59/160.59 & class_Orderings_Olinorder(T_a) )
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> ~ 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))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_left__distrib__number__of,axiom,
% 160.59/160.59 ! [V_v,V_b,V_a,T_b] :
% 160.59/160.59 ( ( class_Int_Onumber(T_b)
% 160.59/160.59 & class_Rings_Osemiring(T_b) )
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_right__distrib__number__of,axiom,
% 160.59/160.59 ! [V_c,V_b,V_v,T_b] :
% 160.59/160.59 ( ( class_Int_Onumber(T_b)
% 160.59/160.59 & class_Rings_Osemiring(T_b) )
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_right__diff__distrib__number__of,axiom,
% 160.59/160.59 ! [V_c,V_b,V_v,T_b] :
% 160.59/160.59 ( ( class_Int_Onumber(T_b)
% 160.59/160.59 & class_Rings_Oring(T_b) )
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_left__diff__distrib__number__of,axiom,
% 160.59/160.59 ! [V_v,V_b,V_a,T_b] :
% 160.59/160.59 ( ( class_Int_Onumber(T_b)
% 160.59/160.59 & class_Rings_Oring(T_b) )
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__number__of,axiom,
% 160.59/160.59 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.59 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 & class_Rings_Olinordered__idom(T_a) )
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__number__of,axiom,
% 160.59/160.59 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.59 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 & class_Rings_Olinordered__idom(T_a) )
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_min__number__of,axiom,
% 160.59/160.59 ! [V_v,V_u,T_b] :
% 160.59/160.59 ( ( class_Int_Onumber(T_b)
% 160.59/160.59 & class_Orderings_Oord(T_b) )
% 160.59/160.59 => ( ( 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)))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => 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) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_max__number__of,axiom,
% 160.59/160.59 ! [V_v,V_u,T_b] :
% 160.59/160.59 ( ( class_Int_Onumber(T_b)
% 160.59/160.59 & class_Orderings_Oord(T_b) )
% 160.59/160.59 => ( ( 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)))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => 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) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_number__of__add,axiom,
% 160.59/160.59 ! [V_w,V_v,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_add__number__of__eq,axiom,
% 160.59/160.59 ! [V_w,V_v,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_add__number__of__left,axiom,
% 160.59/160.59 ! [V_z,V_w,V_v,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_number__of__mult,axiom,
% 160.59/160.59 ! [V_w,V_v,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_arith__simps_I32_J,axiom,
% 160.59/160.59 ! [V_w,V_v,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_mult__number__of__left,axiom,
% 160.59/160.59 ! [V_z,V_w,V_v,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_number__of__diff,axiom,
% 160.59/160.59 ! [V_w,V_v,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_arith__simps_I30_J,axiom,
% 160.59/160.59 ! [V_w,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_number__of__minus,axiom,
% 160.59/160.59 ! [V_w,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Ints__number__of,axiom,
% 160.59/160.59 ! [V_w_2,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_eq__divide__eq__number__of1,axiom,
% 160.59/160.59 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 160.59/160.59 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.59 & class_Int_Onumber(T_a) )
% 160.59/160.59 => ( 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))
% 160.59/160.59 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 => 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 )
% 160.59/160.59 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_eq__divide__eq__number__of,axiom,
% 160.59/160.59 ! [V_c_2,V_b_2,V_w_2,T_a] :
% 160.59/160.59 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.59 & class_Int_Onumber(T_a) )
% 160.59/160.59 => ( 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_c_2)
% 160.59/160.59 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2) = V_b_2 )
% 160.59/160.59 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_divide__eq__eq__number__of,axiom,
% 160.59/160.59 ! [V_w_2,V_c_2,V_b_2,T_a] :
% 160.59/160.59 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.59 & class_Int_Onumber(T_a) )
% 160.59/160.59 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)
% 160.59/160.59 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 => 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_c_2) )
% 160.59/160.59 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_divide__eq__eq__number__of1,axiom,
% 160.59/160.59 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 160.59/160.59 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.59 & class_Int_Onumber(T_a) )
% 160.59/160.59 => ( 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
% 160.59/160.59 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 => 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)) )
% 160.59/160.59 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_add__number__of__diff1,axiom,
% 160.59/160.59 ! [V_c,V_w,V_v,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__number__of__mult,axiom,
% 160.59/160.59 ! [V_z,V_w,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_diff__number__of__eq,axiom,
% 160.59/160.59 ! [V_w,V_v,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_divide__less__eq__number__of1,axiom,
% 160.59/160.59 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 160.59/160.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.59 & class_Int_Onumber(T_a) )
% 160.59/160.59 => ( 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))
% 160.59/160.59 <=> ( ( 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)))
% 160.59/160.59 => 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)))) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => ( ( 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)))
% 160.59/160.59 => 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)) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_divide__less__eq__number__of,axiom,
% 160.59/160.59 ! [V_w_2,V_c_2,V_b_2,T_a] :
% 160.59/160.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.59 & class_Int_Onumber(T_a) )
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 160.59/160.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.59 => 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_c_2))) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.59 => 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_c_2)),V_b_2)) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.59 => 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))) ) ) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__divide__eq__number__of,axiom,
% 160.59/160.59 ! [V_c_2,V_b_2,V_w_2,T_a] :
% 160.59/160.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.59 & class_Int_Onumber(T_a) )
% 160.59/160.59 => ( 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_c_2)))
% 160.59/160.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.59 => 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_c_2)),V_b_2)) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.59 => 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_c_2))) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.59 => 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))) ) ) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__divide__eq__number__of1,axiom,
% 160.59/160.59 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 160.59/160.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.59 & class_Int_Onumber(T_a) )
% 160.59/160.59 => ( 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))))
% 160.59/160.59 <=> ( ( 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)))
% 160.59/160.59 => 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)) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => ( ( 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)))
% 160.59/160.59 => 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)))) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_abs__number__of,axiom,
% 160.59/160.59 ! [V_x,T_a] :
% 160.59/160.59 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 & class_Rings_Olinordered__idom(T_a) )
% 160.59/160.59 => ( ( 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)))
% 160.59/160.59 => 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)) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => 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) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_add__number__of__diff2,axiom,
% 160.59/160.59 ! [V_w,V_c,V_v,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_divide__le__eq__number__of1,axiom,
% 160.59/160.59 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 160.59/160.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.59 & class_Int_Onumber(T_a) )
% 160.59/160.59 => ( 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))
% 160.59/160.59 <=> ( ( 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)))
% 160.59/160.59 => 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)))) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => ( ( 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)))
% 160.59/160.59 => 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)) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_divide__le__eq__number__of,axiom,
% 160.59/160.59 ! [V_w_2,V_c_2,V_b_2,T_a] :
% 160.59/160.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.59 & class_Int_Onumber(T_a) )
% 160.59/160.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))
% 160.59/160.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.59 => 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_c_2))) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.59 => 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_c_2)),V_b_2)) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.59 => 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))) ) ) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__divide__eq__number__of,axiom,
% 160.59/160.59 ! [V_c_2,V_b_2,V_w_2,T_a] :
% 160.59/160.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.59 & class_Int_Onumber(T_a) )
% 160.59/160.59 => ( 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_c_2)))
% 160.59/160.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.59 => 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_c_2)),V_b_2)) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 160.59/160.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.59 => 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_c_2))) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.59 => 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))) ) ) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__divide__eq__number__of1,axiom,
% 160.59/160.59 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 160.59/160.59 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.59 & class_Int_Onumber(T_a) )
% 160.59/160.59 => ( 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))))
% 160.59/160.59 <=> ( ( 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)))
% 160.59/160.59 => 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)) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => ( ( 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)))
% 160.59/160.59 => 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)))) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_one__mod__nat__number__of,axiom,
% 160.59/160.59 ! [V_v_H] :
% 160.59/160.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 160.59/160.59 => 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)) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 160.59/160.59 => 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))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_one__div__nat__number__of,axiom,
% 160.59/160.59 ! [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))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_power__number__of__odd__number__of,axiom,
% 160.59/160.59 ! [V_v_2,V_w_2,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => ( ( 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)))
% 160.59/160.59 => 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))) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => 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) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_power__nat__number__of__number__of,axiom,
% 160.59/160.59 ! [V_w,V_v] :
% 160.59/160.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => 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)) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => 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))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__numeral__code_I5_J,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__eq__number__of__int__code,axiom,
% 160.59/160.59 ! [V_l_2,V_k_2] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__number__of__int__code,axiom,
% 160.59/160.59 ! [V_l_2,V_k_2] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_plus__numeral__code_I9_J,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_number__of__is__id,axiom,
% 160.59/160.59 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 160.59/160.59
% 160.59/160.59 fof(fact_times__numeral__code_I5_J,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__number__of__Bit1,axiom,
% 160.59/160.59 ! [V_w_2] :
% 160.59/160.59 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 160.59/160.59 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_rel__simps_I34_J,axiom,
% 160.59/160.59 ! [V_l_2,V_k_2] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__eq__int__code_I16_J,axiom,
% 160.59/160.59 ! [V_k2_2,V_k1_2] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_rel__simps_I17_J,axiom,
% 160.59/160.59 ! [V_l_2,V_k_2] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__int__code_I16_J,axiom,
% 160.59/160.59 ! [V_k2_2,V_k1_2] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_rel__simps_I51_J,axiom,
% 160.59/160.59 ! [V_l_2,V_k_2] :
% 160.59/160.59 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 160.59/160.59 <=> V_k_2 = V_l_2 ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_int__number__of__def,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_bin__less__0__simps_I4_J,axiom,
% 160.59/160.59 ! [V_w_2] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Bit1__def,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__number__of__def,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__number__of,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__number__of__Bit1,axiom,
% 160.59/160.59 ! [V_w_2] :
% 160.59/160.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 160.59/160.59 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 160.59/160.59 => 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)))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_number__of__Bit1,axiom,
% 160.59/160.59 ! [V_w,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_power__number__of__odd,axiom,
% 160.59/160.59 ! [V_z_2,V_w_2,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => ( ( 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)))
% 160.59/160.59 => 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))) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => 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) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zpower__number__of__odd,axiom,
% 160.59/160.59 ! [V_z_2,V_w_2] :
% 160.59/160.59 ( ( 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)))
% 160.59/160.59 => 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))) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => 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) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__numeral__code_I6_J,axiom,
% 160.59/160.59 ! [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))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__imp__number__of__eq__0,axiom,
% 160.59/160.59 ! [V_v] :
% 160.59/160.59 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_int__eq__iff__number__of,axiom,
% 160.59/160.59 ! [V_v_2,V_m_2] :
% 160.59/160.59 ( 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)
% 160.59/160.59 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 160.59/160.59 & 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))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_eq__nat__number__of,axiom,
% 160.59/160.59 ! [V_v_H_2,V_v_2] :
% 160.59/160.59 ( 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)
% 160.59/160.59 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 160.59/160.59 => 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))) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 160.59/160.59 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 160.59/160.59 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 160.59/160.59 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__number__of__add__left,axiom,
% 160.59/160.59 ! [V_k,V_v_H,V_v] :
% 160.59/160.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 160.59/160.59 => 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) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_int__nat__number__of,axiom,
% 160.59/160.59 ! [V_v] :
% 160.59/160.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => 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) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_mod__nat__number__of,axiom,
% 160.59/160.59 ! [V_v_H,V_v] :
% 160.59/160.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 160.59/160.59 => 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))) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_div__nat__number__of,axiom,
% 160.59/160.59 ! [V_v_H,V_v] :
% 160.59/160.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => 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))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_power__nat__number__of,axiom,
% 160.59/160.59 ! [V_n,V_v] :
% 160.59/160.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Suc__nat__number__of__add,axiom,
% 160.59/160.59 ! [V_n,V_v] :
% 160.59/160.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => 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) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_diff__nat__number__of,axiom,
% 160.59/160.59 ! [V_v_2,V_v_H_2] :
% 160.59/160.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_min__number__of__Suc,axiom,
% 160.59/160.59 ! [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)))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_min__Suc__number__of,axiom,
% 160.59/160.59 ! [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)))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_rel__simps_I46_J,axiom,
% 160.59/160.59 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 160.59/160.59
% 160.59/160.59 fof(fact_rel__simps_I39_J,axiom,
% 160.59/160.59 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_succ__Pls,axiom,
% 160.59/160.59 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__Pls,axiom,
% 160.59/160.59 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 160.59/160.59
% 160.59/160.59 fof(fact_succ__pred,axiom,
% 160.59/160.59 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 160.59/160.59
% 160.59/160.59 fof(fact_mult__Pls,axiom,
% 160.59/160.59 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 160.59/160.59
% 160.59/160.59 fof(fact_add__Pls,axiom,
% 160.59/160.59 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 160.59/160.59
% 160.59/160.59 fof(fact_add__Pls__right,axiom,
% 160.59/160.59 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 160.59/160.59
% 160.59/160.59 fof(fact_rel__simps_I2_J,axiom,
% 160.59/160.59 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_rel__simps_I19_J,axiom,
% 160.59/160.59 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Pls__def,axiom,
% 160.59/160.59 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_diff__bin__simps_I1_J,axiom,
% 160.59/160.59 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 160.59/160.59
% 160.59/160.59 fof(fact_semiring__norm_I112_J,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_number__of__Pls,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_add__numeral__0__right,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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 ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_add__numeral__0,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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 ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_bin__less__0__simps_I1_J,axiom,
% 160.59/160.59 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_semiring__norm_I113_J,axiom,
% 160.59/160.59 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__number__of__Pls,axiom,
% 160.59/160.59 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zero__is__num__zero,axiom,
% 160.59/160.59 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_rel__simps_I22_J,axiom,
% 160.59/160.59 ! [V_k_2] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_rel__simps_I12_J,axiom,
% 160.59/160.59 ! [V_k_2] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Suc__diff__number__of,axiom,
% 160.59/160.59 ! [V_m,V_v] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_not__neg__number__of__Pls,axiom,
% 160.59/160.59 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__1__add__number__of,axiom,
% 160.59/160.59 ! [V_v] :
% 160.59/160.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__number__of__add__1,axiom,
% 160.59/160.59 ! [V_v] :
% 160.59/160.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__iff__pred__less,axiom,
% 160.59/160.59 ! [V_l_2,V_k_2] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__Bit1,axiom,
% 160.59/160.59 ! [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))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_pred__def,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__number__of__diff__1,axiom,
% 160.59/160.59 ! [V_v] :
% 160.59/160.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_mult__numeral__1,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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 ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_mult__numeral__1__right,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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 ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_divide__Numeral0,axiom,
% 160.59/160.59 ! [V_x,T_a] :
% 160.59/160.59 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.59 & class_Int_Onumber__ring(T_a) )
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_numeral__1__eq__1,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_semiring__norm_I110_J,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_eq__number__of__0,axiom,
% 160.59/160.59 ! [V_v_2] :
% 160.59/160.59 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_eq__0__number__of,axiom,
% 160.59/160.59 ! [V_v_2] :
% 160.59/160.59 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_number__of2,axiom,
% 160.59/160.59 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))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_rel__simps_I29_J,axiom,
% 160.59/160.59 ! [V_k_2] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_rel__simps_I5_J,axiom,
% 160.59/160.59 ! [V_k_2] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__nat__number__of,axiom,
% 160.59/160.59 ! [V_v_H_2,V_v_2] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 160.59/160.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_divide__numeral__1,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( ( class_Fields_Ofield(T_a)
% 160.59/160.59 & class_Int_Onumber__ring(T_a) )
% 160.59/160.59 => 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 ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_divide__Numeral1,axiom,
% 160.59/160.59 ! [V_x,T_a] :
% 160.59/160.59 ( ( class_Fields_Ofield(T_a)
% 160.59/160.59 & class_Int_Onumber__ring(T_a) )
% 160.59/160.59 => 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 ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__nat__number__of,axiom,
% 160.59/160.59 ! [V_v_H_2,V_v_2] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 160.59/160.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_one__is__num__one,axiom,
% 160.59/160.59 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Numeral1__eq1__nat,axiom,
% 160.59/160.59 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__numeral__1__eq__1,axiom,
% 160.59/160.59 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 160.59/160.59 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_succ__def,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__special_I3_J,axiom,
% 160.59/160.59 ! [V_x_2,T_a] :
% 160.59/160.59 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 & class_Rings_Olinordered__idom(T_a) )
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__special_I1_J,axiom,
% 160.59/160.59 ! [V_y_2,T_a] :
% 160.59/160.59 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 & class_Rings_Olinordered__idom(T_a) )
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__special_I1_J,axiom,
% 160.59/160.59 ! [V_y_2,T_a] :
% 160.59/160.59 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 & class_Rings_Olinordered__idom(T_a) )
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__special_I3_J,axiom,
% 160.59/160.59 ! [V_x_2,T_a] :
% 160.59/160.59 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 & class_Rings_Olinordered__idom(T_a) )
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__0__number__of,axiom,
% 160.59/160.59 ! [V_v_2] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_numeral__1__eq__Suc__0,axiom,
% 160.59/160.59 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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_numeral__3__eq__3,axiom,
% 160.59/160.59 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)))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_power3__eq__cube,axiom,
% 160.59/160.59 ! [V_a,T_a] :
% 160.59/160.59 ( class_Groups_Omonoid__mult(T_a)
% 160.59/160.59 => 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) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 160.59/160.59 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))))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Suc3__eq__add__3,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_add__nat__number__of,axiom,
% 160.59/160.59 ! [V_v_H,V_v] :
% 160.59/160.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 160.59/160.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 160.59/160.59 => 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)) ) ) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 160.59/160.59 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)))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 160.59/160.59 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)))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_number__of__succ,axiom,
% 160.59/160.59 ! [V_k,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_number__of__pred,axiom,
% 160.59/160.59 ! [V_w,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__special_I4_J,axiom,
% 160.59/160.59 ! [V_x_2,T_a] :
% 160.59/160.59 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 & class_Rings_Olinordered__idom(T_a) )
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__special_I2_J,axiom,
% 160.59/160.59 ! [V_y_2,T_a] :
% 160.59/160.59 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 & class_Rings_Olinordered__idom(T_a) )
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__special_I4_J,axiom,
% 160.59/160.59 ! [V_x_2,T_a] :
% 160.59/160.59 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 & class_Rings_Olinordered__idom(T_a) )
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__special_I2_J,axiom,
% 160.59/160.59 ! [V_y_2,T_a] :
% 160.59/160.59 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 & class_Rings_Olinordered__idom(T_a) )
% 160.59/160.59 => ( 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)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_add__special_I2_J,axiom,
% 160.59/160.59 ! [V_w,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_add__special_I3_J,axiom,
% 160.59/160.59 ! [V_v,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 160.59/160.59 ! [V_m,V_n] :
% 160.59/160.59 ( 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))
% 160.59/160.59 => 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)))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__number__of__mult__left,axiom,
% 160.59/160.59 ! [V_k,V_v_H,V_v] :
% 160.59/160.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 160.59/160.59 => 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) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_mult__nat__number__of,axiom,
% 160.59/160.59 ! [V_v_H,V_v] :
% 160.59/160.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 160.59/160.59 => 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) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__number__of__pred__iff__0,axiom,
% 160.59/160.59 ! [V_v_2] :
% 160.59/160.59 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 160.59/160.59 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_div__Suc__eq__div__add3,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Suc__div__eq__add3__div,axiom,
% 160.59/160.59 ! [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) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_diff__special_I2_J,axiom,
% 160.59/160.59 ! [V_v,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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)))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_diff__special_I1_J,axiom,
% 160.59/160.59 ! [V_w,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => 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))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Suc__eq__number__of,axiom,
% 160.59/160.59 ! [V_v_2,V_n_2] :
% 160.59/160.59 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 160.59/160.59 <=> 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))))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_eq__number__of__Suc,axiom,
% 160.59/160.59 ! [V_n_2,V_v_2] :
% 160.59/160.59 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 160.59/160.59 <=> 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))))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__case__number__of,axiom,
% 160.59/160.59 ! [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))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__Suc__number__of,axiom,
% 160.59/160.59 ! [V_v_2,V_n_2] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 <=> 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))))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__number__of__Suc,axiom,
% 160.59/160.59 ! [V_n_2,V_v_2] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 <=> 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)))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__number__of__Suc,axiom,
% 160.59/160.59 ! [V_n_2,V_v_2] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 <=> 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)))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_le__Suc__number__of,axiom,
% 160.59/160.59 ! [V_v_2,V_n_2] :
% 160.59/160.59 ( 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)))
% 160.59/160.59 <=> 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))))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_Suc__nat__number__of,axiom,
% 160.59/160.59 ! [V_v] :
% 160.59/160.59 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 160.59/160.59 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_max__number__of__Suc,axiom,
% 160.59/160.59 ! [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)))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_max__Suc__number__of,axiom,
% 160.59/160.59 ! [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)))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__case__add__eq__if,axiom,
% 160.59/160.59 ! [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)))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__rec__add__eq__if,axiom,
% 160.59/160.59 ! [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))))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_eq__special_I4_J,axiom,
% 160.59/160.59 ! [V_x_2,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 160.59/160.59 <=> 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))))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_eq__special_I2_J,axiom,
% 160.59/160.59 ! [V_y_2,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 160.59/160.59 <=> 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)))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__rec__number__of,axiom,
% 160.59/160.59 ! [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)))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_iszero__0,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.59 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_iszero__def,axiom,
% 160.59/160.59 ! [V_z_2,T_a] :
% 160.59/160.59 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.59 => ( c_Int_Oiszero(T_a,V_z_2)
% 160.59/160.59 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_not__iszero__1,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.59 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__rec__0,axiom,
% 160.59/160.59 ! [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 ).
% 160.59/160.59
% 160.59/160.59 fof(fact_nat__rec__Suc,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_iszero__Numeral0,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_iszero__number__of__Bit1,axiom,
% 160.59/160.59 ! [V_w,T_a] :
% 160.59/160.59 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 & class_Int_Oring__char__0(T_a) )
% 160.59/160.59 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_not__iszero__Numeral1,axiom,
% 160.59/160.59 ! [T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_eq__number__of__eq,axiom,
% 160.59/160.59 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 160.59/160.59 <=> 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)))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_eq__special_I3_J,axiom,
% 160.59/160.59 ! [V_x_2,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.59 <=> 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)))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_eq__special_I1_J,axiom,
% 160.59/160.59 ! [V_y_2,T_a] :
% 160.59/160.59 ( class_Int_Onumber__ring(T_a)
% 160.59/160.59 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2)
% 160.59/160.59 <=> 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)))) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_neg__zmod__mult__2,axiom,
% 160.59/160.59 ! [V_b,V_a] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.59 => 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)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_zmod__number__of__Bit1,axiom,
% 160.59/160.59 ! [V_v,V_w] :
% 160.59/160.59 ( ( 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)))
% 160.59/160.59 => 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)) )
% 160.59/160.59 & ( ~ 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)))
% 160.59/160.59 => 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)) ) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_arith__series__int,axiom,
% 160.59/160.59 ! [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)))) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_rel__simps_I50_J,axiom,
% 160.59/160.59 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_rel__simps_I49_J,axiom,
% 160.59/160.59 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_minus__Bit0,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_mult__Bit0,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_diff__bin__simps_I7_J,axiom,
% 160.59/160.59 ! [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)) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__eq__int__code_I13_J,axiom,
% 160.59/160.59 ! [V_k2_2,V_k1_2] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_rel__simps_I31_J,axiom,
% 160.59/160.59 ! [V_l_2,V_k_2] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_less__int__code_I13_J,axiom,
% 160.59/160.59 ! [V_k2_2,V_k1_2] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 160.59/160.59
% 160.59/160.59 fof(fact_rel__simps_I14_J,axiom,
% 160.59/160.59 ! [V_l_2,V_k_2] :
% 160.59/160.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 160.59/160.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I48_J,axiom,
% 160.59/160.60 ! [V_l_2,V_k_2] :
% 160.59/160.60 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 160.59/160.60 <=> V_k_2 = V_l_2 ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Bit0__def,axiom,
% 160.59/160.60 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_add__Bit0__Bit0,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I44_J,axiom,
% 160.59/160.60 ! [V_k_2] :
% 160.59/160.60 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 160.59/160.60 <=> V_k_2 = c_Int_OPls ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I38_J,axiom,
% 160.59/160.60 ! [V_l_2] :
% 160.59/160.60 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 160.59/160.60 <=> c_Int_OPls = V_l_2 ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Bit0__Pls,axiom,
% 160.59/160.60 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 160.59/160.60
% 160.59/160.60 fof(fact_bin__less__0__simps_I3_J,axiom,
% 160.59/160.60 ! [V_w_2] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I27_J,axiom,
% 160.59/160.60 ! [V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I21_J,axiom,
% 160.59/160.60 ! [V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_less__eq__int__code_I14_J,axiom,
% 160.59/160.60 ! [V_k2_2,V_k1_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I32_J,axiom,
% 160.59/160.60 ! [V_l_2,V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I10_J,axiom,
% 160.59/160.60 ! [V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I4_J,axiom,
% 160.59/160.60 ! [V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_less__int__code_I15_J,axiom,
% 160.59/160.60 ! [V_k2_2,V_k1_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I16_J,axiom,
% 160.59/160.60 ! [V_l_2,V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_add__Bit0__Bit1,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_add__Bit1__Bit0,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_diff__bin__simps_I3_J,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_diff__bin__simps_I10_J,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_diff__bin__simps_I9_J,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zdiv__number__of__Bit0,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_neg__number__of__Bit0,axiom,
% 160.59/160.60 ! [V_w_2] :
% 160.59/160.60 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 160.59/160.60 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pred__Bit0,axiom,
% 160.59/160.60 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pred__Bit1,axiom,
% 160.59/160.60 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_iszero__number__of__Bit0,axiom,
% 160.59/160.60 ! [V_w_2,T_a] :
% 160.59/160.60 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 & class_Int_Oring__char__0(T_a) )
% 160.59/160.60 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2)))
% 160.59/160.60 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_succ__Bit1,axiom,
% 160.59/160.60 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_succ__Bit0,axiom,
% 160.59/160.60 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat__number__of__Bit0,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_number__of__Bit0,axiom,
% 160.59/160.60 ! [V_w,T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_less__eq__int__code_I15_J,axiom,
% 160.59/160.60 ! [V_k2_2,V_k1_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I33_J,axiom,
% 160.59/160.60 ! [V_l_2,V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_less__int__code_I14_J,axiom,
% 160.59/160.60 ! [V_k2_2,V_k1_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I15_J,axiom,
% 160.59/160.60 ! [V_l_2,V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_card__UNIV__bool,axiom,
% 160.59/160.60 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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mult__Bit1,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_diff__bin__simps_I8_J,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_add__Bit1__Bit1,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power__number__of__even,axiom,
% 160.59/160.60 ! [V_w_2,V_z_2,T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zpower__number__of__even,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_double__number__of__Bit0,axiom,
% 160.59/160.60 ! [V_w,T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_number__of1,axiom,
% 160.59/160.60 ! [V_n] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( 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))))
% 160.59/160.60 & 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)))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 160.59/160.60 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power__number__of__even__number__of,axiom,
% 160.59/160.60 ! [V_w_2,V_v_2,T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mult__2,axiom,
% 160.59/160.60 ! [V_z,T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mult__2__right,axiom,
% 160.59/160.60 ! [V_z,T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_one__add__one__is__two,axiom,
% 160.59/160.60 ! [T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zero__power2,axiom,
% 160.59/160.60 ! [T_a] :
% 160.59/160.60 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zero__eq__power2,axiom,
% 160.59/160.60 ! [V_a_2,T_a] :
% 160.59/160.60 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 160.59/160.60 => ( 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)
% 160.59/160.60 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_numeral__2__eq__2,axiom,
% 160.59/160.60 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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_semiring__norm_I115_J,axiom,
% 160.59/160.60 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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power2__eq__square,axiom,
% 160.59/160.60 ! [V_a,T_a] :
% 160.59/160.60 ( class_Groups_Omonoid__mult(T_a)
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 160.59/160.60 ! [V_x,T_a] :
% 160.59/160.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.60 => 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)))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 160.59/160.60 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))))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_add__2__eq__Suc_H,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_add__2__eq__Suc,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_one__power2,axiom,
% 160.59/160.60 ! [T_a] :
% 160.59/160.60 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power2__minus,axiom,
% 160.59/160.60 ! [V_a,T_a] :
% 160.59/160.60 ( class_Rings_Oring__1(T_a)
% 160.59/160.60 => 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)))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat__mult__2__right,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat__mult__2,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power__even__eq,axiom,
% 160.59/160.60 ! [V_n,V_a,T_a] :
% 160.59/160.60 ( class_Groups_Omonoid__mult(T_a)
% 160.59/160.60 => 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)))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 160.59/160.60 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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 160.59/160.60 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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power2__abs,axiom,
% 160.59/160.60 ! [V_a,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.60 => 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)))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_abs__power2,axiom,
% 160.59/160.60 ! [V_a,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.60 => 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)))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat__1__add__1,axiom,
% 160.59/160.60 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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mod2__Suc__Suc,axiom,
% 160.59/160.60 ! [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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_div2__Suc__Suc,axiom,
% 160.59/160.60 ! [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))))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zmod__number__of__Bit0,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_add__self__div__2,axiom,
% 160.59/160.60 ! [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 ).
% 160.59/160.60
% 160.59/160.60 fof(fact_half__gt__zero,axiom,
% 160.59/160.60 ! [V_r,T_a] :
% 160.59/160.60 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.60 & class_Int_Onumber__ring(T_a) )
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 160.59/160.60 => 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)))))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_half__gt__zero__iff,axiom,
% 160.59/160.60 ! [V_r_2,T_a] :
% 160.59/160.60 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 160.59/160.60 & class_Int_Onumber__ring(T_a) )
% 160.59/160.60 => ( 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))))))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zero__le__power2,axiom,
% 160.59/160.60 ! [V_a,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.60 => 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)))))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power2__le__imp__le,axiom,
% 160.59/160.60 ! [V_y,V_x,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.60 => ( 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))))))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 160.59/160.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power2__eq__imp__eq,axiom,
% 160.59/160.60 ! [V_y,V_x,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.60 => ( 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))))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 160.59/160.60 => V_x = V_y ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zero__less__power2,axiom,
% 160.59/160.60 ! [V_a_2,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.60 => ( 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))))))
% 160.59/160.60 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power2__less__0,axiom,
% 160.59/160.60 ! [V_a,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.60 => ~ 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_sum__power2__eq__zero__iff,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.60 => ( 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)
% 160.59/160.60 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.60 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power2__eq__square__number__of,axiom,
% 160.59/160.60 ! [V_w,T_b] :
% 160.59/160.60 ( ( class_Groups_Omonoid__mult(T_b)
% 160.59/160.60 & class_Int_Onumber(T_b) )
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_less__2__cases,axiom,
% 160.59/160.60 ! [V_n] :
% 160.59/160.60 ( 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)))))
% 160.59/160.60 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.60 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat__2,axiom,
% 160.59/160.60 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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power2__eq__1__iff,axiom,
% 160.59/160.60 ! [V_a_2,T_a] :
% 160.59/160.60 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 160.59/160.60 => ( 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)
% 160.59/160.60 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a)
% 160.59/160.60 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 160.59/160.60 ! [V_n,V_x,T_a] :
% 160.59/160.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power__minus__even,axiom,
% 160.59/160.60 ! [V_n,V_a,T_a] :
% 160.59/160.60 ( class_Rings_Oring__1(T_a)
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power2__less__imp__less,axiom,
% 160.59/160.60 ! [V_y,V_x,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__semidom(T_a)
% 160.59/160.60 => ( 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))))))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 160.59/160.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_sum__power2__le__zero__iff,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.60 => ( 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)))
% 160.59/160.60 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.60 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_sum__power2__ge__zero,axiom,
% 160.59/160.60 ! [V_y,V_x,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.60 => 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))))))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_sum__power2__gt__zero__iff,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.60 => ( 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)))))))
% 160.59/160.60 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 160.59/160.60 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_not__sum__power2__lt__zero,axiom,
% 160.59/160.60 ! [V_y,V_x,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.60 => ~ 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power2__sum,axiom,
% 160.59/160.60 ! [V_y,V_x,T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zero__le__even__power_H,axiom,
% 160.59/160.60 ! [V_n,V_a,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.60 => 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)))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power__odd__eq,axiom,
% 160.59/160.60 ! [V_n,V_a,T_a] :
% 160.59/160.60 ( class_Groups_Omonoid__mult(T_a)
% 160.59/160.60 => 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))))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 160.59/160.60 ! [V_n,V_x,T_a] :
% 160.59/160.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power__minus1__even,axiom,
% 160.59/160.60 ! [V_n,T_a] :
% 160.59/160.60 ( class_Rings_Oring__1(T_a)
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zdiv__number__of__Bit1,axiom,
% 160.59/160.60 ! [V_v,V_w] :
% 160.59/160.60 ( ( 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)))
% 160.59/160.60 => 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)) )
% 160.59/160.60 & ( ~ 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)))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mod2__gr__0,axiom,
% 160.59/160.60 ! [V_m_2] :
% 160.59/160.60 ( 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))))))
% 160.59/160.60 <=> 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_div__2__gt__zero,axiom,
% 160.59/160.60 ! [V_n] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 160.59/160.60 => 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)))))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power2__diff,axiom,
% 160.59/160.60 ! [V_y,V_x,T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 160.59/160.60 ! [V_n,V_a,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.60 => ( 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)))))
% 160.59/160.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_odd__power__less__zero,axiom,
% 160.59/160.60 ! [V_n,V_a,T_a] :
% 160.59/160.60 ( class_Rings_Olinordered__idom(T_a)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 160.59/160.60 => 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))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power__minus1__odd,axiom,
% 160.59/160.60 ! [V_n,T_a] :
% 160.59/160.60 ( class_Rings_Oring__1(T_a)
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 160.59/160.60 ! [V_n] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.60 => 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)))))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_of__nat__double,axiom,
% 160.59/160.60 ! [V_x,T_a] :
% 160.59/160.60 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 160.59/160.60 => 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))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pos__zmod__mult__2,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pos__zdiv__mult__2,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_neg__zdiv__mult__2,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_int__of__code,axiom,
% 160.59/160.60 ! [V_k] :
% 160.59/160.60 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 160.59/160.60 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 160.59/160.60 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 160.59/160.60 => ( ( 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)
% 160.59/160.60 => 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)))))) )
% 160.59/160.60 & ( 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)
% 160.59/160.60 => 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)) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_of__int__num,axiom,
% 160.59/160.60 ! [V_k_2,T_a] :
% 160.59/160.60 ( class_Rings_Oring__1(T_a)
% 160.59/160.60 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) )
% 160.59/160.60 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => 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))) )
% 160.59/160.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => 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))))) ) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power__m1__odd,axiom,
% 160.59/160.60 ! [V_n,T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I42_J,axiom,
% 160.59/160.60 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I45_J,axiom,
% 160.59/160.60 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I40_J,axiom,
% 160.59/160.60 c_Int_OMin != c_Int_OPls ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I37_J,axiom,
% 160.59/160.60 c_Int_OPls != c_Int_OMin ).
% 160.59/160.60
% 160.59/160.60 fof(fact_code__numeral__zero__minus__one,axiom,
% 160.59/160.60 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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I7_J,axiom,
% 160.59/160.60 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I24_J,axiom,
% 160.59/160.60 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Bit1__Min,axiom,
% 160.59/160.60 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I43_J,axiom,
% 160.59/160.60 ! [V_l_2] :
% 160.59/160.60 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 160.59/160.60 <=> c_Int_OMin = V_l_2 ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I47_J,axiom,
% 160.59/160.60 ! [V_k_2] :
% 160.59/160.60 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 160.59/160.60 <=> V_k_2 = c_Int_OMin ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_bin__less__0__simps_I2_J,axiom,
% 160.59/160.60 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I23_J,axiom,
% 160.59/160.60 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I20_J,axiom,
% 160.59/160.60 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I26_J,axiom,
% 160.59/160.60 ! [V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I30_J,axiom,
% 160.59/160.60 ! [V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I6_J,axiom,
% 160.59/160.60 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I3_J,axiom,
% 160.59/160.60 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I9_J,axiom,
% 160.59/160.60 ! [V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I13_J,axiom,
% 160.59/160.60 ! [V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I28_J,axiom,
% 160.59/160.60 ! [V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I8_J,axiom,
% 160.59/160.60 ! [V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_eq__number__of__Pls__Min,axiom,
% 160.59/160.60 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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Int_OMin__def,axiom,
% 160.59/160.60 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mult__Min,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_neg__number__of__Min,axiom,
% 160.59/160.60 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pred__Pls,axiom,
% 160.59/160.60 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 160.59/160.60
% 160.59/160.60 fof(fact_add__Min__right,axiom,
% 160.59/160.60 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_add__Min,axiom,
% 160.59/160.60 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pred__Min,axiom,
% 160.59/160.60 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nonzero__number__of__Min,axiom,
% 160.59/160.60 ! [T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_succ__Min,axiom,
% 160.59/160.60 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 160.59/160.60
% 160.59/160.60 fof(fact_diff__bin__simps_I2_J,axiom,
% 160.59/160.60 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mult__minus1,axiom,
% 160.59/160.60 ! [V_z,T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mult__minus1__right,axiom,
% 160.59/160.60 ! [V_z,T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_arith__simps_I31_J,axiom,
% 160.59/160.60 ! [T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_number__of__Min,axiom,
% 160.59/160.60 ! [T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_abs__minus__one,axiom,
% 160.59/160.60 ! [T_a] :
% 160.59/160.60 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 & class_Rings_Olinordered__idom(T_a) )
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divide__minus1,axiom,
% 160.59/160.60 ! [V_x,T_a] :
% 160.59/160.60 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.60 & class_Int_Onumber__ring(T_a) )
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I25_J,axiom,
% 160.59/160.60 ! [V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rel__simps_I11_J,axiom,
% 160.59/160.60 ! [V_k_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zmod__minus1__right,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_diff__bin__simps_I4_J,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_minus__Min,axiom,
% 160.59/160.60 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zmult__eq__1__iff,axiom,
% 160.59/160.60 ! [V_n_2,V_m_2] :
% 160.59/160.60 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 160.59/160.60 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 160.59/160.60 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 160.59/160.60 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 160.59/160.60 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 160.59/160.60 ! [V_n,V_m] :
% 160.59/160.60 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 160.59/160.60 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 160.59/160.60 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_diff__bin__simps_I6_J,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_diff__bin__simps_I5_J,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_of__int__m1,axiom,
% 160.59/160.60 ! [T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zdiv__minus1__right,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zero__code__numeral__code,axiom,
% 160.59/160.60 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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_minus1__divide,axiom,
% 160.59/160.60 ! [V_x,T_a] :
% 160.59/160.60 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 160.59/160.60 & class_Int_Onumber__ring(T_a) )
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_abs__power__minus__one,axiom,
% 160.59/160.60 ! [V_n,T_a] :
% 160.59/160.60 ( ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 & class_Rings_Olinordered__idom(T_a) )
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_div__eq__minus1,axiom,
% 160.59/160.60 ! [V_b] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_div__pos__neg__trivial,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => 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) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zmod__minus1,axiom,
% 160.59/160.60 ! [V_b] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_one__code__numeral__code,axiom,
% 160.59/160.60 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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_power__m1__even,axiom,
% 160.59/160.60 ! [V_n,T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_int__ge__less__than__def,axiom,
% 160.59/160.60 ! [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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_int__ge__less__than2__def,axiom,
% 160.59/160.60 ! [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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_code__numeral_Osize_I1_J,axiom,
% 160.59/160.60 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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat__of__aux__code,axiom,
% 160.59/160.60 ! [V_n,V_i] :
% 160.59/160.60 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 160.59/160.60 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 160.59/160.60 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__int__rel__def,axiom,
% 160.59/160.60 ! [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))))))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Nitpick_Oprod__def,axiom,
% 160.59/160.60 ! [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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__int__correct,axiom,
% 160.59/160.60 ! [V_a,V_b] :
% 160.59/160.60 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Nitpick_OFrac__def,axiom,
% 160.59/160.60 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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 160.59/160.60 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.60 => ( 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)
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_code__numeral_Osize_I2_J,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_code__numeral_Oinject,axiom,
% 160.59/160.60 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 160.59/160.60 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 160.59/160.60 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 160.59/160.60 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Suc__code__numeral__minus__one,axiom,
% 160.59/160.60 ! [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 ).
% 160.59/160.60
% 160.59/160.60 fof(fact_code__numeral_Osize_I4_J,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 160.59/160.60 ! [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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zmult2__lemma,axiom,
% 160.59/160.60 ! [V_c,V_r,V_q,V_b,V_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 160.59/160.60 => 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)))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_sup__Un__eq2,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 <=> 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inf__Int__eq2,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 <=> 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pred__equals__eq2,axiom,
% 160.59/160.60 ! [V_S_2,V_R_2,T_b,T_a] :
% 160.59/160.60 ( 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)
% 160.59/160.60 <=> V_R_2 = V_S_2 ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_bot__empty__eq2,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 <=> 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)))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pred__subset__eq2,axiom,
% 160.59/160.60 ! [V_S_2,V_R_2,T_b,T_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 <=> 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_unique__remainder,axiom,
% 160.59/160.60 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => V_r = V_r_H ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_unique__quotient,axiom,
% 160.59/160.60 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => V_q = V_q_H ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_self__remainder,axiom,
% 160.59/160.60 ! [V_r,V_q,V_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__int__rel__0,axiom,
% 160.59/160.60 ! [V_b] :
% 160.59/160.60 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => 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)))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_SUP__UN__eq2,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 <=> 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_INF__INT__eq2,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 <=> 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_self__quotient,axiom,
% 160.59/160.60 ! [V_r,V_q,V_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__int__rel__mod,axiom,
% 160.59/160.60 ! [V_r,V_q,V_b,V_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__int__rel__div,axiom,
% 160.59/160.60 ! [V_r,V_q,V_b,V_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__int__mod__div,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__int__rel__div__mod,axiom,
% 160.59/160.60 ! [V_a,V_b] :
% 160.59/160.60 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => 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)))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat__gcd_Osimps,axiom,
% 160.59/160.60 ! [V_x,V_y] :
% 160.59/160.60 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.60 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 160.59/160.60 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zadd1__lemma,axiom,
% 160.59/160.60 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => 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)))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zminus1__lemma,axiom,
% 160.59/160.60 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => 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))))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__int__relI,axiom,
% 160.59/160.60 ! [V_r,V_q,V_b,V_a] :
% 160.59/160.60 ( 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)
% 160.59/160.60 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 160.59/160.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 160.59/160.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 160.59/160.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 160.59/160.60 => 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))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_code__numeral_Osize_I3_J,axiom,
% 160.59/160.60 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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_zmult1__lemma,axiom,
% 160.59/160.60 ! [V_a,V_r,V_q,V_c,V_b] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => 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)))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pair__imageI,axiom,
% 160.59/160.60 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_norm__frac_Osimps,axiom,
% 160.59/160.60 ! [V_a_2,V_b_2] :
% 160.59/160.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => 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)) )
% 160.59/160.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 160.59/160.60 => 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)) )
% 160.59/160.60 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 160.59/160.60 => 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))) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_adjust__def,axiom,
% 160.59/160.60 ! [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))))))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_sup2E,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_sup2CI,axiom,
% 160.59/160.60 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] :
% 160.59/160.60 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inf2E,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 160.59/160.60 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inf2I,axiom,
% 160.59/160.60 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mem__splitI,axiom,
% 160.59/160.60 ! [T_c,T_b,V_b_2,V_a_2,V_c_2,V_z_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
% 160.59/160.60 => 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_c_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_splitI,axiom,
% 160.59/160.60 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_prod__caseI,axiom,
% 160.59/160.60 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_bot2E,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_splitD_H,axiom,
% 160.59/160.60 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] :
% 160.59/160.60 ( 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_c_2))
% 160.59/160.60 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_less__by__empty,axiom,
% 160.59/160.60 ! [V_B_2,T_a,V_A_2] :
% 160.59/160.60 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rev__predicate2D,axiom,
% 160.59/160.60 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 160.59/160.60 => ( 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))
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_predicate2D,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_sup2I1,axiom,
% 160.59/160.60 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_sup2I2,axiom,
% 160.59/160.60 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inf2D2,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inf2D1,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Pair__inject,axiom,
% 160.59/160.60 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 160.59/160.60 ( 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)
% 160.59/160.60 => ~ ( V_a = V_a_H
% 160.59/160.60 => V_b != V_b_H ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Pair__eq,axiom,
% 160.59/160.60 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
% 160.59/160.60 ( 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)
% 160.59/160.60 <=> ( V_a_2 = V_a_H_2
% 160.59/160.60 & V_b_2 = V_b_H_2 ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_split__paired__All,axiom,
% 160.59/160.60 ! [T_b,T_a,V_P_2] :
% 160.59/160.60 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 160.59/160.60 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_split__weak__cong,axiom,
% 160.59/160.60 ! [V_c_2,T_c,T_b,T_a,V_q_2,V_p_2] :
% 160.59/160.60 ( V_p_2 = V_q_2
% 160.59/160.60 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_c_2),V_q_2) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_split__twice,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_split__conv,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_prod_Osimps_I2_J,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_splitD,axiom,
% 160.59/160.60 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_split__eta,axiom,
% 160.59/160.60 ! [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 ).
% 160.59/160.60
% 160.59/160.60 fof(fact_The__split__eq,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_split__paired__The,axiom,
% 160.59/160.60 ! [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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_adjust__eq,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_in__rel__def,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2))
% 160.59/160.60 <=> 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_div__mod__code__numeral__def,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 160.59/160.60 ! [V_w] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ( 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))))
% 160.59/160.60 => 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))) )
% 160.59/160.60 & ( ~ 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))))
% 160.59/160.60 => 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)))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_negDivAlg__correct,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_negDivAlg__div__mod,axiom,
% 160.59/160.60 ! [V_l,V_k] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_negDivAlg__minus1,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_negDivAlg_Osimps,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( ( ( 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)))
% 160.59/160.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 160.59/160.60 => 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)) )
% 160.59/160.60 & ( ~ ( 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)))
% 160.59/160.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 160.59/160.60 => 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))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_negDivAlg__eqn,axiom,
% 160.59/160.60 ! [V_a,V_b] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => ( ( 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)))
% 160.59/160.60 => 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)) )
% 160.59/160.60 & ( ~ 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)))
% 160.59/160.60 => 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))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_negDivAlg__eqn__number__of,axiom,
% 160.59/160.60 ! [V_w,V_v] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ( 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))))
% 160.59/160.60 => 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))) )
% 160.59/160.60 & ( ~ 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))))
% 160.59/160.60 => 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)))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Nitpick_Orefl_H__def,axiom,
% 160.59/160.60 ! [V_r_2,T_a] :
% 160.59/160.60 ( c_Nitpick_Orefl_H(T_a,V_r_2)
% 160.59/160.60 <=> ! [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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 160.59/160.60 ! [V_w] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ( 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)))
% 160.59/160.60 => 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)) )
% 160.59/160.60 & ( ~ 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)))
% 160.59/160.60 => 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)))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_posDivAlg__0,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_posDivAlg__correct,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_posDivAlg__div__mod,axiom,
% 160.59/160.60 ! [V_l,V_k] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_posDivAlg__eqn__number__of,axiom,
% 160.59/160.60 ! [V_w,V_v] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ( 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)))
% 160.59/160.60 => 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)) )
% 160.59/160.60 & ( ~ 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)))
% 160.59/160.60 => 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)))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_posDivAlg__eqn,axiom,
% 160.59/160.60 ! [V_a,V_b] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 160.59/160.60 => 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) )
% 160.59/160.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 160.59/160.60 => 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))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_posDivAlg_Osimps,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 160.59/160.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 160.59/160.60 => 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) )
% 160.59/160.60 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 160.59/160.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 160.59/160.60 => 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))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 160.59/160.60 ! [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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__int__def,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 160.59/160.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => 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)) )
% 160.59/160.60 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => 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))) ) ) ) ) )
% 160.59/160.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 160.59/160.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => 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))) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__nat__step,axiom,
% 160.59/160.60 ! [V_m,V_n] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__nat__zero,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__nat__base,axiom,
% 160.59/160.60 ! [V_n,V_m] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_negateSnd__eq,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__nat__div__mod,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__int__rel__neg,axiom,
% 160.59/160.60 ! [V_qr,V_b,V_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__nat__if,axiom,
% 160.59/160.60 ! [V_m_2,V_n_2] :
% 160.59/160.60 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 160.59/160.60 => 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) )
% 160.59/160.60 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__int__pdivmod,axiom,
% 160.59/160.60 ! [V_l_2,V_k_2] :
% 160.59/160.60 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => 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)) )
% 160.59/160.60 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => 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) )
% 160.59/160.60 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => 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)))) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 160.59/160.60 ! [V_a,V_r,V_q,V_c,V_b] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 160.59/160.60 => 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)))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 160.59/160.60 ! [V_c,V_r,V_q,V_b,V_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 160.59/160.60 => 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)))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_apsnd__conv,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__nat__rel__unique,axiom,
% 160.59/160.60 ! [V_qr_H,V_qr,V_n,V_m] :
% 160.59/160.60 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 160.59/160.60 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 160.59/160.60 => V_qr = V_qr_H ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_apsnd__compose,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 160.59/160.60 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__nat__eq,axiom,
% 160.59/160.60 ! [V_qr,V_n,V_m] :
% 160.59/160.60 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 160.59/160.60 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__nat__def,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mod__eq,axiom,
% 160.59/160.60 ! [V_r,V_q,V_n,V_m] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_div__eq,axiom,
% 160.59/160.60 ! [V_r,V_q,V_n,V_m] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_negateSnd__def,axiom,
% 160.59/160.60 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__nat__rel,axiom,
% 160.59/160.60 ! [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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 160.59/160.60 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 160.59/160.60 => 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)))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pdivmod__def,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pdivmod__posDivAlg,axiom,
% 160.59/160.60 ! [V_k,V_l] :
% 160.59/160.60 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => 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)) )
% 160.59/160.60 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__int__code,axiom,
% 160.59/160.60 ! [V_l_2,V_k_2] :
% 160.59/160.60 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => 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)) )
% 160.59/160.60 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => 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) )
% 160.59/160.60 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 => 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)))) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_negDivAlg_Opsimps,axiom,
% 160.59/160.60 ! [V_b_2,V_a_2] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ( ( 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)))
% 160.59/160.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 160.59/160.60 => 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)) )
% 160.59/160.60 & ( ~ ( 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)))
% 160.59/160.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 160.59/160.60 => 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))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_posDivAlg_Opsimps,axiom,
% 160.59/160.60 ! [V_b_2,V_a_2] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 160.59/160.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 160.59/160.60 => 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) )
% 160.59/160.60 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 160.59/160.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 160.59/160.60 => 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))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mod__pos__neg__1__number__of,axiom,
% 160.59/160.60 ! [V_w] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => 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))))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_snd__def,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_snd__apsnd,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_apsnd__eq__conv,axiom,
% 160.59/160.60 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] :
% 160.59/160.60 ( 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)
% 160.59/160.60 <=> 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_snd__conv,axiom,
% 160.59/160.60 ! [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 ).
% 160.59/160.60
% 160.59/160.60 fof(fact_snd__eqD,axiom,
% 160.59/160.60 ! [V_a,V_y,V_x,T_a,T_b] :
% 160.59/160.60 ( 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
% 160.59/160.60 => V_y = V_a ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mod__int__def,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mod__neg__pos,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mod__pos__pos,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mod__pos__pos__1__number__of,axiom,
% 160.59/160.60 ! [V_w] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mod__pos__neg,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => 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)))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mod__neg__neg,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => 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)))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_norm__frac_Opsimps,axiom,
% 160.59/160.60 ! [V_b_2,V_a_2] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => 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)) )
% 160.59/160.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 160.59/160.60 => 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)) )
% 160.59/160.60 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 160.59/160.60 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 160.59/160.60 => 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))) ) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_negDivAlg_Opinduct,axiom,
% 160.59/160.60 ! [V_P_2,V_a1_2,V_a0_2] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ! [B_a,B_b] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ( ~ ( 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)))
% 160.59/160.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 160.59/160.60 => 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))) )
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_posDivAlg_Opinduct,axiom,
% 160.59/160.60 ! [V_P_2,V_a1_2,V_a0_2] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ! [B_a,B_b] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 160.59/160.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 160.59/160.60 => 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))) )
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mod__nat__def,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_accp__subset,axiom,
% 160.59/160.60 ! [V_R2_2,V_R1_2,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_norm__frac_Opinduct,axiom,
% 160.59/160.60 ! [V_P_2,V_a1_2,V_a0_2] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ! [B_a,B_b] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => 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))) )
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_div__pos__neg__1__number__of,axiom,
% 160.59/160.60 ! [V_w] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => 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))))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_prod__eqI,axiom,
% 160.59/160.60 ! [V_q,V_p,T_b,T_a] :
% 160.59/160.60 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 160.59/160.60 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 160.59/160.60 => V_p = V_q ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Pair__fst__snd__eq,axiom,
% 160.59/160.60 ! [T_b,T_a,V_t_2,V_s_2] :
% 160.59/160.60 ( V_s_2 = V_t_2
% 160.59/160.60 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2)
% 160.59/160.60 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_fst__def,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_fst__conv,axiom,
% 160.59/160.60 ! [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 ).
% 160.59/160.60
% 160.59/160.60 fof(fact_fst__eqD,axiom,
% 160.59/160.60 ! [V_a,V_y,V_x,T_b,T_a] :
% 160.59/160.60 ( 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
% 160.59/160.60 => V_x = V_a ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_fst__apsnd,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_surjective__pairing,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pair__collapse,axiom,
% 160.59/160.60 ! [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 ).
% 160.59/160.60
% 160.59/160.60 fof(fact_prod__case__beta,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_div__int__def,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_split__beta,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_split__comp__eq,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_split__def,axiom,
% 160.59/160.60 ! [V_p_2,V_c_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_c_2),V_p_2) = hAPP(hAPP(V_c_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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_split__comp,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_accp_Osimps,axiom,
% 160.59/160.60 ! [V_a_2,V_r_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2))
% 160.59/160.60 <=> ! [B_x] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 160.59/160.60 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_accp_Oequations,axiom,
% 160.59/160.60 ! [V_a_2,V_r_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2))
% 160.59/160.60 <=> ! [B_x] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 160.59/160.60 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_accp__downward,axiom,
% 160.59/160.60 ! [V_a_2,V_b_2,V_r_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 160.59/160.60 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_The__split,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_div__neg__pos,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_div__pos__pos,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_div__pos__pos__1__number__of,axiom,
% 160.59/160.60 ! [V_w] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_div__pos__neg,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => 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)))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_div__neg__neg,axiom,
% 160.59/160.60 ! [V_b,V_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 160.59/160.60 => 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)))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_prod__size__simp,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat__gcd_Opsimps,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.60 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 160.59/160.60 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.60 => 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)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_conjI__realizer,axiom,
% 160.59/160.60 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] :
% 160.59/160.60 ( hBOOL(hAPP(V_P_2,V_p_2))
% 160.59/160.60 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 160.59/160.60 => ( 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))))
% 160.59/160.60 & 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)))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_div__nat__def,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_divmod__nat__rel__def,axiom,
% 160.59/160.60 ! [V_qr_2,V_n_2,V_m_2] :
% 160.59/160.60 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 160.59/160.60 <=> ( 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))
% 160.59/160.60 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.60 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 160.59/160.60 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 & 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)) ) )
% 160.59/160.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 & 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))) ) ) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_exI__realizer,axiom,
% 160.59/160.60 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 160.59/160.60 => 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)))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat_Osize_I2_J,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_in__measure,axiom,
% 160.59/160.60 ! [V_f_2,V_y_2,V_x_2,T_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 <=> 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat__def,axiom,
% 160.59/160.60 ! [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)))))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Rep__Integ__inject,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2] :
% 160.59/160.60 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 160.59/160.60 <=> V_x_2 = V_y_2 ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat_Osize_I1_J,axiom,
% 160.59/160.60 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat__gcd_Opinduct,axiom,
% 160.59/160.60 ! [V_P_2,V_a1_2,V_a0_2] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ! [B_x,B_y] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mlex__leq,axiom,
% 160.59/160.60 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( 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))
% 160.59/160.60 => 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))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mlex__less,axiom,
% 160.59/160.60 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_finite__psubset__def,axiom,
% 160.59/160.60 ! [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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat_Osize_I4_J,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_prod_Orecs,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat__size,axiom,
% 160.59/160.60 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat_Osize_I3_J,axiom,
% 160.59/160.60 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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_in__finite__psubset,axiom,
% 160.59/160.60 ! [V_B_2,V_A_2,T_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.60 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Nats__number__of,axiom,
% 160.59/160.60 ! [V_w_2,T_a] :
% 160.59/160.60 ( class_Int_Onumber__ring(T_a)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 160.59/160.60 => 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))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 160.59/160.60 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.60 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 160.59/160.60 | ? [B_x,B_y] :
% 160.59/160.60 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 160.59/160.60 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2))
% 160.59/160.60 & 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) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_in__lex__prod,axiom,
% 160.59/160.60 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 <=> ( 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))
% 160.59/160.60 | ( V_a_2 = V_a_H_2
% 160.59/160.60 & 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)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Nats__0,axiom,
% 160.59/160.60 ! [T_a] :
% 160.59/160.60 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.60 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Nats__add,axiom,
% 160.59/160.60 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.60 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 160.59/160.60 => 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))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Nats__mult,axiom,
% 160.59/160.60 ! [V_b_2,V_a_2,T_a] :
% 160.59/160.60 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)))
% 160.59/160.60 => 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))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Nats__1,axiom,
% 160.59/160.60 ! [T_a] :
% 160.59/160.60 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.60 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_of__nat__in__Nats,axiom,
% 160.59/160.60 ! [V_n_2,T_a] :
% 160.59/160.60 ( class_Rings_Osemiring__1(T_a)
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_same__fstI,axiom,
% 160.59/160.60 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] :
% 160.59/160.60 ( hBOOL(hAPP(V_P_2,V_x_2))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => 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))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_apfst__apsnd,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_apsnd__apfst,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_apfst__conv,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_apfst__compose,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_snd__apfst,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_fst__apfst,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_apfst__eq__conv,axiom,
% 160.59/160.60 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] :
% 160.59/160.60 ( 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)
% 160.59/160.60 <=> 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_apsnd__apfst__commute,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pair__lessI2,axiom,
% 160.59/160.60 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_max__ext__additive,axiom,
% 160.59/160.60 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => 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))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pair__lessI1,axiom,
% 160.59/160.60 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 160.59/160.60 ! [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 ).
% 160.59/160.60
% 160.59/160.60 fof(fact_max__extp__max__ext__eq,axiom,
% 160.59/160.60 ! [V_xa_2,V_x_2,V_R_2,T_a] :
% 160.59/160.60 ( 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)
% 160.59/160.60 <=> 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pair__leqI2,axiom,
% 160.59/160.60 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_smax__insertI,axiom,
% 160.59/160.60 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 160.59/160.60 => ( 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))
% 160.59/160.60 => ( 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))
% 160.59/160.60 => 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)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_smax__emptyI,axiom,
% 160.59/160.60 ! [V_Y_2] :
% 160.59/160.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 160.59/160.60 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_max__strict__def,axiom,
% 160.59/160.60 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pair__leqI1,axiom,
% 160.59/160.60 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_wmin__insertI,axiom,
% 160.59/160.60 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 160.59/160.60 => ( 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))
% 160.59/160.60 => ( 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))
% 160.59/160.60 => 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)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_wmax__insertI,axiom,
% 160.59/160.60 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 160.59/160.60 => ( 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))
% 160.59/160.60 => ( 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))
% 160.59/160.60 => 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)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_smin__insertI,axiom,
% 160.59/160.60 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 160.59/160.60 => ( 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))
% 160.59/160.60 => ( 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))
% 160.59/160.60 => 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)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_wmax__emptyI,axiom,
% 160.59/160.60 ! [V_X_2] :
% 160.59/160.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_wmin__emptyI,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_smin__emptyI,axiom,
% 160.59/160.60 ! [V_X_2] :
% 160.59/160.60 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_max__weak__def,axiom,
% 160.59/160.60 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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_min__weak__def,axiom,
% 160.59/160.60 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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_min__rpair__set,axiom,
% 160.59/160.60 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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_max__rpair__set,axiom,
% 160.59/160.60 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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_min__strict__def,axiom,
% 160.59/160.60 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_less__than__iff,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2] :
% 160.59/160.60 ( 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))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_intrel__iff,axiom,
% 160.59/160.60 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 160.59/160.60 ( 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))
% 160.59/160.60 <=> 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rp__inv__image__rp,axiom,
% 160.59/160.60 ! [V_f_2,T_b,V_P_2,T_a] :
% 160.59/160.60 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 160.59/160.60 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pair__less__def,axiom,
% 160.59/160.60 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mlex__prod__def,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rp__inv__image__def,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_equiv__intrel__iff,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2] :
% 160.59/160.60 ( 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))))
% 160.59/160.60 <=> 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_measure__def,axiom,
% 160.59/160.60 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Image__singleton,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Image__singleton__iff,axiom,
% 160.59/160.60 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] :
% 160.59/160.60 ( 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))))))
% 160.59/160.60 <=> 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inv__image__def,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Image__empty,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Image__Un,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Image__UN,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Image__Int__subset,axiom,
% 160.59/160.60 ! [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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Image__mono,axiom,
% 160.59/160.60 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 160.59/160.60 => 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))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Un__Image,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_in__inv__image,axiom,
% 160.59/160.60 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 <=> 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Image__INT__subset,axiom,
% 160.59/160.60 ! [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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Image__iff,axiom,
% 160.59/160.60 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)))
% 160.59/160.60 <=> ? [B_x] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 160.59/160.60 & 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_rev__ImageI,axiom,
% 160.59/160.60 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.60 => ( 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))
% 160.59/160.60 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Image__eq__UN,axiom,
% 160.59/160.60 ! [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))))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_of__int,axiom,
% 160.59/160.60 ! [V_j_2,V_i_2,T_a] :
% 160.59/160.60 ( class_Rings_Oring__1(T_a)
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_One__int__def,axiom,
% 160.59/160.60 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))))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mult,axiom,
% 160.59/160.60 ! [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))))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Rep__Integ__inverse,axiom,
% 160.59/160.60 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 160.59/160.60
% 160.59/160.60 fof(fact_minus,axiom,
% 160.59/160.60 ! [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))))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Zero__int__def,axiom,
% 160.59/160.60 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))))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_int__def,axiom,
% 160.59/160.60 ! [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))))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_add,axiom,
% 160.59/160.60 ! [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))))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_nat,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_minus__int__def,axiom,
% 160.59/160.60 ! [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))))))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_less,axiom,
% 160.59/160.60 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 160.59/160.60 ( 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)))))))
% 160.59/160.60 <=> 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_le,axiom,
% 160.59/160.60 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 160.59/160.60 ( 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)))))))
% 160.59/160.60 <=> 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_irrefl__def,axiom,
% 160.59/160.60 ! [V_r_2,T_a] :
% 160.59/160.60 ( c_Relation_Oirrefl(T_a,V_r_2)
% 160.59/160.60 <=> ! [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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_eq__Abs__Integ,axiom,
% 160.59/160.60 ! [V_z_2] :
% 160.59/160.60 ~ ! [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))))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Field__insert,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Field__Union,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Field__empty,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_mono__Field,axiom,
% 160.59/160.60 ! [V_s_2,V_r_2,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Field__Un,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_finite__Field,axiom,
% 160.59/160.60 ! [V_r_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 160.59/160.60 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Id__on__def,axiom,
% 160.59/160.60 ! [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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_quotient__def,axiom,
% 160.59/160.60 ! [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)))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_ImageE,axiom,
% 160.59/160.60 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)))
% 160.59/160.60 => ~ ! [B_x] :
% 160.59/160.60 ( 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))
% 160.59/160.60 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_quotient__is__empty,axiom,
% 160.59/160.60 ! [V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_quotient__is__empty2,axiom,
% 160.59/160.60 ! [V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( 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)
% 160.59/160.60 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_quotient__empty,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Id__on__def_H,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Id__on__empty,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Image__Id__on,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_quotientI,axiom,
% 160.59/160.60 ! [V_r_2,V_A_2,V_x_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Id__on__eqI,axiom,
% 160.59/160.60 ! [V_A_2,T_a,V_b_2,V_a_2] :
% 160.59/160.60 ( V_a_2 = V_b_2
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.60 => 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))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Id__on__iff,axiom,
% 160.59/160.60 ! [V_A_2,V_y_2,V_x_2,T_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 <=> ( V_x_2 = V_y_2
% 160.59/160.60 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_singleton__quotient,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_equiv__class__nondisjoint,axiom,
% 160.59/160.60 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => ( 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)))))))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_subset__equiv__class,axiom,
% 160.59/160.60 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => ( 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))))))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 160.59/160.60 => 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)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_quotientE,axiom,
% 160.59/160.60 ! [V_r_2,V_A_2,V_X_2,T_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ~ ! [B_x] :
% 160.59/160.60 ( 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))))
% 160.59/160.60 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_equiv__intrel,axiom,
% 160.59/160.60 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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Union__quotient,axiom,
% 160.59/160.60 ! [V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => 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 ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_equiv__class__self,axiom,
% 160.59/160.60 ! [V_a_2,V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.60 => 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)))))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_quotient__disj,axiom,
% 160.59/160.60 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => ( V_X_2 = V_Y_2
% 160.59/160.60 | 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)) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_equiv__class__eq,axiom,
% 160.59/160.60 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => ( 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))
% 160.59/160.60 => 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)))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_quotient__eq__iff,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
% 160.59/160.60 => ( V_X_2 = V_Y_2
% 160.59/160.60 <=> 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)) ) ) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_quotient__eqI,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2))
% 160.59/160.60 => ( 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))
% 160.59/160.60 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_equiv__class__eq__iff,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => ( 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))
% 160.59/160.60 <=> ( 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))))
% 160.59/160.60 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.60 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_eq__equiv__class,axiom,
% 160.59/160.60 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] :
% 160.59/160.60 ( 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))))
% 160.59/160.60 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2))
% 160.59/160.60 => 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)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_eq__equiv__class__iff,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 160.59/160.60 => ( 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))))
% 160.59/160.60 <=> 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)) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_equiv__class__subset,axiom,
% 160.59/160.60 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => ( 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))
% 160.59/160.60 => 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)))))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_eq__equiv__class__iff2,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 160.59/160.60 => ( 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)
% 160.59/160.60 <=> 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)) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_UN__equiv__class2,axiom,
% 160.59/160.60 ! [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] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 160.59/160.60 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 160.59/160.60 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2))
% 160.59/160.60 => 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) ) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_UN__equiv__class,axiom,
% 160.59/160.60 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.60 => 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) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_equivp__equiv,axiom,
% 160.59/160.60 ! [V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2)
% 160.59/160.60 <=> 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_equivp__transp,axiom,
% 160.59/160.60 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_equivp__symp,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_R_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_equivp__reflp,axiom,
% 160.59/160.60 ! [V_x_2,V_R_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 160.59/160.60 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_equivp__def,axiom,
% 160.59/160.60 ! [V_R_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequivp(T_a,V_R_2)
% 160.59/160.60 <=> ! [B_x,B_y] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 160.59/160.60 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_identity__equivp,axiom,
% 160.59/160.60 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_congruent2__implies__congruent,axiom,
% 160.59/160.60 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2)
% 160.59/160.60 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.60 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_congruent2D,axiom,
% 160.59/160.60 ! [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] :
% 160.59/160.60 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2)
% 160.59/160.60 => ( 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))
% 160.59/160.60 => ( 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))
% 160.59/160.60 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_congruentD,axiom,
% 160.59/160.60 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2)
% 160.59/160.60 => ( 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))
% 160.59/160.60 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_congruent2__implies__congruent__UN,axiom,
% 160.59/160.60 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 160.59/160.60 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 160.59/160.60 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2))
% 160.59/160.60 => 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)) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_UN__equiv__class__inject,axiom,
% 160.59/160.60 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 160.59/160.60 => ( 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)
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => ( ! [B_x] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.60 => ! [B_y] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2))
% 160.59/160.60 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 160.59/160.60 => 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)) ) ) )
% 160.59/160.60 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_UN__equiv__class__type2,axiom,
% 160.59/160.60 ! [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] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2)
% 160.59/160.60 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2)
% 160.59/160.60 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => ( ! [B_x1] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2))
% 160.59/160.60 => ! [B_x2] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2))
% 160.59/160.60 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 160.59/160.60 => 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)) ) ) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_UN__equiv__class__type,axiom,
% 160.59/160.60 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.60 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2)
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => ( ! [B_x] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.60 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 160.59/160.60 => 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)) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Integ__def,axiom,
% 160.59/160.60 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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Id__onE,axiom,
% 160.59/160.60 ! [V_A_2,V_c_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_c_2),c_Relation_OId__on(T_a,V_A_2)))
% 160.59/160.60 => ~ ! [B_x] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.60 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_card__quotient__disjoint,axiom,
% 160.59/160.60 ! [V_r_2,V_A_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.60 => ( 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)
% 160.59/160.60 => 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) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__empty,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__uminus,axiom,
% 160.59/160.60 ! [V_A_2,T_a] :
% 160.59/160.60 ( class_Groups_Oordered__ab__group__add(T_a)
% 160.59/160.60 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__imageI2,axiom,
% 160.59/160.60 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] :
% 160.59/160.60 ( 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)
% 160.59/160.60 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_subset__inj__on,axiom,
% 160.59/160.60 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.60 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__Int,axiom,
% 160.59/160.60 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__diff,axiom,
% 160.59/160.60 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__id2,axiom,
% 160.59/160.60 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__def,axiom,
% 160.59/160.60 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 <=> ! [B_x] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.60 => ! [B_xa] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 160.59/160.60 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 160.59/160.60 => B_x = B_xa ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__onD,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 160.59/160.60 => V_x_2 = V_y_2 ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__iff,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 160.59/160.60 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 160.59/160.60 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__contraD,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 => ( V_x_2 != V_y_2
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 160.59/160.60 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 160.59/160.60 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 => ( 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)
% 160.59/160.60 <=> V_A_2 = V_B_2 ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__imageI,axiom,
% 160.59/160.60 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] :
% 160.59/160.60 ( 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)
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_comp__inj__on,axiom,
% 160.59/160.60 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 => ( 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))
% 160.59/160.60 => 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) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_comp__inj__on__iff,axiom,
% 160.59/160.60 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 => ( 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))
% 160.59/160.60 <=> 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) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_card__image,axiom,
% 160.59/160.60 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 => 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) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_finite__imageD,axiom,
% 160.59/160.60 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)))
% 160.59/160.60 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)
% 160.59/160.60 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__image__eq__iff,axiom,
% 160.59/160.60 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.60 => ( 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)
% 160.59/160.60 <=> V_A_2 = V_B_2 ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__eq,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.60 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 160.59/160.60 <=> V_x_2 = V_y_2 ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_injD,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.60 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 160.59/160.60 => V_x_2 = V_y_2 ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__fun,axiom,
% 160.59/160.60 ! [T_c,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__comp,axiom,
% 160.59/160.60 ! [V_g_2,T_c,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.60 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 160.59/160.60 => 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))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__strict__subset,axiom,
% 160.59/160.60 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.60 => 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))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__image__mem__iff,axiom,
% 160.59/160.60 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_range__ex1__eq,axiom,
% 160.59/160.60 ! [V_b_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.60 => ( 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)))))
% 160.59/160.60 <=> ? [B_x] :
% 160.59/160.60 ( V_b_2 = hAPP(V_f_2,B_x)
% 160.59/160.60 & ! [B_y] :
% 160.59/160.60 ( V_b_2 = hAPP(V_f_2,B_y)
% 160.59/160.60 => B_y = B_x ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__iff__surj,axiom,
% 160.59/160.60 ! [V_A_H_2,T_b,T_a,V_A_2] :
% 160.59/160.60 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.60 => ( ? [B_f] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 160.59/160.60 & 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)) )
% 160.59/160.60 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_endo__inj__surj,axiom,
% 160.59/160.60 ! [V_f_2,V_A_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.60 => ( 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))
% 160.59/160.60 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2)
% 160.59/160.60 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_finite__surj__inj,axiom,
% 160.59/160.60 ! [V_f_2,V_A_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_finite__UNIV__surj__inj,axiom,
% 160.59/160.60 ! [V_f_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 160.59/160.60 => ( 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))
% 160.59/160.60 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_finite__UNIV__inj__surj,axiom,
% 160.59/160.60 ! [V_f_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 160.59/160.60 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__image__subset__iff,axiom,
% 160.59/160.60 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.60 => ( 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)))
% 160.59/160.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__image__Int,axiom,
% 160.59/160.60 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 160.59/160.60 => 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)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_image__Int,axiom,
% 160.59/160.60 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_eq__card__imp__inj__on,axiom,
% 160.59/160.60 ! [V_f_2,T_b,V_A_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.60 => ( 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)
% 160.59/160.60 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__iff__eq__card,axiom,
% 160.59/160.60 ! [V_f_2,T_b,V_A_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.60 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 <=> 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) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__image__set__diff,axiom,
% 160.59/160.60 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 160.59/160.60 => 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)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_image__set__diff,axiom,
% 160.59/160.60 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_setsum__reindex,axiom,
% 160.59/160.60 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
% 160.59/160.60 ( class_Groups_Ocomm__monoid__add(T_c)
% 160.59/160.60 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 160.59/160.60 => 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) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_pigeonhole,axiom,
% 160.59/160.60 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( 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)))
% 160.59/160.60 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__fun__updI,axiom,
% 160.59/160.60 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 160.59/160.60 => 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) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_setprod__reindex,axiom,
% 160.59/160.60 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] :
% 160.59/160.60 ( class_Groups_Ocomm__monoid__mult(T_c)
% 160.59/160.60 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 160.59/160.60 => 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) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_setprod__reindex__cong,axiom,
% 160.59/160.60 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 160.59/160.60 ( class_Groups_Ocomm__monoid__mult(T_c)
% 160.59/160.60 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 160.59/160.60 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)
% 160.59/160.60 => 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) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__singleton,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_Rep__Integ,axiom,
% 160.59/160.60 ! [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)) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_setsum_Oreindex,axiom,
% 160.59/160.60 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
% 160.59/160.60 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.60 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
% 160.59/160.60 => 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) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_card__bij__eq,axiom,
% 160.59/160.60 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 => ( 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))
% 160.59/160.60 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2)
% 160.59/160.60 => ( 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))
% 160.59/160.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 160.59/160.60 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_setprod_Oreindex,axiom,
% 160.59/160.60 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] :
% 160.59/160.60 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.60 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2)
% 160.59/160.60 => 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) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__image__Compl__subset,axiom,
% 160.59/160.60 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.60 => 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)))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__insert,axiom,
% 160.59/160.60 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))
% 160.59/160.60 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 & ~ 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))))))) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__Un,axiom,
% 160.59/160.60 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 160.59/160.60 & 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__iff__card__le,axiom,
% 160.59/160.60 ! [V_B_2,T_b,V_A_2,T_a] :
% 160.59/160.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 160.59/160.60 => ( ? [B_f] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 160.59/160.60 & 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)) )
% 160.59/160.60 <=> 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))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_card__inj__on__le,axiom,
% 160.59/160.60 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.60 => ( 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))
% 160.59/160.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 160.59/160.60 => 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))) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_fold__image__reindex,axiom,
% 160.59/160.60 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] :
% 160.59/160.60 ( class_Groups_Oab__semigroup__mult(T_c)
% 160.59/160.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.60 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2)
% 160.59/160.60 => 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) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_quotient__diff1,axiom,
% 160.59/160.60 ! [V_a_2,V_A_2,V_r_2,T_a] :
% 160.59/160.60 ( 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)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_folding__image_Oreindex,axiom,
% 160.59/160.60 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 160.59/160.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.60 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 160.59/160.60 => 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) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_image__INT,axiom,
% 160.59/160.60 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2)
% 160.59/160.60 => ( ! [B_x] :
% 160.59/160.60 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 160.59/160.60 => 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)) )
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2))
% 160.59/160.60 => 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)) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_type__definition__Integ,axiom,
% 160.59/160.60 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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__Suc,axiom,
% 160.59/160.60 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__on__add__nat,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__of__nat,axiom,
% 160.59/160.60 ! [T_a] :
% 160.59/160.60 ( class_Nat_Osemiring__char__0(T_a)
% 160.59/160.60 => 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))) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__int,axiom,
% 160.59/160.60 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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_swap__inj__on,axiom,
% 160.59/160.60 ! [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) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_folding__image_Odistrib,axiom,
% 160.59/160.60 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 160.59/160.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.60 => 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)) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_inj__graph,axiom,
% 160.59/160.60 ! [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))) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_folding__image_Oeq__fold,axiom,
% 160.59/160.60 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] :
% 160.59/160.60 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2)
% 160.59/160.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 160.59/160.60 => 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) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_type__definition_ORep__range,axiom,
% 160.59/160.60 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 160.59/160.60 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 160.59/160.60 => 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 ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_type__definition_OAbs__image,axiom,
% 160.59/160.60 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 160.59/160.60 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 160.59/160.60 => 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)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_type__definition_OAbs__inject,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 160.59/160.60 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 160.59/160.60 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 160.59/160.60 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_type__definition_ORep__inverse,axiom,
% 160.59/160.60 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 160.59/160.60 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 160.59/160.60 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_type__definition_ORep__inject,axiom,
% 160.59/160.60 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 160.59/160.60 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 160.59/160.60 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 160.59/160.60 <=> V_x_2 = V_y_2 ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_type__definition_ORep,axiom,
% 160.59/160.60 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 160.59/160.60 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 160.59/160.60 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_type__definition_OAbs__inverse,axiom,
% 160.59/160.60 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] :
% 160.59/160.60 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2)
% 160.59/160.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 160.59/160.60 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 160.59/160.60
% 160.59/160.60 fof(fact_the__inv__into__comp,axiom,
% 160.59/160.60 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] :
% 160.59/160.60 ( 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))
% 160.59/160.60 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2)
% 160.59/160.61 => ( 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))))
% 160.59/160.61 => 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) ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_the__inv__into__into,axiom,
% 160.59/160.61 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 160.59/160.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.61 => 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)) ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_inj__vimage__singleton,axiom,
% 160.59/160.61 ! [V_a_2,V_f_2,T_b,T_a] :
% 160.59/160.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.61 => 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))))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimageI,axiom,
% 160.59/160.61 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] :
% 160.59/160.61 ( hAPP(V_f_2,V_a_2) = V_b_2
% 160.59/160.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2))
% 160.59/160.61 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__UNIV,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__empty,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__Un,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__Collect__eq,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__Compl,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__ident,axiom,
% 160.59/160.61 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__code,axiom,
% 160.59/160.61 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2))
% 160.59/160.61 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__INT,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__Int,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__mono,axiom,
% 160.59/160.61 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.59/160.61 => 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))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__compose,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__UN,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__Diff,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__eq,axiom,
% 160.59/160.61 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)))
% 160.59/160.61 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimageD,axiom,
% 160.59/160.61 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)))
% 160.59/160.61 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimageI2,axiom,
% 160.59/160.61 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2))
% 160.59/160.61 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_image__vimage__subset,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_surj__image__vimage__eq,axiom,
% 160.59/160.61 ! [V_A_2,V_f_2,T_a,T_b] :
% 160.59/160.61 ( 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))
% 160.59/160.61 => 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 ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__def,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__Union,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__singleton__eq,axiom,
% 160.59/160.61 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] :
% 160.59/160.61 ( 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))))))
% 160.59/160.61 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__insert,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_finite__vimageD,axiom,
% 160.59/160.61 ! [V_F_2,V_h_2,T_b,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2)))
% 160.59/160.61 => ( 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))
% 160.59/160.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__subsetD,axiom,
% 160.59/160.61 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] :
% 160.59/160.61 ( 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))
% 160.59/160.61 => ( 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))
% 160.59/160.61 => 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))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_image__vimage__eq,axiom,
% 160.59/160.61 ! [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)))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_finite__vimageI,axiom,
% 160.59/160.61 ! [V_h_2,T_b,V_F_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 160.59/160.61 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 160.59/160.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_inj__vimage__image__eq,axiom,
% 160.59/160.61 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.61 => 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 ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__const,axiom,
% 160.59/160.61 ! [T_b,V_A_2,V_c_2,T_a] :
% 160.59/160.61 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.59/160.61 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) )
% 160.59/160.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.59/160.61 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__eq__UN,axiom,
% 160.59/160.61 ! [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))))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_the__inv__into__f__f,axiom,
% 160.59/160.61 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.61 => 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 ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_the__inv__into__f__eq,axiom,
% 160.59/160.61 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.61 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 160.59/160.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.59/160.61 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_the__inv__f__f,axiom,
% 160.59/160.61 ! [V_x_2,V_f_2,T_b,T_a] :
% 160.59/160.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.61 => 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 ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_the__inv__into__onto,axiom,
% 160.59/160.61 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.61 => 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 ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_inj__on__the__inv__into,axiom,
% 160.59/160.61 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.61 => 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)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__subsetI,axiom,
% 160.59/160.61 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 160.59/160.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.59/160.61 => ( 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)))
% 160.59/160.61 => 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)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_the__inv__into__def,axiom,
% 160.59/160.61 ! [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))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__if,axiom,
% 160.59/160.61 ! [V_B_2,T_b,V_d_2,V_A_2,V_c_2,T_a] :
% 160.59/160.61 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.59/160.61 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 160.59/160.61 => 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_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) )
% 160.59/160.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 160.59/160.61 => 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_c_2)),V_d_2)),V_A_2) = V_B_2 ) ) )
% 160.59/160.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2))
% 160.59/160.61 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 160.59/160.61 => 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_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) )
% 160.59/160.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2))
% 160.59/160.61 => 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_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_f__the__inv__into__f,axiom,
% 160.59/160.61 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] :
% 160.59/160.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))
% 160.59/160.61 => 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 ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_strong__setprod__reindex__cong,axiom,
% 160.59/160.61 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 160.59/160.61 ( class_Groups_Ocomm__monoid__mult(T_c)
% 160.59/160.61 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.59/160.61 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 160.59/160.61 => ( ! [B_x] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.61 => 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) )
% 160.59/160.61 => 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) ) ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_accp__acc__eq,axiom,
% 160.59/160.61 ! [V_x_2,V_r_2,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_rel__comp__def,axiom,
% 160.59/160.61 ! [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))))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_rel__compI,axiom,
% 160.59/160.61 ! [V_s_2,V_c_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 => ( 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_c_2)),V_s_2))
% 160.59/160.61 => 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_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_rel__comp__UNION__distrib,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_rel__comp__UNION__distrib2,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_rel__comp__empty1,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_rel__comp__empty2,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_rel__comp__distrib,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_rel__comp__distrib2,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_O__assoc,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_rel__comp__mono,axiom,
% 160.59/160.61 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 => ( 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))
% 160.59/160.61 => 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))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_union__comp__emptyR,axiom,
% 160.59/160.61 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 => ( 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))
% 160.59/160.61 => 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)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_union__comp__emptyL,axiom,
% 160.59/160.61 ! [V_B_2,V_C_2,V_A_2,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 => ( 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))
% 160.59/160.61 => 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)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_acc__subset,axiom,
% 160.59/160.61 ! [V_R2_2,V_R1_2,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 => 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))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_acc__downward,axiom,
% 160.59/160.61 ! [V_a_2,V_r_2,V_b_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 160.59/160.61 => ( 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))
% 160.59/160.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_acc_Osimps,axiom,
% 160.59/160.61 ! [V_r_2,V_a_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 160.59/160.61 <=> ! [B_x] :
% 160.59/160.61 ( 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))
% 160.59/160.61 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_max__ext__compat,axiom,
% 160.59/160.61 ! [V_S_2,V_R_2,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 => 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))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_min__ext__compat,axiom,
% 160.59/160.61 ! [V_S_2,V_R_2,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 => 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))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_pred__comp__rel__comp__eq,axiom,
% 160.59/160.61 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_s_2)),V_x_2),V_y_2))
% 160.59/160.61 <=> 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))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_reduction__pairI,axiom,
% 160.59/160.61 ! [V_S_2,V_R_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_R_2)
% 160.59/160.61 => ( 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))
% 160.59/160.61 => 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)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_max__extp_Oequations,axiom,
% 160.59/160.61 ! [V_a2_2,V_a1_2,V_R_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2)
% 160.59/160.61 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2))
% 160.59/160.61 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
% 160.59/160.61 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.61 & ! [B_x] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2))
% 160.59/160.61 => ? [B_xa] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2))
% 160.59/160.61 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__less__than,axiom,
% 160.59/160.61 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_pred__comp_Ointros,axiom,
% 160.59/160.61 ! [T_c,T_b,T_a,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 160.59/160.61 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
% 160.59/160.61 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2),V_a_2),V_c_2)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__empty,axiom,
% 160.59/160.61 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__inv__image,axiom,
% 160.59/160.61 ! [V_f_2,T_b,V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__lex__prod,axiom,
% 160.59/160.61 ! [V_rb_2,T_b,V_ra_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_ra_2)
% 160.59/160.61 => ( c_Wellfounded_Owf(T_b,V_rb_2)
% 160.59/160.61 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__measure,axiom,
% 160.59/160.61 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__comp__self,axiom,
% 160.59/160.61 ! [V_R_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_R_2)
% 160.59/160.61 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__not__refl,axiom,
% 160.59/160.61 ! [V_a_2,V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => ~ 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)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__not__sym,axiom,
% 160.59/160.61 ! [V_x_2,V_a_2,V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => ( 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))
% 160.59/160.61 => ~ 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)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__asym,axiom,
% 160.59/160.61 ! [V_x_2,V_a_2,V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => ( 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))
% 160.59/160.61 => ~ 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)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__irrefl,axiom,
% 160.59/160.61 ! [V_a_2,V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => ~ 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)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_min__ext__wf,axiom,
% 160.59/160.61 ! [V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__finite__psubset,axiom,
% 160.59/160.61 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__subset,axiom,
% 160.59/160.61 ! [V_p_2,V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => ( 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))
% 160.59/160.61 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__Int1,axiom,
% 160.59/160.61 ! [V_r_H_2,V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => 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)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__Int2,axiom,
% 160.59/160.61 ! [V_r_H_2,V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => 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)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_pred__comp_Oequations,axiom,
% 160.59/160.61 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2),V_a1_2),V_a3_2))
% 160.59/160.61 <=> ? [B_b] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 160.59/160.61 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__mlex,axiom,
% 160.59/160.61 ! [V_f_2,V_R_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_R_2)
% 160.59/160.61 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__pair__less,axiom,
% 160.59/160.61 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_max__ext__wf,axiom,
% 160.59/160.61 ! [V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__less,axiom,
% 160.59/160.61 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)))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__int__ge__less__than,axiom,
% 160.59/160.61 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__int__ge__less__than2,axiom,
% 160.59/160.61 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_acc__wfD,axiom,
% 160.59/160.61 ! [V_x_2,V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__acc__iff,axiom,
% 160.59/160.61 ! [V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__no__loop,axiom,
% 160.59/160.61 ! [V_R_2,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__union__merge,axiom,
% 160.59/160.61 ! [V_S_2,V_R_2,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 <=> 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)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 160.59/160.61 ! [V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 <=> ~ ? [B_f] :
% 160.59/160.61 ! [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)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wfE__pf,axiom,
% 160.59/160.61 ! [V_A_2,V_R_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_R_2)
% 160.59/160.61 => ( 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)))
% 160.59/160.61 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__union__compatible,axiom,
% 160.59/160.61 ! [V_S_2,V_R_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_R_2)
% 160.59/160.61 => ( c_Wellfounded_Owf(T_a,V_S_2)
% 160.59/160.61 => ( 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))
% 160.59/160.61 => 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)) ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf,axiom,
% 160.59/160.61 ! [T_a] :
% 160.59/160.61 ( class_Orderings_Owellorder(T_a)
% 160.59/160.61 => 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)))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_reduction__pair__def,axiom,
% 160.59/160.61 ! [V_P_2,T_a] :
% 160.59/160.61 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 160.59/160.61 <=> ( 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))
% 160.59/160.61 & 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))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_reduction__pair__lemma,axiom,
% 160.59/160.61 ! [V_S_2,V_R_2,V_P_2,T_a] :
% 160.59/160.61 ( c_FunDef_Oreduction__pair(T_a,V_P_2)
% 160.59/160.61 => ( 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)))
% 160.59/160.61 => ( 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)))
% 160.59/160.61 => ( c_Wellfounded_Owf(T_a,V_S_2)
% 160.59/160.61 => 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)) ) ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__lenlex,axiom,
% 160.59/160.61 ! [V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__if__measure,axiom,
% 160.59/160.61 ! [T_a,V_g_2,V_f_2,V_P_2] :
% 160.59/160.61 ( ! [B_x] :
% 160.59/160.61 ( hBOOL(hAPP(V_P_2,B_x))
% 160.59/160.61 => 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))) )
% 160.59/160.61 => 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))))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_max__ext_Ointros,axiom,
% 160.59/160.61 ! [V_R_2,V_Y_2,V_X_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2))
% 160.59/160.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2))
% 160.59/160.61 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.61 => ( ! [B_x] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2))
% 160.59/160.61 => ? [B_xa] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2))
% 160.59/160.61 & 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)) ) )
% 160.59/160.61 => 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))) ) ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_pred__nat__def,axiom,
% 160.59/160.61 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))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__lex,axiom,
% 160.59/160.61 ! [V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__lexn,axiom,
% 160.59/160.61 ! [V_n_2,V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_lex__def,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_lexn_Osimps_I1_J,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__pred__nat,axiom,
% 160.59/160.61 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__same__fst,axiom,
% 160.59/160.61 ! [T_a,V_R_2,T_b,V_P_2] :
% 160.59/160.61 ( ! [B_x] :
% 160.59/160.61 ( hBOOL(hAPP(V_P_2,B_x))
% 160.59/160.61 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) )
% 160.59/160.61 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 160.59/160.61 ! [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))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_inj__on__Inter,axiom,
% 160.59/160.61 ! [V_f_2,T_b,T_a,V_S_2] :
% 160.59/160.61 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))
% 160.59/160.61 => ( ! [B_A] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2))
% 160.59/160.61 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) )
% 160.59/160.61 => 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)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Nitpick_Oone__frac__def,axiom,
% 160.59/160.61 ! [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))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 160.59/160.61 ! [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))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Nitpick_Ofrac__def,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Range__Collect__split,axiom,
% 160.59/160.61 ! [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))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_image__split__eq__Sigma,axiom,
% 160.59/160.61 ! [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))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wfP__def,axiom,
% 160.59/160.61 ! [V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 160.59/160.61 <=> 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))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wfP__empty,axiom,
% 160.59/160.61 ! [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))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_SigmaI,axiom,
% 160.59/160.61 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.61 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 160.59/160.61 => 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))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_RangeI,axiom,
% 160.59/160.61 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Times__eq__cancel2,axiom,
% 160.59/160.61 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2))
% 160.59/160.61 => ( 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))
% 160.59/160.61 <=> V_A_2 = V_B_2 ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Sigma__Diff__distrib2,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Times__Diff__distrib1,axiom,
% 160.59/160.61 ! [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))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Sigma__Diff__distrib1,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wfP__accp__iff,axiom,
% 160.59/160.61 ! [V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 160.59/160.61 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_accp__wfPD,axiom,
% 160.59/160.61 ! [V_x_2,V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 160.59/160.61 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Range__Id__on,axiom,
% 160.59/160.61 ! [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 ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Sigma__Union,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Sigma__empty1,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_card__cartesian__product,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_setsum__cartesian__product,axiom,
% 160.59/160.61 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 160.59/160.61 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.59/160.61 => 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))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Sigma__empty2,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Times__empty,axiom,
% 160.59/160.61 ! [V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.61 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Compl__Times__UNIV1,axiom,
% 160.59/160.61 ! [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))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Compl__Times__UNIV2,axiom,
% 160.59/160.61 ! [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)))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_setprod__cartesian__product,axiom,
% 160.59/160.61 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] :
% 160.59/160.61 ( class_Groups_Ocomm__monoid__mult(T_a)
% 160.59/160.61 => 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))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wfP__subset,axiom,
% 160.59/160.61 ! [V_p_2,V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 160.59/160.61 => ( 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))
% 160.59/160.61 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Sigma__Un__distrib1,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Times__Un__distrib1,axiom,
% 160.59/160.61 ! [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))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Sigma__Un__distrib2,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_rel__comp__subset__Sigma,axiom,
% 160.59/160.61 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 160.59/160.61 ( 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))))
% 160.59/160.61 => ( 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))))
% 160.59/160.61 => 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)))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_swap__product,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_finite__cartesian__product,axiom,
% 160.59/160.61 ! [V_B_2,T_b,V_A_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 160.59/160.61 => 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)))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_equiv__type,axiom,
% 160.59/160.61 ! [V_r_2,V_A_2,T_a] :
% 160.59/160.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.59/160.61 => 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)))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Sigma__Int__distrib2,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Times__Int__distrib1,axiom,
% 160.59/160.61 ! [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))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Sigma__Int__distrib1,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Id__on__subset__Times,axiom,
% 160.59/160.61 ! [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)))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Range__Diff__subset,axiom,
% 160.59/160.61 ! [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)))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_UNIV__Times__UNIV,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_SigmaE2,axiom,
% 160.59/160.61 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 160.59/160.61 ( 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)))
% 160.59/160.61 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.61 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_SigmaD2,axiom,
% 160.59/160.61 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 160.59/160.61 ( 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)))
% 160.59/160.61 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_SigmaD1,axiom,
% 160.59/160.61 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 160.59/160.61 ( 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)))
% 160.59/160.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_mem__Sigma__iff,axiom,
% 160.59/160.61 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] :
% 160.59/160.61 ( 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)))
% 160.59/160.61 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.59/160.61 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Range__Union,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Range__empty,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Range__empty__iff,axiom,
% 160.59/160.61 ! [V_r_2,T_a,T_b] :
% 160.59/160.61 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.61 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Range__Un__eq,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_finite__Range,axiom,
% 160.59/160.61 ! [V_r_2,T_b,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2))
% 160.59/160.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_snd__eq__Range,axiom,
% 160.59/160.61 ! [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) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_card__cartesian__product__singleton,axiom,
% 160.59/160.61 ! [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) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Times__subset__cancel2,axiom,
% 160.59/160.61 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2))
% 160.59/160.61 => ( 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))))
% 160.59/160.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Image__subset,axiom,
% 160.59/160.61 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 160.59/160.61 ( 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))))
% 160.59/160.61 => 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)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_finite__cartesian__productD2,axiom,
% 160.59/160.61 ! [V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.61 ( 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))))
% 160.59/160.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_finite__cartesian__productD1,axiom,
% 160.59/160.61 ! [V_B_2,V_A_2,T_b,T_a] :
% 160.59/160.61 ( 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))))
% 160.59/160.61 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 160.59/160.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_SetCompr__Sigma__eq,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Collect__split,axiom,
% 160.59/160.61 ! [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))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_fst__image__times,axiom,
% 160.59/160.61 ! [V_A_2,T_b,T_a,V_B_2] :
% 160.59/160.61 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.61 => 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)) )
% 160.59/160.61 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.61 => 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 ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_snd__image__times,axiom,
% 160.59/160.61 ! [V_B_2,T_b,T_a,V_A_2] :
% 160.59/160.61 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.61 => 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)) )
% 160.59/160.61 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.61 => 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 ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Range__iff,axiom,
% 160.59/160.61 ! [V_r_2,T_b,V_a_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)))
% 160.59/160.61 <=> ? [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)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Range__insert,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Range__Int__subset,axiom,
% 160.59/160.61 ! [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)))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_insert__times__insert,axiom,
% 160.59/160.61 ! [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)))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_finite__equiv__class,axiom,
% 160.59/160.61 ! [V_X_2,V_r_2,V_A_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.61 => ( 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))))
% 160.59/160.61 => ( 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)))
% 160.59/160.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__Times,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_UN__Times__distrib,axiom,
% 160.59/160.61 ! [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))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Sigma__def,axiom,
% 160.59/160.61 ! [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))))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_finite__quotient,axiom,
% 160.59/160.61 ! [V_r_2,V_A_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.61 => ( 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))))
% 160.59/160.61 => 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))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__in__rel,axiom,
% 160.59/160.61 ! [V_R_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_R_2)
% 160.59/160.61 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wfP__wf__eq,axiom,
% 160.59/160.61 ! [V_r_2,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 160.59/160.61 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] :
% 160.59/160.61 ( class_Rings_Osemiring__0(T_c)
% 160.59/160.61 => ( 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)))
% 160.59/160.61 => 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))))))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_RangeP__Range__eq,axiom,
% 160.59/160.61 ! [V_x_2,V_r_2,T_b,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 160.59/160.61 ! [V_A_2,V_I_2,T_b,T_a] :
% 160.59/160.61 ? [B_f] :
% 160.59/160.61 ( 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))
% 160.59/160.61 & 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))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_RangeP_Ointros,axiom,
% 160.59/160.61 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 160.59/160.61 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_image__id,axiom,
% 160.59/160.61 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ).
% 160.59/160.61
% 160.59/160.61 fof(fact_inj__on__id,axiom,
% 160.59/160.61 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_apfst__id,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_apsnd__id,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_RangeP_Oequations,axiom,
% 160.59/160.61 ! [V_a2_2,V_r_2,T_b,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2))
% 160.59/160.61 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_id__def,axiom,
% 160.59/160.61 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 160.59/160.61
% 160.59/160.61 fof(fact_id__apply,axiom,
% 160.59/160.61 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 160.59/160.61
% 160.59/160.61 fof(fact_o__eq__id__dest,axiom,
% 160.59/160.61 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_a,T_b,T_c] :
% 160.59/160.61 ( 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_c_2)
% 160.59/160.61 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_id__o,axiom,
% 160.59/160.61 ! [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 ).
% 160.59/160.61
% 160.59/160.61 fof(fact_o__id,axiom,
% 160.59/160.61 ! [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 ).
% 160.59/160.61
% 160.59/160.61 fof(fact_of__int__eq__id,axiom,
% 160.59/160.61 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_vimage__id,axiom,
% 160.59/160.61 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ).
% 160.59/160.61
% 160.59/160.61 fof(fact_surj__id,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_folding_Oempty,axiom,
% 160.59/160.61 ! [V_F_2,V_f_2,T_b,T_a] :
% 160.59/160.61 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2)
% 160.59/160.61 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_split__Pair,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_setsum__reindex__id,axiom,
% 160.59/160.61 ! [V_B_2,V_f_2,T_a,T_b] :
% 160.59/160.61 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.59/160.61 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 160.59/160.61 => 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)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_setprod__reindex__id,axiom,
% 160.59/160.61 ! [V_B_2,V_f_2,T_a,T_b] :
% 160.59/160.61 ( class_Groups_Ocomm__monoid__mult(T_b)
% 160.59/160.61 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 160.59/160.61 => 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)) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_setprod__Sigma,axiom,
% 160.59/160.61 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 160.59/160.61 ( class_Groups_Ocomm__monoid__mult(T_c)
% 160.59/160.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.61 => ( ! [B_x] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 160.59/160.61 => 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)) ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_setsum__Sigma,axiom,
% 160.59/160.61 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 160.59/160.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 160.59/160.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.61 => ( ! [B_x] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 160.59/160.61 => 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)) ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_fold__image__Sigma,axiom,
% 160.59/160.61 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] :
% 160.59/160.61 ( class_Groups_Ocomm__monoid__mult(T_c)
% 160.59/160.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.61 => ( ! [B_x] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 160.59/160.61 => 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)) ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_card__SigmaI,axiom,
% 160.59/160.61 ! [V_B_2,T_b,V_A_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.61 => ( ! [B_x] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) )
% 160.59/160.61 => 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) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_finite__SigmaI,axiom,
% 160.59/160.61 ! [V_B_2,T_b,V_A_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.59/160.61 => ( ! [B_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 160.59/160.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) )
% 160.59/160.61 => 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))) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_RangeE,axiom,
% 160.59/160.61 ! [V_r_2,T_b,V_b_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)))
% 160.59/160.61 => ~ ! [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)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_SigmaE,axiom,
% 160.59/160.61 ! [V_B_2,V_A_2,V_c_2,T_b,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)))
% 160.59/160.61 => ~ ! [B_x] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.59/160.61 => ! [B_y] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x)))
% 160.59/160.61 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wfP__acyclicP,axiom,
% 160.59/160.61 ! [V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_OwfP(T_a,V_r_2)
% 160.59/160.61 => 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))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__Un,axiom,
% 160.59/160.61 ! [V_s_2,V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => ( c_Wellfounded_Owf(T_a,V_s_2)
% 160.59/160.61 => ( 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))
% 160.59/160.61 => 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)) ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_DomainI,axiom,
% 160.59/160.61 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_acyclic__subset,axiom,
% 160.59/160.61 ! [V_r_2,V_s_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Oacyclic(T_a,V_s_2)
% 160.59/160.61 => ( 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))
% 160.59/160.61 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Domain__Id__on,axiom,
% 160.59/160.61 ! [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 ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__acyclic,axiom,
% 160.59/160.61 ! [V_r_2,T_a] :
% 160.59/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Domain__empty__iff,axiom,
% 160.59/160.61 ! [V_r_2,T_b,T_a] :
% 160.59/160.61 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.59/160.61 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Domain__empty,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Domain__mono,axiom,
% 160.59/160.61 ! [V_s_2,V_r_2,T_b,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 => 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))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Domain__Un__eq,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_finite__Domain,axiom,
% 160.59/160.61 ! [V_r_2,T_b,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2))
% 160.59/160.61 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_fst__eq__Domain,axiom,
% 160.59/160.61 ! [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) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Domain__iff,axiom,
% 160.59/160.61 ! [V_r_2,T_b,V_a_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
% 160.59/160.61 <=> ? [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)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Domain__insert,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 160.59/160.61 ! [V_r_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 160.59/160.61 => ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.59/160.61 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_finite__acyclic__wf,axiom,
% 160.59/160.61 ! [V_r_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 160.59/160.61 => ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 160.59/160.61 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Domain__Int__subset,axiom,
% 160.59/160.61 ! [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)))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Domain__Diff__subset,axiom,
% 160.59/160.61 ! [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)))) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Field__def,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Domain__Union,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Domain__Collect__split,axiom,
% 160.59/160.61 ! [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)) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_DomainP__Domain__eq,axiom,
% 160.59/160.61 ! [V_x_2,V_r_2,T_b,T_a] :
% 160.59/160.61 ( 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))
% 160.59/160.61 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_Nitpick_Owf_H__def,axiom,
% 160.59/160.61 ! [V_r_2,T_a] :
% 160.59/160.61 ( c_Nitpick_Owf_H(T_a,V_r_2)
% 160.59/160.61 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 160.59/160.61 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 160.59/160.61 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_DomainE,axiom,
% 160.59/160.61 ! [V_r_2,T_b,V_a_2,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)))
% 160.59/160.61 => ~ ! [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)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_DomainP_Ointros,axiom,
% 160.59/160.61 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
% 160.59/160.61 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 160.59/160.61 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_DomainP_Oequations,axiom,
% 160.59/160.61 ! [V_a1_2,V_r_2,T_b,T_a] :
% 160.59/160.61 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2))
% 160.59/160.61 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 160.59/160.61
% 160.59/160.61 fof(fact_map__pair__surj,axiom,
% 160.59/160.61 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] :
% 160.59/160.61 ( 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))
% 160.93/160.61 => ( 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))
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_map__pair__inj__on,axiom,
% 160.93/160.61 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] :
% 160.93/160.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.93/160.61 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2)
% 160.93/160.61 => 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_map__pair__imageI,axiom,
% 160.93/160.61 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_snd__comp__map__pair,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_fst__comp__map__pair,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_map__pair_Ocomp,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_map__pair__compose,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_map__pair_Ocompositionality,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_map__pair__ident,axiom,
% 160.93/160.61 ! [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 ).
% 160.93/160.61
% 160.93/160.61 fof(fact_map__pair__simp,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_fst__map__pair,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_snd__prod__fun,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_map__pair_Oidentity,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_apsnd__def,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_apfst__def,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_map__pair_Oid,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_map__pair__def,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_map__pair__surj__on,axiom,
% 160.93/160.61 ! [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] :
% 160.93/160.61 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2
% 160.93/160.61 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_wf__map__pair__image,axiom,
% 160.93/160.61 ! [V_f_2,T_b,V_r_2,T_a] :
% 160.93/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.93/160.61 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_prod__fun__imageE,axiom,
% 160.93/160.61 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_c_2,T_b,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_c_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)))
% 160.93/160.61 => ~ ! [B_x,B_y] :
% 160.93/160.61 ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
% 160.93/160.61 => ~ 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_refl__on__def,axiom,
% 160.93/160.61 ! [V_r_2,V_A_2,T_a] :
% 160.93/160.61 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 160.93/160.61 <=> ( 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))))
% 160.93/160.61 & ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.93/160.61 => 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)) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_refl__on__Id__on,axiom,
% 160.93/160.61 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_refl__on__empty,axiom,
% 160.93/160.61 ! [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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_refl__on__Un,axiom,
% 160.93/160.61 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
% 160.93/160.61 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 160.93/160.61 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_refl__on__Int,axiom,
% 160.93/160.61 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] :
% 160.93/160.61 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 160.93/160.61 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2)
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_refl__onD1,axiom,
% 160.93/160.61 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 160.93/160.61 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 160.93/160.61 => ( 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))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_refl__onD2,axiom,
% 160.93/160.61 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] :
% 160.93/160.61 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 160.93/160.61 => ( 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))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_refl__onD,axiom,
% 160.93/160.61 ! [V_a_2,V_r_2,V_A_2,T_a] :
% 160.93/160.61 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 160.93/160.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2))
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_reflp__def,axiom,
% 160.93/160.61 ! [V_r_2,T_a] :
% 160.93/160.61 ( c_Predicate_Oreflp(T_a,V_r_2)
% 160.93/160.61 <=> 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_refl__onI,axiom,
% 160.93/160.61 ! [V_A_2,V_r_2,T_a] :
% 160.93/160.61 ( 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))))
% 160.93/160.61 => ( ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.93/160.61 => 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)) )
% 160.93/160.61 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_reflpE,axiom,
% 160.93/160.61 ! [V_x_2,V_r_2,T_a] :
% 160.93/160.61 ( c_Predicate_Oreflp(T_a,V_r_2)
% 160.93/160.61 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Rep__Integ__induct,axiom,
% 160.93/160.61 ! [V_P_2,V_y_2] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 160.93/160.61 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 160.93/160.61 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Rep__Integ__cases,axiom,
% 160.93/160.61 ! [V_y_2] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 160.93/160.61 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_inj__on__INTER,axiom,
% 160.93/160.61 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] :
% 160.93/160.61 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.93/160.61 => ( ! [B_i] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2))
% 160.93/160.61 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) )
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_refl__on__def_H,axiom,
% 160.93/160.61 ! [V_r_2,V_A_2,T_a] :
% 160.93/160.61 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 160.93/160.61 <=> ( ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2))
% 160.93/160.61 => 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)) )
% 160.93/160.61 & ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.93/160.61 => 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)) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_ball__UNIV,axiom,
% 160.93/160.61 ! [V_P_2,T_a] :
% 160.93/160.61 ( ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 160.93/160.61 => hBOOL(hAPP(V_P_2,B_x)) )
% 160.93/160.61 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_INFI__bool__eq,axiom,
% 160.93/160.61 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Powp__def,axiom,
% 160.93/160.61 ! [V_B_2,V_A_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2))
% 160.93/160.61 <=> ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2))
% 160.93/160.61 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_ball__empty,axiom,
% 160.93/160.61 ! [V_P_2,T_a,B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 160.93/160.61 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Collect__ball__eq,axiom,
% 160.93/160.61 ! [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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_congruent__def,axiom,
% 160.93/160.61 ! [V_f_2,V_r_2,T_b,T_a] :
% 160.93/160.61 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2)
% 160.93/160.61 <=> ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2))
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_INTER__def,axiom,
% 160.93/160.61 ! [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)))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Inf__Sup,axiom,
% 160.93/160.61 ! [V_A_2,T_a] :
% 160.93/160.61 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.93/160.61 => 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))))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Sup__Inf,axiom,
% 160.93/160.61 ! [V_A_2,T_a] :
% 160.93/160.61 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.93/160.61 => 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)))))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Abs__Integ__cases,axiom,
% 160.93/160.61 ! [V_x_2] :
% 160.93/160.61 ~ ! [B_y] :
% 160.93/160.61 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 160.93/160.61 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Abs__Integ__induct,axiom,
% 160.93/160.61 ! [V_x_2,V_P_2] :
% 160.93/160.61 ( ! [B_y] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 160.93/160.61 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 160.93/160.61 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_triples__valid__Suc,axiom,
% 160.93/160.61 ! [V_n_2,V_ts_2,T_a] :
% 160.93/160.61 ( ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 160.93/160.61 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) )
% 160.93/160.61 => ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 160.93/160.61 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_hoare__valids__def,axiom,
% 160.93/160.61 ! [V_ts_2,V_Ga_2,T_a] :
% 160.93/160.61 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2)
% 160.93/160.61 <=> ! [B_n] :
% 160.93/160.61 ( ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_Ga_2))
% 160.93/160.61 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) )
% 160.93/160.61 => ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2))
% 160.93/160.61 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Inter__eq,axiom,
% 160.93/160.61 ! [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)))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_inj__on__diff__nat,axiom,
% 160.93/160.61 ! [V_k_2,V_N_2] :
% 160.93/160.61 ( ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 160.93/160.61 => 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) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_wfP__SUP,axiom,
% 160.93/160.61 ! [T_a,V_r_2,T_b] :
% 160.93/160.61 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i))
% 160.93/160.61 => ( ! [B_i,B_j] :
% 160.93/160.61 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 160.93/160.61 => 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)) )
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_mem__splitI2,axiom,
% 160.93/160.61 ! [V_c_2,V_z_2,T_c,T_b,T_a,V_p_2] :
% 160.93/160.61 ( ! [B_a,B_b] :
% 160.93/160.61 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
% 160.93/160.61 => 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_c_2),V_p_2))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_mem__splitE,axiom,
% 160.93/160.61 ! [V_p_2,V_c_2,T_c,T_b,V_z_2,T_a] :
% 160.93/160.61 ( 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_c_2),V_p_2)))
% 160.93/160.61 => ~ ! [B_x,B_y] :
% 160.93/160.61 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)
% 160.93/160.61 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Eps__split,axiom,
% 160.93/160.61 ! [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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_wfI__pf,axiom,
% 160.93/160.61 ! [V_R_2,T_a] :
% 160.93/160.61 ( ! [B_A] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) )
% 160.93/160.61 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_someI,axiom,
% 160.93/160.61 ! [T_a,V_x_2,V_P_2] :
% 160.93/160.61 ( hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.61 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_tfl__some,axiom,
% 160.93/160.61 ! [T_a,B_P] :
% 160.93/160.61 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 160.93/160.61 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_some__sym__eq__trivial,axiom,
% 160.93/160.61 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 160.93/160.61
% 160.93/160.61 fof(fact_some__eq__trivial,axiom,
% 160.93/160.61 ! [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 ).
% 160.93/160.61
% 160.93/160.61 fof(fact_some__eq__ex,axiom,
% 160.93/160.61 ! [T_a,V_P_2] :
% 160.93/160.61 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2)))
% 160.93/160.61 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_someI__ex,axiom,
% 160.93/160.61 ! [T_a,V_P_2] :
% 160.93/160.61 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 160.93/160.61 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_exE__some,axiom,
% 160.93/160.61 ! [T_a,V_c_2,V_P_2] :
% 160.93/160.61 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 160.93/160.61 => ( V_c_2 = c_Hilbert__Choice_OEps(T_a,V_P_2)
% 160.93/160.61 => hBOOL(hAPP(V_P_2,V_c_2)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Eps__split__eq,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_split__paired__Eps,axiom,
% 160.93/160.61 ! [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)))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_LeastM__def,axiom,
% 160.93/160.61 ! [V_P_2,V_m_2,T_a,T_b] :
% 160.93/160.61 ( class_Orderings_Oord(T_b)
% 160.93/160.61 => 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))))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_GreatestM__def,axiom,
% 160.93/160.61 ! [V_P_2,V_m_2,T_a,T_b] :
% 160.93/160.61 ( class_Orderings_Oord(T_b)
% 160.93/160.61 => 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))))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_LeastM__nat__le,axiom,
% 160.93/160.61 ! [T_a,V_m_2,V_x_2,V_P_2] :
% 160.93/160.61 ( hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.61 => 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_LeastM__nat__lemma,axiom,
% 160.93/160.61 ! [V_m_2,T_a,V_k_2,V_P_2] :
% 160.93/160.61 ( hBOOL(hAPP(V_P_2,V_k_2))
% 160.93/160.61 => ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2)))
% 160.93/160.61 & ! [B_y] :
% 160.93/160.61 ( hBOOL(hAPP(V_P_2,B_y))
% 160.93/160.61 => 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))) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Greatest__def,axiom,
% 160.93/160.61 ! [T_a] :
% 160.93/160.61 ( class_Orderings_Oord(T_a)
% 160.93/160.61 => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Sigma__mono,axiom,
% 160.93/160.61 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2))
% 160.93/160.61 => ( ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.93/160.61 => 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))) )
% 160.93/160.61 => 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_LeastM__natI,axiom,
% 160.93/160.61 ! [V_m_2,T_a,V_k_2,V_P_2] :
% 160.93/160.61 ( hBOOL(hAPP(V_P_2,V_k_2))
% 160.93/160.61 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_not__acc__down,axiom,
% 160.93/160.61 ! [V_R_2,V_x_2,T_a] :
% 160.93/160.61 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2)))
% 160.93/160.61 => ~ ! [B_z] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_acc_OaccI,axiom,
% 160.93/160.61 ! [V_r_2,V_x_2,T_a] :
% 160.93/160.61 ( ! [B_y] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) )
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_max__ext_Osimps,axiom,
% 160.93/160.61 ! [V_R_2,V_a2_2,V_a1_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2))
% 160.93/160.61 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2))
% 160.93/160.61 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.93/160.61 & ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2))
% 160.93/160.61 => ? [B_xa] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2))
% 160.93/160.61 & 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)) ) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_wf__no__infinite__down__chainE,axiom,
% 160.93/160.61 ! [V_f_2,V_r_2,T_a] :
% 160.93/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.93/160.61 => ~ ! [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)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_setsum__reindex__cong,axiom,
% 160.93/160.61 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 160.93/160.61 ( class_Groups_Ocomm__monoid__add(T_c)
% 160.93/160.61 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 160.93/160.61 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)
% 160.93/160.61 => ( ! [B_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 160.93/160.61 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 160.93/160.61 => 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) ) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_scomp__unfold,axiom,
% 160.93/160.61 ! [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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Pair__scomp,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_scomp__Pair,axiom,
% 160.93/160.61 ! [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 ).
% 160.93/160.61
% 160.93/160.61 fof(fact_scomp__scomp,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_scomp__apply,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_scomp__def,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_iterate_Osimps,axiom,
% 160.93/160.61 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
% 160.93/160.61 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 160.93/160.61 => 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) )
% 160.93/160.61 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_less__eq,axiom,
% 160.93/160.61 ! [V_n_2,V_m_2] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_wf__trancl,axiom,
% 160.93/160.61 ! [V_r_2,T_a] :
% 160.93/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.93/160.61 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_less__than__def,axiom,
% 160.93/160.61 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_acyclic__def,axiom,
% 160.93/160.61 ! [V_r_2,T_a] :
% 160.93/160.61 ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 160.93/160.61 <=> ! [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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl_Or__into__trancl,axiom,
% 160.93/160.61 ! [V_r_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__subset__Field2,axiom,
% 160.93/160.61 ! [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))))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_r__into__trancl_H,axiom,
% 160.93/160.61 ! [V_r_2,V_p_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__empty,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__domain,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__range,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_finite__trancl,axiom,
% 160.93/160.61 ! [V_r_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 160.93/160.61 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__trans,axiom,
% 160.93/160.61 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ( 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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 160.93/160.61 => 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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 160.93/160.61 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ( 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_c_2)),V_r_2))
% 160.93/160.61 => 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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__into__trancl2,axiom,
% 160.93/160.61 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => ( 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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 160.93/160.61 => 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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_r__r__into__trancl,axiom,
% 160.93/160.61 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => ( 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_c_2)),V_R_2))
% 160.93/160.61 => 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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__mono,axiom,
% 160.93/160.61 ! [V_s_2,V_r_2,V_p_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2)))
% 160.93/160.61 => ( 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))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__unfold,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__subset__Sigma,axiom,
% 160.93/160.61 ! [V_A_2,V_r_2,T_a] :
% 160.93/160.61 ( 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))))
% 160.93/160.61 => 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)))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__Int__subset,axiom,
% 160.93/160.61 ! [V_s_2,V_r_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => ( 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))
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_log_Osimps,axiom,
% 160.93/160.61 ! [V_i,V_b] :
% 160.93/160.61 ( ( ( 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)))
% 160.93/160.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 160.93/160.61 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 160.93/160.61 & ( ~ ( 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)))
% 160.93/160.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 160.93/160.61 => 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_minus__shift__def,axiom,
% 160.93/160.61 ! [V_r,V_l,V_k] :
% 160.93/160.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 160.93/160.61 => 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) )
% 160.93/160.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 160.93/160.61 => 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) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_inc__shift__def,axiom,
% 160.93/160.61 ! [V_k,V_v] :
% 160.93/160.61 ( ( V_v = V_k
% 160.93/160.61 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 160.93/160.61 & ( V_v != V_k
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_range,axiom,
% 160.93/160.61 ! [V_s,V_k] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => 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)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__insert,axiom,
% 160.93/160.61 ! [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)))))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_reflcl__set__eq,axiom,
% 160.93/160.61 ! [V_y_2,V_x_2,V_r_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 <=> 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)))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_r__into__rtrancl,axiom,
% 160.93/160.61 ! [V_r_2,V_p_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 160.93/160.61 ! [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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_IdI,axiom,
% 160.93/160.61 ! [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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__into__rtrancl,axiom,
% 160.93/160.61 ! [V_r_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__unfold__left,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__unfold__right,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__reflcl,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_reflcl__trancl,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__trancl__absorb,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__rtrancl__absorb,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Domain__rtrancl,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Range__rtrancl,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__empty,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__idemp,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__trans,axiom,
% 160.93/160.61 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 160.93/160.61 => 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_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 160.93/160.61 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ( 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_c_2)),V_r_2))
% 160.93/160.61 => 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_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 160.93/160.61 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 160.93/160.61 => 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_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_in__rtrancl__UnI,axiom,
% 160.93/160.61 ! [V_S_2,V_R_2,V_x_2,T_a] :
% 160.93/160.61 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 160.93/160.61 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) )
% 160.93/160.61 => 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)))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__reflcl__absorb,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__Un__rtrancl,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__reflcl,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__unfold,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__idemp__self__comp,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_r__comp__rtrancl__eq,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__r__diff__Id,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_refl__rtrancl,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_R__O__Id,axiom,
% 160.93/160.61 ! [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 ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Id__O__R,axiom,
% 160.93/160.61 ! [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 ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Image__Id,axiom,
% 160.93/160.61 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__Int__subset,axiom,
% 160.93/160.61 ! [V_r_2,V_s_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => ( 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))
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__Un__subset,axiom,
% 160.93/160.61 ! [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)))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__subset__rtrancl,axiom,
% 160.93/160.61 ! [V_s_2,V_r_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__subset,axiom,
% 160.93/160.61 ! [V_S_2,V_R_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => ( 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)))
% 160.93/160.61 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__mono,axiom,
% 160.93/160.61 ! [V_s_2,V_r_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Image__closed__trancl,axiom,
% 160.93/160.61 ! [V_X_2,V_r_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_pair__in__Id__conv,axiom,
% 160.93/160.61 ! [V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 <=> V_a_2 = V_b_2 ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__trancl__trancl,axiom,
% 160.93/160.61 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ( 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)))
% 160.93/160.61 => 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__rtrancl__trancl,axiom,
% 160.93/160.61 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 160.93/160.61 => 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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__into__trancl1,axiom,
% 160.93/160.61 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ( 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_c_2)),V_r_2))
% 160.93/160.61 => 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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtranclD,axiom,
% 160.93/160.61 ! [V_R_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ( V_a_2 = V_b_2
% 160.93/160.61 | ( V_a_2 != V_b_2
% 160.93/160.61 & 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))) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__into__trancl2,axiom,
% 160.93/160.61 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))
% 160.93/160.61 => 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_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__eq__or__trancl,axiom,
% 160.93/160.61 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 <=> ( V_x_2 = V_y_2
% 160.93/160.61 | ( V_x_2 != V_y_2
% 160.93/160.61 & 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))) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Domain__Id,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Range__Id,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_refl__Id,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_pair__leq__def,axiom,
% 160.93/160.61 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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Not__Domain__rtrancl,axiom,
% 160.93/160.61 ! [V_y_2,V_R_2,V_x_2,T_a] :
% 160.93/160.61 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2)))
% 160.93/160.61 => ( 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)))
% 160.93/160.61 <=> V_x_2 = V_y_2 ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_acc__downwards__aux,axiom,
% 160.93/160.61 ! [V_r_2,V_a_2,V_b_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_acc__downwards,axiom,
% 160.93/160.61 ! [V_b_2,V_r_2,V_a_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 160.93/160.61 => ( 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)))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_wf__insert,axiom,
% 160.93/160.61 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 <=> ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.93/160.61 & ~ 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_acyclic__insert,axiom,
% 160.93/160.61 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 160.93/160.61 & ~ 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_refl__reflcl,axiom,
% 160.93/160.61 ! [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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Id__def,axiom,
% 160.93/160.61 ! [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))))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_irrefl__diff__Id,axiom,
% 160.93/160.61 ! [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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_pred__nat__trancl__eq__le,axiom,
% 160.93/160.61 ! [V_n_2,V_m_2] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__subset__Sigma__aux,axiom,
% 160.93/160.61 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ( 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))))
% 160.93/160.61 => ( V_a_2 = V_b_2
% 160.93/160.61 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_irrefl__tranclI,axiom,
% 160.93/160.61 ! [V_x_2,V_r_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => ~ 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_sequence__trans,axiom,
% 160.93/160.61 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] :
% 160.93/160.61 ( ! [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)))
% 160.93/160.61 => 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__converse,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_converse__Id,axiom,
% 160.93/160.61 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_acyclic__converse,axiom,
% 160.93/160.61 ! [V_r_2,T_a] :
% 160.93/160.61 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 160.93/160.61 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_converseD,axiom,
% 160.93/160.61 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => 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)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_converseI,axiom,
% 160.93/160.61 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_converse__iff,axiom,
% 160.93/160.61 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 <=> 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)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_converse__Id__on,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_finite__converse,axiom,
% 160.93/160.61 ! [V_r_2,T_b,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)))
% 160.93/160.61 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_converse__Int,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_converse__converse,axiom,
% 160.93/160.61 ! [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 ).
% 160.93/160.61
% 160.93/160.61 fof(fact_converse__inv__image,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Field__converse,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_converse__Un,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_converse__rel__comp,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_converse__UNION,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_refl__on__converse,axiom,
% 160.93/160.61 ! [V_r_2,V_A_2,T_a] :
% 160.93/160.61 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 160.93/160.61 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_converse__INTER,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__converse,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_wf__converse__trancl,axiom,
% 160.93/160.61 ! [V_r_2,T_a] :
% 160.93/160.61 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 160.93/160.61 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_equiv__comp__eq,axiom,
% 160.93/160.61 ! [V_r_2,V_A_2,T_a] :
% 160.93/160.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.93/160.61 => 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 ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Range__def,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Domain__converse,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Range__converse,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__converseI,axiom,
% 160.93/160.61 ! [V_r_2,V_x_2,V_y_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => 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)))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__converseD,axiom,
% 160.93/160.61 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( 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))))
% 160.93/160.61 => 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__converseI,axiom,
% 160.93/160.61 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( 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))))
% 160.93/160.61 => 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)))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__converseD,axiom,
% 160.93/160.61 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( 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))))
% 160.93/160.61 => 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)))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Image__subset__eq,axiom,
% 160.93/160.61 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 <=> 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))))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_refl__on__comp__subset,axiom,
% 160.93/160.61 ! [V_r_2,V_A_2,T_a] :
% 160.93/160.61 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 160.93/160.61 => 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_comp__equivI,axiom,
% 160.93/160.61 ! [V_A_2,V_r_2,T_a] :
% 160.93/160.61 ( 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
% 160.93/160.61 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2
% 160.93/160.61 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_finite__acyclic__wf__converse,axiom,
% 160.93/160.61 ! [V_r_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2))
% 160.93/160.61 => ( c_Wellfounded_Oacyclic(T_a,V_r_2)
% 160.93/160.61 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_converse__def,axiom,
% 160.93/160.61 ! [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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Image__INT__eq,axiom,
% 160.93/160.61 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] :
% 160.93/160.61 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))
% 160.93/160.61 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_total__on__diff__Id,axiom,
% 160.93/160.61 ! [V_r_2,V_A_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_single__valued__Id,axiom,
% 160.93/160.61 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_single__valued__Id__on,axiom,
% 160.93/160.61 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_single__valued__rel__comp,axiom,
% 160.93/160.61 ! [V_s_2,T_c,V_r_2,T_b,T_a] :
% 160.93/160.61 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 160.93/160.61 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_single__valued__subset,axiom,
% 160.93/160.61 ! [V_s_2,V_r_2,T_b,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2)
% 160.93/160.61 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_total__on__empty,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_total__on__converse,axiom,
% 160.93/160.61 ! [V_r_2,V_A_2,T_a] :
% 160.93/160.61 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2))
% 160.93/160.61 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_single__valuedD,axiom,
% 160.93/160.61 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] :
% 160.93/160.61 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 160.93/160.61 => ( 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))
% 160.93/160.61 => ( 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))
% 160.93/160.61 => V_y_2 = V_z_2 ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_single__valued__def,axiom,
% 160.93/160.61 ! [V_r_2,T_b,T_a] :
% 160.93/160.61 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2)
% 160.93/160.61 <=> ! [B_x,B_y] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => ! [B_z] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => B_y = B_z ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_total__on__def,axiom,
% 160.93/160.61 ! [V_r_2,V_A_2,T_a] :
% 160.93/160.61 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2)
% 160.93/160.61 <=> ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.93/160.61 => ! [B_xa] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 160.93/160.61 => ( B_x != B_xa
% 160.93/160.61 => ( 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))
% 160.93/160.61 | 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)) ) ) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_single__valued__confluent,axiom,
% 160.93/160.61 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] :
% 160.93/160.61 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2)
% 160.93/160.61 => ( 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)))
% 160.93/160.61 => ( 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)))
% 160.93/160.61 => ( 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)))
% 160.93/160.61 | 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))) ) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Image__Int__eq,axiom,
% 160.93/160.61 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] :
% 160.93/160.61 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2))
% 160.93/160.61 => 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)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 160.93/160.61 ! [V_R_2,V_p_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 160.93/160.61 => 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)))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_acyclicI,axiom,
% 160.93/160.61 ! [V_r_2,T_a] :
% 160.93/160.61 ( ! [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)))
% 160.93/160.61 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_single__valued__rel__pow,axiom,
% 160.93/160.61 ! [V_n_2,V_R_2,T_a] :
% 160.93/160.61 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2)
% 160.93/160.61 => 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)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_wf__exp,axiom,
% 160.93/160.61 ! [V_R_2,V_n_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => c_Wellfounded_Owf(T_a,V_R_2) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_funpow__swap1,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_funpow__mult,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_comp__funpow,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rel__pow__commute,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rel__pow__1,axiom,
% 160.93/160.61 ! [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 ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__power,axiom,
% 160.93/160.61 ! [V_R_2,V_p_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2)))
% 160.93/160.61 <=> ? [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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rel__pow__imp__rtrancl,axiom,
% 160.93/160.61 ! [V_R_2,V_n_2,V_p_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_relpow_Osimps_I2_J,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rel__pow__add,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_relpow_Osimps_I1_J,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rel__pow__0__E,axiom,
% 160.93/160.61 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => V_x_2 = V_y_2 ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rel__pow__0__I,axiom,
% 160.93/160.61 ! [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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rel__pow__Suc__I,axiom,
% 160.93/160.61 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ( 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))
% 160.93/160.61 => 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rel__pow__Suc__I2,axiom,
% 160.93/160.61 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => ( 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)))
% 160.93/160.61 => 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_funpow_Osimps_I2_J,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_funpow__add,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_funpow_Osimps_I1_J,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_trancl__power,axiom,
% 160.93/160.61 ! [V_R_2,V_p_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2)))
% 160.93/160.61 <=> ? [B_n] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 160.93/160.61 & 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_funpow__code__def,axiom,
% 160.93/160.61 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rel__pow__E2,axiom,
% 160.93/160.61 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.61 => V_x_2 != V_z_2 )
% 160.93/160.61 => ~ ! [B_y,B_m] :
% 160.93/160.61 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 160.93/160.61 => ( 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))
% 160.93/160.61 => ~ 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))) ) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rel__pow__E,axiom,
% 160.93/160.61 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.61 => V_x_2 != V_z_2 )
% 160.93/160.61 => ~ ! [B_y,B_m] :
% 160.93/160.61 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 160.93/160.61 => ( 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)))
% 160.93/160.61 => ~ 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)) ) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 160.93/160.61 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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))))
% 160.93/160.61 => ( ! [B_x] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ! [B_y] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => B_y = B_x ) )
% 160.93/160.61 => 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__Un__separatorE,axiom,
% 160.93/160.61 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] :
% 160.93/160.61 ( 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))))
% 160.93/160.61 => ( ! [B_x] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ! [B_y] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => B_x = B_y ) )
% 160.93/160.61 => 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rel__pow__Suc__D2,axiom,
% 160.93/160.61 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ? [B_y] :
% 160.93/160.61 ( 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))
% 160.93/160.61 & 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rel__pow__Suc__E,axiom,
% 160.93/160.61 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ~ ! [B_y] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ~ 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rel__pow__Suc__E2,axiom,
% 160.93/160.61 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ~ ! [B_y] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => ~ 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_tranclD2,axiom,
% 160.93/160.61 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ? [B_z] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 & 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_tranclD,axiom,
% 160.93/160.61 ! [V_R_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ? [B_z] :
% 160.93/160.61 ( 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))
% 160.93/160.61 & 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_IdE,axiom,
% 160.93/160.61 ! [V_p_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a)))
% 160.93/160.61 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_nat__intermed__int__val,axiom,
% 160.93/160.61 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 160.93/160.61 ( ! [B_i] :
% 160.93/160.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 160.93/160.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 160.93/160.61 => 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))) )
% 160.93/160.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 160.93/160.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 160.93/160.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 160.93/160.61 => ? [B_i] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 160.93/160.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 160.93/160.61 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_mod__div__decomp,axiom,
% 160.93/160.61 ! [V_b,V_a,T_a] :
% 160.93/160.61 ( class_Divides_Osemiring__div(T_a)
% 160.93/160.61 => 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)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_wf__eq__minimal,axiom,
% 160.93/160.61 ! [V_r_2,T_a] :
% 160.93/160.61 ( c_Wellfounded_Owf(T_a,V_r_2)
% 160.93/160.61 <=> ! [B_Q] :
% 160.93/160.61 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q))
% 160.93/160.61 => ? [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q))
% 160.93/160.61 & ! [B_y] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) ) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_transfer__nat__int__set__cong,axiom,
% 160.93/160.61 ! [V_P_H_2,V_P_2] :
% 160.93/160.61 ( ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 160.93/160.61 => ( hBOOL(hAPP(V_P_2,B_x))
% 160.93/160.61 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 160.93/160.61 => 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)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Int__Collect__mono,axiom,
% 160.93/160.61 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.93/160.61 => ( ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.93/160.61 => ( hBOOL(hAPP(V_P_2,B_x))
% 160.93/160.61 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 160.93/160.61 => 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)))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_UnionE,axiom,
% 160.93/160.61 ! [V_C_2,V_A_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ~ ! [B_X] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X))
% 160.93/160.61 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_converseE,axiom,
% 160.93/160.61 ! [V_r_2,V_yx_2,T_b,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ~ ! [B_x,B_y] :
% 160.93/160.61 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x)
% 160.93/160.61 => ~ 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rel__compE,axiom,
% 160.93/160.61 ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ~ ! [B_x,B_y,B_z] :
% 160.93/160.61 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)
% 160.93/160.61 => ( 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))
% 160.93/160.61 => ~ 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)) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 160.93/160.61 ! [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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 160.93/160.61 ! [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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Nitpick_Oof__frac__def,axiom,
% 160.93/160.61 ! [V_q,T_a,T_b] :
% 160.93/160.61 ( ( class_Rings_Oinverse(T_b)
% 160.93/160.61 & class_Rings_Oring__1(T_b) )
% 160.93/160.61 => 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 160.93/160.61 ! [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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Nitpick_Oless__frac__def,axiom,
% 160.93/160.61 ! [V_r_2,V_q_2,T_a] :
% 160.93/160.61 ( c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2)
% 160.93/160.61 <=> 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 160.93/160.61 ! [V_r_2,V_q_2,T_a] :
% 160.93/160.61 ( c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2)
% 160.93/160.61 <=> 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Nitpick_Onum__def,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Nitpick_Odenom__def,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_setprod__pos,axiom,
% 160.93/160.61 ! [V_f_2,V_A_2,T_a,T_b] :
% 160.93/160.61 ( class_Rings_Olinordered__semidom(T_b)
% 160.93/160.61 => ( ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
% 160.93/160.61 => 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_internal__split__def,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_internal__split__conv,axiom,
% 160.93/160.61 ! [V_b_2,V_a_2,V_c_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_b,T_c,T_a),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_setprod__nonneg,axiom,
% 160.93/160.61 ! [V_f_2,V_A_2,T_a,T_b] :
% 160.93/160.61 ( class_Rings_Olinordered__semidom(T_b)
% 160.93/160.61 => ( ! [B_x] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) )
% 160.93/160.61 => 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_bool_Osize_I1_J,axiom,
% 160.93/160.61 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_bool_Osize_I2_J,axiom,
% 160.93/160.61 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_finite__less__ub,axiom,
% 160.93/160.61 ! [V_u_2,V_f_2] :
% 160.93/160.61 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 160.93/160.61 => 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)))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_lenlex__def,axiom,
% 160.93/160.61 ! [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)))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_lexn__length,axiom,
% 160.93/160.61 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2
% 160.93/160.61 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_neq__if__length__neq,axiom,
% 160.93/160.61 ! [V_ys,V_xs,T_a] :
% 160.93/160.61 ( 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)
% 160.93/160.61 => V_xs != V_ys ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_lenlex__conv,axiom,
% 160.93/160.61 ! [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)))))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_length__sublist,axiom,
% 160.93/160.61 ! [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)))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_lexn_Osimps_I2_J,axiom,
% 160.93/160.61 ! [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)))))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_impossible__Cons,axiom,
% 160.93/160.61 ! [V_x,V_ys,V_xs,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_not__Cons__self,axiom,
% 160.93/160.61 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_not__Cons__self2,axiom,
% 160.93/160.61 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 160.93/160.61
% 160.93/160.61 fof(fact_list_Oinject,axiom,
% 160.93/160.61 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] :
% 160.93/160.61 ( 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)
% 160.93/160.61 <=> ( V_a_2 = V_a_H_2
% 160.93/160.61 & V_list_2 = V_list_H_2 ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_list_Osize_I4_J,axiom,
% 160.93/160.61 ! [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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Cons__in__lex,axiom,
% 160.93/160.61 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 <=> ( ( 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))
% 160.93/160.61 & 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) )
% 160.93/160.61 | ( V_x_2 = V_y_2
% 160.93/160.61 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_set__Cons__def,axiom,
% 160.93/160.61 ! [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)))))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_pick_Osimps,axiom,
% 160.93/160.61 ! [V_xs,V_x,T_a,V_i] :
% 160.93/160.61 ( ( 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)))
% 160.93/160.61 => 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) )
% 160.93/160.61 & ( ~ 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)))
% 160.93/160.61 => 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_select__weight__cons__zero,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_lexord__cons__cons,axiom,
% 160.93/160.61 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 <=> ( 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))
% 160.93/160.61 | ( V_a_2 = V_b_2
% 160.93/160.61 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_lexord__lex,axiom,
% 160.93/160.61 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 & 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) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 160.93/160.61 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_list_Osize_I2_J,axiom,
% 160.93/160.61 ! [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))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Cons__acc__listrel1I,axiom,
% 160.93/160.61 ! [V_xs_2,V_r_2,V_x_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2)))
% 160.93/160.61 => ( 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))))
% 160.93/160.61 => 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)))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 160.93/160.61 ! [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)))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel1__converse,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel1__mono,axiom,
% 160.93/160.61 ! [V_s_2,V_r_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel1I2,axiom,
% 160.93/160.61 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 160.93/160.61 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel1__eq__len,axiom,
% 160.93/160.61 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 => 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) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 160.93/160.61 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 160.93/160.61 => 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) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_in__listrel1__converse,axiom,
% 160.93/160.61 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 160.93/160.61 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Cons__listrel1__Cons,axiom,
% 160.93/160.61 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 <=> ( ( 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))
% 160.93/160.61 & V_xs_2 = V_ys_2 )
% 160.93/160.61 | ( V_x_2 = V_y_2
% 160.93/160.61 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel1I1,axiom,
% 160.93/160.61 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel__Cons,axiom,
% 160.93/160.61 ! [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))))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_lexord__linear,axiom,
% 160.93/160.61 ! [V_y_2,V_x_2,V_r_2,T_a] :
% 160.93/160.61 ( ! [B_a,B_b] :
% 160.93/160.61 ( 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))
% 160.93/160.61 | B_a = B_b
% 160.93/160.61 | 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)) )
% 160.93/160.61 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 | V_x_2 = V_y_2
% 160.93/160.61 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel__rtrancl__refl,axiom,
% 160.93/160.61 ! [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)))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel__mono,axiom,
% 160.93/160.61 ! [V_s_2,V_r_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 160.93/160.61 ! [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)))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel__eq__len,axiom,
% 160.93/160.61 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 => 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) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel__rtrancl__trans,axiom,
% 160.93/160.61 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 160.93/160.61 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 160.93/160.61 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel1__subset__listrel,axiom,
% 160.93/160.61 ! [V_r_H_2,V_r_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2)
% 160.93/160.61 => 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 160.93/160.61 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel_OCons,axiom,
% 160.93/160.61 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrelp__listrel__eq,axiom,
% 160.93/160.61 ! [V_xa_2,V_x_2,V_r_2,T_a] :
% 160.93/160.61 ( 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)
% 160.93/160.61 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel__Cons1,axiom,
% 160.93/160.61 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 => ~ ! [B_y,B_ys] :
% 160.93/160.61 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys)
% 160.93/160.61 => ( 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))
% 160.93/160.61 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrelp_OCons,axiom,
% 160.93/160.61 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 160.93/160.61 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2)
% 160.93/160.61 => 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)) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrelp_Oequations_I2_J,axiom,
% 160.93/160.61 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] :
% 160.93/160.61 ( 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))
% 160.93/160.61 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 160.93/160.61 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel__Cons2,axiom,
% 160.93/160.61 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 => ~ ! [B_x,B_xs] :
% 160.93/160.61 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs)
% 160.93/160.61 => ( 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))
% 160.93/160.61 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel__subset,axiom,
% 160.93/160.61 ! [V_A_2,V_r_2,T_a] :
% 160.93/160.61 ( 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))))
% 160.93/160.61 => 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))))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_lists__UNIV,axiom,
% 160.93/160.61 ! [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)) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_lists__mono,axiom,
% 160.93/160.61 ! [V_B_2,V_A_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.93/160.61 => 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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_equiv__listrel,axiom,
% 160.93/160.61 ! [V_r_2,V_A_2,T_a] :
% 160.93/160.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2)
% 160.93/160.61 => 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)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel__refl__on,axiom,
% 160.93/160.61 ! [V_r_2,V_A_2,T_a] :
% 160.93/160.61 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2)
% 160.93/160.61 => 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)) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_Cons__in__lists__iff,axiom,
% 160.93/160.61 ! [V_A_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.93/160.61 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_lists__accD,axiom,
% 160.93/160.61 ! [V_r_2,V_xs_2,T_a] :
% 160.93/160.61 ( 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))))
% 160.93/160.61 => 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)))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_lists__accI,axiom,
% 160.93/160.61 ! [V_r_2,V_xs_2,T_a] :
% 160.93/160.61 ( 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))))
% 160.93/160.61 => 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)))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_listrel__iff__nth,axiom,
% 160.93/160.61 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.61 <=> ( 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)
% 160.93/160.61 & ! [B_n] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => 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)) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_lexord__irreflexive,axiom,
% 160.93/160.61 ! [V_y_2,V_r_2,T_a] :
% 160.93/160.61 ( ! [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))
% 160.93/160.61 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_infinite__UNIV__listI,axiom,
% 160.93/160.61 ! [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)))) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_list__eq__iff__nth__eq,axiom,
% 160.93/160.61 ! [T_a,V_ys_2,V_xs_2] :
% 160.93/160.61 ( V_xs_2 = V_ys_2
% 160.93/160.61 <=> ( 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)
% 160.93/160.61 & ! [B_i] :
% 160.93/160.61 ( 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)))
% 160.93/160.61 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_nth__Cons__Suc,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_nth__Cons__0,axiom,
% 160.93/160.61 ! [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 ).
% 160.93/160.61
% 160.93/160.61 fof(fact_nth_Osimps,axiom,
% 160.93/160.61 ! [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) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_nth__Cons_H,axiom,
% 160.93/160.61 ! [V_xs,V_x,T_a,V_n] :
% 160.93/160.61 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.61 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 160.93/160.61 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.61 => 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_nth__Cons__number__of,axiom,
% 160.93/160.61 ! [V_xs,V_x,T_a,V_v] :
% 160.93/160.61 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.61 => 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 )
% 160.93/160.61 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.61 => 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))) ) ) ).
% 160.93/160.61
% 160.93/160.61 fof(fact_lexord__take__index__conv,axiom,
% 160.93/160.61 ! [V_r_2,V_y_2,V_x_2,T_a] :
% 160.93/160.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.62 <=> ( ( 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)))
% 160.93/160.62 & 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 )
% 160.93/160.62 | ? [B_i] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2)
% 160.93/160.62 & 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)) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__sublist,axiom,
% 160.93/160.62 ! [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))))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_finite__set,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__subset__Cons,axiom,
% 160.93/160.62 ! [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)))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__all,axiom,
% 160.93/160.62 ! [V_n,V_xs,T_a] :
% 160.93/160.62 ( 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))
% 160.93/160.62 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__take__subset,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__take__subset__set__take,axiom,
% 160.93/160.62 ! [V_xs_2,T_a,V_n_2,V_m_2] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.93/160.62 => 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)))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__sublist__subset,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nth__take,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_n,V_i] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__Suc__Cons,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__ConsD,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,V_y_2,T_a] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 => ( V_y_2 = V_x_2
% 160.93/160.62 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_in__set__sublistD,axiom,
% 160.93/160.62 ! [V_I_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_in__set__takeD,axiom,
% 160.93/160.62 ! [V_xs_2,V_n_2,V_x_2,T_a] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_notin__set__sublistI,axiom,
% 160.93/160.62 ! [V_I_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => ~ 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)))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__take,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__take,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_sublist__upt__eq__take,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_card__length,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_all__set__conv__all__nth,axiom,
% 160.93/160.62 ! [V_P_2,V_xs_2,T_a] :
% 160.93/160.62 ( ! [B_x] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => hBOOL(hAPP(V_P_2,B_x)) )
% 160.93/160.62 <=> ! [B_i] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__size__estimation,axiom,
% 160.93/160.62 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 160.93/160.62 => 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))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__size__estimation_H,axiom,
% 160.93/160.62 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 160.93/160.62 => 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))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_in__lists__conv__set,axiom,
% 160.93/160.62 ! [V_A_2,V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
% 160.93/160.62 <=> ! [B_x] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__pos__if__in__set,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nth__mem,axiom,
% 160.93/160.62 ! [V_xs_2,T_a,V_n_2] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_in__set__conv__nth,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 <=> ? [B_i] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_lists__eq__set,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__conv__nth,axiom,
% 160.93/160.62 ! [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))))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_finite__lists__length__eq,axiom,
% 160.93/160.62 ! [V_n_2,V_A_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.93/160.62 => 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))))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_finite__lists__length__le,axiom,
% 160.93/160.62 ! [V_n_2,V_A_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.93/160.62 => 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))))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_WT__bodies__def,axiom,
% 160.93/160.62 ( c_Com_OWT__bodies
% 160.93/160.62 <=> ! [B_x] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listrel__iff__zip,axiom,
% 160.93/160.62 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.62 <=> ( 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)
% 160.93/160.62 & ! [B_x] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 => 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)) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__zip,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__zip,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip__Cons__Cons,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__eq__iff__zip__eq,axiom,
% 160.93/160.62 ! [T_a,V_ys_2,V_xs_2] :
% 160.93/160.62 ( V_xs_2 = V_ys_2
% 160.93/160.62 <=> ( 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)
% 160.93/160.62 & ! [B_x] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_in__set__zipE,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__zip__rightD,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__zip__leftD,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip__same,axiom,
% 160.93/160.62 ! [V_xs_2,V_b_2,V_a_2,T_a] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 & V_a_2 = V_b_2 ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nth__zip,axiom,
% 160.93/160.62 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => ( 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)))
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__zip,axiom,
% 160.93/160.62 ! [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)))))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_greaterThanLessThan__upto,axiom,
% 160.93/160.62 ! [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)))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__setsum__nth,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 160.93/160.62 ! [V_ns_2] :
% 160.93/160.62 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.62 <=> ! [B_x] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 160.93/160.62 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__upto,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_atLeastAtMost__upto,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_elem__le__listsum__nat,axiom,
% 160.93/160.62 ! [V_ns,V_k] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__simps_I2_J,axiom,
% 160.93/160.62 ! [V_xs,V_x,T_a] :
% 160.93/160.62 ( class_Groups_Omonoid__add(T_a)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_atLeastLessThan__upto,axiom,
% 160.93/160.62 ! [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)))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_greaterThanAtMost__upto,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nat__list__def,axiom,
% 160.93/160.62 ! [V_l_2] :
% 160.93/160.62 ( c_List_Onat__list(V_l_2)
% 160.93/160.62 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__size__pointwise,axiom,
% 160.93/160.62 ! [V_g_2,V_f_2,V_xs_2,T_a] :
% 160.93/160.62 ( ! [B_x] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__update__nat,axiom,
% 160.93/160.62 ! [V_n,V_ns,V_k] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_butlast__take,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_n] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__update__beyond,axiom,
% 160.93/160.62 ! [V_x,V_i,V_xs,T_a] :
% 160.93/160.62 ( 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))
% 160.93/160.62 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nth__list__update__neq,axiom,
% 160.93/160.62 ! [V_x,V_xs,T_a,V_j,V_i] :
% 160.93/160.62 ( V_i != V_j
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__update__id,axiom,
% 160.93/160.62 ! [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 ).
% 160.93/160.62
% 160.93/160.62 fof(fact_butlast__list__update,axiom,
% 160.93/160.62 ! [V_x,V_xs,T_a,V_k] :
% 160.93/160.62 ( ( 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))
% 160.93/160.62 => 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) )
% 160.93/160.62 & ( 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))
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__list__update,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip__update,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_update__zip,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__update__overwrite,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__update__swap,axiom,
% 160.93/160.62 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 160.93/160.62 ( V_i != V_i_H
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__update__code_I3_J,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__update_Osimps_I2_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__update__code_I2_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_in__set__butlastD,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2))))
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__update__subsetI,axiom,
% 160.93/160.62 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] :
% 160.93/160.62 ( 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))
% 160.93/160.62 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__update__subset__insert,axiom,
% 160.93/160.62 ! [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)))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nth__list__update,axiom,
% 160.93/160.62 ! [V_x,V_j,V_xs,T_a,V_i] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => ( ( V_i = V_j
% 160.93/160.62 => 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 )
% 160.93/160.62 & ( V_i != V_j
% 160.93/160.62 => 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) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__update__same__conv,axiom,
% 160.93/160.62 ! [V_x_2,V_xs_2,T_a,V_i_2] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 160.93/160.62 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nth__list__update__eq,axiom,
% 160.93/160.62 ! [V_x,V_xs,T_a,V_i] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__butlast,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_n] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__butlast,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__update__memI,axiom,
% 160.93/160.62 ! [V_x_2,V_xs_2,T_a,V_n_2] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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)))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_butlast__conv__take,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listrel1__iff__update,axiom,
% 160.93/160.62 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.62 <=> ? [B_y,B_n] :
% 160.93/160.62 ( 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))
% 160.93/160.62 & 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)))
% 160.93/160.62 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__list__update,axiom,
% 160.93/160.62 ! [V_i_2,V_a_2,V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.62 => ( ~ 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))))))
% 160.93/160.62 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__upto,axiom,
% 160.93/160.62 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__take,axiom,
% 160.93/160.62 ! [V_i,V_xs,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 160.93/160.62 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__sublistI,axiom,
% 160.93/160.62 ! [V_I_2,V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.62 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__zipI1,axiom,
% 160.93/160.62 ! [V_ys,T_b,V_xs,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 160.93/160.62 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__zipI2,axiom,
% 160.93/160.62 ! [V_xs,T_b,V_ys,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 160.93/160.62 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct_Osimps_I2_J,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))
% 160.93/160.62 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_card__distinct,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__card,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__conv__nth,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.62 <=> ! [B_i] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => ! [B_j] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => ( B_i != B_j
% 160.93/160.62 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nth__eq__iff__index__eq,axiom,
% 160.93/160.62 ! [V_j_2,V_i_2,V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.62 => ( 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)))
% 160.93/160.62 => ( 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)))
% 160.93/160.62 => ( 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)
% 160.93/160.62 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.93/160.62 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Nitpick_Ocard_H__def,axiom,
% 160.93/160.62 ! [V_A_2,T_a] :
% 160.93/160.62 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.93/160.62 => 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)))) )
% 160.93/160.62 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.93/160.62 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_dom__map__upds,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__upds__apply__nontin,axiom,
% 160.93/160.62 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__upds__list__update2__drop,axiom,
% 160.93/160.62 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] :
% 160.93/160.62 ( 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))
% 160.93/160.62 => ( 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)))
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nth__take__lemma,axiom,
% 160.93/160.62 ! [V_ys,V_xs,T_a,V_k] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => ( 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)))
% 160.93/160.62 => ( ! [B_i] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 160.93/160.62 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 160.93/160.62 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_restrict__map__upds,axiom,
% 160.93/160.62 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => ( 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))
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_restrict__map__insert,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_restrict__restrict,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_restrict__in,axiom,
% 160.93/160.62 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_dom__restrict,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_fun__upd__restrict,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_restrict__fun__upd,axiom,
% 160.93/160.62 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 160.93/160.62 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 160.93/160.62 => 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) )
% 160.93/160.62 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_fun__upd__restrict__conv,axiom,
% 160.93/160.62 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__remove1__eq,axiom,
% 160.93/160.62 ! [V_x_2,V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.62 => 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)))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__Cons__number__of,axiom,
% 160.93/160.62 ! [V_xs,V_x,T_a,V_v] :
% 160.93/160.62 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.62 => 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) )
% 160.93/160.62 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_lists_ONil,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listrel__Nil1,axiom,
% 160.93/160.62 ! [V_r_2,V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.62 => V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listrel__Nil2,axiom,
% 160.93/160.62 ! [V_r_2,V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.62 => V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__update__nonempty,axiom,
% 160.93/160.62 ! [V_x_2,V_k_2,V_xs_2,T_a] :
% 160.93/160.62 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a)
% 160.93/160.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__update_Osimps_I1_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__update__code_I1_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__empty2,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2)
% 160.93/160.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__empty,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.93/160.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__0__conv,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list_Osize_I3_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__simps_I1_J,axiom,
% 160.93/160.62 ! [T_a] :
% 160.93/160.62 ( class_Groups_Omonoid__add(T_a)
% 160.93/160.62 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip_Osimps_I1_J,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip__Nil,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listrelp_ONil,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listrelp_Oequations_I1_J,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list_Osize_I1_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_remove1_Osimps_I1_J,axiom,
% 160.93/160.62 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_remove1__commute,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_sublist__nil,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__0,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__eq__Nil,axiom,
% 160.93/160.62 ! [V_xs_2,V_n_2,T_a] :
% 160.93/160.62 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 160.93/160.62 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.62 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__Nil,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_upto__empty,axiom,
% 160.93/160.62 ! [V_i,V_j] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 160.93/160.62 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_remove1_Osimps_I2_J,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_y,V_x] :
% 160.93/160.62 ( ( V_x = V_y
% 160.93/160.62 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 160.93/160.62 & ( V_x != V_y
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list_Osimps_I3_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list_Osimps_I2_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_butlast_Osimps_I2_J,axiom,
% 160.93/160.62 ! [V_x,T_a,V_xs] :
% 160.93/160.62 ( ( V_xs = c_List_Olist_ONil(T_a)
% 160.93/160.62 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 160.93/160.62 & ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_butlast_Osimps_I1_J,axiom,
% 160.93/160.62 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_in__set__remove1,axiom,
% 160.93/160.62 ! [V_xs_2,T_a,V_b_2,V_a_2] :
% 160.93/160.62 ( V_a_2 != V_b_2
% 160.93/160.62 => ( 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))))
% 160.93/160.62 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_notin__set__remove1,axiom,
% 160.93/160.62 ! [V_y_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => ~ 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)))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_remove1__idem,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__upds__Nil2,axiom,
% 160.93/160.62 ! [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 ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__upds__Nil1,axiom,
% 160.93/160.62 ! [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 ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct_Osimps_I1_J,axiom,
% 160.93/160.62 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__remove1,axiom,
% 160.93/160.62 ! [V_x,V_xs,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 160.93/160.62 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__butlast,axiom,
% 160.93/160.62 ! [T_a,V_xs] :
% 160.93/160.62 ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.62 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 160.93/160.62 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_sublist__empty,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__remove1__subset,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__greater__0__conv,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__1__Cons,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_not__Nil__listrel1,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_not__listrel1__Nil,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listrel_ONil,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_lexord__Nil__right,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Nil__notin__lex,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Nil2__notin__lex,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__Cons,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_upto_Osimps,axiom,
% 160.93/160.62 ! [V_j,V_i] :
% 160.93/160.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 160.93/160.62 => 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)) )
% 160.93/160.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 160.93/160.62 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_sublist__singleton,axiom,
% 160.93/160.62 ! [V_x_2,T_a,V_A_2] :
% 160.93/160.62 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 160.93/160.62 => 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)) )
% 160.93/160.62 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_lists__empty,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__Cons_H,axiom,
% 160.93/160.62 ! [V_xs,V_x,T_a,V_n] :
% 160.93/160.62 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.62 => 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) )
% 160.93/160.62 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_upto__rec__number__of,axiom,
% 160.93/160.62 ! [V_n,V_m] :
% 160.93/160.62 ( ( 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)))
% 160.93/160.62 => 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))) )
% 160.93/160.62 & ( ~ 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)))
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listrel__Nil,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__Cons__sing__Nil,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__remove1,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => 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)) )
% 160.93/160.62 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_upto_Opsimps,axiom,
% 160.93/160.62 ! [V_j_2,V_i_2] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 160.93/160.62 => 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)) )
% 160.93/160.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 160.93/160.62 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_select,axiom,
% 160.93/160.62 ! [V_s_2,T_a,V_xs_2] :
% 160.93/160.62 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listset_Osimps_I1_J,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip__Cons1,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list_Osimps_I5_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list_Osimps_I4_J,axiom,
% 160.93/160.62 ! [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 ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listset_Osimps_I2_J,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip__Cons,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_sorted__list__of__set__remove,axiom,
% 160.93/160.62 ! [V_x_2,V_A_2,T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_upto_Opinduct,axiom,
% 160.93/160.62 ! [V_P_2,V_a1_2,V_a0_2] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => ( ! [B_i,B_j] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 160.93/160.62 => 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)) )
% 160.93/160.62 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 160.93/160.62 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_sorted__list__of__set__empty,axiom,
% 160.93/160.62 ! [T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_anamorph_Osimps,axiom,
% 160.93/160.62 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] :
% 160.93/160.62 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 160.93/160.62 => 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) )
% 160.93/160.62 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_sublist__Cons,axiom,
% 160.93/160.62 ! [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)))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append1__eq__conv,axiom,
% 160.93/160.62 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 <=> ( V_xs_2 = V_ys_2
% 160.93/160.62 & V_x_2 = V_y_2 ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Cons__eq__append__conv,axiom,
% 160.93/160.62 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a)
% 160.93/160.62 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 )
% 160.93/160.62 | ? [B_ys_H] :
% 160.93/160.62 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2
% 160.93/160.62 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__eq__Cons__conv,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a)
% 160.93/160.62 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) )
% 160.93/160.62 | ? [B_ys_H] :
% 160.93/160.62 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H)
% 160.93/160.62 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Cons__eq__appendI,axiom,
% 160.93/160.62 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 160.93/160.62 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 160.93/160.62 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 160.93/160.62 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__Cons,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__append,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip__append,axiom,
% 160.93/160.62 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => ( 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)
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__append,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__append,axiom,
% 160.93/160.62 ! [V_ys,V_xs,T_a] :
% 160.93/160.62 ( class_Groups_Omonoid__add(T_a)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__assoc,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__eq__append__conv2,axiom,
% 160.93/160.62 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 <=> ? [B_us] :
% 160.93/160.62 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us)
% 160.93/160.62 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 )
% 160.93/160.62 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2
% 160.93/160.62 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_same__append__eq,axiom,
% 160.93/160.62 ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 <=> V_ys_2 = V_zs_2 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__same__eq,axiom,
% 160.93/160.62 ! [V_zs_2,V_xs_2,V_ys_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 <=> V_ys_2 = V_zs_2 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__eq__appendI,axiom,
% 160.93/160.62 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 160.93/160.62 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 160.93/160.62 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 160.93/160.62 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__in__lists__conv,axiom,
% 160.93/160.62 ! [V_A_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2)))
% 160.93/160.62 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_fun__upds__append2__drop,axiom,
% 160.93/160.62 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_fun__upds__append__drop,axiom,
% 160.93/160.62 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_butlast__append,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_ys] :
% 160.93/160.62 ( ( V_ys = c_List_Olist_ONil(T_a)
% 160.93/160.62 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 160.93/160.62 & ( V_ys != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_eq__Nil__appendI,axiom,
% 160.93/160.62 ! [T_a,V_ys,V_xs] :
% 160.93/160.62 ( V_xs = V_ys
% 160.93/160.62 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__self__conv2,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,T_a] :
% 160.93/160.62 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2
% 160.93/160.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__self__conv,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,T_a] :
% 160.93/160.62 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2
% 160.93/160.62 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__is__Nil__conv,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,T_a] :
% 160.93/160.62 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a)
% 160.93/160.62 <=> ( V_xs_2 = c_List_Olist_ONil(T_a)
% 160.93/160.62 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_self__append__conv2,axiom,
% 160.93/160.62 ! [V_xs_2,T_a,V_ys_2] :
% 160.93/160.62 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 160.93/160.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_self__append__conv,axiom,
% 160.93/160.62 ! [V_ys_2,T_a,V_xs_2] :
% 160.93/160.62 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 160.93/160.62 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__Nil2,axiom,
% 160.93/160.62 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Nil__is__append__conv,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,T_a] :
% 160.93/160.62 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)
% 160.93/160.62 <=> ( V_xs_2 = c_List_Olist_ONil(T_a)
% 160.93/160.62 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__Nil,axiom,
% 160.93/160.62 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nth__append__length,axiom,
% 160.93/160.62 ! [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 ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nth__append__length__plus,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__append,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__update__append1,axiom,
% 160.93/160.62 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__update__length,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_remove1__append,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => 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) )
% 160.93/160.62 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_in__set__butlast__appendI,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2))))
% 160.93/160.62 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) )
% 160.93/160.62 => 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))))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_butlast__snoc,axiom,
% 160.93/160.62 ! [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 ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__listrel1I,axiom,
% 160.93/160.62 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.62 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.62 & V_us_2 = V_vs_2 )
% 160.93/160.62 | ( V_xs_2 = V_ys_2
% 160.93/160.62 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) )
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_lexord__append__leftI,axiom,
% 160.93/160.62 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__append,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
% 160.93/160.62 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.62 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
% 160.93/160.62 & 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nth__append,axiom,
% 160.93/160.62 ! [V_ys,V_xs,T_a,V_n] :
% 160.93/160.62 ( ( 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)))
% 160.93/160.62 => 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) )
% 160.93/160.62 & ( ~ 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)))
% 160.93/160.62 => 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))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__update__append,axiom,
% 160.93/160.62 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 160.93/160.62 ( ( 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)))
% 160.93/160.62 => 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) )
% 160.93/160.62 & ( ~ 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)))
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_sublist__append,axiom,
% 160.93/160.62 ! [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)))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listrel1I,axiom,
% 160.93/160.62 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] :
% 160.93/160.62 ( 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))
% 160.93/160.62 => ( 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))
% 160.93/160.62 => ( 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))
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_lexord__append__left__rightI,axiom,
% 160.93/160.62 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] :
% 160.93/160.62 ( 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))
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__Suc__conv__app__nth,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_i] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 160.93/160.62 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.62 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.62 & V_x_2 = V_y_2 )
% 160.93/160.62 | ( V_xs_2 = V_ys_2
% 160.93/160.62 & 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)) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listrel1E,axiom,
% 160.93/160.62 ! [V_r_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.62 => ~ ! [B_x,B_y] :
% 160.93/160.62 ( 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))
% 160.93/160.62 => ! [B_us,B_vs] :
% 160.93/160.62 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs))
% 160.93/160.62 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_lexord__append__leftD,axiom,
% 160.93/160.62 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.62 => ( ! [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))
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate1__def,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__upds__append1,axiom,
% 160.93/160.62 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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)))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_image__map__upd,axiom,
% 160.93/160.62 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 160.93/160.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__rotate1,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__rotate1,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_dom__const,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_domI,axiom,
% 160.93/160.62 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
% 160.93/160.62 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2)
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_insert__dom,axiom,
% 160.93/160.62 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] :
% 160.93/160.62 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct1__rotate,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)))
% 160.93/160.62 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__upd__Some__unfold,axiom,
% 160.93/160.62 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] :
% 160.93/160.62 ( 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)
% 160.93/160.62 <=> ( ( V_x_2 = V_a_2
% 160.93/160.62 & V_b_2 = V_y_2 )
% 160.93/160.62 | ( V_x_2 != V_a_2
% 160.93/160.62 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__upd__triv,axiom,
% 160.93/160.62 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] :
% 160.93/160.62 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 160.93/160.62 => 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 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__upd__eqD1,axiom,
% 160.93/160.62 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] :
% 160.93/160.62 ( 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))
% 160.93/160.62 => V_x_2 = V_y_2 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate1__is__Nil__conv,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
% 160.93/160.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__upds__Cons,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_WT_Oequations_I7_J,axiom,
% 160.93/160.62 ! [V_a_2] :
% 160.93/160.62 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2)))
% 160.93/160.62 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_finite__range__updI,axiom,
% 160.93/160.62 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] :
% 160.93/160.62 ( 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)))))
% 160.93/160.62 => 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))))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_WT__bodiesD,axiom,
% 160.93/160.62 ! [V_b,V_pn] :
% 160.93/160.62 ( c_Com_OWT__bodies
% 160.93/160.62 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
% 160.93/160.62 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__upds__twist,axiom,
% 160.93/160.62 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] :
% 160.93/160.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2)))
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_restrict__upd__same,axiom,
% 160.93/160.62 ! [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))))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate__simps,axiom,
% 160.93/160.62 ! [V_xs,V_x,T_b,T_a] :
% 160.93/160.62 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 160.93/160.62 & 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate1__length01,axiom,
% 160.93/160.62 ! [V_xs,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__upd__upds__conv__if,axiom,
% 160.93/160.62 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] :
% 160.93/160.62 ( ( 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))))
% 160.93/160.62 => 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) )
% 160.93/160.62 & ( ~ 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))))
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option_Osize_I2_J,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option_Osimps_I5_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_inj__Some,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option_Oinject,axiom,
% 160.93/160.62 ! [V_a_H_2,V_a_2,T_a] :
% 160.93/160.62 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2)
% 160.93/160.62 <=> V_a_2 = V_a_H_2 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_the_Osimps,axiom,
% 160.93/160.62 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ).
% 160.93/160.62
% 160.93/160.62 fof(fact_WTs__elim__cases_I7_J,axiom,
% 160.93/160.62 ! [V_P] :
% 160.93/160.62 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P)))
% 160.93/160.62 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Option_Oset_Osimps_I2_J,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_elem__set,axiom,
% 160.93/160.62 ! [V_xo_2,V_x_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2)))
% 160.93/160.62 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_upd__conv__take__nth__drop,axiom,
% 160.93/160.62 ! [V_a,V_xs,T_a,V_i] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_id__take__nth__drop,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_i] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__Nil,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__drop,axiom,
% 160.93/160.62 ! [V_i,V_xs,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 160.93/160.62 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_butlast__drop,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__butlast,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__take,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__drop,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__0,axiom,
% 160.93/160.62 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__drop,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__zip,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__drop,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_in__set__dropD,axiom,
% 160.93/160.62 ! [V_xs_2,V_n_2,V_x_2,T_a] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__drop__subset,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__Suc__Cons,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__1__Cons,axiom,
% 160.93/160.62 ! [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 ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nth__via__drop,axiom,
% 160.93/160.62 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 160.93/160.62 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 160.93/160.62 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__take__drop__id,axiom,
% 160.93/160.62 ! [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 ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__drop__subset__set__drop,axiom,
% 160.93/160.62 ! [V_xs_2,T_a,V_m_2,V_n_2] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 160.93/160.62 => 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)))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__all,axiom,
% 160.93/160.62 ! [V_n,V_xs,T_a] :
% 160.93/160.62 ( 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))
% 160.93/160.62 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__eq__Nil,axiom,
% 160.93/160.62 ! [V_xs_2,V_n_2,T_a] :
% 160.93/160.62 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 160.93/160.62 <=> 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__append,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__eq__conv__conj,axiom,
% 160.93/160.62 ! [V_zs_2,V_ys_2,V_xs_2,T_a] :
% 160.93/160.62 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2
% 160.93/160.62 <=> ( 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)
% 160.93/160.62 & 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__Cons,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__Cons_H,axiom,
% 160.93/160.62 ! [V_xs,V_x,T_a,V_n] :
% 160.93/160.62 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.62 => 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) )
% 160.93/160.62 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nth__drop,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_i,V_n] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__eq__append__conv__if,axiom,
% 160.93/160.62 ! [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] :
% 160.93/160.62 ( 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)
% 160.93/160.62 <=> ( ( 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)))
% 160.93/160.62 => ( 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)
% 160.93/160.62 & 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) ) )
% 160.93/160.62 & ( ~ 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)))
% 160.93/160.62 => ( 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
% 160.93/160.62 & 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 ) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nth__drop_H,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_i] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__Cons__number__of,axiom,
% 160.93/160.62 ! [V_xs,V_x,T_a,V_v] :
% 160.93/160.62 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.62 => 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) )
% 160.93/160.62 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__add,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_j,V_i] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip__append2,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip__append1,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__hd__drop,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_n] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_hd__drop__conv__nth,axiom,
% 160.93/160.62 ! [V_n,T_a,V_xs] :
% 160.93/160.62 ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.62 => ( 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)))
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_hd_Osimps,axiom,
% 160.93/160.62 ! [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 ).
% 160.93/160.62
% 160.93/160.62 fof(fact_hd__append2,axiom,
% 160.93/160.62 ! [V_ys,T_a,V_xs] :
% 160.93/160.62 ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_hd__append,axiom,
% 160.93/160.62 ! [V_ys,T_a,V_xs] :
% 160.93/160.62 ( ( V_xs = c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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) )
% 160.93/160.62 & ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_hd__in__set,axiom,
% 160.93/160.62 ! [T_a,V_xs_2] :
% 160.93/160.62 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_hd__conv__nth,axiom,
% 160.93/160.62 ! [T_a,V_xs] :
% 160.93/160.62 ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate1__hd__tl,axiom,
% 160.93/160.62 ! [T_a,V_xs] :
% 160.93/160.62 ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option_Osize_I4_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__tl,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_tl__drop,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_tl_Osimps_I1_J,axiom,
% 160.93/160.62 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__tl,axiom,
% 160.93/160.62 ! [V_xs,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 160.93/160.62 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_tl_Osimps_I2_J,axiom,
% 160.93/160.62 ! [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 ).
% 160.93/160.62
% 160.93/160.62 fof(fact_tl__append2,axiom,
% 160.93/160.62 ! [V_ys,T_a,V_xs] :
% 160.93/160.62 ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__tl,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__Suc,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_tl__append,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__tl,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_tl__take,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__Suc,axiom,
% 160.93/160.62 ! [V_n,T_a,V_xs] :
% 160.93/160.62 ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_fold1__set,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 160.93/160.62 => ( V_xs_2 != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_hd__rotate__conv__nth,axiom,
% 160.93/160.62 ! [V_n,T_a,V_xs] :
% 160.93/160.62 ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__rotate,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_foldl__append,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_foldl__Cons,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__rotate,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_start__le__sum,axiom,
% 160.93/160.62 ! [V_ns_2,V_n_2,V_m_2] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_foldl__assoc,axiom,
% 160.93/160.62 ! [V_zs_2,V_y_2,V_x_2,T_a] :
% 160.93/160.62 ( class_Groups_Osemigroup__add(T_a)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate__rotate,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_foldl__absorb0,axiom,
% 160.93/160.62 ! [V_zs_2,V_x_2,T_a] :
% 160.93/160.62 ( class_Groups_Omonoid__add(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate0,axiom,
% 160.93/160.62 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate__add,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__rotate,axiom,
% 160.93/160.62 ! [V_xs_2,V_n_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)))
% 160.93/160.62 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_foldl__Nil,axiom,
% 160.93/160.62 ! [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 ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate__is__Nil__conv,axiom,
% 160.93/160.62 ! [V_xs_2,V_n_2,T_a] :
% 160.93/160.62 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 160.93/160.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate1__rotate__swap,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate__def,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate__conv__mod,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate__Suc,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__foldl,axiom,
% 160.93/160.62 ! [T_a] :
% 160.93/160.62 ( class_Groups_Omonoid__add(T_a)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_sum__eq__0__conv,axiom,
% 160.93/160.62 ! [V_ns_2,V_m_2] :
% 160.93/160.62 ( 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)
% 160.93/160.62 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.62 & ! [B_x] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 160.93/160.62 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate__id,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_n] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate__length01,axiom,
% 160.93/160.62 ! [V_n,V_xs,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 160.93/160.62 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] :
% 160.93/160.62 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Sup__set__fold,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Inf__set__fold,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Sup__fin__set__fold,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( class_Lattices_Olattice(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Inf__fin__set__fold,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( class_Lattices_Olattice(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Min__fin__set__fold,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Max__fin__set__fold,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_SUPR__set__fold,axiom,
% 160.93/160.62 ! [V_f_2,V_xs_2,T_b,T_a] :
% 160.93/160.62 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_INFI__set__fold,axiom,
% 160.93/160.62 ! [V_f_2,V_xs_2,T_b,T_a] :
% 160.93/160.62 ( class_Complete__Lattice_Ocomplete__lattice(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__upds__fold__map__upd,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_elem__le__sum,axiom,
% 160.93/160.62 ! [V_ns_2,V_n_2] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate__drop__take,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_ran__def,axiom,
% 160.93/160.62 ! [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)))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_lexord__append__rightI,axiom,
% 160.93/160.62 ! [V_r_2,V_x_2,T_a,V_y_2] :
% 160.93/160.62 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z)
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_ranI,axiom,
% 160.93/160.62 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] :
% 160.93/160.62 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2)
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_sorted__list__of__set__insert,axiom,
% 160.93/160.62 ! [V_x_2,V_A_2,T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.93/160.62 => 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)))))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_lexord__Nil__left,axiom,
% 160.93/160.62 ! [V_r_2,V_y_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 160.93/160.62 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__insort,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_b)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_insort__key_Osimps_I1_J,axiom,
% 160.93/160.62 ! [V_x_2,V_f_2,T_a,T_b] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_b)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_insort__key_Osimps_I2_J,axiom,
% 160.93/160.62 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => ( ( 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)))
% 160.93/160.62 => 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)) )
% 160.93/160.62 & ( ~ 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)))
% 160.93/160.62 => 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)) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__insort,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_b)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_fun__left__comm__insort,axiom,
% 160.93/160.62 ! [T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_insort__left__comm,axiom,
% 160.93/160.62 ! [V_xs_2,V_y_2,V_x_2,T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_insort__key__left__comm,axiom,
% 160.93/160.62 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_remove1__insort,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => 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 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_insort__not__Nil,axiom,
% 160.93/160.62 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_b)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__insort,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_b)
% 160.93/160.62 => ( 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)))
% 160.93/160.62 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_insort__insert__insort__key,axiom,
% 160.93/160.62 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => ( ~ 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))))
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_insort__insert__insort,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__insort__insert,axiom,
% 160.93/160.62 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_b)
% 160.93/160.62 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.62 => 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))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_insort__insert__triv,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__insort__insert,axiom,
% 160.93/160.62 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_insort__insert__key__triv,axiom,
% 160.93/160.62 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] :
% 160.93/160.62 ( class_Orderings_Olinorder(T_a)
% 160.93/160.62 => ( 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))))
% 160.93/160.62 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_last__list__update,axiom,
% 160.93/160.62 ! [V_x,V_k,T_a,V_xs] :
% 160.93/160.62 ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.62 => ( ( 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))
% 160.93/160.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 160.93/160.62 & ( 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))
% 160.93/160.62 => 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) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_last__conv__nth,axiom,
% 160.93/160.62 ! [T_a,V_xs] :
% 160.93/160.62 ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_last__append,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_ys] :
% 160.93/160.62 ( ( V_ys = c_List_Olist_ONil(T_a)
% 160.93/160.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 160.93/160.62 & ( V_ys != c_List_Olist_ONil(T_a)
% 160.93/160.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_last__appendR,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_ys] :
% 160.93/160.62 ( V_ys != c_List_Olist_ONil(T_a)
% 160.93/160.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_last__appendL,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_ys] :
% 160.93/160.62 ( V_ys = c_List_Olist_ONil(T_a)
% 160.93/160.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_last_Osimps,axiom,
% 160.93/160.62 ! [V_x,T_a,V_xs] :
% 160.93/160.62 ( ( V_xs = c_List_Olist_ONil(T_a)
% 160.93/160.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 160.93/160.62 & ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_last__ConsR,axiom,
% 160.93/160.62 ! [V_x,T_a,V_xs] :
% 160.93/160.62 ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_last__ConsL,axiom,
% 160.93/160.62 ! [V_x,T_a,V_xs] :
% 160.93/160.62 ( V_xs = c_List_Olist_ONil(T_a)
% 160.93/160.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_last__in__set,axiom,
% 160.93/160.62 ! [T_a,V_as_2] :
% 160.93/160.62 ( V_as_2 != c_List_Olist_ONil(T_a)
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_last__snoc,axiom,
% 160.93/160.62 ! [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 ).
% 160.93/160.62
% 160.93/160.62 fof(fact_last__drop,axiom,
% 160.93/160.62 ! [V_xs,T_a,V_n] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_snoc__eq__iff__butlast,axiom,
% 160.93/160.62 ! [V_ys_2,V_x_2,V_xs_2,T_a] :
% 160.93/160.62 ( 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
% 160.93/160.62 <=> ( V_ys_2 != c_List_Olist_ONil(T_a)
% 160.93/160.62 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2
% 160.93/160.62 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__butlast__last__id,axiom,
% 160.93/160.62 ! [T_a,V_xs] :
% 160.93/160.62 ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_lists_Osimps,axiom,
% 160.93/160.62 ! [V_A_2,V_a_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2)))
% 160.93/160.62 <=> ( V_a_2 = c_List_Olist_ONil(T_a)
% 160.93/160.62 | ? [B_a,B_l] :
% 160.93/160.62 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l)
% 160.93/160.62 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2))
% 160.93/160.62 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__zip__upd,axiom,
% 160.93/160.62 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => ( 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)
% 160.93/160.62 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 160.93/160.62 => ( 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))
% 160.93/160.62 => 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)) ) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_finite__dom__map__of,axiom,
% 160.93/160.62 ! [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)))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__zip__inject,axiom,
% 160.93/160.62 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => ( 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)
% 160.93/160.62 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 160.93/160.62 => ( 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))
% 160.93/160.62 => V_ys_2 = V_zs_2 ) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_body__def,axiom,
% 160.93/160.62 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__Cons__code_I2_J,axiom,
% 160.93/160.62 ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
% 160.93/160.62 ( ( V_l = V_k
% 160.93/160.62 => 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) )
% 160.93/160.62 & ( V_l != V_k
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__eq__dom,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 160.93/160.62 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_finite__range__map__of,axiom,
% 160.93/160.62 ! [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))))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__SomeD,axiom,
% 160.93/160.62 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__is__SomeD,axiom,
% 160.93/160.62 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_dom__map__of__conv__image__fst,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__zip__is__Some,axiom,
% 160.93/160.62 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 <=> ? [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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_dom__map__of__zip,axiom,
% 160.93/160.62 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of_Osimps_I2_J,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_ran__distinct,axiom,
% 160.93/160.62 ! [V_al_2,T_b,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__map__of__compr,axiom,
% 160.93/160.62 ! [V_xs_2,T_b,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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)))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_inj__mapI,axiom,
% 160.93/160.62 ! [V_f_2,T_b,T_a] :
% 160.93/160.62 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__abs,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 160.93/160.62 => 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)))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_foldl__map,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip__map__map,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip__map1,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__zip__map,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__zip__map2,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip__map2,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_List_Omap_Ocomp,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__comp__map,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_List_Omap_Ocompositionality,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__map,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_List_Omap_Oid,axiom,
% 160.93/160.62 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_List_Omap_Oidentity,axiom,
% 160.93/160.62 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__size__map,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nth__map,axiom,
% 160.93/160.62 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__fun__upd,axiom,
% 160.93/160.62 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] :
% 160.93/160.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__tl,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__map,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__eq__imp__length__eq,axiom,
% 160.93/160.62 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__map,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__append,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map_Osimps_I2_J,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__update,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__eq__conv,axiom,
% 160.93/160.62 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] :
% 160.93/160.62 ( 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)
% 160.93/160.62 <=> ! [B_x] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 160.93/160.62 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__addf,axiom,
% 160.93/160.62 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 160.93/160.62 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__0,axiom,
% 160.93/160.62 ! [V_xs_2,T_b,T_a] :
% 160.93/160.62 ( class_Groups_Omonoid__add(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__const__mult,axiom,
% 160.93/160.62 ! [V_xs_2,V_f_2,V_c_2,T_b,T_a] :
% 160.93/160.62 ( class_Rings_Osemiring__0(T_a)
% 160.93/160.62 => 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_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__mult__const,axiom,
% 160.93/160.62 ! [V_xs_2,V_c_2,V_f_2,T_b,T_a] :
% 160.93/160.62 ( class_Rings_Osemiring__0(T_a)
% 160.93/160.62 => 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_c_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_c_2) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__subtractf,axiom,
% 160.93/160.62 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 160.93/160.62 ( class_Groups_Oab__group__add(T_a)
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__ident,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ).
% 160.93/160.62
% 160.93/160.62 fof(fact_take__map,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__butlast,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__is__Nil__conv,axiom,
% 160.93/160.62 ! [V_xs_2,V_f_2,T_a,T_b] :
% 160.93/160.62 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 160.93/160.62 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map_Osimps_I1_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Nil__is__map__conv,axiom,
% 160.93/160.62 ! [V_xs_2,V_f_2,T_b,T_a] :
% 160.93/160.62 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)
% 160.93/160.62 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__injective,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 160.93/160.62 => V_xs_2 = V_ys_2 ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_inj__map__eq__map,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
% 160.93/160.62 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.93/160.62 => ( 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)
% 160.93/160.62 <=> V_xs_2 = V_ys_2 ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_hd__map,axiom,
% 160.93/160.62 ! [V_f_2,T_b,T_a,V_xs_2] :
% 160.93/160.62 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_drop__map,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_inj__on__map__eq__map,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => ( 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)
% 160.93/160.62 <=> V_xs_2 = V_ys_2 ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__inj__on,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => ( 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)))
% 160.93/160.62 => V_xs_2 = V_ys_2 ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_rotate__map,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__map,axiom,
% 160.93/160.62 ! [V_xs_2,V_f_2,T_b,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)))
% 160.93/160.62 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 160.93/160.62 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_last__map,axiom,
% 160.93/160.62 ! [V_f_2,T_b,T_a,V_xs_2] :
% 160.93/160.62 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_uminus__listsum__map,axiom,
% 160.93/160.62 ! [V_xs_2,V_f_2,T_b,T_a] :
% 160.93/160.62 ( class_Groups_Oab__group__add(T_a)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_inj__on__mapI,axiom,
% 160.93/160.62 ! [V_A_2,V_f_2,T_b,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__fst__zip,axiom,
% 160.93/160.62 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => 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 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__snd__zip,axiom,
% 160.93/160.62 ! [V_ys_2,T_b,V_xs_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => 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 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip__map__fst__snd,axiom,
% 160.93/160.62 ! [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 ).
% 160.93/160.62
% 160.93/160.62 fof(fact_inj__mapD,axiom,
% 160.93/160.62 ! [V_f_2,T_b,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_inj__map,axiom,
% 160.93/160.62 ! [V_f_2,T_b,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_pick__member,axiom,
% 160.93/160.62 ! [V_xs_2,T_a,V_i_2] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 => 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)))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 160.93/160.62 ! [V_f_2,V_xs_2,T_a,T_b] :
% 160.93/160.62 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.93/160.62 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip__eq__conv,axiom,
% 160.93/160.62 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2
% 160.93/160.62 <=> ( 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
% 160.93/160.62 & 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 ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__triv,axiom,
% 160.93/160.62 ! [V_xs_2,V_r_2,T_b,T_a] :
% 160.93/160.62 ( class_Rings_Osemiring__1(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__inject__set,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => ( 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)))
% 160.93/160.62 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2)
% 160.93/160.62 <=> 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) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__map__remove1,axiom,
% 160.93/160.62 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] :
% 160.93/160.62 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.93/160.62 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => 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)))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_select__weight__member,axiom,
% 160.93/160.62 ! [V_s_2,V_xs_2,T_a] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 => 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)))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_select__weight__def,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__mapk__SomeI,axiom,
% 160.93/160.62 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] :
% 160.93/160.62 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.93/160.62 => ( 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)
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__is__SomeI,axiom,
% 160.93/160.62 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => ( 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)))
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__eq__Some__iff,axiom,
% 160.93/160.62 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => ( 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)
% 160.93/160.62 <=> 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))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Some__eq__map__of__iff,axiom,
% 160.93/160.62 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => ( 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)
% 160.93/160.62 <=> 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))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 160.93/160.62 ! [V_f_2,V_A_2,T_a,T_b] :
% 160.93/160.62 ( class_Groups_Ocomm__monoid__add(T_b)
% 160.93/160.62 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.93/160.62 => 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))))) )
% 160.93/160.62 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.93/160.62 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsum__mono,axiom,
% 160.93/160.62 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] :
% 160.93/160.62 ( ( class_Groups_Omonoid__add(T_b)
% 160.93/160.62 & class_Groups_Oordered__ab__semigroup__add(T_b) )
% 160.93/160.62 => ( ! [B_x] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 160.93/160.62 => 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)))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zip__same__conv__map,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_list__size__conv__listsum,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 160.93/160.62 ! [V_j_2,V_i_2,V_f_2,T_a] :
% 160.93/160.62 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 160.93/160.62 ! [V_l_2,V_k_2,V_f_2,T_a] :
% 160.93/160.62 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__map__restrict,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__map__keys,axiom,
% 160.93/160.62 ! [V_m_2,T_b,V_xs_2,T_a] :
% 160.93/160.62 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2)
% 160.93/160.62 => 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 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_select__weigth__select,axiom,
% 160.93/160.62 ! [T_a,V_xs_2] :
% 160.93/160.62 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_pick__same,axiom,
% 160.93/160.62 ! [V_xs_2,T_a,V_l_2] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__map,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Option_Omap_Ocomp,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Option_Omap_Ocompositionality,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option__map__comp,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option__map__o__map__upd,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_number__of__code__numeral__def,axiom,
% 160.93/160.62 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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Option_Omap_Oid,axiom,
% 160.93/160.62 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Option_Omap_Oidentity,axiom,
% 160.93/160.62 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 160.93/160.62 ! [V_y_2,V_x_2] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 160.93/160.62 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 160.93/160.62 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 160.93/160.62 <=> V_x_2 = V_y_2 ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_less__code__numeral__code,axiom,
% 160.93/160.62 ! [V_m_2,V_n_2] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option__map__eq__Some,axiom,
% 160.93/160.62 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] :
% 160.93/160.62 ( 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)
% 160.93/160.62 <=> ? [B_z] :
% 160.93/160.62 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z)
% 160.93/160.62 & hAPP(V_f_2,B_z) = V_y_2 ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option__map__Some,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_dom__option__map,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 160.93/160.62 ! [V_m_2,V_n_2] :
% 160.93/160.62 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 160.93/160.62 <=> V_n_2 = V_m_2 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_times__code__numeral__code,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 160.93/160.62 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_zero__code__numeral__def,axiom,
% 160.93/160.62 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_one__code__numeral__def,axiom,
% 160.93/160.62 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_plus__code__numeral__code,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_less__eq__code__numeral__code,axiom,
% 160.93/160.62 ! [V_m_2,V_n_2] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_code__numeral__not__eq__zero,axiom,
% 160.93/160.62 ! [V_i_2] :
% 160.93/160.62 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 160.93/160.62 <=> 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_select__def,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_subtract__code__numeral__code,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_type__definition__code__numeral,axiom,
% 160.93/160.62 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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nat__of__of__nat,axiom,
% 160.93/160.62 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 160.93/160.62
% 160.93/160.62 fof(fact_of__nat__nat__of,axiom,
% 160.93/160.62 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nat__of__inverse,axiom,
% 160.93/160.62 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 160.93/160.62
% 160.93/160.62 fof(fact_times__code__numeral__def,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_code__numeral_Onat__of__inject,axiom,
% 160.93/160.62 ! [V_y_2,V_x_2] :
% 160.93/160.62 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 160.93/160.62 <=> V_x_2 = V_y_2 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 160.93/160.62 ! [V_l_2,V_k_2] :
% 160.93/160.62 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 160.93/160.62 <=> V_k_2 = V_l_2 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_less__code__numeral__def,axiom,
% 160.93/160.62 ! [V_m_2,V_n_2] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 160.93/160.62 <=> 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nat__of,axiom,
% 160.93/160.62 ! [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)))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nat__of__number,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_int__of__def,axiom,
% 160.93/160.62 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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_less__eq__code__numeral__def,axiom,
% 160.93/160.62 ! [V_m_2,V_n_2] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 160.93/160.62 <=> 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nat__of__code,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_nat__of__aux__def,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Suc__code__numeral__def,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_minus__code__numeral__def,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_of__nat__inverse,axiom,
% 160.93/160.62 ! [V_y_2] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 160.93/160.62 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_plus__code__numeral__def,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_div__code__numeral__def,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_subtract__code__numeral__def,axiom,
% 160.93/160.62 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_minus__code__numeral__code,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_mod__code__numeral__def,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_code__numeral__decr,axiom,
% 160.93/160.62 ! [V_k] :
% 160.93/160.62 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_weak__map__of__SomeI,axiom,
% 160.93/160.62 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 => ? [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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__zip__map,axiom,
% 160.93/160.62 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] :
% 160.93/160.62 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => 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)) )
% 160.93/160.62 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_partition__set,axiom,
% 160.93/160.62 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option__map__o__empty,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option__map__None,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option__map__is__None,axiom,
% 160.93/160.62 ! [V_opt_2,V_f_2,T_a,T_b] :
% 160.93/160.62 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a)
% 160.93/160.62 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__Cons__code_I1_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Option_Oset_Osimps_I1_J,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__empty__eq,axiom,
% 160.93/160.62 ! [V_xo_2,T_a] :
% 160.93/160.62 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.93/160.62 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_empty__upd__none,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_dom__def,axiom,
% 160.93/160.62 ! [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)))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_domIff,axiom,
% 160.93/160.62 ! [V_m_2,T_b,V_a_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2)))
% 160.93/160.62 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_dom__eq__empty__conv,axiom,
% 160.93/160.62 ! [V_f_2,T_b,T_a] :
% 160.93/160.62 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 160.93/160.62 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_dom__empty,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_restrict__out,axiom,
% 160.93/160.62 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 160.93/160.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.93/160.62 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_restrict__map__def,axiom,
% 160.93/160.62 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] :
% 160.93/160.62 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.93/160.62 => 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) )
% 160.93/160.62 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 160.93/160.62 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_restrict__map__empty,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_restrict__map__to__empty,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option_Osimps_I4_J,axiom,
% 160.93/160.62 ! [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 ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__upd__nonempty,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option_Osimps_I2_J,axiom,
% 160.93/160.62 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option_Osimps_I3_J,axiom,
% 160.93/160.62 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_not__Some__eq,axiom,
% 160.93/160.62 ! [T_a,V_x_2] :
% 160.93/160.62 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y)
% 160.93/160.62 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_not__None__eq,axiom,
% 160.93/160.62 ! [T_a,V_x_2] :
% 160.93/160.62 ( V_x_2 != c_Option_Ooption_ONone(T_a)
% 160.93/160.62 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_ran__empty,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of_Osimps_I1_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_Option_Omap__def,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option_Osize_I3_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_option_Osize_I1_J,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_dom__minus,axiom,
% 160.93/160.62 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] :
% 160.93/160.62 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a)
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_WT_OBody,axiom,
% 160.93/160.62 ! [V_pn] :
% 160.93/160.62 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom)
% 160.93/160.62 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_partition__P,axiom,
% 160.93/160.62 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => ( ! [B_x] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2)))
% 160.93/160.62 => hBOOL(hAPP(V_P_2,B_x)) )
% 160.93/160.62 & ! [B_x] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2)))
% 160.93/160.62 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_partition_Osimps_I1_J,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_ran__map__upd,axiom,
% 160.93/160.62 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] :
% 160.93/160.62 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__zip__is__None,axiom,
% 160.93/160.62 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] :
% 160.93/160.62 ( 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)
% 160.93/160.62 => ( 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)
% 160.93/160.62 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_partition_Osimps_I2_J,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_dom__fun__upd,axiom,
% 160.93/160.62 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] :
% 160.93/160.62 ( ( V_y_2 = c_Option_Ooption_ONone(T_a)
% 160.93/160.62 => 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)))) )
% 160.93/160.62 & ( V_y_2 != c_Option_Ooption_ONone(T_a)
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_restrict__complement__singleton__eq,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__eq__None__iff,axiom,
% 160.93/160.62 ! [V_x_2,V_xys_2,T_a,T_b] :
% 160.93/160.62 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a)
% 160.93/160.62 <=> ~ 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)))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_UNIV__option__conv,axiom,
% 160.93/160.62 ! [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)))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_dom__eq__singleton__conv,axiom,
% 160.93/160.62 ! [V_x_2,V_f_2,T_b,T_a] :
% 160.93/160.62 ( 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)))
% 160.93/160.62 <=> ? [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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_fun__upd__None__restrict,axiom,
% 160.93/160.62 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] :
% 160.93/160.62 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 160.93/160.62 => 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))))) )
% 160.93/160.62 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2))
% 160.93/160.62 => 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) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_lists__IntI,axiom,
% 160.93/160.62 ! [V_B_2,V_A_2,V_l_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2)))
% 160.93/160.62 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2)))
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_lists__Int__eq,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsp_ONil,axiom,
% 160.93/160.62 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_append__in__listsp__conv,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,V_A_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)))
% 160.93/160.62 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2))
% 160.93/160.62 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsp_Oequations_I2_J,axiom,
% 160.93/160.62 ! [V_a2_2,V_a1_2,V_A_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2)))
% 160.93/160.62 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 160.93/160.62 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_in__listsp__conv__set,axiom,
% 160.93/160.62 ! [V_xs_2,V_A_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2))
% 160.93/160.62 <=> ! [B_x] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.62 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsp__conj__eq,axiom,
% 160.93/160.62 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 160.93/160.62 ( 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))
% 160.93/160.62 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2))
% 160.93/160.62 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsp__inf__eq,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsp__infI,axiom,
% 160.93/160.62 ! [V_B_2,V_l_2,V_A_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2))
% 160.93/160.62 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2))
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsp_Oequations_I1_J,axiom,
% 160.93/160.62 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsp__mono,axiom,
% 160.93/160.62 ! [V_B_2,V_A_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_listsp__lists__eq,axiom,
% 160.93/160.62 ! [V_x_2,V_A_2,T_a] :
% 160.93/160.62 ( 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))
% 160.93/160.62 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_product_Osimps_I2_J,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_product_Osimps_I1_J,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__product,axiom,
% 160.93/160.62 ! [V_ys,T_b,V_xs,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 160.93/160.62 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 160.93/160.62 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_product__list__set,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_sublists__powset,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__sublists,axiom,
% 160.93/160.62 ! [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)) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_sublists_Osimps_I1_J,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_sublists_Osimps_I2_J,axiom,
% 160.93/160.62 ! [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))))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__set__sublists,axiom,
% 160.93/160.62 ! [V_xs_2,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.62 => 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)))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_set__n__lists,axiom,
% 160.93/160.62 ! [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)))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_enum__the__def,axiom,
% 160.93/160.62 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_distinct__n__lists,axiom,
% 160.93/160.62 ! [V_n,V_xs,T_a] :
% 160.93/160.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 160.93/160.62 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_n__lists__Nil,axiom,
% 160.93/160.62 ! [T_a,V_n] :
% 160.93/160.62 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.62 => 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))) )
% 160.93/160.62 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.62 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_n__lists_Osimps_I1_J,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__n__lists,axiom,
% 160.93/160.62 ! [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) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_length__n__lists__elem,axiom,
% 160.93/160.62 ! [V_xs_2,V_n_2,V_ys_2,T_a] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_full__small__int__def,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_small_H_Osimps,axiom,
% 160.93/160.62 ! [V_f_2,V_i_2,V_d_2] :
% 160.93/160.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 160.93/160.62 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 160.93/160.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 160.93/160.62 => 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)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_small_H_Opsimps,axiom,
% 160.93/160.62 ! [V_i_2,V_d_2,V_f_2] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 160.93/160.62 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 160.93/160.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 160.93/160.62 => 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)) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_small__int__def,axiom,
% 160.93/160.62 ! [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))) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_small__prod__def,axiom,
% 160.93/160.62 ! [V_d_2,V_f_2,T_a,T_b] :
% 160.93/160.62 ( ( class_Smallcheck_Osmall(T_b)
% 160.93/160.62 & class_Smallcheck_Osmall(T_a) )
% 160.93/160.62 => 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) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_small_H_Opinduct,axiom,
% 160.93/160.62 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 => ( ! [B_f,B_d,B_i] :
% 160.93/160.62 ( 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))))
% 160.93/160.62 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 160.93/160.62 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
% 160.93/160.62 => 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)))) ) )
% 160.93/160.62 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) )
% 160.93/160.62 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_map__of__zip__enum__inject,axiom,
% 160.93/160.62 ! [V_ys_2,V_xs_2,T_a,T_b] :
% 160.93/160.62 ( ( class_Enum_Oenum(T_b)
% 160.93/160.62 & class_Enum_Oenum(T_a) )
% 160.93/160.62 => ( 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))
% 160.93/160.62 => ( 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))
% 160.93/160.62 => ( 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)))
% 160.93/160.62 => V_xs_2 = V_ys_2 ) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_enum__prod__def,axiom,
% 160.93/160.62 ! [T_b,T_a] :
% 160.93/160.62 ( ( class_Enum_Oenum(T_a)
% 160.93/160.62 & class_Enum_Oenum(T_b) )
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_enum__UNIV,axiom,
% 160.93/160.62 ! [T_a] :
% 160.93/160.62 ( class_Enum_Oenum(T_a)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_UNIV__enum,axiom,
% 160.93/160.62 ! [T_a] :
% 160.93/160.62 ( class_Enum_Oenum(T_a)
% 160.93/160.62 => 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)) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_in__enum,axiom,
% 160.93/160.62 ! [V_x_2,T_a] :
% 160.93/160.62 ( class_Enum_Oenum(T_a)
% 160.93/160.62 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_enum__option__def,axiom,
% 160.93/160.62 ! [T_a] :
% 160.93/160.62 ( class_Enum_Oenum(T_a)
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_enum__distinct,axiom,
% 160.93/160.62 ! [T_a] :
% 160.93/160.62 ( class_Enum_Oenum(T_a)
% 160.93/160.62 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_enum__fun__code,axiom,
% 160.93/160.62 ! [T_b,T_a] :
% 160.93/160.62 ( ( class_Enum_Oenum(T_a)
% 160.93/160.62 & class_HOL_Oequal(T_a)
% 160.93/160.62 & class_Enum_Oenum(T_b) )
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_enum__fun__def,axiom,
% 160.93/160.62 ! [T_b,T_a] :
% 160.93/160.62 ( ( class_Enum_Oenum(T_a)
% 160.93/160.62 & class_Enum_Oenum(T_b) )
% 160.93/160.62 => 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))) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_ex__n__lists__def,axiom,
% 160.93/160.62 ! [V_n_2,V_P_2,T_a] :
% 160.93/160.62 ( class_Enum_Oenum(T_a)
% 160.93/160.62 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2)
% 160.93/160.62 <=> ? [B_x] :
% 160.93/160.62 ( 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)))))
% 160.93/160.62 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_all__n__lists__def,axiom,
% 160.93/160.62 ! [V_n_2,V_P_2,T_a] :
% 160.93/160.62 ( class_Enum_Oenum(T_a)
% 160.93/160.62 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2)
% 160.93/160.62 <=> ! [B_x] :
% 160.93/160.62 ( 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)))))
% 160.93/160.62 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_enum__all__fun__def,axiom,
% 160.93/160.62 ! [V_P_2,T_a,T_b] :
% 160.93/160.62 ( ( class_Enum_Oenum(T_b)
% 160.93/160.62 & class_Enum_Oenum(T_a) )
% 160.93/160.62 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
% 160.93/160.62 <=> 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))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_enum__ex__fun__def,axiom,
% 160.93/160.62 ! [V_P_2,T_a,T_b] :
% 160.93/160.62 ( ( class_Enum_Oenum(T_b)
% 160.93/160.62 & class_Enum_Oenum(T_a) )
% 160.93/160.62 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
% 160.93/160.62 <=> 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))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_enum__ex__prod__def,axiom,
% 160.93/160.62 ! [V_P_2,T_a,T_b] :
% 160.93/160.62 ( ( class_Enum_Oenum(T_b)
% 160.93/160.62 & class_Enum_Oenum(T_a) )
% 160.93/160.62 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2))
% 160.93/160.62 <=> 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))))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_enum__all__prod__def,axiom,
% 160.93/160.62 ! [V_P_2,T_a,T_b] :
% 160.93/160.62 ( ( class_Enum_Oenum(T_b)
% 160.93/160.62 & class_Enum_Oenum(T_a) )
% 160.93/160.62 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2))
% 160.93/160.62 <=> 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))))) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_enum__ex,axiom,
% 160.93/160.62 ! [V_P_2,T_a] :
% 160.93/160.62 ( class_Enum_Oenum(T_a)
% 160.93/160.62 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2))
% 160.93/160.62 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 160.93/160.62
% 160.93/160.62 fof(fact_enum__all,axiom,
% 160.93/160.62 ! [V_P_2,T_a] :
% 160.93/160.62 ( class_Enum_Oenum(T_a)
% 160.93/160.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2))
% 160.93/160.63 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_exists__code,axiom,
% 160.93/160.63 ! [V_P_2,T_a] :
% 160.93/160.63 ( class_Enum_Oenum(T_a)
% 160.93/160.63 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 160.93/160.63 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_all__code,axiom,
% 160.93/160.63 ! [V_P_2,T_a] :
% 160.93/160.63 ( class_Enum_Oenum(T_a)
% 160.93/160.63 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 160.93/160.63 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_enum__ex__option__def,axiom,
% 160.93/160.63 ! [V_P_2,T_a] :
% 160.93/160.63 ( class_Enum_Oenum(T_a)
% 160.93/160.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2))
% 160.93/160.63 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a)))
% 160.93/160.63 | 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)))) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_enum__all__option__def,axiom,
% 160.93/160.63 ! [V_P_2,T_a] :
% 160.93/160.63 ( class_Enum_Oenum(T_a)
% 160.93/160.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2))
% 160.93/160.63 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a)))
% 160.93/160.63 & 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)))) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_order__fun_I1_J,axiom,
% 160.93/160.63 ! [V_g_2,V_f_2,T_a,T_b] :
% 160.93/160.63 ( ( class_Orderings_Oorder(T_b)
% 160.93/160.63 & class_Enum_Oenum(T_a) )
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 160.93/160.63 <=> 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))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_order__fun_I2_J,axiom,
% 160.93/160.63 ! [V_g_2,V_f_2,T_a,T_b] :
% 160.93/160.63 ( ( class_Orderings_Oorder(T_b)
% 160.93/160.63 & class_Enum_Oenum(T_a) )
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 160.93/160.63 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 160.93/160.63 & 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)))) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_enum__ex__fun__code,axiom,
% 160.93/160.63 ! [V_P_2,T_a,T_b] :
% 160.93/160.63 ( ( class_Enum_Oenum(T_b)
% 160.93/160.63 & class_Enum_Oenum(T_a)
% 160.93/160.63 & class_HOL_Oequal(T_a) )
% 160.93/160.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2))
% 160.93/160.63 <=> 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))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_enum__all__fun__code,axiom,
% 160.93/160.63 ! [V_P_2,T_a,T_b] :
% 160.93/160.63 ( ( class_Enum_Oenum(T_b)
% 160.93/160.63 & class_Enum_Oenum(T_a)
% 160.93/160.63 & class_HOL_Oequal(T_a) )
% 160.93/160.63 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2))
% 160.93/160.63 <=> 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))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__of__zip__enum__is__Some,axiom,
% 160.93/160.63 ! [V_x,V_ys,T_b,T_a] :
% 160.93/160.63 ( class_Enum_Oenum(T_a)
% 160.93/160.63 => ( 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))
% 160.93/160.63 => ? [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) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__def,axiom,
% 160.93/160.63 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 160.93/160.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 160.93/160.63 <=> ( 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)
% 160.93/160.63 & ! [B_x] :
% 160.93/160.63 ( 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))))
% 160.93/160.63 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__lengthD,axiom,
% 160.93/160.63 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 160.93/160.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__dropI,axiom,
% 160.93/160.63 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] :
% 160.93/160.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2)
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__takeI,axiom,
% 160.93/160.63 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 160.93/160.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__eq,axiom,
% 160.93/160.63 ! [T_a,V_ys_2,V_xs_2] :
% 160.93/160.63 ( V_xs_2 = V_ys_2
% 160.93/160.63 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__appendI,axiom,
% 160.93/160.63 ! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_b,T_a] :
% 160.93/160.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2)
% 160.93/160.63 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_c_2,V_d_2)
% 160.93/160.63 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_b),V_b_2),V_d_2)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__Nil2,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_b,T_a] :
% 160.93/160.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b))
% 160.93/160.63 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__Nil,axiom,
% 160.93/160.63 ! [V_ys_2,V_P_2,T_b,T_a] :
% 160.93/160.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2)
% 160.93/160.63 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__append,axiom,
% 160.93/160.63 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
% 160.93/160.63 ( 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)
% 160.93/160.63 => ( 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))
% 160.93/160.63 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 160.93/160.63 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__map1,axiom,
% 160.93/160.63 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] :
% 160.93/160.63 ( 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)
% 160.93/160.63 <=> 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__map2,axiom,
% 160.93/160.63 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] :
% 160.93/160.63 ( 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))
% 160.93/160.63 <=> 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__Cons,axiom,
% 160.93/160.63 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] :
% 160.93/160.63 ( 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))
% 160.93/160.63 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 160.93/160.63 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__conv__all__nth,axiom,
% 160.93/160.63 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 160.93/160.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 160.93/160.63 <=> ( 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)
% 160.93/160.63 & ! [B_i] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => 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))) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__nthD,axiom,
% 160.93/160.63 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 160.93/160.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 160.93/160.63 => ( 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)))
% 160.93/160.63 => 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))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__nthD2,axiom,
% 160.93/160.63 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 160.93/160.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 160.93/160.63 => ( 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)))
% 160.93/160.63 => 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))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__update__cong,axiom,
% 160.93/160.63 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 160.93/160.63 => 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)) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__update__cong2,axiom,
% 160.93/160.63 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 160.93/160.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2)
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 160.93/160.63 => ( 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)))
% 160.93/160.63 => 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)) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2I,axiom,
% 160.93/160.63 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] :
% 160.93/160.63 ( ! [B_x] :
% 160.93/160.63 ( 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))))
% 160.93/160.63 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) )
% 160.93/160.63 => ( 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)
% 160.93/160.63 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_all__nth__imp__all__set,axiom,
% 160.93/160.63 ! [V_x_2,V_P_2,V_xs_2,T_a] :
% 160.93/160.63 ( ! [B_i] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) )
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 160.93/160.63 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] :
% 160.93/160.63 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2)
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__removeAll__inj__on,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_distinct__remdups,axiom,
% 160.93/160.63 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__remdups__leq,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_removeAll__id,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_distinct__remdups__id,axiom,
% 160.93/160.63 ! [V_xs,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 160.93/160.63 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_distinct__removeAll,axiom,
% 160.93/160.63 ! [V_x,V_xs,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 160.93/160.63 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_remdups__id__iff__distinct,axiom,
% 160.93/160.63 ! [V_xs_2,T_a] :
% 160.93/160.63 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2
% 160.93/160.63 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_remove1__remdups,axiom,
% 160.93/160.63 ! [V_x,V_xs,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__remdups__eq,axiom,
% 160.93/160.63 ! [V_xs_2,T_a] :
% 160.93/160.63 ( 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)
% 160.93/160.63 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_set__remdups,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_remdups__remdups,axiom,
% 160.93/160.63 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_removeAll__append,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_remdups__eq__nil__iff,axiom,
% 160.93/160.63 ! [V_x_2,T_a] :
% 160.93/160.63 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a)
% 160.93/160.63 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_removeAll_Osimps_I1_J,axiom,
% 160.93/160.63 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_remdups__eq__nil__right__iff,axiom,
% 160.93/160.63 ! [V_x_2,T_a] :
% 160.93/160.63 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2)
% 160.93/160.63 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_remdups_Osimps_I1_J,axiom,
% 160.93/160.63 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_remdups__map__remdups,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_removeAll_Osimps_I2_J,axiom,
% 160.93/160.63 ! [V_xs,T_a,V_y,V_x] :
% 160.93/160.63 ( ( V_x = V_y
% 160.93/160.63 => 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) )
% 160.93/160.63 & ( V_x != V_y
% 160.93/160.63 => 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)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_distinct__remove1__removeAll,axiom,
% 160.93/160.63 ! [V_x,V_xs,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 160.93/160.63 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_remdups_Osimps_I2_J,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => 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) )
% 160.93/160.63 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => 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)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__remdups__card__conv,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__removeAll__inj,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 160.93/160.63 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_set__removeAll,axiom,
% 160.93/160.63 ! [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)))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__remdups__concat,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 160.93/160.63 ! [V_xs_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_concat_Osimps_I2_J,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__concat,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_concat__eq__Nil__conv,axiom,
% 160.93/160.63 ! [V_xss_2,T_a] :
% 160.93/160.63 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a)
% 160.93/160.63 <=> ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)))
% 160.93/160.63 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_Nil__eq__concat__conv,axiom,
% 160.93/160.63 ! [V_xss_2,T_a] :
% 160.93/160.63 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2)
% 160.93/160.63 <=> ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)))
% 160.93/160.63 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_concat_Osimps_I1_J,axiom,
% 160.93/160.63 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sort__key__simps_I1_J,axiom,
% 160.93/160.63 ! [V_f_2,T_a,T_b] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_b)
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_concat__conv__foldl,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_foldl__conv__concat,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_set__sort,axiom,
% 160.93/160.63 ! [V_xs_2,V_f_2,T_a,T_b] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_b)
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__sort,axiom,
% 160.93/160.63 ! [V_xs_2,V_f_2,T_a,T_b] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_b)
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_distinct__sort,axiom,
% 160.93/160.63 ! [V_xs_2,V_f_2,T_a,T_b] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_b)
% 160.93/160.63 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)))
% 160.93/160.63 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__concat,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_set__concat,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sort__key__simps_I2_J,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_b)
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_concat__append,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sort__foldl__insort,axiom,
% 160.93/160.63 ! [V_xs_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_concat__injective,axiom,
% 160.93/160.63 ! [V_ys_2,V_xs_2,T_a] :
% 160.93/160.63 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2)
% 160.93/160.63 => ( 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)
% 160.93/160.63 => ( ! [B_x] :
% 160.93/160.63 ( 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))))
% 160.93/160.63 => 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)) )
% 160.93/160.63 => V_xs_2 = V_ys_2 ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_concat__eq__concat__iff,axiom,
% 160.93/160.63 ! [V_ys_2,V_xs_2,T_a] :
% 160.93/160.63 ( ! [B_x] :
% 160.93/160.63 ( 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))))
% 160.93/160.63 => 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)) )
% 160.93/160.63 => ( 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)
% 160.93/160.63 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2)
% 160.93/160.63 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_concat__map__singleton,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_n__lists_Osimps_I2_J,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose_Osimps_I3_J,axiom,
% 160.93/160.63 ! [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))))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose__aux__filter__head,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter__concat,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter__sort,axiom,
% 160.93/160.63 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_b)
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose_Osimps_I2_J,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_partition__filter2,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_distinct__filter,axiom,
% 160.93/160.63 ! [V_P_2,V_xs_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.63 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sum__length__filter__compl,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__filter__le,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter__is__subset,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter__id__conv,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2
% 160.93/160.63 <=> ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter__insort__triv,axiom,
% 160.93/160.63 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_b)
% 160.93/160.63 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => 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) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter__remove1,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_remove1__filter__not,axiom,
% 160.93/160.63 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 160.93/160.63 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter__filter,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_partition__filter1,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter__append,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter_Osimps_I1_J,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose_Osimps_I1_J,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter__empty__conv,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a)
% 160.93/160.63 <=> ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter_Osimps_I2_J,axiom,
% 160.93/160.63 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 160.93/160.63 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => 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)) )
% 160.93/160.63 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => 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) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter__map,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_removeAll__filter__not__eq,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_remdups__filter,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_removeAll__filter__not,axiom,
% 160.93/160.63 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 160.93/160.63 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_nth__transpose,axiom,
% 160.93/160.63 ! [V_xs_2,T_a,V_i_2] :
% 160.93/160.63 ( 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))))
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose__map__map,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_set__filter,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__filter__map,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__filter__less,axiom,
% 160.93/160.63 ! [V_P_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => 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))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_partition__filter__conv,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_set__minus__filter__out,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter__in__sublist,axiom,
% 160.93/160.63 ! [V_s_2,V_xs_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose__empty,axiom,
% 160.93/160.63 ! [V_xs_2,T_a] :
% 160.93/160.63 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a))
% 160.93/160.63 <=> ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 160.93/160.63 => B_x = c_List_Olist_ONil(T_a) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__filter__conv__card,axiom,
% 160.93/160.63 ! [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))))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose__aux__filter__tail,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose_Opsimps_I3_J,axiom,
% 160.93/160.63 ! [V_xss_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => 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))))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__filter__def,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__filter__simps_I2_J,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__of__filter__in,axiom,
% 160.93/160.63 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] :
% 160.93/160.63 ( 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)
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2))
% 160.93/160.63 => 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) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__filter__simps_I1_J,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sublist__shift__lemma__Suc,axiom,
% 160.93/160.63 ! [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)))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_select__weigth__drop__zero,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_pick__drop__zero,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose_Opsimps_I1_J,axiom,
% 160.93/160.63 ! [T_a] :
% 160.93/160.63 ( 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))))
% 160.93/160.63 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__filter__map__filter,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose_Opsimps_I2_J,axiom,
% 160.93/160.63 ! [V_xss_2,T_a] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose__max__length,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose__aux__max,axiom,
% 160.93/160.63 ! [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)))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_foldr__append,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_foldr_Osimps_I1_J,axiom,
% 160.93/160.63 ! [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 ).
% 160.93/160.63
% 160.93/160.63 fof(fact_foldr_Osimps_I2_J,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_foldr__conv__foldl,axiom,
% 160.93/160.63 ! [V_a_2,V_xs_2,T_a] :
% 160.93/160.63 ( class_Groups_Oab__semigroup__add(T_a)
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_foldr__map,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_foldl__foldr1__lemma,axiom,
% 160.93/160.63 ! [V_xs_2,V_a_2,T_a] :
% 160.93/160.63 ( class_Groups_Omonoid__add(T_a)
% 160.93/160.63 => 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))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_foldl__foldr1,axiom,
% 160.93/160.63 ! [V_xs_2,T_a] :
% 160.93/160.63 ( class_Groups_Omonoid__add(T_a)
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__transpose,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sublist__def,axiom,
% 160.93/160.63 ! [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))))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sublist__shift__lemma,axiom,
% 160.93/160.63 ! [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))))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_set__upt,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_atLeastLessThan__upt,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__upt,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_upt__Suc__append,axiom,
% 160.93/160.63 ! [V_j,V_i] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 160.93/160.63 => 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))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_upt__Suc,axiom,
% 160.93/160.63 ! [V_j,V_i] :
% 160.93/160.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 160.93/160.63 => 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))) )
% 160.93/160.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 160.93/160.63 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_upt__rec,axiom,
% 160.93/160.63 ! [V_j,V_i] :
% 160.93/160.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 160.93/160.63 => 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)) )
% 160.93/160.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 160.93/160.63 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_upt__conv__Cons,axiom,
% 160.93/160.63 ! [V_j,V_i] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_upt__conv__Nil,axiom,
% 160.93/160.63 ! [V_i,V_j] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 160.93/160.63 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_upt__eq__Nil__conv,axiom,
% 160.93/160.63 ! [V_j_2,V_i_2] :
% 160.93/160.63 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 160.93/160.63 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 160.93/160.63 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_upt__0,axiom,
% 160.93/160.63 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_upt__add__eq__append,axiom,
% 160.93/160.63 ! [V_k,V_j,V_i] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 160.93/160.63 => 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))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__list__of__set__range,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_take__upt,axiom,
% 160.93/160.63 ! [V_n,V_m,V_i] :
% 160.93/160.63 ( 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))
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_hd__upt,axiom,
% 160.93/160.63 ! [V_j,V_i] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 160.93/160.63 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_drop__upt,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_distinct__upt,axiom,
% 160.93/160.63 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_upt__rec__number__of,axiom,
% 160.93/160.63 ! [V_n,V_m] :
% 160.93/160.63 ( ( 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)))
% 160.93/160.63 => 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))) )
% 160.93/160.63 & ( ~ 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)))
% 160.93/160.63 => 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) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_upt__eq__Cons__conv,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 160.93/160.63 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 160.93/160.63 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 160.93/160.63 & V_i_2 = V_x_2
% 160.93/160.63 & 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 ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_last__upt,axiom,
% 160.93/160.63 ! [V_j,V_i] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__Suc__upt,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_atLeastAtMost__upt,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_atLeast__upt,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_nth__upt,axiom,
% 160.93/160.63 ! [V_j,V_k,V_i] :
% 160.93/160.63 ( 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))
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_greaterThanAtMost__upt,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_greaterThanLessThan__upt,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_atMost__upto,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__nth,axiom,
% 160.93/160.63 ! [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 ).
% 160.93/160.63
% 160.93/160.63 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 160.93/160.63 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 160.93/160.63 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.93/160.63 => 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))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 160.93/160.63 ! [V_n_2,V_m_2,V_f_2,T_a] :
% 160.93/160.63 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.93/160.63 => 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))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_nth__map__upt,axiom,
% 160.93/160.63 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose__rectangle,axiom,
% 160.93/160.63 ! [V_n_2,T_a,V_xs_2] :
% 160.93/160.63 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a))
% 160.93/160.63 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 160.93/160.63 => ( ! [B_i] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => 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 )
% 160.93/160.63 => 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)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_insort__key__remove1,axiom,
% 160.93/160.63 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_b)
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
% 160.93/160.63 => ( 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
% 160.93/160.63 => 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 ) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted_ONil,axiom,
% 160.93/160.63 ! [T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__single,axiom,
% 160.93/160.63 ! [V_x,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__upt,axiom,
% 160.93/160.63 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__Cons,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 160.93/160.63 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 160.93/160.63 & ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__sort,axiom,
% 160.93/160.63 ! [V_xs_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__insort,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( 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))
% 160.93/160.63 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__drop,axiom,
% 160.93/160.63 ! [V_n,V_xs,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 160.93/160.63 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__remove1,axiom,
% 160.93/160.63 ! [V_a,V_xs,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 160.93/160.63 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__upto,axiom,
% 160.93/160.63 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__take,axiom,
% 160.93/160.63 ! [V_n,V_xs,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 160.93/160.63 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__tl,axiom,
% 160.93/160.63 ! [V_xs,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 160.93/160.63 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__insort__insert,axiom,
% 160.93/160.63 ! [V_x_2,V_xs_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 160.93/160.63 => 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)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__butlast,axiom,
% 160.93/160.63 ! [V_xs,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 160.93/160.63 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted_Oequations_I1_J,axiom,
% 160.93/160.63 ! [T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__many,axiom,
% 160.93/160.63 ! [V_zs,V_y,V_x,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 160.93/160.63 => 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))) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__many__eq,axiom,
% 160.93/160.63 ! [V_zs_2,V_y_2,V_x_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( 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)))
% 160.93/160.63 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2))
% 160.93/160.63 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__remdups,axiom,
% 160.93/160.63 ! [V_l,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 160.93/160.63 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__distinct__set__unique,axiom,
% 160.93/160.63 ! [V_ys_2,V_xs_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 160.93/160.63 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2)
% 160.93/160.63 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2))
% 160.93/160.63 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2)
% 160.93/160.63 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__sort__key,axiom,
% 160.93/160.63 ! [V_xs_2,V_f_2,T_b,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => 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))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__insort__insert__key,axiom,
% 160.93/160.63 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 160.93/160.63 => 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))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__map__remove1,axiom,
% 160.93/160.63 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 160.93/160.63 => 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))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__insort__key,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( 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)))
% 160.93/160.63 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__filter,axiom,
% 160.93/160.63 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 160.93/160.63 => 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))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__map__same,axiom,
% 160.93/160.63 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => 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))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__same,axiom,
% 160.93/160.63 ! [V_xs_2,V_g_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__append,axiom,
% 160.93/160.63 ! [V_ys_2,V_xs_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 160.93/160.63 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 160.93/160.63 & c_List_Olinorder__class_Osorted(T_a,V_ys_2)
% 160.93/160.63 & ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => ! [B_xa] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2)))
% 160.93/160.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter__insort,axiom,
% 160.93/160.63 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))
% 160.93/160.63 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => 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)) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted_Oequations_I2_J,axiom,
% 160.93/160.63 ! [V_a1_2,V_a2_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2))
% 160.93/160.63 <=> ( ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2)))
% 160.93/160.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) )
% 160.93/160.63 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__list__of__set,axiom,
% 160.93/160.63 ! [V_A_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.93/160.63 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2
% 160.93/160.63 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))
% 160.93/160.63 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_insort__remove1,axiom,
% 160.93/160.63 ! [V_xs_2,V_a_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 160.93/160.63 => 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 ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__equals__nth__mono,axiom,
% 160.93/160.63 ! [V_xs_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 160.93/160.63 <=> ! [B_j] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => ! [B_i] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 160.93/160.63 => 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))) ) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__nth__mono,axiom,
% 160.93/160.63 ! [V_j,V_i,V_xs,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 160.93/160.63 => ( 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)))
% 160.93/160.63 => 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))) ) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__sorted__distinct__set__unique,axiom,
% 160.93/160.63 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_b)
% 160.93/160.63 => ( 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)))
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))
% 160.93/160.63 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)))
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))
% 160.93/160.63 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)))
% 160.93/160.63 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2)
% 160.93/160.63 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose__column,axiom,
% 160.93/160.63 ! [V_i_2,V_xs_2,T_a] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => ( 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)))
% 160.93/160.63 => 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) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_nth__nth__transpose__sorted,axiom,
% 160.93/160.63 ! [V_j_2,V_i_2,V_xs_2,T_a] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => ( 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))))
% 160.93/160.63 => ( 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))))
% 160.93/160.63 => 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) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_inj__on__rev,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_distinct__rev,axiom,
% 160.93/160.63 ! [V_xs_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2)))
% 160.93/160.63 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev__append,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev__is__Nil__conv,axiom,
% 160.93/160.63 ! [V_xs_2,T_a] :
% 160.93/160.63 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a)
% 160.93/160.63 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_Nil__is__rev__conv,axiom,
% 160.93/160.63 ! [V_xs_2,T_a] :
% 160.93/160.63 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2)
% 160.93/160.63 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev_Osimps_I1_J,axiom,
% 160.93/160.63 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev__singleton__conv,axiom,
% 160.93/160.63 ! [V_x_2,V_xs_2,T_a] :
% 160.93/160.63 ( 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))
% 160.93/160.63 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_singleton__rev__conv,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( 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)
% 160.93/160.63 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev__eq__Cons__iff,axiom,
% 160.93/160.63 ! [V_ys_2,V_y_2,V_xs_2,T_a] :
% 160.93/160.63 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)
% 160.93/160.63 <=> 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))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev_Osimps_I2_J,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev__concat,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev__map,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev__filter,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_zip__rev,axiom,
% 160.93/160.63 ! [V_ys,T_b,V_xs,T_a] :
% 160.93/160.63 ( 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)
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_set__rev,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__rev,axiom,
% 160.93/160.63 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 160.93/160.63 ( 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))
% 160.93/160.63 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__rev1,axiom,
% 160.93/160.63 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] :
% 160.93/160.63 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2)
% 160.93/160.63 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_listsum__rev,axiom,
% 160.93/160.63 ! [V_xs,T_a] :
% 160.93/160.63 ( class_Groups_Ocomm__monoid__add(T_a)
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev__rev__ident,axiom,
% 160.93/160.63 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev__swap,axiom,
% 160.93/160.63 ! [V_ys_2,V_xs_2,T_a] :
% 160.93/160.63 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2
% 160.93/160.63 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev__is__rev__conv,axiom,
% 160.93/160.63 ! [V_ys_2,V_xs_2,T_a] :
% 160.93/160.63 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2)
% 160.93/160.63 <=> V_xs_2 = V_ys_2 ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__rev,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_foldr__foldl,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_foldl__foldr,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_hd__rev,axiom,
% 160.93/160.63 ! [T_a,V_xs] :
% 160.93/160.63 ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.63 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_last__rev,axiom,
% 160.93/160.63 ! [T_a,V_xs] :
% 160.93/160.63 ( V_xs != c_List_Olist_ONil(T_a)
% 160.93/160.63 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__transpose,axiom,
% 160.93/160.63 ! [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)))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev__foldl__cons,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev__take,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev__drop,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rotate__rev,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev__nth,axiom,
% 160.93/160.63 ! [V_xs,T_a,V_n] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => 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))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_rev__update,axiom,
% 160.93/160.63 ! [V_y,V_xs,T_a,V_k] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__rev__nth__mono,axiom,
% 160.93/160.63 ! [V_j,V_i,V_xs,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 160.93/160.63 => ( 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)))
% 160.93/160.63 => 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))) ) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_foldr__max__sorted,axiom,
% 160.93/160.63 ! [V_y_2,V_xs_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2))
% 160.93/160.63 => ( ( V_xs_2 = c_List_Olist_ONil(T_a)
% 160.93/160.63 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 )
% 160.93/160.63 & ( V_xs_2 != c_List_Olist_ONil(T_a)
% 160.93/160.63 => 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) ) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__transpose__sorted,axiom,
% 160.93/160.63 ! [V_xs_2,T_a] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a))
% 160.93/160.63 => 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) )
% 160.93/160.63 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a))
% 160.93/160.63 => 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))) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose__column__length,axiom,
% 160.93/160.63 ! [V_i_2,V_xs_2,T_a] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => ( 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)))
% 160.93/160.63 => 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)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transpose__transpose,axiom,
% 160.93/160.63 ! [V_xs_2,T_a] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 160.93/160.63 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__takeWhile,axiom,
% 160.93/160.63 ! [V_P_2,V_xs_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 160.93/160.63 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__takeWhile__le,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_takeWhile__eq__all__conv,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2
% 160.93/160.63 <=> ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_set__takeWhileD,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,V_x_2,T_a] :
% 160.93/160.63 ( 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))))
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_zip__takeWhile__fst,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_zip__takeWhile__snd,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_takeWhile__map,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_takeWhile__tail,axiom,
% 160.93/160.63 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] :
% 160.93/160.63 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 160.93/160.63 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 160.93/160.63 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => 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)) )
% 160.93/160.63 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => 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) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_takeWhile__eq__take,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_distinct__takeWhile,axiom,
% 160.93/160.63 ! [V_P_2,V_xs_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.63 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_return__list__def,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_takeWhile__append1,axiom,
% 160.93/160.63 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => 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) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_takeWhile__nth,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a,V_j_2] :
% 160.93/160.63 ( 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))))
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_nth__length__takeWhile,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => ~ 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))))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_takeWhile__not__last,axiom,
% 160.93/160.63 ! [T_a,V_xs_2] :
% 160.93/160.63 ( V_xs_2 != c_List_Olist_ONil(T_a)
% 160.93/160.63 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.63 => 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) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 160.93/160.63 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( 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)))
% 160.93/160.63 => 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) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 160.93/160.63 ! [V_l] :
% 160.93/160.63 ( c_List_Onat__list(V_l)
% 160.93/160.63 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_embed__list__def,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_takeWhile__neq__rev,axiom,
% 160.93/160.63 ! [V_x_2,V_xs_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => 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))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_dropWhile__neq__rev,axiom,
% 160.93/160.63 ! [V_x_2,V_xs_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => 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))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_takeWhile__dropWhile__id,axiom,
% 160.93/160.63 ! [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 ).
% 160.93/160.63
% 160.93/160.63 fof(fact_dropWhile__map,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__dropWhile,axiom,
% 160.93/160.63 ! [V_P_2,V_xs_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 160.93/160.63 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__dropWhile__le,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a)
% 160.93/160.63 <=> ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 160.93/160.63 ! [V_xs_2,T_a,V_x_2,V_P_2] :
% 160.93/160.63 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => 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) )
% 160.93/160.63 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => 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) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_hd__dropWhile,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a)
% 160.93/160.63 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_distinct__dropWhile,axiom,
% 160.93/160.63 ! [V_P_2,V_xs_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2))
% 160.93/160.63 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_dropWhile__append1,axiom,
% 160.93/160.63 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => 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) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 160.93/160.63 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( 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)
% 160.93/160.63 <=> ( 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))
% 160.93/160.63 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_dropWhile__eq__drop,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_dropWhile__nth,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a,V_j_2] :
% 160.93/160.63 ( 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))))
% 160.93/160.63 => 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)))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_listsum__map__filter,axiom,
% 160.93/160.63 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] :
% 160.93/160.63 ( class_Groups_Omonoid__add(T_b)
% 160.93/160.63 => ( ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => ( ~ hBOOL(hAPP(V_P_2,B_x))
% 160.93/160.63 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) )
% 160.93/160.63 => 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)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted__nth__monoI,axiom,
% 160.93/160.63 ! [V_xs,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( ! [B_i,B_j] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 160.93/160.63 => ( 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)))
% 160.93/160.63 => 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))) ) )
% 160.93/160.63 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_takeWhile__eq__filter,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( ! [B_x] :
% 160.93/160.63 ( 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))))
% 160.93/160.63 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 160.93/160.63 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 160.93/160.63 ! [V_P_2,V_xs_2,T_a,V_n_2] :
% 160.93/160.63 ( ! [B_i] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 160.93/160.63 => ( 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)))
% 160.93/160.63 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) )
% 160.93/160.63 => ( ( 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)))
% 160.93/160.63 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) )
% 160.93/160.63 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__takeWhile__less__P__nth,axiom,
% 160.93/160.63 ! [V_xs_2,T_a,V_P_2,V_j_2] :
% 160.93/160.63 ( ! [B_i] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 160.93/160.63 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) )
% 160.93/160.63 => ( 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)))
% 160.93/160.63 => 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)))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted_Osimps,axiom,
% 160.93/160.63 ! [V_a_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2)
% 160.93/160.63 <=> ( V_a_2 = c_List_Olist_ONil(T_a)
% 160.93/160.63 | ? [B_xs,B_x] :
% 160.93/160.63 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs)
% 160.93/160.63 & ! [B_xa] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs)))
% 160.93/160.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) )
% 160.93/160.63 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__upds__def,axiom,
% 160.93/160.63 ! [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)))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__comp__def,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__of__append,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__comp__empty_I2_J,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__comp__empty_I1_J,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__comp__Some__iff,axiom,
% 160.93/160.63 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
% 160.93/160.63 ( 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)
% 160.93/160.63 <=> ? [B_k_H] :
% 160.93/160.63 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H)
% 160.93/160.63 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__add__find__right,axiom,
% 160.93/160.63 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] :
% 160.93/160.63 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2)
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__comp__simps_I2_J,axiom,
% 160.93/160.63 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] :
% 160.93/160.63 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2)
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__add__upd,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__add__Some__iff,axiom,
% 160.93/160.63 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 160.93/160.63 ( 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)
% 160.93/160.63 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 160.93/160.63 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 160.93/160.63 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__add__SomeD,axiom,
% 160.93/160.63 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 160.93/160.63 ( 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)
% 160.93/160.63 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2)
% 160.93/160.63 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 160.93/160.63 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_empty__map__add,axiom,
% 160.93/160.63 ! [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 ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__add__empty,axiom,
% 160.93/160.63 ! [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 ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__add__None,axiom,
% 160.93/160.63 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] :
% 160.93/160.63 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a)
% 160.93/160.63 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 160.93/160.63 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__comp__simps_I1_J,axiom,
% 160.93/160.63 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] :
% 160.93/160.63 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a)
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__add__upds,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_dom__map__add,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__add__dom__app__simps_I1_J,axiom,
% 160.93/160.63 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2)))
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__add__dom__app__simps_I3_J,axiom,
% 160.93/160.63 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] :
% 160.93/160.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2)))
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__add__dom__app__simps_I2_J,axiom,
% 160.93/160.63 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] :
% 160.93/160.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2)))
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__add__assoc,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_inj__on__map__add__dom,axiom,
% 160.93/160.63 ! [V_m_H_2,V_m_2,T_b,T_a] :
% 160.93/160.63 ( 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))
% 160.93/160.63 <=> 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__add__def,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__add__comm,axiom,
% 160.93/160.63 ! [V_m2_2,V_m1_2,T_b,T_a] :
% 160.93/160.63 ( 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))
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__comp__None__iff,axiom,
% 160.93/160.63 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] :
% 160.93/160.63 ( 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)
% 160.93/160.63 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 160.93/160.63 | ? [B_k_H] :
% 160.93/160.63 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H)
% 160.93/160.63 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__add__map__of__foldr,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__add__upd__left,axiom,
% 160.93/160.63 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] :
% 160.93/160.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2)))
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_finite__range__map__of__map__add,axiom,
% 160.93/160.63 ! [V_l_2,V_f_2,T_b,T_a] :
% 160.93/160.63 ( 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)))))
% 160.93/160.63 => 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))))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_List_Oinsert__def,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 )
% 160.93/160.63 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => 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) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_not__in__set__insert,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_distinct__insert,axiom,
% 160.93/160.63 ! [V_x,V_xs,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 160.93/160.63 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_insert__remdups,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_in__set__insert,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_List_Oset__insert,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_insert__Nil,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_maps__def,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_concat__map__maps,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_maps__simps_I2_J,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_maps__simps_I1_J,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_distinct__concat,axiom,
% 160.93/160.63 ! [V_xs_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2))
% 160.93/160.63 => ( ! [B_ys] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 160.93/160.63 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) )
% 160.93/160.63 => ( ! [B_ys] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 160.93/160.63 => ! [B_zs] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)))
% 160.93/160.63 => ( B_ys != B_zs
% 160.93/160.63 => 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)) ) ) )
% 160.93/160.63 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_ran__restrictD,axiom,
% 160.93/160.63 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] :
% 160.93/160.63 ( 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))))
% 160.93/160.63 => ? [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 160.93/160.63 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_measures__lesseq,axiom,
% 160.93/160.63 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => ( 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)))
% 160.93/160.63 => 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)))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_in__measures_I2_J,axiom,
% 160.93/160.63 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] :
% 160.93/160.63 ( 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))))
% 160.93/160.63 <=> ( 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)))
% 160.93/160.63 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 160.93/160.63 & 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))) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_wf__measures,axiom,
% 160.93/160.63 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_in__measures_I1_J,axiom,
% 160.93/160.63 ! [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))))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_measures__def,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_measures__less,axiom,
% 160.93/160.63 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => 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)))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_foldl__apply,axiom,
% 160.93/160.63 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] :
% 160.93/160.63 ( ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => 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)) )
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_zip__obtain__same__length,axiom,
% 160.93/160.63 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] :
% 160.93/160.63 ( ( 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))
% 160.93/160.63 => 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)))) )
% 160.93/160.63 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_map__of__eqI,axiom,
% 160.93/160.63 ! [V_ys_2,V_xs_2,T_b,T_a] :
% 160.93/160.63 ( 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))
% 160.93/160.63 => ( ! [B_x] :
% 160.93/160.63 ( 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))))
% 160.93/160.63 => 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) )
% 160.93/160.63 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_pos__not__random__dseq__def,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_dropWhile__append2,axiom,
% 160.93/160.63 ! [V_ys_2,V_P_2,V_xs_2,T_a] :
% 160.93/160.63 ( ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => hBOOL(hAPP(V_P_2,B_x)) )
% 160.93/160.63 => 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) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all2__all__nthI,axiom,
% 160.93/160.63 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] :
% 160.93/160.63 ( 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)
% 160.93/160.63 => ( ! [B_n] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => 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))) )
% 160.93/160.63 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_finite__map__freshness,axiom,
% 160.93/160.63 ! [V_f_2,T_b,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2)))
% 160.93/160.63 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 160.93/160.63 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_finite__sorted__distinct__unique,axiom,
% 160.93/160.63 ! [V_A_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2))
% 160.93/160.63 => ? [B_x] :
% 160.93/160.63 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2
% 160.93/160.63 & c_List_Olinorder__class_Osorted(T_a,B_x)
% 160.93/160.63 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x))
% 160.93/160.63 & ! [B_y] :
% 160.93/160.63 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2
% 160.93/160.63 & c_List_Olinorder__class_Osorted(T_a,B_y)
% 160.93/160.63 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) )
% 160.93/160.63 => B_y = B_x ) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_takeWhile__append2,axiom,
% 160.93/160.63 ! [V_ys_2,V_P_2,V_xs_2,T_a] :
% 160.93/160.63 ( ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => hBOOL(hAPP(V_P_2,B_x)) )
% 160.93/160.63 => 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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_insort__is__Cons,axiom,
% 160.93/160.63 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_b)
% 160.93/160.63 => ( ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 160.93/160.63 => 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) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_Cons__eq__filter__iff,axiom,
% 160.93/160.63 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( 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)
% 160.93/160.63 <=> ? [B_us,B_vs] :
% 160.93/160.63 ( 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))
% 160.93/160.63 & ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us)))
% 160.93/160.63 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 160.93/160.63 & hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_filter__eq__Cons__iff,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] :
% 160.93/160.63 ( 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)
% 160.93/160.63 <=> ? [B_us,B_vs] :
% 160.93/160.63 ( 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))
% 160.93/160.63 & ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us)))
% 160.93/160.63 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 160.93/160.63 & hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__ball__nth,axiom,
% 160.93/160.63 ! [V_P_2,V_xs_2,T_a,V_n_2] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => ( ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => hBOOL(hAPP(V_P_2,B_x)) )
% 160.93/160.63 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_sorted_OCons,axiom,
% 160.93/160.63 ! [V_x_2,V_xs_2,T_a] :
% 160.93/160.63 ( class_Orderings_Olinorder(T_a)
% 160.93/160.63 => ( ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) )
% 160.93/160.63 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2)
% 160.93/160.63 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__ex__length,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 160.93/160.63 <=> ? [B_n] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_in__set__conv__decomp__first,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 <=> ? [B_ys] :
% 160.93/160.63 ( ? [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))
% 160.93/160.63 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__ex__simps_I2_J,axiom,
% 160.93/160.63 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__ex__append,axiom,
% 160.93/160.63 ! [V_ys_2,V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 160.93/160.63 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 160.93/160.63 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__ex__iff,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2)
% 160.93/160.63 <=> ? [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__ex__rev,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2))
% 160.93/160.63 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__ex__simps_I1_J,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 160.93/160.63 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_in__set__conv__decomp,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 <=> ? [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)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_in__set__conv__decomp__last,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 <=> ? [B_ys,B_zs] :
% 160.93/160.63 ( 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))
% 160.93/160.63 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_option_Orecs_I2_J,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_option_Orecs_I1_J,axiom,
% 160.93/160.63 ! [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 ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all__length,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 160.93/160.63 <=> ! [B_n] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_finite__induct,axiom,
% 160.93/160.63 ! [V_P_2,V_F_2,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2))
% 160.93/160.63 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 160.93/160.63 => ( ! [B_x,B_F] :
% 160.93/160.63 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F))
% 160.93/160.63 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F))
% 160.93/160.63 => ( hBOOL(hAPP(V_P_2,B_F))
% 160.93/160.63 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F))) ) ) )
% 160.93/160.63 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all__simps_I1_J,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 160.93/160.63 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 & c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all__rev,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2))
% 160.93/160.63 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_Ball__set__list__all,axiom,
% 160.93/160.63 ! [V_P_2,V_xs_2,T_a] :
% 160.93/160.63 ( ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => hBOOL(hAPP(V_P_2,B_x)) )
% 160.93/160.63 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all__iff,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 160.93/160.63 <=> ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all__append,axiom,
% 160.93/160.63 ! [V_ys_2,V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))
% 160.93/160.63 <=> ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 160.93/160.63 & c_List_Olist__all(T_a,V_P_2,V_ys_2) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all__simps_I2_J,axiom,
% 160.93/160.63 ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__all__iff__raw,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_Olist__all(T_a,V_P_2,V_xs_2)
% 160.93/160.63 <=> ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__ex1__simps_I2_J,axiom,
% 160.93/160.63 ! [V_xs_2,V_x_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))
% 160.93/160.63 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => 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) )
% 160.93/160.63 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 160.93/160.63 => c_List_Olist__ex1(T_a,V_P_2,V_xs_2) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_measure__function__int,axiom,
% 160.93/160.63 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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__ex1__simps_I1_J,axiom,
% 160.93/160.63 ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_measure__size,axiom,
% 160.93/160.63 ! [T_a] :
% 160.93/160.63 ( class_Nat_Osize(T_a)
% 160.93/160.63 => c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_is__measure_Osimps,axiom,
% 160.93/160.63 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_is__measure_Oequations,axiom,
% 160.93/160.63 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_is__measure_Ointros,axiom,
% 160.93/160.63 ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_exists1__code,axiom,
% 160.93/160.63 ! [V_P_2,T_a] :
% 160.93/160.63 ( class_Enum_Oenum(T_a)
% 160.93/160.63 => ( ? [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(V_P_2,B_x))
% 160.93/160.63 & ! [B_y] :
% 160.93/160.63 ( hBOOL(hAPP(V_P_2,B_y))
% 160.93/160.63 => B_y = B_x ) )
% 160.93/160.63 <=> c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_measure__snd,axiom,
% 160.93/160.63 ! [T_b,V_f_2,T_a] :
% 160.93/160.63 ( c_FunDef_Ois__measure(T_a,V_f_2)
% 160.93/160.63 => 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))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_measure__fst,axiom,
% 160.93/160.63 ! [T_b,V_f_2,T_a] :
% 160.93/160.63 ( c_FunDef_Ois__measure(T_a,V_f_2)
% 160.93/160.63 => 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))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_list__ex1__iff,axiom,
% 160.93/160.63 ! [V_xs_2,V_P_2,T_a] :
% 160.93/160.63 ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2)
% 160.93/160.63 <=> ? [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 & hBOOL(hAPP(V_P_2,B_x))
% 160.93/160.63 & ! [B_y] :
% 160.93/160.63 ( ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2)))
% 160.93/160.63 & hBOOL(hAPP(V_P_2,B_y)) )
% 160.93/160.63 => B_y = B_x ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_equal__fun__def,axiom,
% 160.93/160.63 ! [V_g_2,V_f_2,T_a,T_b] :
% 160.93/160.63 ( ( class_HOL_Oequal(T_b)
% 160.93/160.63 & class_Enum_Oenum(T_a) )
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 160.93/160.63 <=> ! [B_x] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a))))
% 160.93/160.63 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_transfer__morphism__int__nat,axiom,
% 160.93/160.63 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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_equal,axiom,
% 160.93/160.63 ! [T_a] :
% 160.93/160.63 ( class_HOL_Oequal(T_a)
% 160.93/160.63 => c_HOL_Oequal__class_Oequal(T_a) = c_fequal ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_equal__refl,axiom,
% 160.93/160.63 ! [V_x,T_a] :
% 160.93/160.63 ( class_HOL_Oequal(T_a)
% 160.93/160.63 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_equal__eq,axiom,
% 160.93/160.63 ! [V_y_2,V_x_2,T_a] :
% 160.93/160.63 ( class_HOL_Oequal(T_a)
% 160.93/160.63 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2))
% 160.93/160.63 <=> V_x_2 = V_y_2 ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__equal,axiom,
% 160.93/160.63 ! [T_a] :
% 160.93/160.63 ( class_HOL_Oequal(T_a)
% 160.93/160.63 => c_fequal = c_HOL_Oequal__class_Oequal(T_a) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_bool_Osize_I3_J,axiom,
% 160.93/160.63 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_bool_Osize_I4_J,axiom,
% 160.93/160.63 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_size__code,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 160.93/160.63 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] :
% 160.93/160.63 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 160.93/160.63 => 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) )
% 160.93/160.63 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 160.93/160.63 => 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)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I5_J,axiom,
% 160.93/160.63 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I2_J,axiom,
% 160.93/160.63 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I8_J,axiom,
% 160.93/160.63 ! [V_k2_2] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2)))
% 160.93/160.63 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I12_J,axiom,
% 160.93/160.63 ! [V_k1_2] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin))
% 160.93/160.63 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I3_J,axiom,
% 160.93/160.63 ! [V_k2_2] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2)))
% 160.93/160.63 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I9_J,axiom,
% 160.93/160.63 ! [V_k1_2] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls))
% 160.93/160.63 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I14_J,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I15_J,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_equal__int__def,axiom,
% 160.93/160.63 ! [V_l_2,V_k_2] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2))
% 160.93/160.63 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I4_J,axiom,
% 160.93/160.63 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I10_J,axiom,
% 160.93/160.63 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I6_J,axiom,
% 160.93/160.63 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__number__of__int__code,axiom,
% 160.93/160.63 ! [V_l_2,V_k_2] :
% 160.93/160.63 ( 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)))
% 160.93/160.63 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I16_J,axiom,
% 160.93/160.63 ! [V_k2_2,V_k1_2] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 160.93/160.63 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I1_J,axiom,
% 160.93/160.63 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I13_J,axiom,
% 160.93/160.63 ! [V_k2_2,V_k1_2] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 160.93/160.63 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I7_J,axiom,
% 160.93/160.63 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__code_I11_J,axiom,
% 160.93/160.63 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_lazy__sequence__size__code,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_eq__int__refl,axiom,
% 160.93/160.63 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_seq__case,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_yieldn__def,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 160.93/160.63 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_pos__empty__def,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_pos__bind__def,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact__01,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_lazy__sequence_Oinject,axiom,
% 160.93/160.63 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_a] :
% 160.93/160.63 ( 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)
% 160.93/160.63 <=> ( V_a_2 = V_a_H_2
% 160.93/160.63 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_pos__map__def,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 160.93/160.63 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] :
% 160.93/160.63 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 160.93/160.63 => 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) )
% 160.93/160.63 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 160.93/160.63 => 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)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_pos__single__def,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_New__DSequence_Opos__single__def,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_neg__bind__def,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact__02,axiom,
% 160.93/160.63 ! [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)))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_neg__map__def,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_small__lazy__list_Osimps,axiom,
% 160.93/160.63 ! [V_d_2,T_a] :
% 160.93/160.63 ( class_Lazy__Sequence_Osmall__lazy(T_a)
% 160.93/160.63 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_a),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_a),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),c_Lazy__Sequence_Oproduct(T_a,tc_List_Olist(T_a),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),T_a),hAPP(c_COMBB(tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a)),tc_List_Olist(T_a)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_a)))),c_List_Olist_OCons(T_a))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_a)))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_small__lazy__prod__def,axiom,
% 160.93/160.63 ! [V_d,T_b,T_a] :
% 160.93/160.63 ( ( class_Lazy__Sequence_Osmall__lazy(T_a)
% 160.93/160.63 & class_Lazy__Sequence_Osmall__lazy(T_b) )
% 160.93/160.63 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact__03,axiom,
% 160.93/160.63 ! [V_yq,V_xq,V_x,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_neg__single__def,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_New__DSequence_Opos__union__def,axiom,
% 160.93/160.63 ! [V_i_2,V_yq_2,V_xq_2,T_a] : hAPP(c_New__DSequence_Opos__union(T_a,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_a,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 160.93/160.63 ! [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) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_pos__union__def,axiom,
% 160.93/160.63 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_a] : c_New__Random__Sequence_Opos__union(T_a,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_a,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_small__lazy_H_Osimps,axiom,
% 160.93/160.63 ! [V_i,V_d] :
% 160.93/160.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 160.93/160.63 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 160.93/160.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 160.93/160.63 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i),c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_small__lazy_H_Opsimps,axiom,
% 160.93/160.63 ! [V_i_2,V_d_2] :
% 160.93/160.63 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2)))
% 160.93/160.63 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 160.93/160.63 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 160.93/160.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 160.93/160.63 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i_2),c_Lazy__Sequence_Osmall__lazy_H(V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_small__lazy__int__def,axiom,
% 160.93/160.63 ! [V_d] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,V_d) = c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_small__lazy_H_Opinduct,axiom,
% 160.93/160.63 ! [V_P_2,V_a1_2,V_a0_2] :
% 160.93/160.63 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 160.93/160.63 => ( ! [B_d,B_i] :
% 160.93/160.63 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i)))
% 160.93/160.63 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 160.93/160.63 => hBOOL(hAPP(hAPP(V_P_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
% 160.93/160.63 => hBOOL(hAPP(hAPP(V_P_2,B_d),B_i)) ) )
% 160.93/160.63 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_hb__flat_Osimps_I2_J,axiom,
% 160.93/160.63 ! [V_xqq_2,V_xq_2,T_a] : c_Lazy__Sequence_Ohb__flat(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_xq_2,V_xqq_2)) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(T_a),hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)),tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)),c_Lazy__Sequence_Ohit__bound(T_a),c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))),V_xq_2),c_Lazy__Sequence_Ohb__flat(T_a,V_xqq_2)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_New__DSequence_Oneg__union__def,axiom,
% 160.93/160.63 ! [V_i_2,V_y_2,V_x_2,T_a] : hAPP(c_New__DSequence_Oneg__union(T_a,V_x_2,V_y_2),V_i_2) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(T_a),hAPP(V_x_2,V_i_2),hAPP(V_y_2,V_i_2)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_hb__bind__def,axiom,
% 160.93/160.63 ! [V_f_2,V_xq_2,T_a,T_b] : c_Lazy__Sequence_Ohb__bind(T_b,T_a,V_xq_2,V_f_2) = c_Lazy__Sequence_Ohb__flat(T_a,c_Lazy__Sequence_Ohb__map(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)),V_f_2,V_xq_2)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_hb__map_Osimps_I2_J,axiom,
% 160.93/160.63 ! [V_xq_2,V_x_2,V_f_2,T_a,T_b] : c_Lazy__Sequence_Ohb__map(T_b,T_a,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(T_b),V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(T_a),hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_x_2),c_Lazy__Sequence_Ohb__map(T_b,T_a,V_f_2,V_xq_2)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_neg__union__def,axiom,
% 160.93/160.63 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_a] : c_New__Random__Sequence_Oneg__union(T_a,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__union(T_a,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_New__DSequence_Oneg__map__def,axiom,
% 160.93/160.63 ! [V_i_2,V_xq_2,V_f_2,T_a,T_b] : c_New__DSequence_Oneg__map(T_b,T_a,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Ohb__map(T_b,T_a,V_f_2,hAPP(V_xq_2,V_i_2)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_length__splice,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_acyclicP__converse,axiom,
% 160.93/160.63 ! [V_r_2,T_a] :
% 160.93/160.63 ( 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))))
% 160.93/160.63 <=> 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))) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_splice_Osimps_I3_J,axiom,
% 160.93/160.63 ! [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))) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_conversep__noteq,axiom,
% 160.93/160.63 ! [V_y_2,V_x_2,T_a] :
% 160.93/160.63 ( 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))
% 160.93/160.63 <=> V_x_2 != V_y_2 ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_conversep__eq,axiom,
% 160.93/160.63 ! [T_a] : c_Predicate_Oconversep(T_a,T_a,c_fequal) = c_fequal ).
% 160.93/160.63
% 160.93/160.63 fof(fact_conversep__conversep,axiom,
% 160.93/160.63 ! [V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Oconversep(T_a,T_b,V_r_2)) = V_r_2 ).
% 160.93/160.63
% 160.93/160.63 fof(fact_conversep__iff,axiom,
% 160.93/160.63 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2))
% 160.93/160.63 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_conversep_Oequations,axiom,
% 160.93/160.63 ! [V_a1_2,V_a2_2,V_r_2,T_b,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a2_2),V_a1_2))
% 160.93/160.63 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_conversep_Ointros,axiom,
% 160.93/160.63 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 160.93/160.63 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_b_2),V_a_2)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_conversepD,axiom,
% 160.93/160.63 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2))
% 160.93/160.63 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_converse__pred__comp,axiom,
% 160.93/160.63 ! [V_s_2,V_r_2,T_c,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Opred__comp(T_b,T_c,T_a,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_a,T_c,T_b,c_Predicate_Oconversep(T_c,T_a,V_s_2),c_Predicate_Oconversep(T_b,T_c,V_r_2)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_converse__join,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_converse__meet,axiom,
% 160.93/160.63 ! [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)) ).
% 160.93/160.63
% 160.93/160.63 fof(fact_splice_Osimps_I1_J,axiom,
% 160.93/160.63 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 160.93/160.63
% 160.93/160.63 fof(fact_splice__Nil2,axiom,
% 160.93/160.63 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 160.93/160.63
% 160.93/160.63 fof(fact_conversep__converse__eq,axiom,
% 160.93/160.63 ! [V_y_2,V_x_2,V_r_2,T_b,T_a] :
% 160.93/160.63 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2),V_y_2))
% 160.93/160.63 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2))) ) ).
% 160.93/160.63
% 160.93/160.63 %----Arity declarations (235)
% 160.93/160.63 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 160.93/160.63 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Lattices_Obounded__lattice(T_1)
% 160.93/160.63 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 160.93/160.63 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Lattices_Obounded__lattice(T_1)
% 160.93/160.63 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Lattices_Obounded__lattice(T_1)
% 160.93/160.63 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Lattices_Olattice(T_1)
% 160.93/160.63 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Lattices_Olattice(T_1)
% 160.93/160.63 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Lattices_Odistrib__lattice(T_1)
% 160.93/160.63 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Lattices_Oboolean__algebra(T_1)
% 160.93/160.63 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Orderings_Opreorder,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Orderings_Opreorder(T_1)
% 160.93/160.63 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 160.93/160.63 ! [T_1,T_2] :
% 160.93/160.63 ( ( class_Finite__Set_Ofinite(T_2)
% 160.93/160.63 & class_Finite__Set_Ofinite(T_1) )
% 160.93/160.63 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Lattices_Olattice,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Lattices_Olattice(T_1)
% 160.93/160.63 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Orderings_Oorder,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Orderings_Oorder(T_1)
% 160.93/160.63 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Orderings_Otop,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Orderings_Otop(T_1)
% 160.93/160.63 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Orderings_Oord,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Orderings_Oord(T_1)
% 160.93/160.63 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Orderings_Obot,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Orderings_Obot(T_1)
% 160.93/160.63 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Groups_Ouminus,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Groups_Ouminus(T_1)
% 160.93/160.63 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Groups_Ominus,axiom,
% 160.93/160.63 ! [T_2,T_1] :
% 160.93/160.63 ( class_Groups_Ominus(T_1)
% 160.93/160.63 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__HOL_Oequal,axiom,
% 160.93/160.63 ! [T_1,T_2] :
% 160.93/160.63 ( ( class_Enum_Oenum(T_2)
% 160.93/160.63 & class_HOL_Oequal(T_1) )
% 160.93/160.63 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_fun__Enum_Oenum,axiom,
% 160.93/160.63 ! [T_1,T_2] :
% 160.93/160.63 ( ( class_Enum_Oenum(T_2)
% 160.93/160.63 & class_Enum_Oenum(T_1) )
% 160.93/160.63 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Com__Ocom__HOL_Oequal,axiom,
% 160.93/160.63 class_HOL_Oequal(tc_Com_Ocom) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Com__Ocom__Nat_Osize,axiom,
% 160.93/160.63 class_Nat_Osize(tc_Com_Ocom) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 160.93/160.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 160.93/160.63 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 160.93/160.63 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 160.93/160.63 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 160.93/160.63 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 160.93/160.63 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 160.93/160.63 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 160.93/160.63 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 160.93/160.63 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 160.93/160.63 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 160.93/160.63 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 160.93/160.63 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 160.93/160.63 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 160.93/160.63 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 160.93/160.63 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 160.93/160.63 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 160.93/160.63 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 160.93/160.63 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 160.93/160.63 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 160.93/160.63 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 160.93/160.63 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 160.93/160.63 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
% 160.93/160.63 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 160.93/160.63 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 160.93/160.63 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 160.93/160.63 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 160.93/160.63 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 160.93/160.63 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 160.93/160.63 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 160.93/160.63 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 160.93/160.63 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 160.93/160.63 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 160.93/160.63 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 160.93/160.63 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 160.93/160.63 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 160.93/160.63 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 160.93/160.63 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 160.93/160.63 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 160.93/160.63 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 160.93/160.63 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 160.93/160.63 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 160.93/160.63 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 160.93/160.63 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 160.93/160.63 class_Orderings_Opreorder(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 160.93/160.63 class_Orderings_Olinorder(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 160.93/160.63 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 160.93/160.63 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 160.93/160.63 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
% 160.93/160.63 class_Smallcheck_Osmall(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 160.93/160.63 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 160.93/160.63 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 160.93/160.63 class_Lattices_Olattice(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 160.93/160.63 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 160.93/160.63 class_Divides_Oring__div(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 160.93/160.63 class_Rings_Omult__zero(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 160.93/160.63 class_Orderings_Oorder(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 160.93/160.63 class_Int_Oring__char__0(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 160.93/160.63 class_Int_Onumber__ring(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 160.93/160.63 class_Rings_Osemiring(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 160.93/160.63 class_Orderings_Oord(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 160.93/160.63 class_Groups_Ouminus(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 160.93/160.63 class_Groups_Osgn__if(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 160.93/160.63 class_Groups_Oabs__if(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 160.93/160.63 class_Rings_Oring__1(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 160.93/160.63 class_Groups_Ominus(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Power_Opower,axiom,
% 160.93/160.63 class_Power_Opower(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 160.93/160.63 class_Groups_Ozero(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Oring,axiom,
% 160.93/160.63 class_Rings_Oring(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 160.93/160.63 class_Rings_Oidom(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Int_Onumber,axiom,
% 160.93/160.63 class_Int_Onumber(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__Groups_Oone,axiom,
% 160.93/160.63 class_Groups_Oone(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Int__Oint__HOL_Oequal,axiom,
% 160.93/160.63 class_HOL_Oequal(tc_Int_Oint) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 160.93/160.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 160.93/160.63 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 160.93/160.63 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 160.93/160.63 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 160.93/160.63 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 160.93/160.63 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 160.93/160.63 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 160.93/160.63 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 160.93/160.63 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 160.93/160.63 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 160.93/160.63 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 160.93/160.63 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 160.93/160.63 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 160.93/160.63 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 160.93/160.63 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 160.93/160.63 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 160.93/160.63 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 160.93/160.63 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 160.93/160.63 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 160.93/160.63 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 160.93/160.63 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 160.93/160.63 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 160.93/160.63 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 160.93/160.63 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 160.93/160.63 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 160.93/160.63 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 160.93/160.63 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 160.93/160.63 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 160.93/160.63 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 160.93/160.63 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 160.93/160.63 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 160.93/160.63 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 160.93/160.63 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 160.93/160.63 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 160.93/160.63 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 160.93/160.63 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 160.93/160.63 class_Lattices_Olattice(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 160.93/160.63 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 160.93/160.63 class_Orderings_Oorder(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 160.93/160.63 class_Rings_Osemiring(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 160.93/160.63 class_Orderings_Oord(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 160.93/160.63 class_Orderings_Obot(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 160.93/160.63 class_Groups_Ominus(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Power_Opower,axiom,
% 160.93/160.63 class_Power_Opower(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 160.93/160.63 class_Groups_Ozero(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 160.93/160.63 class_Int_Onumber(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 160.93/160.63 class_Groups_Oone(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__HOL_Oequal,axiom,
% 160.93/160.63 class_HOL_Oequal(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 160.93/160.63 class_Nat_Osize(tc_Nat_Onat) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 160.93/160.63 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 160.93/160.63 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 160.93/160.63 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 160.93/160.63 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 160.93/160.63 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 160.93/160.63 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 160.93/160.63 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 160.93/160.63 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 160.93/160.63 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 160.93/160.63 class_Lattices_Olattice(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 160.93/160.63 class_Orderings_Oorder(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 160.93/160.63 class_Orderings_Otop(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 160.93/160.63 class_Orderings_Oord(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 160.93/160.63 class_Orderings_Obot(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 160.93/160.63 class_Groups_Ouminus(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 160.93/160.63 class_Groups_Ominus(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__HOL_Oequal,axiom,
% 160.93/160.63 class_HOL_Oequal(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 160.93/160.63 class_Enum_Oenum(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 160.93/160.63 class_Nat_Osize(tc_HOL_Obool) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Com__Ostate__HOL_Oequal,axiom,
% 160.93/160.63 class_HOL_Oequal(tc_Com_Ostate) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Com__Ostate__Nat_Osize,axiom,
% 160.93/160.63 class_Nat_Osize(tc_Com_Ostate) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
% 160.93/160.63 ! [T_1] :
% 160.93/160.63 ( class_Lazy__Sequence_Osmall__lazy(T_1)
% 160.93/160.63 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_List__Olist__HOL_Oequal,axiom,
% 160.93/160.63 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_List__Olist__Nat_Osize,axiom,
% 160.93/160.63 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 160.93/160.63 ! [T_1,T_2] :
% 160.93/160.63 ( ( class_Finite__Set_Ofinite(T_2)
% 160.93/160.63 & class_Finite__Set_Ofinite(T_1) )
% 160.93/160.63 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_sum__HOL_Oequal,axiom,
% 160.93/160.63 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_sum__Enum_Oenum,axiom,
% 160.93/160.63 ! [T_1,T_2] :
% 160.93/160.63 ( ( class_Enum_Oenum(T_2)
% 160.93/160.63 & class_Enum_Oenum(T_1) )
% 160.93/160.63 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_sum__Nat_Osize,axiom,
% 160.93/160.63 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 160.93/160.63 ! [T_1] :
% 160.93/160.63 ( class_Finite__Set_Ofinite(T_1)
% 160.93/160.63 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Option__Ooption__HOL_Oequal,axiom,
% 160.93/160.63 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 160.93/160.63 ! [T_1] :
% 160.93/160.63 ( class_Enum_Oenum(T_1)
% 160.93/160.63 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 160.93/160.63 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
% 160.93/160.63 ! [T_1,T_2] :
% 160.93/160.63 ( ( class_Lazy__Sequence_Osmall__lazy(T_2)
% 160.93/160.63 & class_Lazy__Sequence_Osmall__lazy(T_1) )
% 160.93/160.63 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 160.93/160.63 ! [T_1,T_2] :
% 160.93/160.63 ( ( class_Finite__Set_Ofinite(T_2)
% 160.93/160.63 & class_Finite__Set_Ofinite(T_1) )
% 160.93/160.63 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_prod__Smallcheck_Osmall,axiom,
% 160.93/160.63 ! [T_1,T_2] :
% 160.93/160.63 ( ( class_Smallcheck_Osmall(T_2)
% 160.93/160.63 & class_Smallcheck_Osmall(T_1) )
% 160.93/160.63 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_prod__HOL_Oequal,axiom,
% 160.93/160.63 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_prod__Enum_Oenum,axiom,
% 160.93/160.63 ! [T_1,T_2] :
% 160.93/160.63 ( ( class_Enum_Oenum(T_2)
% 160.93/160.63 & class_Enum_Oenum(T_1) )
% 160.93/160.63 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_prod__Nat_Osize,axiom,
% 160.93/160.63 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
% 160.93/160.63 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 160.93/160.63 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
% 160.93/160.63 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom,
% 160.93/160.63 class_HOL_Oequal(tc_Product__Type_Ounit) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 160.93/160.63 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 160.93/160.63 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom,
% 160.93/160.63 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 160.93/160.63 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom,
% 160.93/160.63 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 160.93/160.63 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 160.93/160.63 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.63
% 160.93/160.63 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 160.93/160.63 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.63
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 160.93/160.64 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 160.93/160.64 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 160.93/160.64 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 160.93/160.64 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 160.93/160.64 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 160.93/160.64 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 160.93/160.64 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 160.93/160.64 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 160.93/160.64 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 160.93/160.64 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 160.93/160.64 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 160.93/160.64 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 160.93/160.64 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 160.93/160.64 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 160.93/160.64 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 160.93/160.64 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 160.93/160.64 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 160.93/160.64 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 160.93/160.64 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 160.93/160.64 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 160.93/160.64 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 160.93/160.64 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 160.93/160.64 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 160.93/160.64 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 160.93/160.64 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 160.93/160.64 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 160.93/160.64 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 160.93/160.64 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 160.93/160.64 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 160.93/160.64 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 160.93/160.64 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 160.93/160.64 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 160.93/160.64 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 160.93/160.64 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 160.93/160.64 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 160.93/160.64 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 160.93/160.64 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 160.93/160.64 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom,
% 160.93/160.64 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 160.93/160.64 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom,
% 160.93/160.64 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 160.93/160.64
% 160.93/160.64 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 160.93/160.64 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 160.93/160.64
% 160.93/160.64 %----Helper facts (20)
% 160.93/160.64 fof(help_c__COMBI__1,axiom,
% 160.93/160.64 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__COMBK__1,axiom,
% 160.93/160.64 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__COMBB__1,axiom,
% 160.93/160.64 ! [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)) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__COMBC__1,axiom,
% 160.93/160.64 ! [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) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__COMBS__1,axiom,
% 160.93/160.64 ! [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)) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__fequal__1,axiom,
% 160.93/160.64 ! [V_y_2,V_x_2] :
% 160.93/160.64 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 160.93/160.64 | V_x_2 = V_y_2 ) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__fequal__2,axiom,
% 160.93/160.64 ! [V_y_2,V_x_2] :
% 160.93/160.64 ( V_x_2 != V_y_2
% 160.93/160.64 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__fFalse__1,axiom,
% 160.93/160.64 ~ hBOOL(c_fFalse) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__fTrue__1,axiom,
% 160.93/160.64 hBOOL(c_fTrue) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__fNot__1,axiom,
% 160.93/160.64 ! [V_P_2] :
% 160.93/160.64 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 160.93/160.64 | ~ hBOOL(V_P_2) ) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__fNot__2,axiom,
% 160.93/160.64 ! [V_P_2] :
% 160.93/160.64 ( ~ ~ hBOOL(V_P_2)
% 160.93/160.64 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__fconj__1,axiom,
% 160.93/160.64 ! [V_Q_2,V_P_2] :
% 160.93/160.64 ( ~ hBOOL(V_P_2)
% 160.93/160.64 | ~ hBOOL(V_Q_2)
% 160.93/160.64 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__fconj__2,axiom,
% 160.93/160.64 ! [V_Q_2,V_P_2] :
% 160.93/160.64 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 160.93/160.64 | hBOOL(V_P_2) ) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__fconj__3,axiom,
% 160.93/160.64 ! [V_Q_2,V_P_2] :
% 160.93/160.64 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 160.93/160.64 | hBOOL(V_Q_2) ) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__fdisj__1,axiom,
% 160.93/160.64 ! [V_Q_2,V_P_2] :
% 160.93/160.64 ( ~ hBOOL(V_P_2)
% 160.93/160.64 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__fdisj__2,axiom,
% 160.93/160.64 ! [V_P_2,V_Q_2] :
% 160.93/160.64 ( ~ hBOOL(V_Q_2)
% 160.93/160.64 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__fdisj__3,axiom,
% 160.93/160.64 ! [V_Q_2,V_P_2] :
% 160.93/160.64 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
% 160.93/160.64 | hBOOL(V_P_2)
% 160.93/160.64 | hBOOL(V_Q_2) ) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__fimplies__1,axiom,
% 160.93/160.64 ! [V_Q_2,V_P_2] :
% 160.93/160.64 ( hBOOL(V_P_2)
% 160.93/160.64 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__fimplies__2,axiom,
% 160.93/160.64 ! [V_P_2,V_Q_2] :
% 160.93/160.64 ( ~ hBOOL(V_Q_2)
% 160.93/160.64 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 160.93/160.64
% 160.93/160.64 fof(help_c__fimplies__3,axiom,
% 160.93/160.64 ! [V_Q_2,V_P_2] :
% 160.93/160.64 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
% 160.93/160.64 | ~ hBOOL(V_P_2)
% 160.93/160.64 | hBOOL(V_Q_2) ) ).
% 160.93/160.64
% 160.93/160.64 %----Conjectures (2)
% 160.93/160.64 fof(conj_0,hypothesis,
% 160.93/160.64 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),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),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))),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),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)) ).
% 160.93/160.64
% 160.93/160.64 fof(conj_1,conjecture,
% 160.93/160.64 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),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal)),c_Com_Ocom_OBODY)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Opname),c_Natural_Oevalc),c_Com_Ocom_OBODY))),v_Procs)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_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_Ocom,tc_fun(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate)),v_Sledgehammer_058P_H__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_Sledgehammer_058Q_H__2)),v_Procs)) ).
% 160.93/160.64
% 160.93/160.64 %------------------------------------------------------------------------------
% 160.93/160.64 %-------------------------------------------
% 160.93/160.64 % Proof found
% 160.93/160.64 % SZS status Theorem for theBenchmark
% 160.93/160.64 % SZS output start Proof
% 160.93/160.64 %ClaNum:10220(EqnAxiom:2889)
% 160.93/160.64 %VarNum:70191(SingletonVarNum:20434)
% 160.93/160.64 %MaxLitNum:8
% 160.93/160.64 %MaxfuncDepth:15
% 160.93/160.64 %SharedTerms:1129
% 160.93/160.64 %goalClause: 4579
% 160.93/160.64 %singleGoalClaCount:1
% 160.93/160.64 [2893]P1(a195)
% 160.93/160.64 [2894]P2(a876)
% 160.93/160.64 [2895]P2(a881)
% 160.93/160.64 [2896]P2(a1)
% 160.93/160.64 [2897]P99(a876)
% 160.93/160.64 [2898]P99(a881)
% 160.93/160.64 [2899]P99(a1)
% 160.93/160.64 [2900]P3(a876)
% 160.93/160.64 [2901]P101(a876)
% 160.93/160.64 [2902]P101(a881)
% 160.93/160.64 [2903]P4(a876)
% 160.93/160.64 [2904]P4(a884)
% 160.93/160.64 [2905]P65(a876)
% 160.93/160.64 [2906]P65(a881)
% 160.93/160.64 [2907]P65(a1)
% 160.93/160.64 [2908]P65(a103)
% 160.93/160.64 [2909]P100(a876)
% 160.93/160.64 [2910]P100(a881)
% 160.93/160.64 [2911]P100(a1)
% 160.93/160.64 [2912]P97(a876)
% 160.93/160.64 [2913]P97(a881)
% 160.93/160.64 [2914]P97(a1)
% 160.93/160.64 [2915]P66(a1)
% 160.93/160.64 [2916]P67(a1)
% 160.93/160.64 [2917]P77(a881)
% 160.93/160.64 [2918]P77(a1)
% 160.93/160.64 [2919]P77(a103)
% 160.93/160.64 [2920]P105(a1)
% 160.93/160.64 [2921]P68(a881)
% 160.93/160.64 [2922]P68(a1)
% 160.93/160.64 [2923]P68(a103)
% 160.93/160.64 [2924]P5(a876)
% 160.93/160.64 [2925]P78(a881)
% 160.93/160.64 [2926]P78(a1)
% 160.93/160.64 [2927]P78(a103)
% 160.93/160.64 [2928]P136(a881)
% 160.93/160.64 [2929]P136(a1)
% 160.93/160.64 [2930]P136(a103)
% 160.93/160.64 [2931]P74(a881)
% 160.93/160.64 [2932]P74(a1)
% 160.93/160.64 [2933]P74(a103)
% 160.93/160.64 [2934]P106(a881)
% 160.93/160.64 [2935]P106(a1)
% 160.93/160.64 [2936]P106(a103)
% 160.93/160.64 [2937]P125(a1)
% 160.93/160.64 [2938]P107(a876)
% 160.93/160.64 [2939]P107(a881)
% 160.93/160.64 [2940]P107(a1)
% 160.93/160.64 [2941]P107(a103)
% 160.93/160.64 [2942]P108(a881)
% 160.93/160.64 [2943]P108(a1)
% 160.93/160.64 [2944]P108(a103)
% 160.93/160.64 [2945]P109(a876)
% 160.93/160.64 [2946]P109(a881)
% 160.93/160.64 [2947]P109(a1)
% 160.93/160.64 [2948]P109(a103)
% 160.93/160.64 [2949]P110(a876)
% 160.93/160.64 [2950]P110(a881)
% 160.93/160.64 [2951]P110(a1)
% 160.93/160.64 [2952]P110(a103)
% 160.93/160.64 [2953]P111(a1)
% 160.93/160.64 [2954]P137(a881)
% 160.93/160.64 [2955]P137(a1)
% 160.93/160.64 [2956]P137(a103)
% 160.93/160.64 [2957]P112(a881)
% 160.93/160.64 [2958]P112(a1)
% 160.93/160.64 [2959]P112(a103)
% 160.93/160.64 [2960]P123(a1)
% 160.93/160.64 [2961]P124(a1)
% 160.93/160.64 [2962]P117(a881)
% 160.93/160.64 [2963]P117(a1)
% 160.93/160.64 [2964]P117(a103)
% 160.93/160.64 [2965]P126(a881)
% 160.93/160.64 [2966]P126(a1)
% 160.93/160.64 [2967]P126(a103)
% 160.93/160.64 [2968]P81(a881)
% 160.93/160.64 [2969]P81(a1)
% 160.93/160.64 [2970]P81(a103)
% 160.93/160.64 [2971]P75(a1)
% 160.93/160.64 [2972]P69(a881)
% 160.93/160.64 [2973]P69(a1)
% 160.93/160.64 [2974]P69(a103)
% 160.93/160.64 [2975]P70(a881)
% 160.93/160.64 [2976]P70(a1)
% 160.93/160.64 [2977]P70(a103)
% 160.93/160.64 [2978]P71(a881)
% 160.93/160.64 [2979]P71(a1)
% 160.93/160.64 [2980]P71(a103)
% 160.93/160.64 [2981]P82(a881)
% 160.93/160.64 [2982]P82(a1)
% 160.93/160.64 [2983]P82(a103)
% 160.93/160.64 [2984]P86(a881)
% 160.93/160.64 [2985]P86(a1)
% 160.93/160.64 [2986]P86(a103)
% 160.93/160.64 [2987]P72(a881)
% 160.93/160.64 [2988]P72(a1)
% 160.93/160.64 [2989]P72(a103)
% 160.93/160.64 [2990]P130(a881)
% 160.93/160.64 [2991]P130(a1)
% 160.93/160.64 [2992]P130(a103)
% 160.93/160.64 [2993]P138(a1)
% 160.93/160.64 [2994]P131(a881)
% 160.93/160.64 [2995]P131(a1)
% 160.93/160.64 [2996]P131(a103)
% 160.93/160.64 [2997]P79(a881)
% 160.93/160.64 [2998]P79(a1)
% 160.93/160.64 [2999]P79(a103)
% 160.93/160.64 [3000]P83(a1)
% 160.93/160.64 [3001]P80(a881)
% 160.93/160.64 [3002]P80(a1)
% 160.93/160.64 [3003]P80(a103)
% 160.93/160.64 [3004]P141(a881)
% 160.93/160.64 [3005]P141(a1)
% 160.93/160.64 [3006]P141(a103)
% 160.93/160.64 [3007]P118(a881)
% 160.93/160.64 [3008]P118(a1)
% 160.93/160.64 [3009]P118(a103)
% 160.93/160.64 [3010]P143(a881)
% 160.93/160.64 [3011]P143(a1)
% 160.93/160.64 [3012]P139(a1)
% 160.93/160.64 [3013]P90(a1)
% 160.93/160.64 [3014]P102(a881)
% 160.93/160.64 [3015]P102(a1)
% 160.93/160.64 [3016]P102(a103)
% 160.93/160.64 [3017]P142(a881)
% 160.93/160.64 [3018]P142(a1)
% 160.93/160.64 [3019]P142(a103)
% 160.93/160.64 [3020]P84(a881)
% 160.93/160.64 [3021]P84(a1)
% 160.93/160.64 [3022]P84(a103)
% 160.93/160.64 [3023]P132(a881)
% 160.93/160.64 [3024]P132(a1)
% 160.93/160.64 [3025]P132(a103)
% 160.93/160.64 [3026]P134(a881)
% 160.93/160.64 [3027]P134(a1)
% 160.93/160.64 [3028]P134(a103)
% 160.93/160.64 [3029]P133(a881)
% 160.93/160.64 [3030]P133(a1)
% 160.93/160.64 [3031]P133(a103)
% 160.93/160.64 [3032]P127(a881)
% 160.93/160.64 [3033]P127(a1)
% 160.93/160.64 [3034]P127(a103)
% 160.93/160.64 [3035]P128(a1)
% 160.93/160.64 [3036]P129(a1)
% 160.93/160.64 [3037]P140(a1)
% 160.93/160.64 [3038]P113(a881)
% 160.93/160.64 [3039]P113(a1)
% 160.93/160.64 [3040]P113(a103)
% 160.93/160.64 [3041]P58(a881)
% 160.93/160.64 [3042]P58(a1)
% 160.93/160.64 [3043]P58(a103)
% 160.93/160.64 [3044]P59(a1)
% 160.93/160.64 [3045]P85(a1)
% 160.93/160.64 [3046]P135(a1)
% 160.93/160.64 [3047]P76(a881)
% 160.93/160.64 [3048]P76(a1)
% 160.93/160.64 [3049]P76(a103)
% 160.93/160.64 [3050]P114(a876)
% 160.93/160.64 [3051]P98(a876)
% 160.93/160.64 [3052]P119(a1)
% 160.93/160.64 [3053]P94(a876)
% 160.93/160.64 [3054]P87(a876)
% 160.93/160.64 [3055]P87(a1)
% 160.93/160.64 [3056]P116(a1)
% 160.93/160.64 [3057]P73(a1)
% 160.93/160.64 [3058]P88(a1)
% 160.93/160.64 [3059]P91(a881)
% 160.93/160.64 [3060]P91(a1)
% 160.93/160.64 [3061]P91(a103)
% 160.93/160.64 [3062]P93(a1)
% 160.93/160.64 [3063]P115(a881)
% 160.93/160.64 [3064]P89(a881)
% 160.93/160.64 [3065]P89(a1)
% 160.93/160.64 [3066]P89(a103)
% 160.93/160.64 [3067]P144(a1)
% 160.93/160.64 [3068]P144(a884)
% 160.93/160.64 [3069]P60(a876)
% 160.93/160.64 [3070]P60(a884)
% 160.93/160.64 [3071]P92(a876)
% 160.93/160.64 [3072]P92(a877)
% 160.93/160.64 [3073]P92(a878)
% 160.93/160.64 [3074]P92(a881)
% 160.93/160.64 [3075]P92(a1)
% 160.93/160.64 [3076]P92(a884)
% 160.93/160.64 [3077]P92(a103)
% 160.93/160.64 [3078]P92(a330)
% 160.93/160.64 [3079]P104(a876)
% 160.93/160.64 [3080]P104(a877)
% 160.93/160.64 [3081]P104(a878)
% 160.93/160.64 [3082]P104(a881)
% 160.93/160.64 [3083]P104(a884)
% 160.93/160.64 [3084]P104(a103)
% 160.93/160.64 [3085]P104(a330)
% 160.93/160.64 [3086]P103(a1)
% 160.93/160.64 [3087]P103(a884)
% 160.93/160.64 [3088]P96(a876)
% 160.93/160.64 [3108]P39(a881,a253)
% 160.93/160.64 [3109]P39(a881,a324)
% 160.93/160.64 [4472]~E(a101,a83)
% 160.93/160.64 [4473]~P1(a252)
% 160.93/160.64 [2890]E(f2(a1),a83)
% 160.93/160.64 [2891]E(f104(a103),a3)
% 160.93/160.64 [2892]E(f22(a103),a23)
% 160.93/160.64 [3089]E(f196(a881),f2(a881))
% 160.93/160.64 [3090]E(f31(a24),f2(a881))
% 160.93/160.64 [3091]E(f105(a881),f246(a881))
% 160.93/160.64 [3092]E(f114(a881),f247(a881))
% 160.93/160.64 [3093]E(f106(a1),f34(a1))
% 160.93/160.64 [3094]E(f84(a252),f2(a881))
% 160.93/160.64 [3095]E(f84(a195),f2(a881))
% 160.93/160.64 [3096]P6(f2(a1))
% 160.93/160.64 [3097]P6(f78(a1))
% 160.93/160.64 [3146]P1(f334(a25,a24))
% 160.93/160.64 [3159]P39(f887(a881,a881),a35)
% 160.93/160.64 [3511]E(f326(a881,a881,a253,a253),a35)
% 160.93/160.64 [4474]~E(f78(a1),f2(a1))
% 160.93/160.64 [3098]E(f4(f2(a103)),f2(a881))
% 160.93/160.64 [3099]E(f115(f2(a881)),f2(a881))
% 160.93/160.64 [3111]E(f334(f79(a1),a83),a83)
% 160.93/160.64 [3115]E(f334(a3,f2(a881)),f2(a103))
% 160.93/160.64 [3116]E(f334(a116,f2(a881)),f78(a881))
% 160.93/160.64 [3117]E(f334(a108,f78(a1)),f78(a881))
% 160.93/160.64 [3118]E(f334(a3,f78(a881)),f78(a103))
% 160.93/160.64 [3120]E(f334(f107(a1),a83),f2(a1))
% 160.93/160.64 [3121]E(f334(f107(a103),a83),f2(a103))
% 160.93/160.64 [3122]E(f334(a108,f2(a1)),f2(a881))
% 160.93/160.64 [3123]E(f334(f197(a876),a252),f2(a881))
% 160.93/160.64 [3124]E(f334(f197(a876),a195),f2(a881))
% 160.93/160.64 [3125]E(f334(f197(a878),a24),f2(a881))
% 160.93/160.64 [3126]E(f334(f107(a881),a83),f2(a881))
% 160.93/160.64 [3130]E(f334(f79(a1),f78(a1)),a101)
% 160.93/160.64 [3138]E(f334(f197(a103),f2(a103)),f2(a881))
% 160.93/160.64 [3139]E(f334(f104(a1),f2(a881)),f2(a1))
% 160.93/160.64 [3140]E(f334(f104(a1),f78(a881)),f78(a1))
% 160.93/160.64 [3141]E(f334(f79(a1),f2(a1)),f2(a1))
% 160.93/160.64 [3155]E(f334(a108,f78(a1)),f334(a116,f2(a881)))
% 160.93/160.64 [3156]E(f334(f180(a879,a878),a27),a28)
% 160.93/160.64 [3157]E(f325(f887(a881,a881),a35),a36)
% 160.93/160.64 [3158]E(f327(f887(a881,a881),a35),a68)
% 160.93/160.64 [3180]E(f334(f255(a881),f2(a881)),f196(f888(a881,a876)))
% 160.93/160.64 [3181]E(f334(f256(a881),f2(a881)),f257(f888(a881,a876)))
% 160.93/160.64 [3189]P40(f196(f888(a1,a876)))
% 160.93/160.64 [3225]E(f334(f334(f22(a103),f2(a103)),f78(a103)),f2(a103))
% 160.93/160.64 [3303]P1(f334(f334(f249(a1),a101),f2(a1)))
% 160.93/160.64 [3328]P1(f334(f334(f249(a1),f2(a1)),f78(a1)))
% 160.93/160.64 [3330]P1(f334(f334(f248(a1),f2(a1)),f78(a1)))
% 160.93/160.64 [3503]P1(f334(f61(a879),f186(a879,a878,a28)))
% 160.93/160.64 [3541]E(f334(f334(f291(a881,a881,a881),a324),f310(a881,a324)),a253)
% 160.93/160.64 [3579]P42(a1,a881,a108,f334(f248(a1),f2(a1)))
% 160.93/160.64 [3583]E(f334(f334(f41(a881,f888(a881,a876)),f257(f888(a881,a876))),f255(a881)),f257(f888(a881,a876)))
% 160.93/160.64 [3584]E(f334(f334(f41(a881,f888(a881,a876)),f257(f888(a881,a876))),f303(a881)),f257(f888(a881,a876)))
% 160.93/160.64 [3585]E(f334(f334(f41(a881,f888(a881,a876)),f257(f888(a881,a876))),f256(a881)),f257(f888(a881,a876)))
% 160.93/160.64 [3586]E(f334(f334(f42(a881,f888(a881,a876)),f257(f888(a881,a876))),f306(a881)),f196(f888(a881,a876)))
% 160.93/160.64 [3602]P27(a881,a1,f104(a1),f257(f888(a881,a876)))
% 160.93/160.64 [3613]P42(a881,a1,f104(a1),f334(f16(a876,a881),a195))
% 160.93/160.64 [3749]E(f334(f73(a881,a103,a1,a3),a108),f107(a103))
% 160.93/160.64 [3971]P54(a103,a881,a19,a3,f257(f888(a881,a876)))
% 160.93/160.64 [3980]P54(a1,f888(f887(a881,a881),a876),a110,a89,a102)
% 160.93/160.64 [4246]E(f274(a1,a1,a1,a1,f34(a1),f79(a1)),a50)
% 160.93/160.64 [4497]~E(f334(f107(a1),a101),f334(f107(a1),a83))
% 160.93/160.64 [4498]~P1(f334(a201,f2(a1)))
% 160.93/160.64 [4499]~P1(f334(a201,f78(a1)))
% 160.93/160.64 [4540]~P1(f334(f334(f249(a1),a83),f2(a1)))
% 160.93/160.64 [3172]E(f334(f334(f22(a1),a101),a101),a83)
% 160.93/160.64 [3187]E(f334(f104(a1),f334(a116,f2(a881))),f78(a1))
% 160.93/160.64 [3254]E(f334(f37(a884),f257(f888(a884,a876))),f78(a881))
% 160.93/160.64 [3275]P1(f334(a201,f334(f107(a1),a101)))
% 160.93/160.64 [3276]P1(f334(f334(f249(a1),a101),a83))
% 160.93/160.64 [3278]P1(f334(f334(f248(a1),a101),a83))
% 160.93/160.64 [3339]E(f334(f334(f312(a881),f2(a881)),f196(f888(a881,a876))),f334(f303(a881),f2(a881)))
% 160.93/160.64 [3396]P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),a83)))
% 160.93/160.64 [3408]E(f334(f313(a881,a881,a116),f257(f888(a881,a876))),f334(f306(a881),f2(a881)))
% 160.93/160.64 [3447]P8(f887(a881,a881),f257(f888(f887(a881,a881),a876)),a112)
% 160.93/160.64 [3757]E(f334(f73(a881,a1,a103,f104(a1)),a19),a20)
% 160.93/160.64 [3816]P39(a881,f334(f254(f887(a881,a881)),f334(f273(a881,a881,a876),f249(a881))))
% 160.93/160.64 [4529]~P1(f334(a201,f334(f107(a1),a83)))
% 160.93/160.64 [4530]~P1(f334(f334(f249(a1),a83),a83))
% 160.93/160.64 [4531]~P1(f334(f334(f249(a1),a83),a101))
% 160.93/160.64 [4532]~P1(f334(f334(f249(a1),a101),a101))
% 160.93/160.64 [4533]~P1(f334(f334(f248(a1),a83),a101))
% 160.93/160.64 [4534]~P1(f334(f334(f91(a1),a83),a101))
% 160.93/160.64 [4535]~P1(f334(f334(f91(a1),a101),a83))
% 160.93/160.64 [4546]~P1(f334(f61(a881),f257(f888(a881,a876))))
% 160.93/160.64 [4547]~P1(f334(f61(a1),f257(f888(a1,a876))))
% 160.93/160.64 [4417]E(f334(f273(a1,a1,a876),f334(f334(f8(f888(a1,a876),f888(a1,a876),a1),f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f249(a1),f2(a1))))),f334(f334(f7(a1,a1,f888(a1,a876)),f334(f334(f8(f888(a1,f888(a1,a876)),f888(a1,f888(a1,a876)),a1),f7(a1,a1,a876)),f334(f334(f8(f888(a1,a1),f888(a1,f888(a1,a876)),a1),f334(f8(a1,f888(a1,a876),a1),a331)),a230))),f78(a1)))),a226)
% 160.93/160.64 [3484]E(f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101),f334(f79(a1),a101))
% 160.93/160.64 [3524]E(f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101),f334(f334(f22(a1),a83),a101))
% 160.93/160.64 [3683]E(f334(f334(f60(f887(a881,a881)),f257(f888(f887(a881,a881),a876))),a112),a102)
% 160.93/160.64 [3712]E(f334(f107(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f78(a1))
% 160.93/160.64 [3713]E(f334(f107(a103),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f78(a103))
% 160.93/160.64 [3714]E(f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f78(a881))
% 160.93/160.64 [3718]E(f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(a116,f2(a881)))
% 160.93/160.64 [4105]E(f334(f334(f114(f888(f887(f887(a881,a881),f887(a881,a881)),a876)),a35),f310(f887(a881,a881),f196(f888(f887(f887(a881,a881),f887(a881,a881)),a876)))),a70)
% 160.93/160.64 [4177]E(f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),f2(a881)),f2(a881))),f196(f888(f887(a881,a881),a876))))),f2(a1))
% 160.93/160.64 [4178]E(f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),f78(a881)),f2(a881))),f196(f888(f887(a881,a881),a876))))),f78(a1))
% 160.93/160.64 [4193]E(f334(f254(f887(a881,a881)),f334(f273(a881,a881,a876),f334(f334(f8(a881,f888(a881,a876),a881),f334(f7(a881,a881,a876),a331)),a116))),a324)
% 160.93/160.64 [4163]E(f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),f334(a116,f334(a116,f2(a881))))
% 160.93/160.64 [4166]E(f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),f334(f334(f80(a881),f78(a881)),f78(a881)))
% 160.93/160.64 [4167]E(f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),f334(f37(a876),f257(f888(a876,a876))))
% 160.93/160.64 [4232]P6(f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))
% 160.93/160.64 [4304]P28(f888(f887(a881,a881),a876),f334(f334(f269(f888(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),a876),f888(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),a876)),a36),a69))
% 160.93/160.64 [4305]P28(f888(f887(a881,a881),a876),f334(f334(f269(f888(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),a876),f888(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),a876)),a68),a71))
% 160.93/160.64 [4345]E(f334(f334(f114(f888(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),a876)),f327(f887(a881,a881),a70)),f334(f334(f312(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f334(f334(f269(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),f196(f888(f887(a881,a881),a876))),f196(f888(f887(a881,a881),a876)))),f196(f888(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),a876)))),a71)
% 160.93/160.64 [4346]E(f334(f334(f114(f888(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),a876)),f325(f887(a881,a881),a70)),f334(f334(f312(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f334(f334(f269(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),f196(f888(f887(a881,a881),a876))),f196(f888(f887(a881,a881),a876)))),f196(f888(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),a876)))),a69)
% 160.93/160.64 [4234]E(f334(a108,f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f334(a116,f334(a116,f2(a881))))
% 160.93/160.64 [4281]E(f334(f104(a1),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))
% 160.93/160.64 [4316]P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))
% 160.93/160.64 [4317]E(f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),a101)),f334(a116,f334(a116,f334(a116,f2(a881)))))
% 160.93/160.64 [4359]P6(f334(f107(a1),f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),a101)))
% 160.93/160.64 [4438]P26(a877,f334(f334(f114(f888(f880(a877),a876)),a889),f334(f313(a879,f880(a877),f334(f334(f18(a879,f888(a877,f888(a877,a876)),f880(a877)),f334(f334(f8(a878,f888(f888(a877,f888(a877,a876)),f880(a877)),a879),f334(f92(a877),a331)),a26)),f334(f334(f8(a878,f888(a877,f888(a877,a876)),a879),a202),a26))),a890)),f334(f313(a879,f880(a877),f334(f334(f18(a879,f888(a877,f888(a877,a876)),f880(a877)),f334(f334(f8(a878,f888(f888(a877,f888(a877,a876)),f880(a877)),a879),f334(f92(a877),a331)),f334(f334(f8(f885(a878),a878,a879),f245(a878)),a28))),f334(f334(f8(a878,f888(a877,f888(a877,a876)),a879),a202),f334(f334(f8(f885(a878),a878,a879),f245(a878)),a28)))),a890))
% 160.93/160.64 [4579]~P26(a877,f334(f334(f114(f888(f880(a877),a876)),a889),f334(f313(a879,f880(a877),f334(f334(f18(a879,f888(a877,f888(a877,a876)),f880(a877)),f334(f334(f8(a878,f888(f888(a877,f888(a877,a876)),f880(a877)),a879),f334(f92(a877),a331)),a26)),f334(f334(f8(a878,f888(a877,f888(a877,a876)),a879),a202),a26))),a890)),f334(f313(a879,f880(a877),f334(f334(f18(a879,f888(a877,f888(a877,a876)),f880(a877)),f334(f334(f18(a879,a878,f888(f888(a877,f888(a877,a876)),f880(a877))),f334(f334(f8(f888(a877,f888(a877,a876)),f888(a878,f888(f888(a877,f888(a877,a876)),f880(a877))),a879),f92(a877)),a891)),f334(f334(f8(f885(a878),a878,a879),f245(a878)),a28))),a892)),a890))
% 160.93/160.64 [4387]E(f334(f104(a1),f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),a101))),f334(f107(a1),f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),a101)))
% 160.93/160.64 [4402]P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),a101))))
% 160.93/160.64 [3110]P7(x31101,a331)
% 160.93/160.64 [3512]P27(a881,a881,a116,x35121)
% 160.93/160.64 [3100]P92(f880(x31001))
% 160.93/160.64 [3101]P92(f885(x31011))
% 160.93/160.64 [3102]P92(f882(x31021))
% 160.93/160.64 [3103]P92(f883(x31031))
% 160.93/160.64 [3104]P104(f880(x31041))
% 160.93/160.64 [3105]P104(f885(x31051))
% 160.93/160.64 [3106]P104(f882(x31061))
% 160.93/160.64 [3107]P104(f883(x31071))
% 160.93/160.64 [3127]P39(a1,f109(x31271))
% 160.93/160.64 [3128]P39(a1,f111(x31281))
% 160.93/160.64 [3177]P39(f888(x31771,a876),f309(x31771))
% 160.93/160.64 [3201]E(f258(x32011,x32011,a331),a331)
% 160.93/160.64 [3216]E(f44(a1,x32161,x32161),f2(a1))
% 160.93/160.64 [3272]P17(x32721,f888(x32721,a876),f312(x32721))
% 160.93/160.64 [4476]~E(f334(a26,x44761),a24)
% 160.93/160.64 [4478]~E(f334(a116,x44781),x44781)
% 160.93/160.64 [4488]~E(f334(a116,x44881),f2(a881))
% 160.93/160.64 [3112]E(f334(f197(a881),x31121),x31121)
% 160.93/160.64 [3113]E(f334(f107(a1),x31131),x31131)
% 160.93/160.64 [3129]E(f334(a89,f335(x31291)),x31291)
% 160.93/160.64 [3142]E(f118(x31421,f117(x31421)),f117(x31421))
% 160.93/160.64 [3143]E(f154(x31431,f117(x31431)),f117(x31431))
% 160.93/160.64 [3147]E(f31(f334(a26,x31471)),f2(a881))
% 160.93/160.64 [3152]E(f334(f170(x31521),f117(x31521)),f117(x31521))
% 160.93/160.64 [3153]E(f334(f173(x31531),f117(x31531)),f117(x31531))
% 160.93/160.64 [3154]E(f334(f171(x31541),f117(x31541)),f117(x31541))
% 160.93/160.64 [3160]E(f334(f107(a1),x31601),f334(f106(a1),x31601))
% 160.93/160.64 [3161]E(f334(a89,f334(a110,x31611)),x31611)
% 160.93/160.64 [3163]E(f334(a3,f334(a19,x31631)),x31631)
% 160.93/160.64 [3164]E(f334(a19,f334(a3,x31641)),x31641)
% 160.93/160.64 [3165]P6(f334(f104(a1),x31651))
% 160.93/160.64 [3170]E(f334(f197(f885(x31701)),f210(x31701)),f2(a881))
% 160.93/160.64 [3171]E(f334(f197(f882(x31711)),f117(x31711)),f2(a881))
% 160.93/160.64 [3176]E(f334(f197(a878),f334(a26,x31761)),f2(a881))
% 160.93/160.64 [3185]E(f240(x31851,f210(x31851)),f196(f888(x31851,a876)))
% 160.93/160.64 [3192]E(f334(f334(f22(a881),x31921),f2(a881)),x31921)
% 160.93/160.64 [3193]E(f334(f334(f80(a881),x31931),f2(a881)),x31931)
% 160.93/160.64 [3194]E(f334(f334(f80(a1),x31941),f2(a1)),x31941)
% 160.93/160.64 [3195]E(f334(f334(f81(a881),x31951),f78(a881)),x31951)
% 160.93/160.64 [3196]E(f334(f334(f81(a1),x31961),f78(a1)),x31961)
% 160.93/160.64 [3197]E(f334(f334(f247(a881),x31971),f2(a881)),x31971)
% 160.93/160.64 [3198]E(f334(f334(f81(a881),x31981),f2(a881)),f2(a881))
% 160.93/160.64 [3199]E(f334(f334(f38(a1),x31991),f2(a1)),f2(a1))
% 160.93/160.64 [3200]E(f334(f334(f246(a881),x32001),f2(a881)),f2(a881))
% 160.93/160.64 [3207]E(f334(f174(x32071),f117(x32071)),f196(f888(x32071,a876)))
% 160.93/160.64 [3211]P1(f334(f139(x32111),f117(x32111)))
% 160.93/160.64 [3217]E(f334(f156(x32171,x32171),f5(x32171)),f34(f882(x32171)))
% 160.93/160.64 [3218]E(f334(f156(x32181,x32181),f34(x32181)),f34(f882(x32181)))
% 160.93/160.64 [3219]E(f334(f211(x32191,x32191),f5(x32191)),f34(f885(x32191)))
% 160.93/160.64 [3220]E(f334(f211(x32201,x32201),f34(x32201)),f34(f885(x32201)))
% 160.93/160.64 [3221]E(f44(a1,x32211,f2(a1)),x32211)
% 160.93/160.64 [3222]E(f334(f248(a881),f334(a116,x32221)),f334(f249(a881),x32221))
% 160.93/160.64 [3223]E(f334(f255(a881),f334(a116,x32231)),f334(f303(a881),x32231))
% 160.93/160.64 [3224]E(f334(f256(a881),f334(a116,x32241)),f334(f306(a881),x32241))
% 160.93/160.64 [3226]E(f44(a1,f2(a1),x32261),f2(a1))
% 160.93/160.64 [3238]E(f334(f334(f80(a881),x32381),f78(a881)),f334(a116,x32381))
% 160.93/160.64 [3248]E(f334(f304(a881,x32481),f2(a881)),f196(f888(a881,a876)))
% 160.93/160.64 [3260]E(f305(a881,f2(a881),x32601),f334(f303(a881),x32601))
% 160.93/160.64 [3306]E(f334(f334(f22(a881),f334(a116,x33061)),f78(a881)),x33061)
% 160.93/160.64 [3319]E(f46(f2(a1),x33191),f334(f334(f269(a1,a1),f2(a1)),f2(a1)))
% 160.93/160.64 [3368]P1(f334(f334(f249(a881),x33681),f334(a116,x33681)))
% 160.93/160.64 [3380]P1(f334(f334(f249(a881),f2(a881)),f334(a116,x33801)))
% 160.93/160.64 [3669]E(f334(f334(f22(a103),f334(a3,f334(a116,f334(a19,x36691)))),f78(a103)),x36691)
% 160.93/160.64 [3741]P1(f334(f334(f248(a1),f334(f79(a1),f334(f104(a1),x37411))),f2(a1)))
% 160.93/160.64 [3887]P1(f334(f334(f249(a1),f334(f79(a1),f334(f104(a1),f334(a116,x38871)))),f2(a1)))
% 160.93/160.64 [4504]~E(f257(f888(x45041,a876)),f196(f888(x45041,a876)))
% 160.93/160.64 [4543]~P1(f334(f334(f249(a881),x45431),f2(a881)))
% 160.93/160.64 [4555]~P1(f334(f334(f249(a1),f334(f104(a1),x45551)),f2(a1)))
% 160.93/160.64 [3175]E(f182(x31751,f117(f882(x31751))),f117(f882(x31751)))
% 160.93/160.64 [3178]E(f334(f334(f81(a1),a83),x31781),a83)
% 160.93/160.64 [3179]E(f334(f334(f80(a1),a83),x31791),x31791)
% 160.93/160.64 [3182]E(f334(a108,f334(f104(a1),x31821)),x31821)
% 160.93/160.64 [3183]E(f334(f334(f22(a1),x31831),a83),x31831)
% 160.93/160.64 [3184]E(f334(f334(f80(a1),x31841),a83),x31841)
% 160.93/160.64 [3186]E(f334(f334(f22(a881),x31861),x31861),f2(a881))
% 160.93/160.64 [3190]E(f334(f37(a881),f334(f255(a881),x31901)),x31901)
% 160.93/160.64 [3191]E(f334(f79(a1),f334(f79(a1),x31911)),x31911)
% 160.93/160.64 [3202]E(f334(f334(f80(a881),f2(a881)),x32021),x32021)
% 160.93/160.64 [3203]E(f334(f334(f80(a1),f2(a1)),x32031),x32031)
% 160.93/160.64 [3204]E(f334(f334(f81(a881),f78(a881)),x32041),x32041)
% 160.93/160.64 [3205]E(f334(f334(f81(a1),f78(a1)),x32051),x32051)
% 160.93/160.64 [3206]E(f334(f334(f247(a881),f2(a881)),x32061),x32061)
% 160.93/160.64 [3212]E(f334(f334(f22(a881),f2(a881)),x32121),f2(a881))
% 160.93/160.64 [3213]E(f334(f334(f81(a881),f2(a881)),x32131),f2(a881))
% 160.93/160.64 [3214]E(f334(f334(f38(a1),f2(a1)),x32141),f2(a1))
% 160.93/160.64 [3215]E(f334(f334(f246(a881),f2(a881)),x32151),f2(a881))
% 160.93/160.64 [3227]E(f127(x32271,f334(f79(a1),x32271)),f134(a1,x32271))
% 160.93/160.64 [3233]E(f334(f304(a881,f2(a881)),x32331),f334(f255(a881),x32331))
% 160.93/160.64 [3234]E(f334(f334(f81(a1),a101),x32341),f334(f79(a1),x32341))
% 160.93/160.64 [3240]E(f334(a108,f334(f107(a1),x32401)),f334(f107(a881),x32401))
% 160.93/160.64 [3241]E(f334(a19,f334(f107(a103),x32411)),f334(f107(a881),x32411))
% 160.93/160.64 [3242]E(f334(f37(a881),f334(f303(a881),x32421)),f334(a116,x32421))
% 160.93/160.64 [3252]E(f334(f334(f80(a881),f78(a881)),x32521),f334(a116,x32521))
% 160.93/160.64 [3256]E(f334(f75(a1),f334(f104(a1),x32561)),f334(f104(a1),x32561))
% 160.93/160.64 [3257]E(f334(f106(a1),f334(f104(a1),x32571)),f334(f104(a1),x32571))
% 160.93/160.64 [3262]E(f334(f37(x32621),f196(f888(x32621,a876))),f2(a881))
% 160.93/160.64 [3264]E(f334(f334(f38(a881),x32641),f334(a116,f2(a881))),x32641)
% 160.93/160.64 [3273]E(f44(a881,x32731,f334(a116,f2(a881))),f2(a881))
% 160.93/160.64 [3274]E(f44(a1,x32741,f334(f107(a1),a101)),f2(a1))
% 160.93/160.64 [3290]E(f334(f334(f38(a1),x32901),f334(f107(a1),a101)),f334(f79(a1),x32901))
% 160.93/160.64 [3294]E(f141(a881,f334(f304(a881,x32941),f2(a881))),f117(a881))
% 160.93/160.64 [3295]E(f334(f334(f80(a1),x32951),f78(a1)),f334(f334(f22(a1),x32951),a101))
% 160.93/160.64 [3296]E(f334(f334(f22(a1),x32961),f78(a1)),f334(f334(f80(a1),x32961),a101))
% 160.93/160.64 [3300]P1(f334(f334(f248(a881),x33001),x33001))
% 160.93/160.64 [3301]P1(f334(f334(f248(a1),x33011),x33011))
% 160.93/160.64 [3302]P1(f334(f334(f91(a1),x33021),x33021))
% 160.93/160.64 [3307]E(f334(f79(a1),f334(f107(a1),x33071)),f334(f107(a1),f334(f79(a1),x33071)))
% 160.93/160.64 [3308]P1(f334(f61(a881),f334(f255(a881),x33081)))
% 160.93/160.64 [3309]P1(f334(f61(a881),f334(f303(a881),x33091)))
% 160.93/160.64 [3317]E(f163(x33171,f257(f888(x33171,a876))),f257(f888(f882(x33171),a876)))
% 160.93/160.64 [3322]P1(f334(f334(f248(a881),f2(a881)),x33221))
% 160.93/160.64 [3332]E(f334(f334(f80(a881),f115(x33321)),f334(a116,f2(a881))),f115(f334(a116,x33321)))
% 160.93/160.64 [3333]E(f334(f254(x33331),f334(f16(a876,x33331),a252)),f196(f888(x33331,a876)))
% 160.93/160.64 [3334]E(f334(f254(x33341),f334(f16(a876,x33341),a195)),f257(f888(x33341,a876)))
% 160.93/160.64 [3338]E(f334(f334(f312(a881),x33381),f334(f255(a881),x33381)),f334(f255(a881),f334(a116,x33381)))
% 160.93/160.64 [3350]E(f334(f334(f80(a1),f78(a1)),f334(f104(a1),x33501)),f334(f104(a1),f334(a116,x33501)))
% 160.93/160.64 [3352]E(f334(f334(f153(f882(x33521)),f117(x33521)),f117(f882(x33521))),f53(x33521,f117(x33521)))
% 160.93/160.64 [3371]E(f196(f888(f887(x33711,x33711),a876)),f266(x33711,f196(f888(x33711,a876))))
% 160.93/160.64 [3372]E(f334(f311(x33721),f257(f888(x33721,a876))),f257(f888(f888(x33721,a876),a876)))
% 160.93/160.64 [3373]E(f334(f79(f888(x33731,a876)),f196(f888(x33731,a876))),f257(f888(x33731,a876)))
% 160.93/160.64 [3374]E(f334(f79(f888(x33741,a876)),f257(f888(x33741,a876))),f196(f888(x33741,a876)))
% 160.93/160.64 [3376]P1(f334(f61(x33761),f196(f888(x33761,a876))))
% 160.93/160.64 [3378]E(f334(f304(a881,x33781),f334(a116,x33781)),f334(f334(f312(a881),x33781),f196(f888(a881,a876))))
% 160.93/160.64 [3379]E(f85(f887(a881,a881),f47(x33791,f2(a881))),f334(f334(f269(a881,a881),f2(a881)),x33791))
% 160.93/160.64 [3391]P1(f334(f334(f334(a202,a24),x33911),x33911))
% 160.93/160.64 [3395]E(f334(f334(f312(a881),f334(a116,x33951)),f334(f303(a881),x33951)),f334(f303(a881),f334(a116,x33951)))
% 160.93/160.64 [3399]P39(x33991,f196(f888(f887(x33991,x33991),a876)))
% 160.93/160.64 [3402]P1(f334(f334(f248(a1),f2(a1)),f334(f104(a1),x34021)))
% 160.93/160.64 [3410]E(f334(f334(f80(a881),f334(f197(a881),x34101)),f334(a116,f2(a881))),f334(f197(a881),f334(a116,x34101)))
% 160.93/160.64 [3519]P40(f334(f313(a881,a1,f104(a1)),x35191))
% 160.93/160.64 [3557]P41(x35571,f196(f888(x35571,a876)),f196(f888(f887(x35571,x35571),a876)))
% 160.93/160.64 [3576]E(f334(f334(f269(a1,a1),f334(f107(a1),a101)),f334(f334(f22(a1),x35761),f78(a1))),f49(f334(f107(a1),a101),x35761))
% 160.93/160.64 [3625]P57(x36251,f334(f16(f888(x36251,a876),x36251),f334(f16(a876,x36251),a252)))
% 160.93/160.64 [3828]P1(f334(f334(f336(f888(f887(a881,a881),a876)),f335(x38281)),a102))
% 160.93/160.64 [3853]P1(f334(f334(f336(f888(f887(a881,a881),a876)),f334(a110,x38531)),a102))
% 160.93/160.64 [3989]P27(x39891,f888(x39891,a876),f334(f334(f7(x39891,f888(x39891,a876),f888(x39891,a876)),f312(x39891)),f196(f888(x39891,a876))),f257(f888(x39891,a876)))
% 160.93/160.64 [4501]~E(f334(f334(f80(a1),x45011),x45011),a101)
% 160.93/160.64 [4528]~E(f334(a3,f334(a116,f334(a19,x45281))),f2(a103))
% 160.93/160.64 [4536]~P1(f334(a201,f334(f104(a1),x45361)))
% 160.93/160.64 [4539]~P1(f334(f334(f249(a881),x45391),x45391))
% 160.93/160.64 [4548]~P1(f334(f334(f248(a881),f334(a116,x45481)),x45481))
% 160.93/160.64 [3324]E(f334(a108,f334(f79(a1),f334(f104(a1),x33241))),f2(a881))
% 160.93/160.64 [3327]E(f334(f334(f80(a1),f334(f79(a1),x33271)),x33271),f2(a1))
% 160.93/160.64 [3331]E(f334(f37(a1),f334(f304(a1,f2(a1)),x33311)),f334(a108,x33311))
% 160.93/160.64 [3343]E(f334(f334(f259(a881),f334(a116,f2(a881))),x33431),f334(a116,f2(a881)))
% 160.93/160.64 [3444]E(f334(f287(x34441),f196(f888(f887(x34441,x34441),a876))),f196(f888(x34441,a876)))
% 160.93/160.64 [3452]E(f39(f888(x34521,a876),f196(f888(f888(x34521,a876),a876))),f196(f888(x34521,a876)))
% 160.93/160.64 [3453]E(f39(f888(x34531,a876),f257(f888(f888(x34531,a876),a876))),f257(f888(x34531,a876)))
% 160.93/160.64 [3454]E(f40(f888(x34541,a876),f196(f888(f888(x34541,a876),a876))),f257(f888(x34541,a876)))
% 160.93/160.64 [3455]E(f40(f888(x34551,a876),f257(f888(f888(x34551,a876),a876))),f196(f888(x34551,a876)))
% 160.93/160.64 [3501]E(f334(f334(f312(f882(x35011)),f117(x35011)),f196(f888(f882(x35011),a876))),f163(x35011,f196(f888(x35011,a876))))
% 160.93/160.64 [3502]E(f334(f334(f312(f882(x35021)),f117(x35021)),f196(f888(f882(x35021),a876))),f164(x35021,f117(f888(x35021,a876))))
% 160.93/160.64 [3540]E(f334(f334(f80(a881),f4(x35401)),f334(a116,f2(a881))),f4(f334(a3,f334(a116,f334(a19,x35401)))))
% 160.93/160.64 [3568]E(f334(f37(a1),f334(f313(a881,a1,f104(a1)),x35681)),f334(f37(a881),x35681))
% 160.93/160.64 [3571]P1(f334(f334(f248(a881),x35711),f334(f334(f81(a881),x35711),x35711)))
% 160.93/160.64 [3606]E(f334(f313(a1,a881,a108),f305(a1,f2(a1),f334(f104(a1),x36061))),f334(f303(a881),x36061))
% 160.93/160.64 [3620]E(f334(f334(f38(a881),f334(a116,f2(a881))),f334(f107(a881),x36201)),f334(a108,f334(f334(f38(a1),f78(a1)),f334(f107(a1),x36201))))
% 160.93/160.64 [3622]E(f334(f174(a881),f141(a881,f334(f304(a881,f2(a881)),f334(a116,x36221)))),f334(f303(a881),x36221))
% 160.93/160.64 [3623]E(f334(f334(f80(a881),f334(f197(a103),x36231)),f334(a116,f2(a881))),f334(f197(a103),f334(a3,f334(a116,f334(a19,x36231)))))
% 160.93/160.64 [3643]E(f334(f313(a1,a881,a108),f334(f313(a881,a1,f104(a1)),x36431)),x36431)
% 160.93/160.64 [3675]E(f334(f334(f312(a881),f2(a881)),f334(f313(a881,a881,a116),f334(f255(a881),x36751))),f334(f255(a881),f334(a116,x36751)))
% 160.93/160.64 [3682]P52(x36821,x36821,f310(x36821,f196(f888(f887(x36821,x36821),a876))))
% 160.93/160.64 [3688]P1(f334(a201,f334(f79(a1),f334(f104(a1),f334(a116,x36881)))))
% 160.93/160.64 [3699]E(f334(f334(f22(f888(a881,a876)),f334(f256(a881),x36991)),f334(f334(f312(a881),x36991),f196(f888(a881,a876)))),f334(f256(a881),f334(a116,x36991)))
% 160.93/160.64 [3715]E(f334(f334(f80(a1),f334(f334(f22(a1),a83),x37151)),f334(f334(f22(a1),a83),x37151)),f334(f334(f22(a1),a83),f334(f334(f80(a1),x37151),x37151)))
% 160.93/160.64 [3731]E(f334(f334(f312(f888(x37311,a876)),f196(f888(x37311,a876))),f196(f888(f888(x37311,a876),a876))),f334(f311(x37311),f196(f888(x37311,a876))))
% 160.93/160.64 [3758]E(f334(f334(f22(f888(a881,a876)),f334(f306(a881),x37581)),f334(f334(f312(a881),f334(a116,x37581)),f196(f888(a881,a876)))),f334(f306(a881),f334(a116,x37581)))
% 160.93/160.64 [3766]E(f334(f334(f312(f885(x37661)),f210(x37661)),f334(f313(x37661,f885(x37661),f241(x37661)),f257(f888(x37661,a876)))),f257(f888(f885(x37661),a876)))
% 160.93/160.64 [3865]E(f334(f107(a881),f334(f334(f80(a1),x38651),x38651)),f334(f334(f86(a881,a881),f334(f107(a881),x38651)),f334(f334(f18(a881,a881,a881),f80(a881)),f5(a881))))
% 160.93/160.64 [4255]P17(x42551,f888(x42551,a876),f334(f334(f8(f888(x42551,a876),f888(f888(x42551,a876),f888(x42551,a876)),x42551),f334(f7(f888(x42551,a876),f888(x42551,a876),f888(x42551,a876)),f22(f888(x42551,a876)))),f334(f334(f7(x42551,f888(x42551,a876),f888(x42551,a876)),f312(x42551)),f196(f888(x42551,a876)))))
% 160.93/160.64 [4344]E(f334(f254(f887(a1,a1)),f334(f273(a1,a1,a876),f334(f334(f8(f888(a1,a876),f888(a1,a876),a1),f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f248(a1),x43441)))),f249(a1)))),f111(x43441))
% 160.93/160.64 [4377]E(f334(f254(f887(a1,a1)),f334(f273(a1,a1,a876),f334(f334(f18(a1,f888(a1,a876),f888(a1,a876)),f334(f334(f8(f888(a876,a876),f888(f888(a1,a876),f888(a1,a876)),a1),f8(a876,a876,a1)),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f248(a1),x43771)))),f249(a1)))),f109(x43771))
% 160.93/160.64 [4432]E(f334(f254(f887(f888(x44321,a876),f888(x44321,a876))),f334(f273(f888(x44321,a876),f888(x44321,a876),a876),f334(f334(f7(f888(x44321,a876),f888(f888(x44321,a876),a876),f888(f888(x44321,a876),a876)),f334(f334(f8(f888(f888(x44321,a876),f888(a876,a876)),f888(f888(f888(x44321,a876),a876),f888(f888(x44321,a876),a876)),f888(x44321,a876)),f18(f888(x44321,a876),a876,a876)),f334(f334(f8(f888(f888(x44321,a876),a876),f888(f888(x44321,a876),f888(a876,a876)),f888(x44321,a876)),f334(f8(a876,f888(a876,a876),f888(x44321,a876)),a332)),f249(f888(x44321,a876))))),f61(x44321)))),f309(x44321))
% 160.93/160.64 [4552]~P1(f334(f61(f882(x45521)),f257(f888(f882(x45521),a876))))
% 160.93/160.64 [4557]~P1(f334(f334(f91(a1),a101),f334(f334(f80(a1),x45571),x45571)))
% 160.93/160.64 [4567]~P1(f334(f334(f248(a1),f2(a1)),f334(f79(a1),f334(f104(a1),f334(a116,x45671)))))
% 160.93/160.64 [3478]E(f334(f334(f22(a1),f334(f334(f80(a1),x34781),a101)),a101),x34781)
% 160.93/160.64 [3494]E(f334(f174(a881),f141(a881,f334(f304(a881,f2(a881)),x34941))),f334(f255(a881),x34941))
% 160.93/160.64 [3737]E(f334(f334(f80(a1),f334(f334(f80(a1),f78(a1)),x37371)),x37371),f334(f334(f22(a1),f334(f334(f80(a1),x37371),x37371)),a101))
% 160.93/160.64 [3783]E(f334(f289(x37831,x37831),f310(x37831,f196(f888(f887(x37831,x37831),a876)))),f310(x37831,f196(f888(f887(x37831,x37831),a876))))
% 160.93/160.64 [3831]P1(f334(f334(f248(a881),x38311),f334(f334(f81(a881),x38311),f334(f334(f81(a881),x38311),x38311))))
% 160.93/160.64 [4109]P1(f334(f61(a881),f334(f254(a881),f334(f334(f7(a881,a881,a876),f249(a881)),x41091))))
% 160.93/160.64 [4110]P1(f334(f61(a881),f334(f254(a881),f334(f334(f7(a881,a881,a876),f248(a881)),x41101))))
% 160.93/160.64 [4397]E(f334(f254(f887(x43971,x43971)),f334(f334(f8(f888(x43971,a876),a876,f887(x43971,x43971)),f87(x43971)),f334(f334(f7(f887(x43971,x43971),f888(x43971,f887(x43971,x43971)),f888(x43971,a876)),f334(f334(f8(f888(f887(x43971,x43971),a876),f888(f888(x43971,f887(x43971,x43971)),f888(x43971,a876)),f887(x43971,x43971)),f8(f887(x43971,x43971),a876,x43971)),a331)),f334(f334(f18(x43971,x43971,f887(x43971,x43971)),f269(x43971,x43971)),f5(x43971))))),f310(x43971,f196(f888(f887(x43971,x43971),a876))))
% 160.93/160.64 [4554]~E(f334(f334(f22(a1),f334(f334(f80(a1),x45541),x45541)),a101),a83)
% 160.93/160.64 [4556]~E(f334(f334(f80(a1),f334(f334(f80(a1),f78(a1)),x45561)),x45561),f2(a1))
% 160.93/160.64 [4564]~P1(f334(f334(f91(a1),f334(f334(f80(a1),x45641),x45641)),a101))
% 160.93/160.64 [3876]E(f334(f334(f80(a1),f334(f334(f22(a1),a101),x38761)),f334(f334(f22(a1),a101),x38761)),f334(f334(f22(a1),a101),f334(f334(f22(a1),f334(f334(f80(a1),x38761),x38761)),a101)))
% 160.93/160.64 [3998]E(f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),a101),x39981)),f334(f334(f22(a1),a101),x39981))),a101),f334(f334(f22(a1),a101),f334(f334(f80(a1),x39981),x39981)))
% 160.93/160.64 [4032]E(f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f80(a1),x40321),a101)),f334(f334(f80(a1),x40321),a101))),a101),f334(f334(f80(a1),f334(f334(f80(a1),x40321),x40321)),a101))
% 160.93/160.64 [4071]E(f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),a101),x40711)),f334(f334(f22(a1),a101),x40711))),a101),f334(f334(f22(a1),a83),f334(f334(f22(a1),f334(f334(f80(a1),x40711),x40711)),a101)))
% 160.93/160.64 [4173]E(f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x41731),f2(a881))),f196(f888(f887(a881,a881),a876))))),f334(f104(a1),x41731))
% 160.93/160.64 [4183]E(f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),f339(x41831)),f533(x41831))),f196(f888(f887(a881,a881),a876))))),x41831)
% 160.93/160.64 [4217]E(f334(f254(a1),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f248(a1),f2(a1)))),x42171)),f334(f313(a881,a1,f104(a1)),f334(f254(a881),f334(f334(f8(a1,a876,a881),x42171),f104(a1)))))
% 160.93/160.64 [4263]P40(f334(f254(a1),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f248(a1),f2(a1)))),x42631)))
% 160.93/160.64 [4284]P1(f334(f334(f336(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f334(f334(f269(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),x42841),f196(f888(f887(a881,a881),a876)))),a71))
% 160.93/160.64 [4290]E(f334(f313(a1,a881,a108),f334(f254(a1),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f248(a1),f2(a1)))),f334(f334(f8(a881,a876,a1),x42901),a108)))),f334(f254(a881),x42901))
% 160.93/160.64 [4447]E(f315(a881,f334(f334(f41(f887(a881,a881),f888(a881,a876)),f334(a110,x44471)),f334(f273(a881,a881,f888(a881,a876)),f334(f334(f7(a881,f888(a881,a876),f888(a881,f888(a881,a876))),f334(f334(f8(f888(a881,f888(f888(a881,a876),f888(a881,a876))),f888(f888(a881,a876),f888(a881,f888(a881,a876))),a881),f7(a881,f888(a881,a876),f888(a881,a876))),f334(f334(f8(f888(a881,a881),f888(a881,f888(f888(a881,a876),f888(a881,a876))),a881),f334(f8(a881,f888(f888(a881,a876),f888(a881,a876)),a881),f312(a881))),f22(a881)))),f196(f888(a881,a876)))))),f334(a108,x44471))
% 160.93/160.64 [4569]~P1(f334(f334(f91(a1),a83),f334(f334(f22(a1),f334(f334(f80(a1),x45691),x45691)),a101)))
% 160.93/160.64 [3920]E(f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),x39201),x39201)),a101)),a101),f334(f334(f80(a1),x39201),x39201))
% 160.93/160.64 [3972]E(f334(f334(f22(a1),f334(f334(f22(a1),f334(f334(f80(a1),x39721),x39721)),a101)),a101),f334(f334(f80(a1),f334(f334(f22(a1),x39721),a101)),f334(f334(f22(a1),x39721),a101)))
% 160.93/160.64 [4191]E(f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f80(a1),f334(f79(a1),x41911)),a101)),f334(f334(f80(a1),f334(f79(a1),x41911)),a101))),a101),f334(f79(a1),f334(f334(f22(a1),f334(f334(f80(a1),x41911),x41911)),a101)))
% 160.93/160.64 [4577]~P1(f334(f334(f91(a1),f334(f334(f22(a1),f334(f334(f80(a1),x45771),x45771)),a101)),a83))
% 160.93/160.64 [4235]E(f334(f334(f80(a881),x42351),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f334(a116,f334(a116,x42351)))
% 160.93/160.64 [4236]E(f334(f334(f81(a881),x42361),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f334(f334(f80(a881),x42361),x42361))
% 160.93/160.64 [4237]E(f334(f334(f38(a881),f334(f334(f80(a881),x42371),x42371)),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x42371)
% 160.93/160.64 [4319]E(f44(a881,f334(a116,f334(a116,x43191)),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f44(a881,x43191,f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))
% 160.93/160.64 [4462]E(f334(a89,f334(f334(f41(f887(a881,a881),f888(f887(a881,a881),a876)),f334(a110,x44621)),f334(f273(a881,a881,f888(f887(a881,a881),a876)),f334(f334(f8(f888(a881,f888(f887(a881,a881),a876)),f888(a881,f888(f887(a881,a881),a876)),a881),f334(f8(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876),a881),f288(f887(a881,a881),f887(a881,a881),a112))),f334(f334(f7(a881,f888(f887(a881,a881),a876),f888(a881,f888(f887(a881,a881),a876))),f334(f334(f8(f888(a881,f888(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f888(f888(f887(a881,a881),a876),f888(a881,f888(f887(a881,a881),a876))),a881),f7(a881,f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f334(f334(f8(f888(a881,f887(a881,a881)),f888(a881,f888(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),a881),f334(f8(f887(a881,a881),f888(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),a881),f312(f887(a881,a881)))),f334(f7(a881,a881,f887(a881,a881)),f269(a881,a881))))),f196(f888(f887(a881,a881),a876))))))),f334(f79(a1),x44621))
% 160.93/160.64 [4314]E(f334(f334(f80(a881),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x43141),f334(a116,f334(a116,x43141)))
% 160.93/160.64 [4315]E(f334(f334(f81(a881),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x43151),f334(f334(f80(a881),x43151),x43151))
% 160.93/160.64 [4349]E(f334(f334(f38(a881),f334(a116,f334(a116,x43491))),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f334(a116,f334(f334(f38(a881),x43491),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))))
% 160.93/160.64 [4403]E(f334(f334(f80(a881),f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),a101))),x44031),f334(a116,f334(a116,f334(a116,x44031))))
% 160.93/160.64 [4470]E(f334(f273(a1,a1,f887(a1,a1)),f334(f334(f18(a1,f888(a1,f887(a1,a1)),f888(a1,f887(a1,a1))),f334(f334(f8(f888(a1,f888(f887(a1,a1),f887(a1,a1))),f888(f888(a1,f887(a1,a1)),f888(a1,f887(a1,a1))),a1),f18(a1,f887(a1,a1),f887(a1,a1))),f334(f334(f8(f888(a1,f887(a1,a1)),f888(a1,f888(f887(a1,a1),f887(a1,a1))),a1),f334(f18(a1,f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),f334(f334(f8(a876,f888(f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),a1),f100(f887(a1,a1))),f334(f334(f8(a1,a876,a1),f334(f248(a1),f2(a1))),f334(f334(f7(a1,a1,a1),f22(a1)),x44701))))),f334(f334(f7(a1,f888(a1,a1),f888(a1,f887(a1,a1))),f334(f334(f8(f888(a1,f887(a1,a1)),f888(f888(a1,a1),f888(a1,f887(a1,a1))),a1),f8(a1,f887(a1,a1),a1)),f334(f334(f8(a1,f888(a1,f887(a1,a1)),a1),f269(a1,a1)),f334(f334(f7(a1,a1,a1),f334(f334(f8(a1,f888(a1,a1),a1),f80(a1)),f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))),f78(a1))))),f334(f334(f7(a1,a1,a1),f22(a1)),x44701))))),f334(f334(f8(a1,f888(a1,f887(a1,a1)),a1),f269(a1,a1)),f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))))),f43(x44701))
% 160.93/160.64 [3148]P92(f886(x31481,x31482))
% 160.93/160.64 [3149]P92(f887(x31491,x31492))
% 160.93/160.64 [3150]P104(f886(x31501,x31502))
% 160.93/160.64 [3151]P104(f887(x31511,x31512))
% 160.93/160.64 [3168]P16(a1,f181(x31681,x31682))
% 160.93/160.64 [3169]P39(x31691,f155(x31691,x31692))
% 160.93/160.64 [3235]P33(x32351,x32352,f117(x32351))
% 160.93/160.64 [3268]P41(x32681,x32682,f266(x32681,x32682))
% 160.93/160.64 [3269]P52(x32691,x32691,f266(x32691,x32692))
% 160.93/160.64 [3543]P27(x35431,x35431,f5(x35431),x35432)
% 160.93/160.64 [3544]P27(x35441,x35441,f34(x35441),x35442)
% 160.93/160.64 [3552]P34(x35521,x35522,f117(x35521),f117(x35521))
% 160.93/160.64 [3553]P27(x35531,f885(x35531),f241(x35531),x35532)
% 160.93/160.64 [3562]P27(f882(x35621),f882(x35621),f171(x35621),x35622)
% 160.93/160.64 [4481]~E(f33(x44811,x44812),a24)
% 160.93/160.64 [4482]~E(f32(x44821,x44822),a24)
% 160.93/160.64 [4511]~P35(x45111,x45112,f117(x45111))
% 160.93/160.64 [4512]~P37(x45121,x45122,f117(x45121))
% 160.93/160.64 [3131]E(f334(f5(x31311),x31312),x31312)
% 160.93/160.64 [3132]E(f334(f254(x31321),x31322),x31322)
% 160.93/160.64 [3134]E(f334(f34(x31341),x31342),x31342)
% 160.93/160.64 [3144]E(f334(f199(x31441),x31442),f119(x31441))
% 160.93/160.64 [3166]E(f85(x31661,f334(a331,x31662)),x31662)
% 160.93/160.64 [3167]E(f90(x31671,f334(a331,x31672)),x31672)
% 160.93/160.64 [3188]E(f334(f138(x31881,x31882),f117(x31881)),f117(x31881))
% 160.93/160.64 [3208]E(f310(x32081,f310(x32081,x32082)),f310(x32081,x32082))
% 160.93/160.64 [3209]E(f154(x32091,f154(x32091,x32092)),f154(x32091,x32092))
% 160.93/160.64 [3230]E(f334(f334(f136(x32301),x32302),f117(x32301)),x32302)
% 160.93/160.64 [3236]E(f175(x32361,x32362,f117(x32361)),x32362)
% 160.93/160.64 [3237]E(f175(x32371,f117(x32371),x32372),x32372)
% 160.93/160.64 [3243]E(f334(f334(f177(x32431),x32432),f117(x32431)),f117(x32431))
% 160.93/160.64 [3244]E(f334(f334(f140(x32441),x32442),f117(x32441)),f117(x32441))
% 160.93/160.64 [3246]E(f157(x32461,x32462,f117(x32461)),f2(a881))
% 160.93/160.64 [3247]E(f242(x32471,x32472,f210(x32471)),f2(a881))
% 160.93/160.64 [3249]E(f172(x32491,x32492,f117(x32491)),f117(x32491))
% 160.93/160.64 [3250]E(f179(x32501,x32502,f117(x32501)),f117(x32501))
% 160.93/160.64 [3251]E(f178(x32511,f117(x32511),x32512),f117(x32511))
% 160.93/160.64 [3255]E(f334(f174(x32551),f154(x32551,x32552)),f334(f174(x32551),x32552))
% 160.93/160.64 [3258]E(f334(f265(x32581,x32581),f266(x32581,x32582)),x32582)
% 160.93/160.64 [3259]E(f334(f267(x32591,x32591),f266(x32591,x32592)),x32592)
% 160.93/160.64 [3267]E(f334(f289(x32671,x32671),f266(x32671,x32672)),f266(x32671,x32672))
% 160.93/160.64 [3282]E(f310(f882(x32821),f159(x32821,x32822)),f160(x32821,f310(x32821,x32822)))
% 160.93/160.64 [3284]P1(f334(f139(a1),f181(x32841,x32842)))
% 160.93/160.64 [3292]E(f334(f265(x32921,x32921),f310(x32921,x32922)),f257(f888(x32921,a876)))
% 160.93/160.64 [3293]E(f334(f267(x32931,x32931),f310(x32931,x32932)),f257(f888(x32931,a876)))
% 160.93/160.64 [3297]P1(f334(f139(x32971),f154(x32971,x32972)))
% 160.93/160.64 [3299]P1(f334(f162(x32991,x32992),f117(x32991)))
% 160.93/160.64 [3305]E(f334(f174(a1),f181(x33051,x33052)),f305(a1,x33051,x33052))
% 160.93/160.64 [3320]P53(x33201,f196(f888(x33201,a876)),x33202)
% 160.93/160.64 [3325]E(f334(f272(a1,a1),f45(x33251,x33252)),f44(a1,x33251,x33252))
% 160.93/160.64 [3326]E(f334(f304(a881,x33261),f334(a116,x33262)),f305(a881,x33261,x33262))
% 160.93/160.64 [3342]E(f334(f334(f153(x33421),x33422),f117(x33421)),f142(x33421,x33422,f117(x33421)))
% 160.93/160.64 [3354]E(f305(a881,f334(a116,x33541),x33542),f307(a881,x33541,x33542))
% 160.93/160.64 [3357]P41(x33571,f257(f888(x33571,a876)),f310(x33571,x33572))
% 160.93/160.64 [3421]E(f334(f334(f22(a881),x34211),f334(a116,x34212)),f334(f37(a881),f308(a881,x34212,x34211)))
% 160.93/160.64 [3479]E(f169(x34791,x34792,f117(x34791)),f334(f334(f269(f882(x34791),f882(x34791)),f117(x34791)),f117(x34791)))
% 160.93/160.64 [3499]E(f334(f273(x34991,x34992,f887(x34991,x34992)),f269(x34991,x34992)),f34(f887(x34991,x34992)))
% 160.93/160.64 [3504]P1(f334(f334(f336(f882(x35041)),f117(x35041)),f163(x35041,x35042)))
% 160.93/160.64 [3505]E(f334(f197(f882(x35051)),f118(x35051,x35052)),f334(f334(f22(a881),f334(f197(f882(x35051)),x35052)),f78(a881)))
% 160.93/160.64 [3513]P1(f334(f61(a881),f305(a881,x35131,x35132)))
% 160.93/160.64 [3514]P1(f334(f61(a881),f308(a881,x35141,x35142)))
% 160.93/160.64 [3515]P1(f334(f61(a881),f307(a881,x35151,x35152)))
% 160.93/160.64 [3516]P1(f334(f61(a1),f305(a1,x35161,x35162)))
% 160.93/160.64 [3517]P1(f334(f61(a1),f308(a1,x35171,x35172)))
% 160.93/160.64 [3518]P1(f334(f61(a1),f307(a1,x35181,x35182)))
% 160.93/160.64 [3619]E(f334(f313(a881,a881,a116),f305(a881,x36191,x36192)),f305(a881,f334(a116,x36191),f334(a116,x36192)))
% 160.93/160.64 [3640]E(f334(f334(f291(x36401,x36401,x36401),f310(x36401,x36402)),f310(x36401,x36402)),f310(x36401,x36402))
% 160.93/160.64 [3673]E(f334(f334(f269(a1,a1),f334(f334(f38(a1),x36731),x36732)),f44(a1,x36731,x36732)),f45(x36731,x36732))
% 160.93/160.64 [3674]E(f334(f334(f269(a103,a103),f334(f334(f38(a103),x36741),x36742)),f44(a103,x36741,x36742)),f21(x36741,x36742))
% 160.93/160.64 [3703]E(f334(f334(f269(a881,a881),f334(f334(f38(a881),x37031),x37032)),f44(a881,x37031,x37032)),f85(f887(a881,a881),f47(x37031,x37032)))
% 160.93/160.64 [3754]P1(f334(f334(f249(a881),f334(f334(f22(a881),x37541),x37542)),f334(a116,x37541)))
% 160.93/160.64 [3852]E(f334(f334(f80(a1),f334(f334(f81(a1),x38521),f334(f334(f38(a1),x38522),x38521))),f44(a1,x38522,x38521)),x38522)
% 160.93/160.64 [3856]E(f334(f334(f41(a881,f888(f887(f882(x38561),f882(x38561)),a876)),f257(f888(a881,a876))),f145(x38561,x38562)),f147(x38561,x38562))
% 160.93/160.64 [4084]P1(f334(f334(f336(f887(f882(x40841),f882(x40841))),f334(f334(f269(f882(x40841),f882(x40841)),f117(x40841)),f117(x40841))),f160(x40841,x40842)))
% 160.93/160.64 [4248]E(f274(x42481,x42481,x42482,x42482,f5(x42481),f5(x42482)),f34(f887(x42481,x42482)))
% 160.93/160.64 [4250]E(f274(x42501,x42501,x42502,x42502,f34(x42501),f34(x42502)),f34(f887(x42501,x42502)))
% 160.93/160.64 [4490]~E(f334(f241(x44901),x44902),f210(x44901))
% 160.93/160.64 [3228]E(f334(f245(x32281),f334(f241(x32281),x32282)),x32282)
% 160.93/160.64 [3229]E(f334(f171(x32291),f334(f171(x32291),x32292)),x32292)
% 160.93/160.64 [3231]E(f334(f334(f140(x32311),f2(a881)),x32312),x32312)
% 160.93/160.64 [3245]E(f334(f334(f177(x32451),f2(a881)),x32452),f117(x32451))
% 160.93/160.64 [3253]E(f334(f334(f136(x32531),f117(x32531)),x32532),x32532)
% 160.93/160.64 [3261]E(f334(f197(f885(x32611)),f334(f241(x32611),x32612)),f2(a881))
% 160.93/160.64 [3263]E(f39(f888(x32631,a876),f334(f311(x32631),x32632)),x32632)
% 160.93/160.64 [3265]E(f334(f174(x32651),f334(f170(x32651),x32652)),f334(f174(x32651),x32652))
% 160.93/160.64 [3266]E(f334(f174(x32661),f334(f171(x32661),x32662)),f334(f174(x32661),x32662))
% 160.93/160.64 [3271]E(f334(f334(f22(a103),x32711),x32712),f334(f334(a23,x32711),x32712))
% 160.93/160.64 [3286]E(f334(f334(f80(a881),x32861),x32862),f334(f334(f80(a881),x32862),x32861))
% 160.93/160.64 [3287]E(f334(f334(f80(a1),x32871),x32872),f334(f334(f80(a1),x32872),x32871))
% 160.93/160.64 [3288]E(f334(f334(f81(a881),x32881),x32882),f334(f334(f81(a881),x32882),x32881))
% 160.93/160.64 [3289]E(f334(f334(f81(a1),x32891),x32892),f334(f334(f81(a1),x32892),x32891))
% 160.93/160.64 [3312]E(f334(f334(f191(x33121,x33121),f2(a881)),x33122),f34(x33121))
% 160.93/160.64 [3313]E(f334(f197(f882(x33131)),f334(f170(x33131),x33132)),f334(f197(f882(x33131)),x33132))
% 160.93/160.64 [3314]E(f334(f197(f882(x33141)),f334(f171(x33141),x33142)),f334(f197(f882(x33141)),x33142))
% 160.93/160.64 [3315]E(f178(x33151,x33152,f196(f888(a881,a876))),f117(x33151))
% 160.93/160.64 [3316]E(f334(f334(f156(x33161,x33161),f5(x33161)),x33162),x33162)
% 160.93/160.64 [3318]E(f334(f268(a1,a1),f45(x33181,x33182)),f334(f334(f38(a1),x33181),x33182))
% 160.93/160.64 [3335]E(f334(f197(f882(x33351)),f154(x33351,x33352)),f334(f37(x33351),f334(f174(x33351),x33352)))
% 160.93/160.64 [3336]E(f31(f32(x33361,x33362)),f334(f334(f80(a881),f31(x33362)),f334(a116,f2(a881))))
% 160.93/160.64 [3337]E(f334(f287(x33371),f334(f289(x33371,x33371),x33372)),f334(f287(x33371),x33372))
% 160.93/160.64 [3341]P1(f334(f61(x33411),f334(f174(x33411),x33412)))
% 160.93/160.64 [3349]E(f334(f334(f80(a1),x33491),f334(f79(a1),x33492)),f334(f334(f22(a1),x33491),x33492))
% 160.93/160.64 [3356]P26(x33561,x33562,f196(f888(f880(x33561),a876)))
% 160.93/160.64 [3358]E(f334(f313(x33581,x33581,f5(x33581)),x33582),x33582)
% 160.93/160.64 [3359]E(f334(f313(x33591,x33591,f34(x33591)),x33592),x33592)
% 160.93/160.64 [3360]E(f334(f314(x33601,x33601,f5(x33601)),x33602),x33602)
% 160.93/160.64 [3361]E(f334(f314(x33611,x33611,f34(x33611)),x33612),x33612)
% 160.93/160.64 [3362]P1(f334(f257(f888(x33621,a876)),x33622))
% 160.93/160.64 [3364]E(f334(f37(a881),f334(f304(a881,x33641),x33642)),f334(f334(f22(a881),x33642),x33641))
% 160.93/160.64 [3365]E(f334(f304(a881,f334(a116,x33651)),x33652),f308(a881,x33651,x33652))
% 160.93/160.64 [3377]E(f334(f334(f312(x33771),x33772),f196(f888(x33771,a876))),f334(f254(x33771),f334(a331,x33772)))
% 160.93/160.64 [3381]E(f334(f334(f312(x33811),x33812),f196(f888(x33811,a876))),f240(x33811,f334(f241(x33811),x33812)))
% 160.93/160.64 [3383]E(f310(x33831,f334(f289(x33831,x33831),x33832)),f334(f289(x33831,x33831),f310(x33831,x33832)))
% 160.93/160.64 [3388]E(f334(f334(f80(a881),f334(a116,x33881)),x33882),f334(f334(f80(a881),x33881),f334(a116,x33882)))
% 160.93/160.64 [3389]E(f334(f334(f22(a881),f334(a116,x33891)),f334(a116,x33892)),f334(f334(f22(a881),x33891),x33892))
% 160.93/160.64 [3397]E(f54(x33971,f2(a881),x33972),f334(f334(f153(f882(x33971)),f117(x33971)),f117(f882(x33971))))
% 160.93/160.64 [3398]E(f334(f37(a881),f307(a881,x33981,x33982)),f334(f334(f22(a881),x33982),x33981))
% 160.93/160.64 [3407]P39(x34071,f334(f334(f290(a881,x34071),a253),x34072))
% 160.93/160.64 [3409]P16(a881,f141(a881,f334(f304(a881,x34091),x34092)))
% 160.93/160.64 [3411]P1(f334(f61(a881),f334(f304(a881,x34111),x34112)))
% 160.93/160.64 [3412]P1(f334(f61(a1),f334(f304(a1,x34121),x34122)))
% 160.93/160.64 [3414]E(f334(f289(f882(x34141),f882(x34141)),f159(x34141,x34142)),f159(x34141,f334(f289(x34141,x34141),x34142)))
% 160.93/160.64 [3415]E(f334(f197(a878),f32(x34151,x34152)),f334(f334(f80(a881),f334(f197(a878),x34152)),f334(a116,f2(a881))))
% 160.93/160.64 [3417]E(f334(f304(a1,x34171),f334(f334(f80(a1),x34172),f78(a1))),f305(a1,x34171,x34172))
% 160.93/160.64 [3420]E(f334(f334(f38(a1),f334(f79(a1),x34201)),f334(f79(a1),x34202)),f334(f334(f38(a1),x34201),x34202))
% 160.93/160.64 [3428]E(f186(x34281,x34282,f334(f16(f885(x34282),x34281),f210(x34282))),f196(f888(x34281,a876)))
% 160.93/160.64 [3429]E(f188(x34291,x34292,f334(f16(f885(x34292),x34291),f210(x34292))),f196(f888(x34292,a876)))
% 160.93/160.64 [3430]E(f334(f334(f191(f887(x34301,x34301),a876),f78(a881)),x34302),x34302)
% 160.93/160.64 [3432]E(f334(f334(f114(f888(x34321,a876)),x34322),f196(f888(x34321,a876))),x34322)
% 160.93/160.64 [3433]E(f334(f334(f22(f888(x34331,a876)),x34332),f196(f888(x34331,a876))),x34332)
% 160.93/160.64 [3434]E(f334(f334(f105(f888(x34341,a876)),x34342),f257(f888(x34341,a876))),x34342)
% 160.93/160.64 [3435]E(f334(f268(a881,a881),f85(f887(a881,a881),f47(x34351,x34352))),f334(f334(f38(a881),x34351),x34352))
% 160.93/160.64 [3442]E(f316(x34421,f334(a20,x34422),f334(f79(a1),f334(a20,x34422))),f334(f334(f319(a1),x34421),x34422))
% 160.93/160.64 [3443]E(f305(a1,f334(f334(f80(a1),x34431),f78(a1)),x34432),f307(a1,x34431,x34432))
% 160.93/160.64 [3448]E(f334(f272(a881,a881),f85(f887(a881,a881),f47(x34481,x34482))),f44(a881,x34481,x34482))
% 160.93/160.64 [3456]E(f317(x34561,f334(a20,x34562),f334(f79(a1),f334(a20,x34562))),f318(a1,x34561,x34562))
% 160.93/160.64 [3459]P1(f334(f334(f336(x34591),x34592),f257(f888(x34591,a876))))
% 160.93/160.64 [3464]E(f334(f334(f22(a881),f334(a116,x34641)),x34642),f334(f37(a881),f305(a881,x34642,x34641)))
% 160.93/160.64 [3490]E(f334(f334(f114(f888(x34901,a876)),x34902),f257(f888(x34901,a876))),f257(f888(x34901,a876)))
% 160.93/160.64 [3491]E(f334(f334(f22(f888(x34911,a876)),x34912),f257(f888(x34911,a876))),f196(f888(x34911,a876)))
% 160.93/160.64 [3492]E(f334(f334(f105(f888(x34921,a876)),x34922),f196(f888(x34921,a876))),f196(f888(x34921,a876)))
% 160.93/160.64 [3508]E(f44(a1,f334(f104(a1),x35081),f334(f104(a1),x35082)),f334(f104(a1),f44(a881,x35081,x35082)))
% 160.93/160.64 [3509]E(f44(a1,f334(f79(a1),x35091),f334(f79(a1),x35092)),f334(f79(a1),f44(a1,x35091,x35092)))
% 160.93/160.64 [3520]E(f334(f197(f882(x35201)),f334(f173(x35201),x35202)),f334(f334(f22(a881),f334(f197(f882(x35201)),x35202)),f78(a881)))
% 160.93/160.64 [3545]E(f334(f334(f38(a1),f44(a1,x35451,x35452)),x35452),f2(a1))
% 160.93/160.64 [3555]E(f334(a3,f44(a881,f334(a19,x35551),f334(a19,x35552))),f44(a103,x35551,x35552))
% 160.93/160.64 [3588]E(f334(a3,f334(f334(f22(a881),f334(a19,x35881)),f334(a19,x35882))),f334(f334(f22(a103),x35881),x35882))
% 160.93/160.64 [3589]E(f334(a3,f334(f334(f80(a881),f334(a19,x35891)),f334(a19,x35892))),f334(f334(f80(a103),x35891),x35892))
% 160.93/160.64 [3590]E(f334(a3,f334(f334(f81(a881),f334(a19,x35901)),f334(a19,x35902))),f334(f334(f81(a103),x35901),x35902))
% 160.93/160.64 [3591]E(f334(a3,f334(f334(f38(a881),f334(a19,x35911)),f334(a19,x35912))),f334(f334(f38(a103),x35911),x35912))
% 160.93/160.64 [3600]E(f334(f313(a881,a881,a116),f334(f304(a881,x36001),x36002)),f334(f304(a881,f334(a116,x36001)),f334(a116,x36002)))
% 160.93/160.64 [3624]P1(f334(f47(x36241,x36242),f85(f887(a881,a881),f47(x36241,x36242))))
% 160.93/160.64 [3646]E(f334(f334(f80(a881),f334(f334(f80(a881),f31(x36461)),f31(x36462))),f334(a116,f2(a881))),f31(f33(x36461,x36462)))
% 160.93/160.64 [3647]E(f44(a881,f334(a116,f44(a881,x36471,x36472)),x36472),f44(a881,f334(a116,x36471),x36472))
% 160.93/160.64 [3661]E(f334(f334(f41(f888(x36611,a876),f888(x36611,a876)),x36612),f5(f888(x36611,a876))),f39(f888(x36611,a876),x36612))
% 160.93/160.64 [3662]E(f334(f334(f42(f888(x36621,a876),f888(x36621,a876)),x36622),f5(f888(x36621,a876))),f40(f888(x36621,a876),x36622))
% 160.93/160.64 [3663]E(f334(f313(f882(x36631),f888(x36631,a876),f174(x36631)),f334(f174(f882(x36631)),f53(x36631,x36632))),f334(f311(x36631),f334(f174(x36631),x36632)))
% 160.93/160.64 [3666]P1(f334(f334(f336(f888(x36661,a876)),x36662),f334(f311(x36661),x36662)))
% 160.93/160.64 [3672]E(f44(a1,f334(f79(a1),f44(a1,x36721,x36722)),x36722),f44(a1,f334(f79(a1),x36721),x36722))
% 160.93/160.64 [3684]P1(f334(f334(f248(f888(x36841,a876)),x36842),f257(f888(x36841,a876))))
% 160.93/160.64 [3686]E(f334(f334(f291(x36861,x36861,x36861),f310(x36861,x36862)),f310(x36861,f310(x36861,x36862))),f310(x36861,x36862))
% 160.93/160.64 [3687]E(f334(f334(f114(f888(x36871,a876)),f334(f267(x36871,x36871),x36872)),f334(f265(x36871,x36871),x36872)),f334(f287(x36871),x36872))
% 160.93/160.64 [3708]E(f321(x37081,x37082,f257(f888(x37081,a876)),f257(f888(x37082,a876))),f257(f888(f886(x37081,x37082),a876)))
% 160.93/160.64 [3759]P1(f334(f334(f248(a881),f44(a881,x37591,x37592)),x37591))
% 160.93/160.64 [3781]P1(f334(f334(f248(a1),f334(f79(a1),f334(f104(a1),x37811))),f334(f104(a1),x37812)))
% 160.93/160.64 [3807]P1(f334(f334(f336(f888(x38071,a876)),f196(f888(x38071,a876))),f334(f311(x38071),x38072)))
% 160.93/160.64 [3812]E(f310(x38121,f334(f334(f291(x38121,x38121,x38121),x38122),f310(x38121,x38122))),f310(x38121,x38122))
% 160.93/160.64 [3815]E(f334(f334(f291(x38151,x38151,x38151),f310(x38151,x38152)),x38152),f334(f334(f291(x38151,x38151,x38151),x38152),f310(x38151,x38152)))
% 160.93/160.64 [3817]E(f334(a108,f334(f334(f80(a1),f334(f334(f22(a1),x38171),x38172)),f78(a1))),f334(f37(a1),f305(a1,x38172,x38171)))
% 160.93/160.64 [3832]E(f334(f265(x38321,x38321),f334(f334(f291(x38321,x38321,x38321),x38322),f310(x38321,x38322))),f334(f265(x38321,x38321),x38322))
% 160.93/160.64 [3833]E(f334(f267(x38331,x38331),f334(f334(f291(x38331,x38331,x38331),x38332),f310(x38331,x38332))),f334(f267(x38331,x38331),x38332))
% 160.93/160.64 [3849]E(f334(f334(f80(a881),f334(f334(f80(a881),f334(f197(a878),x38491)),f334(f197(a878),x38492))),f334(a116,f2(a881))),f334(f197(a878),f33(x38491,x38492)))
% 160.93/160.64 [3860]P27(a881,a881,f334(f334(f7(a881,a881,a881),f80(a881)),x38601),x38602)
% 160.93/160.64 [3862]P16(a881,f334(f171(a881),f334(f334(f156(f882(x38621),a881),f197(f882(x38621))),f182(x38621,x38622))))
% 160.93/160.64 [3907]P1(f334(f334(f249(a1),f334(f79(a1),f334(f104(a1),f334(a116,x39071)))),f334(f104(a1),x39072)))
% 160.93/160.64 [3953]E(f334(f144(f882(x39531),x39531,f334(f7(x39531,f882(x39531),f882(x39531)),f153(x39531)),f117(x39531)),x39532),f334(f171(x39531),x39532))
% 160.93/160.64 [4005]P1(f334(f334(f248(f888(f887(f882(x40051),f882(x40051)),a876)),f160(x40051,x40052)),f310(f882(x40051),f159(x40051,x40052))))
% 160.93/160.64 [4036]P1(f334(f47(x40361,x40362),f334(f334(f269(a881,a881),f334(f334(f38(a881),x40361),x40362)),f44(a881,x40361,x40362))))
% 160.93/160.64 [4047]P1(f334(f334(f248(f888(f887(f882(x40471),f882(x40471)),a876)),f159(x40471,f310(x40471,x40472))),f310(f882(x40471),f159(x40471,x40472))))
% 160.93/160.64 [4274]E(f334(f334(f275(f887(a103,a103),a103,f887(a103,a103),f887(x42741,f887(a103,a103))),f279(f334(f168(a103),f334(f334(f156(f887(a103,x42741),a103),f268(a103,x42741)),x42742)))),f334(f334(f8(x42741,f888(f887(a103,a103),f887(x42741,f887(a103,a103))),a103),f269(x42741,f887(a103,a103))),f280(x42741,x42742))),f278(x42741,x42742))
% 160.93/160.64 [4385]E(f334(f243(a881,f887(x43851,f883(x43851)),f2(a881),f334(f273(x43851,f883(x43851),a881),f334(f16(f888(f883(x43851),a881),x43851),f334(f334(f7(f883(x43851),a881,a881),f334(f334(f8(a881,f888(a881,a881),f883(x43851)),f80(a881)),f197(f883(x43851)))),f78(a881))))),f334(f137(x43851),x43852)),f334(f197(f883(x43851)),x43852))
% 160.93/160.64 [4461]E(f334(f273(f888(f887(x44611,x44611),a876),f888(f887(x44611,x44611),a876),f888(f888(x44612,x44611),f887(f888(f887(x44612,x44612),a876),f888(f887(x44612,x44612),a876)))),f334(f334(f7(f888(f887(x44611,x44611),a876),f888(f888(f887(x44611,x44611),a876),f888(f888(x44612,x44611),f888(f887(x44612,x44612),a876))),f888(f888(f887(x44611,x44611),a876),f888(f888(x44612,x44611),f887(f888(f887(x44612,x44612),a876),f888(f887(x44612,x44612),a876))))),f334(f334(f8(f888(f888(f888(x44612,x44611),f888(f887(x44612,x44612),a876)),f888(f888(x44612,x44611),f887(f888(f887(x44612,x44612),a876),f888(f887(x44612,x44612),a876)))),f888(f888(f888(f887(x44611,x44611),a876),f888(f888(x44612,x44611),f888(f887(x44612,x44612),a876))),f888(f888(f887(x44611,x44611),a876),f888(f888(x44612,x44611),f887(f888(f887(x44612,x44612),a876),f888(f887(x44612,x44612),a876))))),f888(f887(x44611,x44611),a876)),f8(f888(f888(x44612,x44611),f888(f887(x44612,x44612),a876)),f888(f888(x44612,x44611),f887(f888(f887(x44612,x44612),a876),f888(f887(x44612,x44612),a876))),f888(f887(x44611,x44611),a876))),f334(f334(f8(f888(f888(x44612,x44611),f888(f888(f887(x44612,x44612),a876),f887(f888(f887(x44612,x44612),a876),f888(f887(x44612,x44612),a876)))),f888(f888(f888(x44612,x44611),f888(f887(x44612,x44612),a876)),f888(f888(x44612,x44611),f887(f888(f887(x44612,x44612),a876),f888(f887(x44612,x44612),a876)))),f888(f887(x44611,x44611),a876)),f18(f888(x44612,x44611),f888(f887(x44612,x44612),a876),f887(f888(f887(x44612,x44612),a876),f888(f887(x44612,x44612),a876)))),f334(f334(f8(f888(f888(x44612,x44611),f888(f887(x44612,x44612),a876)),f888(f888(x44612,x44611),f888(f888(f887(x44612,x44612),a876),f887(f888(f887(x44612,x44612),a876),f888(f887(x44612,x44612),a876)))),f888(f887(x44611,x44611),a876)),f334(f8(f888(f887(x44612,x44612),a876),f888(f888(f887(x44612,x44612),a876),f887(f888(f887(x44612,x44612),a876),f888(f887(x44612,x44612),a876))),f888(x44612,x44611)),f269(f888(f887(x44612,x44612),a876),f888(f887(x44612,x44612),a876)))),f290(x44611,x44612))))),f290(x44611,x44612))),f74(x44611,x44612))
% 160.93/160.64 [4537]~E(f334(f311(x45371),x45372),f196(f888(f888(x45371,a876),a876)))
% 160.93/160.64 [4551]~P1(f334(f334(f336(x45511),x45512),f196(f888(x45511,a876))))
% 160.93/160.64 [4561]~P1(f334(f334(f249(f888(x45611,a876)),x45612),f196(f888(x45611,a876))))
% 160.93/160.64 [3367]E(f334(f334(f22(a881),x33671),f334(f334(f80(a881),x33671),x33672)),f2(a881))
% 160.93/160.64 [3369]E(f334(f334(f114(f888(x33691,a876)),x33692),x33692),x33692)
% 160.93/160.64 [3370]E(f334(f334(f105(f888(x33701,a876)),x33702),x33702),x33702)
% 160.93/160.64 [3400]E(f334(f334(f22(f888(x34001,a876)),x34002),x34002),f196(f888(x34001,a876)))
% 160.93/160.64 [3403]E(f334(f145(x34031,x34032),f2(a881)),f196(f888(f887(f882(x34031),f882(x34031)),a876)))
% 160.93/160.64 [3404]E(f334(f334(f80(a881),x34041),f334(a116,x34042)),f334(a116,f334(f334(f80(a881),x34041),x34042)))
% 160.93/160.64 [3416]E(f203(f334(f104(a1),x34161),f334(f104(a1),x34162)),f334(f104(a1),f334(f334(f22(a881),x34161),x34162)))
% 160.93/160.64 [3419]E(f334(f334(f38(a1),f334(f79(a1),x34191)),x34192),f334(f334(f38(a1),x34191),f334(f79(a1),x34192)))
% 160.93/160.64 [3423]E(f334(f37(a1),f334(f304(a1,x34231),x34232)),f334(a108,f334(f334(f22(a1),x34232),x34231)))
% 160.93/160.64 [3426]E(f334(f334(f80(a881),f334(a116,x34261)),x34262),f334(a116,f334(f334(f80(a881),x34261),x34262)))
% 160.93/160.64 [3431]E(f334(f79(f888(x34311,a876)),f334(f79(f888(x34311,a876)),x34312)),x34312)
% 160.93/160.64 [3445]E(f182(x34451,f334(f334(f153(f882(x34451)),f117(x34451)),x34452)),f182(x34451,x34452))
% 160.93/160.64 [3449]E(f334(f334(f80(a881),x34491),f334(f334(f81(a881),x34491),x34492)),f334(f334(f81(a881),x34491),f334(a116,x34492)))
% 160.93/160.64 [3457]E(f334(f334(a23,f334(a3,x34571)),f334(a3,x34572)),f334(a3,f334(f334(f22(a881),x34571),x34572)))
% 160.93/160.64 [3470]E(f334(f334(f81(a1),f334(f79(a1),x34701)),x34702),f334(f79(a1),f334(f334(f81(a1),x34701),x34702)))
% 160.93/160.64 [3472]E(f334(f334(f259(a1),f334(f104(a1),x34721)),x34722),f334(f104(a1),f334(f334(f259(a881),x34721),x34722)))
% 160.93/160.64 [3473]E(f334(f334(f80(a103),f334(a3,x34731)),f334(a3,x34732)),f334(a3,f334(f334(f80(a881),x34731),x34732)))
% 160.93/160.64 [3474]E(f334(f334(f81(a103),f334(a3,x34741)),f334(a3,x34742)),f334(a3,f334(f334(f81(a881),x34741),x34742)))
% 160.93/160.64 [3475]E(f334(f334(f246(a881),f334(a116,x34751)),f334(a116,x34752)),f334(a116,f334(f334(f246(a881),x34751),x34752)))
% 160.93/160.64 [3476]E(f334(f334(f247(a881),f334(a116,x34761)),f334(a116,x34762)),f334(a116,f334(f334(f247(a881),x34761),x34762)))
% 160.93/160.64 [3482]E(f334(f174(a881),f141(a881,f334(f304(a881,x34821),x34822))),f334(f304(a881,x34821),x34822))
% 160.93/160.64 [3483]E(f315(x34831,f334(f334(f312(x34831),x34832),f196(f888(x34831,a876)))),x34832)
% 160.93/160.64 [3488]E(f334(f265(x34881,x34882),f196(f888(f887(x34881,x34882),a876))),f196(f888(x34882,a876)))
% 160.93/160.64 [3489]E(f334(f267(x34891,x34892),f196(f888(f887(x34891,x34892),a876))),f196(f888(x34891,a876)))
% 160.93/160.64 [3493]E(f334(a108,f334(f334(f22(a1),x34931),x34932)),f334(f37(a1),f307(a1,x34932,x34931)))
% 160.93/160.64 [3498]E(f334(f334(f80(a881),x34981),f334(f334(f81(a881),x34982),x34981)),f334(f334(f81(a881),f334(a116,x34982)),x34981))
% 160.93/160.64 [3500]E(f334(f334(f60(x35001),f196(f888(x35001,a876))),x35002),f196(f888(f888(x35001,a876),a876)))
% 160.93/160.64 [3510]E(f334(f197(f882(a881)),f141(a881,f334(f304(a881,x35101),x35102))),f334(f334(f22(a881),x35102),x35101))
% 160.93/160.64 [3525]E(f334(f334(f114(f888(x35251,a876)),f196(f888(x35251,a876))),x35252),x35252)
% 160.93/160.64 [3526]E(f334(f334(f105(f888(x35261,a876)),f257(f888(x35261,a876))),x35262),x35262)
% 160.93/160.64 [3529]E(f334(f334(f80(a1),f334(f79(a1),x35291)),f334(f79(a1),x35292)),f334(f79(a1),f334(f334(f80(a1),x35291),x35292)))
% 160.93/160.64 [3532]E(f334(f334(f80(a1),f334(f104(a1),x35321)),f334(f104(a1),x35322)),f334(f104(a1),f334(f334(f80(a881),x35321),x35322)))
% 160.93/160.64 [3533]E(f334(f334(f80(a1),f334(f107(a1),x35331)),f334(f107(a1),x35332)),f334(f107(a1),f334(f334(f80(a1),x35331),x35332)))
% 160.93/160.64 [3535]E(f334(f334(f81(a1),f334(f104(a1),x35351)),f334(f104(a1),x35352)),f334(f104(a1),f334(f334(f81(a881),x35351),x35352)))
% 160.93/160.64 [3536]E(f334(f334(f81(a1),f334(f107(a1),x35361)),f334(f107(a1),x35362)),f334(f107(a1),f334(f334(f81(a1),x35361),x35362)))
% 160.93/160.64 [3537]E(f334(f334(f38(a1),f334(f104(a1),x35371)),f334(f104(a1),x35372)),f334(f104(a1),f334(f334(f38(a881),x35371),x35372)))
% 160.93/160.64 [3556]E(f334(f334(f6(x35561,a881),f334(f16(a881,x35561),f78(a881))),x35562),f334(f37(x35561),x35562))
% 160.93/160.64 [3563]E(f334(f79(a1),f44(a1,f334(f79(a1),x35631),x35632)),f44(a1,x35631,f334(f79(a1),x35632)))
% 160.93/160.64 [3565]E(f334(f174(a1),f181(x35651,f334(f334(f22(a1),x35652),f78(a1)))),f334(f304(a1,x35651),x35652))
% 160.93/160.64 [3569]P1(f334(f334(f248(a881),x35691),f334(f334(f80(a881),x35692),x35691)))
% 160.93/160.64 [3570]P1(f334(f334(f248(a881),x35701),f334(f334(f80(a881),x35701),x35702)))
% 160.93/160.64 [3573]E(f334(f334(f114(f888(x35731,a876)),f257(f888(x35731,a876))),x35732),f257(f888(x35731,a876)))
% 160.93/160.64 [3574]E(f334(f334(f22(f888(x35741,a876)),f196(f888(x35741,a876))),x35742),f196(f888(x35741,a876)))
% 160.93/160.64 [3575]E(f334(f334(f105(f888(x35751,a876)),f196(f888(x35751,a876))),x35752),f196(f888(x35751,a876)))
% 160.93/160.64 [3580]E(f334(f334(f269(a1,a1),x35801),f334(f79(a1),x35802)),f334(a50,f334(f334(f269(a1,a1),x35801),x35802)))
% 160.93/160.64 [3581]E(f334(f304(a1,f334(f334(f80(a1),x35811),f78(a1))),x35812),f308(a1,x35811,x35812))
% 160.93/160.64 [3592]E(f334(f334(f81(a881),x35921),f334(f334(f38(a881),x35922),x35921)),f334(f334(f22(a881),x35922),f44(a881,x35922,x35921)))
% 160.93/160.64 [3593]E(f334(f334(f81(a1),x35931),f334(f334(f38(a1),x35932),x35931)),f334(f334(f22(a1),x35932),f44(a1,x35932,x35931)))
% 160.93/160.64 [3597]E(f334(f174(a1),f181(f334(f334(f80(a1),x35971),f78(a1)),x35972)),f307(a1,x35971,x35972))
% 160.93/160.64 [3601]P1(f334(f334(f248(f888(x36011,a876)),x36012),x36012))
% 160.93/160.64 [3604]E(f334(f334(f114(f888(x36041,a876)),x36042),f334(f79(f888(x36041,a876)),x36042)),f257(f888(x36041,a876)))
% 160.93/160.64 [3605]E(f334(f334(f105(f888(x36051,a876)),x36052),f334(f79(f888(x36051,a876)),x36052)),f196(f888(x36051,a876)))
% 160.93/160.64 [3611]E(f334(f334(f22(a881),f334(f334(f22(a881),x36111),f78(a881))),x36112),f334(f334(f22(a881),x36111),f334(a116,x36112)))
% 160.93/160.64 [3616]E(f334(f334(f22(f888(x36161,a876)),f257(f888(x36161,a876))),x36162),f334(f79(f888(x36161,a876)),x36162))
% 160.93/160.64 [3617]E(f334(f334(f22(a1),f334(f107(a1),x36171)),f334(f107(a1),x36172)),f334(f107(a1),f334(f334(f80(a1),x36171),f334(f79(a1),x36172))))
% 160.93/160.64 [3630]E(f334(f174(a881),f141(a881,f334(f304(a881,x36301),f334(a116,x36302)))),f305(a881,x36301,x36302))
% 160.93/160.64 [3638]P1(f334(f334(f334(f334(a204,a24),x36381),x36382),x36381))
% 160.93/160.64 [3644]E(f334(f197(f882(f882(x36441))),f53(x36441,x36442)),f334(f334(f259(a881),f334(a116,f334(a116,f2(a881)))),f334(f197(f882(x36441)),x36442)))
% 160.93/160.64 [3664]E(f334(f334(f191(f887(x36641,x36641),a876),f2(a881)),x36642),f310(x36641,f196(f888(f887(x36641,x36641),a876))))
% 160.93/160.64 [3668]P1(f334(f139(a881),f141(a881,f334(f304(a881,x36681),x36682))))
% 160.93/160.64 [3685]E(f334(f313(a1,a881,a108),f305(a1,f334(f104(a1),x36851),f334(f104(a1),x36852))),f305(a881,x36851,x36852))
% 160.93/160.64 [3695]E(f193(a881,f2(a881),f5(a881),f334(f334(f22(a881),x36951),x36952)),f334(f334(f22(a881),x36951),f334(a116,x36952)))
% 160.93/160.64 [3696]E(f334(a108,f334(f334(f22(a1),x36961),f334(f334(f80(a1),x36962),f78(a1)))),f334(f37(a1),f308(a1,x36962,x36961)))
% 160.93/160.64 [3732]E(f334(f334(f156(a881,a881),a116),f141(a881,f334(f304(a881,x37321),x37322))),f141(a881,f334(f304(a881,f334(a116,x37321)),f334(a116,x37322))))
% 160.93/160.64 [3739]E(f334(f174(a1),f181(f334(f334(f80(a1),x37391),f78(a1)),f334(f334(f22(a1),x37392),f78(a1)))),f308(a1,x37391,x37392))
% 160.93/160.64 [3750]P1(f334(f334(f248(f888(x37501,a876)),f196(f888(x37501,a876))),x37502))
% 160.93/160.64 [3755]E(f85(x37551,f334(f334(f7(x37551,x37551,a876),a331),x37552)),x37552)
% 160.93/160.64 [3756]E(f90(x37561,f334(f334(f7(x37561,x37561,a876),a331),x37562)),x37562)
% 160.93/160.64 [3760]E(f334(f174(a881),f141(a881,f334(f304(a881,f334(a116,x37601)),f334(a116,x37602)))),f307(a881,x37601,x37602))
% 160.93/160.64 [3784]E(f334(f334(f271(x37841,x37842),f257(f888(x37841,a876))),f334(f16(f888(x37842,a876),x37841),f257(f888(x37842,a876)))),f257(f888(f887(x37841,x37842),a876)))
% 160.93/160.64 [3819]E(f334(f254(x38191),f334(f334(f8(a876,a876,x38191),a329),x38192)),f334(f79(f888(x38191,a876)),f334(f254(x38191),x38192)))
% 160.93/160.64 [3822]E(f334(f254(x38221),f334(f334(f7(x38221,x38221,a876),a331),x38222)),f334(f334(f312(x38221),x38222),f196(f888(x38221,a876))))
% 160.93/160.64 [3829]E(f334(f334(f80(a1),f334(f334(f22(a1),x38291),x38292)),f334(f334(f22(a1),x38291),x38292)),f334(f334(f22(a1),f334(f334(f80(a1),x38291),x38291)),f334(f334(f80(a1),x38292),x38292)))
% 160.93/160.64 [3830]E(f334(f334(f80(a1),f334(f334(f80(a1),x38301),x38301)),f334(f334(f80(a1),x38302),x38302)),f334(f334(f80(a1),f334(f334(f80(a1),x38301),x38302)),f334(f334(f80(a1),x38301),x38302)))
% 160.93/160.64 [3846]P1(f334(f334(f248(a881),f334(f37(x38461),f334(f174(x38461),x38462))),f334(f197(f882(x38461)),x38462)))
% 160.93/160.64 [3847]P1(f334(f334(f248(a881),f334(f197(f882(x38471)),f154(x38471,x38472))),f334(f197(f882(x38471)),x38472)))
% 160.93/160.64 [3857]E(f334(f254(x38571),f334(f334(f7(x38571,f888(x38571,a876),a876),f336(x38571)),x38572)),x38572)
% 160.93/160.64 [3872]E(f334(f334(f177(x38721),f334(f334(f22(a881),f334(f197(f882(x38721)),x38722)),f78(a881))),x38722),f118(x38721,x38722))
% 160.93/160.64 [3894]E(f193(a881,f2(a881),f334(f334(f8(a881,a881,a881),a116),f334(f246(a881),x38941)),x38942),f334(f334(f246(a881),f334(a116,x38941)),x38942))
% 160.93/160.64 [3898]E(f39(f888(x38981,a876),f334(f313(f888(f887(x38981,x38981),a876),f888(x38981,a876),f287(x38981)),x38982)),f334(f287(x38981),f39(f888(f887(x38981,x38981),a876),x38982)))
% 160.93/160.64 [3899]E(f193(a881,f334(a116,x38991),f334(f334(f8(a881,a881,a881),a116),f334(f247(a881),x38991)),x38992),f334(f334(f247(a881),f334(a116,x38991)),x38992))
% 160.93/160.64 [3901]E(f334(f334(f269(a1,a1),f334(f334(f38(a1),f334(f75(a1),x39011)),f334(f75(a1),x39012))),f44(a1,f334(f75(a1),x39011),f334(f75(a1),x39012))),f52(x39011,x39012))
% 160.93/160.64 [3923]P1(f334(f334(f248(f888(f888(x39231,a876),a876)),x39232),f334(f311(x39231),f39(f888(x39231,a876),x39232))))
% 160.93/160.64 [3958]E(f334(f334(f41(x39581,f888(x39581,a876)),x39582),f334(f334(f7(x39581,f888(x39581,a876),f888(x39581,a876)),f312(x39581)),f196(f888(x39581,a876)))),x39582)
% 160.93/160.64 [3959]E(f334(f334(f291(x39591,x39591,x39591),f334(f289(x39591,x39591),x39592)),f310(x39591,f334(f289(x39591,x39591),x39592))),f334(f289(x39591,x39591),f334(f334(f291(x39591,x39591,x39591),x39592),f310(x39591,x39592))))
% 160.93/160.64 [4027]E(f334(f174(x40271),f334(f144(f882(x40271),f882(x40271),f136(x40271),f117(x40271)),x40272)),f334(f334(f41(f882(x40271),f888(x40271,a876)),f334(f174(f882(x40271)),x40272)),f174(x40271)))
% 160.93/160.64 [4060]E(f334(f334(f114(f888(f887(x40601,x40601),a876)),f310(x40601,f196(f888(f887(x40601,x40601),a876)))),f334(f334(f291(x40601,x40601,x40601),f310(x40601,x40602)),x40602)),f310(x40601,x40602))
% 160.93/160.64 [4094]E(f334(f334(f184(x40941,x40941),x40942),x40942),f334(f334(f156(x40941,f887(x40941,x40941)),f334(f334(f18(x40941,x40941,f887(x40941,x40941)),f269(x40941,x40941)),f5(x40941))),x40942))
% 160.93/160.64 [4211]E(f334(f144(a881,f882(x42111),f334(f7(f882(x42111),a881,a881),f334(f334(f8(a881,f888(a881,a881),f882(x42111)),f247(a881)),f197(f882(x42111)))),f2(a881)),f334(f171(f882(x42111)),x42112)),f334(f197(f882(f882(x42111))),f182(x42111,x42112)))
% 160.93/160.64 [4289]E(f334(f334(f290(f887(a881,f882(x42891)),f882(x42891)),f326(a881,f882(x42891),a253,f147(x42891,x42892))),f334(f334(f18(f882(x42891),f882(x42891),f887(a881,f882(x42891))),f334(f334(f8(a881,f888(f882(x42891),f887(a881,f882(x42891))),f882(x42891)),f269(a881,f882(x42891))),f197(f882(x42891)))),f5(f882(x42891)))),f148(x42891,x42892))
% 160.93/160.64 [4419]E(f334(f254(x44191),f334(f334(f8(f888(f888(x44191,a876),a876),a876,x44191),f88(f888(x44191,a876))),f334(f334(f8(f888(f888(x44191,a876),a876),f888(f888(x44191,a876),a876),x44191),f334(f18(f888(x44191,a876),a876,a876),f334(f334(f8(a876,f888(a876,a876),f888(x44191,a876)),a337),f334(f334(f7(f888(x44191,a876),f888(f888(x44191,a876),a876),a876),f336(f888(x44191,a876))),x44192)))),f336(x44191)))),f40(f888(x44191,a876),x44192))
% 160.93/160.64 [4562]~P1(f334(f334(f249(a1),f334(f104(a1),x45621)),f334(f79(a1),f334(f104(a1),x45622))))
% 160.93/160.64 [4578]~P1(f334(f334(f91(a1),f334(f334(f22(a1),f334(f334(f80(a1),x45781),x45781)),a101)),f334(f334(f80(a1),x45782),x45782)))
% 160.93/160.64 [3496]E(f334(f334(f22(a881),f334(f334(f80(a881),x34961),x34962)),x34962),x34961)
% 160.93/160.64 [3497]E(f334(f334(f22(a881),f334(f334(f80(a881),x34971),x34972)),x34971),x34972)
% 160.93/160.64 [3564]E(f334(f334(f80(a881),f334(f334(f22(a881),x35641),x35642)),x35642),f334(f334(f247(a881),x35641),x35642))
% 160.93/160.64 [3671]E(f334(f334(f81(a881),f334(f334(f38(a881),x36711),x36712)),x36712),f334(f334(f22(a881),x36711),f44(a881,x36711,x36712)))
% 160.93/160.64 [3700]E(f334(f174(a881),f141(a881,f334(f304(a881,f334(a116,x37001)),x37002))),f308(a881,x37001,x37002))
% 160.93/160.64 [3707]E(f334(f104(a1),f229(f334(a108,f334(f75(a1),x37071)),f334(a108,f334(f75(a1),x37072)))),f334(f334(a230,x37071),x37072))
% 160.93/160.64 [3709]E(f334(f334(f114(f888(x37091,a876)),f334(f79(f888(x37091,a876)),x37092)),x37092),f257(f888(x37091,a876)))
% 160.93/160.64 [3710]E(f334(f334(f105(f888(x37101,a876)),f334(f79(f888(x37101,a876)),x37102)),x37102),f196(f888(x37101,a876)))
% 160.93/160.64 [3728]P1(f334(f334(f248(a881),f334(f334(f22(a881),x37281),x37282)),x37281))
% 160.93/160.64 [3729]P1(f334(f334(f248(a881),f334(f334(f38(a881),x37291),x37292)),x37291))
% 160.93/160.64 [3752]P1(f334(f334(f249(a881),x37521),f334(a116,f334(f334(f80(a881),x37522),x37521))))
% 160.93/160.64 [3753]P1(f334(f334(f249(a881),x37531),f334(a116,f334(f334(f80(a881),x37531),x37532))))
% 160.93/160.64 [3770]E(f334(f334(f81(a881),f334(a108,f334(f75(a1),x37701))),f334(a108,f334(f75(a1),x37702))),f334(a108,f334(f75(a1),f334(f334(f81(a1),x37701),x37702))))
% 160.93/160.64 [3780]P1(f334(f334(f248(a1),f2(a1)),f334(f334(f259(a1),f334(f75(a1),x37801)),x37802)))
% 160.93/160.64 [3851]E(f334(f288(f882(x38511),f882(x38511),f160(x38511,x38512)),f334(f334(f312(f882(x38511)),f117(x38511)),f196(f888(f882(x38511),a876)))),f334(f334(f312(f882(x38511)),f117(x38511)),f196(f888(f882(x38511),a876))))
% 160.93/160.64 [3870]E(f334(f334(f114(f888(f887(x38701,x38701),a876)),f310(x38701,x38702)),f310(x38701,f196(f888(f887(x38701,x38701),a876)))),f310(x38701,x38702))
% 160.93/160.64 [3884]E(f334(f334(f38(a1),f334(f107(a1),f334(f334(f80(a1),x38841),x38841))),f334(f107(a1),f334(f334(f80(a1),x38842),x38842))),f334(f334(f38(a1),f334(f107(a1),x38841)),f334(f107(a1),x38842)))
% 160.93/160.64 [3948]E(f334(f334(f259(a1),x39481),f334(f107(a881),f334(f334(f80(a1),x39482),x39482))),f334(f334(f86(a1,a1),f334(f334(f259(a1),x39481),f334(f107(a881),x39482))),f334(f334(f18(a1,a1,a1),f81(a1)),f5(a1))))
% 160.93/160.64 [3954]E(f334(f254(f888(x39541,a876)),f334(f334(f7(f888(x39541,a876),f888(x39541,a876),a876),f248(f888(x39541,a876))),x39542)),f334(f311(x39541),x39542))
% 160.93/160.64 [3969]E(f334(f334(f156(a1,a881),a108),f334(f334(f136(a1),f334(f334(f156(a881,a1),f104(a1)),x39691)),f334(f334(f156(a881,a1),f104(a1)),x39692))),f334(f334(f136(a881),x39691),x39692))
% 160.93/160.64 [4004]E(f334(f313(a1,a1,f334(f334(f7(a1,a1,a1),f80(a1)),x40041)),f334(f304(a1,f2(a1)),f334(f334(f22(a1),x40042),x40041))),f334(f304(a1,x40041),x40042))
% 160.93/160.64 [4006]P43(x40061,f334(f334(f22(f888(f887(x40061,x40061),a876)),x40062),f310(x40061,f196(f888(f887(x40061,x40061),a876)))))
% 160.93/160.64 [4025]E(f334(f197(f882(x40251)),f334(f144(f882(x40251),f882(x40251),f136(x40251),f117(x40251)),x40252)),f334(f168(a881),f334(f334(f156(f882(x40251),a881),f197(f882(x40251))),x40252)))
% 160.93/160.64 [4030]P41(x40301,f257(f888(x40301,a876)),f334(f334(f114(f888(f887(x40301,x40301),a876)),x40302),f310(x40301,f196(f888(f887(x40301,x40301),a876)))))
% 160.93/160.64 [4074]E(f193(a881,f2(a881),f334(f334(f8(a881,a881,a881),a116),f334(f334(f7(a881,a881,a881),f246(a881)),x40741)),x40742),f334(f334(f246(a881),x40742),f334(a116,x40741)))
% 160.93/160.64 [4077]E(f193(a881,f334(a116,x40771),f334(f334(f8(a881,a881,a881),a116),f334(f334(f7(a881,a881,a881),f247(a881)),x40771)),x40772),f334(f334(f247(a881),x40772),f334(a116,x40771)))
% 160.93/160.64 [4080]E(f334(f313(x40801,f882(x40801),f334(f334(f7(x40801,f882(x40801),f882(x40801)),f153(x40801)),f117(x40801))),x40802),f176(x40801,x40802,f334(f334(f312(f882(x40801)),f117(x40801)),f196(f888(f882(x40801),a876)))))
% 160.93/160.64 [4081]E(f334(f334(f114(f888(f887(x40811,x40811),a876)),f334(f334(f291(x40811,x40811,x40811),x40812),f310(x40811,x40812))),f310(x40811,f196(f888(f887(x40811,x40811),a876)))),f310(x40811,x40812))
% 160.93/160.64 [4089]P1(f334(f334(f248(f888(f887(x40891,x40891),a876)),f266(x40891,x40892)),f334(f334(f271(x40891,x40891),x40892),f334(f16(f888(x40891,a876),x40891),x40892))))
% 160.93/160.64 [4092]E(f334(f313(a1,a881,a108),f334(f334(f114(f888(a1,a876)),f334(f313(a881,a1,f104(a1)),x40921)),f334(f313(a881,a1,f104(a1)),x40922))),f334(f334(f114(f888(a881,a876)),x40921),x40922))
% 160.93/160.64 [4093]E(f334(f313(a1,a881,a108),f334(f334(f105(f888(a1,a876)),f334(f313(a881,a1,f104(a1)),x40931)),f334(f313(a881,a1,f104(a1)),x40932))),f334(f334(f105(f888(a881,a876)),x40931),x40932))
% 160.93/160.64 [4097]E(f334(f254(x40971),f334(f334(f8(a876,a876,x40971),a329),f334(f334(f7(x40971,f888(x40971,a876),a876),f336(x40971)),x40972))),f334(f79(f888(x40971,a876)),x40972))
% 160.93/160.64 [4124]E(f334(f144(f882(x41241),f882(x41241),f136(x41241),f117(x41241)),f334(f334(f156(f882(x41241),f882(x41241)),f171(x41241)),f334(f171(f882(x41241)),x41242))),f334(f171(x41241),f334(f144(f882(x41241),f882(x41241),f136(x41241),f117(x41241)),x41242)))
% 160.93/160.64 [4154]E(f334(f334(f41(a881,f888(f887(x41541,x41541),a876)),f257(f888(a881,a876))),f334(f334(f7(a881,f888(f887(x41541,x41541),a876),f888(f887(x41541,x41541),a876)),f191(f887(x41541,x41541),a876)),x41542)),f310(x41541,x41542))
% 160.93/160.64 [4174]E(f85(x41741,f334(f334(f8(f888(x41741,a876),a876,x41741),f334(a331,x41742)),f334(f334(f7(x41741,f888(x41741,a876),f888(x41741,a876)),f312(x41741)),f196(f888(x41741,a876))))),f315(x41741,x41742))
% 160.93/160.64 [4182]E(f334(f197(f882(x41821)),f154(x41821,f334(f144(f882(x41821),f882(x41821),f136(x41821),f117(x41821)),x41822))),f334(f37(x41821),f334(f334(f41(f882(x41821),f888(x41821,a876)),f334(f174(f882(x41821)),x41822)),f174(x41821))))
% 160.93/160.64 [4198]E(f334(f334(f114(f888(f887(x41981,x41981),a876)),x41982),f334(f334(f291(x41981,x41981,x41981),f334(f334(f291(x41981,x41981,x41981),x41982),f310(x41981,x41982))),x41982)),f334(f334(f291(x41981,x41981,x41981),x41982),f310(x41981,x41982)))
% 160.93/160.64 [4221]P1(f334(f334(f248(f888(f887(x42211,x42211),a876)),f334(f334(f291(x42211,x42211,x42211),x42212),f310(x42211,x42212))),f334(f334(f271(x42211,x42211),f334(f287(x42211),x42212)),f334(f16(f888(x42211,a876),x42211),f334(f287(x42211),x42212)))))
% 160.93/160.64 [4264]E(f334(f254(f882(x42641)),f334(f334(f7(f882(x42641),f888(x42641,a876),a876),f334(f334(f8(f888(x42641,a876),f888(f888(x42641,a876),a876),f882(x42641)),f248(f888(x42641,a876))),f174(x42641))),x42642)),f163(x42641,x42642))
% 160.93/160.64 [4276]E(f334(f158(f882(x42761),x42761,f117(x42761),f334(f334(f8(f882(x42761),f888(f882(x42761),f882(x42761)),x42761),f334(f7(f882(x42761),f882(x42761),f882(x42761)),f136(x42761))),f334(f334(f7(x42761,f882(x42761),f882(x42761)),f153(x42761)),f117(x42761)))),x42762),f334(f170(x42761),x42762))
% 160.93/160.64 [4318]P27(f888(x43181,x43182),f888(f887(x43181,x43182),a876),f334(f334(f8(f888(f887(x43181,x43182),a876),f888(f887(x43181,x43182),a876),f888(x43181,x43182)),f254(f887(x43181,x43182))),f334(f334(f8(f888(x43181,f888(x43182,a876)),f888(f887(x43181,x43182),a876),f888(x43181,x43182)),f273(x43181,x43182,a876)),f334(f8(x43182,f888(x43182,a876),x43181),f334(f7(x43182,x43182,a876),a331)))),f257(f888(f888(x43181,x43182),a876)))
% 160.93/160.64 [4323]E(f44(a1,f334(f107(a1),f334(f334(f80(a1),x43231),x43231)),f334(f107(a1),f334(f334(f80(a1),x43232),x43232))),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f44(a1,f334(f107(a1),x43231),f334(f107(a1),x43232))))
% 160.93/160.64 [4366]E(f334(f334(f41(x43661,f888(f887(x43661,x43661),a876)),x43662),f334(f334(f7(x43661,f888(f887(x43661,x43661),a876),f888(f887(x43661,x43661),a876)),f334(f334(f8(f887(x43661,x43661),f888(f888(f887(x43661,x43661),a876),f888(f887(x43661,x43661),a876)),x43661),f312(f887(x43661,x43661))),f334(f334(f18(x43661,x43661,f887(x43661,x43661)),f269(x43661,x43661)),f5(x43661)))),f196(f888(f887(x43661,x43661),a876)))),f266(x43661,x43662))
% 160.93/160.64 [4374]E(f215(x43741,f334(f334(f269(a1,a1),f334(f79(a1),f334(f334(f73(f887(a1,a1),a1,x43741,f268(a1,a1)),f225(x43741)),x43742))),f334(f334(f73(f887(a1,a1),a1,x43741,f272(a1,a1)),f225(x43741)),x43742))),f233(x43741,x43742))
% 160.93/160.64 [4456]E(f334(f254(f888(x44561,a876)),f334(f334(f8(f888(f888(x44561,a876),a876),a876,f888(x44561,a876)),f87(f888(x44561,a876))),f334(f334(f7(f888(x44561,a876),f888(f888(x44561,a876),a876),f888(f888(x44561,a876),a876)),f334(f334(f8(f888(f888(x44561,a876),f888(a876,a876)),f888(f888(f888(x44561,a876),a876),f888(f888(x44561,a876),a876)),f888(x44561,a876)),f18(f888(x44561,a876),a876,a876)),f334(f334(f8(f888(f888(x44561,a876),a876),f888(f888(x44561,a876),f888(a876,a876)),f888(x44561,a876)),f334(f8(a876,f888(a876,a876),f888(x44561,a876)),a332)),f334(f334(f7(f888(x44561,a876),f888(f888(x44561,a876),f888(x44561,a876)),f888(f888(x44561,a876),a876)),f334(f334(f8(f888(f888(x44561,a876),a876),f888(f888(f888(x44561,a876),f888(x44561,a876)),f888(f888(x44561,a876),a876)),f888(x44561,a876)),f8(f888(x44561,a876),a876,f888(x44561,a876))),a331)),f79(f888(x44561,a876)))))),f334(f334(f8(f888(f888(x44561,a876),a876),a876,f888(x44561,a876)),f334(f336(f888(x44561,a876)),x44562)),f311(x44561))))),f334(f311(x44561),f334(f79(f888(x44561,a876)),x44562)))
% 160.93/160.64 [4559]~E(f334(f334(f80(a1),x45591),x45591),f334(f334(f22(a1),f334(f334(f80(a1),x45592),x45592)),a101))
% 160.93/160.64 [4565]~P1(f334(f334(f249(a881),f334(f334(f80(a881),x45651),x45652)),x45652))
% 160.93/160.64 [4566]~P1(f334(f334(f249(a881),f334(f334(f80(a881),x45661),x45662)),x45661))
% 160.93/160.64 [3785]E(f334(f334(f22(a881),x37851),f334(f334(f81(a881),f334(f334(f38(a881),x37851),x37852)),x37852)),f44(a881,x37851,x37852))
% 160.93/160.64 [3786]E(f334(f334(f22(a1),x37861),f334(f334(f81(a1),f334(f334(f38(a1),x37861),x37862)),x37862)),f44(a1,x37861,x37862))
% 160.93/160.64 [3820]E(f334(f334(f156(a881,x38201),f334(f167(x38201),x38202)),f141(a881,f334(f304(a881,f2(a881)),f334(f197(f882(x38201)),x38202)))),x38202)
% 160.93/160.64 [3880]E(f334(f288(x38801,x38801,f310(x38801,f196(f888(f887(x38801,x38801),a876)))),x38802),x38802)
% 160.93/160.64 [4009]E(f310(x40091,f334(f334(f114(f888(f887(x40091,x40091),a876)),x40092),f310(x40091,f196(f888(f887(x40091,x40091),a876))))),f310(x40091,x40092))
% 160.93/160.64 [4010]E(f310(x40101,f334(f334(f22(f888(f887(x40101,x40101),a876)),x40102),f310(x40101,f196(f888(f887(x40101,x40101),a876))))),f310(x40101,x40102))
% 160.93/160.64 [4063]E(f334(f334(f22(a1),f334(f334(f22(a1),f334(f334(f80(a1),x40631),x40631)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),x40632),x40632)),a101)),f334(f334(f80(a1),f334(f334(f22(a1),x40631),x40632)),f334(f334(f22(a1),x40631),x40632)))
% 160.93/160.64 [4102]E(f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f80(a1),x41021),x41022)),f334(f334(f80(a1),x41021),x41022))),a101),f334(f334(f80(a1),f334(f334(f80(a1),x41021),x41021)),f334(f334(f22(a1),f334(f334(f80(a1),x41022),x41022)),a101)))
% 160.93/160.64 [4128]E(f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),x41281),x41281)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),x41282),x41282)),a101)),f334(f334(f80(a1),f334(f334(f80(a1),x41281),f334(f334(f22(a1),x41282),a101))),f334(f334(f80(a1),x41281),f334(f334(f22(a1),x41282),a101))))
% 160.93/160.64 [4138]E(f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),x41381),x41382)),f334(f334(f22(a1),x41381),x41382))),a101),f334(f334(f22(a1),f334(f334(f22(a1),f334(f334(f80(a1),x41381),x41381)),a101)),f334(f334(f80(a1),x41382),x41382)))
% 160.93/160.64 [4139]E(f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f80(a1),x41391),x41392)),f334(f334(f80(a1),x41391),x41392))),a101),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),x41391),x41391)),a101)),f334(f334(f80(a1),x41392),x41392)))
% 160.93/160.64 [4195]E(f334(f104(a1),f334(f334(f38(a881),f334(f334(f81(a881),f334(a108,f334(f75(a1),x41951))),f334(a108,f334(f75(a1),x41952)))),f229(f334(a108,f334(f75(a1),x41951)),f334(a108,f334(f75(a1),x41952))))),f231(x41951,x41952))
% 160.93/160.64 [4241]E(f334(f334(f275(f887(a103,a103),a103,f887(a103,a103),f887(x42411,f887(a103,a103))),f279(f334(a3,f334(f197(f882(x42411)),x42412)))),f334(f334(f8(x42411,f888(f887(a103,a103),f887(x42411,f887(a103,a103))),a103),f269(x42411,f887(a103,a103))),f334(f334(f8(a881,x42411,a103),f334(f167(x42411),x42412)),a19))),f285(x42411,x42412))
% 160.93/160.64 [4324]E(f334(f144(a881,f882(x43241),f334(f7(f882(x43241),a881,a881),f334(f334(f8(a881,f888(a881,a881),f882(x43241)),f247(a881)),f197(f882(x43241)))),f2(a881)),f334(f171(f882(x43241)),f182(x43241,x43242))),f334(f197(f882(f882(x43241))),f334(f138(f882(x43241),f334(f334(f8(a876,a876,f882(x43241)),a329),f334(f334(f7(f882(x43241),f882(x43241),a876),a331),f117(x43241)))),x43242)))
% 160.93/160.64 [4330]E(f334(f334(f41(a881,f888(x43301,a876)),f257(f888(a881,a876))),f334(f334(f7(a881,f888(a881,f888(x43301,a876)),f888(x43301,a876)),f334(f334(f8(f888(a881,a876),f888(f888(a881,f888(x43301,a876)),f888(x43301,a876)),a881),f41(a881,f888(x43301,a876))),f304(a881,f2(a881)))),x43302)),f334(f334(f41(a881,f888(x43301,a876)),f257(f888(a881,a876))),x43302))
% 160.93/160.64 [4350]P1(f334(f61(a881),f334(f254(a881),f334(f334(f18(a881,a876,a876),f334(f334(f8(a876,f888(a876,a876),a881),a332),x43501)),f334(f334(f7(a881,a881,a876),f249(a881)),x43502)))))
% 160.93/160.64 [4467]E(f334(f254(f887(f882(x44671),f882(x44671))),f334(f273(f882(x44671),f882(x44671),a876),f334(f334(f18(f882(x44671),f888(f882(x44671),a876),f888(f882(x44671),a876)),f334(f334(f8(f888(f882(x44671),f888(a876,a876)),f888(f888(f882(x44671),a876),f888(f882(x44671),a876)),f882(x44671)),f18(f882(x44671),a876,a876)),f334(f334(f8(f888(f882(x44671),a876),f888(f882(x44671),f888(a876,a876)),f882(x44671)),f334(f8(a876,f888(a876,a876),f882(x44671)),a333)),f334(f334(f7(f882(x44671),f888(f882(x44671),a881),f888(f882(x44671),a876)),f334(f334(f8(f888(a881,a876),f888(f888(f882(x44671),a881),f888(f882(x44671),a876)),f882(x44671)),f8(a881,a876,f882(x44671))),f334(f334(f8(a881,f888(a881,a876),f882(x44671)),f249(a881)),f197(f882(x44671))))),f197(f882(x44671)))))),f334(f334(f18(f882(x44671),f888(f882(x44671),a876),f888(f882(x44671),a876)),f334(f334(f8(f888(f882(x44671),f888(a876,a876)),f888(f888(f882(x44671),a876),f888(f882(x44671),a876)),f882(x44671)),f18(f882(x44671),a876,a876)),f334(f334(f8(f888(f882(x44671),a876),f888(f882(x44671),f888(a876,a876)),f882(x44671)),f334(f8(a876,f888(a876,a876),f882(x44671)),a332)),f334(f334(f7(f882(x44671),f888(f882(x44671),a881),f888(f882(x44671),a876)),f334(f334(f8(f888(a881,a876),f888(f888(f882(x44671),a881),f888(f882(x44671),a876)),f882(x44671)),f8(a881,a876,f882(x44671))),f334(f334(f8(a881,f888(a881,a876),f882(x44671)),a331),f197(f882(x44671))))),f197(f882(x44671)))))),f334(f334(f7(f882(x44671),f888(f887(f882(x44671),f882(x44671)),a876),f888(f882(x44671),a876)),f334(f334(f8(f888(f882(x44671),f888(f888(f887(f882(x44671),f882(x44671)),a876),a876)),f888(f888(f887(f882(x44671),f882(x44671)),a876),f888(f882(x44671),a876)),f882(x44671)),f7(f882(x44671),f888(f887(f882(x44671),f882(x44671)),a876),a876)),f334(f334(f8(f888(f882(x44671),f887(f882(x44671),f882(x44671))),f888(f882(x44671),f888(f888(f887(f882(x44671),f882(x44671)),a876),a876)),f882(x44671)),f334(f8(f887(f882(x44671),f882(x44671)),f888(f888(f887(f882(x44671),f882(x44671)),a876),a876),f882(x44671)),f336(f887(f882(x44671),f882(x44671))))),f269(f882(x44671),f882(x44671))))),f147(x44671,x44672)))))),f148(x44671,x44672))
% 160.93/160.64 [4571]~P1(f334(f334(f91(a1),f334(f334(f80(a1),x45711),x45711)),f334(f334(f22(a1),f334(f334(f80(a1),x45712),x45712)),a101)))
% 160.93/160.64 [4131]E(f334(f334(f80(a1),f334(f334(f80(a1),f334(f334(f81(a1),x41311),x41312)),f334(f334(f81(a1),x41311),x41312))),x41312),f334(f334(f81(a1),f334(f334(f22(a1),f334(f334(f80(a1),x41311),x41311)),a101)),x41312))
% 160.93/160.64 [4239]E(f334(a108,f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x42391),x42392)),f196(f888(f887(a881,a881),a876)))))),f334(f334(f22(a881),x42391),x42392))
% 160.93/160.64 [4244]E(f334(f334(f291(x42441,x42441,x42441),f334(f334(f114(f888(f887(x42441,x42441),a876)),x42442),f310(x42441,f196(f888(f887(x42441,x42441),a876))))),f310(x42441,f334(f334(f114(f888(f887(x42441,x42441),a876)),x42442),f310(x42441,f196(f888(f887(x42441,x42441),a876)))))),f310(x42441,x42442))
% 160.93/160.64 [4282]E(f280(x42821,f334(f138(f887(a103,x42821),f334(f273(a103,x42821,a876),f334(f334(f8(a876,f888(x42821,a876),a103),f16(a876,x42821)),f334(f249(a103),f2(a103))))),x42822)),f280(x42821,x42822))
% 160.93/160.64 [4283]E(f278(x42831,f334(f138(f887(a103,x42831),f334(f273(a103,x42831,a876),f334(f334(f8(a876,f888(x42831,a876),a103),f16(a876,x42831)),f334(f249(a103),f2(a103))))),x42832)),f278(x42831,x42832))
% 160.93/160.64 [4285]E(f334(f79(a1),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x42851),x42852)),f196(f888(f887(a881,a881),a876)))))),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x42852),x42851)),f196(f888(f887(a881,a881),a876))))))
% 160.93/160.64 [4342]E(f334(f334(f290(f882(a881),x43421),f147(a881,a253)),f334(f334(f7(x43421,f882(f888(x43421,a881)),f882(a881)),f334(f334(f8(f888(f888(x43421,a881),a881),f888(f882(f888(x43421,a881)),f882(a881)),x43421),f156(f888(x43421,a881),a881)),f334(f7(f888(x43421,a881),x43421,a881),f5(f888(x43421,a881))))),x43422)),f155(x43421,x43422))
% 160.93/160.64 [4363]E(f334(f334(f86(a1,a881),f334(f107(a1),f334(f334(f80(a1),x43631),a101))),f334(f334(f18(a1,a881,a881),f334(f334(f7(a1,a881,f888(a881,a881)),f334(f334(f8(a876,f888(a881,f888(a881,a881)),a1),f100(a881)),a201)),f2(a881))),f334(f334(f8(a881,a881,a1),a116),f334(f334(f8(a881,a881,a1),f334(f246(a881),x43632)),a108)))),f334(f334(f246(a881),f334(a116,x43632)),f334(f107(a881),x43631)))
% 160.93/160.64 [4364]E(f334(f334(f86(a1,a881),f334(f107(a1),f334(f334(f80(a1),x43641),a101))),f334(f334(f18(a1,a881,a881),f334(f334(f7(a1,a881,f888(a881,a881)),f334(f334(f8(a876,f888(a881,f888(a881,a881)),a1),f100(a881)),a201)),f334(a116,x43642))),f334(f334(f8(a881,a881,a1),a116),f334(f334(f8(a881,a881,a1),f334(f247(a881),x43642)),a108)))),f334(f334(f247(a881),f334(a116,x43642)),f334(f107(a881),x43641)))
% 160.93/160.64 [4384]E(f334(f144(f882(x43841),f882(x43841),f136(x43841),f117(x43841)),f334(f334(f156(f882(x43841),f882(x43841)),f158(f882(x43841),x43841,f117(x43841),f334(f334(f8(f882(x43841),f888(f882(x43841),f882(x43841)),x43841),f16(f882(x43841),f882(x43841))),f334(f334(f7(x43841,f882(x43841),f882(x43841)),f153(x43841)),f117(x43841))))),x43842)),f334(f334(f156(f882(x43841),x43841),f143(x43841)),f334(f138(f882(x43841),f334(f334(f8(a876,a876,f882(x43841)),a329),f334(f334(f7(f882(x43841),f882(x43841),a876),a331),f117(x43841)))),x43842)))
% 160.93/160.64 [4448]E(f334(f273(a1,a1,a876),f334(f334(f7(a1,f888(a1,a876),f888(a1,a876)),f334(f334(f8(f888(a1,f888(a876,a876)),f888(f888(a1,a876),f888(a1,a876)),a1),f18(a1,a876,a876)),f334(f334(f8(f888(a1,a876),f888(a1,f888(a876,a876)),a1),f334(f8(a876,f888(a876,a876),a1),a332)),f334(f334(f8(f888(a1,a1),f888(a1,a876),a1),f334(f8(a1,a876,a1),f334(a331,x44481))),f334(f334(f8(a1,f888(a1,a1),a1),f80(a1)),f334(f81(a1),x44482)))))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f334(f8(a876,a876,a1),f334(a337,f334(f334(f249(a1),f2(a1)),x44482))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f248(a1),f2(a1)))),f334(f334(f7(a1,a1,a876),f249(a1)),x44482))))),f334(f334(f8(a876,a876,a1),f334(a337,f334(a329,f334(f334(f249(a1),f2(a1)),x44482)))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f249(a1),x44482))),f334(f334(f7(a1,a1,a876),f248(a1)),f2(a1))))))),f48(x44481,x44482))
% 160.93/160.64 [4450]E(f334(f254(x44501),f334(f334(f8(f888(a881,a876),a876,x44501),f87(a881)),f334(f334(f7(x44501,f888(a881,a876),f888(a881,a876)),f334(f334(f8(f888(a881,f888(a876,a876)),f888(f888(a881,a876),f888(a881,a876)),x44501),f18(a881,a876,a876)),f334(f334(f8(f888(a881,a876),f888(a881,f888(a876,a876)),x44501),f334(f8(a876,f888(a876,a876),a881),a332)),f334(f334(f7(x44501,f888(a881,x44501),f888(a881,a876)),f334(f334(f8(f888(x44501,a876),f888(f888(a881,x44501),f888(a881,a876)),x44501),f8(x44501,a876,a881)),a331)),f334(f167(x44501),x44502))))),f334(f334(f7(a881,a881,a876),f249(a881)),f334(f197(f882(x44501)),x44502))))),f334(f174(x44501),x44502))
% 160.93/160.64 [4254]E(f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),x42541),a101)),x42542)),f334(f334(f22(a1),f334(f334(f80(a1),x42541),a101)),x42542))),a101),f334(f334(f22(a1),f334(f334(f80(a1),x42541),x42541)),f334(f334(f22(a1),f334(f334(f80(a1),x42542),x42542)),a101)))
% 160.93/160.64 [4379]E(f334(f144(f882(f882(x43791)),f882(f882(x43791)),f136(f882(x43791)),f117(f882(x43791))),f334(f334(f156(f882(x43791),f882(f882(x43791))),f158(f882(f882(x43791)),x43791,f117(f882(x43791)),f334(f16(f888(f882(x43791),f882(f882(x43791))),x43791),f334(f334(f7(f882(x43791),f882(f882(x43791)),f882(f882(x43791))),f153(f882(x43791))),f117(f882(x43791)))))),x43792)),f334(f334(f156(f882(x43791),f882(x43791)),f173(x43791)),f334(f138(f882(x43791),f334(f334(f8(a876,a876,f882(x43791)),a329),f334(f334(f7(f882(x43791),f882(x43791),a876),a331),f117(x43791)))),x43792)))
% 160.93/160.64 [4390]E(f334(f334(f86(a1,a881),f334(f107(a1),f334(f334(f80(a1),x43901),a101))),f334(f334(f18(a1,a881,a881),f334(f334(f7(a1,a881,f888(a881,a881)),f334(f334(f8(a876,f888(a881,f888(a881,a881)),a1),f100(a881)),a201)),f2(a881))),f334(f334(f8(a881,a881,a1),a116),f334(f334(f7(a1,a881,a881),f334(f334(f8(a881,f888(a881,a881),a1),f246(a881)),a108)),x43902)))),f334(f334(f246(a881),f334(f107(a881),x43901)),f334(a116,x43902)))
% 160.93/160.64 [4391]E(f334(f334(f86(a1,a881),f334(f107(a1),f334(f334(f80(a1),x43911),a101))),f334(f334(f18(a1,a881,a881),f334(f334(f7(a1,a881,f888(a881,a881)),f334(f334(f8(a876,f888(a881,f888(a881,a881)),a1),f100(a881)),a201)),f334(a116,x43912))),f334(f334(f8(a881,a881,a1),a116),f334(f334(f7(a1,a881,a881),f334(f334(f8(a881,f888(a881,a881),a1),f247(a881)),a108)),x43912)))),f334(f334(f247(a881),f334(f107(a881),x43911)),f334(a116,x43912)))
% 160.93/160.64 [4378]E(f334(f273(x43781,x43781,a876),f334(f334(f18(x43781,a876,f888(x43781,a876)),f334(f334(f8(f888(x43781,f888(a876,a876)),f888(a876,f888(x43781,a876)),x43781),f7(x43781,a876,a876)),f334(f334(f8(f888(x43781,a876),f888(x43781,f888(a876,a876)),x43781),f334(f8(a876,f888(a876,a876),x43781),a332)),a331))),x43782)),f266(x43781,x43782))
% 160.93/160.64 [4425]E(f334(f334(f38(a881),x44251),f334(f334(f80(a881),f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),a101))),x44252)),f334(f334(f38(a881),x44251),f334(a116,f334(a116,f334(a116,x44252)))))
% 160.93/160.64 [4426]E(f44(a881,x44261,f334(f334(f80(a881),f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),a101))),x44262)),f44(a881,x44261,f334(a116,f334(a116,f334(a116,x44262)))))
% 160.93/160.64 [4427]E(f44(a881,f334(f334(f80(a881),f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),a101))),x44271),x44272),f44(a881,f334(a116,f334(a116,f334(a116,x44271))),x44272))
% 160.93/160.64 [4441]E(f126(f334(x44411,f334(f334(f81(a103),f334(f107(a103),f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),a101))),x44412))),f334(f213(x44411),x44412))
% 160.93/160.64 [4442]E(f334(f334(f38(a881),f334(f334(f80(a881),f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),a101))),x44421)),x44422),f334(f334(f38(a881),f334(a116,f334(a116,f334(a116,x44421)))),x44422))
% 160.93/160.64 [4491]~E(f33(x44911,x44912),f334(a26,x44913))
% 160.93/160.64 [4492]~E(f32(x44921,x44922),f334(a26,x44923))
% 160.93/160.64 [4493]~E(f334(a26,x44931),f33(x44932,x44933))
% 160.93/160.64 [4494]~E(f334(a26,x44941),f32(x44942,x44943))
% 160.93/160.64 [4507]~E(f30(x45071,x45072,x45073),a24)
% 160.93/160.64 [4508]~E(f29(x45081,x45082,x45083),a24)
% 160.93/160.64 [3210]E(f334(f200(x32101,x32102),x32103),f123(x32101,x32102))
% 160.93/160.64 [3232]E(f334(f212(x32321,x32322),x32323),f334(f128(x32321),x32322))
% 160.93/160.64 [3310]E(f334(f334(f156(x33101,x33102),x33103),f117(x33101)),f117(x33102))
% 160.93/160.64 [3311]E(f334(f334(f211(x33111,x33112),x33113),f210(x33111)),f210(x33112))
% 160.93/160.64 [3351]E(f334(f192(x33511,x33512,x33513),f2(a881)),x33512)
% 160.93/160.64 [3353]E(f334(f334(f184(x33531,x33532),x33533),f117(x33532)),f117(f887(x33531,x33532)))
% 160.93/160.64 [3387]E(f85(x33871,f62(x33871,x33872,x33873)),f334(f63(x33871,x33872),x33873))
% 160.93/160.64 [3393]E(f258(x33931,x33932,f258(x33932,x33931,x33933)),x33933)
% 160.93/160.64 [3441]E(f142(x34411,x34412,f154(x34411,x34413)),f154(x34411,f142(x34411,x34412,x34413)))
% 160.93/160.64 [3460]E(f334(f268(f882(x34601),f882(x34601)),f169(x34601,x34602,x34603)),f334(f138(x34601,x34602),x34603))
% 160.93/160.64 [3538]E(f193(x35381,x35382,x35383,f2(a881)),x35382)
% 160.93/160.64 [3539]E(f17(x35391,x35392,x35393,f2(a103)),x35392)
% 160.93/160.64 [3546]E(f165(x35461,x35462,x35463,f117(x35461)),f117(x35462))
% 160.93/160.64 [3547]E(f166(x35471,x35472,x35473,f117(x35471)),f117(x35472))
% 160.93/160.64 [3554]E(f334(f334(f167(x35541),f334(f334(f153(x35541),x35542),x35543)),f2(a881)),x35542)
% 160.93/160.64 [3582]E(f59(x35821,x35822,f117(x35821),x35823),f117(f887(x35821,x35822)))
% 160.93/160.64 [3603]P27(x36031,x36032,x36033,f196(f888(x36031,a876)))
% 160.93/160.64 [3761]E(f334(f73(x37611,x37612,x37611,x37613),f34(x37611)),x37613)
% 160.93/160.64 [3938]P1(f334(f334(f336(f887(x39381,x39381)),f334(f334(f269(x39381,x39381),x39382),x39382)),f310(x39381,x39383)))
% 160.93/160.64 [4572]~P1(f334(f334(f336(f887(f882(x45721),f882(x45721))),f334(f334(f269(f882(x45721),f882(x45721)),x45722),f117(x45721))),f147(x45721,x45723)))
% 160.93/160.64 [4573]~P1(f334(f334(f336(f887(f882(x45731),f882(x45731))),f334(f334(f269(f882(x45731),f882(x45731)),x45732),f117(x45731))),f149(x45731,x45733)))
% 160.93/160.64 [4574]~P1(f334(f334(f336(f887(f882(x45741),f882(x45741))),f334(f334(f269(f882(x45741),f882(x45741)),x45742),f117(x45741))),f159(x45741,x45743)))
% 160.93/160.64 [4575]~P1(f334(f334(f336(f887(f882(x45751),f882(x45751))),f334(f334(f269(f882(x45751),f882(x45751)),f117(x45751)),x45752)),f147(x45751,x45753)))
% 160.93/160.64 [4576]~P1(f334(f334(f336(f887(f882(x45761),f882(x45761))),f334(f334(f269(f882(x45761),f882(x45761)),f117(x45761)),x45762)),f159(x45761,x45763)))
% 160.93/160.64 [3285]E(f334(f334(f214(x32851),x32852),x32853),f215(x32851,f228(x32852,x32853)))
% 160.93/160.64 [3340]E(f334(f289(x33401,x33402),f334(f289(x33402,x33401),x33403)),x33403)
% 160.93/160.64 [3363]E(f334(f334(f184(x33631,x33632),f117(x33631)),x33633),f117(f887(x33631,x33632)))
% 160.93/160.64 [3366]E(f178(x33661,x33662,f334(f255(a881),x33663)),f334(f334(f177(x33661),x33663),x33662))
% 160.93/160.64 [3384]E(f154(x33841,f334(f138(x33841,x33842),x33843)),f334(f138(x33841,x33842),f154(x33841,x33843)))
% 160.93/160.64 [3385]E(f334(f265(x33851,x33852),f334(f289(x33852,x33851),x33853)),f334(f267(x33852,x33851),x33853))
% 160.93/160.64 [3386]E(f334(f267(x33861,x33862),f334(f289(x33862,x33861),x33863)),f334(f265(x33862,x33861),x33863))
% 160.93/160.64 [3405]E(f334(f138(x34051,x34052),f334(f171(x34051),x34053)),f334(f171(x34051),f334(f138(x34051,x34052),x34053)))
% 160.93/160.64 [3418]E(f334(f334(f140(x34181),x34182),f334(f173(x34181),x34183)),f334(f334(f140(x34181),f334(a116,x34182)),x34183))
% 160.93/160.64 [3436]E(f31(f29(x34361,x34362,x34363)),f334(f334(f80(a881),f31(x34363)),f334(a116,f2(a881))))
% 160.93/160.64 [3437]E(f334(f313(x34371,x34372,x34373),f196(f888(x34371,a876))),f196(f888(x34372,a876)))
% 160.93/160.64 [3438]E(f334(f288(x34381,x34382,x34383),f196(f888(x34381,a876))),f196(f888(x34382,a876)))
% 160.93/160.64 [3439]E(f334(f314(x34391,x34392,x34393),f196(f888(x34392,a876))),f196(f888(x34391,a876)))
% 160.93/160.64 [3440]E(f334(f314(x34401,x34402,x34403),f257(f888(x34402,a876))),f257(f888(x34401,a876)))
% 160.93/160.64 [3468]E(f334(f334(f312(x34681),x34682),f334(f174(x34681),x34683)),f334(f174(x34681),f142(x34681,x34682,x34683)))
% 160.93/160.64 [3480]E(f242(x34801,x34802,f334(f241(x34801),x34803)),f334(f334(f80(a881),f334(x34802,x34803)),f334(a116,f2(a881))))
% 160.93/160.64 [3558]E(f334(f197(a878),f29(x35581,x35582,x35583)),f334(f334(f80(a881),f334(f197(a878),x35583)),f334(a116,f2(a881))))
% 160.93/160.64 [3559]E(f334(f313(f887(x35591,x35592),x35592,f272(x35591,x35592)),x35593),f334(f265(x35591,x35592),x35593))
% 160.93/160.64 [3560]E(f334(f313(f887(x35601,x35602),x35601,f268(x35601,x35602)),x35603),f334(f267(x35601,x35602),x35603))
% 160.93/160.64 [3629]E(f334(f334(f269(x36291,x36292),f334(f268(x36291,x36292),x36293)),f334(f272(x36291,x36292),x36293)),x36293)
% 160.93/160.64 [3636]E(f334(f197(f883(x36361)),f129(x36361,x36362,x36363)),f334(f334(f80(a881),f334(f197(f883(x36361)),x36363)),f334(a116,f2(a881))))
% 160.93/160.64 [3639]E(f334(f334(f273(x36391,x36392,x36391),f16(x36391,x36392)),x36393),f334(f268(x36391,x36392),x36393))
% 160.93/160.64 [3659]E(f187(x36591,x36592,x36593,f334(f16(f885(x36592),x36591),f210(x36592))),x36593)
% 160.93/160.64 [3660]E(f187(x36601,x36602,f334(f16(f885(x36602),x36601),f210(x36602)),x36603),x36603)
% 160.93/160.64 [3716]E(f31(f30(x37161,x37162,x37163)),f334(f334(f80(a881),f334(f334(f80(a881),f31(x37162)),f31(x37163))),f334(a116,f2(a881))))
% 160.93/160.64 [3765]E(f334(f73(x37651,x37651,x37652,f34(x37651)),x37653),x37653)
% 160.93/160.64 [3873]E(f334(f197(a878),f30(x38731,x38732,x38733)),f334(f334(f80(a881),f334(f334(f80(a881),f334(f197(a878),x38732)),f334(f197(a878),x38733))),f334(a116,f2(a881))))
% 160.93/160.64 [3949]P1(f334(f334(f248(f888(x39491,a876)),f334(f174(x39491),f334(f138(x39491,x39492),x39493))),f334(f174(x39491),x39493)))
% 160.93/160.64 [3994]P1(f334(f334(f248(f888(x39941,a876)),f334(f174(x39941),f334(f334(f177(x39941),x39942),x39943))),f334(f174(x39941),x39943)))
% 160.93/160.64 [3995]P1(f334(f334(f248(f888(x39951,a876)),f334(f174(x39951),f334(f334(f140(x39951),x39952),x39953))),f334(f174(x39951),x39953)))
% 160.93/160.64 [4000]P1(f334(f334(f248(f888(x40001,a876)),f334(f174(x40001),f178(x40001,x40002,x40003))),f334(f174(x40001),x40002)))
% 160.93/160.64 [4001]P1(f334(f334(f248(f888(x40011,a876)),f334(f174(x40011),f172(x40011,x40012,x40013))),f334(f174(x40011),x40013)))
% 160.93/160.64 [4023]P27(f887(x40231,x40232),f887(x40232,x40231),f334(f273(x40231,x40232,f887(x40232,x40231)),f334(f7(x40232,x40231,f887(x40232,x40231)),f269(x40232,x40231))),x40233)
% 160.93/160.64 [4035]E(f334(f334(f334(f191(f882(x40351),f882(x40351)),f44(a881,x40352,f334(f197(f882(x40351)),x40353))),f170(x40351)),x40353),f334(f334(f334(f191(f882(x40351),f882(x40351)),x40352),f170(x40351)),x40353))
% 160.93/160.64 [4078]P1(f334(f334(f336(f887(f882(x40781),f882(x40781))),f334(f334(f269(f882(x40781),f882(x40781)),x40782),x40782)),f160(x40781,f310(x40781,x40783))))
% 160.93/160.64 [4224]E(f85(f887(x42241,x42242),f334(f334(f18(f887(x42241,x42242),x42242,a876),f334(f334(f8(x42241,f888(x42242,a876),f887(x42241,x42242)),x42243),f268(x42241,x42242))),f272(x42241,x42242))),f85(f887(x42241,x42242),f334(f273(x42241,x42242,a876),x42243)))
% 160.93/160.64 [4225]E(f90(f887(x42251,x42252),f334(f334(f18(f887(x42251,x42252),x42252,a876),f334(f334(f8(x42251,f888(x42252,a876),f887(x42251,x42252)),x42253),f268(x42251,x42252))),f272(x42251,x42252))),f90(f887(x42251,x42252),f334(f273(x42251,x42252,a876),x42253)))
% 160.93/160.64 [4261]E(f334(f334(f290(f887(a881,x42611),x42611),f326(a881,x42611,a253,x42612)),f334(f334(f18(x42611,x42611,f887(a881,x42611)),f334(f334(f8(a881,f888(x42611,f887(a881,x42611)),x42611),f269(a881,x42611)),x42613)),f5(x42611))),f328(x42611,x42613,x42612))
% 160.93/160.64 [4326]E(f334(f274(x43261,x43261,x43262,x43262,f5(x43261),f5(x43262)),x43263),x43263)
% 160.93/160.64 [4401]E(f334(f144(f882(f882(x44011)),f882(f882(x44011)),f136(f882(x44011)),f117(f882(x44011))),f334(f334(f156(f882(x44011),f882(f882(x44011))),f334(f334(f7(f882(x44011),f882(x44011),f882(f882(x44011))),f334(f334(f8(f888(x44011,f882(x44011)),f888(f882(x44011),f882(f882(x44011))),f882(x44011)),f156(x44011,f882(x44011))),f334(f7(x44011,f882(x44011),f882(x44011)),f153(x44011)))),x44012)),f54(x44011,x44013,x44012))),f54(x44011,f334(a116,x44013),x44012))
% 160.93/160.64 [4463]E(f334(f243(a881,f887(x44631,f883(x44631)),f2(a881),f334(f273(x44631,f883(x44631),a881),f334(f334(f7(x44631,a881,f888(f883(x44631),a881)),f334(f334(f8(f888(f883(x44631),f888(a881,a881)),f888(a881,f888(f883(x44631),a881)),x44631),f7(f883(x44631),a881,a881)),f334(f334(f8(f888(f883(x44631),a881),f888(f883(x44631),f888(a881,a881)),x44631),f334(f8(a881,f888(a881,a881),f883(x44631)),f80(a881))),f334(f334(f7(x44631,f888(f883(x44631),a881),f888(f883(x44631),a881)),f334(f334(f8(f888(a881,a881),f888(f888(f883(x44631),a881),f888(f883(x44631),a881)),x44631),f8(a881,a881,f883(x44631))),f334(f334(f8(a881,f888(a881,a881),x44631),f80(a881)),x44632))),f131(x44631,x44632))))),f78(a881)))),f334(f137(x44631),x44633)),f334(f131(x44631,x44632),x44633))
% 160.93/160.64 [4466]E(f334(f334(f86(a1,x44661),f231(f334(f334(f73(f887(a1,a1),a1,x44661,f272(a1,a1)),f225(x44661)),x44662),f334(f334(f73(f887(a1,a1),a1,x44661,f272(a1,a1)),f225(x44661)),x44663))),f334(f334(f18(a1,a1,x44661),f334(f334(f8(a1,f888(a1,x44661),a1),f214(x44661)),f334(f334(f18(a1,a1,a1),f334(f334(f8(a1,f888(a1,a1),a1),f80(a1)),f334(f334(f8(a1,a1,a1),f334(f81(a1),f334(f334(f73(f887(a1,a1),a1,x44661,f268(a1,a1)),f225(x44661)),x44662))),f334(f334(f7(a1,a1,a1),f38(a1)),f334(f334(f73(f887(a1,a1),a1,x44661,f272(a1,a1)),f225(x44661)),x44662))))),f334(f334(f8(a1,a1,a1),f334(f81(a1),f334(f334(f73(f887(a1,a1),a1,x44661,f268(a1,a1)),f225(x44661)),x44663))),f334(f334(f7(a1,a1,a1),f38(a1)),f334(f334(f73(f887(a1,a1),a1,x44661,f272(a1,a1)),f225(x44661)),x44663)))))),f5(a1))),f236(x44661,x44662,x44663))
% 160.93/160.64 [4503]~E(f334(f334(f153(x45031),x45032),x45033),x45033)
% 160.93/160.64 [4510]~E(f334(f334(f153(x45101),x45102),x45103),f117(x45101))
% 160.93/160.64 [4526]~E(f334(f334(f312(x45261),x45262),x45263),f196(f888(x45261,a876)))
% 160.93/160.64 [4549]~E(f334(f313(x45491,f888(x45491,a876),x45492),x45493),f334(f311(x45491),x45493))
% 160.93/160.64 [3345]E(f334(f334(f161(x33451,f117(x33451)),x33452),x33453),f117(x33451))
% 160.93/160.64 [3346]E(f334(f143(x33461),f334(f334(f153(x33461),x33462),x33463)),x33462)
% 160.93/160.64 [3347]E(f334(f173(x33471),f334(f334(f153(x33471),x33472),x33473)),x33473)
% 160.93/160.64 [3392]E(f334(f334(f140(x33921),f78(a881)),f334(f334(f153(x33921),x33922),x33923)),x33923)
% 160.93/160.64 [3425]E(f118(x34251,f334(f334(f140(x34251),x34252),x34253)),f334(f334(f140(x34251),x34252),f118(x34251,x34253)))
% 160.93/160.64 [3427]E(f334(f334(f161(x34271,x34272),x34273),f334(f334(f167(x34271),x34272),x34273)),x34272)
% 160.93/160.64 [3451]E(f334(f334(f312(x34511),x34512),f334(f334(f312(x34511),x34512),x34513)),f334(f334(f312(x34511),x34512),x34513))
% 160.93/160.64 [3462]E(f334(f334(f180(x34621,x34622),f117(f887(x34621,x34622))),x34623),f210(x34622))
% 160.93/160.64 [3465]E(f334(f334(f312(x34651),x34652),f334(f174(x34651),x34653)),f334(f174(x34651),f334(f334(f153(x34651),x34652),x34653)))
% 160.93/160.64 [3467]E(f334(f334(f140(x34671),x34672),f334(f173(x34671),x34673)),f334(f173(x34671),f334(f334(f140(x34671),x34672),x34673)))
% 160.93/160.64 [3477]E(f334(f334(f177(x34771),f78(a881)),f334(f334(f153(x34771),x34772),x34773)),f334(f334(f153(x34771),x34772),f117(x34771)))
% 160.93/160.64 [3523]E(f334(f63(x35231,x35232),f334(f334(f312(x35231),x35233),f196(f888(x35231,a876)))),x35233)
% 160.93/160.64 [3566]E(f334(f334(f80(a881),x35661),f334(f334(f80(a881),x35662),x35663)),f334(f334(f80(a881),x35662),f334(f334(f80(a881),x35661),x35663)))
% 160.93/160.64 [3567]E(f334(f334(f80(a1),x35671),f334(f334(f80(a1),x35672),x35673)),f334(f334(f80(a1),x35672),f334(f334(f80(a1),x35671),x35673)))
% 160.93/160.64 [3572]E(f334(f334(f271(x35721,x35722),f196(f888(x35721,a876))),x35723),f196(f888(f887(x35721,x35722),a876)))
% 160.93/160.64 [3595]E(f334(f334(f114(f888(x35951,a876)),x35952),x35953),f334(f334(f114(f888(x35951,a876)),x35953),x35952))
% 160.93/160.64 [3596]E(f334(f334(f105(f888(x35961,a876)),x35962),x35963),f334(f334(f105(f888(x35961,a876)),x35963),x35962))
% 160.93/160.64 [3598]E(f334(f334(f136(x35981),x35982),f334(f334(f153(x35981),x35983),f117(x35981))),f334(f170(x35981),f334(f334(f153(x35981),x35983),x35982)))
% 160.93/160.64 [3599]E(f334(f334(f136(x35991),f334(f171(x35991),x35992)),f334(f171(x35991),x35993)),f334(f171(x35991),f334(f334(f136(x35991),x35993),x35992)))
% 160.93/160.64 [3607]E(f334(f173(x36071),f334(f334(f177(x36071),f334(a116,x36072)),x36073)),f334(f334(f177(x36071),x36072),f334(f173(x36071),x36073)))
% 160.93/160.64 [3614]P1(f334(f334(f336(x36141),x36142),f334(f334(f312(x36141),x36142),x36143)))
% 160.93/160.64 [3618]E(f334(f334(f42(x36181,f888(x36182,a876)),f196(f888(x36181,a876))),x36183),f257(f888(x36182,a876)))
% 160.93/160.64 [3621]E(f334(f288(x36211,x36211,f266(x36211,x36212)),x36213),f334(f334(f105(f888(x36211,a876)),x36212),x36213))
% 160.93/160.64 [3635]E(f334(f197(f882(x36351)),f334(f334(f153(x36351),x36352),x36353)),f334(f334(f80(a881),f334(f197(f882(x36351)),x36353)),f334(a116,f2(a881))))
% 160.93/160.64 [3641]E(f118(x36411,f334(f334(f136(x36411),x36412),f334(f334(f153(x36411),x36413),f117(x36411)))),x36412)
% 160.93/160.64 [3642]E(f146(x36421,f334(f334(f136(x36421),x36422),f334(f334(f153(x36421),x36423),f117(x36421)))),x36423)
% 160.93/160.64 [3648]E(f334(f334(f136(x36481),f334(f334(f177(x36481),x36482),x36483)),f334(f334(f140(x36481),x36482),x36483)),x36483)
% 160.93/160.64 [3657]E(f334(f334(f22(a881),f334(f334(f80(a881),x36571),x36572)),f334(f334(f80(a881),x36573),x36572)),f334(f334(f22(a881),x36571),x36573))
% 160.93/160.64 [3658]E(f334(f334(f22(a881),f334(f334(f80(a881),x36581),x36582)),f334(f334(f80(a881),x36581),x36583)),f334(f334(f22(a881),x36582),x36583))
% 160.93/160.64 [3665]E(f334(f334(f136(x36651),f334(f171(x36651),x36652)),f334(f334(f153(x36651),x36653),f117(x36651))),f334(f171(x36651),f334(f334(f153(x36651),x36653),x36652)))
% 160.93/160.64 [3667]E(f334(f334(f80(a881),f334(f197(f882(x36671)),x36672)),f334(f197(f882(x36671)),x36673)),f334(f197(f882(x36671)),f334(f334(f136(x36671),x36672),x36673)))
% 160.93/160.64 [3670]E(f334(f334(f80(a881),f334(f197(f882(x36701)),x36702)),f334(f197(f882(x36701)),x36703)),f334(f197(f882(x36701)),f175(x36701,x36702,x36703)))
% 160.93/160.64 [3678]E(f334(f334(f114(f888(x36781,a876)),f334(f174(x36781),x36782)),f334(f174(x36781),x36783)),f334(f174(x36781),f334(f334(f136(x36781),x36782),x36783)))
% 160.93/160.64 [3679]E(f44(a881,f334(f334(f81(a881),x36791),x36792),f334(f334(f81(a881),x36791),x36793)),f334(f334(f81(a881),x36791),f44(a881,x36792,x36793)))
% 160.93/160.64 [3692]E(f334(f334(f177(x36921),f334(f334(f22(a881),x36922),f78(a881))),f334(f173(x36921),x36923)),f334(f173(x36921),f334(f334(f177(x36921),x36922),x36923)))
% 160.93/160.64 [3697]E(f334(f334(f105(f888(x36971,a876)),x36972),f334(f79(f888(x36971,a876)),x36973)),f334(f334(f22(f888(x36971,a876)),x36972),x36973))
% 160.93/160.64 [3698]E(f334(f334(f22(f888(x36981,a876)),x36982),f334(f79(f888(x36981,a876)),x36983)),f334(f334(f105(f888(x36981,a876)),x36982),x36983))
% 160.93/160.64 [3720]E(f334(f334(f271(x37201,x37202),x37203),f334(f16(f888(x37202,a876),x37201),f196(f888(x37202,a876)))),f196(f888(f887(x37201,x37202),a876)))
% 160.93/160.64 [3722]E(f334(f334(f22(a881),f334(f334(f81(a881),x37221),x37222)),f334(f334(f81(a881),x37221),x37223)),f334(f334(f81(a881),x37221),f334(f334(f22(a881),x37222),x37223)))
% 160.93/160.64 [3723]E(f334(f334(f80(a881),f334(f334(f81(a881),x37231),x37232)),f334(f334(f81(a881),x37231),x37233)),f334(f334(f81(a881),x37231),f334(f334(f80(a881),x37232),x37233)))
% 160.93/160.64 [3724]E(f334(f334(f22(a1),f334(f334(f81(a1),x37241),x37242)),f334(f334(f81(a1),x37241),x37243)),f334(f334(f81(a1),x37241),f334(f334(f22(a1),x37242),x37243)))
% 160.93/160.64 [3725]E(f334(f334(f80(a1),f334(f334(f81(a1),x37251),x37252)),f334(f334(f81(a1),x37251),x37253)),f334(f334(f81(a1),x37251),f334(f334(f80(a1),x37252),x37253)))
% 160.93/160.64 [3726]E(f334(f334(f81(a1),f334(f334(f259(a1),x37261),x37262)),f334(f334(f259(a1),x37261),x37263)),f334(f334(f259(a1),x37261),f334(f334(f80(a881),x37262),x37263)))
% 160.93/160.64 [3740]E(f334(f334(f41(x37401,f888(x37402,a876)),x37403),f334(f16(f888(x37402,a876),x37401),f196(f888(x37402,a876)))),f196(f888(x37402,a876)))
% 160.93/160.64 [3742]E(f44(a881,f334(f334(f81(a881),x37421),x37422),f334(f334(f81(a881),x37423),x37422)),f334(f334(f81(a881),f44(a881,x37421,x37423)),x37422))
% 160.93/160.64 [3746]E(f44(a1,f334(f334(f22(a1),x37461),f44(a1,x37462,x37463)),x37463),f44(a1,f334(f334(f22(a1),x37461),x37462),x37463))
% 160.93/160.64 [3747]E(f44(a1,f334(f334(f81(a1),x37471),f44(a1,x37472,x37473)),x37473),f44(a1,f334(f334(f81(a1),x37471),x37472),x37473))
% 160.93/160.64 [3748]P1(f334(f334(f248(f888(x37481,a876)),x37482),f334(f334(f312(x37481),x37483),x37482)))
% 160.93/160.64 [3751]E(f334(f313(f887(x37511,x37512),x37511,f268(x37511,x37512)),f334(f174(f887(x37511,x37512)),x37513)),f186(x37511,x37512,f334(f180(x37511,x37512),x37513)))
% 160.93/160.64 [3799]P1(f334(f61(x37991),f186(x37991,x37992,f334(f180(x37991,x37992),x37993))))
% 160.93/160.64 [3824]E(f334(f334(f42(f888(x38241,a876),f888(x38241,a876)),x38242),f334(f114(f888(x38241,a876)),x38243)),f334(f334(f114(f888(x38241,a876)),x38243),f40(f888(x38241,a876),x38242)))
% 160.93/160.64 [3825]E(f334(f334(f41(f888(x38251,a876),f888(x38251,a876)),x38252),f334(f105(f888(x38251,a876)),x38253)),f334(f334(f105(f888(x38251,a876)),x38253),f39(f888(x38251,a876),x38252)))
% 160.93/160.64 [3836]E(f334(f174(x38361),f334(f334(f334(f191(f882(x38361),f882(x38361)),x38362),f170(x38361)),x38363)),f334(f174(x38361),x38363))
% 160.93/160.64 [3840]E(f334(f334(f177(x38401),f334(f197(f882(x38401)),f179(x38401,x38402,x38403))),x38403),f179(x38401,x38402,x38403))
% 160.93/160.64 [3841]E(f186(x38411,x38412,f334(f334(f8(x38412,f885(x38412),x38411),f241(x38412)),x38413)),f257(f888(x38411,a876)))
% 160.93/160.64 [3845]E(f334(f197(f882(x38451)),f334(f334(f334(f191(f882(x38451),f882(x38451)),x38452),f170(x38451)),x38453)),f334(f197(f882(x38451)),x38453))
% 160.93/160.64 [3848]E(f334(f334(f273(x38481,x38482,x38482),f334(f16(f888(x38482,x38482),x38481),f5(x38482))),x38483),f334(f272(x38481,x38482),x38483))
% 160.93/160.64 [3854]E(f44(a1,f334(f334(f22(a1),f44(a1,x38541,x38542)),x38543),x38542),f44(a1,f334(f334(f22(a1),x38541),x38543),x38542))
% 160.93/160.64 [3855]E(f44(a1,f334(f334(f259(a1),f44(a1,x38551,x38552)),x38553),x38552),f44(a1,f334(f334(f259(a1),x38551),x38553),x38552))
% 160.93/160.64 [3858]E(f334(f334(f41(f888(f887(x38581,x38582),a876),f888(x38582,a876)),x38583),f265(x38581,x38582)),f334(f265(x38581,x38582),f39(f888(f887(x38581,x38582),a876),x38583)))
% 160.93/160.64 [3859]E(f334(f334(f41(f888(f887(x38591,x38592),a876),f888(x38591,a876)),x38593),f267(x38591,x38592)),f334(f267(x38591,x38592),f39(f888(f887(x38591,x38592),a876),x38593)))
% 160.93/160.64 [3885]E(f334(f73(x38851,x38851,x38851,x38852),f334(f334(f191(x38851,x38851),x38853),x38852)),f334(f334(f191(x38851,x38851),f334(a116,x38853)),x38852))
% 160.93/160.64 [3895]E(f243(f885(x38951),x38952,f210(x38951),f334(f334(f8(x38951,f885(x38951),x38952),f241(x38951)),x38953)),f334(f211(x38952,x38951),x38953))
% 160.93/160.64 [3902]E(f334(f334(f140(x39021),f334(f334(f22(a881),f334(f197(f882(x39021)),x39022)),x39023)),f334(f171(x39021),x39022)),f334(f171(x39021),f334(f334(f177(x39021),x39023),x39022)))
% 160.93/160.64 [3903]E(f334(f334(f177(x39031),f334(f334(f22(a881),f334(f197(f882(x39031)),x39032)),x39033)),f334(f171(x39031),x39032)),f334(f171(x39031),f334(f334(f140(x39031),x39033),x39032)))
% 160.93/160.64 [3906]E(f334(f334(f80(a881),f334(f168(a881),f334(f334(f156(x39061,a881),x39062),x39063))),f334(f197(f882(x39061)),x39063)),f157(x39061,x39062,x39063))
% 160.93/160.64 [3924]E(f334(f170(x39241),f334(f334(f334(f191(f882(x39241),f882(x39241)),x39242),f170(x39241)),x39243)),f334(f334(f334(f191(f882(x39241),f882(x39241)),f334(a116,x39242)),f170(x39241)),x39243))
% 160.93/160.64 [3939]P1(f334(f334(f248(a881),f334(f197(f882(x39391)),f334(f138(x39391,x39392),x39393))),f334(f197(f882(x39391)),x39393)))
% 160.93/160.64 [3957]E(f334(f334(f114(f888(f888(x39571,a876),a876)),f334(f311(x39571),x39572)),f334(f313(f888(x39571,a876),f888(x39571,a876),f334(f312(x39571),x39573)),f334(f311(x39571),x39572))),f334(f311(x39571),f334(f334(f312(x39571),x39573),x39572)))
% 160.93/160.64 [3976]P26(x39761,x39762,f334(f334(f312(f880(x39761)),f334(f334(f334(f92(x39761),x39763),a24),x39763)),f196(f888(f880(x39761),a876))))
% 160.93/160.64 [3991]P1(f334(f334(f248(a881),f334(f197(f882(x39911)),f179(x39911,x39912,x39913))),f334(f197(f882(x39911)),x39913)))
% 160.93/160.64 [3999]E(f334(f267(x39991,x39992),f334(f254(f887(x39991,x39992)),f334(f273(x39991,x39992,a876),x39993))),f334(f254(x39991),f334(f334(f8(f888(x39992,a876),a876,x39991),f87(x39992)),x39993)))
% 160.93/160.64 [4011]E(f334(f313(a881,a881,f334(f334(f7(a881,a881,a881),f80(a881)),x40111)),f305(a881,x40112,x40113)),f305(a881,f334(f334(f80(a881),x40112),x40111),f334(f334(f80(a881),x40113),x40111)))
% 160.93/160.64 [4013]P1(f334(f61(f885(x40131)),f334(f313(x40132,f885(x40131),f334(f180(x40132,x40131),x40133)),f257(f888(x40132,a876)))))
% 160.93/160.64 [4026]E(f334(f313(a881,a881,f334(f334(f7(a881,a881,a881),f80(a881)),x40261)),f334(f304(a881,x40262),x40263)),f334(f304(a881,f334(f334(f80(a881),x40262),x40261)),f334(f334(f80(a881),x40263),x40261)))
% 160.93/160.64 [4044]E(f334(f334(f184(x40441,x40442),f334(f334(f156(f887(x40441,x40442),x40441),f268(x40441,x40442)),x40443)),f334(f334(f156(f887(x40441,x40442),x40442),f272(x40441,x40442)),x40443)),x40443)
% 160.93/160.64 [4049]E(f334(f334(f80(a881),f334(f334(f81(a881),x40491),f44(a881,f334(f334(f38(a881),x40492),x40491),x40493))),f44(a881,x40492,x40491)),f44(a881,x40492,f334(f334(f81(a881),x40491),x40493)))
% 160.93/160.64 [4064]E(f334(f334(f136(x40641),x40642),f334(f144(f882(x40641),f882(x40641),f136(x40641),f117(x40641)),x40643)),f334(f144(f882(x40641),f882(x40641),f136(x40641),x40642),x40643))
% 160.93/160.64 [4082]P1(f334(f334(f336(f887(x40821,x40821)),f334(f334(f269(x40821,x40821),x40822),x40822)),f334(f334(f191(f887(x40821,x40821),a876),f2(a881)),x40823)))
% 160.93/160.64 [4088]E(f334(f254(x40881),f334(f334(f8(f888(x40882,a876),a876,x40881),f87(x40882)),f334(f7(x40882,x40881,a876),x40883))),f334(f265(x40882,x40881),f334(f254(f887(x40882,x40881)),f334(f273(x40882,x40881,a876),x40883))))
% 160.93/160.64 [4106]E(f334(f334(f114(f888(x41061,a876)),f334(f334(f41(a881,f888(x41061,a876)),f305(a881,f78(a881),x41062)),x41063)),f334(x41063,f2(a881))),f334(f334(f41(a881,f888(x41061,a876)),f334(f303(a881),x41062)),x41063))
% 160.93/160.64 [4121]E(f334(f144(f882(x41211),f882(x41211),f136(x41211),f117(x41211)),f334(f334(f156(f882(x41211),f882(x41211)),f138(x41211,x41212)),x41213)),f334(f138(x41211,x41212),f334(f144(f882(x41211),f882(x41211),f136(x41211),f117(x41211)),x41213)))
% 160.93/160.64 [4126]E(f334(f272(f882(x41261),f882(x41261)),f169(x41261,x41262,x41263)),f334(f138(x41261,f334(f73(a876,a876,x41261,a329),x41262)),x41263))
% 160.93/160.64 [4144]E(f334(f334(f42(x41441,f888(x41442,a876)),f257(f888(x41441,a876))),f334(f334(f8(f888(x41442,a876),f888(x41442,a876),x41441),f254(x41442)),f334(f7(x41442,x41441,a876),x41443))),f334(f254(x41442),f334(f334(f8(f888(x41441,a876),a876,x41442),f88(x41441)),x41443)))
% 160.93/160.64 [4176]E(f334(f334(f80(a1),f334(f334(f80(a1),f334(f334(f81(a1),x41761),f334(f334(f38(a1),x41762),x41761))),f44(a1,x41762,x41761))),x41763),f334(f334(f80(a1),x41762),x41763))
% 160.93/160.64 [4213]E(f334(f334(f80(a1),f334(f334(f80(a1),f334(f334(f81(a1),f334(f334(f38(a1),x42131),x42132)),x42132)),f44(a1,x42131,x42132))),x42133),f334(f334(f80(a1),x42131),x42133))
% 160.93/160.64 [4242]E(f85(f887(x42421,x42422),f334(f273(x42421,x42422,a876),f334(f334(f8(f888(x42422,f887(x42421,x42422)),f888(x42422,a876),x42421),f334(f8(f887(x42421,x42422),a876,x42422),x42423)),f269(x42421,x42422)))),f85(f887(x42421,x42422),x42423))
% 160.93/160.64 [4243]E(f90(f887(x42431,x42432),f334(f273(x42431,x42432,a876),f334(f334(f8(f888(x42432,f887(x42431,x42432)),f888(x42432,a876),x42431),f334(f8(f887(x42431,x42432),a876,x42432),x42433)),f269(x42431,x42432)))),f90(f887(x42431,x42432),x42433))
% 160.93/160.64 [4271]P1(f334(f334(f248(f888(x42711,a876)),f39(f888(x42711,a876),f334(f334(f105(f888(f888(x42711,a876),a876)),x42712),x42713))),f334(f334(f105(f888(x42711,a876)),f39(f888(x42711,a876),x42712)),f39(f888(x42711,a876),x42713))))
% 160.93/160.64 [4272]E(f334(f171(x42721),f334(f334(f334(f191(f882(x42721),f882(x42721)),f334(f334(f22(a881),f334(f197(f882(x42721)),x42722)),f44(a881,x42723,f334(f197(f882(x42721)),x42722)))),f170(x42721)),x42722)),f334(f334(f334(f191(f882(x42721),f882(x42721)),x42723),f170(x42721)),f334(f171(x42721),x42722)))
% 160.93/160.64 [4286]E(f334(f254(x42861),f334(f334(f8(a876,a876,x42861),a329),f334(f334(f7(x42861,f885(x42862),a876),f334(f334(f8(f885(x42862),f888(f885(x42862),a876),x42861),a331),x42863)),f210(x42862)))),f186(x42861,x42862,x42863))
% 160.93/160.64 [4311]P1(f334(f334(f248(a881),f334(f197(f882(x43111)),f334(f334(f140(x43111),f334(f197(f882(x43111)),f179(x43111,x43112,x43113))),x43113))),f334(f197(f882(x43111)),x43113)))
% 160.93/160.64 [4352]E(f334(f254(x43521),f334(f334(f8(f888(x43522,a876),a876,x43521),f87(x43522)),f334(f334(f8(f885(x43521),f888(x43522,a876),x43521),f334(f7(x43522,f885(x43521),a876),f334(f334(f8(f885(x43521),f888(f885(x43521),a876),x43522),a331),x43523))),f241(x43521)))),f188(x43522,x43521,x43523))
% 160.93/160.64 [4563]~P1(f334(f62(x45631,x45632,f196(f888(x45631,a876))),x45633))
% 160.93/160.64 [4570]~P1(f334(f334(f336(f887(x45701,x45701)),f334(f334(f269(x45701,x45701),x45702),x45703)),f155(x45701,f117(f888(x45701,a881)))))
% 160.93/160.64 [3608]E(f334(f197(f882(x36081)),f334(f334(f177(x36081),x36082),x36083)),f334(f334(f246(a881),f334(f197(f882(x36081)),x36083)),x36082))
% 160.93/160.64 [3609]E(f334(f197(f882(x36091)),f334(f334(f140(x36091),x36092),x36093)),f334(f334(f22(a881),f334(f197(f882(x36091)),x36093)),x36092))
% 160.93/160.64 [3634]E(f334(f197(f882(f882(x36341))),f54(x36341,x36342,x36343)),f334(f334(f259(a881),f334(f197(f882(x36341)),x36343)),x36342))
% 160.93/160.64 [3650]E(f334(f334(f38(a881),f334(f334(f38(a881),x36501),x36502)),x36503),f334(f334(f38(a881),x36501),f334(f334(f81(a881),x36502),x36503)))
% 160.93/160.64 [3651]E(f334(f334(f22(a881),f334(f334(f22(a881),x36511),x36512)),x36513),f334(f334(f22(a881),x36511),f334(f334(f80(a881),x36512),x36513)))
% 160.93/160.64 [3652]E(f334(f334(f80(a881),f334(f334(f80(a881),x36521),x36522)),x36523),f334(f334(f80(a881),x36521),f334(f334(f80(a881),x36522),x36523)))
% 160.93/160.64 [3653]E(f334(f334(f80(a1),f334(f334(f80(a1),x36531),x36532)),x36533),f334(f334(f80(a1),x36531),f334(f334(f80(a1),x36532),x36533)))
% 160.93/160.64 [3654]E(f334(f334(f81(a881),f334(f334(f81(a881),x36541),x36542)),x36543),f334(f334(f81(a881),x36541),f334(f334(f81(a881),x36542),x36543)))
% 160.93/160.64 [3655]E(f334(f334(f81(a1),f334(f334(f81(a1),x36551),x36552)),x36553),f334(f334(f81(a1),x36551),f334(f334(f81(a1),x36552),x36553)))
% 160.93/160.64 [3656]E(f334(f334(f259(a1),f334(f334(f259(a1),x36561),x36562)),x36563),f334(f334(f259(a1),x36561),f334(f334(f81(a881),x36562),x36563)))
% 160.93/160.64 [3676]E(f164(x36761,f334(f334(f153(f888(x36761,a876)),x36762),x36763)),f176(x36761,x36762,f164(x36761,x36763)))
% 160.93/160.64 [3721]E(f334(f334(f22(a881),f334(f334(f22(a881),x37211),x37212)),x37213),f334(f334(f22(a881),f334(f334(f22(a881),x37211),x37213)),x37212))
% 160.93/160.64 [3727]E(f334(f241(f887(x37271,f883(x37271))),f334(f334(f269(x37271,f883(x37271)),x37272),x37273)),f334(f137(x37271),f129(x37271,x37272,x37273)))
% 160.93/160.64 [3730]E(f334(f334(f105(f888(x37301,a876)),x37302),f334(f334(f22(f888(x37301,a876)),x37303),x37302)),f196(f888(x37301,a876)))
% 160.93/160.64 [3771]E(f39(f888(x37711,a876),f334(f334(f312(f888(x37711,a876)),x37712),x37713)),f334(f334(f114(f888(x37711,a876)),x37712),f39(f888(x37711,a876),x37713)))
% 160.93/160.64 [3772]E(f40(f888(x37721,a876),f334(f334(f312(f888(x37721,a876)),x37722),x37723)),f334(f334(f105(f888(x37721,a876)),x37722),f40(f888(x37721,a876),x37723)))
% 160.93/160.64 [3774]E(f334(f334(f22(a881),f334(f334(f81(a881),x37741),x37742)),f334(f334(f81(a881),x37743),x37742)),f334(f334(f81(a881),f334(f334(f22(a881),x37741),x37743)),x37742))
% 160.93/160.64 [3775]E(f334(f334(f80(a881),f334(f334(f81(a881),x37751),x37752)),f334(f334(f81(a881),x37753),x37752)),f334(f334(f81(a881),f334(f334(f80(a881),x37751),x37753)),x37752))
% 160.93/160.64 [3776]E(f334(f334(f22(a1),f334(f334(f81(a1),x37761),x37762)),f334(f334(f81(a1),x37763),x37762)),f334(f334(f81(a1),f334(f334(f22(a1),x37761),x37763)),x37762))
% 160.93/160.64 [3777]E(f334(f334(f80(a1),f334(f334(f81(a1),x37771),x37772)),f334(f334(f81(a1),x37773),x37772)),f334(f334(f81(a1),f334(f334(f80(a1),x37771),x37773)),x37772))
% 160.93/160.64 [3779]E(f334(f334(f246(a881),f334(f334(f22(a881),x37791),x37792)),f334(f334(f22(a881),x37793),x37792)),f334(f334(f22(a881),f334(f334(f246(a881),x37791),x37793)),x37792))
% 160.93/160.64 [3802]E(f334(f334(f105(f888(f882(x38021),a876)),f162(x38021,x38022)),f162(x38021,x38023)),f162(x38021,f334(f334(f105(f888(x38021,a876)),x38022),x38023)))
% 160.93/160.64 [3804]E(f334(f334(f114(f888(x38041,a876)),x38042),f334(f334(f114(f888(x38041,a876)),x38042),x38043)),f334(f334(f114(f888(x38041,a876)),x38042),x38043))
% 160.93/160.64 [3805]E(f334(f334(f114(f888(x38051,a876)),x38052),f334(f334(f22(f888(x38051,a876)),x38053),x38052)),f334(f334(f114(f888(x38051,a876)),x38052),x38053))
% 160.93/160.64 [3806]E(f334(f334(f105(f888(x38061,a876)),x38062),f334(f334(f105(f888(x38061,a876)),x38062),x38063)),f334(f334(f105(f888(x38061,a876)),x38062),x38063))
% 160.93/160.64 [3818]E(f334(f334(f291(x38181,x38182,x38182),x38183),f310(x38182,f196(f888(f887(x38182,x38182),a876)))),x38183)
% 160.93/160.64 [3821]E(f334(f334(f114(f888(x38211,a876)),f334(f334(f312(x38211),x38212),f196(f888(x38211,a876)))),x38213),f334(f334(f312(x38211),x38212),x38213))
% 160.93/160.64 [3839]E(f334(f334(f22(a881),f334(f334(f22(a881),f334(a116,x38391)),x38392)),f334(a116,x38393)),f334(f334(f22(a881),f334(f334(f22(a881),x38391),x38392)),x38393))
% 160.93/160.64 [3867]E(f334(f334(f105(f888(f888(x38671,a876),a876)),f334(f311(x38671),x38672)),f334(f311(x38671),x38673)),f334(f311(x38671),f334(f334(f105(f888(x38671,a876)),x38672),x38673)))
% 160.93/160.64 [3871]E(f334(f334(f114(f888(x38711,a876)),f334(f79(f888(x38711,a876)),x38712)),x38713),f334(f79(f888(x38711,a876)),f334(f334(f22(f888(x38711,a876)),x38712),x38713)))
% 160.93/160.64 [3882]E(f334(f334(f312(x38821),x38822),f334(f334(f22(f888(x38821,a876)),x38823),f334(f334(f312(x38821),x38822),f196(f888(x38821,a876))))),f334(f334(f312(x38821),x38822),x38823))
% 160.93/160.64 [3892]P1(f334(f334(f248(f888(x38921,a876)),x38922),f334(f334(f114(f888(x38921,a876)),x38923),x38922)))
% 160.93/160.64 [3893]P1(f334(f334(f248(f888(x38931,a876)),x38932),f334(f334(f114(f888(x38931,a876)),x38932),x38933)))
% 160.93/160.64 [3896]E(f334(f334(f105(f888(x38961,a876)),f334(f79(f888(x38961,a876)),x38962)),f334(f79(f888(x38961,a876)),x38963)),f334(f79(f888(x38961,a876)),f334(f334(f114(f888(x38961,a876)),x38962),x38963)))
% 160.93/160.64 [3897]E(f334(f334(f114(f888(x38971,a876)),f334(f79(f888(x38971,a876)),x38972)),f334(f79(f888(x38971,a876)),x38973)),f334(f79(f888(x38971,a876)),f334(f334(f105(f888(x38971,a876)),x38972),x38973)))
% 160.93/160.64 [3911]P1(f334(f334(f248(f888(x39111,a876)),f334(f174(x39111),x39112)),f334(f174(x39111),f334(f334(f153(x39111),x39113),x39112))))
% 160.93/160.64 [3921]E(f334(f334(f114(f888(x39211,a876)),f334(f334(f22(f888(x39211,a876)),x39212),x39213)),f334(f334(f105(f888(x39211,a876)),x39212),x39213)),x39212)
% 160.93/160.64 [3978]E(f334(f334(f6(x39781,a1),f334(f334(f8(a881,a1,x39781),f104(a1)),x39782)),x39783),f334(f104(a1),f334(f334(f6(x39781,a881),x39782),x39783)))
% 160.93/160.64 [3979]E(f334(f334(f9(x39791,a1),f334(f334(f8(a881,a1,x39791),f104(a1)),x39792)),x39793),f334(f104(a1),f334(f334(f9(x39791,a881),x39792),x39793)))
% 160.93/160.64 [4028]E(f334(f334(f136(x40281),f179(x40281,x40282,x40283)),f334(f334(f140(x40281),f334(f197(f882(x40281)),f179(x40281,x40282,x40283))),x40283)),x40283)
% 160.93/160.64 [4033]E(f334(f79(f888(f887(x40331,x40332),a876)),f334(f334(f271(x40331,x40332),x40333),f334(f16(f888(x40332,a876),x40331),f257(f888(x40332,a876))))),f334(f334(f271(x40331,x40332),f334(f79(f888(x40331,a876)),x40333)),f334(f16(f888(x40332,a876),x40331),f257(f888(x40332,a876)))))
% 160.93/160.64 [4034]E(f334(f79(f888(f887(x40341,x40342),a876)),f334(f334(f271(x40341,x40342),f257(f888(x40341,a876))),f334(f16(f888(x40342,a876),x40341),x40343))),f334(f334(f271(x40341,x40342),f257(f888(x40341,a876))),f334(f16(f888(x40342,a876),x40341),f334(f79(f888(x40342,a876)),x40343))))
% 160.93/160.64 [4058]E(f120(f885(x40581),f334(f243(f883(f885(x40581)),f883(f885(x40581)),f130(x40581),f5(f883(f885(x40581)))),x40582),f125(x40581,x40583)),f125(x40581,f129(f885(f883(f885(x40581))),x40582,x40583)))
% 160.93/160.64 [4083]E(f334(f334(f41(f888(x40831,a876),f888(x40831,a876)),x40832),f334(f334(f7(f888(x40831,a876),f888(x40831,a876),f888(x40831,a876)),f105(f888(x40831,a876))),x40833)),f334(f334(f105(f888(x40831,a876)),f39(f888(x40831,a876),x40832)),x40833))
% 160.93/160.64 [4090]E(f334(f144(f882(x40901),f882(x40901),f136(x40901),f117(x40901)),f334(f334(f153(f882(x40901)),x40902),x40903)),f334(f334(f136(x40901),x40902),f334(f144(f882(x40901),f882(x40901),f136(x40901),f117(x40901)),x40903)))
% 160.93/160.64 [4112]E(f334(f334(f312(f888(x41121,a876)),f334(f288(x41121,x41121,x41122),f334(f334(f312(x41121),x41123),f196(f888(x41121,a876))))),f196(f888(f888(x41121,a876),a876))),f334(f334(f60(x41121),f334(f334(f312(x41121),x41123),f196(f888(x41121,a876)))),x41122))
% 160.93/160.64 [4122]E(f334(f334(f80(a881),f334(f334(f81(a881),x41221),f334(f334(f38(a881),x41222),x41223))),f334(f334(f38(a881),f334(f334(f81(a881),x41221),f44(a881,x41222,x41223))),x41223)),f334(f334(f38(a881),f334(f334(f81(a881),x41221),x41222)),x41223))
% 160.93/160.64 [4123]E(f334(f334(f80(a1),f334(f334(f81(a1),x41231),f334(f334(f38(a1),x41232),x41233))),f334(f334(f38(a1),f334(f334(f81(a1),x41231),f44(a1,x41232,x41233))),x41233)),f334(f334(f38(a1),f334(f334(f81(a1),x41231),x41232)),x41233))
% 160.93/160.64 [4161]E(f334(f334(f22(f888(x41611,a876)),f334(f174(x41611),x41612)),f334(f334(f312(x41611),x41613),f196(f888(x41611,a876)))),f334(f174(x41611),f334(f138(x41611,f334(f334(f8(a876,a876,x41611),a329),f334(a331,x41613))),x41612)))
% 160.93/160.64 [4210]E(f334(f334(f136(x42101),f334(f144(f882(x42101),f882(x42101),f136(x42101),f117(x42101)),x42102)),f334(f144(f882(x42101),f882(x42101),f136(x42101),f117(x42101)),x42103)),f334(f144(f882(x42101),f882(x42101),f136(x42101),f117(x42101)),f334(f334(f136(f882(x42101)),x42102),x42103)))
% 160.93/160.64 [4215]E(f334(f334(f269(f882(x42151),f882(x42151)),f334(f138(x42151,x42152),x42153)),f334(f138(x42151,f334(f73(a876,a876,x42151,a329),x42152)),x42153)),f169(x42151,x42152,x42153))
% 160.93/160.64 [4218]E(f334(f334(f80(a881),f334(f334(f80(a881),f334(f334(f38(a881),x42181),x42182)),f334(f334(f38(a881),x42183),x42182))),f334(f334(f38(a881),f334(f334(f80(a881),f44(a881,x42181,x42182)),f44(a881,x42183,x42182))),x42182)),f334(f334(f38(a881),f334(f334(f80(a881),x42181),x42183)),x42182))
% 160.93/160.64 [4219]E(f334(f334(f80(a1),f334(f334(f80(a1),f334(f334(f38(a1),x42191),x42192)),f334(f334(f38(a1),x42193),x42192))),f334(f334(f38(a1),f334(f334(f80(a1),f44(a1,x42191,x42192)),f44(a1,x42193,x42192))),x42192)),f334(f334(f38(a1),f334(f334(f80(a1),x42191),x42193)),x42192))
% 160.93/160.64 [4275]E(f334(f334(f105(f888(f882(x42751),a876)),f334(f334(f7(f882(x42751),f888(f882(x42751),a876),a876),f336(f882(x42751))),f163(x42751,x42752))),f334(f334(f7(f882(x42751),f888(f882(x42751),a876),a876),f336(f882(x42751))),f163(x42751,x42753))),f162(x42751,f334(f334(f105(f888(x42751,a876)),f334(f334(f7(x42751,f888(x42751,a876),a876),f336(x42751)),x42752)),f334(f334(f7(x42751,f888(x42751,a876),a876),f336(x42751)),x42753))))
% 160.93/160.64 [4288]E(f334(f254(x42881),f334(f334(f18(x42881,a876,a876),f334(f334(f8(a876,f888(a876,a876),x42881),a333),f334(f334(f7(x42881,x42881,a876),a331),x42882))),f334(f334(f7(x42881,f888(x42881,a876),a876),f336(x42881)),x42883))),f334(f334(f312(x42881),x42882),x42883))
% 160.93/160.64 [4308]E(f334(f334(f86(f882(f882(x43081)),f882(f882(x43081))),f53(x43081,x43082)),f334(f334(f18(f882(f882(x43081)),f882(f882(x43081)),f882(f882(x43081))),f334(f334(f8(f882(f882(x43081)),f888(f882(f882(x43081)),f882(f882(x43081))),f882(f882(x43081))),f136(f882(x43081))),f334(f156(f882(x43081),f882(x43081)),f334(f153(x43081),x43083)))),f5(f882(f882(x43081))))),f53(x43081,f334(f334(f153(x43081),x43083),x43082)))
% 160.93/160.64 [4312]E(f334(f254(x43121),f334(f334(f18(x43121,a876,a876),f334(f334(f8(a876,f888(a876,a876),x43121),a333),f334(f334(f7(x43121,f888(x43121,a876),a876),f336(x43121)),x43122))),f334(f334(f7(x43121,f888(x43121,a876),a876),f336(x43121)),x43123))),f334(f334(f114(f888(x43121,a876)),x43122),x43123))
% 160.93/160.64 [4313]E(f334(f254(x43131),f334(f334(f18(x43131,a876,a876),f334(f334(f8(a876,f888(a876,a876),x43131),a332),f334(f334(f7(x43131,f888(x43131,a876),a876),f336(x43131)),x43132))),f334(f334(f7(x43131,f888(x43131,a876),a876),f336(x43131)),x43133))),f334(f334(f105(f888(x43131,a876)),x43132),x43133))
% 160.93/160.64 [4404]E(f334(f334(f41(x44041,f888(f888(x44041,a876),a876)),x44042),f334(f334(f7(x44041,f888(f888(x44041,a876),a876),f888(f888(x44041,a876),a876)),f334(f334(f8(f888(x44041,a876),f888(f888(f888(x44041,a876),a876),f888(f888(x44041,a876),a876)),x44041),f312(f888(x44041,a876))),f334(f334(f8(f888(x44041,a876),f888(x44041,a876),x44041),f288(x44041,x44041,x44043)),f334(f334(f7(x44041,f888(x44041,a876),f888(x44041,a876)),f312(x44041)),f196(f888(x44041,a876)))))),f196(f888(f888(x44041,a876),a876)))),f334(f334(f60(x44041),x44042),x44043))
% 160.93/160.64 [4406]E(f334(f334(f214(x44061),f334(f334(f81(a1),f334(f334(f73(f887(a1,a1),a1,x44061,f268(a1,a1)),f225(x44061)),x44062)),f334(f334(f73(f887(a1,a1),a1,x44061,f268(a1,a1)),f225(x44061)),x44063))),f334(f334(f81(a1),f334(f334(f73(f887(a1,a1),a1,x44061,f272(a1,a1)),f225(x44061)),x44062)),f334(f334(f73(f887(a1,a1),a1,x44061,f272(a1,a1)),f225(x44061)),x44063))),f234(x44061,x44062,x44063))
% 160.93/160.64 [4409]E(f334(f254(f882(x44091)),f334(f334(f18(f882(x44091),a876,a876),f334(f334(f8(a876,f888(a876,a876),f882(x44091)),a332),f334(f334(f7(f882(x44091),a881,a876),f334(f334(f8(a881,f888(a881,a876),f882(x44091)),a331),f197(f882(x44091)))),x44092))),f334(f334(f7(f882(x44091),f888(x44091,a876),a876),f334(f334(f8(f888(x44091,a876),f888(f888(x44091,a876),a876),f882(x44091)),f248(f888(x44091,a876))),f174(x44091))),f334(f174(x44091),x44093)))),f334(f174(f882(x44091)),f54(x44091,x44092,x44093)))
% 160.93/160.64 [3792]E(f44(a881,f334(f334(f80(a881),f334(f334(f81(a881),x37921),x37922)),x37923),x37922),f44(a881,x37923,x37922))
% 160.93/160.64 [3838]E(f141(a881,f334(f304(a881,f334(f334(f80(a881),x38381),x38382)),x38383)),f334(f334(f140(a881),x38382),f141(a881,f334(f304(a881,x38381),x38383))))
% 160.93/160.64 [3881]E(f334(f334(f80(a1),f334(f104(a1),x38811)),f334(f334(f80(a1),f334(f104(a1),x38812)),x38813)),f334(f334(f80(a1),f334(f104(a1),f334(f334(f80(a881),x38811),x38812))),x38813))
% 160.93/160.64 [3888]E(f334(f334(f114(f888(x38881,a876)),f334(f334(f22(f888(x38881,a876)),x38882),x38883)),x38883),f334(f334(f114(f888(x38881,a876)),x38882),x38883))
% 160.93/160.64 [3889]E(f334(f334(f22(f888(x38891,a876)),f334(f334(f22(f888(x38891,a876)),x38892),x38893)),x38893),f334(f334(f22(f888(x38891,a876)),x38892),x38893))
% 160.93/160.64 [3912]E(f334(f334(f291(x39121,x39121,x39122),f310(x39121,f196(f888(f887(x39121,x39121),a876)))),x39123),x39123)
% 160.93/160.64 [3918]E(f334(f334(f114(f888(x39181,a876)),f334(f287(x39181),x39182)),f334(f287(x39181),x39183)),f334(f287(x39181),f334(f334(f114(f888(f887(x39181,x39181),a876)),x39182),x39183)))
% 160.93/160.64 [3929]E(f278(x39291,f334(f334(f153(f887(a103,x39291)),f334(f334(f269(a103,x39291),f2(a103)),x39292)),x39293)),f278(x39291,x39293))
% 160.93/160.64 [3932]E(f334(f334(f114(f888(x39321,a876)),f39(f888(x39321,a876),x39322)),f39(f888(x39321,a876),x39323)),f39(f888(x39321,a876),f334(f334(f114(f888(f888(x39321,a876),a876)),x39322),x39323)))
% 160.93/160.64 [3933]E(f334(f334(f105(f888(x39331,a876)),f40(f888(x39331,a876),x39332)),f40(f888(x39331,a876),x39333)),f40(f888(x39331,a876),f334(f334(f114(f888(f888(x39331,a876),a876)),x39332),x39333)))
% 160.93/160.64 [3970]E(f334(f334(f291(x39701,x39701,x39701),f334(f334(f191(f887(x39701,x39701),a876),x39702),x39703)),x39703),f334(f334(f191(f887(x39701,x39701),a876),f334(a116,x39702)),x39703))
% 160.93/160.64 [4019]P1(f334(f334(f248(f888(x40191,a876)),f334(f334(f22(f888(x40191,a876)),x40192),x40193)),x40192))
% 160.93/160.64 [4020]P1(f334(f334(f248(f888(x40201,a876)),f334(f334(f105(f888(x40201,a876)),x40202),x40203)),x40203))
% 160.93/160.64 [4021]P1(f334(f334(f248(f888(x40211,a876)),f334(f334(f105(f888(x40211,a876)),x40212),x40213)),x40212))
% 160.93/160.64 [4046]E(f310(x40461,f334(f334(f114(f888(f887(x40461,x40461),a876)),f310(x40461,x40462)),f310(x40461,x40463))),f310(x40461,f334(f334(f114(f888(f887(x40461,x40461),a876)),x40462),x40463)))
% 160.93/160.64 [4050]E(f39(f888(x40501,a876),f334(f334(f312(f888(x40501,a876)),x40502),f334(f334(f312(f888(x40501,a876)),x40503),f196(f888(f888(x40501,a876),a876))))),f334(f334(f114(f888(x40501,a876)),x40502),x40503))
% 160.93/160.64 [4051]E(f40(f888(x40511,a876),f334(f334(f312(f888(x40511,a876)),x40512),f334(f334(f312(f888(x40511,a876)),x40513),f196(f888(f888(x40511,a876),a876))))),f334(f334(f105(f888(x40511,a876)),x40512),x40513))
% 160.93/160.64 [4057]E(f334(f334(f291(x40571,x40571,x40571),f334(f334(f191(f887(x40571,x40571),a876),x40572),x40573)),x40573),f334(f334(f291(x40571,x40571,x40571),x40573),f334(f334(f191(f887(x40571,x40571),a876),x40572),x40573)))
% 160.93/160.64 [4127]E(f334(f334(f114(f888(x41271,a876)),f334(f254(x41271),f334(f334(f7(x41271,x41271,a876),a331),x41272))),x41273),f334(f334(f312(x41271),x41272),x41273))
% 160.93/160.64 [4129]E(f334(a108,f334(f334(f6(x41291,a1),f334(f334(f8(a881,a1,x41291),f104(a1)),x41292)),x41293)),f334(f334(f6(x41291,a881),x41292),x41293))
% 160.93/160.64 [4130]E(f334(a108,f334(f334(f9(x41301,a1),f334(f334(f8(a881,a1,x41301),f104(a1)),x41302)),x41303)),f334(f334(f9(x41301,a881),x41302),x41303))
% 160.93/160.64 [4207]E(f334(f158(f882(x42071),x42071,f334(f173(x42071),x42072),f334(f16(f888(f882(x42071),f882(x42071)),x42071),f334(f334(f7(f882(x42071),f882(x42071),f882(x42071)),f136(x42071)),x42072))),x42073),f334(f173(x42071),f334(f334(f136(x42071),x42073),x42072)))
% 160.93/160.64 [4238]P1(f334(f334(f248(f888(f888(x42381,a876),a876)),f334(f334(f114(f888(f888(x42381,a876),a876)),f334(f311(x42381),x42382)),f334(f311(x42381),x42383))),f334(f311(x42381),f334(f334(f114(f888(x42381,a876)),x42382),x42383))))
% 160.93/160.64 [4331]E(f334(f254(x43311),f334(f334(f18(x43311,a876,a876),f334(f334(f8(a876,f888(a876,a876),x43311),a332),f334(f334(f7(x43311,f888(x43311,a876),a876),f336(x43311)),x43312))),f334(f334(f8(a876,a876,x43311),a329),f334(f334(f7(x43311,f888(x43311,a876),a876),f336(x43311)),x43313)))),f334(f334(f22(f888(x43311,a876)),x43312),x43313))
% 160.93/160.64 [4353]E(f334(f37(a881),f334(f254(a881),f334(f334(f18(a881,a876,a876),f334(f334(f8(a876,f888(a876,a876),a881),a332),f334(f334(f7(a881,a881,a876),f249(a881)),f334(f197(f882(x43531)),x43532)))),f334(f334(f8(x43531,a876,a881),x43533),f334(f167(x43531),x43532))))),f334(f197(f882(x43531)),f334(f138(x43531,x43533),x43532)))
% 160.93/160.64 [4355]E(f334(f197(f882(x43551)),f178(x43551,x43552,x43553)),f334(f37(a881),f334(f254(a881),f334(f334(f18(a881,a876,a876),f334(f334(f8(a876,f888(a876,a876),a881),a332),f334(f334(f7(a881,a881,a876),f249(a881)),f334(f197(f882(x43551)),x43552)))),f334(f334(f7(a881,f888(a881,a876),a876),f336(a881)),x43553)))))
% 160.93/160.64 [4453]E(f334(f334(f105(f888(f887(f882(x44531),f882(x44531)),a876)),f334(f313(f887(f887(x44531,f882(x44531)),f887(x44531,f882(x44531))),f887(f882(x44531),f882(x44531)),f274(f887(x44531,f882(x44531)),f882(x44531),f887(x44531,f882(x44531)),f882(x44531),f334(f273(x44531,f882(x44531),f882(x44531)),f153(x44531)),f334(f273(x44531,f882(x44531),f882(x44531)),f153(x44531)))),f326(x44531,f882(x44531),x44532,f334(f145(x44531,x44532),x44533)))),f334(f254(f887(f882(x44531),f882(x44531))),f334(f273(f882(x44531),f882(x44531),a876),f334(f334(f7(f882(x44531),f888(f882(x44531),a876),f888(f882(x44531),a876)),f334(f334(f8(f888(a876,a876),f888(f888(f882(x44531),a876),f888(f882(x44531),a876)),f882(x44531)),f8(a876,a876,f882(x44531))),f334(f334(f8(a876,f888(a876,a876),f882(x44531)),a332),f334(f334(f7(f882(x44531),a881,a876),f334(f334(f8(a881,f888(a881,a876),f882(x44531)),a331),f197(f882(x44531)))),f334(a116,x44533))))),f334(f334(f7(f882(x44531),a881,a876),f334(f334(f8(a881,f888(a881,a876),f882(x44531)),a331),f197(f882(x44531)))),f334(a116,x44533)))))),f334(f145(x44531,x44532),f334(a116,x44533)))
% 160.93/160.64 [3934]E(f44(a881,f334(a116,f334(f334(f80(a881),f334(f334(f81(a881),x39341),x39342)),x39343)),x39342),f44(a881,f334(a116,x39343),x39342))
% 160.93/160.64 [4196]E(f334(f254(x41961),f334(f334(f18(x41961,a876,a876),f334(f334(f8(a876,f888(a876,a876),x41961),a332),x41962)),x41963)),f334(f334(f105(f888(x41961,a876)),f334(f254(x41961),x41962)),f334(f254(x41961),x41963)))
% 160.93/160.64 [4197]E(f334(f254(x41971),f334(f334(f18(x41971,a876,a876),f334(f334(f8(a876,f888(a876,a876),x41971),a333),x41972)),x41973)),f334(f334(f114(f888(x41971,a876)),f334(f254(x41971),x41972)),f334(f254(x41971),x41973)))
% 160.93/160.64 [4199]E(f334(f334(f136(x41991),f334(f334(f140(x41991),f44(a881,x41992,f334(f197(f882(x41991)),x41993))),x41993)),f334(f334(f177(x41991),f44(a881,x41992,f334(f197(f882(x41991)),x41993))),x41993)),f334(f334(f334(f191(f882(x41991),f882(x41991)),x41992),f170(x41991)),x41993))
% 160.93/160.64 [4204]E(f334(f254(x42041),f334(f334(f18(x42041,a876,a876),f334(f334(f8(a876,f888(a876,a876),x42041),a337),x42042)),x42043)),f334(f334(f114(f888(x42041,a876)),f334(f79(f888(x42041,a876)),f334(f254(x42041),x42042))),f334(f254(x42041),x42043)))
% 160.93/160.64 [4220]E(f334(f334(f80(a881),f334(f197(f882(x42201)),f334(f138(x42201,x42202),x42203))),f334(f197(f882(x42201)),f334(f138(x42201,f334(f334(f8(a876,a876,x42201),a329),x42202)),x42203))),f334(f197(f882(x42201)),x42203))
% 160.93/160.64 [4245]P1(f334(f334(f248(f888(x42451,a876)),f334(f334(f114(f888(x42451,a876)),f40(f888(x42451,a876),x42452)),f40(f888(x42451,a876),x42453))),f40(f888(x42451,a876),f334(f334(f105(f888(f888(x42451,a876),a876)),x42452),x42453))))
% 160.93/160.64 [4259]E(f334(f174(x42591),f334(f138(x42591,f334(f334(f8(a876,a876,x42591),a329),f334(f334(f7(x42591,x42591,a876),a331),x42592))),x42593)),f334(f334(f22(f888(x42591,a876)),f334(f174(x42591),x42593)),f334(f334(f312(x42591),x42592),f196(f888(x42591,a876)))))
% 160.93/160.64 [4268]P1(f334(f334(f248(f888(f887(x42681,x42681),a876)),f334(f334(f114(f888(f887(x42681,x42681),a876)),f310(x42681,x42682)),f310(x42681,x42683))),f310(x42681,f334(f334(f114(f888(f887(x42681,x42681),a876)),x42682),x42683))))
% 160.93/160.64 [4293]E(f334(f334(f81(a881),f334(a116,f334(a116,f2(a881)))),f334(f334(f6(a881,a881),f334(f334(f8(a881,a881,a881),f334(f80(a881),x42931)),f334(f334(f7(a881,a881,a881),f81(a881)),x42932))),f334(f255(a881),x42933))),f334(f334(f81(a881),x42933),f334(f334(f80(a881),x42931),f334(f334(f80(a881),x42931),f334(f334(f81(a881),f334(f334(f22(a881),x42933),f78(a881))),x42932)))))
% 160.93/160.64 [4303]E(f334(f254(x43031),f334(f334(f18(x43031,a876,a876),f334(f334(f8(a876,f888(a876,a876),x43031),a332),f334(f334(f7(x43031,f888(x43031,a876),a876),f336(x43031)),f334(f174(x43031),x43032)))),x43033)),f334(f174(x43031),f334(f138(x43031,x43033),x43032)))
% 160.93/160.64 [4452]E(f334(f254(x44521),f334(f334(f8(f888(a881,a876),a876,x44521),f87(a881)),f334(f334(f7(x44521,f888(a881,a876),f888(a881,a876)),f334(f334(f8(f888(a881,f888(a876,a876)),f888(f888(a881,a876),f888(a881,a876)),x44521),f18(a881,a876,a876)),f334(f334(f8(f888(a881,a876),f888(a881,f888(a876,a876)),x44521),f334(f8(a876,f888(a876,a876),a881),a332)),f334(f334(f7(x44521,f888(a881,x44521),f888(a881,a876)),f334(f334(f8(f888(x44521,a876),f888(f888(a881,x44521),f888(a881,a876)),x44521),f8(x44521,a876,a881)),a331)),f334(f167(x44521),x44522))))),f334(f334(f18(a881,a876,a876),f334(f334(f8(a876,f888(a876,a876),a881),a332),f334(f334(f7(a881,a881,a876),f249(a881)),f334(f197(f882(x44521)),x44522)))),f334(f334(f7(a881,f888(a881,a876),a876),f336(a881)),x44523))))),f334(f174(x44521),f178(x44521,x44522,x44523)))
% 160.93/160.64 [4343]E(f334(f254(x43431),f334(f334(f18(x43431,a876,a876),f334(f334(f8(a876,f888(a876,a876),x43431),a337),f334(f334(f8(a876,a876,x43431),a329),f334(f334(f7(x43431,x43431,a876),a331),x43432)))),x43433)),f334(f334(f312(x43431),x43432),f334(f254(x43431),x43433)))
% 160.93/160.64 [4375]E(f334(f334(f156(f887(x43751,a881),x43751),f268(x43751,a881)),f334(f138(f887(x43751,a881),f334(f334(f7(f887(x43751,a881),f888(a881,a876),a876),f334(f334(f8(a881,f888(f888(a881,a876),a876),f887(x43751,a881)),f336(a881)),f272(x43751,a881))),x43752)),f334(f334(f184(x43751,a881),x43753),f141(a881,f334(f304(a881,f2(a881)),f334(f197(f882(x43751)),x43753)))))),f178(x43751,x43753,x43752))
% 160.93/160.64 [4405]E(f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f334(f334(f6(a881,a1),f334(f334(f8(a1,a1,a881),f334(f80(a1),x44051)),f334(f334(f7(a881,a1,a1),f334(f334(f8(a1,f888(a1,a1),a881),f81(a1)),f104(a1))),x44052))),f334(f255(a881),x44053))),f334(f334(f81(a1),f334(f104(a1),x44053)),f334(f334(f80(a1),x44051),f334(f334(f80(a1),x44051),f334(f334(f81(a1),f334(f104(a1),f334(f334(f22(a881),x44053),f78(a881)))),x44052)))))
% 160.93/160.64 [4446]E(f334(f254(f887(x44461,x44462)),f334(f273(x44461,x44462,a876),f334(f334(f7(x44461,f888(f887(x44462,x44461),a876),f888(x44462,a876)),f334(f334(f8(f888(x44462,f888(f888(f887(x44462,x44461),a876),a876)),f888(f888(f887(x44462,x44461),a876),f888(x44462,a876)),x44461),f7(x44462,f888(f887(x44462,x44461),a876),a876)),f334(f334(f8(f888(x44462,f887(x44462,x44461)),f888(x44462,f888(f888(f887(x44462,x44461),a876),a876)),x44461),f334(f8(f887(x44462,x44461),f888(f888(f887(x44462,x44461),a876),a876),x44462),f336(f887(x44462,x44461)))),f334(f7(x44462,x44461,f887(x44462,x44461)),f269(x44462,x44461))))),x44463))),f334(f289(x44462,x44461),x44463))
% 160.93/160.64 [4468]E(f334(f254(f882(x44681)),f334(f334(f8(f888(x44681,a876),a876,f882(x44681)),f87(x44681)),f334(f334(f8(f888(x44681,f888(f882(x44681),a876)),f888(x44681,a876),f882(x44681)),f334(f8(f888(f882(x44681),a876),a876,x44681),f87(f882(x44681)))),f334(f334(f7(f882(x44681),f888(x44681,f888(f882(x44681),a876)),f888(x44681,f888(f882(x44681),a876))),f334(f334(f8(f888(x44681,f888(f888(f882(x44681),a876),f888(f882(x44681),a876))),f888(f888(x44681,f888(f882(x44681),a876)),f888(x44681,f888(f882(x44681),a876))),f882(x44681)),f18(x44681,f888(f882(x44681),a876),f888(f882(x44681),a876))),f334(f334(f8(f888(x44681,f888(f882(x44681),f888(a876,a876))),f888(x44681,f888(f888(f882(x44681),a876),f888(f882(x44681),a876))),f882(x44681)),f334(f8(f888(f882(x44681),f888(a876,a876)),f888(f888(f882(x44681),a876),f888(f882(x44681),a876)),x44681),f18(f882(x44681),a876,a876))),f334(f334(f8(f888(x44681,f888(f882(x44681),a876)),f888(x44681,f888(f882(x44681),f888(a876,a876))),f882(x44681)),f334(f8(f888(f882(x44681),a876),f888(f882(x44681),f888(a876,a876)),x44681),f334(f8(a876,f888(a876,a876),f882(x44681)),a332))),f334(f334(f7(f882(x44681),f888(x44681,f888(f882(x44681),f882(x44681))),f888(x44681,f888(f882(x44681),a876))),f334(f334(f8(f888(f888(f882(x44681),f882(x44681)),f888(f882(x44681),a876)),f888(f888(x44681,f888(f882(x44681),f882(x44681))),f888(x44681,f888(f882(x44681),a876))),f882(x44681)),f8(f888(f882(x44681),f882(x44681)),f888(f882(x44681),a876),x44681)),f334(f334(f8(f888(f882(x44681),a876),f888(f888(f882(x44681),f882(x44681)),f888(f882(x44681),a876)),f882(x44681)),f8(f882(x44681),a876,f882(x44681))),a331))),f153(x44681)))))),f334(f334(f7(x44681,f888(f882(x44681),a876),f888(f882(x44681),a876)),f334(f334(f8(f888(a876,a876),f888(f888(f882(x44681),a876),f888(f882(x44681),a876)),x44681),f8(a876,a876,f882(x44681))),f334(f334(f8(a876,f888(a876,a876),x44681),a332),f334(f334(f7(x44681,f888(x44681,a876),a876),f336(x44681)),x44682)))),f334(f334(f7(f882(x44681),f888(f882(x44681),a876),a876),f336(f882(x44681))),x44683)))))),f176(x44681,x44682,x44683))
% 160.93/160.64 [4465]E(f334(f334(f86(a1,f887(a1,a1)),f334(f334(f22(a1),x44651),x44652)),f334(f334(f7(a1,f887(a1,a1),f887(a1,a1)),f334(f334(f18(a1,f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),f334(f334(f8(a876,f888(f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),a1),f100(f887(a1,a1))),f334(f248(a1),f2(a1)))),f334(f269(a1,a1),f334(f334(f80(a1),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x44653)),f78(a1))))),f334(f334(f269(a1,a1),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x44653)),x44651))),f334(f43(x44652),f334(f334(f269(a1,a1),x44653),x44651)))
% 160.93/160.64 [4496]~E(f32(x44961,x44962),f33(x44963,x44964))
% 160.93/160.64 [4513]~E(f334(a26,x45131),f30(x45132,x45133,x45134))
% 160.93/160.64 [4514]~E(f334(a26,x45141),f29(x45142,x45143,x45144))
% 160.93/160.64 [4515]~E(f30(x45151,x45152,x45153),f334(a26,x45154))
% 160.93/160.64 [4516]~E(f29(x45161,x45162,x45163),f334(a26,x45164))
% 160.93/160.64 [3487]E(f334(f334(f334(f72(x34871,x34872),x34873),x34874),f334(x34873,x34874)),x34873)
% 160.93/160.64 [3495]E(f120(x34951,f334(x34952,x34953),f334(x34954,x34953)),f334(f216(x34951,x34952,x34954),x34953))
% 160.93/160.64 [3506]E(f120(f885(x35061),f334(x35062,x35063),f334(x35064,x35063)),f334(f207(x35061,x35062,x35064),x35063))
% 160.93/160.64 [3548]E(f334(f334(f260(x35481,x35482,x35483),x35484),f2(a881)),x35482)
% 160.93/160.64 [3587]E(f193(x35871,x35872,x35873,f334(a116,x35874)),f334(x35873,x35874))
% 160.93/160.64 [3626]E(f172(x36261,x36262,f172(x36261,x36263,x36264)),f172(x36261,x36263,f172(x36261,x36262,x36264)))
% 160.93/160.64 [3627]E(f120(x36271,f129(x36271,x36272,x36273),x36274),f129(x36271,x36272,f120(x36271,x36273,x36274)))
% 160.93/160.64 [3762]E(f334(f158(x37621,x37622,x37623,x37624),f117(x37622)),x37623)
% 160.93/160.64 [3763]E(f334(f243(x37631,x37632,x37633,x37634),f210(x37632)),x37633)
% 160.93/160.64 [3764]E(f334(f144(x37641,x37642,x37643,x37644),f117(x37642)),x37644)
% 160.93/160.64 [3878]E(f334(f243(f885(x38781),x38782,f210(x38781),f334(f16(f885(x38781),x38782),f210(x38781))),f334(x38783,x38784)),f210(x38781))
% 160.93/160.64 [3922]E(f334(f334(f114(f888(x39221,a876)),f186(x39221,x39222,x39223)),f186(x39221,x39222,x39224)),f186(x39221,x39222,f187(x39221,x39222,x39224,x39223)))
% 160.93/160.64 [3955]E(f334(f334(f275(x39551,x39552,x39553,f887(x39552,x39553)),x39554),f269(x39552,x39553)),x39554)
% 160.93/160.64 [3964]E(f189(x39641,x39642,x39643,x39644,f117(x39642)),x39643)
% 160.93/160.64 [3965]E(f244(x39651,x39652,x39653,x39654,f210(x39652)),x39653)
% 160.93/160.64 [3966]E(f189(x39661,x39662,x39663,f117(x39661),x39664),x39663)
% 160.93/160.64 [4252]P44(x42521,x42522,x42523,x42524,f196(f888(x42521,a876)),x42524)
% 160.93/160.64 [3291]E(f334(f334(f16(x32911,x32912),x32913),x32914),x32913)
% 160.93/160.64 [3406]E(f334(f334(f211(x34061,x34062),x34063),f334(f241(x34061),x34064)),f334(f241(x34062),f334(x34063,x34064)))
% 160.93/160.64 [3578]E(f172(x35781,x35782,f334(f138(x35781,x35783),x35784)),f334(f138(x35781,x35783),f172(x35781,x35782,x35784)))
% 160.93/160.64 [3610]E(f334(f334(f64(x36101,x36102,x36103),x36104),f196(f888(x36101,a876))),x36104)
% 160.93/160.64 [3633]E(f334(f334(f167(x36331),f334(f334(f153(x36331),x36332),x36333)),f334(a116,x36334)),f334(f334(f167(x36331),x36333),x36334))
% 160.93/160.64 [3677]P29(x36771,f2(a881),f334(f334(f334(f92(x36771),x36772),f334(a26,x36773)),x36774))
% 160.93/160.64 [3702]E(f334(f334(x37021,x37022),f334(f192(x37023,x37024,x37021),x37022)),f334(f192(x37023,x37024,x37021),f334(a116,x37022)))
% 160.93/160.64 [3797]E(f334(f334(f161(x37971,f334(f334(f153(x37971),x37972),x37973)),f2(a881)),x37974),f334(f334(f153(x37971),x37974),x37973))
% 160.93/160.64 [3808]E(f334(f334(f41(f888(x38081,a876),f888(x38082,a876)),x38083),f313(x38081,x38082,x38084)),f334(f313(x38081,x38082,x38084),f39(f888(x38081,a876),x38083)))
% 160.93/160.64 [3809]E(f334(f334(f41(f888(x38091,a876),f888(x38092,a876)),x38093),f314(x38092,x38091,x38094)),f334(f314(x38092,x38091,x38094),f39(f888(x38091,a876),x38093)))
% 160.93/160.64 [3905]E(f186(x39051,x39052,f190(x39051,x39052,x39053,x39054)),f334(f334(f105(f888(x39051,a876)),f186(x39051,x39052,x39053)),x39054))
% 160.93/160.64 [3909]E(f334(f131(x39091,x39092),f129(x39091,x39093,x39094)),f334(f334(f80(a881),f334(f334(f80(a881),f334(x39092,x39093)),f334(f131(x39091,x39092),x39094))),f334(a116,f2(a881))))
% 160.93/160.64 [3928]E(f334(f144(x39281,x39282,f334(f7(x39282,x39281,x39281),x39283),x39284),f334(f171(x39282),f117(x39282))),x39284)
% 160.93/160.64 [3977]E(f76(x39771,x39772,x39773,x39774,f196(f888(x39771,a876))),x39773)
% 160.93/160.64 [4022]E(f334(f334(f334(f334(f72(x40221,f885(x40222)),f334(f16(f885(x40222),x40221),f210(x40222))),x40223),f210(x40222)),x40224),f210(x40222))
% 160.93/160.64 [4179]E(f334(f273(x41791,x41792,x41793),f334(f334(f8(f888(x41792,f887(x41791,x41792)),f888(x41792,x41793),x41791),f334(f8(f887(x41791,x41792),x41793,x41792),x41794)),f269(x41791,x41792))),x41794)
% 160.93/160.64 [3485]E(f334(f272(x34851,x34852),f334(f334(f269(x34851,x34852),x34853),x34854)),x34854)
% 160.93/160.64 [3486]E(f334(f268(x34861,x34862),f334(f334(f269(x34861,x34862),x34863),x34864)),x34863)
% 160.93/160.64 [3521]E(f334(f197(f882(x35211)),f334(f334(f161(x35211,x35212),x35213),x35214)),f334(f197(f882(x35211)),x35212))
% 160.93/160.64 [3522]E(f334(f197(f882(x35221)),f334(f334(f156(x35222,x35221),x35223),x35224)),f334(f197(f882(x35222)),x35224))
% 160.93/160.64 [3542]E(f334(f334(f140(x35421),f334(a116,x35422)),f334(f334(f153(x35421),x35423),x35424)),f334(f334(f140(x35421),x35422),x35424))
% 160.93/160.64 [3612]E(f334(f334(f312(x36121),x36122),f334(f334(f312(x36121),x36123),x36124)),f334(f334(f312(x36121),x36123),f334(f334(f312(x36121),x36122),x36124)))
% 160.93/160.64 [3615]E(f334(f334(f156(x36151,x36152),x36153),f118(x36151,x36154)),f118(x36152,f334(f334(f156(x36151,x36152),x36153),x36154)))
% 160.93/160.64 [3631]E(f334(f171(x36311),f334(f334(f156(x36312,x36311),x36313),x36314)),f334(f334(f156(x36312,x36311),x36313),f334(f171(x36312),x36314)))
% 160.93/160.64 [3632]E(f334(f334(f156(x36321,x36322),x36323),f334(f173(x36321),x36324)),f334(f173(x36322),f334(f334(f156(x36321,x36322),x36323),x36324)))
% 160.93/160.64 [3645]E(f334(f334(f177(x36451),f334(a116,x36452)),f334(f334(f153(x36451),x36453),x36454)),f334(f334(f153(x36451),x36453),f334(f334(f177(x36451),x36452),x36454)))
% 160.93/160.64 [3649]E(f334(f174(x36491),f334(f334(f156(x36492,x36491),x36493),x36494)),f334(f313(x36492,x36491,x36493),f334(f174(x36492),x36494)))
% 160.93/160.64 [3701]E(f17(x37011,x37012,x37013,f334(a3,f334(a116,f334(a19,x37014)))),f334(x37013,x37014))
% 160.93/160.64 [3704]E(f334(f334(f136(x37041),f334(f138(x37041,x37042),x37043)),f334(f138(x37041,x37042),x37044)),f334(f138(x37041,x37042),f334(f334(f136(x37041),x37043),x37044)))
% 160.93/160.64 [3717]E(f154(x37171,f334(f334(f156(x37172,x37171),x37173),f154(x37172,x37174))),f154(x37171,f334(f334(f156(x37172,x37171),x37173),x37174)))
% 160.93/160.64 [3733]E(f334(f289(x37331,x37331),f334(f334(f290(x37332,x37331),x37333),x37334)),f334(f334(f290(x37332,x37331),f334(f289(x37332,x37332),x37333)),x37334))
% 160.93/160.64 [3743]E(f334(f334(f291(x37431,x37432,x37433),x37434),f196(f888(f887(x37432,x37433),a876))),f196(f888(f887(x37431,x37433),a876)))
% 160.93/160.64 [3744]E(f334(f334(f177(x37441),f334(f334(f22(a881),x37442),x37443)),f334(f334(f140(x37441),x37443),x37444)),f334(f334(f140(x37441),x37443),f334(f334(f177(x37441),x37442),x37444)))
% 160.93/160.64 [3789]E(f39(f888(x37891,a876),f334(f313(x37892,f888(x37891,a876),x37893),x37894)),f334(f334(f41(x37892,f888(x37891,a876)),x37894),x37893))
% 160.93/160.64 [3790]E(f40(f888(x37901,a876),f334(f313(x37902,f888(x37901,a876),x37903),x37904)),f334(f334(f42(x37902,f888(x37901,a876)),x37904),x37903))
% 160.93/160.64 [3791]E(f334(f197(f882(f887(x37911,x37912))),f334(f334(f184(x37911,x37912),x37913),x37914)),f334(f334(f246(a881),f334(f197(f882(x37911)),x37913)),f334(f197(f882(x37912)),x37914)))
% 160.93/160.64 [3793]E(f334(f314(x37931,x37932,x37933),f334(f79(f888(x37932,a876)),x37934)),f334(f79(f888(x37931,a876)),f334(f314(x37931,x37932,x37933),x37934)))
% 160.93/160.64 [3823]E(f334(f190(x38231,x38232,x38233,f196(f888(x38231,a876))),x38234),f210(x38232))
% 160.93/160.64 [3844]E(f334(f314(x38441,x38442,x38443),f334(f254(x38442),x38444)),f334(f254(x38441),f334(f334(f8(x38442,a876,x38441),x38444),x38443)))
% 160.93/160.64 [3861]E(f334(f334(f167(x38611),f334(f334(f136(x38611),x38612),f334(f334(f153(x38611),x38613),x38614))),f334(f197(f882(x38611)),x38612)),x38613)
% 160.93/160.64 [3866]E(f334(f190(x38661,x38662,f334(f16(f885(x38662),x38661),f210(x38662)),x38663),x38664),f210(x38662))
% 160.93/160.64 [3886]E(f334(f313(x38861,x38862,x38863),f334(f314(x38861,x38862,x38863),x38864)),f334(f334(f105(f888(x38862,a876)),x38864),f334(f313(x38861,x38862,x38863),f257(f888(x38861,a876)))))
% 160.93/160.64 [3904]P1(f334(f334(f336(x39041),f334(x39042,x39043)),f334(f313(x39044,x39041,x39042),f257(f888(x39044,a876)))))
% 160.93/160.64 [3917]E(f334(f334(f271(x39171,x39172),f334(f174(x39171),x39173)),f334(f16(f888(x39172,a876),x39171),f334(f174(x39172),x39174))),f334(f174(f887(x39171,x39172)),f59(x39171,x39172,x39173,x39174)))
% 160.93/160.64 [3931]E(f157(x39311,x39312,f334(f334(f153(x39311),x39313),x39314)),f334(f334(f80(a881),f334(f334(f80(a881),f334(x39312,x39313)),f157(x39311,x39312,x39314))),f334(a116,f2(a881))))
% 160.93/160.64 [3946]E(f193(f882(x39461),f334(f334(f153(x39461),x39462),x39463),f334(f334(f7(a881,f882(x39461),f882(x39461)),f140(x39461)),x39463),x39464),f334(f334(f140(x39461),x39464),f334(f334(f153(x39461),x39462),x39463)))
% 160.93/160.64 [3947]P27(x39471,f887(x39472,x39471),f338(x39473,x39474,x39472,x39471),f334(f334(f41(x39472,f888(x39471,a876)),x39474),x39473))
% 160.93/160.64 [3956]E(f334(f334(f22(f888(x39561,a876)),f334(f334(f22(f888(x39561,a876)),x39562),x39563)),f334(f334(f312(x39561),x39564),f196(f888(x39561,a876)))),f334(f334(f22(f888(x39561,a876)),x39562),f334(f334(f312(x39561),x39564),x39563)))
% 160.93/160.64 [3968]E(f334(f334(f191(f888(x39681,x39682),f888(x39681,x39682)),x39683),f73(x39682,x39682,x39681,x39684)),f73(x39682,x39682,x39681,f334(f334(f191(x39682,x39682),x39683),x39684)))
% 160.93/160.64 [4045]E(f334(f334(f334(f191(f882(x40451),f882(x40451)),x40452),f170(x40451)),f334(f334(f334(f191(f882(x40451),f882(x40451)),x40453),f170(x40451)),x40454)),f334(f334(f334(f191(f882(x40451),f882(x40451)),f334(f334(f80(a881),x40452),x40453)),f170(x40451)),x40454))
% 160.93/160.64 [4132]P1(f334(f334(f248(f888(x41321,a876)),f334(f174(x41321),f334(f334(f161(x41321,x41322),x41323),x41324))),f334(f334(f312(x41321),x41324),f334(f174(x41321),x41322))))
% 160.93/160.64 [4169]E(f334(f334(f41(f888(x41691,a876),f888(f887(x41691,x41692),a876)),x41693),f334(f334(f7(f888(x41691,a876),f888(x41691,f888(x41692,a876)),f888(f887(x41691,x41692),a876)),f271(x41691,x41692)),x41694)),f334(f334(f271(x41691,x41692),f39(f888(x41691,a876),x41693)),x41694))
% 160.93/160.64 [4206]E(f222(x42061,x42062,x42063,f334(f73(x42062,f888(a103,f888(a103,f888(f887(a103,a103),f888(a103,f883(x42062))))),x42061,f217(x42062)),x42064)),f223(x42061,x42062,x42064,x42063))
% 160.93/160.64 [4223]E(f219(x42231,x42232,x42233,f334(f73(x42232,f888(a103,f888(a103,f888(f887(a103,a103),f888(a103,f883(f885(x42232)))))),x42231,f218(x42232)),x42234)),f220(x42231,x42232,x42234,x42233))
% 160.93/160.64 [4228]P1(f334(f66(x42281,x42282,x42283,x42284,f196(f888(x42281,a876))),x42284))
% 160.93/160.64 [4270]E(f334(f334(f41(x42701,f888(x42702,a876)),x42703),f334(f334(f7(x42701,f888(x42702,a876),f888(x42702,a876)),f334(f334(f8(x42702,f888(f888(x42702,a876),f888(x42702,a876)),x42701),f312(x42702)),x42704)),f196(f888(x42702,a876)))),f334(f313(x42701,x42702,x42704),x42703))
% 160.93/160.64 [4277]P1(f334(f334(f248(f888(x42771,a876)),f334(f265(x42772,x42771),f334(f334(f105(f888(f887(x42772,x42771),a876)),x42773),x42774))),f334(f334(f105(f888(x42771,a876)),f334(f265(x42772,x42771),x42773)),f334(f265(x42772,x42771),x42774))))
% 160.93/160.64 [4278]P1(f334(f334(f248(f888(x42781,a876)),f334(f267(x42781,x42782),f334(f334(f105(f888(f887(x42781,x42782),a876)),x42783),x42784))),f334(f334(f105(f888(x42781,a876)),f334(f267(x42781,x42782),x42783)),f334(f267(x42781,x42782),x42784))))
% 160.93/160.64 [4340]P1(f334(f334(f248(f888(f887(x43401,x43402),a876)),f334(f313(x43402,f887(x43401,x43402),f338(x43403,x43404,x43401,x43402)),f334(f334(f41(x43401,f888(x43402,a876)),x43404),x43403))),f334(f334(f271(x43401,x43402),x43404),x43403)))
% 160.93/160.64 [4341]E(f334(f122(x43411,f887(x43411,x43412),x43413),f334(f334(f8(f888(x43412,f883(f887(x43411,x43412))),f883(f887(x43411,x43412)),x43411),f122(x43412,f887(x43411,x43412),x43414)),f334(f334(f8(f888(x43412,f887(x43411,x43412)),f888(x43412,f883(f887(x43411,x43412))),x43411),f334(f8(f887(x43411,x43412),f883(f887(x43411,x43412)),x43412),f128(f887(x43411,x43412)))),f269(x43411,x43412)))),f133(x43411,x43412,x43413,x43414))
% 160.93/160.64 [4381]E(f85(f887(x43811,x43812),f334(f273(x43811,x43812,a876),f334(f334(f7(x43811,f888(x43812,a876),f888(x43812,a876)),f334(f334(f8(f888(a876,a876),f888(f888(x43812,a876),f888(x43812,a876)),x43811),f8(a876,a876,x43812)),f334(f334(f8(a876,f888(a876,a876),x43811),a332),f334(a331,x43813)))),f334(a331,x43814)))),f334(f334(f269(x43811,x43812),x43813),x43814))
% 160.93/160.64 [4382]E(f90(f887(x43821,x43822),f334(f273(x43821,x43822,a876),f334(f334(f7(x43821,f888(x43822,a876),f888(x43822,a876)),f334(f334(f8(f888(a876,a876),f888(f888(x43822,a876),f888(x43822,a876)),x43821),f8(a876,a876,x43822)),f334(f334(f8(a876,f888(a876,a876),x43821),a332),f334(a331,x43823)))),f334(a331,x43824)))),f334(f334(f269(x43821,x43822),x43823),x43824))
% 160.93/160.64 [4454]E(f334(f334(f273(f882(x44541),f882(x44541),f887(f882(x44541),f882(x44541))),f334(f334(f18(f882(x44541),f888(f882(x44541),f887(f882(x44541),f882(x44541))),f888(f882(x44541),f887(f882(x44541),f882(x44541)))),f334(f334(f8(f888(f882(x44541),f888(f887(f882(x44541),f882(x44541)),f887(f882(x44541),f882(x44541)))),f888(f888(f882(x44541),f887(f882(x44541),f882(x44541))),f888(f882(x44541),f887(f882(x44541),f882(x44541)))),f882(x44541)),f18(f882(x44541),f887(f882(x44541),f882(x44541)),f887(f882(x44541),f882(x44541)))),f334(f334(f8(f888(f882(x44541),f887(f882(x44541),f882(x44541))),f888(f882(x44541),f888(f887(f882(x44541),f882(x44541)),f887(f882(x44541),f882(x44541)))),f882(x44541)),f334(f8(f887(f882(x44541),f882(x44541)),f888(f887(f882(x44541),f882(x44541)),f887(f882(x44541),f882(x44541))),f882(x44541)),f334(f100(f887(f882(x44541),f882(x44541))),f334(x44542,x44543)))),f334(f334(f8(f882(x44541),f888(f882(x44541),f887(f882(x44541),f882(x44541))),f882(x44541)),f269(f882(x44541),f882(x44541))),f334(f153(x44541),x44543))))),f334(f334(f7(f882(x44541),f888(f882(x44541),f882(x44541)),f888(f882(x44541),f887(f882(x44541),f882(x44541)))),f334(f334(f8(f888(f882(x44541),f887(f882(x44541),f882(x44541))),f888(f888(f882(x44541),f882(x44541)),f888(f882(x44541),f887(f882(x44541),f882(x44541)))),f882(x44541)),f8(f882(x44541),f887(f882(x44541),f882(x44541)),f882(x44541))),f269(f882(x44541),f882(x44541)))),f334(f153(x44541),x44543)))),f169(x44541,x44542,x44544)),f169(x44541,x44542,f334(f334(f153(x44541),x44543),x44544)))
% 160.93/160.64 [4460]E(f334(f144(f888(x44601,f885(x44602)),f887(x44601,x44602),f334(f7(f887(x44601,x44602),f888(x44601,f885(x44602)),f888(x44601,f885(x44602))),f334(f273(x44601,x44602,f888(f888(x44601,f885(x44602)),f888(x44601,f885(x44602)))),f334(f334(f7(x44601,f888(x44602,f885(x44602)),f888(x44602,f888(f888(x44601,f885(x44602)),f888(x44601,f885(x44602))))),f334(f334(f8(f888(f885(x44602),f888(f888(x44601,f885(x44602)),f888(x44601,f885(x44602)))),f888(f888(x44602,f885(x44602)),f888(x44602,f888(f888(x44601,f885(x44602)),f888(x44601,f885(x44602))))),x44601),f8(f885(x44602),f888(f888(x44601,f885(x44602)),f888(x44601,f885(x44602))),x44602)),f334(f334(f8(f888(f888(x44601,f885(x44602)),f888(f885(x44602),f888(x44601,f885(x44602)))),f888(f885(x44602),f888(f888(x44601,f885(x44602)),f888(x44601,f885(x44602)))),x44601),f7(f888(x44601,f885(x44602)),f885(x44602),f888(x44601,f885(x44602)))),f334(f7(f888(x44601,f885(x44602)),x44601,f888(f885(x44602),f888(x44601,f885(x44602)))),f72(x44601,f885(x44602)))))),f241(x44602)))),x44603),f334(f171(f887(x44601,x44602)),x44604)),f187(x44601,x44602,x44603,f334(f180(x44601,x44602),x44604)))
% 160.93/160.64 [3561]E(f334(f197(f880(x35611)),f334(f334(f334(f92(x35611),x35612),x35613),x35614)),f2(a881))
% 160.93/160.64 [3680]E(f334(f334(f177(x36801),x36802),f334(f334(f177(x36801),x36803),x36804)),f334(f334(f177(x36801),f334(f334(f246(a881),x36802),x36803)),x36804))
% 160.93/160.64 [3681]E(f334(f334(f140(x36811),x36812),f334(f334(f140(x36811),x36813),x36814)),f334(f334(f140(x36811),f334(f334(f80(a881),x36812),x36813)),x36814))
% 160.93/160.64 [3693]E(f334(f334(f136(x36931),f334(f334(f153(x36931),x36932),x36933)),x36934),f334(f334(f153(x36931),x36932),f334(f334(f136(x36931),x36933),x36934)))
% 160.93/160.64 [3694]E(f334(f334(f136(x36941),f334(f334(f136(x36941),x36942),x36943)),x36944),f334(f334(f136(x36941),x36942),f334(f334(f136(x36941),x36943),x36944)))
% 160.93/160.64 [3773]E(f334(f334(f167(x37731),f334(f334(f153(x37731),x37732),x37733)),x37734),f193(x37731,x37732,f334(f167(x37731),x37733),x37734))
% 160.93/160.64 [3782]E(f334(f334(f191(x37821,x37821),x37822),f334(f334(f191(x37821,x37821),x37823),x37824)),f334(f334(f191(x37821,x37821),f334(f334(f81(a881),x37823),x37822)),x37824))
% 160.93/160.64 [3811]E(f334(f334(f114(f888(x38111,a876)),x38112),f334(f334(f312(x38111),x38113),x38114)),f334(f334(f312(x38111),x38113),f334(f334(f114(f888(x38111,a876)),x38112),x38114)))
% 160.93/160.64 [3826]E(f334(f334(f334(f191(x38261,x38261),x38262),x38263),f334(x38263,x38264)),f334(x38263,f334(f334(f334(f191(x38261,x38261),x38262),x38263),x38264)))
% 160.93/160.64 [3834]E(f334(f334(f291(x38341,x38342,x38343),f196(f888(f887(x38341,x38342),a876))),x38344),f196(f888(f887(x38341,x38343),a876)))
% 160.93/160.64 [3850]E(f334(f334(f114(f888(x38501,a876)),f334(f334(f312(x38501),x38502),x38503)),x38504),f334(f334(f312(x38501),x38502),f334(f334(f114(f888(x38501,a876)),x38503),x38504)))
% 160.93/160.64 [3868]E(f187(x38681,x38682,f334(f180(x38681,x38682),x38683),f334(f180(x38681,x38682),x38684)),f334(f180(x38681,x38682),f334(f334(f136(f887(x38681,x38682)),x38684),x38683)))
% 160.93/160.64 [3869]E(f334(f37(f887(x38691,x38692)),f334(f334(f271(x38691,x38692),x38693),f334(f16(f888(x38692,a876),x38691),x38694))),f334(f334(f81(a881),f334(f37(x38691),x38693)),f334(f37(x38692),x38694)))
% 160.93/160.64 [3875]E(f334(f334(f105(f888(x38751,a876)),f334(f334(f312(x38751),x38752),x38753)),f334(f334(f312(x38751),x38752),x38754)),f334(f334(f312(x38751),x38752),f334(f334(f105(f888(x38751,a876)),x38753),x38754)))
% 160.93/160.64 [3890]E(f334(f334(f114(f888(x38901,a876)),x38902),f334(f334(f114(f888(x38901,a876)),x38903),x38904)),f334(f334(f114(f888(x38901,a876)),x38903),f334(f334(f114(f888(x38901,a876)),x38902),x38904)))
% 160.93/160.64 [3891]E(f334(f334(f105(f888(x38911,a876)),x38912),f334(f334(f105(f888(x38911,a876)),x38913),x38914)),f334(f334(f105(f888(x38911,a876)),x38913),f334(f334(f105(f888(x38911,a876)),x38912),x38914)))
% 160.93/160.64 [3900]E(f64(x39001,x39002,f334(f334(f8(x39002,f888(x39002,x39002),x39001),x39003),x39004)),f334(f65(x39002,x39001,x39003),x39004))
% 160.93/160.64 [3910]E(f182(x39101,f334(f334(f156(f882(x39102),f882(x39101)),f334(f156(x39102,x39101),x39103)),x39104)),f334(f334(f156(f882(x39102),f882(x39101)),f334(f156(x39102,x39101),x39103)),f182(x39102,x39104)))
% 160.93/160.64 [3927]E(f334(f144(f882(x39271),f882(x39271),f136(x39271),f117(x39271)),f334(f334(f156(x39272,f882(x39271)),x39273),x39274)),f166(x39272,x39271,x39273,x39274))
% 160.93/160.64 [3930]E(f190(x39301,x39302,x39303,f334(f79(f888(x39301,a876)),f334(f334(f312(x39301),x39304),f196(f888(x39301,a876))))),f334(f334(f334(f72(x39301,f885(x39302)),x39303),x39304),f210(x39302)))
% 160.93/160.64 [3973]E(f334(f334(f334(f72(x39731,f885(x39732)),f334(f180(x39731,x39732),x39733)),f334(f268(x39731,x39732),x39734)),f334(f241(x39732),f334(f272(x39731,x39732),x39734))),f334(f180(x39731,x39732),f334(f334(f153(f887(x39731,x39732)),x39734),x39733)))
% 160.93/160.64 [3990]E(f334(f73(x39901,x39901,x39901,f334(f334(f191(x39901,x39901),x39902),x39903)),f334(f334(f191(x39901,x39901),x39904),x39903)),f334(f334(f191(x39901,x39901),f334(f334(f80(a881),x39902),x39904)),x39903))
% 160.93/160.64 [4014]E(f334(f334(f105(f888(x40141,a876)),f334(f334(f114(f888(x40141,a876)),x40142),x40143)),f334(f334(f114(f888(x40141,a876)),x40142),x40144)),f334(f334(f114(f888(x40141,a876)),x40142),f334(f334(f105(f888(x40141,a876)),x40143),x40144)))
% 160.93/160.64 [4015]E(f334(f334(f105(f888(x40151,a876)),f334(f334(f22(f888(x40151,a876)),x40152),x40153)),f334(f334(f22(f888(x40151,a876)),x40152),x40154)),f334(f334(f22(f888(x40151,a876)),x40152),f334(f334(f114(f888(x40151,a876)),x40153),x40154)))
% 160.93/160.64 [4016]E(f334(f334(f114(f888(x40161,a876)),f334(f334(f22(f888(x40161,a876)),x40162),x40163)),f334(f334(f22(f888(x40161,a876)),x40162),x40164)),f334(f334(f22(f888(x40161,a876)),x40162),f334(f334(f105(f888(x40161,a876)),x40163),x40164)))
% 160.93/160.64 [4017]E(f334(f334(f114(f888(x40171,a876)),f334(f334(f105(f888(x40171,a876)),x40172),x40173)),f334(f334(f105(f888(x40171,a876)),x40172),x40174)),f334(f334(f105(f888(x40171,a876)),x40172),f334(f334(f114(f888(x40171,a876)),x40173),x40174)))
% 160.93/160.64 [4018]E(f334(f334(f22(f888(x40181,a876)),f334(f334(f105(f888(x40181,a876)),x40182),x40183)),f334(f334(f105(f888(x40181,a876)),x40182),x40184)),f334(f334(f105(f888(x40181,a876)),x40182),f334(f334(f22(f888(x40181,a876)),x40183),x40184)))
% 160.93/160.64 [4024]E(f334(f37(f887(x40241,x40242)),f334(f334(f271(x40241,x40242),f334(f334(f312(x40241),x40243),f196(f888(x40241,a876)))),f334(f16(f888(x40242,a876),x40241),x40244))),f334(f37(x40242),x40244))
% 160.93/160.64 [4061]E(f334(f334(f42(x40611,f888(x40612,a876)),x40613),f334(f334(f8(f888(x40612,a876),f888(x40612,a876),x40611),f79(f888(x40612,a876))),x40614)),f334(f79(f888(x40612,a876)),f334(f334(f41(x40611,f888(x40612,a876)),x40613),x40614)))
% 160.93/160.64 [4062]E(f334(f334(f41(x40621,f888(x40622,a876)),x40623),f334(f334(f8(f888(x40622,a876),f888(x40622,a876),x40621),f79(f888(x40622,a876))),x40624)),f334(f79(f888(x40622,a876)),f334(f334(f42(x40621,f888(x40622,a876)),x40623),x40624)))
% 160.93/160.64 [4076]E(f334(f334(f291(x40761,x40761,x40761),f334(f334(f191(f887(x40761,x40761),a876),x40762),x40763)),f334(f334(f191(f887(x40761,x40761),a876),x40764),x40763)),f334(f334(f191(f887(x40761,x40761),a876),f334(f334(f80(a881),x40762),x40764)),x40763))
% 160.93/160.64 [4107]E(f334(f334(f42(x41071,f888(f888(x41072,a876),a876)),x41073),f334(f334(f8(f888(x41072,a876),f888(f888(x41072,a876),a876),x41071),f311(x41072)),x41074)),f334(f311(x41072),f334(f334(f42(x41071,f888(x41072,a876)),x41073),x41074)))
% 160.93/160.64 [4136]E(f334(f334(f41(f888(x41361,a876),f888(x41362,a876)),x41363),f334(f334(f7(f888(x41361,a876),f888(x41361,f888(x41362,a876)),f888(x41362,a876)),f41(x41361,f888(x41362,a876))),x41364)),f334(f334(f41(x41361,f888(x41362,a876)),f39(f888(x41361,a876),x41363)),x41364))
% 160.93/160.64 [4137]E(f334(f334(f42(f888(x41371,a876),f888(x41372,a876)),x41373),f334(f334(f7(f888(x41371,a876),f888(x41371,f888(x41372,a876)),f888(x41372,a876)),f42(x41371,f888(x41372,a876))),x41374)),f334(f334(f42(x41371,f888(x41372,a876)),f39(f888(x41371,a876),x41373)),x41374))
% 160.93/160.64 [4142]E(f334(f334(f156(x41421,x41422),x41423),f334(f144(f882(x41421),f882(x41421),f136(x41421),f117(x41421)),x41424)),f334(f144(f882(x41422),f882(x41422),f136(x41422),f117(x41422)),f334(f334(f156(f882(x41421),f882(x41422)),f334(f156(x41421,x41422),x41423)),x41424)))
% 160.93/160.64 [4147]E(f193(f882(x41471),f117(x41471),f334(f334(f8(f882(x41471),f882(x41471),a881),f334(f153(x41471),x41472)),f334(f334(f7(a881,f882(x41471),f882(x41471)),f177(x41471)),x41473)),x41474),f334(f334(f177(x41471),x41474),f334(f334(f153(x41471),x41472),x41473)))
% 160.93/160.64 [4189]P1(f334(f334(f248(f888(x41891,a876)),f334(f313(x41892,x41891,x41893),f334(f314(x41892,x41891,x41893),x41894))),x41894))
% 160.93/160.64 [4192]E(f334(f313(f887(x41921,x41922),f887(x41922,x41921),f334(f273(x41921,x41922,f887(x41922,x41921)),f334(f7(x41922,x41921,f887(x41922,x41921)),f269(x41922,x41921)))),f334(f334(f271(x41921,x41922),x41923),f334(f16(f888(x41922,a876),x41921),x41924))),f334(f334(f271(x41922,x41921),x41924),f334(f16(f888(x41921,a876),x41922),x41923)))
% 160.93/160.64 [4201]E(f334(f334(f41(x42011,f888(x42012,a876)),x42013),f334(f334(f8(f888(x42011,a876),f888(x42012,a876),x42011),f288(x42011,x42012,x42014)),f334(f334(f7(x42011,f888(x42011,a876),f888(x42011,a876)),f312(x42011)),f196(f888(x42011,a876))))),f334(f288(x42011,x42012,x42014),x42013))
% 160.93/160.64 [4202]E(f334(f334(f41(x42021,f888(x42022,a876)),x42023),f334(f334(f8(f888(x42021,a876),f888(x42022,a876),x42021),f314(x42022,x42021,x42024)),f334(f334(f7(x42021,f888(x42021,a876),f888(x42021,a876)),f312(x42021)),f196(f888(x42021,a876))))),f334(f314(x42022,x42021,x42024),x42023))
% 160.93/160.64 [4292]E(f334(f334(f114(f888(x42921,a876)),f334(f334(f114(f888(x42921,a876)),f334(f334(f105(f888(x42921,a876)),x42922),x42923)),f334(f334(f105(f888(x42921,a876)),x42923),x42924))),f334(f334(f105(f888(x42921,a876)),x42924),x42922)),f334(f334(f105(f888(x42921,a876)),f334(f334(f105(f888(x42921,a876)),f334(f334(f114(f888(x42921,a876)),x42922),x42923)),f334(f334(f114(f888(x42921,a876)),x42923),x42924))),f334(f334(f114(f888(x42921,a876)),x42924),x42922)))
% 160.93/160.64 [4354]E(f334(f144(f882(x43541),f882(x43541),f136(x43541),f117(x43541)),f334(f334(f156(x43542,f882(x43541)),f334(f334(f7(x43542,f882(x43541),f882(x43541)),f334(f334(f8(x43541,f888(f882(x43541),f882(x43541)),x43542),f153(x43541)),x43543)),f117(x43541))),x43544)),f334(f334(f156(x43542,x43541),x43543),x43544))
% 160.93/160.64 [4365]E(f334(f334(f86(a1,x43651),f334(f107(a1),f334(f334(f80(a1),x43652),a101))),f334(f334(f18(a1,x43651,x43651),f334(f334(f7(a1,x43651,f888(x43651,x43651)),f334(f334(f8(a876,f888(x43651,f888(x43651,x43651)),a1),f100(x43651)),a201)),x43653)),f334(f334(f8(a881,x43651,a1),x43654),a108))),f193(x43651,x43653,x43654,f334(f107(a881),x43652)))
% 160.93/160.64 [4568]~P1(f334(f334(f196(f888(x45681,f888(x45682,a876))),x45683),x45684))
% 160.93/160.64 [3837]E(f334(f334(f167(x38371),f334(f334(f136(x38371),x38372),x38373)),f334(f334(f80(a881),f334(f197(f882(x38371)),x38372)),x38374)),f334(f334(f167(x38371),x38373),x38374))
% 160.93/160.64 [3843]E(f334(f334(f140(x38431),x38432),f334(f334(f177(x38431),f334(f334(f80(a881),x38433),x38432)),x38434)),f334(f334(f177(x38431),x38433),f334(f334(f140(x38431),x38432),x38434)))
% 160.93/160.64 [3944]E(f334(f334(f114(f888(x39441,a876)),f334(f265(x39442,x39441),x39443)),f334(f265(x39442,x39441),x39444)),f334(f265(x39442,x39441),f334(f334(f114(f888(f887(x39442,x39441),a876)),x39443),x39444)))
% 160.93/160.64 [3945]E(f334(f334(f114(f888(x39451,a876)),f334(f267(x39451,x39452),x39453)),f334(f267(x39451,x39452),x39454)),f334(f267(x39451,x39452),f334(f334(f114(f888(f887(x39451,x39452),a876)),x39453),x39454)))
% 160.93/160.64 [3950]E(f334(f334(f114(f888(x39501,a876)),f334(f334(f114(f888(x39501,a876)),x39502),x39503)),x39504),f334(f334(f114(f888(x39501,a876)),x39502),f334(f334(f114(f888(x39501,a876)),x39503),x39504)))
% 160.93/160.64 [3951]E(f334(f334(f22(f888(x39511,a876)),f334(f334(f105(f888(x39511,a876)),x39512),x39513)),x39514),f334(f334(f105(f888(x39511,a876)),x39512),f334(f334(f22(f888(x39511,a876)),x39513),x39514)))
% 160.93/160.64 [3952]E(f334(f334(f105(f888(x39521,a876)),f334(f334(f105(f888(x39521,a876)),x39522),x39523)),x39524),f334(f334(f105(f888(x39521,a876)),x39522),f334(f334(f105(f888(x39521,a876)),x39523),x39524)))
% 160.93/160.64 [3992]E(f334(f334(f114(f888(f887(x39921,x39922),a876)),f334(f289(x39922,x39921),x39923)),f334(f289(x39922,x39921),x39924)),f334(f289(x39922,x39921),f334(f334(f114(f888(f887(x39922,x39921),a876)),x39923),x39924)))
% 160.93/160.64 [3993]E(f334(f334(f105(f888(f887(x39931,x39932),a876)),f334(f289(x39932,x39931),x39933)),f334(f289(x39932,x39931),x39934)),f334(f289(x39932,x39931),f334(f334(f105(f888(f887(x39932,x39931),a876)),x39933),x39934)))
% 160.93/160.64 [4007]E(f334(f334(f114(f888(x40071,f888(x40072,a876))),f258(x40072,x40071,x40073)),f258(x40072,x40071,x40074)),f258(x40072,x40071,f334(f334(f114(f888(x40072,f888(x40071,a876))),x40073),x40074)))
% 160.93/160.64 [4008]E(f334(f334(f105(f888(x40081,f888(x40082,a876))),f258(x40082,x40081,x40083)),f258(x40082,x40081,x40084)),f258(x40082,x40081,f334(f334(f105(f888(x40082,f888(x40081,a876))),x40083),x40084)))
% 160.93/160.64 [4065]E(f334(f334(f105(f888(x40651,a876)),f334(f334(f114(f888(x40651,a876)),x40652),x40653)),f334(f334(f114(f888(x40651,a876)),x40654),x40653)),f334(f334(f114(f888(x40651,a876)),f334(f334(f105(f888(x40651,a876)),x40652),x40654)),x40653))
% 160.93/160.64 [4066]E(f334(f334(f114(f888(x40661,a876)),f334(f334(f22(f888(x40661,a876)),x40662),x40663)),f334(f334(f22(f888(x40661,a876)),x40664),x40663)),f334(f334(f22(f888(x40661,a876)),f334(f334(f114(f888(x40661,a876)),x40662),x40664)),x40663))
% 160.93/160.64 [4067]E(f334(f334(f114(f888(x40671,a876)),f334(f334(f105(f888(x40671,a876)),x40672),x40673)),f334(f334(f105(f888(x40671,a876)),x40674),x40673)),f334(f334(f105(f888(x40671,a876)),f334(f334(f114(f888(x40671,a876)),x40672),x40674)),x40673))
% 160.93/160.64 [4068]E(f334(f334(f22(f888(x40681,a876)),f334(f334(f105(f888(x40681,a876)),x40682),x40683)),f334(f334(f105(f888(x40681,a876)),x40684),x40683)),f334(f334(f105(f888(x40681,a876)),f334(f334(f22(f888(x40681,a876)),x40682),x40684)),x40683))
% 160.93/160.64 [4069]E(f334(f334(f22(f888(x40691,a876)),f334(f334(f105(f888(x40691,a876)),x40692),x40693)),f334(f334(f105(f888(x40691,a876)),x40694),x40693)),f334(f334(f22(f888(x40691,a876)),f334(f334(f105(f888(x40691,a876)),x40692),x40693)),x40694))
% 160.93/160.64 [4079]E(f334(f334(f22(f888(x40791,a876)),f334(f334(f22(f888(x40791,a876)),x40792),f334(f334(f312(x40791),x40793),f196(f888(x40791,a876))))),x40794),f334(f334(f22(f888(x40791,a876)),x40792),f334(f334(f312(x40791),x40793),x40794)))
% 160.93/160.64 [4133]E(f334(f334(f114(f888(x41331,a876)),f334(f334(f312(x41331),x41332),f334(f334(f312(x41331),x41333),f196(f888(x41331,a876))))),f334(f287(x41331),x41334)),f334(f287(x41331),f334(f334(f312(f887(x41331,x41331)),f334(f334(f269(x41331,x41331),x41332),x41333)),x41334)))
% 160.93/160.64 [4164]E(f334(f334(f41(a881,f888(x41641,a876)),f334(f303(a881),x41642)),f334(f334(f8(a881,f888(x41641,a876),a881),x41643),f334(f334(f7(a881,a881,a881),f80(a881)),x41644))),f334(f334(f41(a881,f888(x41641,a876)),f305(a881,x41644,f334(f334(f80(a881),x41642),x41644))),x41643))
% 160.93/160.64 [4165]E(f176(x41651,f334(f288(x41651,x41651,x41652),f334(f334(f312(x41651),x41653),f196(f888(x41651,a876)))),f334(f288(f882(x41651),f882(x41651),f160(x41651,x41652)),f334(f334(f312(f882(x41651)),x41654),f196(f888(f882(x41651),a876))))),f334(f288(f882(x41651),f882(x41651),f160(x41651,x41652)),f334(f334(f312(f882(x41651)),f334(f334(f153(x41651),x41653),x41654)),f196(f888(f882(x41651),a876)))))
% 160.93/160.64 [4226]E(f334(f180(x42261,x42262),f334(f334(f156(x42261,f887(x42261,x42262)),f334(f334(f18(x42261,x42262,f887(x42261,x42262)),f269(x42261,x42262)),x42263)),x42264)),f190(x42261,x42262,f334(f73(x42262,f885(x42262),x42261,f241(x42262)),x42263),f334(f174(x42261),x42264)))
% 160.93/160.64 [4231]E(f334(f254(x42311),f334(f334(f7(x42311,f888(x42312,a876),a876),f334(f334(f8(x42312,f888(f888(x42312,a876),a876),x42311),f336(x42312)),x42313)),x42314)),f334(f314(x42311,x42312,x42313),x42314))
% 160.93/160.64 [4325]E(f334(f254(x43251),f334(f334(f7(x43251,f888(f887(x43252,x43251),a876),a876),f334(f334(f8(f887(x43252,x43251),f888(f888(f887(x43252,x43251),a876),a876),x43251),f336(f887(x43252,x43251))),f334(f269(x43252,x43251),x43253))),x43254)),f334(f288(x43252,x43251,x43254),f334(f334(f312(x43252),x43253),f196(f888(x43252,a876)))))
% 160.93/160.64 [4339]E(f334(f334(f156(f887(x43391,a881),x43391),f268(x43391,a881)),f334(f138(f887(x43391,a881),f334(f334(f8(a881,a876,f887(x43391,a881)),x43392),f334(f334(f8(a881,a881,f887(x43391,a881)),a116),f272(x43391,a881)))),f334(f334(f184(x43391,a881),x43393),x43394))),f334(f334(f156(f887(x43391,a881),x43391),f268(x43391,a881)),f334(f138(f887(x43391,a881),f334(f334(f8(a881,a876,f887(x43391,a881)),x43392),f272(x43391,a881))),f334(f334(f184(x43391,a881),x43393),f334(f334(f156(a881,a881),a116),x43394)))))
% 160.93/160.64 [4347]P1(f334(f334(f248(f888(f888(x43471,a876),a876)),f334(f334(f41(x43472,f888(f888(x43471,a876),a876)),x43473),f334(f334(f8(f888(x43471,a876),f888(f888(x43471,a876),a876),x43472),f311(x43471)),x43474))),f334(f311(x43471),f334(f334(f41(x43472,f888(x43471,a876)),x43473),x43474))))
% 160.93/160.64 [4389]E(f334(f334(f86(a1,x43891),f334(f107(a1),f334(f334(f80(a1),x43892),a101))),f334(f334(f18(a1,x43891,x43891),f334(f334(f7(a1,x43891,f888(x43891,x43891)),f334(f334(f8(a876,f888(x43891,f888(x43891,x43891)),a1),f100(x43891)),a201)),x43893)),f334(f334(f18(a1,x43891,x43891),f334(f334(f8(a881,f888(x43891,x43891),a1),x43894),a108)),f334(f334(f8(a881,x43891,a1),f192(x43891,x43893,x43894)),a108)))),f334(f192(x43891,x43893,x43894),f334(f107(a881),x43892)))
% 160.93/160.64 [4392]E(f334(f334(f156(x43921,x43922),f334(f73(f885(x43922),x43922,x43921,f245(x43922)),x43923)),f334(f138(x43921,f334(f334(f8(a876,a876,x43921),a329),f334(f334(f7(x43921,f885(x43922),a876),f334(f334(f8(f885(x43922),f888(f885(x43922),a876),x43921),a331),x43923)),f210(x43922)))),x43924)),f165(x43921,x43922,x43923,x43924))
% 160.93/160.64 [4415]E(f334(f254(f887(x44151,x44152)),f334(f273(x44151,x44152,a876),f334(f334(f7(x44151,f888(x44152,a876),f888(x44152,a876)),f334(f334(f8(f888(a876,a876),f888(f888(x44152,a876),f888(x44152,a876)),x44151),f8(a876,a876,x44152)),f334(f334(f8(a876,f888(a876,a876),x44151),a332),f334(f334(f7(x44151,f888(x44151,a876),a876),f336(x44151)),x44153)))),f334(f334(f7(x44152,f888(x44152,a876),a876),f336(x44152)),x44154)))),f235(x44151,x44152,x44153,x44154))
% 160.93/160.64 [4449]E(f334(f334(f41(x44491,f888(f887(x44491,x44492),a876)),x44493),f334(f334(f18(x44491,f888(x44492,f888(f887(x44491,x44492),a876)),f888(f887(x44491,x44492),a876)),f334(f334(f8(f888(x44492,a876),f888(f888(x44492,f888(f887(x44491,x44492),a876)),f888(f887(x44491,x44492),a876)),x44491),f41(x44492,f888(f887(x44491,x44492),a876))),x44494)),f334(f334(f7(x44491,f888(f887(x44491,x44492),a876),f888(x44492,f888(f887(x44491,x44492),a876))),f334(f334(f8(f888(x44492,f888(f888(f887(x44491,x44492),a876),f888(f887(x44491,x44492),a876))),f888(f888(f887(x44491,x44492),a876),f888(x44492,f888(f887(x44491,x44492),a876))),x44491),f7(x44492,f888(f887(x44491,x44492),a876),f888(f887(x44491,x44492),a876))),f334(f334(f8(f888(x44492,f887(x44491,x44492)),f888(x44492,f888(f888(f887(x44491,x44492),a876),f888(f887(x44491,x44492),a876))),x44491),f334(f8(f887(x44491,x44492),f888(f888(f887(x44491,x44492),a876),f888(f887(x44491,x44492),a876)),x44492),f312(f887(x44491,x44492)))),f269(x44491,x44492)))),f196(f888(f887(x44491,x44492),a876))))),f334(f334(f271(x44491,x44492),x44493),x44494))
% 160.93/160.64 [4002]E(f334(f334(f136(x40021),f334(f334(f177(x40021),x40022),x40023)),f334(f334(f177(x40021),f334(f334(f22(a881),x40022),f334(f197(f882(x40021)),x40023))),x40024)),f334(f334(f177(x40021),x40022),f334(f334(f136(x40021),x40023),x40024)))
% 160.93/160.64 [4003]E(f334(f334(f136(x40031),f334(f334(f140(x40031),x40032),x40033)),f334(f334(f140(x40031),f334(f334(f22(a881),x40032),f334(f197(f882(x40031)),x40033))),x40034)),f334(f334(f140(x40031),x40032),f334(f334(f136(x40031),x40033),x40034)))
% 160.93/160.64 [4054]E(f334(f334(f80(a881),f334(f334(f81(a881),x40541),x40542)),f334(f334(f80(a881),f334(f334(f81(a881),x40543),x40542)),x40544)),f334(f334(f80(a881),f334(f334(f81(a881),f334(f334(f80(a881),x40541),x40543)),x40542)),x40544))
% 160.93/160.64 [4256]P1(f334(f334(f248(f888(x42561,a876)),f334(f334(f22(f888(x42561,a876)),f334(f265(x42562,x42561),x42563)),f334(f265(x42562,x42561),x42564))),f334(f265(x42562,x42561),f334(f334(f22(f888(f887(x42562,x42561),a876)),x42563),x42564))))
% 160.93/160.64 [4257]P1(f334(f334(f248(f888(x42571,a876)),f334(f334(f22(f888(x42571,a876)),f334(f267(x42571,x42572),x42573)),f334(f267(x42571,x42572),x42574))),f334(f267(x42571,x42572),f334(f334(f22(f888(f887(x42571,x42572),a876)),x42573),x42574))))
% 160.93/160.64 [4367]E(f334(f334(f80(a1),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x43671),x43672)),f196(f888(f887(a881,a881),a876)))))),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x43673),x43674)),f196(f888(f887(a881,a881),a876)))))),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),f334(f334(f80(a881),x43671),x43673)),f334(f334(f80(a881),x43672),x43674))),f196(f888(f887(a881,a881),a876))))))
% 160.93/160.64 [4410]E(f334(f334(f81(a1),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x44101),x44102)),f196(f888(f887(a881,a881),a876)))))),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x44103),x44104)),f196(f888(f887(a881,a881),a876)))))),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),f334(f334(f80(a881),f334(f334(f81(a881),x44101),x44103)),f334(f334(f81(a881),x44102),x44104))),f334(f334(f80(a881),f334(f334(f81(a881),x44101),x44104)),f334(f334(f81(a881),x44102),x44103)))),f196(f888(f887(a881,a881),a876))))))
% 160.93/160.64 [4430]E(f334(f254(x44301),f334(f334(f8(f888(x44302,a876),a876,x44301),f88(x44302)),f334(f334(f8(f888(x44302,a876),f888(x44302,a876),x44301),f334(f18(x44302,a876,a876),f334(f334(f8(a876,f888(a876,a876),x44302),a337),f334(f334(f7(x44302,f888(x44302,a876),a876),f336(x44302)),x44303)))),f334(f334(f7(x44301,f888(x44302,f888(x44301,a876)),f888(x44302,a876)),f334(f334(f8(f888(f888(x44301,a876),a876),f888(f888(x44302,f888(x44301,a876)),f888(x44302,a876)),x44301),f8(f888(x44301,a876),a876,x44302)),f336(x44301))),x44304)))),f334(f334(f42(x44302,f888(x44301,a876)),x44303),x44304))
% 160.93/160.64 [4464]E(f334(f334(f291(x44641,x44641,x44641),f334(f334(f312(f887(x44641,x44641)),f334(f334(f269(x44641,x44641),x44642),x44643)),x44644)),f310(x44641,f334(f334(f312(f887(x44641,x44641)),f334(f334(f269(x44641,x44641),x44642),x44643)),x44644))),f334(f334(f114(f888(f887(x44641,x44641),a876)),f334(f334(f291(x44641,x44641,x44641),x44644),f310(x44641,x44644))),f334(f254(f887(x44641,x44641)),f334(f273(x44641,x44641,a876),f334(f334(f7(x44641,f888(x44641,a876),f888(x44641,a876)),f334(f334(f8(f888(a876,a876),f888(f888(x44641,a876),f888(x44641,a876)),x44641),f8(a876,a876,x44641)),f334(f334(f8(a876,f888(a876,a876),x44641),a332),f334(f334(f7(x44641,f888(f887(x44641,x44641),a876),a876),f334(f334(f8(f887(x44641,x44641),f888(f888(f887(x44641,x44641),a876),a876),x44641),f336(f887(x44641,x44641))),f334(f334(f7(x44641,x44641,f887(x44641,x44641)),f269(x44641,x44641)),x44642))),f310(x44641,x44644))))),f334(f334(f7(x44641,f888(f887(x44641,x44641),a876),a876),f334(f334(f8(f887(x44641,x44641),f888(f888(f887(x44641,x44641),a876),a876),x44641),f336(f887(x44641,x44641))),f334(f269(x44641,x44641),x44643))),f310(x44641,x44644)))))))
% 160.93/160.64 [4258]E(f334(f138(x42581,f334(f334(f18(x42581,a876,a876),f334(f334(f8(a876,f888(a876,a876),x42581),a332),x42582)),x42583)),x42584),f334(f138(x42581,x42583),f334(f138(x42581,x42582),x42584)))
% 160.93/160.64 [4361]E(f334(f334(f136(x43611),f334(f334(f334(f100(f882(x43611)),f334(f334(f336(a881),f2(a881)),x43612)),f334(f334(f153(x43611),x43613),f117(x43611))),f117(x43611))),f178(x43611,x43614,f334(f254(a881),f334(f334(f7(a881,f888(a881,a876),a876),f334(f334(f8(a881,f888(f888(a881,a876),a876),a881),f336(a881)),a116)),x43612)))),f178(x43611,f334(f334(f153(x43611),x43613),x43614),x43612))
% 160.93/160.64 [4458]E(f334(f254(f887(x44581,x44582)),f334(f334(f8(f888(a881,a876),a876,f887(x44581,x44582)),f87(a881)),f334(f334(f7(f887(x44581,x44582),f888(a881,a876),f888(a881,a876)),f334(f334(f8(f888(a881,f888(a876,a876)),f888(f888(a881,a876),f888(a881,a876)),f887(x44581,x44582)),f18(a881,a876,a876)),f334(f334(f8(f888(a881,a876),f888(a881,f888(a876,a876)),f887(x44581,x44582)),f334(f8(a876,f888(a876,a876),a881),a332)),f334(f334(f7(f887(x44581,x44582),f888(a881,f887(x44581,x44582)),f888(a881,a876)),f334(f334(f8(f888(f887(x44581,x44582),a876),f888(f888(a881,f887(x44581,x44582)),f888(a881,a876)),f887(x44581,x44582)),f8(f887(x44581,x44582),a876,a881)),a331)),f334(f334(f18(a881,x44582,f887(x44581,x44582)),f334(f334(f8(x44581,f888(x44582,f887(x44581,x44582)),a881),f269(x44581,x44582)),f334(f167(x44581),x44583))),f334(f167(x44582),x44584)))))),f334(f334(f7(a881,a881,a876),f249(a881)),f334(f334(f246(a881),f334(f197(f882(x44581)),x44583)),f334(f197(f882(x44582)),x44584)))))),f334(f174(f887(x44581,x44582)),f334(f334(f184(x44581,x44582),x44583),x44584)))
% 160.93/160.64 [4380]E(f334(f254(f887(x43801,x43802)),f334(f273(x43801,x43802,a876),f334(f334(f7(x43801,f888(x43802,a876),f888(x43802,a876)),f334(f334(f8(f888(a876,a876),f888(f888(x43802,a876),f888(x43802,a876)),x43801),f8(a876,a876,x43802)),f334(f334(f8(a876,f888(a876,a876),x43801),a332),x43803))),x43804))),f334(f334(f271(x43801,x43802),f334(f254(x43801),x43803)),f334(f16(f888(x43802,a876),x43801),f334(f254(x43802),x43804))))
% 160.93/160.64 [4383]E(f334(f254(f887(x43831,x43832)),f334(f273(x43831,x43832,a876),f334(f334(f18(x43831,f888(x43832,a876),f888(x43832,a876)),f334(f334(f8(f888(a876,a876),f888(f888(x43832,a876),f888(x43832,a876)),x43831),f8(a876,a876,x43832)),f334(f334(f8(a876,f888(a876,a876),x43831),a332),x43833))),x43834))),f334(f334(f271(x43831,x43832),f334(f254(x43831),x43833)),f334(f334(f8(f888(x43832,a876),f888(x43832,a876),x43831),f254(x43832)),x43834)))
% 160.93/160.64 [4399]E(f334(f254(x43991),f334(f334(f8(f888(x43992,a876),a876,x43991),f88(x43992)),f334(f334(f8(f888(x43992,a876),f888(x43992,a876),x43991),f334(f18(x43992,a876,a876),f334(f334(f8(a876,f888(a876,a876),x43992),a337),f334(f334(f7(x43992,f888(x43992,a876),a876),f336(x43992)),x43993)))),x43994))),f334(f334(f42(x43992,f888(x43991,a876)),x43993),f334(f334(f8(f888(x43991,a876),f888(x43991,a876),x43992),f254(x43991)),f334(f7(x43991,x43992,a876),x43994))))
% 160.93/160.64 [4444]E(f334(f334(f156(f887(x44441,a881),x44441),f268(x44441,a881)),f334(f138(f887(x44441,a881),f334(f334(f7(f887(x44441,a881),f888(a881,a876),a876),f334(f334(f8(a881,f888(f888(a881,a876),a876),f887(x44441,a881)),f336(a881)),f272(x44441,a881))),x44442)),f334(f334(f184(x44441,a881),x44443),f141(a881,f334(f304(a881,x44444),f334(f334(f80(a881),x44444),f334(f197(f882(x44441)),x44443))))))),f334(f334(f156(f887(x44441,a881),x44441),f268(x44441,a881)),f334(f138(f887(x44441,a881),f334(f334(f7(f887(x44441,a881),f888(a881,a876),a876),f334(f334(f8(a881,f888(f888(a881,a876),a876),f887(x44441,a881)),f336(a881)),f334(f334(f7(f887(x44441,a881),a881,a881),f334(f334(f8(a881,f888(a881,a881),f887(x44441,a881)),f80(a881)),f272(x44441,a881))),x44444))),x44442)),f334(f334(f184(x44441,a881),x44443),f141(a881,f334(f304(a881,f2(a881)),f334(f197(f882(x44441)),x44443)))))))
% 160.93/160.64 [4445]E(f334(a116,f334(f334(f247(a881),f334(f197(f882(x44451)),x44452)),f334(f144(a881,f882(x44453),f334(f7(f882(x44453),a881,a881),f334(f334(f8(a881,f888(a881,a881),f882(x44453)),f247(a881)),f334(f334(f7(f882(x44453),a881,a881),f334(f334(f8(a881,f888(a881,a881),f882(x44453)),f22(a881)),f197(f882(x44453)))),f334(a116,f2(a881))))),f2(a881)),f334(f171(f882(x44453)),f334(f138(f882(x44453),f334(f334(f8(a876,a876,f882(x44453)),a329),f334(f334(f7(f882(x44453),f882(x44453),a876),a331),f117(x44453)))),x44454))))),f334(f334(f247(a881),f334(a116,f334(f197(f882(x44451)),x44452))),f334(f144(a881,f882(x44453),f334(f7(f882(x44453),a881,a881),f334(f334(f8(a881,f888(a881,a881),f882(x44453)),f247(a881)),f197(f882(x44453)))),f2(a881)),f334(f171(f882(x44453)),x44454))))
% 160.93/160.64 [4398]E(f334(f334(f136(x43981),f178(x43981,x43982,x43983)),f178(x43981,x43984,f334(f254(a881),f334(f334(f7(a881,f888(a881,a876),a876),f334(f334(f8(a881,f888(f888(a881,a876),a876),a881),f336(a881)),f334(f334(f7(a881,a881,a881),f80(a881)),f334(f197(f882(x43981)),x43982)))),x43983)))),f178(x43981,f334(f334(f136(x43981),x43982),x43984),x43983))
% 160.93/160.64 [4451]E(f334(f334(f153(f882(x44511)),f334(f334(f153(x44511),x44512),f334(f144(f882(x44511),f882(x44511),f136(x44511),f117(x44511)),f334(f334(f156(f882(x44511),f882(x44511)),f158(f882(x44511),x44511,f117(x44511),f334(f334(f8(f882(x44511),f888(f882(x44511),f882(x44511)),x44511),f16(f882(x44511),f882(x44511))),f334(f334(f7(x44511,f882(x44511),f882(x44511)),f153(x44511)),f117(x44511))))),x44513)))),f182(x44511,f334(f334(f153(f882(x44511)),x44514),f334(f144(f882(f882(x44511)),f882(f882(x44511)),f136(f882(x44511)),f117(f882(x44511))),f334(f334(f156(f882(x44511),f882(f882(x44511))),f158(f882(f882(x44511)),x44511,f117(f882(x44511)),f334(f16(f888(f882(x44511),f882(f882(x44511))),x44511),f334(f334(f7(f882(x44511),f882(f882(x44511)),f882(f882(x44511))),f153(f882(x44511))),f117(f882(x44511)))))),x44513))))),f182(x44511,f334(f334(f153(f882(x44511)),f334(f334(f153(x44511),x44512),x44514)),x44513)))
% 160.93/160.64 [4459]E(f334(f254(f887(x44591,x44591)),f334(f273(x44591,x44591,a876),f334(f334(f7(x44591,f888(f887(x44592,x44592),a876),f888(x44591,a876)),f334(f334(f8(f888(x44591,f888(f888(f887(x44592,x44592),a876),a876)),f888(f888(f887(x44592,x44592),a876),f888(x44591,a876)),x44591),f7(x44591,f888(f887(x44592,x44592),a876),a876)),f334(f334(f8(f888(x44591,f887(x44592,x44592)),f888(x44591,f888(f888(f887(x44592,x44592),a876),a876)),x44591),f334(f8(f887(x44592,x44592),f888(f888(f887(x44592,x44592),a876),a876),x44591),f336(f887(x44592,x44592)))),f334(f334(f7(x44591,f888(x44591,x44592),f888(x44591,f887(x44592,x44592))),f334(f334(f8(f888(x44592,f887(x44592,x44592)),f888(f888(x44591,x44592),f888(x44591,f887(x44592,x44592))),x44591),f8(x44592,f887(x44592,x44592),x44591)),f334(f334(f8(x44592,f888(x44592,f887(x44592,x44592)),x44591),f269(x44592,x44592)),x44593))),x44593)))),x44594))),f334(f334(f290(x44592,x44591),x44594),x44593))
% 160.93/160.64 [4517]~E(f33(x45171,x45172),f30(x45173,x45174,x45175))
% 160.93/160.64 [4518]~E(f33(x45181,x45182),f29(x45183,x45184,x45185))
% 160.93/160.64 [4519]~E(f32(x45191,x45192),f30(x45193,x45194,x45195))
% 160.93/160.64 [4520]~E(f32(x45201,x45202),f29(x45203,x45204,x45205))
% 160.93/160.64 [4521]~E(f30(x45211,x45212,x45213),f33(x45214,x45215))
% 160.93/160.64 [4522]~E(f30(x45221,x45222,x45223),f32(x45224,x45225))
% 160.93/160.64 [4523]~E(f29(x45231,x45232,x45233),f33(x45234,x45235))
% 160.93/160.64 [4524]~E(f29(x45241,x45242,x45243),f32(x45244,x45245))
% 160.93/160.64 [3942]E(f334(f187(x39421,x39422,x39423,x39424),x39425),f334(f243(f885(x39422),x39422,f334(x39423,x39425),f241(x39422)),f334(x39424,x39425)))
% 160.93/160.64 [4029]E(f187(x40291,x40292,f187(x40291,x40292,x40293,x40294),x40295),f187(x40291,x40292,x40293,f187(x40291,x40292,x40294,x40295)))
% 160.93/160.64 [4205]E(f270(x42051,x42052,x42053,f258(x42052,x42051,x42054),f258(x42053,x42052,x42055)),f258(x42053,x42051,f270(x42053,x42052,x42051,x42055,x42054)))
% 160.93/160.64 [4212]E(f334(f334(f114(f888(x42121,a876)),f334(f174(x42121),f334(f334(f177(x42121),f334(f197(f882(x42122)),x42123)),x42124))),f186(x42121,x42122,x42125)),f186(x42121,x42122,f189(x42121,x42122,x42125,x42124,x42123)))
% 160.93/160.64 [3769]E(f334(f334(f273(x37691,x37692,x37693),x37694),x37695),f334(f334(x37694,f334(f268(x37691,x37692),x37695)),f334(f272(x37691,x37692),x37695)))
% 160.93/160.64 [3794]E(f334(f243(x37941,x37942,x37943,x37944),f334(f241(x37942),x37945)),f334(x37944,x37945))
% 160.93/160.64 [3803]E(f334(f334(f334(f65(x38031,x38032,x38033),x38034),x38035),f196(f888(x38032,a876))),x38035)
% 160.93/160.64 [3941]E(f129(f885(x39411),f334(f334(f211(x39412,x39411),x39413),x39414),f124(x39412,x39411,x39413,x39415)),f124(x39412,x39411,x39413,f129(f885(x39412),x39414,x39415)))
% 160.93/160.64 [3974]E(f244(x39741,x39742,x39743,x39744,f334(f241(x39742),x39745)),f334(x39744,x39745))
% 160.93/160.64 [4085]E(f334(f73(f885(x40851),f885(x40852),f885(x40853),f334(f211(x40851,x40852),x40854)),f334(f211(x40853,x40851),x40855)),f334(f211(x40853,x40852),f334(f73(x40851,x40852,x40853,x40854),x40855)))
% 160.93/160.64 [4087]E(f334(f73(f882(x40871),f882(x40872),f882(x40873),f334(f156(x40871,x40872),x40874)),f334(f156(x40873,x40871),x40875)),f334(f156(x40873,x40872),f334(f73(x40871,x40872,x40873,x40874),x40875)))
% 160.93/160.64 [4143]E(f334(f243(x41431,f887(x41432,f883(x41432)),x41433,f334(f273(x41432,f883(x41432),x41431),x41434)),f334(f137(x41432),x41435)),f132(x41431,x41432,x41433,x41434,x41435))
% 160.93/160.64 [4145]E(f125(x41451,f124(x41452,f883(f885(x41451)),f334(f334(f7(x41452,a103,f883(f885(x41451))),x41453),x41454),f334(x41455,x41454))),f334(f205(x41452,x41451,x41455,x41453),x41454))
% 160.93/160.64 [4168]E(f85(x41681,f66(x41682,x41681,x41683,x41684,x41685)),f334(f334(f64(x41682,x41681,x41683),x41684),x41685))
% 160.93/160.64 [4203]E(f334(f334(f80(a881),f334(f334(f80(a881),f334(x42031,f334(f268(x42032,x42033),x42034))),f334(x42035,f334(f272(x42032,x42033),x42034)))),f334(a116,f2(a881))),f277(x42032,x42033,x42031,x42035,x42034))
% 160.93/160.64 [4394]E(f165(x43941,x43942,f334(f334(f7(x43941,f885(x43942),f885(x43942)),f334(f334(f18(x43941,f885(x43942),f888(f885(x43942),f885(x43942))),f334(f334(f8(a876,f888(f885(x43942),f888(f885(x43942),f885(x43942))),x43941),f100(f885(x43942))),x43943)),f334(f334(f8(x43942,f885(x43942),x43941),f241(x43942)),x43944))),f210(x43942)),x43945),f334(f334(f156(x43941,x43942),x43944),f334(f138(x43941,x43943),x43945)))
% 160.93/160.64 [4560]~E(f334(f334(f334(f72(x45601,f885(x45602)),x45603),x45604),f334(f241(x45602),x45605)),f334(f16(f885(x45602),x45601),f210(x45602)))
% 160.93/160.64 [3705]E(f334(f334(f177(x37051),x37052),f334(f334(f156(x37053,x37051),x37054),x37055)),f334(f334(f156(x37053,x37051),x37054),f334(f334(f177(x37053),x37052),x37055)))
% 160.93/160.64 [3706]E(f334(f334(f140(x37061),x37062),f334(f334(f156(x37063,x37061),x37064),x37065)),f334(f334(f156(x37063,x37061),x37064),f334(f334(f140(x37063),x37062),x37065)))
% 160.93/160.64 [3738]E(f334(f334(f156(x37381,x37382),x37383),f334(f334(f153(x37381),x37384),x37385)),f334(f334(f153(x37382),f334(x37383,x37384)),f334(f334(f156(x37381,x37382),x37383),x37385)))
% 160.93/160.64 [3798]E(f334(f313(x37981,x37982,x37983),f334(f334(f312(x37981),x37984),x37985)),f334(f334(f312(x37982),f334(x37983,x37984)),f334(f313(x37981,x37982,x37983),x37985)))
% 160.93/160.64 [3827]E(f175(x38271,f334(f334(f153(x38271),x38272),x38273),f334(f334(f153(x38271),x38274),x38275)),f334(f334(f153(x38271),x38272),f334(f334(f153(x38271),x38274),f175(x38271,x38273,x38275))))
% 160.93/160.64 [3863]E(f334(f334(f184(x38631,x38632),f334(f334(f177(x38631),x38633),x38634)),f334(f334(f177(x38632),x38633),x38635)),f334(f334(f177(f887(x38631,x38632)),x38633),f334(f334(f184(x38631,x38632),x38634),x38635)))
% 160.93/160.64 [3864]E(f334(f334(f184(x38641,x38642),f334(f334(f140(x38641),x38643),x38644)),f334(f334(f140(x38642),x38643),x38645)),f334(f334(f140(f887(x38641,x38642)),x38643),f334(f334(f184(x38641,x38642),x38644),x38645)))
% 160.93/160.64 [3874]E(f334(f334(f161(x38741,f334(f334(f153(x38741),x38742),x38743)),f334(a116,x38744)),x38745),f334(f334(f153(x38741),x38742),f334(f334(f161(x38741,x38743),x38744),x38745)))
% 160.93/160.64 [3877]E(f334(f243(f885(x38771),x38772,f210(x38771),x38773),f334(f334(f16(f885(x38772),x38774),f210(x38772)),x38775)),f210(x38771))
% 160.93/160.64 [3879]E(f334(f334(f136(x38791),f334(f334(f156(x38792,x38791),x38793),x38794)),f334(f334(f156(x38792,x38791),x38793),x38795)),f334(f334(f156(x38792,x38791),x38793),f334(f334(f136(x38792),x38794),x38795)))
% 160.93/160.64 [3883]E(f334(f334(x38831,x38832),f334(f334(f260(x38833,x38834,x38831),x38832),x38835)),f334(f334(f260(x38833,x38834,x38831),x38832),f334(a116,x38835)))
% 160.93/160.64 [3913]E(f166(x39131,x39132,x39133,f334(f334(f153(x39131),x39134),x39135)),f334(f334(f136(x39132),f334(x39133,x39134)),f166(x39131,x39132,x39133,x39135)))
% 160.93/160.64 [3925]E(f334(f334(f291(x39251,x39252,x39253),f334(f289(x39252,x39251),x39254)),f334(f289(x39253,x39252),x39255)),f334(f289(x39253,x39251),f334(f334(f291(x39253,x39252,x39251),x39255),x39254)))
% 160.93/160.64 [3960]E(f334(f334(f334(f191(f882(x39601),f882(x39601)),x39602),f170(x39601)),f334(f334(f156(x39603,x39601),x39604),x39605)),f334(f334(f156(x39603,x39601),x39604),f334(f334(f334(f191(f882(x39603),f882(x39603)),x39602),f170(x39603)),x39605)))
% 160.93/160.64 [3961]E(f334(f334(f275(x39611,x39612,x39611,x39613),f334(f269(x39612,x39611),x39614)),x39615),f334(x39615,x39614))
% 160.93/160.64 [3988]E(f157(x39881,x39882,f334(f334(f156(x39883,x39881),x39884),x39885)),f157(x39883,f334(f73(x39881,a881,x39883,x39882),x39884),x39885))
% 160.93/160.64 [4052]E(f334(f334(f73(f885(x40521),f885(x40522),x40523,f334(f211(x40521,x40522),x40524)),f334(f16(f885(x40521),x40523),f210(x40521))),x40525),f210(x40522))
% 160.93/160.64 [4053]E(f179(f887(x40531,x40532),f334(f73(x40532,a876,f887(x40531,x40532),x40533),f272(x40531,x40532)),f334(f334(f184(x40531,x40532),x40534),x40535)),f334(f334(f184(x40531,x40532),x40534),f179(x40532,x40533,x40535)))
% 160.93/160.64 [4059]E(f334(f313(x40591,x40592,f334(f334(f8(x40593,x40592,x40591),x40594),x40595)),f257(f888(x40591,a876))),f334(f313(x40593,x40592,x40594),f334(f313(x40591,x40593,x40595),f257(f888(x40591,a876)))))
% 160.93/160.64 [4072]E(f179(f887(x40721,x40722),f334(f73(x40721,a876,f887(x40721,x40722),x40723),f268(x40721,x40722)),f334(f334(f184(x40721,x40722),x40724),x40725)),f334(f334(f184(x40721,x40722),f179(x40721,x40723,x40724)),x40725))
% 160.93/160.64 [4091]E(f334(f334(f114(f888(x40911,a876)),f334(f314(x40911,x40912,x40913),f334(f334(f312(x40912),x40914),f196(f888(x40912,a876))))),f334(f314(x40911,x40912,x40913),x40915)),f334(f314(x40911,x40912,x40913),f334(f334(f312(x40912),x40914),x40915)))
% 160.93/160.64 [4152]E(f334(f334(f136(f887(x41521,x41522)),f334(f334(f156(x41522,f887(x41521,x41522)),f334(f269(x41521,x41522),x41523)),x41524)),f59(x41521,x41522,x41525,x41524)),f59(x41521,x41522,f334(f334(f153(x41521),x41523),x41525),x41524))
% 160.93/160.64 [4153]E(f334(f334(f156(x41531,x41532),x41533),f179(x41531,f334(f73(x41532,a876,x41531,x41534),x41533),x41535)),f179(x41532,x41534,f334(f334(f156(x41531,x41532),x41533),x41535)))
% 160.93/160.64 [4159]E(f334(f144(x41591,x41592,f334(f7(x41592,x41591,x41591),f334(f7(x41591,x41592,x41591),x41593)),x41594),f334(f171(x41592),f334(f171(x41592),x41595))),f334(f144(x41591,x41592,x41593,x41594),x41595))
% 160.93/160.64 [4160]E(f334(f334(f334(f72(x41601,f885(x41602)),f190(x41601,x41602,x41603,x41604)),x41605),f334(x41603,x41605)),f190(x41601,x41602,x41603,f334(f334(f312(x41601),x41605),x41604)))
% 160.93/160.64 [4229]E(f334(f243(f882(x42291),x42291,f165(x42292,x42291,x42293,x42294),f334(f334(f7(x42291,f882(x42291),f882(x42291)),f153(x42291)),f165(x42292,x42291,x42293,x42294))),f334(x42293,x42295)),f165(x42292,x42291,x42293,f334(f334(f153(x42292),x42295),x42294)))
% 160.93/160.64 [4266]P1(f334(f334(f248(f888(x42661,a876)),f334(f313(x42662,x42661,x42663),f334(f334(f105(f888(x42662,a876)),x42664),x42665))),f334(f334(f105(f888(x42661,a876)),f334(f313(x42662,x42661,x42663),x42664)),f334(f313(x42662,x42661,x42663),x42665))))
% 160.93/160.64 [4267]P1(f334(f334(f248(f888(x42671,a876)),f334(f288(x42672,x42671,x42673),f334(f334(f105(f888(x42672,a876)),x42674),x42675))),f334(f334(f105(f888(x42671,a876)),f334(f288(x42672,x42671,x42673),x42674)),f334(f288(x42672,x42671,x42673),x42675))))
% 160.93/160.64 [4368]E(f334(f272(x43681,x43682),f334(f274(x43683,x43681,x43682,x43682,x43684,f34(x43682)),x43685)),f334(f272(x43683,x43682),x43685))
% 160.93/160.64 [4369]E(f334(f268(x43691,x43692),f334(f274(x43691,x43691,x43693,x43692,f34(x43691),x43694),x43695)),f334(f268(x43691,x43693),x43695))
% 160.93/160.64 [4455]E(f334(f144(f888(x44551,f885(x44552)),f887(x44551,x44552),f334(f334(f8(f888(x44551,f888(x44552,f888(x44551,f885(x44552)))),f888(f887(x44551,x44552),f888(x44551,f885(x44552))),f888(x44551,f885(x44552))),f273(x44551,x44552,f888(x44551,f885(x44552)))),f334(f334(f7(f888(x44551,f885(x44552)),f888(x44552,f885(x44552)),f888(x44551,f888(x44552,f888(x44551,f885(x44552))))),f334(f334(f8(f888(x44551,f888(f888(x44552,f885(x44552)),f888(x44552,f888(x44551,f885(x44552))))),f888(f888(x44552,f885(x44552)),f888(x44551,f888(x44552,f888(x44551,f885(x44552))))),f888(x44551,f885(x44552))),f7(x44551,f888(x44552,f885(x44552)),f888(x44552,f888(x44551,f885(x44552))))),f334(f334(f8(f888(x44551,f888(f885(x44552),f888(x44551,f885(x44552)))),f888(x44551,f888(f888(x44552,f885(x44552)),f888(x44552,f888(x44551,f885(x44552))))),f888(x44551,f885(x44552))),f334(f8(f888(f885(x44552),f888(x44551,f885(x44552))),f888(f888(x44552,f885(x44552)),f888(x44552,f888(x44551,f885(x44552)))),x44551),f8(f885(x44552),f888(x44551,f885(x44552)),x44552))),f72(x44551,f885(x44552))))),f241(x44552))),x44553),f334(f334(f184(x44551,x44552),x44554),x44555)),f189(x44551,x44552,x44553,x44554,x44555))
% 160.93/160.64 [4457]P26(x44571,x44572,f334(f334(f312(f880(x44571)),f334(f334(f334(f92(x44571),f334(f334(f7(x44571,f888(a877,a876),f888(a877,a876)),f334(f334(f8(f888(a877,f888(a876,a876)),f888(f888(a877,a876),f888(a877,a876)),x44571),f18(a877,a876,a876)),f334(f334(f8(f888(a877,a876),f888(a877,f888(a876,a876)),x44571),f334(f8(a876,f888(a876,a876),a877),a332)),x44573))),f334(f334(f8(a876,a876,a877),a329),x44574))),f32(x44574,x44575)),x44573)),f196(f888(f880(x44571),a876))))
% 160.93/160.64 [3549]E(f334(f334(f334(f334(f217(x35491),x35492),x35493),x35494),x35495),f212(x35491,x35492))
% 160.93/160.64 [3550]E(f334(f334(f334(f334(f218(x35501),x35502),x35503),x35504),x35505),f200(x35501,x35502))
% 160.93/160.64 [3594]E(f97(x35941,x35942,f334(f334(f334(f92(x35941),x35943),x35944),x35945)),f2(a881))
% 160.93/160.64 [3689]E(f334(f334(f334(f334(f72(x36891,x36892),x36893),x36894),x36895),x36894),x36895)
% 160.93/160.64 [3914]E(f334(f334(f41(x39141,f888(x39142,a876)),f334(f334(f312(x39141),x39143),x39144)),x39145),f334(f334(f114(f888(x39142,a876)),f334(x39145,x39143)),f334(f334(f41(x39141,f888(x39142,a876)),x39144),x39145)))
% 160.93/160.64 [3915]E(f334(f334(f42(x39151,f888(x39152,a876)),f334(f334(f312(x39151),x39153),x39154)),x39155),f334(f334(f105(f888(x39152,a876)),f334(x39155,x39153)),f334(f334(f42(x39151,f888(x39152,a876)),x39154),x39155)))
% 160.93/160.64 [3967]E(f334(f122(x39671,x39672,f334(x39673,x39674)),f334(f334(f7(x39671,a103,f883(x39672)),x39675),x39674)),f334(f208(x39671,x39672,x39673,x39675),x39674))
% 160.93/160.64 [3981]E(f334(f334(f114(f888(x39811,a876)),f334(f313(x39812,x39811,x39813),x39814)),f334(f313(x39812,x39811,x39813),x39815)),f334(f313(x39812,x39811,x39813),f334(f334(f114(f888(x39812,a876)),x39814),x39815)))
% 160.93/160.64 [3982]E(f334(f334(f114(f888(x39821,a876)),f334(f288(x39822,x39821,x39823),x39824)),f334(f288(x39822,x39821,x39823),x39825)),f334(f288(x39822,x39821,x39823),f334(f334(f114(f888(x39822,a876)),x39824),x39825)))
% 160.93/160.64 [3983]E(f334(f334(f114(f888(x39831,a876)),f334(f314(x39831,x39832,x39833),x39834)),f334(f314(x39831,x39832,x39833),x39835)),f334(f314(x39831,x39832,x39833),f334(f334(f114(f888(x39832,a876)),x39834),x39835)))
% 160.93/160.64 [3984]E(f334(f334(f22(f888(x39841,a876)),f334(f314(x39841,x39842,x39843),x39844)),f334(f314(x39841,x39842,x39843),x39845)),f334(f314(x39841,x39842,x39843),f334(f334(f22(f888(x39842,a876)),x39844),x39845)))
% 160.93/160.64 [3985]E(f334(f334(f105(f888(x39851,a876)),f334(f314(x39851,x39852,x39853),x39854)),f334(f314(x39851,x39852,x39853),x39855)),f334(f314(x39851,x39852,x39853),f334(f334(f105(f888(x39852,a876)),x39854),x39855)))
% 160.93/160.64 [3987]E(f190(x39871,x39872,f190(x39871,x39872,x39873,x39874),x39875),f190(x39871,x39872,x39873,f334(f334(f105(f888(x39871,a876)),x39874),x39875)))
% 160.93/160.64 [4048]E(f334(f334(f161(x40481,f334(f334(f136(x40481),x40482),f334(f334(f153(x40481),x40483),x40484))),f334(f197(f882(x40481)),x40482)),x40485),f334(f334(f136(x40481),x40482),f334(f334(f153(x40481),x40485),x40484)))
% 160.93/160.64 [4056]E(f334(f334(f42(x40561,f888(x40562,a876)),x40563),f334(f334(f8(f888(x40562,a876),f888(x40562,a876),x40561),f334(f312(x40562),x40564)),x40565)),f334(f334(f312(x40562),x40564),f334(f334(f42(x40561,f888(x40562,a876)),x40563),x40565)))
% 160.93/160.64 [4125]E(f190(x41251,x41252,f334(f334(f334(f72(x41251,f885(x41252)),x41253),x41254),f334(f241(x41252),x41255)),f334(f79(f888(x41251,a876)),f334(f334(f312(x41251),x41254),f196(f888(x41251,a876))))),f190(x41251,x41252,x41253,f334(f79(f888(x41251,a876)),f334(f334(f312(x41251),x41254),f196(f888(x41251,a876))))))
% 160.93/160.64 [4216]E(f334(f334(f156(x42161,x42162),x42163),f334(f138(x42161,f334(f73(x42162,a876,x42161,x42164),x42163)),x42165)),f334(f138(x42162,x42164),f334(f334(f156(x42161,x42162),x42163),x42165)))
% 160.93/160.64 [4222]E(f334(f197(f882(x42221)),f334(f138(x42221,x42222),f334(f334(f156(x42223,x42221),x42224),x42225))),f334(f197(f882(x42223)),f334(f138(x42223,f334(f73(x42221,a876,x42223,x42222),x42224)),x42225)))
% 160.93/160.64 [4360]E(f334(f334(f114(f888(x43601,a876)),f334(f334(f22(f888(x43601,a876)),f186(x43601,x43602,x43603)),f334(f254(x43601),f334(f334(f7(x43601,f888(x43601,a876),a876),f336(x43601)),f334(f334(f22(f888(x43601,a876)),x43604),f186(x43601,x43602,x43605)))))),f334(f254(x43601),f334(f334(f7(x43601,f888(x43601,a876),a876),f336(x43601)),f334(f334(f105(f888(x43601,a876)),x43604),f186(x43601,x43602,x43605))))),f186(x43601,x43602,f76(x43601,f885(x43602),x43603,x43605,x43604)))
% 160.93/160.64 [4435]E(f334(f158(f882(f887(x44351,x44352)),x44352,f117(f887(x44351,x44352)),f334(f334(f7(x44352,f888(f882(x44352),f882(f887(x44351,x44352))),f888(f882(x44352),f882(f887(x44351,x44352)))),f334(f334(f8(f888(f882(f887(x44351,x44352)),f882(f887(x44351,x44352))),f888(f888(f882(x44352),f882(f887(x44351,x44352))),f888(f882(x44352),f882(f887(x44351,x44352)))),x44352),f8(f882(f887(x44351,x44352)),f882(f887(x44351,x44352)),f882(x44352))),f334(f334(f8(f887(x44351,x44352),f888(f882(f887(x44351,x44352)),f882(f887(x44351,x44352))),x44352),f153(f887(x44351,x44352))),f334(f269(x44351,x44352),x44353)))),f334(f184(x44351,x44352),x44354))),x44355),f334(f334(f184(x44351,x44352),f334(f334(f153(x44351),x44353),x44354)),x44355))
% 160.93/160.64 [3908]E(f334(f334(f161(x39081,f334(f334(f161(x39081,x39082),x39083),x39084)),x39083),x39085),f334(f334(f161(x39081,x39082),x39083),x39085))
% 160.93/160.64 [3962]E(f334(f265(x39621,x39622),f334(f334(f312(f887(x39621,x39622)),f334(f334(f269(x39621,x39622),x39623),x39624)),x39625)),f334(f334(f312(x39622),x39624),f334(f265(x39621,x39622),x39625)))
% 160.93/160.64 [3963]E(f334(f267(x39631,x39632),f334(f334(f312(f887(x39631,x39632)),f334(f334(f269(x39631,x39632),x39633),x39634)),x39635)),f334(f334(f312(x39631),x39633),f334(f267(x39631,x39632),x39635)))
% 160.93/160.64 [4041]E(f334(f334(f114(f888(f887(x40411,x40412),a876)),f334(f334(f271(x40411,x40412),x40413),x40414)),f334(f334(f271(x40411,x40412),x40415),x40414)),f334(f334(f271(x40411,x40412),f334(f334(f114(f888(x40411,a876)),x40413),x40415)),x40414))
% 160.93/160.64 [4042]E(f334(f334(f22(f888(f887(x40421,x40422),a876)),f334(f334(f271(x40421,x40422),x40423),x40424)),f334(f334(f271(x40421,x40422),x40425),x40424)),f334(f334(f271(x40421,x40422),f334(f334(f22(f888(x40421,a876)),x40423),x40425)),x40424))
% 160.93/160.64 [4043]E(f334(f334(f105(f888(f887(x40431,x40432),a876)),f334(f334(f271(x40431,x40432),x40433),x40434)),f334(f334(f271(x40431,x40432),x40435),x40434)),f334(f334(f271(x40431,x40432),f334(f334(f105(f888(x40431,a876)),x40433),x40435)),x40434))
% 160.93/160.64 [4103]E(f334(f334(f114(f888(x41031,a876)),f334(f334(f41(x41032,f888(x41031,a876)),x41033),x41034)),f334(f334(f41(x41032,f888(x41031,a876)),x41035),x41034)),f334(f334(f41(x41032,f888(x41031,a876)),f334(f334(f114(f888(x41032,a876)),x41033),x41035)),x41034))
% 160.93/160.64 [4104]E(f334(f334(f105(f888(x41041,a876)),f334(f334(f42(x41042,f888(x41041,a876)),x41043),x41044)),f334(f334(f42(x41042,f888(x41041,a876)),x41045),x41044)),f334(f334(f42(x41042,f888(x41041,a876)),f334(f334(f114(f888(x41042,a876)),x41043),x41045)),x41044))
% 160.93/160.64 [4118]E(f334(f334(f41(x41181,f888(x41182,a876)),x41183),f334(f334(f8(f888(x41182,a876),f888(x41182,a876),x41181),f334(f22(f888(x41182,a876)),x41184)),x41185)),f334(f334(f22(f888(x41182,a876)),x41184),f334(f334(f42(x41181,f888(x41182,a876)),x41183),x41185)))
% 160.93/160.64 [4119]E(f334(f334(f41(x41191,f888(x41192,a876)),x41193),f334(f334(f8(f888(x41192,a876),f888(x41192,a876),x41191),f334(f105(f888(x41192,a876)),x41194)),x41195)),f334(f334(f105(f888(x41192,a876)),x41194),f334(f334(f41(x41191,f888(x41192,a876)),x41193),x41195)))
% 160.93/160.64 [4120]E(f334(f334(f42(x41201,f888(x41202,a876)),x41203),f334(f334(f8(f888(x41202,a876),f888(x41202,a876),x41201),f334(f114(f888(x41202,a876)),x41204)),x41205)),f334(f334(f114(f888(x41202,a876)),x41204),f334(f334(f42(x41201,f888(x41202,a876)),x41203),x41205)))
% 160.93/160.64 [4158]E(f187(x41581,x41582,x41583,f334(f180(x41581,x41582),f334(f171(f887(x41581,x41582)),f334(f334(f184(x41581,x41582),x41584),x41585)))),f189(x41581,x41582,x41583,x41584,x41585))
% 160.93/160.64 [4180]E(f193(f882(x41801),f334(f334(f153(x41801),x41802),x41803),f334(f334(f8(f882(x41801),f882(x41801),a881),f334(f153(x41801),x41804)),f334(f334(f7(a881,x41801,f882(x41801)),f161(x41801,x41803)),x41802)),x41805),f334(f334(f161(x41801,f334(f334(f153(x41801),x41804),x41803)),x41805),x41802))
% 160.93/160.64 [4184]E(f334(f334(f41(x41841,f888(f887(x41842,x41843),a876)),x41844),f334(f334(f8(f888(f887(x41843,x41842),a876),f888(f887(x41842,x41843),a876),x41841),f289(x41843,x41842)),x41845)),f334(f289(x41843,x41842),f334(f334(f41(x41841,f888(f887(x41843,x41842),a876)),x41844),x41845)))
% 160.93/160.64 [4185]E(f334(f334(f42(x41851,f888(f887(x41852,x41853),a876)),x41854),f334(f334(f8(f888(f887(x41853,x41852),a876),f888(f887(x41852,x41853),a876),x41851),f289(x41853,x41852)),x41855)),f334(f289(x41853,x41852),f334(f334(f42(x41851,f888(f887(x41853,x41852),a876)),x41854),x41855)))
% 160.93/160.64 [4240]E(f186(x42401,x42402,f334(f334(f18(x42401,f885(x42403),f885(x42402)),f334(f334(f8(f888(x42403,x42402),f888(f885(x42403),f885(x42402)),x42401),f211(x42403,x42402)),x42404)),x42405)),f186(x42401,x42403,x42405))
% 160.93/160.64 [4291]P1(f334(f334(f248(f888(x42911,a876)),f334(f334(f22(f888(x42911,a876)),f334(f313(x42912,x42911,x42913),x42914)),f334(f313(x42912,x42911,x42913),x42915))),f334(f313(x42912,x42911,x42913),f334(f334(f22(f888(x42912,a876)),x42914),x42915))))
% 160.93/160.64 [4440]E(f334(f158(f882(f887(x44401,x44402)),x44401,f117(f887(x44401,x44402)),f334(f334(f7(x44401,f888(f882(x44401),f882(f887(x44401,x44402))),f888(f882(x44401),f882(f887(x44401,x44402)))),f334(f334(f8(f888(f882(f887(x44401,x44402)),f882(f887(x44401,x44402))),f888(f888(f882(x44401),f882(f887(x44401,x44402))),f888(f882(x44401),f882(f887(x44401,x44402)))),x44401),f8(f882(f887(x44401,x44402)),f882(f887(x44401,x44402)),f882(x44401))),f334(f334(f8(f887(x44401,x44402),f888(f882(f887(x44401,x44402)),f882(f887(x44401,x44402))),x44401),f153(f887(x44401,x44402))),f334(f334(f7(x44401,x44402,f887(x44401,x44402)),f269(x44401,x44402)),x44403)))),f334(f334(f7(f882(x44401),f882(x44402),f882(f887(x44401,x44402))),f184(x44401,x44402)),x44404))),x44405),f334(f334(f184(x44401,x44402),x44405),f334(f334(f153(x44402),x44403),x44404)))
% 160.93/160.64 [4146]E(f334(f334(f114(f888(x41461,a876)),f334(f288(x41462,x41461,x41463),x41464)),f334(f288(x41462,x41461,x41465),x41464)),f334(f288(x41462,x41461,f334(f334(f114(f888(f887(x41462,x41461),a876)),x41463),x41465)),x41464))
% 160.93/160.64 [4187]E(f334(f334(f136(f887(x41871,x41872)),f334(f334(f184(x41871,x41872),x41873),f334(f334(f177(x41872),f334(f197(f882(x41871)),x41873)),x41874))),f334(f334(f184(x41871,x41872),x41875),f334(f334(f140(x41872),f334(f197(f882(x41871)),x41873)),x41874))),f334(f334(f184(x41871,x41872),f334(f334(f136(x41871),x41873),x41875)),x41874))
% 160.93/160.64 [4294]E(f334(f334(f271(x42941,x42942),x42943),f334(f334(f18(x42941,f888(x42942,a876),f888(x42942,a876)),f334(f334(f8(f888(x42942,a876),f888(f888(x42942,a876),f888(x42942,a876)),x42941),f114(f888(x42942,a876))),x42944)),x42945)),f334(f334(f114(f888(f887(x42941,x42942),a876)),f334(f334(f271(x42941,x42942),x42943),x42944)),f334(f334(f271(x42941,x42942),x42943),x42945)))
% 160.93/160.64 [4295]E(f334(f334(f271(x42951,x42952),x42953),f334(f334(f18(x42951,f888(x42952,a876),f888(x42952,a876)),f334(f334(f8(f888(x42952,a876),f888(f888(x42952,a876),f888(x42952,a876)),x42951),f22(f888(x42952,a876))),x42954)),x42955)),f334(f334(f22(f888(f887(x42951,x42952),a876)),f334(f334(f271(x42951,x42952),x42953),x42954)),f334(f334(f271(x42951,x42952),x42953),x42955)))
% 160.93/160.64 [4296]E(f334(f334(f271(x42961,x42962),x42963),f334(f334(f18(x42961,f888(x42962,a876),f888(x42962,a876)),f334(f334(f8(f888(x42962,a876),f888(f888(x42962,a876),f888(x42962,a876)),x42961),f105(f888(x42962,a876))),x42964)),x42965)),f334(f334(f105(f888(f887(x42961,x42962),a876)),f334(f334(f271(x42961,x42962),x42963),x42964)),f334(f334(f271(x42961,x42962),x42963),x42965)))
% 160.93/160.64 [4300]E(f334(f334(f41(x43001,f888(x43002,a876)),x43003),f334(f334(f7(x43001,f888(x43002,a876),f888(x43002,a876)),f334(f334(f8(f888(x43002,a876),f888(f888(x43002,a876),f888(x43002,a876)),x43001),f22(f888(x43002,a876))),x43004)),x43005)),f334(f334(f22(f888(x43002,a876)),f334(f334(f41(x43001,f888(x43002,a876)),x43003),x43004)),x43005))
% 160.93/160.64 [4301]E(f334(f334(f41(x43011,f888(x43012,a876)),x43013),f334(f334(f7(x43011,f888(x43012,a876),f888(x43012,a876)),f334(f334(f8(f888(x43012,a876),f888(f888(x43012,a876),f888(x43012,a876)),x43011),f105(f888(x43012,a876))),x43014)),x43015)),f334(f334(f105(f888(x43012,a876)),f334(f334(f41(x43011,f888(x43012,a876)),x43013),x43014)),x43015))
% 160.93/160.64 [4302]E(f334(f334(f42(x43021,f888(x43022,a876)),x43023),f334(f334(f7(x43021,f888(x43022,a876),f888(x43022,a876)),f334(f334(f8(f888(x43022,a876),f888(f888(x43022,a876),f888(x43022,a876)),x43021),f114(f888(x43022,a876))),x43024)),x43025)),f334(f334(f114(f888(x43022,a876)),f334(f334(f42(x43021,f888(x43022,a876)),x43023),x43024)),x43025))
% 160.93/160.64 [4306]E(f334(f334(f41(x43061,f888(x43062,a876)),x43063),f334(f334(f18(x43061,f888(x43062,a876),f888(x43062,a876)),f334(f334(f8(f888(x43062,a876),f888(f888(x43062,a876),f888(x43062,a876)),x43061),f114(f888(x43062,a876))),x43064)),x43065)),f334(f334(f114(f888(x43062,a876)),f334(f334(f41(x43061,f888(x43062,a876)),x43063),x43064)),f334(f334(f41(x43061,f888(x43062,a876)),x43063),x43065)))
% 160.93/160.64 [4307]E(f334(f334(f42(x43071,f888(x43072,a876)),x43073),f334(f334(f18(x43071,f888(x43072,a876),f888(x43072,a876)),f334(f334(f8(f888(x43072,a876),f888(f888(x43072,a876),f888(x43072,a876)),x43071),f105(f888(x43072,a876))),x43074)),x43075)),f334(f334(f105(f888(x43072,a876)),f334(f334(f42(x43071,f888(x43072,a876)),x43073),x43074)),f334(f334(f42(x43071,f888(x43072,a876)),x43073),x43075)))
% 160.93/160.64 [4321]E(f334(f334(f41(x43211,f888(x43212,a876)),x43213),f334(f334(f18(x43211,f888(x43212,a876),f888(x43212,a876)),f334(f334(f8(f888(x43212,a876),f888(f888(x43212,a876),f888(x43212,a876)),x43211),f114(f888(x43212,a876))),x43214)),x43215)),f334(f334(f114(f888(x43212,a876)),f39(f888(x43212,a876),f334(f313(x43211,f888(x43212,a876),x43214),x43213))),f39(f888(x43212,a876),f334(f313(x43211,f888(x43212,a876),x43215),x43213))))
% 160.93/160.64 [4322]E(f334(f334(f42(x43221,f888(x43222,a876)),x43223),f334(f334(f18(x43221,f888(x43222,a876),f888(x43222,a876)),f334(f334(f8(f888(x43222,a876),f888(f888(x43222,a876),f888(x43222,a876)),x43221),f105(f888(x43222,a876))),x43224)),x43225)),f334(f334(f105(f888(x43222,a876)),f40(f888(x43222,a876),f334(f313(x43221,f888(x43222,a876),x43224),x43223))),f40(f888(x43222,a876),f334(f313(x43221,f888(x43222,a876),x43225),x43223))))
% 160.93/160.64 [4356]E(f334(f334(f140(x43561),f334(f197(f882(x43561)),f179(x43561,x43562,f334(f334(f156(x43563,x43561),x43564),x43565)))),f334(f334(f156(x43563,x43561),x43564),x43565)),f334(f334(f156(x43563,x43561),x43564),f334(f334(f140(x43563),f334(f197(f882(x43563)),f179(x43563,f334(f73(x43561,a876,x43563,x43562),x43564),x43565))),x43565)))
% 160.93/160.64 [4230]E(f334(f334(f136(f887(x42301,x42302)),f334(f334(f184(x42301,x42302),f334(f334(f177(x42301),f334(f197(f882(x42302)),x42303)),x42304)),x42303)),f334(f334(f184(x42301,x42302),f334(f334(f140(x42301),f334(f197(f882(x42302)),x42303)),x42304)),x42305)),f334(f334(f184(x42301,x42302),x42304),f334(f334(f136(x42302),x42303),x42305)))
% 160.93/160.64 [4348]E(f85(x43481,f334(f334(f18(x43481,a876,a876),f334(f334(f8(a876,f888(a876,a876),x43481),a332),f334(f334(f7(x43481,f888(x43481,a876),a876),f336(x43481)),x43482))),f334(f334(f7(x43481,x43483,a876),f334(f334(f8(x43483,f888(x43483,a876),x43481),a331),x43484)),x43485))),f334(f77(x43481,x43483,x43482,x43484),x43485))
% 160.93/160.64 [4400]E(f334(f334(f86(a1,x44001),f334(f107(a1),f334(f334(f80(a1),x44002),a101))),f334(f334(f18(a1,x44001,x44001),f334(f334(f7(a1,x44001,f888(x44001,x44001)),f334(f334(f8(a876,f888(x44001,f888(x44001,x44001)),a1),f100(x44001)),a201)),f193(x44001,x44003,x44004,x44005))),f334(f334(f8(a881,x44001,a1),x44004),f334(f334(f7(a1,a881,a881),f334(f334(f8(a881,f888(a881,a881),a1),f80(a881)),a108)),x44005)))),f193(x44001,x44003,x44004,f334(f334(f80(a881),f334(f107(a881),x44002)),x44005)))
% 160.93/160.64 [4436]E(f334(f180(x44361,x44362),f334(f334(f156(f887(x44361,x44363),f887(x44361,x44362)),f334(f273(x44361,x44363,f887(x44361,x44362)),f334(f334(f7(x44361,f888(x44363,x44362),f888(x44363,f887(x44361,x44362))),f334(f334(f8(f888(x44362,f887(x44361,x44362)),f888(f888(x44363,x44362),f888(x44363,f887(x44361,x44362))),x44361),f8(x44362,f887(x44361,x44362),x44363)),f269(x44361,x44362))),x44364))),x44365)),f334(f73(f885(x44363),f885(x44362),x44361,f334(f211(x44363,x44362),x44364)),f334(f180(x44361,x44363),x44365)))
% 160.93/160.64 [4393]E(f186(x43931,x43932,f334(f334(f18(x43931,f885(x43932),f885(x43932)),f334(f334(f18(x43931,f885(x43932),f888(f885(x43932),f885(x43932))),f334(f334(f8(a876,f888(f885(x43932),f888(f885(x43932),f885(x43932))),x43931),f100(f885(x43932))),x43933)),x43934)),x43935)),f334(f334(f114(f888(x43931,a876)),f334(f334(f105(f888(x43931,a876)),f186(x43931,x43932,x43934)),f334(f254(x43931),x43933))),f334(f334(f105(f888(x43931,a876)),f186(x43931,x43932,x43935)),f334(f254(x43931),f334(f334(f8(a876,a876,x43931),a329),x43933)))))
% 160.93/160.64 [4434]E(f334(f334(f86(a1,x44341),f334(f107(a1),f334(f334(f80(a1),x44342),a101))),f334(f334(f18(a1,x44341,x44341),f334(f334(f7(a1,x44341,f888(x44341,x44341)),f334(f334(f8(a876,f888(x44341,f888(x44341,x44341)),a1),f100(x44341)),a201)),f334(f192(x44341,x44343,x44344),x44345))),f334(f334(f18(a1,x44341,x44341),f334(f334(f8(a881,f888(x44341,x44341),a1),x44344),f334(f334(f7(a1,a881,a881),f334(f334(f8(a881,f888(a881,a881),a1),f80(a881)),a108)),x44345))),f334(f334(f8(a881,x44341,a1),f192(x44341,x44343,x44344)),f334(f334(f7(a1,a881,a881),f334(f334(f8(a881,f888(a881,a881),a1),f80(a881)),a108)),x44345))))),f334(f192(x44341,x44343,x44344),f334(f334(f80(a881),f334(f107(a881),x44342)),x44345)))
% 160.93/160.64 [4469]E(f334(f254(f887(x44691,x44692)),f334(f273(x44691,x44692,a876),f334(f334(f8(f888(x44692,f888(x44693,a876)),f888(x44692,a876),x44691),f334(f8(f888(x44693,a876),a876,x44692),f87(x44693))),f334(f334(f7(x44691,f888(x44692,f888(x44693,a876)),f888(x44692,f888(x44693,a876))),f334(f334(f8(f888(f888(x44693,a876),f888(x44693,a876)),f888(f888(x44692,f888(x44693,a876)),f888(x44692,f888(x44693,a876))),x44691),f8(f888(x44693,a876),f888(x44693,a876),x44692)),f334(f334(f8(f888(x44693,f888(a876,a876)),f888(f888(x44693,a876),f888(x44693,a876)),x44691),f18(x44693,a876,a876)),f334(f334(f8(f888(x44693,a876),f888(x44693,f888(a876,a876)),x44691),f334(f8(a876,f888(a876,a876),x44693),a332)),f334(f334(f7(x44691,f888(f887(x44691,x44693),a876),f888(x44693,a876)),f334(f334(f8(f888(x44693,f888(f888(f887(x44691,x44693),a876),a876)),f888(f888(f887(x44691,x44693),a876),f888(x44693,a876)),x44691),f7(x44693,f888(f887(x44691,x44693),a876),a876)),f334(f334(f8(f888(x44693,f887(x44691,x44693)),f888(x44693,f888(f888(f887(x44691,x44693),a876),a876)),x44691),f334(f8(f887(x44691,x44693),f888(f888(f887(x44691,x44693),a876),a876),x44693),f336(f887(x44691,x44693)))),f269(x44691,x44693)))),x44694))))),f334(f334(f7(x44692,f888(f887(x44693,x44692),a876),f888(x44693,a876)),f334(f334(f8(f888(x44693,f888(f888(f887(x44693,x44692),a876),a876)),f888(f888(f887(x44693,x44692),a876),f888(x44693,a876)),x44692),f7(x44693,f888(f887(x44693,x44692),a876),a876)),f334(f334(f8(f888(x44693,f887(x44693,x44692)),f888(x44693,f888(f888(f887(x44693,x44692),a876),a876)),x44692),f334(f8(f887(x44693,x44692),f888(f888(f887(x44693,x44692),a876),a876),x44693),f336(f887(x44693,x44692)))),f334(f7(x44693,x44692,f887(x44693,x44692)),f269(x44693,x44692))))),x44695))))),f334(f334(f291(x44691,x44693,x44692),x44694),x44695))
% 160.93/160.64 [4545]~E(f29(x45451,x45452,x45453),f30(x45454,x45455,x45456))
% 160.93/160.64 [3997]E(f132(x39971,x39972,x39973,x39974,f129(x39972,x39975,x39976)),f334(f334(x39974,x39975),x39976))
% 160.93/160.64 [4214]E(f189(x42141,x42142,f187(x42141,x42142,x42143,x42144),x42145,x42146),f187(x42141,x42142,x42143,f189(x42141,x42142,x42144,x42145,x42146)))
% 160.93/160.64 [4337]E(f334(f73(f887(x43371,x43372),x43372,f887(x43373,x43374),f272(x43371,x43372)),f274(x43373,x43371,x43374,x43372,x43375,x43376)),f334(f73(x43374,x43372,f887(x43373,x43374),x43376),f272(x43373,x43374)))
% 160.93/160.64 [4338]E(f334(f73(f887(x43381,x43382),x43381,f887(x43383,x43384),f268(x43381,x43382)),f274(x43383,x43381,x43384,x43382,x43385,x43386)),f334(f73(x43383,x43381,f887(x43383,x43384),x43385),f268(x43383,x43384)))
% 160.93/160.64 [3936]E(f334(f334(f73(x39361,x39362,x39363,x39364),x39365),x39366),f334(x39364,f334(x39365,x39366)))
% 160.93/160.64 [3736]E(f334(f334(f273(x37361,x37362,x37363),x37364),f334(f334(f269(x37361,x37362),x37365),x37366)),f334(f334(x37364,x37365),x37366))
% 160.93/160.64 [3795]E(f334(f334(f334(f8(x37951,x37952,x37953),x37954),x37955),x37956),f334(x37954,f334(x37955,x37956)))
% 160.93/160.64 [3796]E(f334(f334(f334(f7(x37961,x37962,x37963),x37964),x37965),x37966),f334(f334(x37964,x37966),x37965))
% 160.93/160.64 [3813]E(f334(f334(f334(f18(x38131,x38132,x38133),x38134),x38135),x38136),f334(f334(x38134,x38136),f334(x38135,x38136)))
% 160.93/160.64 [3835]E(f334(f158(x38351,x38352,x38353,x38354),f334(f334(f153(x38352),x38355),x38356)),f334(f334(x38354,x38355),x38356))
% 160.93/160.64 [3940]E(f334(f334(f153(f887(x39401,x39402)),f334(f334(f269(x39401,x39402),x39403),x39404)),f334(f334(f184(x39401,x39402),x39405),x39406)),f334(f334(f184(x39401,x39402),f334(f334(f153(x39401),x39403),x39405)),f334(f334(f153(x39402),x39404),x39406)))
% 160.93/160.64 [3943]E(f334(f334(f156(x39431,x39432),x39433),f334(f334(f161(x39431,x39434),x39435),x39436)),f334(f334(f161(x39432,f334(f334(f156(x39431,x39432),x39433),x39434)),x39435),f334(x39433,x39436)))
% 160.93/160.64 [3986]E(f334(f144(x39861,x39862,x39863,x39864),f334(f334(f153(x39862),x39865),x39866)),f334(f144(x39861,x39862,x39863,f334(f334(x39863,x39864),x39865)),x39866))
% 160.93/160.64 [4012]E(f276(x40121,x40122,x40123,x40124,f334(f334(f269(x40121,x40122),x40125),x40126)),f334(f334(x40124,x40125),x40126))
% 160.93/160.64 [4096]E(f334(f334(f41(x40961,f888(x40962,a876)),x40963),f334(f73(x40964,f888(x40962,a876),x40961,x40965),x40966)),f334(f334(f41(x40964,f888(x40962,a876)),f334(f313(x40961,x40964,x40966),x40963)),x40965))
% 160.93/160.64 [4149]E(f334(f334(f156(x41491,x41492),x41493),f334(f334(f156(x41494,x41491),x41495),x41496)),f334(f334(f156(x41494,x41492),f334(f73(x41491,x41492,x41494,x41493),x41495)),x41496))
% 160.93/160.64 [4151]E(f334(f334(f211(x41511,x41512),x41513),f334(f334(f211(x41514,x41511),x41515),x41516)),f334(f334(f211(x41514,x41512),f334(f73(x41511,x41512,x41514,x41513),x41515)),x41516))
% 160.93/160.64 [4156]E(f334(f313(x41561,x41562,f334(f73(x41563,x41562,x41561,x41564),x41565)),x41566),f334(f313(x41563,x41562,x41564),f334(f313(x41561,x41563,x41565),x41566)))
% 160.93/160.64 [4157]E(f334(f314(x41571,x41572,f334(f73(x41573,x41572,x41571,x41574),x41575)),x41576),f334(f314(x41571,x41573,x41575),f334(f314(x41573,x41572,x41574),x41576)))
% 160.93/160.64 [4186]E(f187(x41861,x41862,x41863,f334(f334(f334(f72(x41861,f885(x41862)),x41864),x41865),f334(f241(x41862),x41866))),f334(f334(f334(f72(x41861,f885(x41862)),f187(x41861,x41862,x41863,x41864)),x41865),f334(f241(x41862),x41866)))
% 160.93/160.64 [4188]E(f334(f144(x41881,x41882,x41883,f334(f144(x41881,x41882,x41883,x41884),x41885)),x41886),f334(f144(x41881,x41882,x41883,x41884),f334(f334(f136(x41882),x41885),x41886)))
% 160.93/160.64 [4327]E(f334(f274(x43271,x43271,x43272,x43273,f34(x43271),x43274),f334(f334(f269(x43271,x43272),x43275),x43276)),f334(f334(f269(x43271,x43273),x43275),f334(x43274,x43276)))
% 160.93/160.64 [4328]E(f334(f274(x43281,x43282,x43283,x43283,x43284,f34(x43283)),f334(f334(f269(x43281,x43283),x43285),x43286)),f334(f334(f269(x43282,x43283),f334(x43284,x43285)),x43286))
% 160.93/160.64 [4418]E(f334(f334(f156(f887(x44181,x44182),f887(x44181,x44183)),f334(f273(x44181,x44182,f887(x44181,x44183)),f334(f334(f7(x44181,f888(x44182,x44183),f888(x44182,f887(x44181,x44183))),f334(f334(f8(f888(x44183,f887(x44181,x44183)),f888(f888(x44182,x44183),f888(x44182,f887(x44181,x44183))),x44181),f8(x44183,f887(x44181,x44183),x44182)),f269(x44181,x44183))),x44184))),f334(f334(f184(x44181,x44182),x44185),x44186)),f334(f334(f184(x44181,x44183),x44185),f334(f334(f156(x44182,x44183),x44184),x44186)))
% 160.93/160.64 [3800]E(f98(x38001,x38002,x38003,f334(f334(f334(f92(x38001),x38004),x38005),x38006)),f334(f334(f334(x38003,x38004),x38005),x38006))
% 160.93/160.64 [3801]E(f99(x38011,x38012,x38013,f334(f334(f334(f92(x38011),x38014),x38015),x38016)),f334(f334(f334(x38013,x38014),x38015),x38016))
% 160.93/160.64 [3996]E(f334(f334(f73(x39961,x39962,x39963,f334(f16(x39962,x39961),x39964)),x39965),x39966),x39964)
% 160.93/160.64 [4031]E(f334(f313(x40311,x40312,x40313),f334(f313(x40314,x40311,x40315),x40316)),f334(f313(x40314,x40312,f334(f334(f8(x40311,x40312,x40314),x40313),x40315)),x40316))
% 160.93/160.64 [4037]E(f334(f334(f41(x40371,f888(x40372,a876)),f334(f313(x40373,x40371,x40374),x40375)),x40376),f334(f334(f41(x40373,f888(x40372,a876)),x40375),f334(f334(f8(x40371,f888(x40372,a876),x40373),x40376),x40374)))
% 160.93/160.64 [4038]E(f334(f334(f42(x40381,f888(x40382,a876)),f334(f313(x40383,x40381,x40384),x40385)),x40386),f334(f334(f42(x40383,f888(x40382,a876)),x40385),f334(f334(f8(x40381,f888(x40382,a876),x40383),x40386),x40384)))
% 160.93/160.64 [4039]E(f334(f334(f41(x40391,f888(x40392,a876)),x40393),f334(f334(f8(x40394,f888(x40392,a876),x40391),x40395),x40396)),f334(f334(f41(x40394,f888(x40392,a876)),f334(f313(x40391,x40394,x40396),x40393)),x40395))
% 160.93/160.64 [4040]E(f334(f334(f42(x40401,f888(x40402,a876)),x40403),f334(f334(f8(x40404,f888(x40402,a876),x40401),x40405),x40406)),f334(f334(f42(x40404,f888(x40402,a876)),f334(f313(x40401,x40404,x40406),x40403)),x40405))
% 160.93/160.64 [4098]E(f334(f334(f41(x40981,f888(x40982,a876)),x40983),f334(f334(f8(f888(x40984,a876),f888(x40982,a876),x40981),f313(x40984,x40982,x40985)),x40986)),f334(f313(x40984,x40982,x40985),f334(f334(f41(x40981,f888(x40984,a876)),x40983),x40986)))
% 160.93/160.64 [4099]E(f334(f334(f41(x40991,f888(x40992,a876)),x40993),f334(f334(f8(f888(x40994,a876),f888(x40992,a876),x40991),f288(x40994,x40992,x40995)),x40996)),f334(f288(x40994,x40992,x40995),f334(f334(f41(x40991,f888(x40994,a876)),x40993),x40996)))
% 160.93/160.64 [4100]E(f334(f334(f41(x41001,f888(x41002,a876)),x41003),f334(f334(f8(f888(x41004,a876),f888(x41002,a876),x41001),f314(x41002,x41004,x41005)),x41006)),f334(f314(x41002,x41004,x41005),f334(f334(f41(x41001,f888(x41004,a876)),x41003),x41006)))
% 160.93/160.64 [4101]E(f334(f334(f42(x41011,f888(x41012,a876)),x41013),f334(f334(f8(f888(x41014,a876),f888(x41012,a876),x41011),f314(x41012,x41014,x41015)),x41016)),f334(f314(x41012,x41014,x41015),f334(f334(f42(x41011,f888(x41014,a876)),x41013),x41016)))
% 160.93/160.64 [4194]E(f334(f144(x41941,x41942,f334(f7(x41942,x41941,x41941),x41943),x41944),f334(f171(x41942),f334(f334(f153(x41942),x41945),x41946))),f334(f334(x41943,x41945),f334(f144(x41941,x41942,f334(f7(x41942,x41941,x41941),x41943),x41944),f334(f171(x41942),x41946))))
% 160.93/160.64 [4253]E(f334(f334(f18(f887(x42531,x42532),x42532,x42533),f334(f334(f8(x42534,f888(x42532,x42533),f887(x42531,x42532)),x42535),f334(f334(f8(x42531,x42534,f887(x42531,x42532)),x42536),f268(x42531,x42532)))),f272(x42531,x42532)),f334(f273(x42531,x42532,x42533),f334(f334(f8(x42534,f888(x42532,x42533),x42531),x42535),x42536)))
% 160.93/160.64 [4260]E(f334(f144(x42601,x42602,f334(f7(x42602,x42601,x42601),x42603),f334(f144(x42601,x42602,f334(f7(x42602,x42601,x42601),x42603),x42604),f334(f171(x42602),x42605))),f334(f171(x42602),x42606)),f334(f144(x42601,x42602,f334(f7(x42602,x42601,x42601),x42603),x42604),f334(f171(x42602),f334(f334(f136(x42602),x42606),x42605))))
% 160.93/160.64 [4262]E(f334(f334(f156(f887(x42621,x42622),f887(x42623,x42622)),f334(f273(x42621,x42622,f887(x42623,x42622)),f334(f334(f8(x42623,f888(x42622,f887(x42623,x42622)),x42621),f269(x42623,x42622)),x42624))),f334(f334(f184(x42621,x42622),x42625),x42626)),f334(f334(f184(x42623,x42622),f334(f334(f156(x42621,x42623),x42624),x42625)),x42626))
% 160.93/160.64 [4310]P1(f334(f334(f248(f888(x43101,a876)),f334(f288(x43102,x43101,x43103),f334(f334(f42(x43104,f888(x43102,a876)),x43105),x43106))),f334(f334(f42(x43104,f888(x43101,a876)),x43105),f334(f334(f8(f888(x43102,a876),f888(x43101,a876),x43104),f288(x43102,x43101,x43103)),x43106))))
% 160.93/160.64 [4111]E(f334(f334(f184(x41111,x41112),f334(f334(f161(x41111,x41113),x41114),f334(f268(x41111,x41112),x41115))),f334(f334(f161(x41112,x41116),x41114),f334(f272(x41111,x41112),x41115))),f334(f334(f161(f887(x41111,x41112),f334(f334(f184(x41111,x41112),x41113),x41116)),x41114),x41115))
% 160.93/160.64 [4175]E(f334(f334(f114(f888(f887(x41751,x41752),a876)),f334(f334(f291(x41751,x41753,x41752),x41754),x41755)),f334(f334(f291(x41751,x41753,x41752),x41754),x41756)),f334(f334(f291(x41751,x41753,x41752),x41754),f334(f334(f114(f888(f887(x41753,x41752),a876)),x41755),x41756)))
% 160.93/160.64 [4273]E(f334(f334(f312(f887(x42731,x42732)),f334(f334(f269(x42731,x42732),x42733),x42734)),f334(f334(f114(f888(f887(x42731,x42732),a876)),f334(f334(f271(x42731,x42732),x42735),f334(f16(f888(x42732,a876),x42731),f334(f334(f312(x42732),x42734),x42736)))),f334(f334(f271(x42731,x42732),f334(f334(f312(x42731),x42733),x42735)),f334(f16(f888(x42732,a876),x42731),x42736)))),f334(f334(f271(x42731,x42732),f334(f334(f312(x42731),x42733),x42735)),f334(f16(f888(x42732,a876),x42731),f334(f334(f312(x42732),x42734),x42736))))
% 160.93/160.64 [4351]E(f334(f334(f105(f888(x43511,a876)),f334(f314(x43511,x43512,f334(f73(f887(x43512,x43513),x43512,x43511,f268(x43512,x43513)),x43514)),x43515)),f334(f314(x43511,x43513,f334(f73(f887(x43512,x43513),x43513,x43511,f272(x43512,x43513)),x43514)),x43516)),f334(f314(x43511,f887(x43512,x43513),x43514),f334(f334(f271(x43512,x43513),x43515),f334(f16(f888(x43513,a876),x43512),x43516))))
% 160.93/160.64 [4095]E(f334(f334(f334(f72(x40951,x40952),f334(f334(f334(f72(x40951,x40952),x40953),x40954),x40955)),x40954),x40956),f334(f334(f334(f72(x40951,x40952),x40953),x40954),x40956))
% 160.93/160.64 [4200]E(f334(f334(f114(f888(f887(x42001,x42002),a876)),f334(f334(f291(x42001,x42003,x42002),x42004),x42005)),f334(f334(f291(x42001,x42003,x42002),x42006),x42005)),f334(f334(f291(x42001,x42003,x42002),f334(f334(f114(f888(f887(x42001,x42003),a876)),x42004),x42006)),x42005))
% 160.93/160.64 [4335]E(f334(f334(f41(x43351,f888(x43352,a876)),x43353),f334(f334(f7(x43351,f888(x43354,f888(x43352,a876)),f888(x43352,a876)),f334(f334(f8(f888(x43354,a876),f888(f888(x43354,f888(x43352,a876)),f888(x43352,a876)),x43351),f41(x43354,f888(x43352,a876))),x43355)),x43356)),f334(f334(f41(x43354,f888(x43352,a876)),f334(f334(f41(x43351,f888(x43354,a876)),x43353),x43355)),x43356))
% 160.93/160.64 [4336]E(f334(f334(f42(x43361,f888(x43362,a876)),x43363),f334(f334(f7(x43361,f888(x43364,f888(x43362,a876)),f888(x43362,a876)),f334(f334(f8(f888(x43364,a876),f888(f888(x43364,f888(x43362,a876)),f888(x43362,a876)),x43361),f42(x43364,f888(x43362,a876))),x43365)),x43366)),f334(f334(f42(x43364,f888(x43362,a876)),f334(f334(f41(x43361,f888(x43364,a876)),x43363),x43365)),x43366))
% 160.93/160.64 [4388]E(f334(f273(x43881,x43882,f887(x43883,x43884)),f334(f334(f7(x43881,f888(x43882,x43884),f888(x43882,f887(x43883,x43884))),f334(f334(f8(f888(x43884,f887(x43883,x43884)),f888(f888(x43882,x43884),f888(x43882,f887(x43883,x43884))),x43881),f8(x43884,f887(x43883,x43884),x43882)),f334(f334(f8(x43883,f888(x43884,f887(x43883,x43884)),x43881),f269(x43883,x43884)),x43885))),x43886)),f274(x43881,x43883,x43882,x43884,x43885,x43886))
% 160.93/160.64 [4309]E(f334(f334(f334(f72(x43091,f885(x43092)),f190(x43091,x43092,x43093,f334(f334(f22(f888(x43091,a876)),x43094),f334(f334(f312(x43091),x43095),f196(f888(x43091,a876)))))),x43095),x43096),f334(f334(f334(f72(x43091,f885(x43092)),f190(x43091,x43092,x43093,x43094)),x43095),x43096))
% 160.93/160.64 [4413]E(f334(f313(x44131,x44132,f334(f334(f18(x44131,x44132,x44132),f334(f334(f18(x44131,x44132,f888(x44132,x44132)),f334(f334(f8(a876,f888(x44132,f888(x44132,x44132)),x44131),f100(x44132)),x44133)),x44134)),x44135)),x44136),f334(f334(f114(f888(x44132,a876)),f334(f313(x44131,x44132,x44134),f334(f334(f105(f888(x44131,a876)),x44136),f334(f254(x44131),x44133)))),f334(f313(x44131,x44132,x44135),f334(f334(f105(f888(x44131,a876)),x44136),f334(f254(x44131),f334(f334(f8(a876,a876,x44131),a329),x44133))))))
% 160.93/160.64 [4424]E(f334(f313(x44241,f887(x44242,x44243),f334(f334(f18(x44241,x44243,f887(x44242,x44243)),f334(f334(f8(x44242,f888(x44243,f887(x44242,x44243)),x44241),f269(x44242,x44243)),x44244)),x44245)),x44246),f334(f334(f271(x44242,x44243),f334(f313(x44241,x44242,x44244),x44246)),f334(f334(f8(f888(x44241,a876),f888(x44243,a876),x44242),f313(x44241,x44243,x44245)),f334(f334(f7(x44242,f888(x44241,a876),f888(x44241,a876)),f334(f334(f8(f888(x44241,a876),f888(f888(x44241,a876),f888(x44241,a876)),x44242),f105(f888(x44241,a876))),f334(f334(f8(f888(x44242,a876),f888(x44241,a876),x44242),f314(x44241,x44242,x44244)),f334(f334(f7(x44242,f888(x44242,a876),f888(x44242,a876)),f312(x44242)),f196(f888(x44242,a876)))))),x44246))))
% 160.93/160.64 [4370]E(f334(f272(x43701,x43702),f334(f274(x43703,x43701,x43704,x43702,x43705,x43706),x43707)),f334(x43706,f334(f272(x43703,x43704),x43707)))
% 160.93/160.64 [4371]E(f334(f268(x43711,x43712),f334(f274(x43713,x43711,x43714,x43712,x43715,x43716),x43717)),f334(x43715,f334(f268(x43713,x43714),x43717)))
% 160.93/160.64 [4073]E(f334(f334(f184(x40731,x40732),f334(f334(f161(x40731,x40733),x40734),x40735)),f334(f334(f161(x40732,x40736),x40734),x40737)),f334(f334(f161(f887(x40731,x40732),f334(f334(f184(x40731,x40732),x40733),x40736)),x40734),f334(f334(f269(x40731,x40732),x40735),x40737)))
% 160.93/160.64 [4141]E(f334(f334(f334(f275(x41411,x41412,x41413,x41414),x41415),x41416),x41417),f334(f334(f273(x41412,x41413,x41414),x41416),f334(x41415,x41417)))
% 160.93/160.64 [4155]E(f334(f334(f334(f275(x41551,x41552,x41553,x41554),x41555),x41556),x41557),f334(f334(x41556,f334(f268(x41552,x41553),f334(x41555,x41557))),f334(f272(x41552,x41553),f334(x41555,x41557))))
% 160.93/160.64 [4190]E(f189(x41901,x41902,f334(f334(f334(f72(x41901,f885(x41902)),x41903),x41904),f334(f241(x41902),x41905)),x41906,x41907),f189(x41901,x41902,x41903,f334(f334(f153(x41901),x41904),x41906),f334(f334(f153(x41902),x41905),x41907)))
% 160.93/160.64 [4208]E(f334(f73(x42081,x42082,x42083,x42084),f334(f73(x42085,x42081,x42083,x42086),x42087)),f334(f73(x42085,x42082,x42083,f334(f73(x42081,x42082,x42085,x42084),x42086)),x42087))
% 160.93/160.64 [4269]E(f334(f73(f885(x42691),f885(x42692),x42693,f334(f211(x42691,x42692),x42694)),f334(f334(f334(f72(x42693,f885(x42691)),x42695),x42696),f334(f241(x42691),x42697))),f334(f334(f334(f72(x42693,f885(x42692)),f334(f73(f885(x42691),f885(x42692),x42693,f334(f211(x42691,x42692),x42694)),x42695)),x42696),f334(f241(x42692),f334(x42694,x42697))))
% 160.93/160.64 [4395]E(f334(f274(x43951,x43952,x43953,x43953,x43954,f34(x43953)),f334(f274(x43951,x43951,x43955,x43953,f34(x43951),x43956),x43957)),f334(f334(f269(x43952,x43953),f334(x43954,f334(f268(x43951,x43955),x43957))),f334(x43956,f334(f272(x43951,x43955),x43957))))
% 160.93/160.64 [4396]E(f334(f274(x43961,x43961,x43962,x43963,f34(x43961),x43964),f334(f274(x43965,x43961,x43962,x43962,x43966,f34(x43962)),x43967)),f334(f334(f269(x43961,x43963),f334(x43966,f334(f268(x43965,x43962),x43967))),f334(x43964,f334(f272(x43965,x43962),x43967))))
% 160.93/160.64 [4411]E(f334(f274(x44111,x44112,x44113,x44113,x44114,f34(x44113)),f334(f274(x44115,x44111,x44113,x44113,x44116,f34(x44113)),x44117)),f334(f274(x44115,x44112,x44113,x44113,f334(f73(x44111,x44112,x44115,x44114),x44116),f34(x44113)),x44117))
% 160.93/160.64 [4412]E(f334(f274(x44121,x44121,x44122,x44123,f34(x44121),x44124),f334(f274(x44121,x44121,x44125,x44122,f34(x44121),x44126),x44127)),f334(f274(x44121,x44121,x44125,x44123,f34(x44121),f334(f73(x44122,x44123,x44125,x44124),x44126)),x44127))
% 160.93/160.64 [4421]E(f334(f274(x44211,x44212,x44213,x44213,x44214,f34(x44213)),f334(f274(x44211,x44211,x44215,x44213,f34(x44211),x44216),x44217)),f334(f274(x44212,x44212,x44215,x44213,f34(x44212),x44216),f334(f274(x44211,x44212,x44215,x44215,x44214,f34(x44215)),x44217)))
% 160.93/160.64 [4108]E(f334(f334(f291(x41081,x41082,x41083),f334(f334(f291(x41081,x41084,x41082),x41085),x41086)),x41087),f334(f334(f291(x41081,x41084,x41083),x41085),f334(f334(f291(x41084,x41082,x41083),x41086),x41087)))
% 160.93/160.64 [4181]E(f334(f334(f273(x41811,x41812,x41813),f334(f73(x41814,f888(x41812,x41813),x41811,x41815),x41816)),x41817),f334(f334(x41815,f334(x41816,f334(f268(x41811,x41812),x41817))),f334(f272(x41811,x41812),x41817)))
% 160.93/160.64 [4233]E(f334(f73(x42331,x42332,x42333,x42334),f334(f334(f334(f72(x42333,x42331),x42335),x42336),x42337)),f334(f334(f334(f72(x42333,x42332),f334(f73(x42331,x42332,x42333,x42334),x42335)),x42336),f334(x42334,x42337)))
% 160.93/160.64 [4265]E(f334(f144(x42651,x42652,f334(f7(x42652,x42651,x42651),x42653),x42654),f334(f171(x42652),f334(f334(f156(x42655,x42652),x42656),x42657))),f334(f144(x42651,x42655,f334(f7(x42655,x42651,x42651),f334(f73(x42652,f888(x42651,x42651),x42655,x42653),x42656)),x42654),f334(f171(x42655),x42657)))
% 160.93/160.64 [4209]E(f334(f334(f41(x42091,f888(f887(x42092,x42093),a876)),x42094),f334(f334(f8(f888(f887(x42095,x42093),a876),f888(f887(x42092,x42093),a876),x42091),f334(f291(x42092,x42095,x42093),x42096)),x42097)),f334(f334(f291(x42092,x42095,x42093),x42096),f334(f334(f41(x42091,f888(f887(x42095,x42093),a876)),x42094),x42097)))
% 160.93/160.64 [4357]E(f334(f334(f41(x43571,f888(f887(x43572,x43573),a876)),x43574),f334(f334(f7(x43571,f888(f887(x43575,x43573),a876),f888(f887(x43572,x43573),a876)),f334(f334(f8(f888(f887(x43572,x43575),a876),f888(f888(f887(x43575,x43573),a876),f888(f887(x43572,x43573),a876)),x43571),f291(x43572,x43575,x43573)),x43576)),x43577)),f334(f334(f291(x43572,x43575,x43573),f334(f334(f41(x43571,f888(f887(x43572,x43575),a876)),x43574),x43576)),x43577))
% 160.93/160.64 [4358]E(f334(f144(x43581,x43582,f334(f334(f7(x43581,f888(x43582,x43583),f888(x43582,x43581)),f334(f334(f8(f888(x43583,x43581),f888(f888(x43582,x43583),f888(x43582,x43581)),x43581),f8(x43583,x43581,x43582)),x43584)),x43585),x43586),x43587),f334(f144(x43581,x43583,x43584,x43586),f334(f334(f156(x43582,x43583),x43585),x43587)))
% 160.93/160.64 [4422]E(f334(f334(f42(x44221,f888(x44222,a876)),x44223),f334(f334(f8(f888(x44224,f888(x44222,a876)),f888(x44222,a876),x44221),f334(f42(x44224,f888(x44222,a876)),x44225)),f334(f334(f7(x44221,f888(x44224,f888(x44222,a876)),f888(x44224,f888(x44222,a876))),f334(f334(f8(f888(f888(x44222,a876),f888(x44222,a876)),f888(f888(x44224,f888(x44222,a876)),f888(x44224,f888(x44222,a876))),x44221),f8(f888(x44222,a876),f888(x44222,a876),x44224)),f334(f334(f8(f888(x44222,a876),f888(f888(x44222,a876),f888(x44222,a876)),x44221),f114(f888(x44222,a876))),x44226))),x44227))),f334(f334(f114(f888(x44222,a876)),f334(f334(f42(x44221,f888(x44222,a876)),x44223),x44226)),f334(f334(f42(x44224,f888(x44222,a876)),x44225),x44227)))
% 160.93/160.64 [4423]E(f334(f334(f41(x44231,f888(x44232,a876)),x44233),f334(f334(f8(f888(x44234,f888(x44232,a876)),f888(x44232,a876),x44231),f334(f41(x44234,f888(x44232,a876)),x44235)),f334(f334(f7(x44231,f888(x44234,f888(x44232,a876)),f888(x44234,f888(x44232,a876))),f334(f334(f8(f888(f888(x44232,a876),f888(x44232,a876)),f888(f888(x44234,f888(x44232,a876)),f888(x44234,f888(x44232,a876))),x44231),f8(f888(x44232,a876),f888(x44232,a876),x44234)),f334(f334(f8(f888(x44232,a876),f888(f888(x44232,a876),f888(x44232,a876)),x44231),f105(f888(x44232,a876))),x44236))),x44237))),f334(f334(f105(f888(x44232,a876)),f334(f334(f41(x44231,f888(x44232,a876)),x44233),x44236)),f334(f334(f41(x44234,f888(x44232,a876)),x44235),x44237)))
% 160.93/160.64 [4416]E(f208(x44161,x44162,f334(f334(f334(x44163,x44164),x44165),x44166),f334(f334(f7(x44161,f887(a103,a103),f888(a103,f883(x44162))),f334(f334(f7(x44161,a103,f888(f887(a103,a103),f888(a103,f883(x44162)))),f334(f334(f7(x44161,a103,f888(a103,f888(f887(a103,a103),f888(a103,f883(x44162))))),x44167),x44164)),x44165)),x44166)),f334(f334(f334(f222(x44161,x44162,x44163,x44167),x44164),x44165),x44166))
% 160.93/160.64 [4429]E(f209(x44291,x44292,f334(f334(f334(x44293,x44294),x44295),x44296),f334(f334(f7(x44291,f887(a103,a103),f888(a103,f883(x44292))),f334(f334(f7(x44291,a103,f888(f887(a103,a103),f888(a103,f883(x44292)))),f334(f334(f7(x44291,a103,f888(a103,f888(f887(a103,a103),f888(a103,f883(x44292))))),x44297),x44294)),x44295)),x44296)),f224(x44291,x44292,x44293,x44297,x44294,x44295,x44296))
% 160.93/160.64 [4420]E(f205(x44201,x44202,f334(f334(f334(x44203,x44204),x44205),x44206),f334(f334(f7(x44201,f887(a103,a103),f888(a103,f883(f885(x44202)))),f334(f334(f7(x44201,a103,f888(f887(a103,a103),f888(a103,f883(f885(x44202))))),f334(f334(f7(x44201,a103,f888(a103,f888(f887(a103,a103),f888(a103,f883(f885(x44202)))))),x44207),x44204)),x44205)),x44206)),f334(f334(f334(f219(x44201,x44202,x44203,x44207),x44204),x44205),x44206))
% 160.93/160.64 [4431]E(f206(x44311,x44312,f334(f334(f334(x44313,x44314),x44315),x44316),f334(f334(f7(x44311,f887(a103,a103),f888(a103,f883(f885(x44312)))),f334(f334(f7(x44311,a103,f888(f887(a103,a103),f888(a103,f883(f885(x44312))))),f334(f334(f7(x44311,a103,f888(a103,f888(f887(a103,a103),f888(a103,f883(f885(x44312)))))),x44317),x44314)),x44315)),x44316)),f221(x44311,x44312,x44313,x44317,x44314,x44315,x44316))
% 160.93/160.64 [4329]E(f334(f274(x43291,x43292,x43293,x43294,x43295,x43296),f334(f334(f269(x43291,x43293),x43297),x43298)),f334(f334(f269(x43292,x43294),f334(x43295,x43297)),f334(x43296,x43298)))
% 160.93/160.64 [4433]E(f334(f334(f156(f887(x44331,x44332),f887(x44333,x44334)),f334(f273(x44331,x44332,f887(x44333,x44334)),f334(f334(f7(x44331,f888(x44332,x44334),f888(x44332,f887(x44333,x44334))),f334(f334(f8(f888(x44334,f887(x44333,x44334)),f888(f888(x44332,x44334),f888(x44332,f887(x44333,x44334))),x44331),f8(x44334,f887(x44333,x44334),x44332)),f334(f334(f8(x44333,f888(x44334,f887(x44333,x44334)),x44331),f269(x44333,x44334)),x44335))),x44336))),f334(f334(f184(x44331,x44332),x44337),x44338)),f334(f334(f184(x44333,x44334),f334(f334(f156(x44331,x44333),x44335),x44337)),f334(f334(f156(x44332,x44334),x44336),x44338)))
% 160.93/160.64 [4437]E(f334(f334(f156(f887(x44371,x44372),x44373),f334(f273(x44371,x44372,x44373),f334(f334(f8(f888(x44372,f887(x44371,x44374)),f888(x44372,x44373),x44371),f334(f8(f887(x44371,x44374),x44373,x44372),x44375)),f334(f334(f7(x44371,f888(x44372,x44374),f888(x44372,f887(x44371,x44374))),f334(f334(f8(f888(x44374,f887(x44371,x44374)),f888(f888(x44372,x44374),f888(x44372,f887(x44371,x44374))),x44371),f8(x44374,f887(x44371,x44374),x44372)),f269(x44371,x44374))),x44376)))),f334(f334(f184(x44371,x44372),x44377),x44378)),f334(f334(f156(f887(x44371,x44374),x44373),x44375),f334(f334(f184(x44371,x44374),x44377),f334(f334(f156(x44372,x44374),x44376),x44378))))
% 160.93/160.64 [4362]E(f334(f334(f156(f887(x43621,x43622),x43623),f334(f273(x43621,x43622,x43623),f334(f334(f8(f888(x43622,f887(x43624,x43622)),f888(x43622,x43623),x43621),f334(f8(f887(x43624,x43622),x43623,x43622),x43625)),f334(f334(f8(x43624,f888(x43622,f887(x43624,x43622)),x43621),f269(x43624,x43622)),x43626)))),f334(f334(f184(x43621,x43622),x43627),x43628)),f334(f334(f156(f887(x43624,x43622),x43623),x43625),f334(f334(f184(x43624,x43622),f334(f334(f156(x43621,x43624),x43626),x43627)),x43628)))
% 160.93/160.64 [4320]E(f334(f334(f273(x43201,x43202,x43203),f334(f334(f8(f888(x43202,f887(x43204,x43205)),f888(x43202,x43203),x43201),f334(f8(f887(x43204,x43205),x43203,x43202),f334(f273(x43204,x43205,x43203),x43206))),x43207)),x43208),f334(f334(f273(x43204,x43205,x43203),x43206),f334(f334(f273(x43201,x43202,f887(x43204,x43205)),x43207),x43208)))
% 160.93/160.64 [4439]E(f334(f334(f41(f887(x44391,x44392),f888(f887(x44393,x44394),a876)),f334(f334(f271(x44391,x44392),x44395),f334(f16(f888(x44392,a876),x44391),x44396))),f334(f273(x44391,x44392,f888(f887(x44393,x44394),a876)),f334(f334(f7(x44391,f888(x44392,f888(x44393,f888(x44394,a876))),f888(x44392,f888(f887(x44393,x44394),a876))),f334(f334(f8(f888(f888(x44393,f888(x44394,a876)),f888(f887(x44393,x44394),a876)),f888(f888(x44392,f888(x44393,f888(x44394,a876))),f888(x44392,f888(f887(x44393,x44394),a876))),x44391),f8(f888(x44393,f888(x44394,a876)),f888(f887(x44393,x44394),a876),x44392)),f334(f334(f8(f888(x44393,a876),f888(f888(x44393,f888(x44394,a876)),f888(f887(x44393,x44394),a876)),x44391),f271(x44393,x44394)),x44397))),f334(f334(f8(f888(x44394,a876),f888(x44393,f888(x44394,a876)),x44392),f16(f888(x44394,a876),x44393)),x44398)))),f334(f334(f271(x44393,x44394),f334(f334(f41(x44391,f888(x44393,a876)),x44395),x44397)),f334(f16(f888(x44394,a876),x44393),f334(f334(f41(x44392,f888(x44394,a876)),x44396),x44398))))
% 160.93/160.64 [4376]E(f334(f334(f275(x43761,x43762,x43763,x43764),f334(f334(f275(x43761,x43765,x43766,f887(x43762,x43763)),x43767),x43768)),x43769),f334(f334(f275(x43761,x43765,x43766,x43764),x43767),f334(f334(f7(x43765,f888(x43762,f888(x43763,x43764)),f888(x43766,x43764)),f334(f334(f8(f888(x43766,f887(x43762,x43763)),f888(f888(x43762,f888(x43763,x43764)),f888(x43766,x43764)),x43765),f275(x43766,x43762,x43763,x43764)),x43768)),x43769)))
% 160.93/160.64 [4408]E(f334(f73(f887(x44081,x44082),f887(x44083,x44084),f887(x44085,x44086),f274(x44081,x44083,x44082,x44084,x44087,x44088)),f274(x44085,x44081,x44086,x44082,x44089,x440810)),f274(x44085,x44083,x44086,x44084,f334(f73(x44081,x44083,x44085,x44087),x44089),f334(f73(x44082,x44084,x44086,x44088),x440810)))
% 160.93/160.64 [4414]E(f334(f274(x44141,x44142,x44143,x44144,x44145,x44146),f334(f274(x44147,x44141,x44148,x44143,x44149,x441410),x441411)),f334(f274(x44147,x44142,x44148,x44144,f334(f73(x44141,x44142,x44147,x44145),x44149),f334(f73(x44143,x44144,x44148,x44146),x441410)),x441411))
% 160.93/160.64 [6458]P9(a5000)+P1(f334(f334(f336(f887(a879,a878)),a685),f334(f174(f887(a879,a878)),a27)))
% 160.93/160.64 [8456]P9(a5000)+~P1(f334(f334(f273(a879,a878,a876),f334(f16(f888(a878,a876),a879),a25)),a685))
% 160.93/160.64 [4581]~P92(x45811)+E(f91(x45811),a331)
% 160.93/160.64 [4582]~P4(x45821)+P4(f885(x45821))
% 160.93/160.64 [4583]~P60(x45831)+P60(f885(x45831))
% 160.93/160.64 [4584]~P103(x45841)+P103(f882(x45841))
% 160.93/160.64 [4587]~P136(x45871)+~E(f78(x45871),f2(x45871))
% 160.93/160.64 [4589]~E(x45891,f2(a103))+E(f334(a20,x45891),f2(a1))
% 160.93/160.64 [4590]~E(x45901,f2(a1))+E(f82(a1,x45901),f2(a1))
% 160.93/160.64 [4596]~P142(x45961)+P32(x45961,f2(x45961))
% 160.93/160.64 [4598]~P108(x45981)+P16(x45981,f117(x45981))
% 160.93/160.64 [4607]P1(x46071)+P1(f334(a329,x46071))
% 160.93/160.64 [4650]~P142(x46501)+~P32(x46501,f78(x46501))
% 160.93/160.64 [4697]~P1(x46971)+~P1(f334(a329,x46971))
% 160.93/160.64 [4720]E(f334(a108,x47201),f2(a881))+~P1(f334(a201,x47201))
% 160.93/160.64 [4784]~P99(x47841)+P17(x47841,x47841,f114(x47841))
% 160.93/160.64 [4785]~P100(x47851)+P17(x47851,x47851,f105(x47851))
% 160.93/160.64 [4786]~P95(x47861)+P17(x47861,x47861,f81(x47861))
% 160.93/160.64 [4787]~P108(x47871)+P17(x47871,x47871,f246(x47871))
% 160.93/160.64 [4788]~P108(x47881)+P17(x47881,x47881,f247(x47881))
% 160.93/160.64 [4789]~P70(x47891)+P18(x47891,x47891,f81(x47891))
% 160.93/160.64 [4593]~E(x45931,f2(a881))+E(f334(f104(a1),x45931),f2(a1))
% 160.93/160.64 [4600]~P93(x46001)+E(f334(f107(x46001),a83),f2(x46001))
% 160.93/160.64 [4603]~E(f598(x46031),f2(a881))+E(f334(f168(a881),x46031),f2(a881))
% 160.93/160.64 [4604]~P110(x46041)+E(f250(x46041,f248(x46041)),f246(x46041))
% 160.93/160.64 [4605]~P110(x46051)+E(f251(x46051,f248(x46051)),f247(x46051))
% 160.93/160.64 [4606]~P88(x46061)+E(f82(x46061,f2(x46061)),f2(x46061))
% 160.93/160.64 [4615]~P142(x46151)+E(f334(f104(x46151),f2(a881)),f2(x46151))
% 160.93/160.64 [4616]~P142(x46161)+E(f334(f104(x46161),f78(a881)),f78(x46161))
% 160.93/160.64 [4617]~P139(x46171)+E(f334(f106(x46171),f2(a1)),f2(x46171))
% 160.93/160.64 [4618]~P139(x46181)+E(f334(f106(x46181),f78(a1)),f78(x46181))
% 160.93/160.64 [4619]E(x46191,f2(a881))+~E(f334(f104(a1),x46191),f2(a1))
% 160.93/160.64 [4644]~P85(x46441)+E(f334(f75(x46441),f2(x46441)),f2(x46441))
% 160.93/160.64 [4645]~P111(x46451)+E(f334(f75(x46451),f78(x46451)),f78(x46451))
% 160.93/160.64 [4646]~P94(x46461)+E(f334(f79(x46461),f196(x46461)),f257(x46461))
% 160.93/160.64 [4647]~P66(x46471)+E(f334(f79(x46471),f2(x46471)),f2(x46471))
% 160.93/160.64 [4648]~P94(x46481)+E(f334(f79(x46481),f257(x46481)),f196(x46481))
% 160.93/160.64 [4649]~P79(x46491)+E(f334(f168(x46491),f117(x46491)),f2(x46491))
% 160.93/160.64 [4670]~P38(x46701)+P40(f334(f174(a1),x46701))
% 160.93/160.64 [4702]~P93(x47021)+E(f334(f79(x47021),f78(x47021)),f334(f107(x47021),a101))
% 160.93/160.64 [4719]~P93(x47191)+P32(x47191,f334(f107(x47191),a83))
% 160.93/160.64 [4736]~P60(x47361)+E(f334(f174(x47361),f55(x47361)),f257(f888(x47361,a876)))
% 160.93/160.64 [4746]P38(x47461)+~P40(f334(f174(a1),x47461))
% 160.93/160.64 [4747]~P60(x47471)+P1(f334(f139(x47471),f55(x47471)))
% 160.93/160.64 [4790]E(f334(f104(a1),f334(a108,x47901)),x47901)+P1(f334(a201,x47901))
% 160.93/160.64 [4807]~P110(x48071)+E(f93(x48071,x48071,f5(x48071)),f94(x48071))
% 160.93/160.64 [4860]~P113(x48601)+E(f260(x48601,f78(x48601),f81(x48601)),f259(x48601))
% 160.93/160.64 [4890]~P93(x48901)+~P32(x48901,f334(f107(x48901),a101))
% 160.93/160.64 [4900]E(f334(a28,x49001),f210(a878))+P1(f334(a25,f334(a26,x49001)))
% 160.93/160.64 [5030]E(f334(f75(a1),x50301),x50301)+P1(f334(f334(f249(a1),x50301),f2(a1)))
% 160.93/160.64 [5051]~E(f334(a108,x50511),f2(a881))+P1(f334(f334(f248(a1),x50511),f2(a1)))
% 160.93/160.64 [5111]~P1(f334(a201,x51111))+P1(f334(f334(f249(a1),x51111),f2(a1)))
% 160.93/160.64 [5151]~P139(x51511)+P1(f334(f334(f336(x51511),f2(x51511)),f113(x51511)))
% 160.93/160.64 [5152]~P142(x51521)+P1(f334(f334(f336(x51521),f2(x51521)),f194(x51521)))
% 160.93/160.64 [5153]~P139(x51531)+P1(f334(f334(f336(x51531),f78(x51531)),f113(x51531)))
% 160.93/160.64 [5154]~P142(x51541)+P1(f334(f334(f336(x51541),f78(x51541)),f194(x51541)))
% 160.93/160.64 [5155]~P106(x51551)+P1(f334(f334(f249(x51551),f2(x51551)),f78(x51551)))
% 160.93/160.64 [5156]~P106(x51561)+P1(f334(f334(f248(x51561),f2(x51561)),f78(x51561)))
% 160.93/160.64 [5158]E(f334(f241(a878),f695(x51581)),f334(a28,x51581))+~P1(f334(a25,f334(a26,x51581)))
% 160.93/160.64 [5159]E(f334(f241(a878),f709(x51591)),f334(a28,x51591))+~P1(f334(a25,f334(a26,x51591)))
% 160.93/160.64 [5214]E(x52141,f2(a881))+~P1(f334(f334(f248(a881),x52141),f2(a881)))
% 160.93/160.64 [5259]E(f334(a108,x52591),f2(a881))+~P1(f334(f334(f248(a1),x52591),f2(a1)))
% 160.93/160.64 [5319]P1(f334(a201,x53191))+~P1(f334(f334(f249(a1),x53191),f2(a1)))
% 160.93/160.64 [5324]~P108(x53241)+P18(x53241,f882(x53241),f150(x53241,x53241,f5(x53241)))
% 160.93/160.64 [5341]P40(x53411)+~P1(f334(f334(f248(a1),f2(a1)),f342(x53411)))
% 160.93/160.64 [5347]E(f334(f75(a1),x53471),f334(f79(a1),x53471))+~P1(f334(f334(f249(a1),x53471),f2(a1)))
% 160.93/160.64 [5519]~P106(x55191)+~P1(f334(f334(f249(x55191),f78(x55191)),f2(x55191)))
% 160.93/160.64 [5520]~P106(x55201)+~P1(f334(f334(f248(x55201),f78(x55201)),f2(x55201)))
% 160.93/160.64 [5530]~E(x55301,f2(a1))+P1(f334(f334(f249(a1),f334(f75(a1),x55301)),f78(a1)))
% 160.93/160.64 [5531]~E(x55311,f2(a881))+P1(f334(f334(f248(a1),f334(f104(a1),x55311)),f2(a1)))
% 160.93/160.64 [5650]~P79(x56501)+E(f144(x56501,x56501,f80(x56501),f2(x56501)),f168(x56501))
% 160.93/160.64 [5821]~P102(x58211)+P27(a881,x58211,f104(x58211),f257(f888(a881,a876)))
% 160.93/160.64 [6014]E(x60141,f2(a881))+~P1(f334(f334(f248(a1),f334(f104(a1),x60141)),f2(a1)))
% 160.93/160.64 [6015]E(x60151,f2(a1))+~P1(f334(f334(f249(a1),f334(f75(a1),x60151)),f78(a1)))
% 160.93/160.64 [6813]~P1(f334(f334(f249(a1),x68131),f2(a1)))+P1(f334(f334(f249(a1),f334(f334(f80(a1),x68131),x68131)),f2(a1)))
% 160.93/160.64 [7361]P1(f334(f334(f249(a1),x73611),f2(a1)))+~P1(f334(f334(f249(a1),f334(f334(f80(a1),x73611),x73611)),f2(a1)))
% 160.93/160.64 [7915]E(x79151,f334(a3,f2(a881)))+P1(f334(f334(f249(a881),f334(f334(f22(a881),f334(a19,x79151)),f334(a116,f2(a881)))),f334(a19,x79151)))
% 160.93/160.64 [8691]~P1(f334(f334(f249(a1),x86911),f2(a1)))+P1(f334(f334(f249(a1),f334(f334(f22(a1),f334(f334(f80(a1),x86911),x86911)),a101)),f2(a1)))
% 160.93/160.64 [8777]~P1(f334(f334(f249(a1),x87771),f2(a1)))+P1(f334(f334(f249(a1),f334(f334(f80(a1),f334(f334(f80(a1),f78(a1)),x87771)),x87771)),f2(a1)))
% 160.93/160.64 [9103]P1(f334(f334(f249(a1),x91031),f2(a1)))+~P1(f334(f334(f249(a1),f334(f334(f22(a1),f334(f334(f80(a1),x91031),x91031)),a101)),f2(a1)))
% 160.93/160.64 [9167]P1(f334(f334(f249(a1),x91671),f2(a1)))+~P1(f334(f334(f249(a1),f334(f334(f80(a1),f334(f334(f80(a1),f78(a1)),x91671)),x91671)),f2(a1)))
% 160.93/160.64 [4690]~E(a83,x46901)+E(f334(f334(f80(a1),x46901),x46901),a83)
% 160.93/160.64 [4691]~E(x46911,a83)+E(f334(f334(f80(a1),x46911),x46911),a83)
% 160.93/160.64 [4705]E(x47051,f2(a1))+E(f334(f334(f38(a1),x47051),x47051),f78(a1))
% 160.93/160.64 [4836]E(x48361,a83)+~E(f334(f334(f80(a1),x48361),x48361),a83)
% 160.93/160.64 [4837]E(a83,x48371)+~E(f334(f334(f80(a1),x48371),x48371),a83)
% 160.93/160.64 [4850]~P5(x48501)+E(f39(x48501,f196(f888(x48501,a876))),f196(x48501))
% 160.93/160.64 [4851]~P5(x48511)+E(f39(x48511,f257(f888(x48511,a876))),f257(x48511))
% 160.93/160.64 [4852]~P5(x48521)+E(f40(x48521,f196(f888(x48521,a876))),f257(x48521))
% 160.93/160.64 [4853]~P5(x48531)+E(f40(x48531,f257(f888(x48531,a876))),f196(x48531))
% 160.93/160.64 [4854]~P108(x48541)+E(f141(x48541,f196(f888(x48541,a876))),f117(x48541))
% 160.93/160.64 [4989]E(x49891,f2(a881))+P1(f334(f334(f249(a881),f2(a881)),x49891))
% 160.93/160.64 [5008]~P6(x50081)+P1(f334(f334(f248(a1),f2(a1)),x50081))
% 160.93/160.64 [5042]~E(f334(f107(a881),x50421),f2(a881))+P1(f334(f334(f248(a1),x50421),a83))
% 160.93/160.64 [5047]P40(x50471)+P1(f334(f334(f336(a1),f342(x50471)),x50471))
% 160.93/160.64 [5048]E(x50481,f334(a3,f2(a881)))+P1(f334(f334(f248(a103),f78(a103)),x50481))
% 160.93/160.64 [5085]P1(f334(a201,x50851))+P1(f334(f334(f248(a1),f2(a1)),x50851))
% 160.93/160.64 [5133]E(f334(f104(a1),f334(a108,x51331)),f2(a1))+P1(f334(f334(f248(a1),f2(a1)),x51331))
% 160.93/160.64 [5200]E(f334(f104(a1),f334(f107(a881),x52001)),f334(f107(a1),x52001))+P1(f334(a201,f334(f107(a1),x52001)))
% 160.93/160.64 [5220]E(f334(f107(a881),x52201),f2(a881))+~P1(f334(a201,f334(f107(a1),x52201)))
% 160.93/160.64 [5221]E(f334(f107(a881),x52211),f2(a881))+~P1(f334(f334(f248(a1),x52211),a83))
% 160.93/160.64 [5256]P6(x52561)+~P1(f334(f334(f248(a1),f2(a1)),x52561))
% 160.93/160.64 [5327]E(f334(a116,f826(x53271)),x53271)+~P1(f334(f334(f249(a881),f2(a881)),x53271))
% 160.93/160.64 [5335]E(f334(a116,f334(f107(a881),x53351)),f78(a881))+~P1(f334(a201,f334(f107(a1),x53351)))
% 160.93/160.64 [5343]E(f334(f104(a1),f417(x53431)),x53431)+~P1(f334(f334(f249(a1),f2(a1)),x53431))
% 160.93/160.64 [5350]~E(x53501,f334(a3,f2(a881)))+~P1(f334(f334(f248(a103),f78(a103)),x53501))
% 160.93/160.64 [5357]E(f334(f104(a1),f334(f107(a881),x53571)),f2(a1))+~P1(f334(a201,f334(f107(a1),x53571)))
% 160.93/160.64 [5383]E(f334(f168(a881),x53831),f2(a881))+P1(f334(f334(f336(a881),f598(x53831)),f334(f174(a881),x53831)))
% 160.93/160.64 [5404]E(f334(f104(a1),f334(a108,x54041)),x54041)+~P1(f334(f334(f248(a1),f2(a1)),x54041))
% 160.93/160.64 [5413]~P1(f334(a201,x54131))+~P1(f334(f334(f248(a1),f2(a1)),x54131))
% 160.93/160.64 [5512]E(f334(f334(f80(a881),f78(a881)),f334(f107(a881),x55121)),f78(a881))+~P1(f334(f334(f249(a1),x55121),a83))
% 160.93/160.64 [5570]E(x55701,f2(a881))+~P1(f334(f334(f249(a881),x55701),f334(a116,f2(a881))))
% 160.93/160.64 [5609]E(f334(f334(f22(a881),f334(f107(a881),x56091)),f78(a881)),f2(a881))+~P1(f334(f334(f248(a1),x56091),a83))
% 160.93/160.64 [5610]E(f334(f334(f80(a881),f334(f107(a881),x56101)),f78(a881)),f78(a881))+~P1(f334(f334(f249(a1),x56101),a83))
% 160.93/160.64 [5620]~P40(x56201)+E(f334(f37(a881),f334(f313(a1,a881,a108),x56201)),f334(f37(a1),x56201))
% 160.93/160.64 [5651]~P108(x56511)+E(f250(x56511,f334(f7(x56511,x56511,a876),f248(x56511))),f247(x56511))
% 160.93/160.64 [5652]~P108(x56521)+E(f251(x56521,f334(f7(x56521,x56521,a876),f248(x56521))),f246(x56521))
% 160.93/160.64 [5662]E(f44(a881,f334(a116,f2(a881)),f334(f107(a881),x56621)),f334(a116,f2(a881)))+~P1(f334(a201,f334(f107(a1),x56621)))
% 160.93/160.64 [5671]P1(f334(f334(f249(a1),f2(a1)),x56711))+~P1(f334(f334(f248(a1),f78(a1)),x56711))
% 160.93/160.64 [5672]~P1(f334(f334(f249(a1),f2(a1)),x56721))+P1(f334(f334(f248(a1),f78(a1)),x56721))
% 160.93/160.64 [5683]E(f334(a116,f334(f334(f22(a881),x56831),f78(a881))),x56831)+~P1(f334(f334(f249(a881),f2(a881)),x56831))
% 160.93/160.64 [5740]P1(f334(f334(f249(a881),f2(a881)),f417(x57401)))+~P1(f334(f334(f249(a1),f2(a1)),x57401))
% 160.93/160.64 [5799]E(f44(a1,f334(f107(a1),a101),x57991),f334(f334(f22(a1),x57991),f78(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x57991))
% 160.93/160.64 [5833]~P1(f334(f334(f249(a1),a83),x58331))+P1(f334(f334(f249(a881),f2(a881)),f334(f107(a881),x58331)))
% 160.93/160.64 [5883]P1(f334(f334(f249(a881),f2(a881)),f334(a108,x58831)))+~P1(f334(f334(f249(a1),f2(a1)),x58831))
% 160.93/160.64 [5934]~P1(f334(f334(f249(a881),f2(a881)),x59341))+P1(f334(f334(f249(a1),f2(a1)),f334(f104(a1),x59341)))
% 160.93/160.64 [5970]~P1(f334(f334(f249(a881),f2(a881)),f334(a108,x59701)))+P1(f334(f334(f249(a1),f2(a1)),x59701))
% 160.93/160.64 [5984]~P40(x59841)+E(f334(f313(a881,a1,f104(a1)),f334(f313(a1,a881,a108),x59841)),x59841)
% 160.93/160.64 [5995]P1(f334(f334(f249(a1),a83),x59951))+~P1(f334(f334(f249(a881),f2(a881)),f334(f107(a881),x59951)))
% 160.93/160.64 [6043]~P60(x60431)+E(f334(f334(f153(f885(x60431)),f210(x60431)),f334(f334(f156(x60431,f885(x60431)),f241(x60431)),f55(x60431))),f55(f885(x60431)))
% 160.93/160.64 [6054]P1(f334(f334(f249(a881),f2(a881)),x60541))+~P1(f334(f334(f249(a1),f2(a1)),f334(f104(a1),x60541)))
% 160.93/160.64 [6169]E(f334(f313(a881,a1,f104(a1)),f334(f255(a881),f334(a108,x61691))),f334(f304(a1,f2(a1)),x61691))+~P1(f334(f334(f248(a1),f2(a1)),x61691))
% 160.93/160.64 [6187]~P106(x61871)+P1(f334(f334(f249(x61871),f2(x61871)),f334(f334(f80(x61871),f78(x61871)),f78(x61871))))
% 160.93/160.64 [6238]P1(f334(f334(f249(a881),f334(a116,f2(a881))),f334(a108,x62381)))+~P1(f334(f334(f249(a1),f78(a1)),x62381))
% 160.93/160.64 [6333]E(x63331,f2(a1))+P1(f334(f48(f2(a1),x63331),f334(f334(f269(a1,a1),f2(a1)),f2(a1))))
% 160.93/160.64 [6497]~P1(f334(f334(f249(a881),f334(a116,f2(a881))),f334(a108,x64971)))+P1(f334(f334(f249(a1),f78(a1)),x64971))
% 160.93/160.64 [6924]~P115(x69241)+P39(x69241,f334(f254(f887(x69241,x69241)),f334(f273(x69241,x69241,a876),f249(x69241))))
% 160.93/160.64 [5557]E(f334(f107(a881),f334(f334(f22(a1),x55571),a101)),f334(a116,f334(f107(a881),x55571)))+P1(f334(a201,f334(f107(a1),x55571)))
% 160.93/160.64 [5573]~P38(x55731)+E(f334(f334(f156(a881,a1),f104(a1)),f334(f334(f156(a1,a881),a108),x55731)),x55731)
% 160.93/160.64 [5689]E(f334(f79(a1),f334(f104(a1),f334(a116,f451(x56891)))),x56891)+~P1(f334(f334(f249(a1),x56891),f2(a1)))
% 160.93/160.64 [5699]E(f334(f334(f80(a881),f78(a881)),f334(f107(a881),x56991)),f334(f107(a881),f334(f334(f22(a1),x56991),a101)))+P1(f334(f334(f249(a1),x56991),a83))
% 160.93/160.64 [5742]E(f334(f334(f38(a1),f334(f107(a1),a101)),x57421),f334(f107(a1),a101))+~P1(f334(f334(f249(a1),f2(a1)),x57421))
% 160.93/160.64 [5829]E(f334(f334(f22(a881),f334(f107(a881),x58291)),f78(a881)),f334(f107(a881),f334(f334(f80(a1),x58291),a101)))+P1(f334(f334(f248(a1),x58291),a83))
% 160.93/160.64 [5830]E(f334(f334(f80(a881),f334(f107(a881),x58301)),f78(a881)),f334(f107(a881),f334(f334(f22(a1),x58301),a101)))+P1(f334(f334(f249(a1),x58301),a83))
% 160.93/160.64 [5871]E(f334(a108,f334(f334(f80(a1),f78(a1)),x58711)),f334(a116,f334(a108,x58711)))+~P1(f334(f334(f248(a1),f2(a1)),x58711))
% 160.93/160.64 [5907]E(f334(a116,f334(f334(f22(a881),x59071),f334(a116,f2(a881)))),x59071)+~P1(f334(f334(f249(a881),f2(a881)),x59071))
% 160.93/160.64 [6114]E(f44(a881,f334(a116,f2(a881)),f334(f107(a881),x61141)),f334(a108,f44(a1,f78(a1),f334(f107(a1),x61141))))+P1(f334(a201,f334(f107(a1),x61141)))
% 160.93/160.64 [6159]~P1(f334(f334(f249(a1),a83),x61591))+P1(f334(f334(f249(a1),a83),f334(f334(f80(a1),x61591),x61591)))
% 160.93/160.64 [6160]~P1(f334(f334(f249(a1),a101),x61601))+P1(f334(f334(f249(a1),a101),f334(f334(f80(a1),x61601),x61601)))
% 160.93/160.64 [6161]~P1(f334(f334(f248(a1),a83),x61611))+P1(f334(f334(f248(a1),a83),f334(f334(f80(a1),x61611),x61611)))
% 160.93/160.64 [6162]~P1(f334(f334(f249(a1),a101),x61621))+P1(f334(f334(f248(a1),a101),f334(f334(f80(a1),x61621),x61621)))
% 160.93/160.64 [6163]~P1(f334(f334(f91(a1),a83),x61631))+P1(f334(f334(f91(a1),a83),f334(f334(f80(a1),x61631),x61631)))
% 160.93/160.64 [6346]~P1(f334(f61(x63461),f257(f888(x63461,a876))))+P1(f334(f61(f885(x63461)),f257(f888(f885(x63461),a876))))
% 160.93/160.64 [6430]~P1(f334(f334(f248(a1),f2(a1)),x64301))+P1(f334(f334(f249(a1),f2(a1)),f334(f334(f80(a1),f78(a1)),x64301)))
% 160.93/160.64 [6437]E(f334(f268(a1,a1),f46(f78(a1),f334(f107(a1),x64371))),f334(f334(f38(a1),f78(a1)),f334(f107(a1),x64371)))+~P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),x64371)))
% 160.93/160.64 [6457]E(f334(f272(a1,a1),f46(f78(a1),f334(f107(a1),x64571))),f44(a1,f78(a1),f334(f107(a1),x64571)))+~P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),x64571)))
% 160.93/160.64 [6469]P1(f334(f61(x64691),f257(f888(x64691,a876))))+~P1(f334(f61(f885(x64691)),f257(f888(f885(x64691),a876))))
% 160.93/160.64 [6498]P1(f334(f334(f249(a1),a83),x64981))+~P1(f334(f334(f249(a1),a83),f334(f334(f80(a1),x64981),x64981)))
% 160.93/160.64 [6499]P1(f334(f334(f249(a1),a101),x64991))+~P1(f334(f334(f249(a1),a101),f334(f334(f80(a1),x64991),x64991)))
% 160.93/160.64 [6500]P1(f334(f334(f249(a1),a101),x65001))+~P1(f334(f334(f248(a1),a101),f334(f334(f80(a1),x65001),x65001)))
% 160.93/160.64 [6501]P1(f334(f334(f248(a1),a83),x65011))+~P1(f334(f334(f248(a1),a83),f334(f334(f80(a1),x65011),x65011)))
% 160.93/160.64 [6502]P1(f334(f334(f91(a1),a83),x65021))+~P1(f334(f334(f91(a1),a83),f334(f334(f80(a1),x65021),x65021)))
% 160.93/160.64 [6817]~P1(f334(f61(x68171),f257(f888(x68171,a876))))+P1(f334(f334(f249(a881),f2(a881)),f334(f37(x68171),f257(f888(x68171,a876)))))
% 160.93/160.64 [7403]P1(f334(f61(a881),x74031))+~P1(f334(f61(a1),f334(f313(a881,a1,f104(a1)),x74031)))
% 160.93/160.64 [5487]~E(a101,x54871)+E(f334(f334(f22(a1),f334(f334(f80(a1),x54871),x54871)),a101),a101)
% 160.93/160.64 [5488]~E(x54881,a101)+E(f334(f334(f22(a1),f334(f334(f80(a1),x54881),x54881)),a101),a101)
% 160.93/160.64 [5990]E(x59901,a101)+~E(f334(f334(f22(a1),f334(f334(f80(a1),x59901),x59901)),a101),a101)
% 160.93/160.64 [5991]E(a101,x59911)+~E(f334(f334(f22(a1),f334(f334(f80(a1),x59911),x59911)),a101),a101)
% 160.93/160.64 [6399]~E(f334(f107(a881),x63991),f2(a881))+P1(f334(a201,f334(f107(a1),f334(f334(f80(a1),x63991),a101))))
% 160.93/160.64 [6744]~P1(f334(a201,f334(f107(a1),x67441)))+P1(f334(a201,f334(f107(a1),f334(f334(f80(a1),x67441),x67441))))
% 160.93/160.64 [6745]~P1(f334(f334(f249(a1),x67451),a83))+P1(f334(f334(f249(a1),f334(f334(f80(a1),x67451),x67451)),a83))
% 160.93/160.64 [6746]~P1(f334(f334(f248(a1),x67461),a101))+P1(f334(f334(f249(a1),f334(f334(f80(a1),x67461),x67461)),a101))
% 160.93/160.64 [6747]~P1(f334(f334(f248(a1),x67471),a83))+P1(f334(f334(f248(a1),f334(f334(f80(a1),x67471),x67471)),a83))
% 160.93/160.64 [6748]~P1(f334(f334(f248(a1),x67481),a101))+P1(f334(f334(f248(a1),f334(f334(f80(a1),x67481),x67481)),a101))
% 160.93/160.64 [6749]~P1(f334(f334(f91(a1),x67491),a83))+P1(f334(f334(f91(a1),f334(f334(f80(a1),x67491),x67491)),a83))
% 160.93/160.64 [7069]E(f334(f107(a881),x70691),f2(a881))+~P1(f334(a201,f334(f107(a1),f334(f334(f80(a1),x70691),a101))))
% 160.93/160.64 [7310]~P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),x73101)))+P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),f334(f334(f80(a1),x73101),x73101))))
% 160.93/160.64 [7311]P1(f334(a201,f334(f107(a1),x73111)))+~P1(f334(a201,f334(f107(a1),f334(f334(f80(a1),x73111),x73111))))
% 160.93/160.64 [7312]P1(f334(f334(f249(a1),x73121),a83))+~P1(f334(f334(f249(a1),f334(f334(f80(a1),x73121),x73121)),a83))
% 160.93/160.64 [7313]P1(f334(f334(f248(a1),x73131),a83))+~P1(f334(f334(f248(a1),f334(f334(f80(a1),x73131),x73131)),a83))
% 160.93/160.64 [7314]P1(f334(f334(f248(a1),x73141),a101))+~P1(f334(f334(f249(a1),f334(f334(f80(a1),x73141),x73141)),a101))
% 160.93/160.64 [7315]P1(f334(f334(f248(a1),x73151),a101))+~P1(f334(f334(f248(a1),f334(f334(f80(a1),x73151),x73151)),a101))
% 160.93/160.64 [7316]P1(f334(f334(f91(a1),x73161),a83))+~P1(f334(f334(f91(a1),f334(f334(f80(a1),x73161),x73161)),a83))
% 160.93/160.64 [7685]E(f334(a110,f585(x76851)),x76851)+~P1(f334(f334(f336(f888(f887(a881,a881),a876)),x76851),a102))
% 160.93/160.64 [6319]~P93(x63191)+E(f334(f107(x63191),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f78(x63191))
% 160.93/160.64 [6796]~P1(f334(a201,f334(f107(a1),x67961)))+E(f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),x67961),x67961)),a101)),f2(a881))
% 160.93/160.64 [7860]~P1(f334(f334(f249(a1),f334(f107(a1),x78601)),f2(a1)))+E(f334(f268(a1,a1),f334(a50,f49(f334(f79(a1),f78(a1)),f334(f79(a1),f334(f107(a1),x78601))))),f334(f334(f38(a1),f78(a1)),f334(f107(a1),x78601)))
% 160.93/160.64 [7873]~P1(f334(f334(f249(a1),f334(f107(a1),x78731)),f2(a1)))+E(f334(f272(a1,a1),f334(a50,f49(f334(f79(a1),f78(a1)),f334(f79(a1),f334(f107(a1),x78731))))),f44(a1,f78(a1),f334(f107(a1),x78731)))
% 160.93/160.64 [7921]~P1(f334(f334(f248(a1),a83),x79211))+P1(f334(f334(f249(a1),a83),f334(f334(f22(a1),f334(f334(f80(a1),x79211),x79211)),a101)))
% 160.93/160.64 [7922]~P1(f334(f334(f249(a1),a101),x79221))+P1(f334(f334(f249(a1),a101),f334(f334(f22(a1),f334(f334(f80(a1),x79221),x79221)),a101)))
% 160.93/160.64 [7923]~P1(f334(f334(f248(a1),a83),x79231))+P1(f334(f334(f248(a1),a83),f334(f334(f22(a1),f334(f334(f80(a1),x79231),x79231)),a101)))
% 160.93/160.64 [7924]~P1(f334(f334(f248(a1),a101),x79241))+P1(f334(f334(f248(a1),a101),f334(f334(f22(a1),f334(f334(f80(a1),x79241),x79241)),a101)))
% 160.93/160.64 [7925]~P1(f334(f334(f91(a1),a101),x79251))+P1(f334(f334(f91(a1),a101),f334(f334(f22(a1),f334(f334(f80(a1),x79251),x79251)),a101)))
% 160.93/160.64 [8237]~P93(x82371)+~P32(x82371,f334(f107(x82371),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))
% 160.93/160.64 [8415]P1(f334(f334(f249(a1),a101),x84151))+~P1(f334(f334(f249(a1),a101),f334(f334(f22(a1),f334(f334(f80(a1),x84151),x84151)),a101)))
% 160.93/160.64 [8416]P1(f334(f334(f248(a1),a83),x84161))+~P1(f334(f334(f249(a1),a83),f334(f334(f22(a1),f334(f334(f80(a1),x84161),x84161)),a101)))
% 160.93/160.64 [8417]P1(f334(f334(f248(a1),a83),x84171))+~P1(f334(f334(f248(a1),a83),f334(f334(f22(a1),f334(f334(f80(a1),x84171),x84171)),a101)))
% 160.93/160.64 [8418]P1(f334(f334(f248(a1),a101),x84181))+~P1(f334(f334(f248(a1),a101),f334(f334(f22(a1),f334(f334(f80(a1),x84181),x84181)),a101)))
% 160.93/160.64 [8419]P1(f334(f334(f91(a1),a101),x84191))+~P1(f334(f334(f91(a1),a101),f334(f334(f22(a1),f334(f334(f80(a1),x84191),x84191)),a101)))
% 160.93/160.64 [8735]E(f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),x87351),x87351)),a101)),f334(f334(f86(a881,a881),f334(f107(a881),x87351)),f334(f334(f8(a881,a881,a881),a116),f334(f334(f18(a881,a881,a881),f80(a881)),f5(a881)))))+P1(f334(a201,f334(f107(a1),x87351)))
% 160.93/160.64 [9586]E(x95861,f196(f888(f887(a881,a881),a876)))+P1(f334(f334(f336(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f334(f334(f269(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),x95861),f196(f888(f887(a881,a881),a876)))),a68))
% 160.93/160.64 [8666]~P1(f334(a201,f334(f107(a1),x86661)))+P1(f334(a201,f334(f107(a1),f334(f334(f22(a1),f334(f334(f80(a1),x86661),x86661)),a101))))
% 160.93/160.64 [8667]~P1(f334(f334(f249(a1),x86671),a83))+P1(f334(f334(f249(a1),f334(f334(f22(a1),f334(f334(f80(a1),x86671),x86671)),a101)),a83))
% 160.93/160.64 [8668]~P1(f334(f334(f249(a1),x86681),a101))+P1(f334(f334(f249(a1),f334(f334(f22(a1),f334(f334(f80(a1),x86681),x86681)),a101)),a101))
% 160.93/160.64 [8669]~P1(f334(f334(f249(a1),x86691),a83))+P1(f334(f334(f248(a1),f334(f334(f22(a1),f334(f334(f80(a1),x86691),x86691)),a101)),a83))
% 160.93/160.64 [8670]~P1(f334(f334(f248(a1),x86701),a101))+P1(f334(f334(f248(a1),f334(f334(f22(a1),f334(f334(f80(a1),x86701),x86701)),a101)),a101))
% 160.93/160.64 [8671]~P1(f334(f334(f91(a1),x86711),a101))+P1(f334(f334(f91(a1),f334(f334(f22(a1),f334(f334(f80(a1),x86711),x86711)),a101)),a101))
% 160.93/160.64 [8770]~P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),x87701)))+P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),f334(f334(f22(a1),f334(f334(f80(a1),x87701),x87701)),a101))))
% 160.93/160.64 [8928]~P93(x89281)+E(f334(f334(f80(x89281),f78(x89281)),f78(x89281)),f334(f107(x89281),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))
% 160.93/160.64 [9087]P1(f334(a201,f334(f107(a1),x90871)))+~P1(f334(a201,f334(f107(a1),f334(f334(f22(a1),f334(f334(f80(a1),x90871),x90871)),a101))))
% 160.93/160.64 [9088]P1(f334(f334(f249(a1),x90881),a83))+~P1(f334(f334(f249(a1),f334(f334(f22(a1),f334(f334(f80(a1),x90881),x90881)),a101)),a83))
% 160.93/160.64 [9089]P1(f334(f334(f249(a1),x90891),a83))+~P1(f334(f334(f248(a1),f334(f334(f22(a1),f334(f334(f80(a1),x90891),x90891)),a101)),a83))
% 160.93/160.64 [9090]P1(f334(f334(f249(a1),x90901),a101))+~P1(f334(f334(f249(a1),f334(f334(f22(a1),f334(f334(f80(a1),x90901),x90901)),a101)),a101))
% 160.93/160.64 [9091]P1(f334(f334(f248(a1),x90911),a101))+~P1(f334(f334(f248(a1),f334(f334(f22(a1),f334(f334(f80(a1),x90911),x90911)),a101)),a101))
% 160.93/160.64 [9092]P1(f334(f334(f91(a1),x90921),a101))+~P1(f334(f334(f91(a1),f334(f334(f22(a1),f334(f334(f80(a1),x90921),x90921)),a101)),a101))
% 160.93/160.64 [9632]~P1(f334(f61(f887(a881,a881)),x96321))+P1(f334(f334(f336(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f334(f334(f269(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),f196(f888(f887(a881,a881),a876))),x96321)),a69))
% 160.93/160.64 [9415]~P142(x94151)+E(f334(f334(f259(x94151),f2(x94151)),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f2(x94151))
% 160.93/160.64 [9416]~P142(x94161)+E(f334(f334(f259(x94161),f78(x94161)),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f78(x94161))
% 160.93/160.64 [9863]~P1(f334(f334(f249(a881),f78(a881)),x98631))+P1(f334(f334(f249(a881),f2(a881)),f334(f334(f38(a881),x98631),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))))
% 160.93/160.64 [9875]~P1(f334(f334(f249(a881),f2(a881)),x98751))+P1(f334(f334(f249(a881),f2(a881)),f334(f334(f38(a881),f334(f334(f80(a881),x98751),f78(a881))),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))))
% 160.93/160.64 [9917]~E(f44(a881,x99171,f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f78(a881))+P1(f334(f334(f249(a881),f2(a881)),f44(a881,x99171,f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))))
% 160.93/160.64 [9936]E(f44(a881,x99361,f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f78(a881))+~P1(f334(f334(f249(a881),f2(a881)),f44(a881,x99361,f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))))
% 160.93/160.64 [4623]~P39(x46231,x46232)+P55(x46231,x46232)
% 160.93/160.64 [4624]~P45(x46241,x46242)+P55(x46241,x46242)
% 160.93/160.64 [4585]~E(x45851,x45852)+E(f281(x45851,x45852),f78(a103))
% 160.93/160.64 [4588]E(f229(x45881,x45882),x45881)+~E(x45882,f2(a881))
% 160.93/160.64 [4595]~E(x45952,f117(x45951))+E(f154(x45951,x45952),f117(x45951))
% 160.93/160.64 [4614]~E(f154(x46142,x46141),f117(x46142))+E(x46141,f117(x46142))
% 160.93/160.64 [4628]~P2(x46282)+P2(f888(x46281,x46282))
% 160.93/160.64 [4629]~P2(x46292)+P99(f888(x46291,x46292))
% 160.93/160.64 [4630]~P96(x46302)+P3(f888(x46301,x46302))
% 160.93/160.64 [4631]~P101(x46312)+P101(f888(x46311,x46312))
% 160.93/160.64 [4632]~P65(x46322)+P65(f888(x46321,x46322))
% 160.93/160.64 [4633]~P2(x46332)+P100(f888(x46331,x46332))
% 160.93/160.64 [4634]~P97(x46342)+P97(f888(x46341,x46342))
% 160.93/160.64 [4635]~P5(x46352)+P5(f888(x46351,x46352))
% 160.93/160.64 [4636]~P107(x46362)+P107(f888(x46361,x46362))
% 160.93/160.64 [4637]~P109(x46372)+P109(f888(x46371,x46372))
% 160.93/160.64 [4638]~P110(x46382)+P110(f888(x46381,x46382))
% 160.93/160.64 [4639]~P114(x46392)+P114(f888(x46391,x46392))
% 160.93/160.64 [4640]~P96(x46402)+P98(f888(x46401,x46402))
% 160.93/160.64 [4641]~P94(x46412)+P94(f888(x46411,x46412))
% 160.93/160.64 [4642]~P87(x46422)+P87(f888(x46421,x46422))
% 160.93/160.64 [4643]~P96(x46432)+P96(f888(x46431,x46432))
% 160.93/160.64 [4655]E(x46551,x46552)+~E(f334(a26,x46551),f334(a26,x46552))
% 160.93/160.64 [4657]E(x46571,x46572)+~E(f334(a116,x46571),f334(a116,x46572))
% 160.93/160.64 [4658]E(x46581,x46582)+~E(f334(a110,x46581),f334(a110,x46582))
% 160.93/160.64 [4659]E(x46591,x46592)+~E(f334(a3,x46591),f334(a3,x46592))
% 160.93/160.64 [4661]E(x46611,x46612)+~E(f334(a19,x46611),f334(a19,x46612))
% 160.93/160.64 [4763]~P58(x47631)+E(f44(x47631,x47632,x47632),f2(x47631))
% 160.93/160.64 [4797]~P39(x47971,x47972)+P39(f882(x47971),f148(x47971,x47972))
% 160.93/160.64 [4798]~P39(x47981,x47982)+P39(f882(x47981),f147(x47981,x47982))
% 160.93/160.64 [4895]~P39(x48951,x48952)+P39(f888(x48951,a876),f325(x48951,x48952))
% 160.93/160.64 [4896]~P39(x48961,x48962)+P39(f888(x48961,a876),f327(x48961,x48962))
% 160.93/160.64 [5014]~P6(x50141)+P40(f305(a1,x50141,x50142))
% 160.93/160.64 [5114]~P39(x51141,x51142)+P57(x51141,f67(x51141,x51141,x51142))
% 160.93/160.64 [5614]~P83(x56141)+P27(x56141,x56141,f79(x56141),x56142)
% 160.93/160.64 [4609]~E(x46092,f117(x46091))+E(f334(f170(x46091),x46092),f117(x46091))
% 160.93/160.64 [4610]~E(x46102,f117(x46101))+E(f334(f171(x46101),x46102),f117(x46101))
% 160.93/160.64 [4665]E(x46651,f334(a108,x46652))+~E(f334(f104(a1),x46651),x46652)
% 160.93/160.64 [4668]E(x46681,f117(x46682))+~E(f334(f170(x46682),x46681),f117(x46682))
% 160.93/160.64 [4669]E(x46691,f117(x46692))+~E(f334(f171(x46692),x46691),f117(x46692))
% 160.93/160.64 [4687]~P93(x46871)+E(f334(f107(x46871),x46872),f334(f106(x46871),x46872))
% 160.93/160.64 [4694]~E(x46942,f210(x46941))+E(f240(x46941,x46942),f196(f888(x46941,a876)))
% 160.93/160.64 [4696]~P4(x46961)+P1(f334(f61(x46961),x46962))
% 160.93/160.64 [4703]E(x47031,f210(x47032))+E(f334(f241(x47032),f688(x47032,x47031)),x47031)
% 160.93/160.64 [4704]E(x47041,f210(x47042))+E(f334(f241(x47042),f721(x47042,x47041)),x47041)
% 160.93/160.64 [4706]~E(f722(x47062,x47061),f117(x47061))+E(f182(x47061,x47062),f117(f882(x47061)))
% 160.93/160.64 [4715]~E(x47152,f117(x47151))+E(f334(f174(x47151),x47152),f196(f888(x47151,a876)))
% 160.93/160.64 [4716]~E(x47162,f117(x47161))+E(f196(f888(x47161,a876)),f334(f174(x47161),x47162))
% 160.93/160.64 [4718]E(x47181,x47182)+~E(f334(f104(a1),x47181),f334(f104(a1),x47182))
% 160.93/160.64 [4721]E(f227(x47211,x47212),f2(a881))+P1(f334(f61(x47211),x47212))
% 160.93/160.64 [4741]~P111(x47411)+E(f82(x47411,f82(x47411,x47412)),f82(x47411,x47412))
% 160.93/160.64 [4754]~P80(x47541)+E(f334(f334(f259(x47541),x47542),f78(a881)),x47542)
% 160.93/160.64 [4755]~P118(x47551)+E(f334(f334(f259(x47551),x47552),f78(a881)),x47552)
% 160.93/160.64 [4757]E(x47571,x47572)+E(f281(x47571,x47572),f334(f334(f80(a103),x47572),f78(a103)))
% 160.93/160.64 [4760]E(f334(f37(x47601),x47602),f2(a881))+P1(f334(f61(x47601),x47602))
% 160.93/160.64 [4764]~E(f154(x47641,x47642),x47642)+P1(f334(f139(x47641),x47642))
% 160.93/160.64 [4767]~P3(x47671)+E(f334(f334(f114(x47671),x47672),f196(x47671)),x47672)
% 160.93/160.64 [4768]~P66(x47681)+E(f334(f334(f22(x47681),x47682),f2(x47681)),x47682)
% 160.93/160.64 [4769]~P98(x47691)+E(f334(f334(f105(x47691),x47692),f257(x47691)),x47692)
% 160.93/160.64 [4770]~P68(x47701)+E(f334(f334(f80(x47701),x47702),f2(x47701)),x47702)
% 160.93/160.64 [4771]~P79(x47711)+E(f334(f334(f80(x47711),x47712),f2(x47711)),x47712)
% 160.93/160.64 [4772]~P118(x47721)+E(f334(f334(f80(x47721),x47722),f2(x47721)),x47722)
% 160.93/160.64 [4773]~P74(x47731)+E(f334(f334(f81(x47731),x47732),f78(x47731)),x47732)
% 160.93/160.64 [4774]~P80(x47741)+E(f334(f334(f81(x47741),x47742),f78(x47741)),x47742)
% 160.93/160.64 [4775]~P118(x47751)+E(f334(f334(f81(x47751),x47752),f78(x47751)),x47752)
% 160.93/160.64 [4776]~P58(x47761)+E(f334(f334(f38(x47761),x47762),f78(x47761)),x47762)
% 160.93/160.64 [4777]~P120(x47771)+E(f334(f334(f292(x47771),x47772),f78(x47771)),x47772)
% 160.93/160.64 [4778]~P118(x47781)+E(f334(f334(f259(x47781),x47782),f2(a881)),f78(x47781))
% 160.93/160.64 [4779]~P113(x47791)+E(f334(f334(f259(x47791),x47792),f2(a881)),f78(x47791))
% 160.93/160.64 [4780]~E(x47802,f196(f888(x47801,a876)))+E(f334(f37(x47801),x47802),f2(a881))
% 160.93/160.64 [4791]~P58(x47911)+E(f44(x47911,x47912,f2(x47911)),x47912)
% 160.93/160.64 [4799]~P98(x47991)+E(f334(f334(f114(x47991),x47992),f257(x47991)),f257(x47991))
% 160.93/160.64 [4800]~P3(x48001)+E(f334(f334(f105(x48001),x48002),f196(x48001)),f196(x48001))
% 160.93/160.64 [4801]~P131(x48011)+E(f334(f334(f81(x48011),x48012),f2(x48011)),f2(x48011))
% 160.93/160.64 [4802]~P118(x48021)+E(f334(f334(f81(x48021),x48022),f2(x48021)),f2(x48021))
% 160.93/160.64 [4803]~P58(x48031)+E(f334(f334(f38(x48031),x48032),f2(x48031)),f2(x48031))
% 160.93/160.64 [4804]~P121(x48041)+E(f334(f334(f292(x48041),x48042),f2(x48041)),f2(x48041))
% 160.93/160.64 [4805]E(x48051,f210(x48052))+~E(f240(x48052,x48051),f196(f888(x48052,a876)))
% 160.93/160.64 [4808]~P58(x48081)+E(f44(x48081,x48082,f78(x48081)),f2(x48081))
% 160.93/160.64 [4809]~P58(x48091)+E(f44(x48091,f2(x48091),x48092),f2(x48091))
% 160.93/160.64 [4838]E(x48381,f2(a881))+E(f54(x48382,x48381,f117(x48382)),f117(f882(x48382)))
% 160.93/160.64 [4862]P39(x48621,x48622)+~E(f599(x48622,x48621),f196(f888(x48621,a876)))
% 160.93/160.64 [4863]E(x48631,f117(x48632))+~E(f334(f174(x48632),x48631),f196(f888(x48632,a876)))
% 160.93/160.64 [4864]E(x48641,f117(x48642))+~E(f196(f888(x48642,a876)),f334(f174(x48642),x48641))
% 160.93/160.64 [4867]~E(x48671,x48672)+P1(f334(f334(a331,x48671),x48672))
% 160.93/160.64 [4877]P1(x48771)+P1(f334(f334(a337,x48771),x48772))
% 160.93/160.64 [4878]E(x48781,f117(x48782))+E(f334(f334(f167(x48782),x48781),f2(a881)),f334(f143(x48782),x48781))
% 160.93/160.64 [4881]E(f154(x48811,x48812),x48812)+~P1(f334(f139(x48811),x48812))
% 160.93/160.64 [4886]~P1(x48862)+P1(f334(f334(a337,x48861),x48862))
% 160.93/160.64 [4887]~P1(x48872)+P1(f334(f334(a333,x48871),x48872))
% 160.93/160.64 [4888]~P1(x48881)+P1(f334(f334(a333,x48881),x48882))
% 160.93/160.64 [4898]~E(f689(x48982,x48981),f694(x48982,x48981))+P1(f334(f139(x48981),x48982))
% 160.93/160.64 [4906]E(f334(f254(x49061),x49062),f196(f888(x49061,a876)))+P1(f334(x49062,f340(x49062)))
% 160.93/160.64 [4907]E(f196(f888(x49071,a876)),f334(f254(x49071),x49072))+P1(f334(x49072,f341(x49072)))
% 160.93/160.64 [4971]~P111(x49711)+E(f334(f334(f81(x49711),x49712),f82(x49711,x49712)),f334(f75(x49711),x49712))
% 160.93/160.64 [4982]~E(x49821,f2(a1))+E(f45(x49821,x49822),f334(f334(f269(a1,a1),f2(a1)),f2(a1)))
% 160.93/160.64 [5013]~P55(x50131,x50132)+P55(x50131,f334(f289(x50131,x50131),x50132))
% 160.93/160.64 [5031]~E(f334(a28,x50311),f334(f241(a878),x50312))+P1(f334(a25,f334(a26,x50311)))
% 160.93/160.64 [5036]E(x50361,x50362)+~P1(f334(f334(a331,x50361),x50362))
% 160.93/160.64 [5040]~P1(f334(a25,x50402))+P1(f334(a25,f32(x50401,x50402)))
% 160.93/160.64 [5049]P1(x50491)+~P1(f334(f334(a332,x50492),x50491))
% 160.93/160.64 [5050]P1(x50501)+~P1(f334(f334(a332,x50501),x50502))
% 160.93/160.64 [5054]~P114(x50541)+P1(f334(f334(f248(x50541),x50542),f257(x50541)))
% 160.93/160.64 [5058]E(x50581,x50582)+~E(f334(x50581,f445(x50582,x50581)),f334(x50582,f445(x50582,x50581)))
% 160.93/160.64 [5087]E(x50871,f2(a881))+E(f229(x50871,f44(a881,x50872,x50871)),f229(x50872,x50871))
% 160.93/160.64 [5092]~P108(x50921)+P16(x50921,f334(f334(f153(x50921),x50922),f117(x50921)))
% 160.93/160.64 [5094]E(x50941,f2(a1))+P1(f334(f48(x50942,x50941),f45(x50942,x50941)))
% 160.93/160.64 [5112]~E(x51121,x51122)+P1(f334(f334(f249(a881),x51121),f334(a116,x51122)))
% 160.93/160.64 [5122]~E(x51221,f2(a881))+P1(f334(f334(f249(a881),x51221),f334(a116,x51222)))
% 160.93/160.64 [5132]P1(f334(x51321,x51322))+P1(f334(f334(f248(a1),f2(a1)),f344(x51321)))
% 160.93/160.64 [5168]P1(f334(a25,x51681))+~P1(f334(a25,f32(x51682,x51681)))
% 160.93/160.64 [5170]P1(f334(a25,x51701))+~P1(f334(a25,f33(x51702,x51701)))
% 160.93/160.64 [5172]P1(f334(a25,x51721))+~P1(f334(a25,f33(x51721,x51722)))
% 160.93/160.64 [5204]P55(x52041,x52042)+~P55(x52041,f334(f289(x52041,x52041),x52042))
% 160.93/160.64 [5207]~E(f44(a881,x52072,x52071),f2(a881))+E(f334(f334(f81(a881),x52071),f446(x52071,x52072)),x52072)
% 160.93/160.64 [5208]~E(f44(a1,x52082,x52081),f2(a1))+E(f334(f334(f81(a1),x52081),f416(x52081,x52082)),x52082)
% 160.93/160.64 [5235]~P1(f334(x52351,x52352))+P1(f334(f334(f248(a1),f2(a1)),f343(x52351)))
% 160.93/160.64 [5247]E(f334(f334(f22(a881),f334(a108,x52471)),f334(a108,x52472)),f334(a108,x52471))+~P1(f334(a201,x52472))
% 160.93/160.64 [5276]E(f282(x52761,x52762),f78(a103))+~P1(f334(f334(f248(a103),x52761),f78(a103)))
% 160.93/160.64 [5369]E(f334(f334(f167(x53691),x53692),f689(x53692,x53691)),f334(f334(f167(x53691),x53692),f694(x53692,x53691)))+P1(f334(f139(x53691),x53692))
% 160.93/160.64 [5414]~P1(f334(x54141,f90(x54142,x54141)))+P1(f334(x54141,f614(x54142,x54141)))
% 160.93/160.64 [5477]P57(x54771,x54772)+~P1(f334(f322(x54771,x54772),f539(x54772,x54771)))
% 160.93/160.64 [5621]~E(f334(a116,f44(a881,x56211,x56212)),x56212)+E(f44(a881,f334(a116,x56211),x56212),f2(a881))
% 160.93/160.64 [5678]P39(x56781,x56782)+P1(f334(f334(f336(x56781),f631(x56782,x56781)),f632(x56782,x56781)))
% 160.93/160.64 [5685]~P139(x56851)+P1(f334(f334(f336(x56851),f334(f104(x56851),x56852)),f113(x56851)))
% 160.93/160.64 [5686]~P142(x56861)+P1(f334(f334(f336(x56861),f334(f104(x56861),x56862)),f194(x56861)))
% 160.93/160.64 [5687]~P139(x56871)+P1(f334(f334(f336(x56871),f334(f106(x56871),x56872)),f113(x56871)))
% 160.93/160.64 [5688]~P93(x56881)+P1(f334(f334(f336(x56881),f334(f107(x56881),x56882)),f113(x56881)))
% 160.93/160.64 [5832]E(f334(a116,f44(a881,x58321,x58322)),x58322)+E(f44(a881,f334(a116,x58321),x58322),f334(a116,f44(a881,x58321,x58322)))
% 160.93/160.64 [6250]P39(x62501,x62502)+~P1(f334(f334(f336(x62501),f540(x62502,x62501)),f323(x62501,x62502)))
% 160.93/160.64 [6285]~P106(x62851)+~P1(f334(f334(f249(x62851),f334(f104(x62851),x62852)),f2(x62851)))
% 160.93/160.64 [6286]~P85(x62861)+~P1(f334(f334(f249(x62861),f334(f75(x62861),x62862)),f2(x62861)))
% 160.93/160.64 [6372]P1(f334(f334(f249(a1),x63721),f44(a1,x63722,x63721)))+~P1(f334(f334(f249(a1),x63721),f2(a1)))
% 160.93/160.64 [6471]E(f334(f334(f312(a881),f334(a116,x64711)),f305(a881,x64712,x64711)),f305(a881,x64712,f334(a116,x64711)))+~P1(f334(f334(f248(a881),x64712),f334(a116,x64711)))
% 160.93/160.64 [6558]~P108(x65581)+P16(x65581,f152(x65581,x65581,f5(x65581),x65582))
% 160.93/160.64 [6688]E(f334(f170(x66881),x66882),x66882)+~P1(f334(f334(f248(a881),f334(f197(f882(x66881)),x66882)),f78(a881)))
% 160.93/160.64 [6708]~P85(x67081)+P1(f334(f334(f248(x67081),f334(f79(x67081),f334(f75(x67081),x67082))),f2(x67081)))
% 160.93/160.64 [6741]~P39(x67411,x67412)+P39(x67411,f334(f334(f291(x67411,x67411,x67411),x67412),f310(x67411,x67412)))
% 160.93/160.64 [6962]~P1(f334(f334(f249(a1),x69622),f2(a1)))+P1(f334(f334(f248(a1),f44(a1,x69621,x69622)),f2(a1)))
% 160.93/160.64 [7358]~P142(x73581)+E(f198(x73581,f334(f334(f7(x73581,x73581,x73581),f80(x73581)),f78(x73581)),x73582,f2(x73581)),f334(f104(x73581),x73582))
% 160.93/160.64 [7386]~P123(x73861)+~P1(f334(f334(f249(x73861),f334(f334(f81(x73861),x73862),x73862)),f2(x73861)))
% 160.93/160.64 [10026]~P111(x100261)+~P1(f334(f334(f249(x100261),f334(f334(f259(x100261),x100262),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f2(x100261)))
% 160.93/160.64 [4666]~E(x46662,f117(x46661))+E(f334(f197(f882(x46661)),x46662),f2(a881))
% 160.93/160.64 [4707]~E(x47071,f2(a881))+E(f334(f334(f80(a881),x47071),x47072),x47072)
% 160.93/160.64 [4708]~E(x47082,f2(a881))+E(f334(f334(f81(a881),x47081),x47082),f2(a881))
% 160.93/160.64 [4710]~E(x47101,f2(a881))+E(f334(f334(f81(a881),x47101),x47102),f2(a881))
% 160.93/160.64 [4711]~E(x47112,f2(a881))+E(f334(f334(f259(a881),x47111),x47112),f78(a881))
% 160.93/160.64 [4712]~E(x47122,f2(a1))+E(f334(f334(f38(a1),x47121),x47122),f2(a1))
% 160.93/160.64 [4722]E(x47221,f117(x47222))+~E(f334(f197(f882(x47222)),x47221),f2(a881))
% 160.93/160.64 [4723]~P2(x47231)+E(f334(f334(f114(x47231),x47232),x47232),x47232)
% 160.93/160.64 [4725]~P99(x47251)+E(f334(f334(f114(x47251),x47252),x47252),x47252)
% 160.93/160.64 [4726]~P2(x47261)+E(f334(f334(f105(x47261),x47262),x47262),x47262)
% 160.93/160.64 [4728]~P100(x47281)+E(f334(f334(f105(x47281),x47282),x47282),x47282)
% 160.93/160.64 [4730]~P95(x47301)+E(f334(f334(f81(x47301),x47302),x47302),x47302)
% 160.93/160.64 [4732]~P108(x47321)+E(f334(f334(f246(x47321),x47322),x47322),x47322)
% 160.93/160.64 [4734]~P108(x47341)+E(f334(f334(f247(x47341),x47342),x47342),x47342)
% 160.93/160.64 [4753]~P66(x47531)+E(f334(f334(f22(x47531),x47532),x47532),f2(x47531))
% 160.93/160.64 [4765]~P66(x47651)+E(f334(f79(x47651),f334(f79(x47651),x47652)),x47652)
% 160.93/160.64 [4766]~P94(x47661)+E(f334(f79(x47661),f334(f79(x47661),x47662)),x47662)
% 160.93/160.64 [4783]~E(x47832,f2(a881))+E(f334(f334(f259(a881),x47831),x47832),f334(a116,f2(a881)))
% 160.93/160.64 [4817]~P3(x48171)+E(f334(f334(f114(x48171),f196(x48171)),x48172),x48172)
% 160.93/160.64 [4818]~P98(x48181)+E(f334(f334(f105(x48181),f257(x48181)),x48182),x48182)
% 160.93/160.64 [4819]~P68(x48191)+E(f334(f334(f80(x48191),f2(x48191)),x48192),x48192)
% 160.93/160.64 [4820]~P79(x48201)+E(f334(f334(f80(x48201),f2(x48201)),x48202),x48202)
% 160.93/160.64 [4821]~P118(x48211)+E(f334(f334(f80(x48211),f2(x48211)),x48212),x48212)
% 160.93/160.64 [4822]~P74(x48221)+E(f334(f334(f81(x48221),f78(x48221)),x48222),x48222)
% 160.93/160.64 [4823]~P80(x48231)+E(f334(f334(f81(x48231),f78(x48231)),x48232),x48232)
% 160.93/160.64 [4824]~P118(x48241)+E(f334(f334(f81(x48241),f78(x48241)),x48242),x48242)
% 160.93/160.64 [4843]~P98(x48431)+E(f334(f334(f114(x48431),f257(x48431)),x48432),f257(x48431))
% 160.93/160.64 [4844]~P3(x48441)+E(f334(f334(f105(x48441),f196(x48441)),x48442),f196(x48441))
% 160.93/160.64 [4845]~P131(x48451)+E(f334(f334(f81(x48451),f2(x48451)),x48452),f2(x48451))
% 160.93/160.64 [4846]~P118(x48461)+E(f334(f334(f81(x48461),f2(x48461)),x48462),f2(x48461))
% 160.93/160.64 [4847]~P80(x48471)+E(f334(f334(f259(x48471),f78(x48471)),x48472),f78(x48471))
% 160.93/160.64 [4848]~P58(x48481)+E(f334(f334(f38(x48481),f2(x48481)),x48482),f2(x48481))
% 160.93/160.64 [4849]~P120(x48491)+E(f334(f334(f292(x48491),f2(x48491)),x48492),f2(x48491))
% 160.93/160.64 [4857]E(x48571,f117(x48572))+E(f146(x48572,f334(f171(x48572),x48571)),f334(f143(x48572),x48571))
% 160.93/160.64 [4858]E(x48581,f117(x48582))+E(f334(f143(x48582),f334(f171(x48582),x48581)),f146(x48582,x48581))
% 160.93/160.64 [4859]E(x48591,f2(a881))+~E(f334(f334(f80(a881),x48592),x48591),x48592)
% 160.93/160.64 [4865]~P139(x48651)+E(f334(f106(x48651),f334(f104(a1),x48652)),f334(f104(x48651),x48652))
% 160.93/160.64 [4866]~P93(x48661)+E(f334(f106(x48661),f334(f107(a1),x48662)),f334(f107(x48661),x48662))
% 160.93/160.64 [4873]E(x48731,f2(a881))+~E(f334(f334(f80(a881),x48732),x48731),f2(a881))
% 160.93/160.64 [4874]E(x48741,f2(a881))+~E(f334(f334(f80(a881),x48741),x48742),f2(a881))
% 160.93/160.64 [4875]E(x48751,f78(a881))+~E(f334(f334(f81(a881),x48752),x48751),f78(a881))
% 160.93/160.64 [4876]E(x48761,f78(a881))+~E(f334(f334(f81(a881),x48761),x48762),f78(a881))
% 160.93/160.64 [4891]~P111(x48911)+E(f334(f75(x48911),f334(f104(x48911),x48912)),f334(f104(x48911),x48912))
% 160.93/160.64 [4892]~P85(x48921)+E(f334(f75(x48921),f334(f75(x48921),x48922)),f334(f75(x48921),x48922))
% 160.93/160.64 [4893]~P85(x48931)+E(f334(f75(x48931),f334(f79(x48931),x48932)),f334(f75(x48931),x48932))
% 160.93/160.64 [4894]~P68(x48941)+E(f334(f168(x48941),f334(f171(x48941),x48942)),f334(f168(x48941),x48942))
% 160.93/160.64 [4899]~E(x48991,f334(a116,f2(a881)))+E(f334(f334(f259(a881),x48991),x48992),f334(a116,f2(a881)))
% 160.93/160.64 [4909]~P66(x49091)+E(f334(f334(f22(x49091),f2(x49091)),x49092),f334(f79(x49091),x49092))
% 160.93/160.64 [4910]~E(x49102,f2(a881))+E(f141(a881,f334(f304(a881,x49101),x49102)),f117(a881))
% 160.93/160.64 [4919]~P93(x49191)+E(f334(f334(f80(x49191),x49192),f334(f107(x49191),a83)),x49192)
% 160.93/160.64 [4920]E(x49201,f2(a1))+E(f46(f334(f75(a1),x49202),f334(f75(a1),x49201)),f52(x49202,x49201))
% 160.93/160.64 [4934]~E(x49341,x49342)+P1(f334(f334(f248(a881),x49341),x49342))
% 160.93/160.64 [4941]~E(x49411,f2(a103))+E(f334(f334(f80(a881),f334(a19,x49411)),x49412),x49412)
% 160.93/160.64 [4942]~E(f334(f107(a1),x49422),f334(f104(a1),x49421))+E(x49421,f334(a108,f334(f107(a1),x49422)))
% 160.93/160.64 [4951]~P6(x49511)+P6(f334(f334(f259(a1),x49511),x49512))
% 160.93/160.64 [4952]~P94(x49521)+E(f334(f334(f114(x49521),x49522),f334(f79(x49521),x49522)),f257(x49521))
% 160.93/160.64 [4953]~P94(x49531)+E(f334(f334(f105(x49531),x49532),f334(f79(x49531),x49532)),f196(x49531))
% 160.93/160.64 [4954]~P66(x49541)+E(f334(f334(f80(x49541),x49542),f334(f79(x49541),x49542)),f2(x49541))
% 160.93/160.64 [4979]E(x49791,f2(a881))+~E(f334(f79(a1),f334(f104(a1),x49792)),f334(f104(a1),x49791))
% 160.93/160.64 [4980]E(x49801,f2(a881))+~E(f334(f79(a1),f334(f104(a1),x49801)),f334(f104(a1),x49802))
% 160.93/160.64 [4990]E(f203(x49901,x49902),f2(a1))+P1(f334(f334(f248(a1),x49902),x49901))
% 160.93/160.64 [4991]E(f181(x49911,x49912),f117(a1))+P1(f334(f334(f248(a1),x49911),x49912))
% 160.93/160.64 [5004]E(x50041,f334(a116,f2(a881)))+~E(f334(f334(f81(a881),x50042),x50041),f334(a116,f2(a881)))
% 160.93/160.64 [5005]E(x50051,f334(a116,f2(a881)))+~E(f334(f334(f81(a881),x50051),x50052),f334(a116,f2(a881)))
% 160.93/160.64 [5006]~P107(x50061)+P1(f334(f334(f248(x50061),x50062),x50062))
% 160.93/160.64 [5007]~P92(x50071)+P1(f334(f334(f91(x50071),x50072),x50072))
% 160.93/160.64 [5010]~P93(x50101)+E(f334(f334(f81(x50101),x50102),f334(f107(x50101),a101)),f334(f79(x50101),x50102))
% 160.93/160.64 [5028]~P139(x50281)+E(f334(f79(x50281),f334(f106(x50281),x50282)),f334(f106(x50281),f334(f79(a1),x50282)))
% 160.93/160.64 [5029]~P93(x50291)+E(f334(f79(x50291),f334(f107(x50291),x50292)),f334(f107(x50291),f334(f79(a1),x50292)))
% 160.93/160.64 [5059]~E(x50591,f334(a116,x50592))+P1(f334(f334(f249(a881),f2(a881)),x50591))
% 160.93/160.64 [5076]~P108(x50761)+E(f334(f79(f888(x50761,a876)),f334(f255(x50761),x50762)),f334(f256(x50761),x50762))
% 160.93/160.64 [5077]~P108(x50771)+E(f334(f79(f888(x50771,a876)),f334(f303(x50771),x50772)),f334(f306(x50771),x50772))
% 160.93/160.64 [5078]~P108(x50781)+E(f334(f79(f888(x50781,a876)),f334(f256(x50781),x50782)),f334(f255(x50781),x50782))
% 160.93/160.64 [5079]~P108(x50791)+E(f334(f79(f888(x50791,a876)),f334(f306(x50791),x50792)),f334(f303(x50791),x50792))
% 160.93/160.64 [5086]~E(f334(f104(a1),x50862),x50861)+P1(f334(f334(f248(a1),f2(a1)),x50861))
% 160.93/160.64 [5093]~E(x50932,f2(a1))+E(f52(x50931,x50932),f334(f334(f269(a1,a1),f2(a1)),f334(f75(a1),x50931)))
% 160.93/160.64 [5095]~P101(x50951)+P1(f334(f334(f248(x50951),f196(x50951)),x50952))
% 160.93/160.64 [5127]E(x51271,x51272)+~E(f334(f334(f80(a1),x51271),x51271),f334(f334(f80(a1),x51272),x51272))
% 160.93/160.64 [5131]~P1(f334(x51311,x51312))+P1(f334(x51311,f334(a108,f343(x51311))))
% 160.93/160.64 [5157]~P111(x51571)+E(f334(f334(f81(x51571),f82(x51571,x51572)),f334(f75(x51571),x51572)),x51572)
% 160.93/160.64 [5166]~E(x51662,f2(a881))+E(f85(f887(a881,a881),f47(x51661,x51662)),f334(f334(f269(a881,a881),f2(a881)),x51661))
% 160.93/160.64 [5177]~E(x51771,x51772)+~P1(f334(f334(f249(a881),x51771),x51772))
% 160.93/160.64 [5178]~E(x51781,x51782)+~P1(f334(f334(f249(a1),x51781),x51782))
% 160.93/160.64 [5181]~P142(x51811)+E(f334(f334(f80(x51811),f78(x51811)),f334(f104(x51811),x51812)),f334(f104(x51811),f334(a116,x51812)))
% 160.93/160.64 [5185]~E(x51851,f2(a881))+~P1(f334(f334(f249(a881),x51852),x51851))
% 160.93/160.64 [5201]E(f154(x52011,x52012),x52012)+~E(f334(f197(f882(x52011)),f154(x52011,x52012)),f334(f197(f882(x52011)),x52012))
% 160.93/160.64 [5202]E(f334(f37(x52021),f334(f174(x52021),x52022)),f334(f197(f882(x52021)),x52022))+~P1(f334(f139(x52021),x52022))
% 160.93/160.64 [5212]~P1(f334(x52121,f345(x52121)))+P1(f334(x52121,f334(f104(a1),x52122)))
% 160.93/160.64 [5223]E(f282(x52231,x52232),f78(a103))+~P1(f334(f334(f249(a103),x52232),x52231))
% 160.93/160.64 [5224]E(f181(x52241,x52242),f117(a1))+~P1(f334(f334(f249(a1),x52242),x52241))
% 160.93/160.64 [5225]E(f127(x52251,x52252),f119(a1))+~P1(f334(f334(f249(a1),x52251),x52252))
% 160.93/160.64 [5228]~P109(x52281)+E(f305(x52281,x52282,x52282),f334(f334(f312(x52281),x52282),f196(f888(x52281,a876))))
% 160.93/160.64 [5250]~E(f334(f334(f22(a881),x52501),x52502),f2(a881))+P1(f334(f334(f248(a881),x52501),x52502))
% 160.93/160.64 [5251]~E(f334(f334(f22(a1),x52511),x52512),f2(a1))+P1(f334(f334(f91(a1),x52511),x52512))
% 160.93/160.64 [5273]~E(x52732,f2(a881))+E(f54(x52731,x52732,f117(x52731)),f334(f334(f153(f882(x52731)),f117(x52731)),f117(f882(x52731))))
% 160.93/160.64 [5277]~P107(x52771)+~P1(f334(f334(f249(x52771),x52772),x52772))
% 160.93/160.64 [5280]~E(f44(a1,x52801,x52802),f2(a1))+E(f44(a1,x52801,f334(f79(a1),x52802)),f2(a1))
% 160.93/160.64 [5282]~E(f44(a1,x52821,x52822),f2(a1))+E(f44(a1,f334(f79(a1),x52821),x52822),f2(a1))
% 160.93/160.64 [5290]E(f334(f304(a881,x52901),f334(a116,x52902)),f196(f888(a881,a876)))+P1(f334(f334(f248(a881),x52901),x52902))
% 160.93/160.64 [5310]E(f141(a881,f334(f304(a881,x53101),x53102)),f117(a881))+P1(f334(f334(f249(a881),x53101),x53102))
% 160.93/160.64 [5315]~E(f334(f37(x53151),f334(f174(x53151),x53152)),f334(f197(f882(x53151)),x53152))+P1(f334(f139(x53151),x53152))
% 160.93/160.64 [5320]~P1(f334(f139(x53201),x53202))+P1(f334(f139(x53201),f334(f170(x53201),x53202)))
% 160.93/160.64 [5321]~P1(f334(f139(x53211),x53212))+P1(f334(f139(x53211),f334(f173(x53211),x53212)))
% 160.93/160.64 [5322]~P1(f334(f139(x53221),x53222))+P1(f334(f139(x53221),f334(f171(x53221),x53222)))
% 160.93/160.64 [5329]P1(f334(x53291,x53292))+~P1(f334(x53291,f334(a108,f344(x53291))))
% 160.93/160.64 [5330]P1(f334(f334(f248(a881),x53302),x53301))+P1(f334(f334(f248(a881),x53301),x53302))
% 160.93/160.64 [5331]P1(f334(f334(f248(a1),x53312),x53311))+P1(f334(f334(f248(a1),x53311),x53312))
% 160.93/160.64 [5333]~P85(x53331)+P1(f334(f334(f248(x53331),x53332),f334(f75(x53331),x53332)))
% 160.93/160.64 [5336]P1(f334(x53361,f346(x53361)))+~P1(f334(x53361,f334(f104(a1),x53362)))
% 160.93/160.64 [5361]E(f334(f334(f22(a881),x53611),x53612),f2(a881))+~P1(f334(f334(f248(a881),x53611),x53612))
% 160.93/160.64 [5362]E(f334(f334(f22(a1),x53621),x53622),f2(a1))+~P1(f334(f334(f91(a1),x53621),x53622))
% 160.93/160.64 [5363]E(f334(f334(f38(a881),x53631),x53632),f2(a881))+~P1(f334(f334(f249(a881),x53631),x53632))
% 160.93/160.64 [5381]E(f44(a881,x53811,x53812),x53811)+~P1(f334(f334(f249(a881),x53811),x53812))
% 160.93/160.64 [5390]E(f44(a1,x53901,f334(f79(a1),x53902)),f293(x53901,x53902))+P1(f334(f334(f248(a1),f2(a1)),x53902))
% 160.93/160.64 [5402]E(f334(f334(f22(a1),x54021),x54022),f203(x54021,x54022))+~P1(f334(f334(f248(a1),x54022),x54021))
% 160.93/160.64 [5421]P1(f334(f334(f248(a1),f2(a1)),f345(x54211)))+P1(f334(x54211,f334(f104(a1),x54212)))
% 160.93/160.64 [5433]~P60(x54331)+P1(f334(f334(f336(x54331),x54332),f334(f174(x54331),f55(x54331))))
% 160.93/160.64 [5435]~P106(x54351)+P1(f334(f334(f248(x54351),f2(x54351)),f334(f104(x54351),x54352)))
% 160.93/160.64 [5436]~P85(x54361)+P1(f334(f334(f248(x54361),f2(x54361)),f334(f75(x54361),x54362)))
% 160.93/160.64 [5463]E(f334(f334(f80(a881),x54631),f347(x54632,x54631)),x54632)+~P1(f334(f334(f248(a881),x54631),x54632))
% 160.93/160.64 [5475]~E(f334(f107(a1),x54751),f334(f104(a1),x54752))+P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),x54751)))
% 160.93/160.64 [5478]E(f305(a1,x54781,x54782),f196(f888(a1,a876)))+~P1(f334(f334(f249(a1),x54782),x54781))
% 160.93/160.64 [5480]~P111(x54801)+E(f334(f334(f81(x54801),f334(f75(x54801),x54802)),f334(f75(x54801),x54802)),f334(f334(f81(x54801),x54802),x54802))
% 160.93/160.64 [5486]E(f141(a881,f334(f304(a881,x54861),f334(a116,x54862))),f117(a881))+P1(f334(f334(f248(a881),x54861),x54862))
% 160.93/160.64 [5490]E(f334(f334(f38(a1),x54901),x54902),f294(x54901,x54902))+~P1(f334(f334(f248(a1),f2(a1)),x54902))
% 160.93/160.64 [5510]P1(f334(f139(x55101),x55102))+~P1(f334(f139(x55101),f334(f170(x55101),x55102)))
% 160.93/160.64 [5511]P1(f334(f139(x55111),x55112))+~P1(f334(f139(x55111),f334(f171(x55111),x55112)))
% 160.93/160.64 [5532]P1(f334(f61(a881),x55321))+P1(f334(f334(f336(a881),f846(x55321,x55322)),x55321))
% 160.93/160.64 [5533]P1(f334(f61(a881),x55331))+P1(f334(f334(f336(a881),f363(x55331,x55332)),x55331))
% 160.93/160.64 [5534]P1(f334(f334(f249(a881),x55342),f334(a116,x55341)))+P1(f334(f334(f249(a881),x55341),x55342))
% 160.93/160.64 [5535]E(f44(a1,x55351,x55352),f293(x55351,x55352))+~P1(f334(f334(f248(a1),f2(a1)),x55352))
% 160.93/160.64 [5538]E(f141(a881,f334(f304(a881,x55381),x55382)),f117(a881))+~P1(f334(f334(f248(a881),x55382),x55381))
% 160.93/160.64 [5539]~P83(x55391)+E(f334(f313(x55391,x55391,f79(x55391)),f334(f255(x55391),x55392)),f334(f306(x55391),f334(f79(x55391),x55392)))
% 160.93/160.64 [5540]~P83(x55401)+E(f334(f313(x55401,x55401,f79(x55401)),f334(f303(x55401),x55402)),f334(f256(x55401),f334(f79(x55401),x55402)))
% 160.93/160.64 [5541]~P83(x55411)+E(f334(f313(x55411,x55411,f79(x55411)),f334(f256(x55411),x55412)),f334(f303(x55411),f334(f79(x55411),x55412)))
% 160.93/160.64 [5542]~P83(x55421)+E(f334(f313(x55421,x55421,f79(x55421)),f334(f306(x55421),x55422)),f334(f255(x55421),f334(f79(x55421),x55422)))
% 160.93/160.64 [5553]E(x55531,f196(f888(x55532,a876)))+P1(f334(f334(f336(x55532),f847(x55531,x55532)),x55531))
% 160.93/160.64 [5554]E(x55541,f196(f888(x55542,a876)))+P1(f334(f334(f336(x55542),f872(x55541,x55542)),x55541))
% 160.93/160.64 [5565]~P1(f334(f334(f249(a881),x55651),x55652))+P1(f334(f334(f248(a881),x55651),x55652))
% 160.93/160.64 [5566]~P1(f334(f334(f249(a1),x55661),x55662))+P1(f334(f334(f248(a1),x55661),x55662))
% 160.93/160.64 [5582]E(f46(x55821,x55822),f334(f334(f269(a1,a1),f2(a1)),x55821))+~P1(f334(f334(f249(a1),x55821),x55822))
% 160.93/160.64 [5583]E(f228(f334(f79(a1),x55831),f334(f79(a1),x55832)),f228(x55831,x55832))+~P1(f334(f334(f249(a1),x55832),f2(a1)))
% 160.93/160.64 [5591]E(x55911,x55912)+~P1(f334(f334(f334(a202,a24),x55911),x55912))
% 160.93/160.64 [5595]E(x55951,x55952)+~E(f334(a3,f334(a116,f334(a19,x55951))),f334(a3,f334(a116,f334(a19,x55952))))
% 160.93/160.64 [5600]E(f46(x56001,x56002),f334(f334(f269(a1,a1),f2(a1)),x56001))+~P1(f334(f334(f248(a1),x56002),f2(a1)))
% 160.93/160.64 [5627]E(f44(a881,f334(f107(a881),x56271),f334(f107(a881),x56272)),f2(a881))+~P1(f334(a201,f334(f107(a1),x56271)))
% 160.93/160.64 [5642]P1(f334(f334(f248(a1),f2(a1)),f346(x56421)))+~P1(f334(x56421,f334(f104(a1),x56422)))
% 160.93/160.64 [5676]P40(f305(a1,x56761,x56762))+~P1(f334(f334(f248(a1),f2(a1)),x56761))
% 160.93/160.64 [5681]~P1(f334(f61(x56811),x56812))+P1(f334(f61(f888(x56811,a876)),f334(f311(x56811),x56812)))
% 160.93/160.64 [5694]E(f334(f334(f80(a1),x56941),f334(f104(a1),f370(x56942,x56941))),x56942)+~P1(f334(f334(f248(a1),x56941),x56942))
% 160.93/160.64 [5702]P1(f334(f334(f248(a881),x57021),x57022))+P1(f334(f334(f248(a881),f334(a116,x57022)),x57021))
% 160.93/160.64 [5746]E(f334(f334(f38(a881),f334(f107(a881),x57461)),f334(f107(a881),x57462)),f2(a881))+~P1(f334(a201,f334(f107(a1),x57461)))
% 160.93/160.64 [5747]E(f334(f334(f81(a881),f334(f107(a881),x57471)),f334(f107(a881),x57472)),f2(a881))+~P1(f334(f334(f249(a1),x57471),a83))
% 160.93/160.64 [5749]P1(f334(f334(f249(a881),x57491),f334(a116,x57492)))+~P1(f334(f334(f249(a881),x57491),x57492))
% 160.93/160.64 [5751]P1(f334(f334(f249(a881),x57511),f334(a116,x57512)))+~P1(f334(f334(f248(a881),x57511),x57512))
% 160.93/160.64 [5753]P1(f334(f334(f248(a881),x57531),f334(a116,x57532)))+~P1(f334(f334(f248(a881),x57531),x57532))
% 160.93/160.64 [5756]~E(x57561,x57562)+P1(f334(f334(f249(a1),x57561),f334(f334(f80(a1),x57562),f78(a1))))
% 160.93/160.64 [5759]E(f44(a1,x57591,x57592),f2(a1))+E(f334(f334(f22(a1),x57592),f44(a1,x57591,x57592)),f44(a1,f334(f79(a1),x57591),x57592))
% 160.93/160.64 [5768]E(x57681,f117(x57682))+P1(f334(f334(f336(x57682),f146(x57682,x57681)),f334(f174(x57682),x57681)))
% 160.93/160.64 [5780]E(f85(f887(a881,a881),f47(x57801,x57802)),f334(f334(f269(a881,a881),f2(a881)),x57801))+~P1(f334(f334(f249(a881),x57801),x57802))
% 160.93/160.64 [5813]E(f334(f334(f22(a881),f334(f107(a881),x58131)),f334(f107(a881),x58132)),f334(f107(a881),x58131))+~P1(f334(f334(f249(a1),x58132),a83))
% 160.93/160.64 [5814]E(f334(f334(f80(a881),f334(f107(a881),x58141)),f334(f107(a881),x58142)),f334(f107(a881),x58142))+~P1(f334(f334(f249(a1),x58141),a83))
% 160.93/160.64 [5819]E(f334(a116,f334(f334(f80(a881),x58191),f827(x58192,x58191))),x58192)+~P1(f334(f334(f249(a881),x58191),x58192))
% 160.93/160.64 [5842]P1(f334(x58421,x58422))+~P1(f334(x58421,f334(a89,f600(x58422,x58421))))
% 160.93/160.64 [5850]~P1(f334(f334(f249(a881),x58501),f334(a116,x58502)))+P1(f334(f334(f248(a881),x58501),x58502))
% 160.93/160.64 [5896]E(f334(f334(f312(a881),x58961),f334(f304(a881,x58962),x58961)),f334(f304(a881,x58962),f334(a116,x58961)))+~P1(f334(f334(f248(a881),x58962),x58961))
% 160.93/160.64 [5900]E(x59001,f117(x59002))+E(f334(f334(f136(x59002),f118(x59002,x59001)),f334(f334(f153(x59002),f146(x59002,x59001)),f117(x59002))),x59001)
% 160.93/160.64 [5914]P1(f334(f61(x59141),x59142))+~P1(f334(f334(f249(a881),f2(a881)),f334(f37(x59141),x59142)))
% 160.93/160.64 [5916]~E(x59161,f196(f888(x59162,a876)))+~P1(f334(f334(f249(a881),f2(a881)),f334(f37(x59162),x59161)))
% 160.93/160.64 [5928]~P1(f334(f334(f249(a881),x59281),x59282))+P1(f334(f334(f248(a881),f334(a116,x59281)),x59282))
% 160.93/160.64 [5935]~P108(x59351)+E(f152(x59351,x59351,f5(x59351),f154(x59351,x59352)),f141(x59351,f334(f174(x59351),x59352)))
% 160.93/160.64 [5938]E(x59381,f117(x59382))+P1(f334(f334(f336(x59382),f334(f143(x59382),x59381)),f334(f174(x59382),x59381)))
% 160.93/160.64 [5944]~P106(x59441)+P1(f334(f334(f249(x59441),x59442),f334(f334(f80(x59441),x59442),f78(x59441))))
% 160.93/160.64 [5946]~P85(x59461)+P1(f334(f334(f248(x59461),f334(f79(x59461),x59462)),f334(f75(x59461),x59462)))
% 160.93/160.64 [5977]P1(f334(f61(a881),x59771))+~P1(f334(f334(f249(a881),f846(x59771,x59772)),x59772))
% 160.93/160.64 [5978]P1(f334(f61(a881),x59781))+~P1(f334(f334(f248(a881),f363(x59781,x59782)),x59782))
% 160.93/160.64 [5981]~P1(f334(f61(f887(x59811,x59811)),x59812))+P1(f334(f61(x59811),f334(f287(x59811),x59812)))
% 160.93/160.64 [6035]~P1(f334(f334(f249(a881),x60352),f334(a116,x60351)))+~P1(f334(f334(f249(a881),x60351),x60352))
% 160.93/160.64 [6036]~P109(x60361)+E(f334(f334(f105(f888(x60361,a876)),f334(f303(x60361),x60362)),f334(f256(x60361),x60362)),f334(f334(f312(x60361),x60362),f196(f888(x60361,a876))))
% 160.93/160.64 [6049]P1(f334(f61(x60491),x60492))+~P1(f334(f61(f888(x60491,a876)),f334(f311(x60491),x60492)))
% 160.93/160.64 [6074]P1(f334(f334(f249(a881),f334(a116,x60741)),f334(a116,x60742)))+~P1(f334(f334(f249(a881),x60741),x60742))
% 160.93/160.64 [6075]P1(f334(f334(f249(a881),f334(a19,x60751)),f334(a19,x60752)))+~P1(f334(f334(f249(a103),x60751),x60752))
% 160.93/160.64 [6076]P1(f334(f334(f249(a103),f334(a3,x60761)),f334(a3,x60762)))+~P1(f334(f334(f249(a881),x60761),x60762))
% 160.93/160.64 [6077]P1(f334(f334(f248(a881),f334(a116,x60771)),f334(a116,x60772)))+~P1(f334(f334(f248(a881),x60771),x60772))
% 160.93/160.64 [6078]P1(f334(f334(f248(a881),f334(a19,x60781)),f334(a19,x60782)))+~P1(f334(f334(f248(a103),x60781),x60782))
% 160.93/160.64 [6079]P1(f334(f334(f248(a103),f334(a3,x60791)),f334(a3,x60792)))+~P1(f334(f334(f248(a881),x60791),x60792))
% 160.93/160.64 [6082]E(x60821,x60822)+~E(f334(f313(a881,a1,f104(a1)),x60821),f334(f313(a881,a1,f104(a1)),x60822))
% 160.93/160.64 [6098]P1(f334(f334(f249(a881),x60981),x60982))+~P1(f334(f334(f249(a881),f334(a116,x60981)),x60982))
% 160.93/160.64 [6101]P1(f334(f334(f249(a881),x61011),x61012))+~P1(f334(f334(f248(a881),f334(a116,x61011)),x61012))
% 160.93/160.64 [6102]P1(f334(f334(f248(a881),x61021),x61022))+~P1(f334(f334(f248(a881),f334(a116,x61021)),x61022))
% 160.93/160.64 [6117]E(f44(a1,x61171,x61172),f2(a1))+E(f334(f334(f22(a1),f44(a1,x61171,x61172)),x61172),f44(a1,x61171,f334(f79(a1),x61172)))
% 160.93/160.64 [6190]E(f334(f37(f888(x61901,a876)),f334(f311(x61901),x61902)),f334(f334(f259(a881),f334(a116,f334(a116,f2(a881)))),f334(f37(x61901),x61902)))+~P1(f334(f61(x61901),x61902))
% 160.93/160.64 [6193]E(x61931,f117(x61932))+E(f334(f334(f167(x61932),x61931),f334(f334(f22(a881),f334(f197(f882(x61932)),x61931)),f78(a881))),f146(x61932,x61931))
% 160.93/160.64 [6218]E(x62181,f117(x62182))+E(f334(f334(f136(x62182),f334(f173(x62182),x62181)),f334(f334(f153(x62182),f334(f143(x62182),x62181)),f117(x62182))),f334(f170(x62182),x62181))
% 160.93/160.64 [6247]~P1(f334(f61(x62471),f39(f888(x62471,a876),x62472)))+P1(f334(f61(f888(x62471,a876)),x62472))
% 160.93/160.64 [6270]P1(f334(f334(f248(a881),f334(f107(a881),x62701)),f334(f107(a881),x62702)))+~P1(f334(f334(f248(a1),x62701),a83))
% 160.93/160.64 [6287]~P1(f334(f334(f249(a1),x62871),x62872))+P1(f334(f334(f249(a1),x62871),f334(f334(f80(a1),x62872),f78(a1))))
% 160.93/160.64 [6288]~P1(f334(f334(f248(a1),x62881),x62882))+P1(f334(f334(f249(a1),x62881),f334(f334(f80(a1),x62882),f78(a1))))
% 160.93/160.64 [6289]~P1(f334(f334(f249(a1),x62891),x62892))+P1(f334(f334(f248(a1),x62891),f334(f334(f22(a1),x62892),f78(a1))))
% 160.93/160.64 [6292]~P1(f334(f334(f249(a881),x62921),x62922))+P1(f334(f334(f249(a1),f334(f104(a1),x62921)),f334(f104(a1),x62922)))
% 160.93/160.64 [6293]~P1(f334(f334(f249(a1),x62931),x62932))+P1(f334(f334(f249(a1),f334(f107(a1),x62931)),f334(f107(a1),x62932)))
% 160.93/160.64 [6294]~P1(f334(f334(f248(a1),x62941),x62942))+P1(f334(f334(f248(a881),f334(f107(a881),x62941)),f334(f107(a881),x62942)))
% 160.93/160.64 [6296]~P1(f334(f334(f248(a881),x62961),x62962))+P1(f334(f334(f248(a1),f334(f104(a1),x62961)),f334(f104(a1),x62962)))
% 160.93/160.64 [6297]~P1(f334(f334(f248(a1),x62971),x62972))+P1(f334(f334(f248(a1),f334(f107(a1),x62971)),f334(f107(a1),x62972)))
% 160.93/160.64 [6298]~P1(f334(f334(f91(a1),x62981),x62982))+P1(f334(f334(f91(a1),f334(f107(a1),x62981)),f334(f107(a1),x62982)))
% 160.93/160.64 [6316]~P1(f334(f334(f248(a881),x63161),x63162))+~P1(f334(f334(f248(a881),f334(a116,x63162)),x63161))
% 160.93/160.64 [6359]~P1(f334(f334(f249(a881),f334(a116,x63591)),f334(a116,x63592)))+P1(f334(f334(f249(a881),x63591),x63592))
% 160.93/160.64 [6360]~P1(f334(f334(f249(a103),f334(a3,x63601)),f334(a3,x63602)))+P1(f334(f334(f249(a881),x63601),x63602))
% 160.93/160.64 [6361]~P1(f334(f334(f249(a881),f334(a108,x63611)),f334(a108,x63612)))+P1(f334(f334(f249(a1),x63611),x63612))
% 160.93/160.64 [6362]~P1(f334(f334(f249(a881),f334(a19,x63621)),f334(a19,x63622)))+P1(f334(f334(f249(a103),x63621),x63622))
% 160.93/160.64 [6363]~P1(f334(f334(f248(a881),f334(a116,x63631)),f334(a116,x63632)))+P1(f334(f334(f248(a881),x63631),x63632))
% 160.93/160.64 [6364]~P1(f334(f334(f248(a103),f334(a3,x63641)),f334(a3,x63642)))+P1(f334(f334(f248(a881),x63641),x63642))
% 160.93/160.64 [6365]~P1(f334(f334(f248(a881),f334(a19,x63651)),f334(a19,x63652)))+P1(f334(f334(f248(a103),x63651),x63652))
% 160.93/160.64 [6405]~P1(f334(f334(f249(a881),f334(a108,x64052)),f334(a108,x64051)))+P1(f334(f334(f249(a1),f2(a1)),x64051))
% 160.93/160.64 [6436]P1(f334(f334(f248(a1),f2(a1)),f44(a1,x64361,x64362)))+~P1(f334(f334(f249(a1),f2(a1)),x64362))
% 160.93/160.64 [6593]P39(x65931,x65932)+~E(f334(f334(f291(x65931,x65931,x65931),x65932),x65932),f196(f888(f887(x65931,x65931),a876)))
% 160.93/160.64 [6605]~P39(x66051,x66052)+P39(x66051,f334(f334(f291(x66051,x66051,x66051),x66052),x66052))
% 160.93/160.64 [6617]P1(f334(f334(f249(a1),x66171),x66172))+~P1(f334(f334(f248(a1),x66171),f334(f334(f22(a1),x66172),f78(a1))))
% 160.93/160.64 [6618]P1(f334(f334(f248(a1),x66181),x66182))+~P1(f334(f334(f249(a1),x66181),f334(f334(f80(a1),x66182),f78(a1))))
% 160.93/160.64 [6621]P1(f334(f334(f249(a881),x66211),x66212))+~P1(f334(f334(f249(a1),f334(f104(a1),x66211)),f334(f104(a1),x66212)))
% 160.93/160.64 [6622]P1(f334(f334(f249(a1),x66221),x66222))+~P1(f334(f334(f249(a881),f334(f107(a881),x66221)),f334(f107(a881),x66222)))
% 160.93/160.64 [6623]P1(f334(f334(f249(a1),x66231),x66232))+~P1(f334(f334(f249(a1),f334(f107(a1),x66231)),f334(f107(a1),x66232)))
% 160.93/160.64 [6625]P1(f334(f334(f248(a881),x66251),x66252))+~P1(f334(f334(f248(a1),f334(f104(a1),x66251)),f334(f104(a1),x66252)))
% 160.93/160.64 [6626]P1(f334(f334(f248(a1),x66261),x66262))+~P1(f334(f334(f248(a1),f334(f107(a1),x66261)),f334(f107(a1),x66262)))
% 160.93/160.64 [6627]P1(f334(f334(f91(a1),x66271),x66272))+~P1(f334(f334(f91(a1),f334(f107(a1),x66271)),f334(f107(a1),x66272)))
% 160.93/160.64 [6721]~E(f737(x67212,x67211),f117(x67211))+E(f334(f144(f882(x67211),f882(x67211),f136(x67211),f117(x67211)),x67212),f117(x67211))
% 160.93/160.64 [6722]~E(f738(x67222,x67221),f117(x67221))+E(f334(f144(f882(x67221),f882(x67221),f136(x67221),f117(x67221)),x67222),f117(x67221))
% 160.93/160.64 [6729]~P5(x67291)+E(f334(f144(x67291,x67291,f114(x67291),f196(x67291)),x67292),f39(x67291,f334(f174(x67291),x67292)))
% 160.93/160.64 [6730]~P5(x67301)+E(f334(f144(x67301,x67301,f105(x67301),f257(x67301)),x67302),f40(x67301,f334(f174(x67301),x67302)))
% 160.93/160.64 [6742]E(x67421,f2(a103))+E(f334(f334(f80(a881),f334(a19,f334(f334(f22(a103),x67421),f78(a103)))),f334(a116,x67422)),f334(f334(f80(a881),f334(a19,x67421)),x67422))
% 160.93/160.64 [6792]P1(f334(f334(f249(a1),f334(f334(f22(a1),x67921),x67922)),f2(a1)))+~P1(f334(f334(f249(a1),x67921),x67922))
% 160.93/160.64 [6819]~P108(x68191)+E(f334(f334(f114(f888(x68191,a876)),f334(f334(f312(x68191),x68192),f196(f888(x68191,a876)))),f334(f306(x68191),x68192)),f334(f256(x68191),x68192))
% 160.93/160.64 [6895]~P57(x68951,x68952)+P39(x68951,f334(f254(f887(x68951,x68951)),f334(f273(x68951,x68951,a876),x68952)))
% 160.93/160.64 [6896]~P57(x68961,x68962)+P55(x68961,f334(f254(f887(x68961,x68961)),f334(f273(x68961,x68961,a876),x68962)))
% 160.93/160.64 [6897]E(x68971,f196(f888(x68972,a876)))+~P1(f334(f334(f248(f888(x68972,a876)),x68971),f196(f888(x68972,a876))))
% 160.93/160.64 [6978]~P1(f334(f334(f249(a881),f2(a881)),x69782))+P1(f334(f334(f249(a881),f44(a881,x69781,x69782)),x69782))
% 160.93/160.64 [6980]~P1(f334(f334(f249(a1),f2(a1)),x69802))+P1(f334(f334(f249(a1),f44(a1,x69801,x69802)),x69802))
% 160.93/160.64 [6981]~P1(f334(f334(f249(a881),f2(a881)),x69812))+P1(f334(f334(f248(a881),f44(a881,x69811,x69812)),x69812))
% 160.93/160.64 [6982]~P1(f334(f334(f248(a1),f2(a1)),x69821))+P1(f334(f334(f248(a1),f44(a1,x69821,x69822)),x69821))
% 160.93/160.64 [7058]~P109(x70581)+E(f334(f334(f22(f888(x70581,a876)),f334(f334(f312(x70581),x70582),f196(f888(x70581,a876)))),f334(f255(x70581),x70582)),f334(f334(f312(x70581),x70582),f196(f888(x70581,a876))))
% 160.93/160.64 [7131]~P50(x71311,x71312)+P41(x71311,f257(f888(x71311,a876)),f334(f254(f887(x71311,x71311)),f334(f273(x71311,x71311,a876),x71312)))
% 160.93/160.64 [7132]P1(f334(x71321,x71322))+P1(f334(f334(f336(f888(f887(a881,a881),a876)),f600(x71322,x71321)),a102))
% 160.93/160.64 [7177]E(f334(f334(f136(a881),f141(a881,f334(f304(a881,x71771),x71772))),f334(f334(f153(a881),x71772),f117(a881))),f141(a881,f334(f304(a881,x71771),f334(a116,x71772))))+~P1(f334(f334(f248(a881),x71771),x71772))
% 160.93/160.64 [7320]E(x73201,f2(a881))+~E(f334(f144(a881,a881,f80(a881),x73201),x73202),f2(a881))
% 160.93/160.64 [7348]~P1(f334(f334(f249(a1),f334(f334(f22(a1),x73481),x73482)),f2(a1)))+P1(f334(f334(f249(a1),x73481),x73482))
% 160.93/160.64 [7377]P39(x73771,x73772)+~P39(x73771,f334(f334(f291(x73771,x73771,x73771),x73772),x73772))
% 160.93/160.64 [7406]~P1(f334(f334(f248(a881),f334(a116,x74061)),x74062))+P1(f193(a876,a252,f334(f248(a881),x74061),x74062))
% 160.93/160.64 [7564]P27(a881,a881,f334(f334(f7(a881,a881,a881),f22(a881)),x75641),x75642)+P1(f334(f334(f336(a881),f606(x75641,x75642)),x75642))
% 160.93/160.64 [7622]E(f334(f334(f334(f65(a881,x76221,f80(a881)),f334(f16(a881,x76221),f78(a881))),f2(a881)),x76222),f334(f37(x76221),x76222))+~P1(f334(f61(x76221),x76222))
% 160.93/160.64 [7664]P27(a881,a881,f334(f334(f7(a881,a881,a881),f22(a881)),x76641),x76642)+~P1(f334(f334(f248(a881),x76641),f606(x76641,x76642)))
% 160.93/160.64 [7720]P39(x77201,x77202)+P1(f334(f334(f248(f888(x77201,a876)),f599(x77202,x77201)),f334(f288(x77201,x77201,x77202),f599(x77202,x77201))))
% 160.93/160.64 [7725]P57(x77251,x77252)+~P39(x77251,f334(f254(f887(x77251,x77251)),f334(f273(x77251,x77251,a876),x77252)))
% 160.93/160.64 [7793]P1(f334(f334(f248(a881),f334(a116,x77931)),x77932))+~P1(f193(a876,a252,f334(f248(a881),x77931),x77932))
% 160.93/160.64 [7848]P1(f334(f334(f336(f887(a881,a881)),f334(f334(f269(a881,a881),x78481),x78482)),f310(a881,a324)))+~P1(f334(f334(f248(a881),x78481),x78482))
% 160.93/160.64 [7945]P50(x79451,x79452)+~P41(x79451,f257(f888(x79451,a876)),f334(f254(f887(x79451,x79451)),f334(f273(x79451,x79451,a876),x79452)))
% 160.93/160.64 [8000]~P1(f334(f139(x80001),x80002))+P1(f334(f139(f888(x80001,a876)),f334(f334(f156(f882(x80001),f888(x80001,a876)),f174(x80001)),f53(x80001,x80002))))
% 160.93/160.64 [8211]~P39(x82111,f334(f289(x82111,x82111),x82112))+P39(x82111,f334(f289(x82111,x82111),f334(f334(f291(x82111,x82111,x82111),x82112),f310(x82111,x82112))))
% 160.93/160.64 [8335]P1(f334(f61(f887(x83351,x83351)),f334(f334(f291(x83351,x83351,x83351),x83352),f310(x83351,x83352))))+~P1(f334(f61(f887(x83351,x83351)),x83352))
% 160.93/160.64 [8366]E(x83661,f2(a1))+P1(f334(f48(x83662,x83661),f334(f334(f269(a1,a1),f334(f334(f38(a1),x83662),x83661)),f44(a1,x83662,x83661))))
% 160.93/160.64 [8377]~P1(f334(f334(f336(f887(a881,a881)),f334(f334(f269(a881,a881),x83771),x83772)),f310(a881,a324)))+P1(f334(f334(f248(a881),x83771),x83772))
% 160.93/160.64 [8392]~P79(x83921)+E(f334(f144(x83921,x83921,f334(f7(x83921,x83921,x83921),f80(x83921)),f2(x83921)),f334(f171(x83921),x83922)),f334(f144(x83921,x83921,f80(x83921),f2(x83921)),x83922))
% 160.93/160.64 [8571]~P108(x85711)+E(f334(f144(f882(x85711),x85711,f334(f7(x85711,f882(x85711),f882(x85711)),f150(x85711,x85711,f5(x85711))),f117(x85711)),x85712),f152(x85711,x85711,f5(x85711),x85712))
% 160.93/160.64 [8676]~P55(x86761,f334(f254(f887(x86761,x86761)),f334(f273(x86761,x86761,a876),x86762)))+P55(x86761,f334(f254(f887(x86761,x86761)),f334(f273(x86761,x86761,a876),f258(x86761,x86761,x86762))))
% 160.93/160.64 [8690]P1(f334(f334(f336(f887(a881,a881)),f334(f334(f269(a881,a881),x86901),x86902)),f334(f334(f291(a881,a881,a881),a324),f310(a881,a324))))+~P1(f334(f334(f249(a881),x86901),x86902))
% 160.93/160.64 [8733]~P1(f334(f61(f887(x87331,x87331)),f334(f334(f291(x87331,x87331,x87331),x87332),f310(x87331,x87332))))+P1(f334(f61(f887(x87331,x87331)),x87332))
% 160.93/160.64 [8784]~P55(x87841,f334(f254(f887(x87841,x87841)),f334(f273(x87841,x87841,a876),f258(x87841,x87841,x87842))))+P55(x87841,f334(f254(f887(x87841,x87841)),f334(f273(x87841,x87841,a876),x87842)))
% 160.93/160.64 [8987]P55(x89871,x89872)+P1(f334(f334(f336(f887(x89871,x89871)),f334(f334(f269(x89871,x89871),f621(x89872,x89871)),f621(x89872,x89871))),f334(f334(f291(x89871,x89871,x89871),x89872),f310(x89871,x89872))))
% 160.93/160.64 [8988]P55(x89881,x89882)+P1(f334(f334(f336(f887(x89881,x89881)),f334(f334(f269(x89881,x89881),f636(x89882,x89881)),f636(x89882,x89881))),f334(f334(f291(x89881,x89881,x89881),x89882),f310(x89881,x89882))))
% 160.93/160.64 [9106]~P1(f334(f334(f336(f887(a881,a881)),f334(f334(f269(a881,a881),x91061),x91062)),f334(f334(f291(a881,a881,a881),a324),f310(a881,a324))))+P1(f334(f334(f249(a881),x91061),x91062))
% 160.93/160.64 [5072]~P93(x50721)+E(f334(f334(f80(x50721),f334(f107(x50721),a83)),x50722),x50722)
% 160.93/160.64 [5100]~P94(x51001)+E(f334(f334(f114(x51001),f334(f79(x51001),x51002)),x51002),f257(x51001))
% 160.93/160.64 [5101]~P94(x51011)+E(f334(f334(f105(x51011),f334(f79(x51011),x51012)),x51012),f196(x51011))
% 160.93/160.64 [5102]~P66(x51021)+E(f334(f334(f80(x51021),f334(f79(x51021),x51022)),x51022),f2(x51021))
% 160.93/160.64 [5103]~P67(x51031)+E(f334(f334(f80(x51031),f334(f79(x51031),x51032)),x51032),f2(x51031))
% 160.93/160.64 [5135]~P93(x51351)+E(f334(f334(f81(x51351),f334(f107(x51351),a101)),x51352),f334(f79(x51351),x51352))
% 160.93/160.64 [5304]~P116(x53041)+E(f334(f334(f81(x53041),f334(f79(x53041),f78(x53041))),x53042),f334(f79(x53041),x53042))
% 160.93/160.64 [5346]E(f334(f75(a1),x53461),f78(a1))+~E(f334(f75(a1),f334(f334(f81(a1),x53461),x53462)),f78(a1))
% 160.93/160.64 [5438]~P93(x54381)+E(f334(f334(f80(x54381),f78(x54381)),f334(f107(x54381),x54382)),f334(f107(x54381),f334(f334(f22(a1),x54382),a101)))
% 160.93/160.64 [5491]~P2(x54911)+E(f10(x54911,f334(f334(f312(x54911),x54912),f196(f888(x54911,a876)))),x54912)
% 160.93/160.64 [5492]~P2(x54921)+E(f11(x54921,f334(f334(f312(x54921),x54922),f196(f888(x54921,a876)))),x54922)
% 160.93/160.64 [5493]~P5(x54931)+E(f39(x54931,f334(f334(f312(x54931),x54932),f196(f888(x54931,a876)))),x54932)
% 160.93/160.64 [5494]~P108(x54941)+E(f14(x54941,f334(f334(f312(x54941),x54942),f196(f888(x54941,a876)))),x54942)
% 160.93/160.64 [5495]~P108(x54951)+E(f15(x54951,f334(f334(f312(x54951),x54952),f196(f888(x54951,a876)))),x54952)
% 160.93/160.64 [5496]~P5(x54961)+E(f40(x54961,f334(f334(f312(x54961),x54962),f196(f888(x54961,a876)))),x54962)
% 160.93/160.64 [5518]E(f334(f334(f80(a881),x55181),f334(f334(f22(a881),x55182),x55181)),x55182)+P1(f334(f334(f249(a881),x55182),x55181))
% 160.93/160.64 [5548]E(x55481,f117(x55482))+P1(f334(f334(f249(a881),f2(a881)),f334(f197(f882(x55482)),x55481)))
% 160.93/160.64 [5673]~P108(x56731)+E(f12(x56731,f247(x56731),f334(f334(f312(x56731),x56732),f196(f888(x56731,a876)))),x56732)
% 160.93/160.64 [5674]~P108(x56741)+E(f13(x56741,f246(x56741),f334(f334(f312(x56741),x56742),f196(f888(x56741,a876)))),x56742)
% 160.93/160.64 [5736]E(f334(f334(f22(a881),x57361),f334(f334(f22(a881),x57361),x57362)),x57362)+~P1(f334(f334(f248(a881),x57362),x57361))
% 160.93/160.64 [5737]E(f334(f334(f80(a881),x57371),f334(f334(f22(a881),x57372),x57371)),x57372)+~P1(f334(f334(f248(a881),x57371),x57372))
% 160.93/160.64 [5758]E(f44(a881,f334(f334(f22(a881),x57581),x57582),x57582),f44(a881,x57581,x57582))+P1(f334(f334(f249(a881),x57581),x57582))
% 160.93/160.64 [5769]E(f334(f79(a1),f334(f334(f38(a1),x57691),f334(f79(a1),x57692))),f294(x57691,x57692))+P1(f334(f334(f248(a1),f2(a1)),x57692))
% 160.93/160.64 [5771]~E(x57712,f2(a881))+P1(f334(f334(f249(a881),f2(a881)),f334(f334(f259(a881),x57711),x57712)))
% 160.93/160.64 [5822]~P93(x58221)+E(f334(f334(f80(x58221),f334(f79(x58221),f78(x58221))),f334(f107(x58221),x58222)),f334(f107(x58221),f334(f334(f80(a1),x58222),a101)))
% 160.93/160.64 [5823]E(f334(f334(f259(a881),f334(f107(a881),x58231)),x58232),f334(f334(f259(a881),f2(a881)),x58232))+~P1(f334(a201,f334(f107(a1),x58231)))
% 160.93/160.64 [5920]E(f334(f143(a881),f141(a881,f334(f304(a881,x59201),x59202))),x59201)+~P1(f334(f334(f249(a881),x59201),x59202))
% 160.93/160.64 [5939]E(f334(f334(f81(a881),f334(f107(a881),x59391)),f334(f107(a881),x59392)),f334(f107(a881),f334(f334(f81(a1),x59391),x59392)))+P1(f334(f334(f249(a1),x59391),a83))
% 160.93/160.64 [5945]~P123(x59451)+P1(f334(f334(f248(x59451),f2(x59451)),f334(f334(f81(x59451),x59452),x59452)))
% 160.93/160.64 [5957]E(f334(f334(f22(a881),f334(a116,x59571)),x59572),f334(a116,f334(f334(f22(a881),x59571),x59572)))+~P1(f334(f334(f248(a881),x59572),x59571))
% 160.93/160.64 [5960]E(f44(a881,f334(f334(f22(a881),x59601),x59602),x59602),f44(a881,x59601,x59602))+~P1(f334(f334(f248(a881),x59602),x59601))
% 160.93/160.64 [6010]E(f334(f334(f259(a881),f334(a108,x60101)),x60102),f334(a108,f334(f334(f259(a1),x60101),x60102)))+~P1(f334(f334(f248(a1),f2(a1)),x60101))
% 160.93/160.64 [6026]P1(f334(f139(x60261),x60262))+P1(f334(f334(f249(a881),f689(x60262,x60261)),f334(f197(f882(x60261)),x60262)))
% 160.93/160.64 [6027]P1(f334(f139(x60271),x60272))+P1(f334(f334(f249(a881),f694(x60272,x60271)),f334(f197(f882(x60271)),x60272)))
% 160.93/160.64 [6042]~E(x60421,f117(x60422))+~P1(f334(f334(f249(a881),f2(a881)),f334(f197(f882(x60422)),x60421)))
% 160.93/160.64 [6056]E(f146(a881,f141(a881,f334(f304(a881,x60561),x60562))),f334(f334(f22(a881),x60562),f78(a881)))+~P1(f334(f334(f249(a881),x60561),x60562))
% 160.93/160.64 [6059]E(f334(f334(f80(a1),x60591),f334(f104(a1),f334(a116,f873(x60592,x60591)))),x60592)+~P1(f334(f334(f249(a1),x60591),x60592))
% 160.93/160.64 [6066]E(x60661,f2(a881))+E(f334(f334(f81(a881),x60662),f334(f334(f259(a881),x60662),f334(f334(f22(a881),x60661),f78(a881)))),f334(f334(f259(a881),x60662),x60661))
% 160.93/160.64 [6092]E(f334(f334(f81(a881),f334(a108,x60921)),f334(a108,x60922)),f334(a108,f334(f334(f81(a1),x60921),x60922)))+~P1(f334(f334(f248(a1),f2(a1)),x60921))
% 160.93/160.64 [6093]E(f334(f334(f38(a881),f334(a108,x60931)),f334(a108,x60932)),f334(a108,f334(f334(f38(a1),x60931),x60932)))+~P1(f334(f334(f248(a1),f2(a1)),x60931))
% 160.93/160.64 [6107]~P118(x61071)+E(f334(f334(f80(x61071),x61072),x61072),f334(f334(f81(x61071),f334(f334(f80(x61071),f78(x61071)),f78(x61071))),x61072))
% 160.93/160.64 [6124]E(f334(f334(f22(a1),f334(f104(a1),x61241)),f334(f104(a1),x61242)),f334(f104(a1),f334(f334(f22(a881),x61241),x61242)))+~P1(f334(f334(f248(a881),x61242),x61241))
% 160.93/160.64 [6126]E(f334(f334(f269(a1,a1),f334(f107(a1),a101)),f334(f334(f80(a1),x61261),x61262)),f49(x61261,x61262))+~P1(f334(f334(f248(a1),x61262),f2(a1)))
% 160.93/160.64 [6166]E(f182(x61661,x61662),f117(f882(x61661)))+P1(f334(f334(f336(f882(x61661)),f722(x61662,x61661)),f334(f174(f882(x61661)),x61662)))
% 160.93/160.64 [6177]E(f120(a1,f334(f128(a1),x61771),f127(x61772,f334(f334(f80(a1),x61771),f78(a1)))),f127(x61772,x61771))+P1(f334(f334(f249(a1),x61772),x61771))
% 160.93/160.64 [6253]E(f334(f334(f153(a1),x62531),f181(f334(f334(f80(a1),x62531),f78(a1)),x62532)),f181(x62531,x62532))+~P1(f334(f334(f248(a1),x62531),x62532))
% 160.93/160.64 [6290]~P1(f334(f334(f249(a881),x62902),x62901))+P1(f334(f334(f249(a881),f2(a881)),f334(f334(f22(a881),x62901),x62902)))
% 160.93/160.64 [6321]~P1(f334(f334(f249(a881),x63211),f334(a108,x63212)))+P1(f334(f334(f249(a1),f334(f104(a1),x63211)),x63212))
% 160.93/160.64 [6350]~P108(x63501)+E(f334(f334(f114(f888(x63501,a876)),f334(f255(x63501),x63502)),f334(f334(f312(x63501),x63502),f196(f888(x63501,a876)))),f334(f303(x63501),x63502))
% 160.93/160.64 [6353]~P1(f334(f334(f249(a881),f2(a881)),x63531))+P1(f334(f334(f249(a881),f2(a881)),f334(f334(f259(a881),x63531),x63532)))
% 160.93/160.64 [6354]~P1(f334(f334(f248(a1),f2(a1)),x63541))+P1(f334(f334(f248(a1),f2(a1)),f334(f334(f259(a1),x63541),x63542)))
% 160.93/160.64 [6381]~E(f334(x63811,f2(a881)),f2(a881))+E(f334(f334(f6(a881,a881),x63811),f305(a881,f334(a116,f2(a881)),x63812)),f334(f334(f6(a881,a881),x63811),f305(a881,f2(a881),x63812)))
% 160.93/160.64 [6444]~P93(x64441)+E(f334(f334(f81(x64441),f334(f334(f80(x64441),f78(x64441)),f78(x64441))),f334(f107(x64441),x64442)),f334(f107(x64441),f334(f334(f80(a1),x64442),x64442)))
% 160.93/160.64 [6460]E(f334(f334(f312(a1),x64601),f305(a1,f334(f334(f80(a1),x64601),f78(a1)),x64602)),f305(a1,x64601,x64602))+P1(f334(f334(f249(a1),x64602),x64601))
% 160.93/160.64 [6461]P1(f334(f334(f249(a881),x64611),f334(a108,x64612)))+~P1(f334(f334(f249(a1),f334(f104(a1),x64611)),x64612))
% 160.93/160.64 [6561]E(f334(a108,f334(f334(f38(a1),f334(f107(a1),x65611)),f334(f107(a1),x65612))),f334(f334(f38(a881),f334(f107(a881),x65611)),f334(f107(a881),x65612)))+P1(f334(a201,f334(f107(a1),x65611)))
% 160.93/160.64 [6619]P1(f334(f334(f249(a881),x66191),x66192))+~P1(f334(f334(f249(a881),f2(a881)),f334(f334(f22(a881),x66192),x66191)))
% 160.93/160.64 [6664]P1(f334(f334(f249(a881),f2(a881)),x66641))+~P1(f334(f334(f249(a881),f2(a881)),f334(f334(f81(a881),x66642),x66641)))
% 160.93/160.64 [6665]P1(f334(f334(f249(a881),f2(a881)),x66651))+~P1(f334(f334(f249(a881),f2(a881)),f334(f334(f81(a881),x66651),x66652)))
% 160.93/160.64 [6682]~P1(f334(f334(f248(a1),x66821),f2(a1)))+E(f334(f334(f81(a881),f334(a108,f334(f79(a1),x66821))),f334(a108,f334(f79(a1),x66822))),f334(a108,f334(f334(f81(a1),x66821),x66822)))
% 160.93/160.64 [6740]~E(x67402,f196(f888(x67401,a876)))+P1(f334(f334(f248(f888(x67401,a876)),x67402),f334(f79(f888(x67401,a876)),x67402)))
% 160.93/160.64 [6803]~P93(x68031)+E(f334(f334(f80(x68031),f334(f334(f80(x68031),f2(x68031)),f334(f107(x68031),x68032))),f334(f107(x68031),x68032)),f334(f107(x68031),f334(f334(f80(a1),x68032),x68032)))
% 160.93/160.64 [6859]~P1(f334(f334(f249(a1),x68591),x68592))+P1(f334(f334(f248(a1),f334(f334(f80(a1),x68591),f78(a1))),x68592))
% 160.93/160.64 [6925]E(x69251,f2(a881))+~P1(f334(f334(f248(a1),f334(f104(a1),x69252)),f334(f79(a1),f334(f104(a1),x69251))))
% 160.93/160.64 [6926]E(x69261,f2(a881))+~P1(f334(f334(f248(a1),f334(f104(a1),x69261)),f334(f79(a1),f334(f104(a1),x69262))))
% 160.93/160.64 [7029]E(f334(f334(f269(a1,a1),f334(f107(a1),a101)),f334(f334(f80(a1),x70291),x70292)),f49(x70291,x70292))+~P1(f334(f334(f248(a1),f2(a1)),f334(f334(f80(a1),x70291),x70292)))
% 160.93/160.64 [7071]~P28(x70711,x70712)+P39(x70711,f334(f268(f888(f887(x70711,x70711),a876),f888(f887(x70711,x70711),a876)),x70712))
% 160.93/160.64 [7089]~P1(f334(f334(f248(a881),f334(a116,f2(a881))),x70891))+P1(f334(f334(f248(a881),f334(a116,f2(a881))),f334(f334(f259(a881),x70891),x70892)))
% 160.93/160.64 [7254]~P1(f334(f334(f249(a1),x72541),x72542))+P1(f334(f334(f249(a1),f334(f334(f80(a1),x72541),x72541)),f334(f334(f80(a1),x72542),x72542)))
% 160.93/160.64 [7266]~P1(f334(f334(f248(a1),x72661),x72662))+P1(f334(f334(f248(a1),f334(f334(f80(a1),x72661),x72661)),f334(f334(f80(a1),x72662),x72662)))
% 160.93/160.64 [7267]~P1(f334(f334(f91(a1),x72671),x72672))+P1(f334(f334(f91(a1),f334(f334(f80(a1),x72671),x72671)),f334(f334(f80(a1),x72672),x72672)))
% 160.93/160.64 [7322]~P1(f334(f334(f249(a881),f2(a881)),x73221))+P1(f334(f334(f249(a881),f334(f334(f22(a881),x73221),f334(a116,x73222))),x73221))
% 160.93/160.64 [7359]P1(f334(f334(f248(a881),f334(a116,f2(a881))),x73591))+~P1(f334(f334(f248(a881),f334(a116,f2(a881))),f334(f334(f81(a881),x73592),x73591)))
% 160.93/160.64 [7360]P1(f334(f334(f248(a881),f334(a116,f2(a881))),x73601))+~P1(f334(f334(f248(a881),f334(a116,f2(a881))),f334(f334(f81(a881),x73601),x73602)))
% 160.93/160.64 [7364]P1(f334(f334(f248(a881),f334(f334(f167(a881),x73641),x73642)),f334(f168(a881),x73641)))+~P1(f334(f334(f249(a881),x73642),f334(f197(f882(a881)),x73641)))
% 160.93/160.64 [7405]P1(f334(f334(f249(a1),x74051),x74052))+~P1(f334(f334(f248(a1),f334(f334(f80(a1),x74051),f78(a1))),x74052))
% 160.93/160.64 [7449]P1(f334(f61(x74491),f257(f888(x74491,a876))))+~P1(f334(f61(f888(x74492,x74491)),f257(f888(f888(x74492,x74491),a876))))
% 160.93/160.64 [7450]P1(f334(f61(x74501),f257(f888(x74501,a876))))+~P1(f334(f61(f886(x74502,x74501)),f257(f888(f886(x74502,x74501),a876))))
% 160.93/160.64 [7451]P1(f334(f61(x74511),f257(f888(x74511,a876))))+~P1(f334(f61(f886(x74511,x74512)),f257(f888(f886(x74511,x74512),a876))))
% 160.93/160.64 [7493]E(x74931,f196(f888(x74932,a876)))+~P1(f334(f334(f248(f888(x74932,a876)),x74931),f334(f79(f888(x74932,a876)),x74931)))
% 160.93/160.64 [7632]E(f334(f144(f882(x76321),f882(x76321),f136(x76321),f117(x76321)),x76322),f117(x76321))+P1(f334(f334(f336(f882(x76321)),f737(x76322,x76321)),f334(f174(f882(x76321)),x76322)))
% 160.93/160.64 [7633]E(f334(f144(f882(x76331),f882(x76331),f136(x76331),f117(x76331)),x76332),f117(x76331))+P1(f334(f334(f336(f882(x76331)),f738(x76332,x76331)),f334(f174(f882(x76331)),x76332)))
% 160.93/160.64 [7867]P1(f334(f334(f249(a1),x78671),x78672))+~P1(f334(f334(f249(a1),f334(f334(f80(a1),x78671),x78671)),f334(f334(f80(a1),x78672),x78672)))
% 160.93/160.64 [7870]P1(f334(f334(f248(a1),x78701),x78702))+~P1(f334(f334(f248(a1),f334(f334(f80(a1),x78701),x78701)),f334(f334(f80(a1),x78702),x78702)))
% 160.93/160.64 [7871]P1(f334(f334(f91(a1),x78711),x78712))+~P1(f334(f334(f91(a1),f334(f334(f80(a1),x78711),x78711)),f334(f334(f80(a1),x78712),x78712)))
% 160.93/160.64 [7965]~P118(x79651)+E(f334(f334(f81(x79651),f334(f334(f80(x79651),f78(x79651)),f78(x79651))),f334(f334(f6(a881,x79651),f104(x79651)),f305(a881,f78(a881),x79652))),f334(f334(f81(x79651),f334(f104(x79651),x79652)),f334(f334(f80(x79651),f334(f104(x79651),x79652)),f78(x79651))))
% 160.93/160.64 [8014]P1(f334(f334(f336(a881),x80141),x80142))+~P1(f334(f334(f336(a1),f334(f104(a1),x80141)),f334(f313(a881,a1,f104(a1)),x80142)))
% 160.93/160.64 [8179]~P1(f334(f61(x81791),x81792))+E(f334(f313(a881,x81791,f457(x81792,x81791)),f334(f254(a881),f334(f334(f7(a881,a881,a876),f249(a881)),f458(x81792,x81791)))),x81792)
% 160.93/160.64 [8465]P43(x84651,x84652)+P1(f334(f334(f336(f887(x84651,x84651)),f334(f334(f269(x84651,x84651),f526(x84652,x84651)),f526(x84652,x84651))),x84652))
% 160.93/160.64 [8612]~P93(x86121)+E(f334(f334(f22(x86121),f78(x86121)),f334(f107(x86121),x86122)),f334(f107(x86121),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f79(a1),x86122))))
% 160.93/160.64 [8729]~P1(f334(f334(f249(f888(a881,a876)),x87291),x87292))+P1(f334(f334(f249(f888(a1,a876)),f334(f313(a881,a1,f104(a1)),x87291)),f334(f313(a881,a1,f104(a1)),x87292)))
% 160.93/160.64 [8758]~P1(f334(f334(f249(a1),x87581),x87582))+P1(f334(f334(f249(a1),f334(f334(f22(a1),f334(f334(f80(a1),x87581),x87581)),a101)),f334(f334(f80(a1),x87582),x87582)))
% 160.93/160.64 [8760]~P1(f334(f334(f249(a1),x87601),x87602))+P1(f334(f334(f248(a1),f334(f334(f22(a1),f334(f334(f80(a1),x87601),x87601)),a101)),f334(f334(f80(a1),x87602),x87602)))
% 160.93/160.64 [8830]~P1(f334(f334(f336(a881),x88301),f334(f174(a881),x88302)))+P1(f334(f334(f248(a881),x88301),f334(f144(a881,a881,f80(a881),f2(a881)),x88302)))
% 160.93/160.64 [8922]P47(x89221,x89222)+~P1(f334(f334(f336(f887(x89221,x89221)),f334(f334(f269(x89221,x89221),f516(x89222,x89221)),f516(x89222,x89221))),x89222))
% 160.93/160.64 [9069]~P1(f334(f334(f249(f888(a1,a876)),f334(f313(a881,a1,f104(a1)),x90691)),f334(f313(a881,a1,f104(a1)),x90692)))+P1(f334(f334(f249(f888(a881,a876)),x90691),x90692))
% 160.93/160.64 [9070]~P1(f334(f334(f248(f888(a1,a876)),f334(f313(a881,a1,f104(a1)),x90701)),f334(f313(a881,a1,f104(a1)),x90702)))+P1(f334(f334(f248(f888(a881,a876)),x90701),x90702))
% 160.93/160.64 [9154]P1(f334(f334(f249(a1),x91541),x91542))+~P1(f334(f334(f249(a1),f334(f334(f22(a1),f334(f334(f80(a1),x91541),x91541)),a101)),f334(f334(f80(a1),x91542),x91542)))
% 160.93/160.64 [9156]P1(f334(f334(f249(a1),x91561),x91562))+~P1(f334(f334(f248(a1),f334(f334(f22(a1),f334(f334(f80(a1),x91561),x91561)),a101)),f334(f334(f80(a1),x91562),x91562)))
% 160.93/160.64 [10046]~P103(x100461)+E(f120(f882(x100461),f334(f128(f882(x100461)),f117(x100461)),f334(f334(f334(f100(f883(f882(x100461))),f334(f334(f249(a1),f2(a1)),x100462)),f334(f122(f887(x100461,f882(x100461)),f882(x100461),f133(x100461,f882(x100461),f134(x100461,f334(f334(f22(a1),x100462),f78(a1))),f134(f882(x100461),f334(f334(f22(a1),x100462),f78(a1))))),f334(f273(x100461,f882(x100461),f883(f882(x100461))),f334(f334(f8(f888(f882(x100461),f882(x100461)),f888(f882(x100461),f883(f882(x100461))),x100461),f334(f8(f882(x100461),f883(f882(x100461)),f882(x100461)),f128(f882(x100461)))),f153(x100461))))),f119(f882(x100461)))),f134(f882(x100461),x100462))
% 160.93/160.64 [10068]~P1(f334(f61(x100681),x100682))+E(f334(f197(f882(x100681)),f90(f882(x100681),f334(f334(f18(f882(x100681),a876,a876),f334(f334(f8(a876,f888(a876,a876),f882(x100681)),a332),f334(f334(f7(f882(x100681),f888(x100681,a876),a876),f334(f334(f8(f888(x100681,a876),f888(f888(x100681,a876),a876),f882(x100681)),a331),f174(x100681))),x100682))),f139(x100681)))),f227(x100681,x100682))
% 160.93/160.64 [10204]~P26(a877,x102041,f334(f334(f312(f880(a877)),f334(f334(f334(f92(a877),a331),x102042),f334(a202,x102042))),f196(f888(f880(a877),a876))))+P26(a877,x102041,f334(f334(f312(f880(a877)),f334(f334(f334(f92(a877),f334(f334(f8(f888(a877,f888(a877,a876)),f888(a877,a876),a877),f334(f8(f888(a877,a876),a876,a877),f88(a877))),f334(f334(f8(f888(a877,a876),f888(a877,f888(a877,a876)),a877),f334(f7(a877,f888(a877,a876),f888(a877,a876)),f334(f334(f8(f888(a877,f888(a876,a876)),f888(f888(a877,a876),f888(a877,a876)),a877),f18(a877,a876,a876)),f334(f334(f8(f888(a877,a876),f888(a877,f888(a876,a876)),a877),f334(f8(a876,f888(a876,a876),a877),a337)),f334(a202,x102042))))),a331))),x102042),a331)),f196(f888(f880(a877),a876))))
% 160.93/160.64 [6055]E(f334(f334(f80(a881),f334(f334(f22(a881),x60551),x60552)),x60552),x60551)+~P1(f334(f334(f248(a881),x60552),x60551))
% 160.93/160.64 [6120]E(f334(f334(f38(a881),f334(f334(f81(a881),x61201),x61202)),x61202),x61201)+~P1(f334(f334(f249(a881),f2(a881)),x61202))
% 160.93/160.64 [6121]E(f334(f334(f38(a881),f334(f334(f81(a881),x61211),x61212)),x61211),x61212)+~P1(f334(f334(f249(a881),f2(a881)),x61211))
% 160.93/160.64 [6125]~P68(x61251)+E(f334(f334(f6(a881,x61251),f334(f167(x61251),x61252)),f334(f304(a881,f2(a881)),f334(f197(f882(x61251)),x61252))),f334(f168(x61251),x61252))
% 160.93/160.64 [6245]E(f44(a881,f334(a116,f334(f334(f81(a881),x62451),x62452)),x62451),f78(a881))+~P1(f334(f334(f249(a881),f78(a881)),x62451))
% 160.93/160.64 [6251]E(f334(a116,f334(f334(f80(a881),f334(f107(a881),x62511)),x62512)),f334(f334(f80(a881),f78(a881)),x62512))+~P1(f334(a201,f334(f107(a1),x62511)))
% 160.93/160.64 [6279]E(f334(a108,f334(f334(f259(a1),f334(f107(a1),x62791)),x62792)),f334(f334(f259(a881),f334(f107(a881),x62791)),x62792))+P1(f334(a201,f334(f107(a1),x62791)))
% 160.93/160.64 [6514]E(f334(f334(f22(a881),x65141),f334(f107(a881),f334(f334(f80(a1),x65142),a101))),f334(f334(f22(a881),f334(a116,x65141)),f334(f107(a881),x65142)))+~P1(f334(f334(f249(a1),a83),x65142))
% 160.93/160.64 [6592]E(x65921,f2(a881))+E(f334(a116,f334(f334(f80(a881),f334(f334(f22(a881),x65921),f78(a881))),x65922)),f334(f334(f80(a881),x65921),x65922))
% 160.93/160.64 [6633]E(x66331,f2(a1))+P1(f334(f334(f249(a1),f2(a1)),f334(f334(f259(a1),f334(f75(a1),x66331)),x66332)))
% 160.93/160.64 [6649]~E(x66492,f2(a881))+P1(f334(f334(f249(a1),f2(a1)),f334(f334(f259(a1),f334(f75(a1),x66491)),x66492)))
% 160.93/160.64 [6686]E(x66861,f2(a881))+E(f334(f334(f80(a881),x66862),f334(f334(f81(a881),f334(f334(f22(a881),x66861),f78(a881))),x66862)),f334(f334(f81(a881),x66861),x66862))
% 160.93/160.64 [6734]~P1(f334(f334(f248(a1),x67341),x67342))+P1(f334(f334(f249(a1),f334(f334(f80(a1),x67341),a101)),x67342))
% 160.93/160.64 [6862]E(f334(f334(f153(a881),x68621),f141(a881,f334(f304(a881,f334(a116,x68621)),x68622))),f141(a881,f334(f304(a881,x68621),x68622)))+~P1(f334(f334(f249(a881),x68621),x68622))
% 160.93/160.64 [7062]E(x70621,x70622)+~E(f334(f334(f22(a1),f334(f334(f80(a1),x70621),x70621)),a101),f334(f334(f22(a1),f334(f334(f80(a1),x70622),x70622)),a101))
% 160.93/160.64 [7065]E(x70651,f117(x70652))+E(f278(x70652,f334(f334(f156(x70652,f887(a103,x70652)),f334(f269(a103,x70652),f78(a103))),x70651)),f285(x70652,x70651))
% 160.93/160.64 [7291]P1(f334(f334(f248(a1),x72911),x72912))+~P1(f334(f334(f249(a1),f334(f334(f80(a1),x72911),a101)),x72912))
% 160.93/160.64 [7770]~P1(f334(f334(f249(a881),x77701),x77702))+P1(f334(f334(f336(f887(a881,a881)),f334(f334(f269(a881,a881),x77701),x77702)),a253))
% 160.93/160.64 [7991]~P1(f334(f334(f249(a103),f2(a103)),x79911))+P1(f334(f334(f249(a103),f334(f268(a103,f887(a103,a103)),f334(f279(x79911),x79912))),x79911))
% 160.93/160.64 [8313]~P85(x83131)+P1(f334(f334(f248(x83131),f334(f75(x83131),f334(f168(x83131),x83132))),f334(f168(x83131),f334(f334(f156(x83131,x83131),f75(x83131)),x83132))))
% 160.93/160.64 [8337]P1(f334(f334(f249(a881),x83371),x83372))+~P1(f334(f334(f336(f887(a881,a881)),f334(f334(f269(a881,a881),x83371),x83372)),a253))
% 160.93/160.64 [8486]E(f334(f334(f269(x84861,x84861),f634(x84862,x84861)),f634(x84862,x84861)),x84862)+~P1(f334(f334(f336(f887(x84861,x84861)),x84862),f310(x84861,f196(f888(f887(x84861,x84861),a876)))))
% 160.93/160.64 [8530]E(f334(f304(a881,x85301),f334(f334(f80(a881),x85301),f334(f37(a881),x85302))),x85302)+~P1(f334(f334(f248(f888(a881,a876)),x85302),f334(f304(a881,x85301),f334(f334(f80(a881),x85301),f334(f37(a881),x85302)))))
% 160.93/160.64 [8869]E(f334(f334(f38(a1),f334(f107(a1),f334(f334(f22(a1),f334(f334(f80(a1),x88691),x88691)),a101))),f334(f107(a1),f334(f334(f80(a1),x88692),x88692))),f334(f334(f38(a1),f334(f107(a1),x88691)),f334(f107(a1),x88692)))+~P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),x88692)))
% 160.93/160.64 [8998]E(f179(f882(x89981),f334(f334(f8(a876,a876,f882(x89981)),a329),f334(f334(f7(f882(x89981),f882(x89981),a876),a331),f117(x89981))),x89982),f182(x89981,f182(x89981,x89982)))+~P16(a881,f334(f171(a881),f334(f334(f156(f882(x89981),a881),f197(f882(x89981))),x89982)))
% 160.93/160.64 [9001]E(f334(f334(f38(a1),f334(f107(a1),f334(f334(f22(a1),f334(f334(f80(a1),x90011),x90011)),a101))),f334(f107(a1),f334(f334(f80(a1),x90012),x90012))),f334(f334(f38(a1),f334(f334(f80(a1),f334(f107(a1),x90011)),f78(a1))),f334(f107(a1),x90012)))+P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),x90012)))
% 160.93/160.64 [9692]P26(a877,x96921,f334(f334(f312(f880(a877)),f334(f334(f334(f92(a877),a331),f334(a26,x96922)),f334(a202,f334(a26,x96922)))),f196(f888(f880(a877),a876))))+~P26(a877,f334(f334(f312(f880(a877)),f334(f334(f334(f92(a877),a331),f334(a26,x96922)),f334(a202,f334(a26,x96922)))),x96921),f334(f334(f312(f880(a877)),f334(f334(f334(f92(a877),a331),f334(f245(a878),f334(a28,x96922))),f334(a202,f334(f245(a878),f334(a28,x96922))))),f196(f888(f880(a877),a876))))
% 160.93/160.64 [9842]P1(f334(a201,x98422))+E(f334(f334(f86(a1,a881),f334(f334(f22(a1),x98421),x98422)),f334(f334(f18(a1,a881,a881),f334(f334(f7(a1,a881,f888(a881,a881)),f334(f334(f8(a876,f888(a881,f888(a881,a881)),a1),f100(a881)),a201)),f2(a881))),a108)),f334(f334(f22(a881),f334(a108,x98421)),f334(a108,x98422)))
% 160.93/160.64 [9850]E(f334(f334(f86(a1,a881),f334(f107(a1),f334(f334(f80(a1),x98501),f334(f79(a1),x98502)))),f334(f334(f18(a1,a881,a881),f334(f334(f7(a1,a881,f888(a881,a881)),f334(f334(f8(a876,f888(a881,f888(a881,a881)),a1),f100(a881)),a201)),f2(a881))),a108)),f334(f334(f22(a881),f334(f107(a881),x98501)),f334(f107(a881),x98502)))+P1(f334(f334(f249(a1),x98502),a83))
% 160.93/160.64 [9851]~P28(x98511,x98512)+P1(f334(f334(f248(f888(f887(x98511,x98511),a876)),f334(f334(f291(x98511,x98511,x98511),f334(f268(f888(f887(x98511,x98511),a876),f888(f887(x98511,x98511),a876)),x98512)),f334(f272(f888(f887(x98511,x98511),a876),f888(f887(x98511,x98511),a876)),x98512))),f334(f268(f888(f887(x98511,x98511),a876),f888(f887(x98511,x98511),a876)),x98512)))
% 160.93/160.64 [9918]~E(f334(f37(a881),f334(f254(a881),f334(f334(f18(a881,a876,a876),f334(f334(f8(a876,f888(a876,a876),a881),a332),f334(f334(f7(a881,f888(a881,a876),a876),f336(a881)),x99181))),f334(f334(f7(a881,a881,a876),f249(a881)),f334(a116,x99182))))),f2(a881))+~P1(f334(f334(f336(a881),f2(a881)),x99181))
% 160.93/160.64 [9974]E(f44(a1,f334(f107(a1),f334(f334(f22(a1),f334(f334(f80(a1),x99741),x99741)),a101)),f334(f107(a1),f334(f334(f80(a1),x99742),x99742))),f334(f334(f80(a1),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f44(a1,f334(f107(a1),x99741),f334(f107(a1),x99742)))),f78(a1)))+~P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),x99742)))
% 160.93/160.64 [9983]E(f44(a1,f334(f107(a1),f334(f334(f22(a1),f334(f334(f80(a1),x99831),x99831)),a101)),f334(f107(a1),f334(f334(f80(a1),x99832),x99832))),f334(f334(f22(a1),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f44(a1,f334(f334(f80(a1),f334(f107(a1),x99831)),f78(a1)),f334(f107(a1),x99832)))),f78(a1)))+P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),x99832)))
% 160.93/160.64 [10035]~P5(x100351)+E(f39(x100351,f334(f254(x100351),f334(f334(f8(f888(x100351,a876),a876,x100351),f88(x100351)),f334(f334(f8(f888(x100351,a876),f888(x100351,a876),x100351),f334(f18(x100351,a876,a876),f334(f334(f8(a876,f888(a876,a876),x100351),a337),f334(f334(f7(x100351,f888(x100351,a876),a876),f336(x100351)),x100352)))),f248(x100351))))),f40(x100351,x100352))
% 160.93/160.64 [10061]~P39(x100611,x100612)+P57(x100611,f334(f334(f7(x100611,f888(f887(x100611,x100611),a876),f888(x100611,a876)),f334(f334(f8(f888(x100611,f888(f888(f887(x100611,x100611),a876),a876)),f888(f888(f887(x100611,x100611),a876),f888(x100611,a876)),x100611),f7(x100611,f888(f887(x100611,x100611),a876),a876)),f334(f334(f8(f888(x100611,f887(x100611,x100611)),f888(x100611,f888(f888(f887(x100611,x100611),a876),a876)),x100611),f334(f8(f887(x100611,x100611),f888(f888(f887(x100611,x100611),a876),a876),x100611),f336(f887(x100611,x100611)))),f269(x100611,x100611)))),x100612))
% 160.93/160.64 [10062]~P8(x100621,f257(f888(x100621,a876)),x100622)+P7(x100621,f334(f334(f7(x100621,f888(f887(x100621,x100621),a876),f888(x100621,a876)),f334(f334(f8(f888(x100621,f888(f888(f887(x100621,x100621),a876),a876)),f888(f888(f887(x100621,x100621),a876),f888(x100621,a876)),x100621),f7(x100621,f888(f887(x100621,x100621),a876),a876)),f334(f334(f8(f888(x100621,f887(x100621,x100621)),f888(x100621,f888(f888(f887(x100621,x100621),a876),a876)),x100621),f334(f8(f887(x100621,x100621),f888(f888(f887(x100621,x100621),a876),a876),x100621),f336(f887(x100621,x100621)))),f269(x100621,x100621)))),x100622))
% 160.93/160.64 [10099]P39(x100991,x100992)+~P57(x100991,f334(f334(f7(x100991,f888(f887(x100991,x100991),a876),f888(x100991,a876)),f334(f334(f8(f888(x100991,f888(f888(f887(x100991,x100991),a876),a876)),f888(f888(f887(x100991,x100991),a876),f888(x100991,a876)),x100991),f7(x100991,f888(f887(x100991,x100991),a876),a876)),f334(f334(f8(f888(x100991,f887(x100991,x100991)),f888(x100991,f888(f888(f887(x100991,x100991),a876),a876)),x100991),f334(f8(f887(x100991,x100991),f888(f888(f887(x100991,x100991),a876),a876),x100991),f336(f887(x100991,x100991)))),f269(x100991,x100991)))),x100992))
% 160.93/160.64 [10100]P8(x101001,f257(f888(x101001,a876)),x101002)+~P7(x101001,f334(f334(f7(x101001,f888(f887(x101001,x101001),a876),f888(x101001,a876)),f334(f334(f8(f888(x101001,f888(f888(f887(x101001,x101001),a876),a876)),f888(f888(f887(x101001,x101001),a876),f888(x101001,a876)),x101001),f7(x101001,f888(f887(x101001,x101001),a876),a876)),f334(f334(f8(f888(x101001,f887(x101001,x101001)),f888(x101001,f888(f888(f887(x101001,x101001),a876),a876)),x101001),f334(f8(f887(x101001,x101001),f888(f888(f887(x101001,x101001),a876),a876),x101001),f336(f887(x101001,x101001)))),f269(x101001,x101001)))),x101002))
% 160.93/160.64 [7242]E(f334(f334(f80(a881),f334(f107(a881),f334(f334(f22(a1),x72421),a101))),x72422),f334(a116,f334(f334(f80(a881),f334(f107(a881),x72421)),x72422)))+P1(f334(a201,f334(f107(a1),x72421)))
% 160.93/160.64 [7689]~P93(x76891)+E(f334(f334(f80(x76891),f334(f334(f80(x76891),f78(x76891)),f334(f107(x76891),x76892))),f334(f107(x76891),x76892)),f334(f107(x76891),f334(f334(f22(a1),f334(f334(f80(a1),x76892),x76892)),a101)))
% 160.93/160.64 [8339]~P1(f334(f334(f248(a1),x83391),x83392))+P1(f334(f334(f249(a1),f334(f334(f80(a1),x83391),x83391)),f334(f334(f22(a1),f334(f334(f80(a1),x83392),x83392)),a101)))
% 160.93/160.64 [8341]~P1(f334(f334(f248(a1),x83411),x83412))+P1(f334(f334(f248(a1),f334(f334(f80(a1),x83411),x83411)),f334(f334(f22(a1),f334(f334(f80(a1),x83412),x83412)),a101)))
% 160.93/160.64 [8762]P1(f334(f334(f248(a1),x87621),x87622))+~P1(f334(f334(f249(a1),f334(f334(f80(a1),x87621),x87621)),f334(f334(f22(a1),f334(f334(f80(a1),x87622),x87622)),a101)))
% 160.93/160.64 [8764]P1(f334(f334(f248(a1),x87641),x87642))+~P1(f334(f334(f248(a1),f334(f334(f80(a1),x87641),x87641)),f334(f334(f22(a1),f334(f334(f80(a1),x87642),x87642)),a101)))
% 160.93/160.64 [9057]~P1(f334(f334(f249(a1),x90571),x90572))+P1(f334(f334(f249(a1),f334(f334(f22(a1),f334(f334(f80(a1),x90571),x90571)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),x90572),x90572)),a101)))
% 160.93/160.64 [9059]~P1(f334(f334(f248(a1),x90591),x90592))+P1(f334(f334(f248(a1),f334(f334(f22(a1),f334(f334(f80(a1),x90591),x90591)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),x90592),x90592)),a101)))
% 160.93/160.64 [9060]~P1(f334(f334(f91(a1),x90601),x90602))+P1(f334(f334(f91(a1),f334(f334(f22(a1),f334(f334(f80(a1),x90601),x90601)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),x90602),x90602)),a101)))
% 160.93/160.64 [9327]P1(f334(f334(f249(a1),x93271),x93272))+~P1(f334(f334(f249(a1),f334(f334(f22(a1),f334(f334(f80(a1),x93271),x93271)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),x93272),x93272)),a101)))
% 160.93/160.64 [9329]P1(f334(f334(f248(a1),x93291),x93292))+~P1(f334(f334(f248(a1),f334(f334(f22(a1),f334(f334(f80(a1),x93291),x93291)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),x93292),x93292)),a101)))
% 160.93/160.64 [9330]P1(f334(f334(f91(a1),x93301),x93302))+~P1(f334(f334(f91(a1),f334(f334(f22(a1),f334(f334(f80(a1),x93301),x93301)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),x93302),x93302)),a101)))
% 160.93/160.64 [9362]~P1(f334(f61(x93621),x93622))+P1(f334(f61(f888(x93621,a876)),f334(f254(f888(x93621,a876)),f334(f334(f7(f888(x93621,a876),f888(x93621,a876),a876),f248(f888(x93621,a876))),x93622))))
% 160.93/160.64 [9410]~E(f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),x94101),f196(f888(f887(a881,a881),a876)))),f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),x94102),f196(f888(f887(a881,a881),a876)))))+P1(f334(f334(f336(f887(f887(a881,a881),f887(a881,a881))),f334(f334(f269(f887(a881,a881),f887(a881,a881)),x94101),x94102)),a112))
% 160.93/160.64 [9494]E(f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),x94941),f196(f888(f887(a881,a881),a876)))),f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),x94942),f196(f888(f887(a881,a881),a876)))))+~P1(f334(f334(f336(f887(f887(a881,a881),f887(a881,a881))),f334(f334(f269(f887(a881,a881),f887(a881,a881)),x94941),x94942)),a112))
% 160.93/160.64 [9533]P1(f334(f334(f248(a1),f2(a1)),f660(x95331,x95332)))+E(f334(f254(a1),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f248(a1),f2(a1)))),x95331)),f334(f254(a1),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f248(a1),f2(a1)))),x95332)))
% 160.93/160.64 [10045]~P5(x100451)+E(f40(x100451,f334(f254(x100451),f334(f334(f8(f888(x100451,a876),a876,x100451),f88(x100451)),f334(f334(f8(f888(x100451,a876),f888(x100451,a876),x100451),f334(f18(x100451,a876,a876),f334(f334(f8(a876,f888(a876,a876),x100451),a337),f334(f334(f7(x100451,f888(x100451,a876),a876),f336(x100451)),x100452)))),f334(f7(x100451,x100451,a876),f248(x100451)))))),f39(x100451,x100452))
% 160.93/160.65 [10067]P1(f334(f334(f336(a881),f2(a881)),x100671))+E(f334(f37(a881),f334(f254(a881),f334(f334(f18(a881,a876,a876),f334(f334(f8(a876,f888(a876,a876),a881),a332),f334(f334(f7(a881,f888(a881,a876),a876),f334(f334(f8(a881,f888(f888(a881,a876),a876),a881),f336(a881)),a116)),x100671))),f334(f334(f7(a881,a881,a876),f249(a881)),x100672)))),f334(f37(a881),f334(f254(a881),f334(f334(f18(a881,a876,a876),f334(f334(f8(a876,f888(a876,a876),a881),a332),f334(f334(f7(a881,f888(a881,a876),a876),f336(a881)),x100671))),f334(f334(f7(a881,a881,a876),f249(a881)),f334(a116,x100672))))))
% 160.93/160.65 [7558]~P93(x75581)+E(f334(f334(f81(x75581),x75582),f334(f107(x75581),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),x75582)
% 160.93/160.65 [7818]~P93(x78181)+E(f334(f334(f80(x78181),f334(f107(x78181),x78182)),f78(x78181)),f334(f107(x78181),f334(f334(f80(a1),x78182),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))
% 160.93/160.65 [7963]P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),x79632)))+E(f334(f334(f259(a1),x79631),f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),x79632),x79632)),a101))),f78(a1))
% 160.93/160.65 [9387]~P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),x93872)))+E(f334(f334(f259(a1),x93871),f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),x93872),x93872)),a101))),f334(f334(f86(a1,a1),f334(f334(f259(a1),x93871),f334(f107(a881),x93872))),f334(f334(f18(a1,a1,a1),f334(f334(f8(a1,f888(a1,a1),a1),f81(a1)),f334(f81(a1),x93871))),f5(a1))))
% 160.93/160.65 [9757]~P1(f334(f334(f248(a881),f671(x97572,x97571)),f334(x97571,f671(x97572,x97571))))+P1(f334(f61(a881),f334(f254(a881),f334(f334(f7(a881,a881,a876),f334(f334(f8(a881,f888(a881,a876),a881),f248(a881)),x97571)),x97572))))
% 160.93/160.65 [9908]~P1(f334(f334(f249(a881),f334(f107(a881),x99081)),f334(a116,x99082)))+P1(f334(f334(f86(a1,a876),f334(f107(a1),f334(f334(f80(a1),x99081),a101))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a337),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f7(a1,a881,a876),f334(f334(f8(a881,f888(a881,a876),a1),f249(a881)),a108)),x99082))))
% 160.93/160.65 [9909]~P1(f334(f334(f248(a881),f334(f107(a881),x99091)),f334(a116,x99092)))+P1(f334(f334(f86(a1,a876),f334(f107(a1),f334(f334(f80(a1),x99091),a101))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a337),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f7(a1,a881,a876),f334(f334(f8(a881,f888(a881,a876),a1),f248(a881)),a108)),x99092))))
% 160.93/160.65 [9958]P1(f334(f334(f249(a881),f334(f107(a881),x99581)),f334(a116,x99582)))+~P1(f334(f334(f86(a1,a876),f334(f107(a1),f334(f334(f80(a1),x99581),a101))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a337),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f7(a1,a881,a876),f334(f334(f8(a881,f888(a881,a876),a1),f249(a881)),a108)),x99582))))
% 160.93/160.65 [9959]P1(f334(f334(f248(a881),f334(f107(a881),x99591)),f334(a116,x99592)))+~P1(f334(f334(f86(a1,a876),f334(f107(a1),f334(f334(f80(a1),x99591),a101))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a337),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f7(a1,a881,a876),f334(f334(f8(a881,f888(a881,a876),a1),f248(a881)),a108)),x99592))))
% 160.93/160.65 [9989]~P1(f334(f334(f249(a881),f334(a116,x99892)),f334(f107(a881),x99891)))+P1(f334(f334(f86(a1,a876),f334(f107(a1),f334(f334(f80(a1),x99891),a101))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a337),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f8(a881,a876,a1),f334(f249(a881),x99892)),a108)))))
% 160.93/160.65 [9990]~P1(f334(f334(f248(a881),f334(a116,x99902)),f334(f107(a881),x99901)))+P1(f334(f334(f86(a1,a876),f334(f107(a1),f334(f334(f80(a1),x99901),a101))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a337),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f8(a881,a876,a1),f334(f248(a881),x99902)),a108)))))
% 160.93/160.65 [10033]P1(f334(f334(f249(a881),f334(a116,x100331)),f334(f107(a881),x100332)))+~P1(f334(f334(f86(a1,a876),f334(f107(a1),f334(f334(f80(a1),x100332),a101))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a337),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f8(a881,a876,a1),f334(f249(a881),x100331)),a108)))))
% 160.93/160.65 [10034]P1(f334(f334(f248(a881),f334(a116,x100341)),f334(f107(a881),x100342)))+~P1(f334(f334(f86(a1,a876),f334(f107(a1),f334(f334(f80(a1),x100342),a101))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a337),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f8(a881,a876,a1),f334(f248(a881),x100341)),a108)))))
% 160.93/160.65 [10107]~P1(f334(f334(f336(a881),f2(a881)),x101071))+E(f334(a116,f334(f37(a881),f334(f254(a881),f334(f334(f18(a881,a876,a876),f334(f334(f8(a876,f888(a876,a876),a881),a332),f334(f334(f7(a881,f888(a881,a876),a876),f334(f334(f8(a881,f888(f888(a881,a876),a876),a881),f336(a881)),a116)),x101071))),f334(f334(f7(a881,a881,a876),f249(a881)),x101072))))),f334(f37(a881),f334(f254(a881),f334(f334(f18(a881,a876,a876),f334(f334(f8(a876,f888(a876,a876),a881),a332),f334(f334(f7(a881,f888(a881,a876),a876),f336(a881)),x101071))),f334(f334(f7(a881,a881,a876),f249(a881)),f334(a116,x101072))))))
% 160.93/160.65 [8514]~P93(x85141)+E(f334(f334(f81(x85141),f334(f107(x85141),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),x85142),x85142)
% 160.93/160.65 [8580]~P93(x85801)+E(f334(f334(f80(x85801),f78(x85801)),f334(f107(x85801),x85802)),f334(f107(x85801),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),x85802)))
% 160.93/160.65 [8639]~P93(x86391)+E(f334(f334(f22(x86391),f334(f107(x86391),x86392)),f78(x86391)),f334(f107(x86391),f334(f334(f80(a1),x86392),f334(f79(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))
% 160.93/160.65 [8780]~P1(f334(f334(f249(a881),f334(f107(a881),a83)),x87802))+E(f334(f334(f22(a881),x87801),f334(f334(f22(a881),x87802),f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f334(f334(f22(a881),f334(a116,x87801)),x87802))
% 160.93/160.65 [9426]~P118(x94261)+E(f334(f334(f81(x94261),x94262),x94262),f334(f334(f259(x94261),x94262),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))
% 160.93/160.65 [9427]~P80(x94271)+E(f334(f334(f259(x94271),x94272),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f334(f334(f81(x94271),x94272),x94272))
% 160.93/160.65 [9429]~P93(x94291)+E(f334(f334(f81(x94291),x94292),f334(f107(x94291),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f334(f334(f80(x94291),x94292),x94292))
% 160.93/160.65 [9675]~P111(x96751)+E(f334(f334(f259(x96751),f334(f75(x96751),x96752)),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f334(f334(f259(x96751),x96752),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))
% 160.93/160.65 [9676]~P139(x96761)+E(f334(f334(f259(x96761),f334(f79(x96761),x96762)),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f334(f334(f259(x96761),x96762),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))
% 160.93/160.65 [9672]~P93(x96721)+E(f334(f334(f81(x96721),f334(f107(x96721),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x96722),f334(f334(f80(x96721),x96722),x96722))
% 160.93/160.65 [9797]~P111(x97971)+E(f334(f75(x97971),f334(f334(f259(x97971),x97972),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x97971),x97972),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))
% 160.93/160.65 [9860]~P111(x98601)+P1(f334(f334(f248(x98601),f2(x98601)),f334(f334(f259(x98601),x98602),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))))
% 160.93/160.65 [10024]~E(f334(a116,x100242),f334(f107(a881),x100241))+P1(f334(f334(f86(a1,a876),f334(f107(a1),f334(f334(f80(a1),x100241),a101))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a337),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f7(a1,a881,a876),f334(f334(f8(a881,f888(a881,a876),a1),a331),a108)),x100242)))))
% 160.93/160.65 [10025]~E(f334(f107(a881),x100251),f334(a116,x100252))+P1(f334(f334(f86(a1,a876),f334(f107(a1),f334(f334(f80(a1),x100251),a101))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a337),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f7(a1,a881,a876),f334(f334(f8(a881,f888(a881,a876),a1),a331),a108)),x100252)))))
% 160.93/160.65 [10070]E(f334(a116,x100701),f334(f107(a881),x100702))+~P1(f334(f334(f86(a1,a876),f334(f107(a1),f334(f334(f80(a1),x100702),a101))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a337),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f7(a1,a881,a876),f334(f334(f8(a881,f888(a881,a876),a1),a331),a108)),x100701)))))
% 160.93/160.65 [10071]E(f334(f107(a881),x100711),f334(a116,x100712))+~P1(f334(f334(f86(a1,a876),f334(f107(a1),f334(f334(f80(a1),x100711),a101))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a337),f334(f334(f8(a876,a876,a1),a329),a201))),f334(f334(f7(a1,a881,a876),f334(f334(f8(a881,f888(a881,a876),a1),a331),a108)),x100712)))))
% 160.93/160.65 [9856]~P93(x98561)+E(f334(f334(f259(x98561),f334(f107(x98561),a101)),f334(f334(f81(a881),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x98562)),f78(x98561))
% 160.93/160.65 [9857]~P139(x98571)+E(f334(f334(f259(x98571),f334(f79(x98571),f78(x98571))),f334(f334(f81(a881),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x98572)),f78(x98571))
% 160.93/160.65 [9862]~P80(x98621)+E(f334(f334(f259(x98621),x98622),f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),a101))),f334(f334(f81(x98621),f334(f334(f81(x98621),x98622),x98622)),x98622))
% 160.93/160.65 [10049]~P1(f334(f334(f248(a1),f2(a1)),x100492))+E(f44(a1,f334(f334(f80(a1),f78(a1)),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x100491)),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x100492)),f334(f334(f80(a1),f78(a1)),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f44(a1,x100491,x100492))))
% 160.93/160.65 [10073]~P1(f334(f334(f248(a1),f2(a1)),x100732))+E(f334(f334(f38(a1),f334(f334(f80(a1),f78(a1)),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x100731))),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x100732)),f334(f334(f38(a1),x100731),x100732))
% 160.93/160.65 [10075]~P1(f334(f334(f248(a1),x100752),f2(a1)))+E(f334(f334(f38(a1),f334(f334(f80(a1),f78(a1)),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x100751))),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x100752)),f334(f334(f38(a1),f334(f334(f80(a1),x100751),f78(a1))),x100752))
% 160.93/160.65 [10076]~P1(f334(f334(f248(a1),x100762),f2(a1)))+E(f44(a1,f334(f334(f80(a1),f78(a1)),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x100761)),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x100762)),f334(f334(f22(a1),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f44(a1,f334(f334(f80(a1),x100761),f78(a1)),x100762))),f78(a1)))
% 160.93/160.65 [9949]~P93(x99491)+E(f334(f334(f259(x99491),f334(f107(x99491),a101)),f334(a116,f334(f334(f81(a881),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x99492))),f334(f107(x99491),a101))
% 160.93/160.65 [9951]~P139(x99511)+E(f334(f334(f259(x99511),f334(f79(x99511),f78(x99511))),f334(a116,f334(f334(f81(a881),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x99512))),f334(f79(x99511),f78(x99511)))
% 160.93/160.65 [5108]~P26(x51081,x51082,x51083)+P30(x51081,x51082,x51083)
% 160.93/160.65 [8029]~E(x80292,x80293)+P36(x80291,x80291,a331,x80292,x80293)
% 160.93/160.65 [8593]E(x85931,x85932)+~P36(x85933,x85933,a331,x85931,x85932)
% 160.93/160.65 [5113]~P39(x51131,x51133)+P39(x51131,f328(x51131,x51132,x51133))
% 160.93/160.65 [5285]P29(x52851,x52852,x52853)+~P29(x52851,f334(a116,x52852),x52853)
% 160.93/160.65 [5370]~P8(x53701,x53702,x53703)+P8(f882(x53701),f163(x53701,x53702),f160(x53701,x53703))
% 160.93/160.65 [5371]~P41(x53711,x53712,x53713)+P41(f882(x53711),f163(x53711,x53712),f160(x53711,x53713))
% 160.93/160.65 [5483]P52(x54831,x54832,x54833)+~E(f616(x54833,x54832,x54831),f617(x54833,x54832,x54831))
% 160.93/160.65 [5484]P53(x54841,x54842,x54843)+~E(f629(x54843,x54842,x54841),f630(x54843,x54842,x54841))
% 160.93/160.65 [6419]P30(x64191,x64192,x64193)+~P29(x64191,f601(x64193,x64192,x64191),f604(x64193,x64192,x64191))
% 160.93/160.65 [4663]~E(x46631,f210(x46632))+~E(x46631,f334(f241(x46632),x46633))
% 160.93/160.65 [4713]~E(f334(f171(x47132),x47131),x47133)+E(x47131,f334(f171(x47132),x47133))
% 160.93/160.65 [4714]~E(x47142,f334(f171(x47141),x47143))+E(f334(f171(x47141),x47142),x47143)
% 160.93/160.65 [4761]E(x47611,x47612)+~E(f334(f241(x47613),x47611),f334(f241(x47613),x47612))
% 160.93/160.65 [4762]E(x47621,x47622)+~E(f334(f171(x47623),x47621),f334(f171(x47623),x47622))
% 160.93/160.65 [4967]~P7(x49673,x49671)+P1(f334(f334(x49671,x49672),x49672))
% 160.93/160.65 [4968]~P50(x49683,x49681)+P1(f334(f334(x49681,x49682),x49682))
% 160.93/160.65 [4970]~P57(x49701,x49702)+P1(f334(f322(x49701,x49702),x49703))
% 160.93/160.65 [5032]~P39(x50321,x50322)+P39(f882(x50321),f334(f145(x50321,x50322),x50323))
% 160.93/160.65 [5037]~P1(f334(x50372,x50373))+~E(f334(f254(x50371),x50372),f196(f888(x50371,a876)))
% 160.93/160.65 [5038]~P1(f334(x50382,x50383))+~E(f196(f888(x50381,a876)),f334(f254(x50381),x50382))
% 160.93/160.65 [5069]~P1(f334(x50691,x50693))+P1(f334(x50691,f90(x50692,x50691)))
% 160.93/160.65 [5193]~E(x51932,x51933)+P1(f334(f334(f336(x51931),x51932),f334(a331,x51933)))
% 160.93/160.65 [5205]P1(f334(x52051,x52052))+~P1(f334(x52051,f570(x52051,x52053)))
% 160.93/160.65 [5252]E(f334(f171(x52521),x52522),f334(f334(f153(x52521),x52523),f117(x52521)))+~E(x52522,f334(f334(f153(x52521),x52523),f117(x52521)))
% 160.93/160.65 [5253]~E(x52533,f334(f334(f153(x52531),x52532),f117(x52531)))+E(f334(f334(f153(x52531),x52532),f117(x52531)),f334(f171(x52531),x52533))
% 160.93/160.65 [5278]~E(x52783,f334(f16(f885(x52782),x52781),f210(x52782)))+E(f186(x52781,x52782,x52783),f196(f888(x52781,a876)))
% 160.93/160.65 [5299]~P35(x52991,x52992,x52993)+P35(x52991,x52992,f334(f171(x52991),x52993))
% 160.93/160.65 [5300]~P33(x53001,x53002,x53003)+P33(x53001,x53002,f334(f171(x53001),x53003))
% 160.93/160.65 [5303]E(f334(f37(x53031),f782(x53032,x53033,x53031)),x53032)+~E(f334(f37(x53031),x53033),f334(a116,x53032))
% 160.93/160.65 [5309]~P39(x53091,x53093)+P1(f334(f334(f336(x53091),x53092),f323(x53091,x53093)))
% 160.93/160.65 [5312]~E(f334(f171(x53122),x53121),f334(f334(f153(x53122),x53123),f117(x53122)))+E(x53121,f334(f334(f153(x53122),x53123),f117(x53122)))
% 160.93/160.65 [5313]~E(f334(f334(f153(x53132),x53133),f117(x53132)),f334(f171(x53132),x53131))+E(x53131,f334(f334(f153(x53132),x53133),f117(x53132)))
% 160.93/160.65 [5328]E(x53281,f334(f16(f885(x53282),x53283),f210(x53282)))+~E(f186(x53283,x53282,x53281),f196(f888(x53283,a876)))
% 160.93/160.65 [5334]E(f85(f887(a881,a881),f47(x53341,x53342)),x53343)+~P1(f334(f47(x53341,x53342),x53343))
% 160.93/160.65 [5342]~E(x53423,f334(f241(x53421),x53422))+P1(f334(f334(f336(x53421),x53422),f240(x53421,x53423)))
% 160.93/160.65 [5374]P35(x53741,x53742,x53743)+~P35(x53741,x53742,f334(f171(x53741),x53743))
% 160.93/160.65 [5375]P33(x53751,x53752,x53753)+~P33(x53751,x53752,f334(f171(x53751),x53753))
% 160.93/160.65 [5437]~E(x54372,f117(x54371))+P1(f334(f334(f336(f882(x54371)),x54372),f163(x54371,x54373)))
% 160.93/160.65 [5444]~P41(x54441,x54442,x54443)+P41(x54441,x54442,f334(f289(x54441,x54441),x54443))
% 160.93/160.65 [5445]~P53(x54451,x54452,x54453)+P53(x54451,x54452,f334(f289(x54451,x54451),x54453))
% 160.93/160.65 [5464]~P58(x54641)+E(f44(x54641,f44(x54641,x54642,x54643),x54643),f44(x54641,x54642,x54643))
% 160.93/160.65 [5559]E(x55591,x55592)+~P1(f334(f334(f336(x55593),x55591),f334(a331,x55592)))
% 160.93/160.65 [5605]~P142(x56051)+E(f198(x56051,x56052,f2(a881),x56053),x56053)
% 160.93/160.65 [5625]P41(x56251,x56252,x56253)+~P41(x56251,x56252,f334(f289(x56251,x56251),x56253))
% 160.93/160.65 [5626]P53(x56261,x56262,x56263)+~P53(x56261,x56262,f334(f289(x56261,x56261),x56263))
% 160.93/160.65 [5630]~P108(x56302)+E(f152(x56301,x56302,x56303,f117(x56301)),f117(x56301))
% 160.93/160.65 [5643]E(f172(x56431,x56432,f154(x56431,x56433)),f154(x56431,f172(x56431,x56432,x56433)))+~P1(f334(f139(x56431),x56433))
% 160.93/160.65 [5649]E(x56491,f334(f241(x56492),x56493))+~P1(f334(f334(f336(x56492),x56493),f240(x56492,x56491)))
% 160.93/160.65 [5734]~P1(f334(a25,x57343))+P1(f334(a25,f29(x57341,x57342,x57343)))
% 160.93/160.65 [5745]E(f334(f138(x57451,x57452),x57453),f117(x57451))+P1(f334(x57452,f735(x57453,x57452,x57451)))
% 160.93/160.65 [5888]~P1(f334(f139(x58881),x58882))+P1(f334(f139(x58881),f178(x58881,x58882,x58883)))
% 160.93/160.65 [5889]~P1(f334(f139(x58891),x58893))+P1(f334(f139(x58891),f172(x58891,x58892,x58893)))
% 160.93/160.65 [5890]~P1(f334(f139(x58901),x58903))+P1(f334(f139(x58901),f179(x58901,x58902,x58903)))
% 160.93/160.65 [5891]~P1(f334(f139(x58911),x58913))+P1(f334(f139(x58911),f142(x58911,x58912,x58913)))
% 160.93/160.65 [5892]~P145(x58921,x58922,x58923)+P1(f334(x58921,f44(a1,x58922,x58923)))
% 160.93/160.65 [5911]~P35(x59113,x59111,x59112)+P1(f334(x59111,f785(x59112,x59111,x59113)))
% 160.93/160.65 [5912]~P37(x59123,x59121,x59122)+P1(f334(x59121,f811(x59122,x59121,x59123)))
% 160.93/160.65 [5933]E(f334(f138(x59331,x59332),x59333),f179(x59331,x59332,x59333))+P1(f334(x59332,f762(x59333,x59332,x59331)))
% 160.93/160.65 [5973]~P1(f334(f139(x59731),x59733))+P1(f334(f139(f882(x59731)),f54(x59731,x59732,x59733)))
% 160.93/160.65 [6005]~P109(x60051)+E(f334(f334(f105(f888(x60051,a876)),f334(f255(x60051),x60052)),f305(x60051,x60052,x60053)),f196(f888(x60051,a876)))
% 160.93/160.65 [6006]~P109(x60061)+E(f334(f334(f105(f888(x60061,a876)),f334(f303(x60061),x60062)),f308(x60061,x60062,x60063)),f196(f888(x60061,a876)))
% 160.93/160.65 [6007]~P109(x60071)+E(f334(f334(f105(f888(x60071,a876)),f334(f303(x60071),x60072)),f307(x60071,x60072,x60073)),f196(f888(x60071,a876)))
% 160.93/160.65 [6154]P1(f334(a25,x61541))+~P1(f334(a25,f29(x61542,x61543,x61541)))
% 160.93/160.65 [6156]P1(f334(a25,x61561))+~P1(f334(a25,f30(x61562,x61563,x61561)))
% 160.93/160.65 [6158]P1(f334(a25,x61581))+~P1(f334(a25,f30(x61582,x61581,x61583)))
% 160.93/160.65 [6241]E(f334(f138(x62411,x62412),x62413),x62413)+~P1(f334(x62412,f736(x62413,x62412,x62411)))
% 160.93/160.65 [6243]E(f334(f334(f312(x62431),f812(x62432,x62433,x62431)),f782(x62432,x62433,x62431)),x62433)+~E(f334(f37(x62431),x62433),f334(a116,x62432))
% 160.93/160.65 [6259]P145(x62591,x62592,x62593)+~P1(f334(x62591,f44(a1,x62592,x62593)))
% 160.93/160.65 [6306]P33(x63061,x63062,x63063)+~P1(f334(x63062,f806(x63062,x63063,x63061)))
% 160.93/160.65 [6307]P33(x63071,x63072,x63073)+~P1(f334(x63072,f809(x63073,x63072,x63071)))
% 160.93/160.65 [6308]P33(x63081,x63082,x63083)+~P1(f334(x63082,f810(x63083,x63082,x63081)))
% 160.93/160.65 [6310]E(f179(x63101,x63102,x63103),x63103)+~P1(f334(x63102,f757(x63103,x63102,x63101)))
% 160.93/160.65 [6388]~P1(f334(x63882,f596(x63883,x63882,x63881)))+P1(f334(f262(x63881,x63882),x63883))
% 160.93/160.65 [6389]~P1(f334(x63892,f725(x63893,x63892,x63891)))+P1(f334(f162(x63891,x63892),x63893))
% 160.93/160.65 [6634]~P1(f334(f322(x66341,x66342),f505(x66343,x66342,x66341)))+P1(f334(f322(x66341,x66342),x66343))
% 160.93/160.65 [6635]~P1(f334(f322(x66351,x66352),f525(x66353,x66352,x66351)))+P1(f334(f322(x66351,x66352),x66353))
% 160.93/160.65 [7243]~P58(x72431)+E(f334(f334(f80(x72431),f334(f334(f81(x72431),x72432),f334(f334(f38(x72431),x72433),x72432))),f44(x72431,x72433,x72432)),x72433)
% 160.93/160.65 [7712]E(f334(f334(f269(x77121,x77121),f542(x77122,x77123,x77121)),f542(x77122,x77123,x77121)),x77123)+~P1(f334(f334(f336(f887(x77121,x77121)),x77123),f266(x77121,x77122)))
% 160.93/160.65 [7826]~P1(f334(f334(f336(x78261),f554(x78263,x78262,x78261)),f323(x78261,x78263)))+P1(f334(f334(f336(x78261),x78262),f323(x78261,x78263)))
% 160.93/160.65 [7827]~P1(f334(f334(f336(x78271),f618(x78273,x78272,x78271)),f323(x78271,x78273)))+P1(f334(f334(f336(x78271),x78272),f323(x78271,x78273)))
% 160.93/160.65 [7828]~P1(f334(f334(f336(x78281),f620(x78283,x78282,x78281)),f323(x78281,x78283)))+P1(f334(f334(f336(x78281),x78282),f323(x78281,x78283)))
% 160.93/160.65 [8010]~P58(x80101)+E(f334(f334(f80(x80101),f334(f334(f81(x80101),f334(f334(f38(x80101),x80102),x80103)),x80103)),f44(x80101,x80102,x80103)),x80102)
% 160.93/160.65 [8055]~E(f334(f37(x80551),x80552),f334(a116,x80553))+~P1(f334(f334(f336(x80551),f812(x80553,x80552,x80551)),f782(x80553,x80552,x80551)))
% 160.93/160.65 [8692]P1(f334(f334(f248(f888(f887(x86921,x86921),a876)),f310(x86921,x86922)),f310(x86921,x86923)))+~P1(f334(f334(f248(f888(f887(x86921,x86921),a876)),x86922),f310(x86921,x86923)))
% 160.93/160.65 [8965]E(x89651,f117(x89652))+~P1(f334(f334(f336(f887(f882(x89652),f882(x89652))),f334(f334(f269(f882(x89652),f882(x89652)),x89651),f117(x89652))),f160(x89652,x89653)))
% 160.93/160.65 [8992]E(x89921,f117(x89922))+~P1(f334(f334(f336(f887(f882(x89922),f882(x89922))),f334(f334(f269(f882(x89922),f882(x89922)),f117(x89922)),x89921)),f160(x89922,x89923)))
% 160.93/160.65 [9118]E(f334(f334(f153(x91181),f712(x91182,x91183,x91181)),f713(x91182,x91183,x91181)),x91183)+~P1(f334(f334(f336(f887(f882(x91181),f882(x91181))),f334(f334(f269(f882(x91181),f882(x91181)),f117(x91181)),x91183)),f149(x91181,x91182)))
% 160.93/160.65 [9355]~P123(x93551)+~P1(f334(f334(f249(x93551),f334(f334(f80(x93551),f334(f334(f81(x93551),x93552),x93552)),f334(f334(f81(x93551),x93553),x93553))),f2(x93551)))
% 160.93/160.65 [9404]P1(f334(f61(x94041),x94042))+~P1(f334(f334(f336(f887(f888(x94041,a876),f888(x94041,a876))),f334(f334(f269(f888(x94041,a876),f888(x94041,a876)),x94043),x94042)),f309(x94041)))
% 160.93/160.65 [9698]~P48(x96981,x96982,x96983)+P1(f334(f334(f249(a1),f334(f334(f73(f887(a1,a1),a1,x96981,f268(a1,a1)),f225(x96981)),f236(x96981,x96982,f233(x96981,x96983)))),f2(a1)))
% 160.93/160.65 [9699]~P49(x96991,x96992,x96993)+P1(f334(f334(f248(a1),f334(f334(f73(f887(a1,a1),a1,x96991,f268(a1,a1)),f225(x96991)),f236(x96991,x96992,f233(x96991,x96993)))),f2(a1)))
% 160.93/160.65 [9826]P48(x98261,x98262,x98263)+~P1(f334(f334(f249(a1),f334(f334(f73(f887(a1,a1),a1,x98261,f268(a1,a1)),f225(x98261)),f236(x98261,x98262,f233(x98261,x98263)))),f2(a1)))
% 160.93/160.65 [9827]P49(x98271,x98272,x98273)+~P1(f334(f334(f248(a1),f334(f334(f73(f887(a1,a1),a1,x98271,f268(a1,a1)),f225(x98271)),f236(x98271,x98272,f233(x98271,x98273)))),f2(a1)))
% 160.93/160.65 [10150]~P111(x101501)+~P1(f334(f334(f249(x101501),f334(f334(f80(x101501),f334(f334(f259(x101501),x101502),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x101501),x101503),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))),f2(x101501)))
% 160.93/160.65 [4744]~E(x47443,f117(x47441))+E(f334(f334(f136(x47441),x47442),x47443),x47442)
% 160.93/160.65 [4745]~E(x47452,f117(x47451))+E(f334(f334(f136(x47451),x47452),x47453),x47453)
% 160.93/160.65 [4752]~E(x47522,f2(a881))+E(f334(f334(f177(x47521),x47522),x47523),f117(x47521))
% 160.93/160.65 [4756]~E(x47563,f117(x47561))+E(f334(f334(f177(x47561),x47562),x47563),f117(x47561))
% 160.93/160.65 [4796]~E(x47961,x47963)+E(x47961,f334(f334(f136(x47962),f117(x47962)),x47963))
% 160.93/160.65 [4884]~P101(x48842)+E(f334(f196(f888(x48841,x48842)),x48843),f196(x48842))
% 160.93/160.65 [4885]~P114(x48852)+E(f334(f257(f888(x48851,x48852)),x48853),f257(x48852))
% 160.93/160.65 [4904]E(x49041,f117(x49042))+~E(f334(f334(f136(x49042),x49043),x49041),x49043)
% 160.93/160.65 [4905]E(x49051,f117(x49052))+~E(f334(f334(f136(x49052),x49051),x49053),x49053)
% 160.93/160.65 [4913]E(x49131,f117(x49132))+~E(f334(f334(f136(x49132),x49133),x49131),f117(x49132))
% 160.93/160.65 [4914]E(x49141,f117(x49142))+~E(f334(f334(f136(x49142),x49141),x49143),f117(x49142))
% 160.93/160.65 [4937]~E(x49372,f2(a881))+E(f334(f334(f81(a881),x49371),x49372),f334(f334(f81(a881),x49373),x49372))
% 160.93/160.65 [4939]~E(x49391,f2(a881))+E(f334(f334(f81(a881),x49391),x49392),f334(f334(f81(a881),x49391),x49393))
% 160.93/160.65 [4992]~P2(x49921)+E(f334(f334(f114(x49921),x49922),x49923),f334(f334(f114(x49921),x49923),x49922))
% 160.93/160.65 [4994]~P99(x49941)+E(f334(f334(f114(x49941),x49942),x49943),f334(f334(f114(x49941),x49943),x49942))
% 160.93/160.65 [4995]~P2(x49951)+E(f334(f334(f105(x49951),x49952),x49953),f334(f334(f105(x49951),x49953),x49952))
% 160.93/160.65 [4997]~P100(x49971)+E(f334(f334(f105(x49971),x49972),x49973),f334(f334(f105(x49971),x49973),x49972))
% 160.93/160.65 [4998]~P118(x49981)+E(f334(f334(f80(x49981),x49982),x49983),f334(f334(f80(x49981),x49983),x49982))
% 160.93/160.65 [4999]~P118(x49991)+E(f334(f334(f81(x49991),x49992),x49993),f334(f334(f81(x49991),x49993),x49992))
% 160.93/160.65 [5001]~P108(x50011)+E(f334(f334(f246(x50011),x50012),x50013),f334(f334(f246(x50011),x50013),x50012))
% 160.93/160.65 [5003]~P108(x50031)+E(f334(f334(f247(x50031),x50032),x50033),f334(f334(f247(x50031),x50033),x50032))
% 160.93/160.65 [5064]E(f44(a881,x50641,x50642),f2(a881))+~E(x50641,f334(f334(f81(a881),x50642),x50643))
% 160.93/160.65 [5065]E(f44(a1,x50651,x50652),f2(a1))+~E(x50651,f334(f334(f81(a1),x50652),x50653))
% 160.93/160.65 [5125]E(x51251,x51252)+~E(f334(f334(f80(a881),x51253),x51251),f334(f334(f80(a881),x51253),x51252))
% 160.93/160.65 [5126]E(x51261,x51262)+~E(f334(f334(f80(a881),x51261),x51263),f334(f334(f80(a881),x51262),x51263))
% 160.93/160.65 [5136]~P94(x51361)+E(f334(f334(f105(x51361),x51362),f334(f79(x51361),x51363)),f334(f334(f22(x51361),x51362),x51363))
% 160.93/160.65 [5137]~P66(x51371)+E(f334(f334(f80(x51371),x51372),f334(f79(x51371),x51373)),f334(f334(f22(x51371),x51372),x51373))
% 160.93/160.65 [5138]~P67(x51381)+E(f334(f334(f80(x51381),x51382),f334(f79(x51381),x51383)),f334(f334(f22(x51381),x51382),x51383))
% 160.93/160.65 [5139]~P116(x51391)+E(f334(f334(f80(x51391),x51392),f334(f79(x51391),x51393)),f334(f334(f22(x51391),x51392),x51393))
% 160.93/160.65 [5140]~P66(x51401)+E(f334(f334(f22(x51401),x51402),f334(f79(x51401),x51403)),f334(f334(f80(x51401),x51402),x51403))
% 160.93/160.65 [5186]~P1(f334(x51863,x51862))+P1(f334(f334(f336(x51861),x51862),x51863))
% 160.93/160.65 [5188]~P68(x51882)+E(f334(f334(f6(x51881,x51882),x51883),f196(f888(x51881,a876))),f2(x51882))
% 160.93/160.65 [5190]~P74(x51902)+E(f334(f334(f9(x51901,x51902),x51903),f196(f888(x51901,a876))),f78(x51902))
% 160.93/160.65 [5240]~E(x52402,f334(f334(f80(a881),x52401),x52403))+P1(f334(f334(f248(a881),x52401),x52402))
% 160.93/160.65 [5243]~E(x52432,f196(f888(x52431,a876)))+E(f334(f334(f60(x52431),x52432),x52433),f196(f888(f888(x52431,a876),a876)))
% 160.93/160.65 [5244]~E(x52442,f196(f888(x52441,a876)))+E(f196(f888(f888(x52441,a876),a876)),f334(f334(f60(x52441),x52442),x52443))
% 160.93/160.65 [5317]~E(f334(f265(x53172,x53173),x53171),f196(f888(x53173,a876)))+E(x53171,f196(f888(f887(x53172,x53173),a876)))
% 160.93/160.65 [5318]~E(f334(f267(x53182,x53183),x53181),f196(f888(x53182,a876)))+E(x53181,f196(f888(f887(x53182,x53183),a876)))
% 160.93/160.65 [5348]E(f334(f265(x53481,x53482),x53483),f196(f888(x53482,a876)))+~E(x53483,f196(f888(f887(x53481,x53482),a876)))
% 160.93/160.65 [5349]E(f334(f267(x53491,x53492),x53493),f196(f888(x53491,a876)))+~E(x53493,f196(f888(f887(x53491,x53492),a876)))
% 160.93/160.65 [5352]E(f284(x53521,x53522,x53523),f334(f334(f22(a103),x53522),x53523))+P1(f334(f334(f249(a103),x53522),x53523))
% 160.93/160.65 [5368]P1(f334(x53681,x53682))+~P1(f334(f334(f336(x53683),x53682),x53681))
% 160.93/160.65 [5407]E(x54071,x54072)+~E(f334(f79(f888(x54073,a876)),x54071),f334(f79(f888(x54073,a876)),x54072))
% 160.93/160.65 [5412]E(f316(x54121,x54122,x54123),f210(f882(a330)))+~P1(f334(f334(f249(a1),x54122),x54123))
% 160.93/160.65 [5417]~E(x54171,f196(f888(x54172,a876)))+~P1(f334(f334(f336(x54172),x54173),x54171))
% 160.93/160.65 [5446]~E(x54462,f334(f334(f80(a1),x54461),f334(f104(a1),x54463)))+P1(f334(f334(f248(a1),x54461),x54462))
% 160.93/160.65 [5462]E(f334(f334(f312(x54621),x54622),x54623),x54623)+~P1(f334(f334(f336(x54621),x54622),x54623))
% 160.93/160.65 [5473]E(x54731,f196(f888(x54732,a876)))+~E(f334(f334(f60(x54732),x54731),x54733),f196(f888(f888(x54732,a876),a876)))
% 160.93/160.65 [5474]E(x54741,f196(f888(x54742,a876)))+~E(f196(f888(f888(x54742,a876),a876)),f334(f334(f60(x54742),x54741),x54743))
% 160.93/160.65 [5481]~P105(x54811)+E(f334(f334(f81(x54811),f334(f79(x54811),x54812)),f334(f79(x54811),x54813)),f334(f334(f81(x54811),x54812),x54813))
% 160.93/160.65 [5482]~P61(x54821)+E(f334(f334(f292(x54821),f334(f79(x54821),x54822)),f334(f79(x54821),x54823)),f334(f334(f292(x54821),x54822),x54823))
% 160.93/160.65 [5514]~P1(f334(x55143,x55142))+P1(f334(f334(f336(x55141),x55142),f334(f254(x55141),x55143)))
% 160.93/160.65 [5552]E(f172(x55521,x55522,x55523),x55523)+P1(f334(f334(f336(x55521),x55522),f334(f174(x55521),x55523)))
% 160.93/160.65 [5634]~P1(f334(f139(x56341),x56343))+P1(f334(f139(x56341),f334(f138(x56341,x56342),x56343)))
% 160.93/160.65 [5679]~P58(x56791)+E(f334(f334(f38(x56791),f44(x56791,x56792,x56793)),x56793),f2(x56791))
% 160.93/160.65 [5698]E(f178(x56981,f334(f334(f153(x56981),x56982),f117(x56981)),x56983),f117(x56981))+P1(f334(f334(f336(a881),f2(a881)),x56983))
% 160.93/160.65 [5755]E(f334(f334(f153(x57551),x57552),x57553),f142(x57551,x57552,x57553))+P1(f334(f334(f336(x57551),x57552),f334(f174(x57551),x57553)))
% 160.93/160.65 [5764]E(x57641,x57642)+~E(f334(f334(f81(a881),f334(a116,x57643)),x57641),f334(f334(f81(a881),f334(a116,x57643)),x57642))
% 160.93/160.65 [5765]~E(x57652,f334(f334(f80(a1),x57651),f334(f104(a1),f334(a116,x57653))))+P1(f334(f334(f249(a1),x57651),x57652))
% 160.93/160.65 [5870]~E(x58703,f117(x58701))+E(f334(f334(f334(f191(f882(x58701),f882(x58701)),x58702),f170(x58701)),x58703),f117(x58701))
% 160.93/160.65 [5874]P1(f334(x58741,x58742))+~P1(f334(f334(f336(x58743),x58742),f334(f254(x58743),x58741)))
% 160.93/160.65 [5906]E(x59061,x59062)+~E(f334(f334(f312(x59063),x59061),f196(f888(x59063,a876))),f334(f334(f312(x59063),x59062),f196(f888(x59063,a876))))
% 160.93/160.65 [5917]~P109(x59171)+E(f334(f334(f105(f888(x59171,a876)),f334(f255(x59171),x59172)),f334(f304(x59171,x59172),x59173)),f196(f888(x59171,a876)))
% 160.93/160.65 [5959]E(f142(x59591,x59592,x59593),x59593)+~P1(f334(f334(f336(x59591),x59592),f334(f174(x59591),x59593)))
% 160.93/160.65 [5980]~P83(x59801)+E(f334(f313(x59801,x59801,f79(x59801)),f334(f304(x59801,x59802),x59803)),f307(x59801,f334(f79(x59801),x59803),f334(f79(x59801),x59802)))
% 160.93/160.65 [5989]E(f334(f197(f882(x59891)),f172(x59891,x59892,x59893)),f334(f197(f882(x59891)),x59893))+P1(f334(f334(f336(x59891),x59892),f334(f174(x59891),x59893)))
% 160.93/160.65 [6041]~P109(x60411)+E(f334(f334(f105(f888(x60411,a876)),f334(f304(x60411,x60412),x60413)),f334(f256(x60411),x60413)),f196(f888(x60411,a876)))
% 160.93/160.65 [6064]~P83(x60641)+E(f334(f313(x60641,x60641,f79(x60641)),f305(x60641,x60642,x60643)),f305(x60641,f334(f79(x60641),x60643),f334(f79(x60641),x60642)))
% 160.93/160.65 [6065]~P83(x60651)+E(f334(f313(x60651,x60651,f79(x60651)),f308(x60651,x60652,x60653)),f308(x60651,f334(f79(x60651),x60653),f334(f79(x60651),x60652)))
% 160.93/160.65 [6122]E(f178(x61221,f334(f334(f153(x61221),x61222),f117(x61221)),x61223),f334(f334(f153(x61221),x61222),f117(x61221)))+~P1(f334(f334(f336(a881),f2(a881)),x61223))
% 160.93/160.65 [6129]~P83(x61291)+E(f334(f313(x61291,x61291,f79(x61291)),f307(x61291,x61292,x61293)),f334(f304(x61291,f334(f79(x61291),x61293)),f334(f79(x61291),x61292)))
% 160.93/160.65 [6149]~P59(x61491)+E(f44(x61491,f334(f79(x61491),f44(x61491,x61492,x61493)),x61493),f44(x61491,f334(f79(x61491),x61492),x61493))
% 160.93/160.65 [6256]~P1(f334(f61(f887(x62562,x62561)),x62563))+P1(f334(f61(x62561),f334(f265(x62562,x62561),x62563)))
% 160.93/160.65 [6257]~P1(f334(f61(f887(x62571,x62572)),x62573))+P1(f334(f61(x62571),f334(f267(x62571,x62572),x62573)))
% 160.93/160.65 [6263]~P109(x62631)+E(f334(f334(f105(f888(x62631,a876)),f305(x62631,x62632,x62633)),f334(f306(x62631),x62633)),f196(f888(x62631,a876)))
% 160.93/160.65 [6264]~P109(x62641)+E(f334(f334(f105(f888(x62641,a876)),f308(x62641,x62642,x62643)),f334(f256(x62641),x62643)),f196(f888(x62641,a876)))
% 160.93/160.65 [6265]~P109(x62651)+E(f334(f334(f105(f888(x62651,a876)),f307(x62651,x62652,x62653)),f334(f306(x62651),x62653)),f196(f888(x62651,a876)))
% 160.93/160.65 [6331]E(f334(f334(f167(x63311),x63312),f655(x63312,x63313,x63311)),x63313)+~P1(f334(f334(f336(x63311),x63313),f334(f174(x63311),x63312)))
% 160.93/160.65 [6470]E(x64701,f117(x64702))+~E(f334(f334(f334(f191(f882(x64702),f882(x64702)),x64703),f170(x64702)),x64701),f117(x64702))
% 160.93/160.65 [6571]~P1(f334(f61(f887(x65712,x65711)),x65713))+P1(f334(f61(f887(x65711,x65712)),f334(f289(x65712,x65711),x65713)))
% 160.93/160.65 [6723]P53(x67231,x67232,x67233)+P1(f334(f334(f336(x67231),f630(x67233,x67232,x67231)),x67232))
% 160.93/160.65 [6724]P53(x67241,x67242,x67243)+P1(f334(f334(f336(x67241),f629(x67243,x67242,x67241)),x67242))
% 160.93/160.65 [6736]P1(f334(f322(x67361,x67362),x67363))+P1(f334(f334(x67362,f505(x67363,x67362,x67361)),x67363))
% 160.93/160.65 [6737]P1(f334(f322(x67371,x67372),x67373))+P1(f334(f334(x67372,f525(x67373,x67372,x67371)),x67373))
% 160.93/160.65 [6768]E(f334(f197(f882(x67681)),f172(x67681,x67682,x67683)),f334(f334(f22(a881),f334(f197(f882(x67681)),x67683)),f78(a881)))+~P1(f334(f334(f336(x67681),x67682),f334(f174(x67681),x67683)))
% 160.93/160.65 [6808]P1(f334(f262(x68081,x68082),x68083))+P1(f334(f334(f336(x68081),f596(x68083,x68082,x68081)),x68083))
% 160.93/160.65 [6818]~P1(f334(f61(f887(x68182,x68181)),f334(f289(x68181,x68182),x68183)))+P1(f334(f61(f887(x68181,x68182)),x68183))
% 160.93/160.65 [6875]~P1(f334(f334(f336(x68751),x68752),f334(f174(x68751),f118(x68751,x68753))))+P1(f334(f334(f336(x68751),x68752),f334(f174(x68751),x68753)))
% 160.93/160.65 [6880]P30(x68801,x68802,x68803)+P1(f334(f334(f336(f880(x68801)),f604(x68803,x68802,x68801)),x68803))
% 160.93/160.65 [6908]E(f334(f138(x69081,x69082),x69083),x69083)+P1(f334(f334(f336(x69081),f736(x69083,x69082,x69081)),f334(f174(x69081),x69083)))
% 160.93/160.65 [6923]E(f334(f138(x69231,x69232),x69233),f117(x69231))+P1(f334(f334(f336(x69231),f735(x69233,x69232,x69231)),f334(f174(x69231),x69233)))
% 160.93/160.65 [6946]P33(x69461,x69462,x69463)+P1(f334(f334(f336(x69461),f809(x69463,x69462,x69461)),f334(f174(x69461),x69463)))
% 160.93/160.65 [6947]P33(x69471,x69472,x69473)+P1(f334(f334(f336(x69471),f810(x69473,x69472,x69471)),f334(f174(x69471),x69473)))
% 160.93/160.65 [6948]P33(x69481,x69482,x69483)+P1(f334(f334(f336(x69481),f806(x69482,x69483,x69481)),f334(f174(x69481),x69483)))
% 160.93/160.65 [6951]E(f179(x69511,x69512,x69513),x69513)+P1(f334(f334(f336(x69511),f757(x69513,x69512,x69511)),f334(f174(x69511),x69513)))
% 160.93/160.65 [7030]P1(f334(f162(x70301,x70302),x70303))+P1(f334(f334(f336(x70301),f725(x70303,x70302,x70301)),f334(f174(x70301),x70303)))
% 160.93/160.65 [7039]~P35(x70391,x70393,x70392)+P1(f334(f334(f336(x70391),f785(x70392,x70393,x70391)),f334(f174(x70391),x70392)))
% 160.93/160.65 [7040]~P37(x70401,x70403,x70402)+P1(f334(f334(f336(x70401),f811(x70402,x70403,x70401)),f334(f174(x70401),x70402)))
% 160.93/160.65 [7075]P1(f334(f334(f336(x70751),x70752),f657(x70753,x70752,x70751)))+~P1(f334(f334(f336(x70751),x70752),f39(f888(x70751,a876),x70753)))
% 160.93/160.65 [7076]~P68(x70761)+E(f334(f334(f80(x70761),f334(f334(f6(a881,x70761),x70762),f334(f255(a881),x70763))),f334(x70762,x70763)),f334(f334(f6(a881,x70761),x70762),f334(f255(a881),f334(a116,x70763))))
% 160.93/160.65 [7165]~P35(x71652,x71651,x71653)+P1(f334(x71651,f334(f334(f167(x71652),x71653),f797(x71653,x71651,x71652))))
% 160.93/160.65 [7178]~P1(f334(f334(f336(x71781),x71782),f506(x71782,x71783,x71781)))+P1(f334(f334(f336(x71781),x71782),f40(f888(x71781,a876),x71783)))
% 160.93/160.65 [7210]~P68(x72101)+E(f334(f334(f80(x72101),f334(f334(f6(a881,x72101),x72102),f334(f303(a881),x72103))),f334(x72102,f334(a116,x72103))),f334(f334(f6(a881,x72101),x72102),f334(f303(a881),f334(a116,x72103))))
% 160.93/160.65 [7345]P1(f334(f334(f336(f882(x73451)),x73452),f163(x73451,x73453)))+P1(f334(f334(f336(x73451),f680(x73453,x73452,x73451)),f334(f174(x73451),x73452)))
% 160.93/160.65 [7362]~P1(f334(f334(f336(f882(x73621)),x73622),f163(x73621,f323(x73621,x73623))))+P1(f334(f334(f336(f882(x73621)),x73622),f323(f882(x73621),f159(x73621,x73623))))
% 160.93/160.65 [7387]~P1(f334(f334(f336(f882(x73871)),x73872),f323(f882(x73871),f159(x73871,x73873))))+P1(f334(f334(f336(f882(x73871)),x73872),f163(x73871,f323(x73871,x73873))))
% 160.93/160.65 [7423]E(f334(f334(f334(f191(f882(x74231),f882(x74231)),x74232),f170(x74231)),x74233),x74233)+~P1(f334(f334(f248(a881),f334(f197(f882(x74231)),x74233)),f78(a881)))
% 160.93/160.65 [7458]E(f334(f334(f136(x74581),f802(x74582,x74583,x74581)),f334(f334(f153(x74581),x74583),f803(x74582,x74583,x74581))),x74582)+~P1(f334(f334(f336(x74581),x74583),f334(f174(x74581),x74582)))
% 160.93/160.65 [7459]E(f334(f334(f136(x74591),f798(x74592,x74593,x74591)),f334(f334(f153(x74591),x74593),f799(x74592,x74593,x74591))),x74592)+~P1(f334(f334(f336(x74591),x74593),f334(f174(x74591),x74592)))
% 160.93/160.65 [7460]E(f334(f334(f136(x74601),f804(x74602,x74603,x74601)),f334(f334(f153(x74601),x74603),f805(x74602,x74603,x74601))),x74602)+~P1(f334(f334(f336(x74601),x74603),f334(f174(x74601),x74602)))
% 160.93/160.65 [7484]~P27(x74841,x74842,x74843,f257(f888(x74841,a876)))+P27(f882(x74841),f882(x74842),f334(f156(x74841,x74842),x74843),f257(f888(f882(x74841),a876)))
% 160.93/160.65 [7635]E(x76351,f334(f334(f80(a881),f334(f334(f81(a881),f334(f268(a881,a881),x76352)),x76353)),f334(f272(a881,a881),x76352)))+~P1(f334(f47(x76351,x76353),x76352))
% 160.93/160.65 [7643]P27(x76431,x76432,x76433,f257(f888(x76431,a876)))+~P27(f882(x76431),f882(x76432),f334(f156(x76431,x76432),x76433),f257(f888(f882(x76431),a876)))
% 160.93/160.65 [7684]P1(f334(f334(f336(f888(x76841,a876)),f506(x76842,x76843,x76841)),x76843))+P1(f334(f334(f336(x76841),x76842),f40(f888(x76841,a876),x76843)))
% 160.93/160.65 [7774]P1(f334(f334(f336(f882(x77741)),x77742),f163(x77741,x77743)))+~P1(f334(f334(f336(x77741),f680(x77743,x77742,x77741)),x77743))
% 160.93/160.65 [7815]P1(f334(f334(f334(f334(a204,x78151),x78152),f464(x78153,x78152,x78151)),x78153))+~P1(f334(f334(f334(a202,x78151),x78152),x78153))
% 160.93/160.65 [7875]P33(x78751,x78752,x78753)+~P1(f334(x78752,f334(f334(f167(x78751),x78753),f801(x78753,x78752,x78751))))
% 160.93/160.65 [7900]E(x79001,x79002)+~E(f334(f334(f7(x79003,f888(x79003,a876),a876),f336(x79003)),x79001),f334(f334(f7(x79003,f888(x79003,a876),a876),f336(x79003)),x79002))
% 160.93/160.65 [7906]~P1(f334(f334(f336(f887(x79061,x79061)),x79063),f266(x79061,x79062)))+P1(f334(f334(f336(x79061),f542(x79062,x79063,x79061)),x79062))
% 160.93/160.65 [7908]~P1(f334(f334(f336(x79081),x79083),f39(f888(x79081,a876),x79082)))+P1(f334(f334(f336(f888(x79081,a876)),f657(x79082,x79083,x79081)),x79082))
% 160.93/160.65 [8083]~P1(f334(f334(f336(x80831),x80832),f334(f174(x80831),f798(x80833,x80832,x80831))))+~P1(f334(f334(f336(x80831),x80832),f334(f174(x80831),x80833)))
% 160.93/160.65 [8084]~P1(f334(f334(f336(x80841),x80842),f334(f174(x80841),f805(x80843,x80842,x80841))))+~P1(f334(f334(f336(x80841),x80842),f334(f174(x80841),x80843)))
% 160.93/160.65 [8178]E(f334(f243(f885(f882(a330)),f882(a330),f316(x81781,x81782,f334(f334(f80(a1),x81783),f78(a1))),f241(f882(a330))),f334(x81781,x81783)),f316(x81781,x81782,x81783))+P1(f334(f334(f249(a1),x81782),x81783))
% 160.93/160.65 [8285]E(x82851,f117(x82852))+P1(f334(f334(f336(x82852),f334(f268(x82852,f887(a103,a103)),f334(f285(x82852,x82851),x82853))),f334(f174(x82852),x82851)))
% 160.93/160.65 [8382]~P69(x83821)+E(f334(f144(x83821,x83821,f334(f7(x83821,x83821,x83821),f80(x83821)),x83822),f334(f171(x83821),x83823)),f334(f144(x83821,x83821,f80(x83821),x83822),x83823))
% 160.93/160.65 [8875]~P108(x88751)+E(f334(f174(x88751),f151(x88751,x88751,f5(x88751),x88752,x88753)),f334(f334(f312(x88751),x88752),f334(f174(x88751),x88753)))
% 160.93/160.65 [8886]P1(f334(f334(f249(a881),f2(a881)),f637(x88861,x88862,x88863)))+~P1(f334(f334(f336(f887(x88863,x88863)),x88862),f334(f334(f291(x88863,x88863,x88863),x88861),f310(x88863,x88861))))
% 160.93/160.65 [9178]~P55(x91781,x91782)+~P1(f334(f334(f336(f887(x91781,x91781)),f334(f334(f269(x91781,x91781),x91783),x91783)),f334(f334(f291(x91781,x91781,x91781),x91782),f310(x91781,x91782))))
% 160.93/160.65 [9310]~E(f334(f334(f105(f888(f887(x93101,x93101),a876)),f334(f289(x93101,x93101),x93102)),f310(x93101,x93102)),f196(f888(f887(x93101,x93101),a876)))+~P1(f334(f334(f336(f887(x93101,x93101)),f334(f334(f269(x93101,x93101),x93103),x93103)),f334(f334(f291(x93101,x93101,x93101),x93102),f310(x93101,x93102))))
% 160.93/160.65 [9489]~P1(f334(f61(x94891),x94892))+P1(f334(f334(f248(a881),f334(f37(x94891),f334(f334(f22(f888(x94891,a876)),x94892),f334(f334(f312(x94891),x94893),f196(f888(x94891,a876)))))),f334(f37(x94891),x94892)))
% 160.93/160.65 [5053]~E(x50533,f117(x50531))+E(f146(x50531,f334(f334(f153(x50531),x50532),x50533)),x50532)
% 160.93/160.65 [5061]~E(x50613,f117(x50611))+E(f118(x50611,f334(f334(f153(x50611),x50612),x50613)),f117(x50611))
% 160.93/160.65 [5089]E(x50891,f117(x50892))+E(f146(x50892,f334(f334(f153(x50892),x50893),x50891)),f146(x50892,x50891))
% 160.93/160.65 [5091]E(x50911,f117(x50912))+E(f146(x50912,f334(f334(f136(x50912),x50913),x50911)),f146(x50912,x50911))
% 160.93/160.65 [5096]~E(x50963,f117(x50961))+E(f118(x50961,f334(f334(f136(x50961),x50962),x50963)),f118(x50961,x50962))
% 160.93/160.65 [5098]~E(x50983,f117(x50981))+E(f146(x50981,f334(f334(f136(x50981),x50982),x50983)),f146(x50981,x50982))
% 160.93/160.65 [5130]E(x51301,f117(x51302))+E(f334(f143(x51302),f334(f334(f136(x51302),x51301),x51303)),f334(f143(x51302),x51301))
% 160.93/160.65 [5160]~E(x51602,f117(x51601))+E(f334(f143(x51601),f334(f334(f136(x51601),x51602),x51603)),f334(f143(x51601),x51603))
% 160.93/160.65 [5215]~P2(x52151)+E(f334(f334(f114(x52151),x52152),f334(f334(f105(x52151),x52152),x52153)),x52152)
% 160.93/160.65 [5216]~P2(x52161)+E(f334(f334(f105(x52161),x52162),f334(f334(f114(x52161),x52162),x52163)),x52162)
% 160.93/160.65 [5217]~P108(x52171)+E(f334(f334(f246(x52171),x52172),f334(f334(f247(x52171),x52172),x52173)),x52172)
% 160.93/160.65 [5218]~P108(x52181)+E(f334(f334(f247(x52181),x52182),f334(f334(f246(x52181),x52182),x52183)),x52182)
% 160.93/160.65 [5238]~P58(x52381)+E(f44(x52381,f334(f334(f81(x52381),x52382),x52383),x52383),f2(x52381))
% 160.93/160.65 [5239]~P58(x52391)+E(f44(x52391,f334(f334(f81(x52391),x52392),x52393),x52392),f2(x52391))
% 160.93/160.65 [5311]~P67(x53111)+E(f334(f79(x53111),f334(f334(f22(x53111),x53112),x53113)),f334(f334(f22(x53111),x53113),x53112))
% 160.93/160.65 [5372]E(x53721,f117(x53722))+E(f118(x53722,f334(f334(f153(x53722),x53723),x53721)),f334(f334(f153(x53722),x53723),f118(x53722,x53721)))
% 160.93/160.65 [5373]E(x53731,f117(x53732))+E(f118(x53732,f334(f334(f136(x53732),x53733),x53731)),f334(f334(f136(x53732),x53733),f118(x53732,x53731)))
% 160.93/160.65 [5376]~P5(x53761)+E(f39(x53761,f334(f334(f312(x53761),x53762),x53763)),f334(f334(f114(x53761),x53762),f39(x53761,x53763)))
% 160.93/160.65 [5377]~P5(x53771)+E(f40(x53771,f334(f334(f312(x53771),x53772),x53773)),f334(f334(f105(x53771),x53772),f40(x53771,x53773)))
% 160.93/160.65 [5422]~P2(x54221)+E(f334(f334(f114(x54221),x54222),f334(f334(f114(x54221),x54222),x54223)),f334(f334(f114(x54221),x54222),x54223))
% 160.93/160.65 [5424]~P99(x54241)+E(f334(f334(f114(x54241),x54242),f334(f334(f114(x54241),x54242),x54243)),f334(f334(f114(x54241),x54242),x54243))
% 160.93/160.65 [5425]~P2(x54251)+E(f334(f334(f105(x54251),x54252),f334(f334(f105(x54251),x54252),x54253)),f334(f334(f105(x54251),x54252),x54253))
% 160.93/160.65 [5427]~P100(x54271)+E(f334(f334(f105(x54271),x54272),f334(f334(f105(x54271),x54272),x54273)),f334(f334(f105(x54271),x54272),x54273))
% 160.93/160.65 [5428]~P95(x54281)+E(f334(f334(f81(x54281),x54282),f334(f334(f81(x54281),x54282),x54283)),f334(f334(f81(x54281),x54282),x54283))
% 160.93/160.65 [5430]~P108(x54301)+E(f334(f334(f246(x54301),x54302),f334(f334(f246(x54301),x54302),x54303)),f334(f334(f246(x54301),x54302),x54303))
% 160.93/160.65 [5432]~P108(x54321)+E(f334(f334(f247(x54321),x54322),f334(f334(f247(x54321),x54322),x54323)),f334(f334(f247(x54321),x54322),x54323))
% 160.93/160.65 [5440]~P58(x54401)+E(f44(x54401,f334(f334(f80(x54401),x54402),x54403),x54403),f44(x54401,x54402,x54403))
% 160.93/160.65 [5441]~P58(x54411)+E(f44(x54411,f334(f334(f80(x54411),x54412),x54413),x54412),f44(x54411,x54413,x54412))
% 160.93/160.65 [5447]~P105(x54471)+E(f334(f334(f81(x54471),x54472),f334(f79(x54471),x54473)),f334(f79(x54471),f334(f334(f81(x54471),x54472),x54473)))
% 160.93/160.65 [5448]~P61(x54481)+E(f334(f334(f292(x54481),x54482),f334(f79(x54481),x54483)),f334(f79(x54481),f334(f334(f292(x54481),x54482),x54483)))
% 160.93/160.65 [5449]~P79(x54491)+E(f334(f334(f80(x54491),x54492),f334(f168(x54491),x54493)),f334(f168(x54491),f334(f334(f153(x54491),x54492),x54493)))
% 160.93/160.65 [5479]~P105(x54791)+E(f334(f334(f81(x54791),f334(f79(x54791),x54792)),x54793),f334(f334(f81(x54791),x54792),f334(f79(x54791),x54793)))
% 160.93/160.65 [5485]~P8(x54851,x54852,x54853)+E(f39(f888(x54851,a876),f334(f334(f60(x54851),x54852),x54853)),x54852)
% 160.93/160.65 [5544]~P113(x55441)+E(f334(f334(f81(x55441),x55442),f334(f334(f259(x55441),x55442),x55443)),f334(f334(f259(x55441),x55442),f334(a116,x55443)))
% 160.93/160.65 [5545]~P118(x55451)+E(f334(f334(f81(x55451),x55452),f334(f334(f259(x55451),x55452),x55453)),f334(f334(f259(x55451),x55452),f334(a116,x55453)))
% 160.93/160.65 [5555]~P66(x55551)+E(f334(f334(f80(x55551),f334(f79(x55551),x55552)),f334(f334(f80(x55551),x55552),x55553)),x55553)
% 160.93/160.65 [5578]~P142(x55781)+E(f334(f334(f259(x55781),f334(f104(x55781),x55782)),x55783),f334(f104(x55781),f334(f334(f259(a881),x55782),x55783)))
% 160.93/160.65 [5579]~P139(x55791)+E(f334(f334(f259(x55791),f334(f106(x55791),x55792)),x55793),f334(f106(x55791),f334(f334(f259(a1),x55792),x55793)))
% 160.93/160.65 [5584]~P85(x55841)+E(f334(f75(x55841),f334(f334(f22(x55841),x55842),x55843)),f334(f75(x55841),f334(f334(f22(x55841),x55843),x55842)))
% 160.93/160.65 [5586]~P111(x55861)+E(f334(f334(f81(x55861),f82(x55861,x55862)),f82(x55861,x55863)),f82(x55861,f334(f334(f81(x55861),x55862),x55863)))
% 160.93/160.65 [5590]E(x55901,f117(x55902))+E(f334(f334(f136(x55902),f334(f173(x55902),x55901)),x55903),f334(f173(x55902),f334(f334(f136(x55902),x55901),x55903)))
% 160.93/160.65 [5596]~E(x55962,f334(a116,f334(f334(f80(a881),x55961),x55963)))+P1(f334(f334(f249(a881),x55961),x55962))
% 160.93/160.65 [5597]~P111(x55971)+E(f334(f334(f259(x55971),f334(f75(x55971),x55972)),x55973),f334(f75(x55971),f334(f334(f259(x55971),x55972),x55973)))
% 160.93/160.65 [5598]~P105(x55981)+E(f334(f334(f81(x55981),f334(f79(x55981),x55982)),x55983),f334(f79(x55981),f334(f334(f81(x55981),x55982),x55983)))
% 160.93/160.65 [5599]~P120(x55991)+E(f334(f334(f292(x55991),f334(f79(x55991),x55992)),x55993),f334(f79(x55991),f334(f334(f292(x55991),x55992),x55993)))
% 160.93/160.65 [5697]E(f690(x56971,x56972,x56973),f696(x56971,x56972,x56973))+E(f334(f334(f105(f888(x56973,a876)),x56972),x56971),f196(f888(x56973,a876)))
% 160.93/160.65 [5711]~P68(x57112)+E(f334(f334(f6(x57111,x57112),f334(f16(x57112,x57111),f2(x57112))),x57113),f2(x57112))
% 160.93/160.65 [5712]~P74(x57122)+E(f334(f334(f9(x57121,x57122),f334(f16(x57122,x57121),f78(x57122))),x57123),f78(x57122))
% 160.93/160.65 [5714]~P142(x57141)+E(f334(f334(f80(x57141),f334(f104(x57141),x57142)),f334(f104(x57141),x57143)),f334(f104(x57141),f334(f334(f80(a881),x57142),x57143)))
% 160.93/160.65 [5715]~P142(x57151)+E(f334(f334(f81(x57151),f334(f104(x57151),x57152)),f334(f104(x57151),x57153)),f334(f104(x57151),f334(f334(f81(a881),x57152),x57153)))
% 160.93/160.65 [5716]~P139(x57161)+E(f334(f334(f22(x57161),f334(f106(x57161),x57162)),f334(f106(x57161),x57163)),f334(f106(x57161),f334(f334(f22(a1),x57162),x57163)))
% 160.93/160.65 [5717]~P139(x57171)+E(f334(f334(f80(x57171),f334(f106(x57171),x57172)),f334(f106(x57171),x57173)),f334(f106(x57171),f334(f334(f80(a1),x57172),x57173)))
% 160.93/160.65 [5718]~P139(x57181)+E(f334(f334(f81(x57181),f334(f106(x57181),x57182)),f334(f106(x57181),x57183)),f334(f106(x57181),f334(f334(f81(a1),x57182),x57183)))
% 160.93/160.65 [5719]~P93(x57191)+E(f334(f334(f22(x57191),f334(f107(x57191),x57192)),f334(f107(x57191),x57193)),f334(f107(x57191),f334(f334(f22(a1),x57192),x57193)))
% 160.93/160.65 [5722]~P93(x57221)+E(f334(f334(f80(x57221),f334(f107(x57221),x57222)),f334(f107(x57221),x57223)),f334(f107(x57221),f334(f334(f80(a1),x57222),x57223)))
% 160.93/160.65 [5723]~P93(x57231)+E(f334(f334(f81(x57231),f334(f107(x57231),x57232)),f334(f107(x57231),x57233)),f334(f107(x57231),f334(f334(f81(a1),x57232),x57233)))
% 160.93/160.65 [5772]~E(x57723,x57722)+P1(f334(f334(f248(f888(x57721,a876)),x57722),x57723))
% 160.93/160.65 [5778]~E(x57782,x57783)+P1(f334(f334(f248(f888(x57781,a876)),x57782),x57783))
% 160.93/160.65 [5783]~P111(x57831)+E(f334(f334(f81(x57831),f334(f75(x57831),x57832)),f334(f75(x57831),x57833)),f334(f75(x57831),f334(f334(f81(x57831),x57832),x57833)))
% 160.93/160.65 [5784]~P63(x57841)+E(f334(f334(f292(x57841),f334(f75(x57841),x57842)),f334(f75(x57841),x57843)),f334(f75(x57841),f334(f334(f292(x57841),x57842),x57843)))
% 160.93/160.65 [5785]~P94(x57851)+E(f334(f334(f105(x57851),f334(f79(x57851),x57852)),f334(f79(x57851),x57853)),f334(f79(x57851),f334(f334(f114(x57851),x57852),x57853)))
% 160.93/160.65 [5786]~P94(x57861)+E(f334(f334(f114(x57861),f334(f79(x57861),x57862)),f334(f79(x57861),x57863)),f334(f79(x57861),f334(f334(f105(x57861),x57862),x57863)))
% 160.93/160.65 [5787]~P66(x57871)+E(f334(f334(f80(x57871),f334(f79(x57871),x57872)),f334(f79(x57871),x57873)),f334(f79(x57871),f334(f334(f80(x57871),x57873),x57872)))
% 160.93/160.65 [5788]~P67(x57881)+E(f334(f334(f80(x57881),f334(f79(x57881),x57882)),f334(f79(x57881),x57883)),f334(f79(x57881),f334(f334(f80(x57881),x57882),x57883)))
% 160.93/160.65 [5789]~P75(x57891)+E(f334(f334(f247(x57891),f334(f79(x57891),x57892)),f334(f79(x57891),x57893)),f334(f79(x57891),f334(f334(f246(x57891),x57892),x57893)))
% 160.93/160.65 [5790]~P75(x57901)+E(f334(f334(f246(x57901),f334(f79(x57901),x57902)),f334(f79(x57901),x57903)),f334(f79(x57901),f334(f334(f247(x57901),x57902),x57903)))
% 160.93/160.65 [5791]~P79(x57911)+E(f334(f334(f80(x57911),f334(f168(x57911),x57912)),f334(f168(x57911),x57913)),f334(f168(x57911),f334(f334(f136(x57911),x57912),x57913)))
% 160.93/160.65 [5792]E(x57921,f196(f888(x57922,a876)))+~E(f334(f334(f114(f888(x57922,a876)),x57923),x57921),f196(f888(x57922,a876)))
% 160.93/160.65 [5793]E(x57931,f196(f888(x57932,a876)))+~E(f334(f334(f114(f888(x57932,a876)),x57931),x57933),f196(f888(x57932,a876)))
% 160.93/160.65 [5794]~P146(x57941,x57942,x57943)+P1(f334(x57941,f334(f334(f38(a1),x57942),x57943)))
% 160.93/160.65 [5844]~P1(f334(f61(x58441),x58443))+P1(f334(f61(x58441),f334(f334(f312(x58441),x58442),x58443)))
% 160.93/160.65 [5845]~P1(f334(f139(x58451),x58453))+P1(f334(f139(x58451),f334(f334(f177(x58451),x58452),x58453)))
% 160.93/160.65 [5846]~P1(f334(f139(x58461),x58463))+P1(f334(f139(x58461),f334(f334(f140(x58461),x58462),x58463)))
% 160.93/160.65 [5875]~P2(x58751)+P1(f334(f334(f248(x58751),x58752),f334(f334(f114(x58751),x58753),x58752)))
% 160.93/160.65 [5876]~P99(x58761)+P1(f334(f334(f248(x58761),x58762),f334(f334(f114(x58761),x58763),x58762)))
% 160.93/160.65 [5877]~P2(x58771)+P1(f334(f334(f248(x58771),x58772),f334(f334(f114(x58771),x58772),x58773)))
% 160.93/160.65 [5878]~P99(x58781)+P1(f334(f334(f248(x58781),x58782),f334(f334(f114(x58781),x58782),x58783)))
% 160.93/160.65 [5879]~P108(x58791)+P1(f334(f334(f248(x58791),x58792),f334(f334(f247(x58791),x58793),x58792)))
% 160.93/160.65 [5880]~P108(x58801)+P1(f334(f334(f248(x58801),x58802),f334(f334(f247(x58801),x58802),x58803)))
% 160.93/160.65 [5894]~E(x58941,f2(a881))+E(f334(f334(f38(a881),f334(f334(f81(a881),x58941),x58942)),f334(f334(f81(a881),x58941),x58943)),f2(a881))
% 160.93/160.65 [5975]~P93(x59751)+E(f334(f334(f22(x59751),f334(f107(x59751),x59752)),f334(f107(x59751),x59753)),f334(f107(x59751),f334(f334(f80(a1),x59752),f334(f79(a1),x59753))))
% 160.93/160.65 [6028]E(x60281,f2(a881))+E(f334(f334(f38(a881),f334(f334(f81(a881),x60281),x60282)),f334(f334(f81(a881),x60281),x60283)),f334(f334(f38(a881),x60282),x60283))
% 160.93/160.65 [6062]E(f154(x60621,f334(f334(f153(x60621),x60622),x60623)),f334(f334(f153(x60621),x60622),f154(x60621,x60623)))+P1(f334(f334(f336(x60621),x60622),f334(f174(x60621),x60623)))
% 160.93/160.65 [6096]P146(x60961,x60962,x60963)+~P1(f334(x60961,f334(f334(f38(a1),x60962),x60963)))
% 160.93/160.65 [6171]E(x61711,f117(x61712))+E(f334(f334(f153(x61712),f334(f143(x61712),x61711)),f334(f334(f177(x61712),x61713),f334(f173(x61712),x61711))),f334(f334(f177(x61712),f334(a116,x61713)),x61711))
% 160.93/160.65 [6176]P1(f334(x61761,x61762))+P1(f334(f334(f334(a202,f32(x61761,x61763)),x61762),x61762))
% 160.93/160.65 [6180]E(f334(f334(f22(f888(x61801,a876)),x61802),x61803),x61802)+~E(f334(f334(f105(f888(x61801,a876)),x61802),x61803),f196(f888(x61801,a876)))
% 160.93/160.65 [6194]E(f154(x61941,f334(f334(f153(x61941),x61942),x61943)),f154(x61941,x61943))+~P1(f334(f334(f336(x61941),x61942),f334(f174(x61941),x61943)))
% 160.93/160.65 [6226]~P1(f334(f334(f249(a881),x62261),x62263))+P1(f334(f334(f249(a881),x62261),f334(f334(f80(a881),x62262),x62263)))
% 160.93/160.65 [6228]~P1(f334(f334(f249(a881),x62281),x62282))+P1(f334(f334(f249(a881),x62281),f334(f334(f80(a881),x62282),x62283)))
% 160.93/160.65 [6230]~P1(f334(f334(f248(a881),x62301),x62303))+P1(f334(f334(f248(a881),x62301),f334(f334(f80(a881),x62302),x62303)))
% 160.93/160.65 [6232]~P1(f334(f334(f248(a881),x62321),x62322))+P1(f334(f334(f248(a881),x62321),f334(f334(f80(a881),x62322),x62323)))
% 160.93/160.65 [6271]P1(f334(f61(x62711),x62712))+~P1(f334(f61(x62711),f334(f334(f312(x62711),x62713),x62712)))
% 160.93/160.65 [6272]P1(f334(f139(x62721),x62722))+~P1(f334(f139(x62721),f334(f334(f153(x62721),x62723),x62722)))
% 160.93/160.65 [6273]P1(f334(f139(x62731),x62732))+~P1(f334(f139(x62731),f334(f334(f136(x62731),x62733),x62732)))
% 160.93/160.65 [6274]P1(f334(f139(x62741),x62742))+~P1(f334(f139(x62741),f334(f334(f136(x62741),x62742),x62743)))
% 160.93/160.65 [6320]~P118(x63201)+E(f334(f334(f80(x63201),x63202),f334(f334(f81(x63201),x63203),x63202)),f334(f334(f81(x63201),f334(f334(f80(x63201),x63203),f78(x63201))),x63202))
% 160.93/160.65 [6366]~E(x63661,x63662)+~P1(f334(f334(f249(f888(x63663,a876)),x63661),x63662))
% 160.93/160.65 [6410]P1(f334(f334(f336(x64101),x64102),x64103))+P1(f334(f334(f336(x64101),x64102),f334(f79(f888(x64101,a876)),x64103)))
% 160.93/160.65 [6416]E(f146(x64161,f334(f334(f140(x64161),x64162),x64163)),f146(x64161,x64163))+~P1(f334(f334(f249(a881),x64162),f334(f197(f882(x64161)),x64163)))
% 160.93/160.65 [6417]E(f334(f334(f177(x64171),x64172),f118(x64171,x64173)),f334(f334(f177(x64171),x64172),x64173))+~P1(f334(f334(f249(a881),x64172),f334(f197(f882(x64171)),x64173)))
% 160.93/160.65 [6472]E(f334(f334(f334(f191(f882(x64721),f882(x64721)),x64722),f170(x64721)),x64723),x64723)+~E(f44(a881,x64722,f334(f197(f882(x64721)),x64723)),f2(a881))
% 160.93/160.65 [6479]~P8(x64791,x64793,x64792)+E(f334(f334(f291(x64791,x64791,x64791),f334(f289(x64791,x64791),x64792)),x64792),x64792)
% 160.93/160.65 [6521]~E(f334(f334(f114(f888(x65211,a876)),x65212),x65213),x65213)+P1(f334(f334(f248(f888(x65211,a876)),x65212),x65213))
% 160.93/160.65 [6526]~P52(x65261,x65261,x65263)+P52(x65261,x65261,f334(f334(f191(f887(x65261,x65261),a876),x65262),x65263))
% 160.93/160.65 [6528]~P1(f334(f334(f336(x65281),x65283),f334(f174(x65281),x65282)))+P1(f334(f334(f249(a881),f2(a881)),f334(f197(f882(x65281)),x65282)))
% 160.93/160.65 [6554]~P85(x65541)+E(f334(f75(x65541),f334(f334(f80(x65541),f334(f75(x65541),x65542)),f334(f75(x65541),x65543))),f334(f334(f80(x65541),f334(f75(x65541),x65542)),f334(f75(x65541),x65543)))
% 160.93/160.65 [6564]E(f334(f334(f38(a881),f334(f334(f81(a881),x65641),x65642)),f334(f334(f81(a881),x65641),x65643)),f334(f334(f38(a881),x65642),x65643))+~P1(f334(f334(f249(a881),f2(a881)),x65641))
% 160.93/160.65 [6612]E(x66121,x66122)+~P1(f334(f334(f334(f334(a204,a24),x66121),x66123),x66122))
% 160.93/160.65 [6702]~P1(f334(f61(x67021),x67023))+E(f334(f334(f64(x67021,f888(x67021,a876),f312(x67021)),x67022),x67023),f334(f334(f114(f888(x67021,a876)),x67023),x67022))
% 160.93/160.65 [6761]E(f334(f334(f114(f888(x67611,a876)),x67612),x67613),x67612)+~P1(f334(f334(f248(f888(x67611,a876)),x67613),x67612))
% 160.93/160.65 [6763]E(f334(f334(f114(f888(x67631,a876)),x67632),x67633),x67633)+~P1(f334(f334(f248(f888(x67631,a876)),x67632),x67633))
% 160.93/160.65 [6764]E(f334(f334(f105(f888(x67641,a876)),x67642),x67643),x67643)+~P1(f334(f334(f248(f888(x67641,a876)),x67643),x67642))
% 160.93/160.65 [6765]E(f334(f334(f105(f888(x67651,a876)),x67652),x67653),x67652)+~P1(f334(f334(f248(f888(x67651,a876)),x67652),x67653))
% 160.93/160.65 [6816]~P1(f334(f139(x68161),x68162))+E(f334(f334(f22(f888(x68161,a876)),f334(f174(x68161),x68162)),f334(f334(f312(x68161),x68163),f196(f888(x68161,a876)))),f334(f174(x68161),f172(x68161,x68163,x68162)))
% 160.93/160.65 [6869]P39(x68691,x68692)+~P39(x68691,f334(f334(f191(f887(x68691,x68691),a876),x68693),x68692))
% 160.93/160.65 [6934]P1(f334(f48(x69341,x69342),f334(a50,x69343)))+~P1(f334(f48(f334(f79(a1),x69341),f334(f79(a1),x69342)),x69343))
% 160.93/160.65 [6939]E(f334(f334(f22(f888(x69391,a876)),f334(f334(f312(x69391),x69392),x69393)),f334(f334(f312(x69391),x69392),f196(f888(x69391,a876)))),x69393)+P1(f334(f334(f336(x69391),x69392),x69393))
% 160.93/160.65 [6960]E(f334(f334(f105(f888(x69601,a876)),f334(f174(x69601),x69602)),f334(f174(x69601),x69603)),f196(f888(x69601,a876)))+~P1(f334(f139(x69601),f334(f334(f136(x69601),x69602),x69603)))
% 160.93/160.65 [6976]~P1(f334(f334(f336(x69761),x69762),f334(f174(x69761),x69763)))+~P1(f334(f139(x69761),f334(f334(f153(x69761),x69762),x69763)))
% 160.93/160.65 [7046]P33(x70461,x70462,x70463)+P1(f334(f334(f249(a881),f801(x70463,x70462,x70461)),f334(f197(f882(x70461)),x70463)))
% 160.93/160.65 [7056]E(f334(f334(f105(f888(x70561,a876)),x70562),x70563),f196(f888(x70561,a876)))+P1(f334(f334(f336(x70561),f690(x70563,x70562,x70561)),x70562))
% 160.93/160.65 [7057]E(f334(f334(f105(f888(x70571,a876)),x70572),x70573),f196(f888(x70571,a876)))+P1(f334(f334(f336(x70571),f696(x70573,x70572,x70571)),x70573))
% 160.93/160.65 [7061]E(f118(x70611,f334(f334(f177(x70611),x70612),x70613)),f334(f334(f177(x70611),f334(f334(f22(a881),x70612),f78(a881))),x70613))+~P1(f334(f334(f248(a881),x70612),f334(f197(f882(x70611)),x70613)))
% 160.93/160.65 [7120]~P35(x71203,x71202,x71201)+P1(f334(f334(f249(a881),f797(x71201,x71202,x71203)),f334(f197(f882(x71203)),x71201)))
% 160.93/160.65 [7138]P1(f334(f334(f249(a881),f2(a881)),x71381))+P1(f334(f334(f248(a881),f334(f334(f81(a881),x71382),x71381)),f334(f334(f81(a881),x71383),x71381)))
% 160.93/160.65 [7139]P1(f334(f334(f249(a881),f2(a881)),x71391))+P1(f334(f334(f248(a881),f334(f334(f81(a881),x71391),x71392)),f334(f334(f81(a881),x71391),x71393)))
% 160.93/160.65 [7142]~P1(f334(f334(f336(x71421),x71422),x71423))+~P1(f334(f334(f336(x71421),x71422),f334(f79(f888(x71421,a876)),x71423)))
% 160.93/160.65 [7149]~P1(f334(f334(f249(f888(x71491,a876)),x71492),x71493))+P1(f334(f334(f248(f888(x71491,a876)),x71492),x71493))
% 160.93/160.65 [7250]~P1(f334(f334(f249(a881),x72502),x72503))+P1(f334(f334(f249(a881),f334(f334(f80(a881),x72501),x72502)),f334(f334(f80(a881),x72501),x72503)))
% 160.93/160.65 [7251]~P1(f334(f334(f249(a881),x72511),x72513))+P1(f334(f334(f249(a881),f334(f334(f80(a881),x72511),x72512)),f334(f334(f80(a881),x72513),x72512)))
% 160.93/160.65 [7252]~P1(f334(f334(f249(a1),x72521),x72523))+P1(f334(f334(f249(a1),f334(f334(f80(a1),x72521),x72522)),f334(f334(f80(a1),x72523),x72522)))
% 160.93/160.65 [7255]~P1(f334(f334(f248(a881),x72553),x72552))+P1(f334(f334(f248(a881),f334(f334(f22(a881),x72551),x72552)),f334(f334(f22(a881),x72551),x72553)))
% 160.93/160.65 [7256]~P1(f334(f334(f248(a881),x72561),x72563))+P1(f334(f334(f248(a881),f334(f334(f22(a881),x72561),x72562)),f334(f334(f22(a881),x72563),x72562)))
% 160.93/160.65 [7257]~P1(f334(f334(f248(a881),x72572),x72573))+P1(f334(f334(f248(a881),f334(f334(f80(a881),x72571),x72572)),f334(f334(f80(a881),x72571),x72573)))
% 160.93/160.65 [7258]~P1(f334(f334(f248(a881),x72581),x72583))+P1(f334(f334(f248(a881),f334(f334(f80(a881),x72581),x72582)),f334(f334(f80(a881),x72583),x72582)))
% 160.93/160.65 [7260]~P1(f334(f334(f248(a881),x72602),x72603))+P1(f334(f334(f248(a881),f334(f334(f81(a881),x72601),x72602)),f334(f334(f81(a881),x72601),x72603)))
% 160.93/160.65 [7262]~P1(f334(f334(f248(a881),x72621),x72623))+P1(f334(f334(f248(a881),f334(f334(f81(a881),x72621),x72622)),f334(f334(f81(a881),x72623),x72622)))
% 160.93/160.65 [7263]~P1(f334(f334(f248(a881),x72631),x72633))+P1(f334(f334(f248(a881),f334(f334(f38(a881),x72631),x72632)),f334(f334(f38(a881),x72633),x72632)))
% 160.93/160.65 [7264]~P1(f334(f334(f248(a1),x72642),x72643))+P1(f334(f334(f248(a1),f334(f334(f80(a1),x72641),x72642)),f334(f334(f80(a1),x72641),x72643)))
% 160.93/160.65 [7344]E(x73441,x73442)+~P1(f334(f334(f336(x73443),x73441),f334(f334(f312(x73443),x73442),f196(f888(x73443,a876)))))
% 160.93/160.65 [7346]~E(f334(f334(f105(f888(x73461,a876)),x73462),x73463),f196(f888(x73461,a876)))+P1(f334(f334(f248(f888(x73461,a876)),x73462),f334(f79(f888(x73461,a876)),x73463)))
% 160.93/160.65 [7354]P1(f334(f334(f336(f888(x73541,a876)),x73542),f334(f311(x73541),x73543)))+~P1(f334(f334(f248(f888(x73541,a876)),x73542),x73543))
% 160.93/160.65 [7407]E(f334(f334(f153(x74071),f334(f334(f167(x74071),x74072),x74073)),f334(f334(f140(x74071),f334(a116,x74073)),x74072)),f334(f334(f140(x74071),x74073),x74072))+~P1(f334(f334(f249(a881),x74073),f334(f197(f882(x74071)),x74072)))
% 160.93/160.65 [7434]P1(f334(f334(f336(f887(x74341,x74341)),x74342),f310(x74341,x74343)))+~P1(f334(f334(f336(f887(x74341,x74341)),x74342),x74343))
% 160.93/160.65 [7444]~P1(f334(f334(f336(f888(x74441,a876)),x74442),f334(f311(x74441),x74443)))+P1(f334(f334(f248(f888(x74441,a876)),x74442),x74443))
% 160.93/160.65 [7490]P1(f334(f334(f248(f888(x74901,a876)),x74902),f39(f888(x74901,a876),x74903)))+~P1(f334(f334(f336(f888(x74901,a876)),x74902),x74903))
% 160.93/160.65 [7515]~P139(x75151)+E(f334(f334(f81(x75151),f334(f334(f259(x75151),f334(f79(x75151),f78(x75151))),x75152)),f334(f334(f259(x75151),x75153),x75152)),f334(f334(f259(x75151),f334(f79(x75151),x75153)),x75152))
% 160.93/160.65 [7537]E(f334(f334(f167(x75371),x75372),f334(f334(f22(a881),f334(f197(f882(x75371)),x75372)),f334(a116,x75373))),f334(f334(f167(x75371),f334(f171(x75371),x75372)),x75373))+~P1(f334(f334(f249(a881),x75373),f334(f197(f882(x75371)),x75372)))
% 160.93/160.65 [7554]~E(f334(f334(f105(f888(x75541,a876)),f856(x75543,x75542,x75541)),x75543),f196(f888(x75541,a876)))+E(f334(f334(f105(f888(x75541,a876)),f39(f888(x75541,a876),x75542)),x75543),f196(f888(x75541,a876)))
% 160.93/160.65 [7617]~P1(f334(f334(f336(x76173),x76172),f334(f174(x76173),x76171)))+P1(f334(f334(f249(a881),f655(x76171,x76172,x76173)),f334(f197(f882(x76173)),x76171)))
% 160.93/160.65 [7625]P1(f334(f334(f336(x76251),f334(f334(f167(x76251),x76252),x76253)),f334(f174(x76251),x76252)))+~P1(f334(f334(f249(a881),x76253),f334(f197(f882(x76251)),x76252)))
% 160.93/160.65 [7723]~P1(f334(x77232,f758(x77233,x77232,x77231)))+E(f334(f334(f140(x77231),f334(f197(f882(x77231)),f179(x77231,x77232,x77233))),x77233),f117(x77231))
% 160.93/160.65 [7733]P1(f334(f334(f248(f888(f882(x77331),a876)),f163(x77331,x77332)),f163(x77331,x77333)))+~P1(f334(f334(f248(f888(x77331,a876)),x77332),x77333))
% 160.93/160.65 [7734]P1(f334(f334(f248(f888(f882(x77341),a876)),f162(x77341,x77342)),f162(x77341,x77343)))+~P1(f334(f334(f248(f888(x77341,a876)),x77342),x77343))
% 160.93/160.65 [7760]E(f334(f334(f105(f888(x77601,a876)),f39(f888(x77601,a876),x77602)),x77603),f196(f888(x77601,a876)))+P1(f334(f334(f336(f888(x77601,a876)),f856(x77603,x77602,x77601)),x77602))
% 160.93/160.65 [7763]~P1(f334(f334(f336(f888(x77631,a876)),x77633),x77632))+P1(f334(f334(f248(f888(x77631,a876)),f40(f888(x77631,a876),x77632)),x77633))
% 160.93/160.65 [7765]E(f334(f334(f105(f888(x77651,a876)),x77652),x77653),f196(f888(x77651,a876)))+~P1(f334(f334(f248(f888(x77651,a876)),x77652),f334(f79(f888(x77651,a876)),x77653)))
% 160.93/160.65 [7813]E(f334(f334(f22(a881),f334(f334(f80(a881),f334(f168(a881),x78131)),x78132)),f334(f334(f167(a881),x78131),x78133)),f334(f168(a881),f334(f334(f161(a881,x78131),x78133),x78132)))+~P1(f334(f334(f249(a881),x78133),f334(f197(f882(a881)),x78131)))
% 160.93/160.65 [7863]P1(f334(f334(f249(a881),x78631),x78632))+~P1(f334(f334(f249(a881),f334(f334(f80(a881),x78633),x78631)),f334(f334(f80(a881),x78633),x78632)))
% 160.93/160.65 [7864]P1(f334(f334(f249(a881),x78641),x78642))+~P1(f334(f334(f249(a881),f334(f334(f81(a881),x78643),x78641)),f334(f334(f81(a881),x78643),x78642)))
% 160.93/160.65 [7865]P1(f334(f334(f249(a881),x78651),x78652))+~P1(f334(f334(f249(a881),f334(f334(f81(a881),x78651),x78653)),f334(f334(f81(a881),x78652),x78653)))
% 160.93/160.65 [7868]P1(f334(f334(f248(a881),x78681),x78682))+~P1(f334(f334(f248(a881),f334(f334(f80(a881),x78683),x78681)),f334(f334(f80(a881),x78683),x78682)))
% 160.93/160.65 [7898]P1(f334(f334(f249(a881),f2(a881)),x78981))+~P1(f334(f334(f249(a881),f334(f334(f81(a881),x78982),x78981)),f334(f334(f81(a881),x78983),x78981)))
% 160.93/160.65 [7899]P1(f334(f334(f249(a881),f2(a881)),x78991))+~P1(f334(f334(f249(a881),f334(f334(f81(a881),x78991),x78992)),f334(f334(f81(a881),x78991),x78993)))
% 160.93/160.65 [7973]E(f261(x79731,x79732,x79733),x79732)+~P1(f334(f334(f248(f888(x79731,a876)),x79733),f334(f334(f312(x79731),x79732),f196(f888(x79731,a876)))))
% 160.93/160.65 [8023]~P1(f334(f139(x80231),x80233))+E(f334(f138(x80231,f334(f334(f8(a876,a876,x80231),a329),f334(a331,x80232))),x80233),f172(x80231,x80232,x80233))
% 160.93/160.65 [8046]E(f334(f334(f140(x80461),f334(f197(f882(x80461)),f179(x80461,x80462,x80463))),x80463),f117(x80461))+P1(f334(f334(f336(x80461),f758(x80463,x80462,x80461)),f334(f174(x80461),x80463)))
% 160.93/160.65 [8050]E(f334(f334(f136(x80501),f334(f334(f177(x80501),x80502),x80503)),f334(f334(f153(x80501),f334(f334(f167(x80501),x80503),x80502)),f117(x80501))),f334(f334(f177(x80501),f334(a116,x80502)),x80503))+~P1(f334(f334(f249(a881),x80502),f334(f197(f882(x80501)),x80503)))
% 160.93/160.65 [8113]E(f334(f138(x81131,f334(f334(f8(a876,a876,x81131),a329),f334(a331,x81132))),x81133),x81133)+P1(f334(f334(f336(x81131),x81132),f334(f174(x81131),x81133)))
% 160.93/160.65 [8121]P1(f334(f334(f248(f888(f888(x81211,a876),a876)),f262(x81211,x81212)),f262(x81211,x81213)))+~P1(f334(f334(f248(f888(x81211,a876)),x81212),x81213))
% 160.93/160.65 [8166]~P1(f334(f139(x81661),x81663))+P1(f334(f139(x81661),f334(f334(f334(f191(f882(x81661),f882(x81661)),x81662),f170(x81661)),x81663)))
% 160.93/160.65 [8174]~P1(f334(f334(f249(a881),x81742),x81743))+P1(f334(f334(f249(a881),f334(f334(f81(a881),f334(a116,x81741)),x81742)),f334(f334(f81(a881),f334(a116,x81741)),x81743)))
% 160.93/160.65 [8197]P1(f334(f334(f248(f888(f888(x81971,a876),a876)),f334(f311(x81971),x81972)),f334(f311(x81971),x81973)))+~P1(f334(f334(f248(f888(x81971,a876)),x81972),x81973))
% 160.93/160.65 [8365]~P1(f334(f334(f248(f888(x83651,a876)),x83653),x83652))+P1(f334(f334(f248(f888(x83651,a876)),f334(f79(f888(x83651,a876)),x83652)),f334(f79(f888(x83651,a876)),x83653)))
% 160.93/160.65 [8395]E(f334(f313(a881,a881,f334(f334(f7(a881,a881,a881),f22(a881)),x83951)),f334(f304(a881,x83952),x83953)),f334(f304(a881,f334(f334(f22(a881),x83952),x83951)),f334(f334(f22(a881),x83953),x83951)))+~P1(f334(f334(f249(a881),x83951),x83953))
% 160.93/160.65 [8423]~P79(x84231)+E(f334(f334(f80(x84231),x84232),f334(f144(x84231,x84231,f80(x84231),f2(x84231)),x84233)),f334(f144(x84231,x84231,f80(x84231),x84232),x84233))
% 160.93/160.65 [8498]~P85(x84981)+P1(f334(f334(f248(x84981),f334(f75(x84981),f334(f334(f22(x84981),x84982),x84983))),f334(f334(f80(x84981),f334(f75(x84981),x84982)),f334(f75(x84981),x84983))))
% 160.93/160.65 [8499]~P85(x84991)+P1(f334(f334(f248(x84991),f334(f75(x84991),f334(f334(f80(x84991),x84992),x84993))),f334(f334(f80(x84991),f334(f75(x84991),x84992)),f334(f75(x84991),x84993))))
% 160.93/160.65 [8512]E(f334(f334(f80(a1),f334(f334(f81(a1),x85121),f44(a1,f334(f334(f38(a1),x85122),x85121),x85123))),f44(a1,x85122,x85121)),f44(a1,x85122,f334(f334(f81(a1),x85121),x85123)))+~P1(f334(f334(f249(a1),f2(a1)),x85123))
% 160.93/160.65 [8518]E(f334(f334(f136(x85181),f334(f334(f177(x85181),x85182),x85183)),f334(f334(f153(x85181),f334(f143(x85181),f334(f334(f140(x85181),x85182),x85183))),f117(x85181))),f334(f334(f177(x85181),f334(a116,x85182)),x85183))+~P1(f334(f334(f249(a881),x85182),f334(f197(f882(x85181)),x85183)))
% 160.93/160.65 [8538]E(f334(f280(x85381,f334(f334(f156(x85381,f887(a103,x85381)),f334(f269(a103,x85381),f78(a103))),x85382)),f334(a3,x85383)),f334(f334(f167(x85381),x85382),x85383))+~P1(f334(f334(f249(a881),x85383),f334(f197(f882(x85381)),x85382)))
% 160.93/160.65 [8609]P1(f334(f334(f336(f887(x86091,x86091)),x86092),f334(f334(f291(x86091,x86091,x86091),x86093),f310(x86091,x86093))))+~P1(f334(f334(f336(f887(x86091,x86091)),x86092),x86093))
% 160.93/160.65 [8629]P1(f334(f334(f248(a881),x86291),x86292))+~P1(f334(f334(f248(a881),f334(f334(f81(a881),f334(a116,x86293)),x86291)),f334(f334(f81(a881),f334(a116,x86293)),x86292)))
% 160.93/160.65 [8647]P1(f334(f334(f248(f888(x86471,a876)),x86472),x86473))+~P1(f334(f334(f248(f888(x86471,a876)),f334(f79(f888(x86471,a876)),x86473)),f334(f79(f888(x86471,a876)),x86472)))
% 160.93/160.65 [8665]P1(f334(f139(x86651),x86652))+~P1(f334(f139(x86651),f334(f334(f334(f191(f882(x86651),f882(x86651)),x86653),f170(x86651)),x86652)))
% 160.93/160.65 [8725]E(f334(f313(f887(x87251,x87252),x87252,f272(x87251,x87252)),f334(f174(f887(x87251,x87252)),x87253)),f188(x87251,x87252,f334(f180(x87251,x87252),x87253)))+~P1(f334(f139(x87251),f334(f334(f156(f887(x87251,x87252),x87251),f268(x87251,x87252)),x87253)))
% 160.93/160.65 [8734]E(f334(f288(x87341,x87341,f310(x87341,x87342)),x87343),x87343)+~P1(f334(f334(f248(f888(x87341,a876)),f334(f288(x87341,x87341,x87342),x87343)),x87343))
% 160.93/160.65 [8776]~P108(x87761)+P16(x87761,f334(f138(x87761,f334(f334(f7(x87761,x87761,a876),a331),f334(x87762,x87763))),x87763))
% 160.93/160.65 [8782]~P1(f334(f334(f248(a881),x87821),x87822))+P1(f334(f334(f248(a881),x87821),f334(f144(a881,a881,f80(a881),x87822),x87823)))
% 160.93/160.65 [8859]~P1(f334(f334(f336(f887(x88591,x88591)),x88592),f310(x88591,x88593)))+P1(f334(f334(f336(f887(x88591,x88591)),x88592),f334(f334(f191(f887(x88591,x88591),a876),f635(x88593,x88592,x88591)),x88593)))
% 160.93/160.65 [8951]~P79(x89511)+E(f334(f334(f80(x89511),x89512),f334(f144(x89511,x89511,f334(f7(x89511,x89511,x89511),f80(x89511)),f2(x89511)),f334(f171(x89511),x89513))),f334(f144(x89511,x89511,f80(x89511),x89512),x89513))
% 160.93/160.65 [9224]P52(x92241,x92242,x92243)+P1(f334(f334(f336(f887(x92241,x92242)),f334(f334(f269(x92241,x92242),f626(x92243,x92242,x92241)),f617(x92243,x92242,x92241))),x92243))
% 160.93/160.65 [9225]P52(x92251,x92252,x92253)+P1(f334(f334(f336(f887(x92251,x92252)),f334(f334(f269(x92251,x92252),f626(x92253,x92252,x92251)),f616(x92253,x92252,x92251))),x92253))
% 160.93/160.65 [9295]~P1(f334(f334(f336(f887(x92951,x92951)),x92952),f334(f334(f291(x92951,x92951,x92951),x92953),f310(x92951,x92953))))+P1(f334(f334(f336(f887(x92951,x92951)),x92952),f334(f334(f191(f887(x92951,x92951),a876),f637(x92953,x92952,x92951)),x92953)))
% 160.93/160.65 [9296]~P1(f334(x92961,f334(f334(f167(x92962),x92963),f334(f197(f882(x92962)),f179(x92962,x92961,x92963)))))+~P1(f334(f334(f249(a881),f334(f197(f882(x92962)),f179(x92962,x92961,x92963))),f334(f197(f882(x92962)),x92963)))
% 160.93/160.65 [9385]~P1(f334(f334(f248(f888(x93851,a876)),x93852),x93853))+P1(f334(f334(f248(f888(x93851,a876)),f334(f334(f7(x93851,f888(x93851,a876),a876),f336(x93851)),x93852)),f334(f334(f7(x93851,f888(x93851,a876),a876),f336(x93851)),x93853)))
% 160.93/160.65 [9438]~P1(f334(f334(f336(f887(f888(x94381,a876),f888(x94381,a876))),f334(f334(f269(f888(x94381,a876),f888(x94381,a876)),x94382),x94383)),f309(x94381)))+P1(f334(f334(f249(f888(x94381,a876)),x94382),x94383))
% 160.93/160.65 [9463]P53(x94631,x94632,x94633)+~P1(f334(f334(f336(f887(x94631,x94631)),f334(f334(f269(x94631,x94631),f630(x94633,x94632,x94631)),f629(x94633,x94632,x94631))),x94633))
% 160.93/160.65 [9464]P53(x94641,x94642,x94643)+~P1(f334(f334(f336(f887(x94641,x94641)),f334(f334(f269(x94641,x94641),f629(x94643,x94642,x94641)),f630(x94643,x94642,x94641))),x94643))
% 160.93/160.65 [9500]~P1(f334(f334(f336(f887(f882(x95001),f882(x95001))),f334(f334(f269(f882(x95001),f882(x95001)),x95002),x95002)),f149(x95001,x95003)))+P1(f334(f334(f336(f887(x95001,x95001)),f334(f334(f269(x95001,x95001),f679(x95002,x95003,x95001)),f679(x95002,x95003,x95001))),x95003))
% 160.93/160.65 [9555]P1(f334(f334(f248(f888(x95551,a876)),x95552),x95553))+~P1(f334(f334(f248(f888(x95551,a876)),f334(f334(f7(x95551,f888(x95551,a876),a876),f336(x95551)),x95552)),f334(f334(f7(x95551,f888(x95551,a876),a876),f336(x95551)),x95553)))
% 160.93/160.65 [9636]E(f334(f334(f22(a881),f334(f334(f6(a881,a881),x96361),f334(f255(a881),x96362))),f334(f334(f6(a881,a881),x96363),f334(f255(a881),x96362))),f334(f334(f6(a881,a881),f334(f334(f18(a881,a881,a881),f334(f334(f8(a881,f888(a881,a881),a881),f22(a881)),x96361)),x96363)),f334(f255(a881),x96362)))+~P1(f334(f334(f248(a881),f334(x96363,f421(x96362,x96361,x96363))),f334(x96361,f421(x96362,x96361,x96363))))
% 160.93/160.65 [9943]E(f334(f254(f887(x99431,x99432)),f334(f273(x99431,x99432,a876),f334(f334(f7(x99431,f888(x99432,f885(x99432)),f888(x99432,a876)),f334(f334(f8(f888(f885(x99432),a876),f888(f888(x99432,f885(x99432)),f888(x99432,a876)),x99431),f8(f885(x99432),a876,x99432)),f334(f334(f8(f885(x99432),f888(f885(x99432),a876),x99431),a331),f334(f180(x99431,x99432),x99433)))),f241(x99432)))),f334(f174(f887(x99431,x99432)),x99433))+~P1(f334(f139(x99431),f334(f334(f156(f887(x99431,x99432),x99431),f268(x99431,x99432)),x99433)))
% 160.93/160.65 [5631]~P66(x56311)+E(f334(f334(f22(x56311),f334(f334(f80(x56311),x56312),x56313)),x56313),x56312)
% 160.93/160.65 [5632]~P66(x56321)+E(f334(f334(f80(x56321),f334(f334(f22(x56321),x56322),x56323)),x56323),x56322)
% 160.93/160.65 [5852]~P66(x58521)+E(f334(f334(f80(x58521),x58522),f334(f334(f80(x58521),f334(f79(x58521),x58522)),x58523)),x58523)
% 160.93/160.65 [5936]~P80(x59361)+E(f334(f334(f81(x59361),f334(f334(f259(x59361),x59362),x59363)),x59362),f334(f334(f259(x59361),x59362),f334(a116,x59363)))
% 160.93/160.65 [5937]~P118(x59371)+E(f334(f334(f81(x59371),f334(f334(f259(x59371),x59372),x59373)),x59372),f334(f334(f259(x59371),x59372),f334(a116,x59373)))
% 160.93/160.65 [6146]~P111(x61461)+E(f334(f75(x61461),f334(f334(f259(x61461),f334(f79(x61461),x61462)),x61463)),f334(f75(x61461),f334(f334(f259(x61461),x61462),x61463)))
% 160.93/160.65 [6208]~P80(x62081)+E(f334(f334(f81(x62081),f334(f334(f259(x62081),x62082),x62083)),x62082),f334(f334(f81(x62081),x62082),f334(f334(f259(x62081),x62082),x62083)))
% 160.93/160.65 [6262]E(f334(f334(f22(a103),f334(f334(f80(a103),x62621),x62622)),x62623),f284(x62621,x62622,x62623))+~P1(f334(f334(f249(a103),x62622),x62623))
% 160.93/160.65 [6283]~E(f334(f334(f140(x62831),x62833),x62832),f117(x62831))+P1(f334(f334(f248(a881),f334(f197(f882(x62831)),x62832)),x62833))
% 160.93/160.65 [6415]E(f334(f334(f81(a881),f334(f107(a881),x64151)),f334(f334(f81(a881),f334(f107(a881),x64152)),x64153)),f2(a881))+~P1(f334(f334(f249(a1),x64151),a83))
% 160.93/160.65 [6431]~P61(x64311)+E(f334(f334(f259(x64311),f334(f334(f292(x64311),f78(x64311)),x64312)),x64313),f334(f334(f292(x64311),f78(x64311)),f334(f334(f259(x64311),x64312),x64313)))
% 160.93/160.65 [6508]E(f334(f334(f22(a881),f334(f334(f80(a881),x65081),x65082)),x65083),f334(f334(f22(a881),x65081),f334(f334(f22(a881),x65083),x65082)))+~P1(f334(f334(f248(a881),x65082),x65083))
% 160.93/160.65 [6510]E(f334(f334(f22(a881),f334(f334(f80(a881),x65101),x65102)),x65103),f334(f334(f80(a881),x65101),f334(f334(f22(a881),x65102),x65103)))+~P1(f334(f334(f248(a881),x65103),x65102))
% 160.93/160.65 [6545]~P2(x65451)+P1(f334(f334(f248(x65451),f334(f334(f105(x65451),x65452),x65453)),x65453))
% 160.93/160.65 [6546]~P100(x65461)+P1(f334(f334(f248(x65461),f334(f334(f105(x65461),x65462),x65463)),x65463))
% 160.93/160.65 [6547]~P2(x65471)+P1(f334(f334(f248(x65471),f334(f334(f105(x65471),x65472),x65473)),x65472))
% 160.93/160.65 [6548]~P100(x65481)+P1(f334(f334(f248(x65481),f334(f334(f105(x65481),x65482),x65483)),x65482))
% 160.93/160.65 [6549]~P108(x65491)+P1(f334(f334(f248(x65491),f334(f334(f246(x65491),x65492),x65493)),x65493))
% 160.93/160.65 [6550]~P108(x65501)+P1(f334(f334(f248(x65501),f334(f334(f246(x65501),x65502),x65503)),x65502))
% 160.93/160.65 [6563]E(f334(f334(f38(a1),f334(f334(f38(a1),x65631),x65632)),x65633),f334(f334(f38(a1),x65631),f334(f334(f81(a1),x65632),x65633)))+~P1(f334(f334(f249(a1),f2(a1)),x65633))
% 160.93/160.65 [6615]~P118(x66151)+E(f334(f334(f80(x66151),f334(f334(f81(x66151),x66152),x66153)),x66153),f334(f334(f81(x66151),f334(f334(f80(x66151),x66152),f78(x66151))),x66153))
% 160.93/160.65 [6616]~P93(x66161)+E(f334(f334(f81(x66161),f334(f79(x66161),f334(f107(x66161),x66162))),x66163),f334(f334(f81(x66161),f334(f107(x66161),f334(f79(a1),x66162))),x66163))
% 160.93/160.65 [6689]~P79(x66891)+E(f334(f168(x66891),f334(f334(f156(x66892,x66891),f334(f16(x66891,x66892),f2(x66891))),x66893)),f2(x66891))
% 160.93/160.65 [6705]E(f334(f334(f80(a881),f334(f107(a881),x67051)),f334(f334(f80(a881),f334(f107(a881),x67052)),x67053)),f334(f334(f80(a881),f334(f107(a881),x67052)),x67053))+~P1(f334(a201,f334(f107(a1),x67051)))
% 160.93/160.65 [6719]~P5(x67191)+E(f39(x67191,f334(f334(f312(x67191),x67192),f334(f334(f312(x67191),x67193),f196(f888(x67191,a876))))),f334(f334(f114(x67191),x67192),x67193))
% 160.93/160.65 [6720]~P5(x67201)+E(f40(x67201,f334(f334(f312(x67201),x67202),f334(f334(f312(x67201),x67203),f196(f888(x67201,a876))))),f334(f334(f105(x67201),x67202),x67203))
% 160.93/160.65 [6743]E(f334(f334(f177(x67431),x67432),x67433),x67433)+~P1(f334(f334(f248(a881),f334(f197(f882(x67431)),x67433)),x67432))
% 160.93/160.65 [6756]E(f334(f334(f140(x67561),x67562),x67563),f117(x67561))+~P1(f334(f334(f248(a881),f334(f197(f882(x67561)),x67563)),x67562))
% 160.93/160.65 [6767]E(f334(f334(f80(a881),f334(f334(f22(a881),x67671),x67672)),x67673),f334(f334(f22(a881),f334(f334(f80(a881),x67671),x67673)),x67672))+~P1(f334(f334(f248(a881),x67672),x67671))
% 160.93/160.65 [6781]~P1(f334(f334(f249(a881),x67811),x67813))+P1(f334(f334(f249(a881),f334(f334(f22(a881),x67811),x67812)),x67813))
% 160.93/160.65 [6809]~P108(x68091)+E(f172(x68091,x68092,f334(f334(f150(x68091,x68091,f5(x68091)),x68092),x68093)),x68093)
% 160.93/160.65 [6898]E(f334(f334(f22(a881),f334(f334(f80(a881),x68981),x68982)),f334(a116,x68983)),f334(f334(f22(a881),x68981),f334(a116,f334(f334(f22(a881),x68983),x68982))))+~P1(f334(f334(f248(a881),x68982),x68983))
% 160.93/160.65 [6899]~P111(x68991)+P1(f334(f334(f248(x68991),f2(x68991)),f334(f334(f259(x68991),f334(f75(x68991),x68992)),x68993)))
% 160.93/160.65 [6944]P26(x69441,x69442,x69443)+~P1(f334(f334(f248(f888(f880(x69441),a876)),x69443),x69442))
% 160.93/160.65 [6987]~P1(f334(f61(x69871),x69872))+P1(f334(f61(x69871),f334(f334(f22(f888(x69871,a876)),x69872),x69873)))
% 160.93/160.65 [6988]~P1(f334(f61(x69881),x69883))+P1(f334(f61(x69881),f334(f334(f105(f888(x69881,a876)),x69882),x69883)))
% 160.93/160.65 [6989]~P1(f334(f61(x69891),x69892))+P1(f334(f61(x69891),f334(f334(f105(f888(x69891,a876)),x69892),x69893)))
% 160.93/160.65 [7128]~P39(x71281,x71283)+P39(x71281,f334(f334(f105(f888(f887(x71281,x71281),a876)),x71282),x71283))
% 160.93/160.65 [7129]~P39(x71291,x71292)+P39(x71291,f334(f334(f105(f888(f887(x71291,x71291),a876)),x71292),x71293))
% 160.93/160.65 [7246]~P2(x72461)+E(f10(x72461,f334(f174(x72461),f334(f334(f153(x72461),x72462),x72463))),f334(f144(x72461,x72461,f114(x72461),x72462),x72463))
% 160.93/160.65 [7247]~P2(x72471)+E(f11(x72471,f334(f174(x72471),f334(f334(f153(x72471),x72472),x72473))),f334(f144(x72471,x72471,f105(x72471),x72472),x72473))
% 160.93/160.65 [7248]~P108(x72481)+E(f14(x72481,f334(f174(x72481),f334(f334(f153(x72481),x72482),x72483))),f334(f144(x72481,x72481,f246(x72481),x72482),x72483))
% 160.93/160.65 [7249]~P108(x72491)+E(f15(x72491,f334(f174(x72491),f334(f334(f153(x72491),x72492),x72493))),f334(f144(x72491,x72491,f247(x72491),x72492),x72493))
% 160.93/160.65 [7309]~P1(f334(f61(x73091),x73092))+P1(f334(f334(f248(a881),f334(f37(x73091),x73092)),f334(f37(x73091),f334(f334(f312(x73091),x73093),x73092))))
% 160.93/160.65 [7317]E(f334(f334(f114(f888(a881,a876)),f334(f304(a881,x73171),x73172)),f334(f304(a881,x73172),f334(f334(f80(a881),x73172),x73173))),f334(f304(a881,x73171),f334(f334(f80(a881),x73172),x73173)))+~P1(f334(f334(f248(a881),x73171),x73172))
% 160.93/160.65 [7325]P1(f334(f334(f249(a881),x73251),x73252))+~P1(f334(f334(f249(a881),f334(f334(f80(a881),x73251),x73253)),x73252))
% 160.93/160.65 [7328]P1(f334(f334(f248(a881),x73281),x73282))+~P1(f334(f334(f248(a881),f334(f334(f80(a881),x73283),x73281)),x73282))
% 160.93/160.65 [7329]P1(f334(f334(f248(a881),x73291),x73292))+~P1(f334(f334(f248(a881),f334(f334(f80(a881),x73291),x73293)),x73292))
% 160.93/160.65 [7371]~P108(x73711)+E(f12(x73711,f247(x73711),f334(f174(x73711),f334(f334(f153(x73711),x73712),x73713))),f334(f144(x73711,x73711,f247(x73711),x73712),x73713))
% 160.93/160.65 [7372]~P108(x73721)+E(f13(x73721,f246(x73721),f334(f174(x73721),f334(f334(f153(x73721),x73722),x73723))),f334(f144(x73721,x73721,f246(x73721),x73722),x73723))
% 160.93/160.65 [7376]~E(x73762,f196(f888(f887(x73761,x73761),a876)))+P1(f334(f334(f248(f888(f887(x73761,x73761),a876)),x73762),x73763))
% 160.93/160.65 [7485]E(f334(f334(f114(f888(x74851,a876)),x74852),f334(f334(f22(f888(x74851,a876)),x74853),x74852)),x74853)+~P1(f334(f334(f248(f888(x74851,a876)),x74852),x74853))
% 160.93/160.65 [7486]~P1(f334(f334(f249(a881),x74861),f334(f334(f22(a881),x74863),x74862)))+P1(f334(f334(f249(a881),f334(f334(f80(a881),x74861),x74862)),x74863))
% 160.93/160.65 [7487]~P1(f334(f334(f248(a881),x74871),f334(f334(f80(a881),x74873),x74872)))+P1(f334(f334(f248(a881),f334(f334(f22(a881),x74871),x74872)),x74873))
% 160.93/160.65 [7544]E(x75441,f117(x75442))+E(f334(f143(x75442),f334(f334(f334(f191(f882(x75442),f882(x75442)),x75443),f170(x75442)),x75441)),f334(f334(f167(x75442),x75441),f44(a881,x75443,f334(f197(f882(x75442)),x75441))))
% 160.93/160.65 [7553]E(f334(f334(f312(x75531),x75532),f334(f334(f22(f888(x75531,a876)),x75533),f334(f334(f312(x75531),x75532),f196(f888(x75531,a876))))),x75533)+~P1(f334(f334(f336(x75531),x75532),x75533))
% 160.93/160.65 [7714]P1(f334(f334(f249(a881),x77141),f334(f334(f22(a881),x77142),x77143)))+~P1(f334(f334(f249(a881),f334(f334(f80(a881),x77141),x77143)),x77142))
% 160.93/160.65 [7715]P1(f334(f334(f248(a881),x77151),f334(f334(f80(a881),x77152),x77153)))+~P1(f334(f334(f248(a881),f334(f334(f22(a881),x77151),x77153)),x77152))
% 160.93/160.65 [7737]P1(f334(f61(x77371),x77372))+~P1(f334(f61(x77371),f334(f334(f114(f888(x77371,a876)),x77373),x77372)))
% 160.93/160.65 [7738]P1(f334(f61(x77381),x77382))+~P1(f334(f61(x77381),f334(f334(f114(f888(x77381,a876)),x77382),x77383)))
% 160.93/160.65 [7812]~P47(x78121,x78123)+P1(f334(f334(f336(f887(x78121,x78121)),f334(f334(f269(x78121,x78121),x78122),x78122)),x78123))
% 160.93/160.65 [7946]E(f334(f334(f167(a881),f141(a881,f334(f304(a881,x79461),x79462))),x79463),f334(f334(f80(a881),x79461),x79463))+~P1(f334(f334(f249(a881),f334(f334(f80(a881),x79461),x79463)),x79462))
% 160.93/160.65 [8012]E(f334(f334(f177(a881),x80121),f141(a881,f334(f304(a881,x80122),x80123))),f141(a881,f334(f304(a881,x80122),f334(f334(f80(a881),x80122),x80121))))+~P1(f334(f334(f248(a881),f334(f334(f80(a881),x80122),x80121)),x80123))
% 160.93/160.65 [8065]~P93(x80651)+E(f334(f334(f259(x80651),x80652),f334(f107(a881),f334(f334(f80(a1),x80653),x80653))),f334(f334(f86(x80651,x80651),f334(f334(f259(x80651),x80652),f334(f107(a881),x80653))),f334(f334(f18(x80651,x80651,x80651),f81(x80651)),f5(x80651))))
% 160.93/160.65 [8219]~P1(f334(f334(f334(a202,f334(a26,x82191)),x82192),x82193))+P1(f334(f334(f334(a202,f334(f245(a878),f334(a28,x82191))),x82192),x82193))
% 160.93/160.65 [8345]E(f334(f334(f136(x83451),f334(f334(f177(x83451),x83452),x83453)),f334(f334(f153(x83451),f334(f334(f167(x83451),x83453),x83452)),f334(f334(f140(x83451),f334(a116,x83452)),x83453))),x83453)+~P1(f334(f334(f249(a881),x83452),f334(f197(f882(x83451)),x83453)))
% 160.93/160.65 [8352]P1(f334(f334(f248(f888(x83521,a876)),f322(x83521,x83522)),f322(x83521,x83523)))+~P1(f334(f334(f248(f888(x83521,f888(x83521,a876))),x83523),x83522))
% 160.93/160.65 [8354]~P53(x83541,x83542,x83543)+P53(x83541,x83542,f334(f334(f22(f888(f887(x83541,x83541),a876)),x83543),f310(x83541,f196(f888(f887(x83541,x83541),a876)))))
% 160.93/160.65 [8371]P1(f334(f334(f248(f888(x83711,a876)),f323(x83711,x83712)),f323(x83711,x83713)))+~P1(f334(f334(f248(f888(f887(x83711,x83711),a876)),x83713),x83712))
% 160.93/160.65 [8378]~P123(x83781)+P1(f334(f334(f248(x83781),f2(x83781)),f334(f334(f80(x83781),f334(f334(f81(x83781),x83782),x83782)),f334(f334(f81(x83781),x83783),x83783))))
% 160.93/160.65 [8399]P1(f334(f334(f334(a202,f334(a26,x83991)),x83992),x83993))+~P1(f334(f334(f334(a202,f334(f245(a878),f334(a28,x83991))),x83992),x83993))
% 160.93/160.65 [8412]P1(f334(f334(f248(f888(x84121,a876)),f334(f287(x84121),x84122)),f334(f287(x84121),x84123)))+~P1(f334(f334(f248(f888(f887(x84121,x84121),a876)),x84122),x84123))
% 160.93/160.65 [8441]~P43(x84411,x84412)+~P1(f334(f334(f336(f887(x84411,x84411)),f334(f334(f269(x84411,x84411),x84413),x84413)),x84412))
% 160.93/160.65 [8443]~P39(x84431,x84432)+~P1(f334(f334(f336(f887(x84431,x84431)),f334(f334(f269(x84431,x84431),x84433),x84433)),x84432))
% 160.93/160.65 [8500]P1(f334(f334(f248(f888(x85001,a876)),f39(f888(x85001,a876),x85002)),f39(f888(x85001,a876),x85003)))+~P1(f334(f334(f248(f888(f888(x85001,a876),a876)),x85002),x85003))
% 160.93/160.65 [8501]P1(f334(f334(f248(f888(x85011,a876)),f40(f888(x85011,a876),x85012)),f40(f888(x85011,a876),x85013)))+~P1(f334(f334(f248(f888(f888(x85011,a876),a876)),x85013),x85012))
% 160.93/160.65 [8560]~P8(x85601,x85603,x85602)+P1(f334(f334(f248(f888(f887(x85601,x85601),a876)),x85602),f334(f334(f271(x85601,x85601),x85603),f334(f16(f888(x85601,a876),x85601),x85603))))
% 160.93/160.65 [8561]~P41(x85611,x85613,x85612)+P1(f334(f334(f248(f888(f887(x85611,x85611),a876)),x85612),f334(f334(f271(x85611,x85611),x85613),f334(f16(f888(x85611,a876),x85611),x85613))))
% 160.93/160.65 [8610]~P85(x86101)+P1(f334(f334(f248(x86101),f334(f334(f22(x86101),f334(f75(x86101),x86102)),f334(f75(x86101),x86103))),f334(f75(x86101),f334(f334(f22(x86101),x86103),x86102))))
% 160.93/160.65 [8611]~P85(x86111)+P1(f334(f334(f248(x86111),f334(f334(f22(x86111),f334(f75(x86111),x86112)),f334(f75(x86111),x86113))),f334(f75(x86111),f334(f334(f22(x86111),x86112),x86113))))
% 160.93/160.65 [8645]P1(f334(f334(f248(f888(f887(x86451,x86451),a876)),f310(x86451,x86452)),f310(x86451,x86453)))+~P1(f334(f334(f248(f888(f887(x86451,x86451),a876)),x86452),x86453))
% 160.93/160.65 [8800]P53(x88001,x88002,x88003)+~P53(x88001,x88002,f334(f334(f22(f888(f887(x88001,x88001),a876)),x88003),f310(x88001,f196(f888(f887(x88001,x88001),a876)))))
% 160.93/160.65 [8818]P1(f334(f334(f248(f888(f887(f882(x88181),f882(x88181)),a876)),f159(x88181,x88182)),f159(x88181,x88183)))+~P1(f334(f334(f248(f888(f887(x88181,x88181),a876)),x88182),x88183))
% 160.93/160.65 [8819]P1(f334(f334(f248(f888(f887(f882(x88191),f882(x88191)),a876)),f160(x88191,x88192)),f160(x88191,x88193)))+~P1(f334(f334(f248(f888(f887(x88191,x88191),a876)),x88192),x88193))
% 160.93/160.65 [8838]~P41(x88381,x88383,x88382)+P1(f334(f334(f248(f888(f887(x88381,x88381),a876)),x88382),f334(f334(f291(x88381,x88381,x88381),f334(f289(x88381,x88381),x88382)),x88382)))
% 160.93/160.65 [8887]~P1(f334(f139(x88871),x88872))+E(f334(f138(x88871,f334(f334(f7(x88871,f888(x88871,a876),a876),f336(x88871)),f334(f174(x88871),f178(x88871,x88872,x88873)))),x88872),f178(x88871,x88872,x88873))
% 160.93/160.65 [8949]E(x89491,x89492)+~P1(f334(f334(f336(f887(x89493,x89493)),f334(f334(f269(x89493,x89493),x89491),x89492)),f310(x89493,f196(f888(f887(x89493,x89493),a876)))))
% 160.93/160.65 [9035]P1(f334(f334(f336(x90351),x90352),f323(x90351,x90353)))+P1(f334(f334(f336(f887(x90351,x90351)),f334(f334(f269(x90351,x90351),f554(x90353,x90352,x90351)),x90352)),x90353))
% 160.93/160.65 [9036]P1(f334(f334(f336(x90361),x90362),f323(x90361,x90363)))+P1(f334(f334(f336(f887(x90361,x90361)),f334(f334(f269(x90361,x90361),f618(x90363,x90362,x90361)),x90362)),x90363))
% 160.93/160.65 [9037]P1(f334(f334(f336(x90371),x90372),f323(x90371,x90373)))+P1(f334(f334(f336(f887(x90371,x90371)),f334(f334(f269(x90371,x90371),f620(x90373,x90372,x90371)),x90372)),x90373))
% 160.93/160.65 [9127]~P1(f334(f334(f336(f882(x91271)),x91273),f163(x91271,x91272)))+P1(f334(f162(x91271,f334(f334(f7(x91271,f888(x91271,a876),a876),f336(x91271)),x91272)),x91273))
% 160.93/160.65 [9148]P1(f334(x91483,x91482))+E(f334(f254(x91481),f334(f334(f18(x91481,a876,a876),f334(f334(f8(a876,f888(a876,a876),x91481),a332),f334(a331,x91482))),x91483)),f196(f888(x91481,a876)))
% 160.93/160.65 [9169]~P85(x91691)+P1(f334(f334(f248(x91691),f334(f75(x91691),f334(f334(f22(x91691),f334(f75(x91691),x91692)),f334(f75(x91691),x91693)))),f334(f75(x91691),f334(f334(f22(x91691),x91692),x91693))))
% 160.93/160.65 [9183]~P1(f334(x91833,x91832))+E(f334(f254(x91831),f334(f334(f18(x91831,a876,a876),f334(f334(f8(a876,f888(a876,a876),x91831),a332),f334(a331,x91832))),x91833)),f334(f334(f312(x91831),x91832),f196(f888(x91831,a876))))
% 160.93/160.65 [9190]~P1(f334(f334(f336(f888(x91901,a876)),x91903),f334(f311(x91901),x91902)))+P1(f334(f262(x91901,f334(f334(f7(x91901,f888(x91901,a876),a876),f336(x91901)),x91902)),x91903))
% 160.93/160.65 [9223]P39(x92231,x92232)+P1(f334(f334(f336(f887(x92231,x92231)),f334(f334(f269(x92231,x92231),f334(f564(x92232,x92231),f334(a116,x92233))),f334(f564(x92232,x92231),x92233))),x92232))
% 160.93/160.65 [9364]P1(f334(f334(f336(f882(x93641)),x93642),f163(x93641,x93643)))+~P1(f334(f162(x93641,f334(f334(f7(x93641,f888(x93641,a876),a876),f336(x93641)),x93643)),x93642))
% 160.93/160.65 [9377]P1(f334(f334(f336(f888(x93771,a876)),x93772),f334(f311(x93771),x93773)))+~P1(f334(f262(x93771,f334(f334(f7(x93771,f888(x93771,a876),a876),f336(x93771)),x93773)),x93772))
% 160.93/160.65 [9434]P1(f334(f334(f336(x94341),f334(f280(x94341,x94342),x94343)),f334(f174(x94341),f334(f334(f156(f887(a103,x94341),x94341),f272(a103,x94341)),x94342))))+~P1(f334(f334(f249(a103),x94343),f334(f168(a103),f334(f334(f156(f887(a103,x94341),a103),f268(a103,x94341)),x94342))))
% 160.93/160.65 [9482]P1(f334(f334(f248(f888(f887(f882(x94821),f882(x94821)),a876)),f160(x94821,x94822)),f334(f334(f271(f882(x94821),f882(x94821)),f163(x94821,x94823)),f334(f16(f888(f882(x94821),a876),f882(x94821)),f163(x94821,x94823)))))+~P1(f334(f334(f248(f888(f887(x94821,x94821),a876)),x94822),f334(f334(f271(x94821,x94821),x94823),f334(f16(f888(x94821,a876),x94821),x94823))))
% 160.93/160.65 [9503]P1(f334(f334(f336(x95031),f334(f268(x95031,f887(a103,a103)),f334(f278(x95031,x95032),x95033))),f334(f174(x95031),f334(f334(f156(f887(a103,x95031),x95031),f272(a103,x95031)),x95032))))+~P1(f334(f334(f249(a103),f2(a103)),f334(f168(a103),f334(f334(f156(f887(a103,x95031),a103),f268(a103,x95031)),x95032))))
% 160.93/160.65 [9523]~P1(f334(f334(f248(f888(f887(x95231,x95231),a876)),x95232),f334(f334(f271(x95231,x95231),x95233),f334(f16(f888(x95231,a876),x95231),x95233))))+P1(f334(f334(f248(f888(f887(x95231,x95231),a876)),f334(f334(f291(x95231,x95231,x95231),x95232),f310(x95231,x95232))),f334(f334(f271(x95231,x95231),x95233),f334(f16(f888(x95231,a876),x95231),x95233))))
% 160.93/160.65 [9829]~P39(x98291,x98292)+~P1(f334(f334(f336(f887(x98291,x98291)),f334(f334(f269(x98291,x98291),f334(x98293,f334(a116,f565(x98292,x98291,x98293)))),f334(x98293,f565(x98292,x98291,x98293)))),x98292))
% 160.93/160.65 [9830]~P39(x98301,x98302)+~P1(f334(f334(f336(f887(x98301,x98301)),f334(f334(f269(x98301,x98301),f334(x98303,f334(a116,f624(x98303,x98302,x98301)))),f334(x98303,f624(x98303,x98302,x98301)))),x98302))
% 160.93/160.65 [10084]P1(f334(f334(f248(f888(f887(f888(x100841,a876),f888(x100841,a876)),a876)),f334(f334(f291(f888(x100841,a876),f888(x100841,a876),f888(x100841,a876)),f325(x100841,x100842)),f334(f334(f114(f888(f887(f888(x100841,a876),f888(x100841,a876)),a876)),f325(x100841,x100843)),f334(f334(f312(f887(f888(x100841,a876),f888(x100841,a876))),f334(f334(f269(f888(x100841,a876),f888(x100841,a876)),f196(f888(x100841,a876))),f196(f888(x100841,a876)))),f196(f888(f887(f888(x100841,a876),f888(x100841,a876)),a876)))))),f325(x100841,x100842)))+~P1(f334(f334(f248(f888(f887(x100841,x100841),a876)),f334(f334(f291(x100841,x100841,x100841),x100842),x100843)),x100842))
% 160.93/160.65 [10085]P1(f334(f334(f248(f888(f887(f888(x100851,a876),f888(x100851,a876)),a876)),f334(f334(f291(f888(x100851,a876),f888(x100851,a876),f888(x100851,a876)),f327(x100851,x100852)),f334(f334(f114(f888(f887(f888(x100851,a876),f888(x100851,a876)),a876)),f327(x100851,x100853)),f334(f334(f312(f887(f888(x100851,a876),f888(x100851,a876))),f334(f334(f269(f888(x100851,a876),f888(x100851,a876)),f196(f888(x100851,a876))),f196(f888(x100851,a876)))),f196(f888(f887(f888(x100851,a876),f888(x100851,a876)),a876)))))),f327(x100851,x100852)))+~P1(f334(f334(f248(f888(f887(x100851,x100851),a876)),f334(f334(f291(x100851,x100851,x100851),x100852),x100853)),x100852))
% 160.93/160.65 [7245]~P1(f334(f334(f248(a881),x72452),x72451))+E(f334(f334(f22(a881),f334(a116,f334(f334(f22(a881),x72451),x72452))),x72453),f334(f334(f22(a881),f334(a116,x72451)),f334(f334(f80(a881),x72452),x72453)))
% 160.93/160.65 [7284]~P58(x72841)+E(f334(f334(f80(x72841),f44(x72841,x72842,x72843)),f334(f334(f81(x72841),f334(f334(f38(x72841),x72842),x72843)),x72843)),x72842)
% 160.93/160.65 [7491]E(f334(f334(f81(a881),f334(f107(a881),x74911)),f334(f334(f81(a881),f334(f107(a881),x74912)),x74913)),f334(f334(f81(a881),f334(f107(a881),f334(f334(f81(a1),x74911),x74912))),x74913))+P1(f334(f334(f249(a1),x74911),a83))
% 160.93/160.65 [7955]~P1(f334(f334(f248(a881),x79553),x79552))+P1(f334(f334(f248(a881),x79551),f334(f334(f22(a881),f334(f334(f80(a881),x79552),x79551)),x79553)))
% 160.93/160.65 [8156]~P1(f334(f334(f248(a881),x81561),x81562))+E(f334(f334(f136(a881),f141(a881,f334(f304(a881,x81561),x81562))),f141(a881,f334(f304(a881,x81562),f334(f334(f80(a881),x81562),x81563)))),f141(a881,f334(f304(a881,x81561),f334(f334(f80(a881),x81562),x81563))))
% 160.93/160.65 [8420]~P1(f334(f61(x84201),x84202))+E(f334(a116,f334(f37(x84201),f334(f334(f22(f888(x84201,a876)),x84202),f334(f334(f312(x84201),x84203),f196(f888(x84201,a876)))))),f334(f37(x84201),f334(f334(f312(x84201),x84203),x84202)))
% 160.93/160.65 [8462]~P1(f334(f61(x84621),x84622))+E(f334(f334(f80(a881),f78(a881)),f334(f37(x84621),f334(f334(f22(f888(x84621,a876)),x84622),f334(f334(f312(x84621),x84623),f196(f888(x84621,a876)))))),f334(f37(x84621),f334(f334(f312(x84621),x84623),x84622)))
% 160.93/160.65 [8654]E(f334(f334(f22(a881),f334(f37(x86541),x86542)),f334(f37(x86541),f334(f334(f105(f888(x86541,a876)),x86542),x86543))),f334(f37(x86541),f334(f334(f22(f888(x86541,a876)),x86542),x86543)))+~P1(f334(f61(x86541),f334(f334(f105(f888(x86541,a876)),x86542),x86543)))
% 160.93/160.65 [8883]~P6(f334(x88832,f424(x88832,x88833,x88831)))+E(f334(f104(a1),f334(f334(f6(x88831,a881),f334(f334(f8(a1,a881,x88831),a108),x88832)),x88833)),f334(f334(f6(x88831,a1),x88832),x88833))
% 160.93/160.65 [8884]~P6(f334(x88842,f425(x88842,x88843,x88841)))+E(f334(f104(a1),f334(f334(f9(x88841,a881),f334(f334(f8(a1,a881,x88841),a108),x88842)),x88843)),f334(f334(f9(x88841,a1),x88842),x88843))
% 160.93/160.65 [8931]~P1(f334(f61(x89311),x89313))+P1(f334(f334(f248(a881),f334(f334(f22(a881),f334(f37(x89311),x89312)),f334(f37(x89311),x89313))),f334(f37(x89311),f334(f334(f22(f888(x89311,a876)),x89312),x89313))))
% 160.93/160.65 [8957]P1(f334(f334(f336(x89571),f424(x89572,x89573,x89571)),x89573))+E(f334(f104(a1),f334(f334(f6(x89571,a881),f334(f334(f8(a1,a881,x89571),a108),x89572)),x89573)),f334(f334(f6(x89571,a1),x89572),x89573))
% 160.93/160.65 [8958]P1(f334(f334(f336(x89581),f425(x89582,x89583,x89581)),x89583))+E(f334(f104(a1),f334(f334(f9(x89581,a881),f334(f334(f8(a1,a881,x89581),a108),x89582)),x89583)),f334(f334(f9(x89581,a1),x89582),x89583))
% 160.93/160.65 [9027]E(f85(x90271,f334(f334(f7(x90271,f888(x90271,a876),a876),f336(x90271)),f334(f334(f22(f888(x90271,a876)),x90272),f334(f334(f312(x90271),x90273),f196(f888(x90271,a876)))))),f261(x90271,x90273,x90272))+P1(f334(f334(f248(f888(x90271,a876)),x90272),f334(f334(f312(x90271),x90273),f196(f888(x90271,a876)))))
% 160.93/160.65 [9378]E(f334(f334(f156(f882(x93781),x93781),f334(f334(f7(f882(x93781),a881,x93781),f167(x93781)),x93782)),f334(f138(f882(x93781),f334(f334(f8(a881,a876,f882(x93781)),f334(f249(a881),x93782)),f197(f882(x93781)))),x93783)),f334(f334(f167(f882(x93781)),f182(x93781,x93783)),x93782))+~P1(f334(f334(f249(a881),x93782),f334(f197(f882(f882(x93781))),f182(x93781,x93783))))
% 160.93/160.65 [9451]E(f334(f138(x94511,x94512),x94513),f179(x94511,x94512,x94513))+P1(f334(f334(f336(x94511),f762(x94513,x94512,x94511)),f334(f174(x94511),f334(f334(f140(x94511),f334(f197(f882(x94511)),f179(x94511,x94512,x94513))),x94513))))
% 160.93/160.65 [9595]E(f334(f334(f140(x95951),f334(f197(f882(x95951)),f179(x95951,x95952,x95953))),x95953),f117(x95951))+~P1(f334(x95952,f334(f143(x95951),f334(f334(f140(x95951),f334(f197(f882(x95951)),f179(x95951,x95952,x95953))),x95953))))
% 160.93/160.65 [9690]~P1(f334(f334(f336(f887(x96901,x96901)),x96902),f310(x96901,x96903)))+P1(f334(f334(f336(f887(x96901,x96901)),x96902),f334(f334(f41(a881,f888(f887(x96901,x96901),a876)),f257(f888(a881,a876))),f334(f334(f7(a881,f888(f887(x96901,x96901),a876),f888(f887(x96901,x96901),a876)),f191(f887(x96901,x96901),a876)),x96903))))
% 160.93/160.65 [9747]~P1(f334(f334(f248(f888(x97471,a876)),f334(f334(f41(a881,f888(x97471,a876)),f334(f304(a881,f2(a881)),f480(x97473,x97472,x97471))),x97472)),x97473))+P1(f334(f334(f248(f888(x97471,a876)),f334(f334(f41(a881,f888(x97471,a876)),f257(f888(a881,a876))),x97472)),x97473))
% 160.93/160.65 [9805]~P1(f334(f334(f249(a1),f2(a1)),x98053))+P1(f334(f334(f249(a1),x98051),f334(f334(f80(a1),x98052),f334(f334(f81(a1),f334(f334(f80(a1),f334(f75(a1),f334(f334(f22(a1),x98052),x98051))),f78(a1))),x98053))))
% 160.93/160.65 [9816]~P39(x98161,f334(f334(f114(f888(f887(x98161,x98161),a876)),x98162),x98163))+P39(x98161,f334(f334(f114(f888(f887(x98161,x98161),a876)),f334(f334(f114(f888(f887(x98161,x98161),a876)),f334(f334(f291(x98161,x98161,x98161),x98162),x98162)),f334(f334(f291(x98161,x98161,x98161),x98163),x98162))),x98163))
% 160.93/160.65 [9899]P39(x98991,f334(f334(f114(f888(f887(x98991,x98991),a876)),x98992),x98993))+~P39(x98991,f334(f334(f114(f888(f887(x98991,x98991),a876)),f334(f334(f114(f888(f887(x98991,x98991),a876)),f334(f334(f291(x98991,x98991,x98991),x98992),x98992)),f334(f334(f291(x98991,x98991,x98991),x98993),x98992))),x98993))
% 160.93/160.65 [9455]~P139(x94551)+E(f334(f106(x94551),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x94552),x94553)),f196(f888(f887(a881,a881),a876)))))),f334(f334(f22(x94551),f334(f104(x94551),x94552)),f334(f104(x94551),x94553)))
% 160.93/160.65 [9541]P1(f334(x95413,x95412))+E(f334(f254(x95411),f334(f334(f18(x95411,a876,a876),f334(f334(f8(a876,f888(a876,a876),x95411),a332),f334(f334(f7(x95411,x95411,a876),a331),x95412))),x95413)),f196(f888(x95411,a876)))
% 160.93/160.65 [9544]~P1(f334(x95443,x95442))+E(f334(f254(x95441),f334(f334(f18(x95441,a876,a876),f334(f334(f8(a876,f888(a876,a876),x95441),a332),f334(f334(f7(x95441,x95441,a876),a331),x95442))),x95443)),f334(f334(f312(x95441),x95442),f196(f888(x95441,a876))))
% 160.93/160.65 [9783]E(x97831,x97832)+P1(f334(f334(f258(x97833,x97833,f334(f334(f8(f888(x97833,a876),f888(x97833,a876),x97833),f334(f8(a876,a876,x97833),a329)),a331)),x97831),x97832))
% 160.93/160.65 [9877]~E(x98771,x98772)+~P1(f334(f334(f258(x98773,x98773,f334(f334(f8(f888(x98773,a876),f888(x98773,a876),x98773),f334(f8(a876,a876,x98773),a329)),a331)),x98771),x98772))
% 160.93/160.65 [9891]~P1(f334(f61(x98911),x98913))+E(f334(f334(f64(x98911,f888(x98911,a876),f334(f334(f8(f888(x98911,a876),f888(f888(x98911,a876),f888(x98911,a876)),x98911),f334(f7(f888(x98911,a876),f888(x98911,a876),f888(x98911,a876)),f22(f888(x98911,a876)))),f334(f334(f7(x98911,f888(x98911,a876),f888(x98911,a876)),f312(x98911)),f196(f888(x98911,a876))))),x98912),x98913),f334(f334(f22(f888(x98911,a876)),x98912),x98913))
% 160.93/160.65 [9923]~P1(f334(f334(f249(a1),f2(a1)),x99233))+P1(f334(f334(f249(a1),f334(f334(f22(a1),x99231),f334(f334(f81(a1),f334(f334(f80(a1),f334(f75(a1),f334(f334(f22(a1),x99231),x99232))),f78(a1))),x99233))),x99232))
% 160.93/160.65 [10146]~P1(f334(f334(f336(x101461),x101463),f323(x101461,x101462)))+P1(f334(f322(x101461,f334(f334(f7(x101461,f888(f887(x101461,x101461),a876),f888(x101461,a876)),f334(f334(f8(f888(x101461,f888(f888(f887(x101461,x101461),a876),a876)),f888(f888(f887(x101461,x101461),a876),f888(x101461,a876)),x101461),f7(x101461,f888(f887(x101461,x101461),a876),a876)),f334(f334(f8(f888(x101461,f887(x101461,x101461)),f888(x101461,f888(f888(f887(x101461,x101461),a876),a876)),x101461),f334(f8(f887(x101461,x101461),f888(f888(f887(x101461,x101461),a876),a876),x101461),f336(f887(x101461,x101461)))),f269(x101461,x101461)))),x101462)),x101463))
% 160.93/160.65 [10158]P1(f334(f334(f336(x101581),x101582),f323(x101581,x101583)))+~P1(f334(f322(x101581,f334(f334(f7(x101581,f888(f887(x101581,x101581),a876),f888(x101581,a876)),f334(f334(f8(f888(x101581,f888(f888(f887(x101581,x101581),a876),a876)),f888(f888(f887(x101581,x101581),a876),f888(x101581,a876)),x101581),f7(x101581,f888(f887(x101581,x101581),a876),a876)),f334(f334(f8(f888(x101581,f887(x101581,x101581)),f888(x101581,f888(f888(f887(x101581,x101581),a876),a876)),x101581),f334(f8(f887(x101581,x101581),f888(f888(f887(x101581,x101581),a876),a876),x101581),f336(f887(x101581,x101581)))),f269(x101581,x101581)))),x101583)),x101582))
% 160.93/160.65 [9745]~P1(f334(f61(x97451),f334(f254(x97451),x97453)))+P1(f334(f61(x97451),f334(f254(x97451),f334(f334(f18(x97451,a876,a876),f334(f334(f8(a876,f888(a876,a876),x97451),a332),x97452)),x97453))))
% 160.93/160.65 [9746]~P1(f334(f61(x97461),f334(f254(x97461),x97462)))+P1(f334(f61(x97461),f334(f254(x97461),f334(f334(f18(x97461,a876,a876),f334(f334(f8(a876,f888(a876,a876),x97461),a332),x97462)),x97463))))
% 160.93/160.65 [9848]P1(f334(f61(x98481),f334(f254(x98481),x98482)))+~P1(f334(f61(x98481),f334(f254(x98481),f334(f334(f18(x98481,a876,a876),f334(f334(f8(a876,f888(a876,a876),x98481),a333),x98483)),x98482))))
% 160.93/160.65 [9849]P1(f334(f61(x98491),f334(f254(x98491),x98492)))+~P1(f334(f61(x98491),f334(f254(x98491),f334(f334(f18(x98491,a876,a876),f334(f334(f8(a876,f888(a876,a876),x98491),a333),x98492)),x98493))))
% 160.93/160.65 [10133]~P1(f334(f61(x101331),x101332))+P1(f334(f61(f882(x101331)),f334(f254(f882(x101331)),f334(f334(f18(f882(x101331),a876,a876),f334(f334(f8(a876,f888(a876,a876),f882(x101331)),a332),f334(f334(f7(f882(x101331),f888(x101331,a876),a876),f334(f334(f8(f888(x101331,a876),f888(f888(x101331,a876),a876),f882(x101331)),f248(f888(x101331,a876))),f174(x101331))),x101332))),f334(f334(f7(f882(x101331),a881,a876),f334(f334(f8(a881,f888(a881,a876),f882(x101331)),a331),f197(f882(x101331)))),x101333)))))
% 160.93/160.65 [10134]~P1(f334(f61(x101341),x101342))+P1(f334(f61(f882(x101341)),f334(f254(f882(x101341)),f334(f334(f18(f882(x101341),a876,a876),f334(f334(f8(a876,f888(a876,a876),f882(x101341)),a332),f334(f334(f7(f882(x101341),f888(x101341,a876),a876),f334(f334(f8(f888(x101341,a876),f888(f888(x101341,a876),a876),f882(x101341)),f248(f888(x101341,a876))),f174(x101341))),x101342))),f334(f334(f7(f882(x101341),a881,a876),f334(f334(f8(a881,f888(a881,a876),f882(x101341)),f248(a881)),f197(f882(x101341)))),x101343)))))
% 160.93/160.65 [9864]~P118(x98641)+E(f334(f334(f259(x98641),x98642),f334(f334(f81(a881),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x98643)),f334(f334(f81(x98641),f334(f334(f259(x98641),x98642),x98643)),f334(f334(f259(x98641),x98642),x98643)))
% 160.93/160.65 [9904]~P80(x99041)+E(f334(f334(f259(x99041),f334(f334(f259(x99041),x99042),x99043)),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f334(f334(f259(x99041),x99042),f334(f334(f81(a881),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x99043)))
% 160.93/160.65 [9950]~P139(x99501)+E(f334(f334(f259(x99501),f334(f79(x99501),x99502)),f334(f334(f81(a881),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x99503)),f334(f334(f259(x99501),x99502),f334(f334(f81(a881),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x99503)))
% 160.93/160.65 [10091]~P111(x100911)+P1(f334(f334(f248(x100911),f2(x100911)),f334(f334(f80(x100911),f334(f334(f259(x100911),x100912),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x100911),x100913),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))))
% 160.93/160.65 [9960]~P118(x99601)+E(f334(f334(f259(x99601),x99602),f334(a116,f334(f334(f81(a881),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x99603))),f334(f334(f81(x99601),x99602),f334(f334(f81(x99601),f334(f334(f259(x99601),x99602),x99603)),f334(f334(f259(x99601),x99602),x99603))))
% 160.93/160.65 [10009]~P80(x100091)+E(f334(f334(f81(x100091),x100092),f334(f334(f259(x100091),f334(f334(f259(x100091),x100092),x100093)),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x100091),x100092),f334(a116,f334(f334(f81(a881),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x100093))))
% 160.93/160.65 [10048]~P111(x100481)+P1(f334(f334(f248(x100481),f2(x100481)),f334(f334(f259(x100481),x100482),f334(f334(f81(a881),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x100483))))
% 160.93/160.65 [10114]~P93(x101141)+E(f334(f334(f22(x101141),f334(f334(f80(x101141),f334(f334(f259(x101141),x101142),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x101141),x101143),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))),f334(f334(f81(x101141),f334(f334(f81(x101141),f334(f107(x101141),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x101142)),x101143)),f334(f334(f259(x101141),f334(f334(f22(x101141),x101142),x101143)),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))
% 160.93/160.65 [10115]~P93(x101151)+E(f334(f334(f80(x101151),f334(f334(f80(x101151),f334(f334(f259(x101151),x101152),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x101151),x101153),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))),f334(f334(f81(x101151),f334(f334(f81(x101151),f334(f107(x101151),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x101152)),x101153)),f334(f334(f259(x101151),f334(f334(f80(x101151),x101152),x101153)),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))
% 160.93/160.65 [10213]~P29(x102131,x102132,x102133)+P1(f99(x102131,a876,f334(f334(f8(f888(a878,f888(f888(x102131,f888(a877,a876)),f888(x102131,a876))),f888(a878,f888(f888(x102131,f888(a877,a876)),a876)),f888(x102131,f888(a877,a876))),f334(f8(f888(f888(x102131,f888(a877,a876)),f888(x102131,a876)),f888(f888(x102131,f888(a877,a876)),a876),a878),f334(f8(f888(x102131,a876),a876,f888(x102131,f888(a877,a876))),f88(x102131)))),f334(f334(f8(f888(a878,f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876)))),f888(a878,f888(f888(x102131,f888(a877,a876)),f888(x102131,a876))),f888(x102131,f888(a877,a876))),f334(f8(f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876))),f888(f888(x102131,f888(a877,a876)),f888(x102131,a876)),a878),f334(f8(f888(x102131,f888(a877,a876)),f888(x102131,a876),f888(x102131,f888(a877,a876))),f334(f8(f888(a877,a876),a876,x102131),f88(a877))))),f334(f334(f7(f888(x102131,f888(a877,a876)),f888(a878,f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876)))),f888(a878,f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876))))),f334(f334(f8(f888(f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876))),f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876)))),f888(f888(a878,f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876)))),f888(a878,f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876))))),f888(x102131,f888(a877,a876))),f8(f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876))),f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876))),a878)),f334(f334(f8(f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876))),f888(f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876))),f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876)))),f888(x102131,f888(a877,a876))),f8(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876)))),f334(f334(f8(f888(x102131,f888(f888(a877,a876),f888(a877,a876))),f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876))),f888(x102131,f888(a877,a876))),f18(x102131,f888(a877,a876),f888(a877,a876))),f334(f334(f8(f888(x102131,f888(a877,f888(a876,a876))),f888(x102131,f888(f888(a877,a876),f888(a877,a876))),f888(x102131,f888(a877,a876))),f334(f8(f888(a877,f888(a876,a876)),f888(f888(a877,a876),f888(a877,a876)),x102131),f18(a877,a876,a876))),f334(f8(f888(a877,a876),f888(a877,f888(a876,a876)),x102131),f334(f8(a876,f888(a876,a876),a877),a337))))))),f334(f334(f8(f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,f888(a877,a876)))),f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876))),a878),f334(f8(f888(x102131,f888(a877,f888(a877,a876))),f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,a876))),f334(f8(f888(a877,f888(a877,a876)),f888(a877,a876),x102131),f334(f8(f888(a877,a876),a876,a877),f88(a877))))),f334(f334(f8(f888(f888(a877,a876),f888(a877,f888(a877,a876))),f888(f888(x102131,f888(a877,a876)),f888(x102131,f888(a877,f888(a877,a876)))),a878),f8(f888(a877,a876),f888(a877,f888(a877,a876)),x102131)),f334(f334(f8(f888(a877,f888(f888(a877,a876),f888(a877,a876))),f888(f888(a877,a876),f888(a877,f888(a877,a876))),a878),f7(a877,f888(a877,a876),f888(a877,a876))),f334(f334(f8(f888(a877,f888(a877,f888(a876,a876))),f888(a877,f888(f888(a877,a876),f888(a877,a876))),a878),f334(f8(f888(a877,f888(a876,a876)),f888(f888(a877,a876),f888(a877,a876)),a877),f18(a877,a876,a876))),f334(f334(f8(f888(a877,f888(a877,a876)),f888(a877,f888(a877,f888(a876,a876))),a878),f334(f8(f888(a877,a876),f888(a877,f888(a876,a876)),a877),f334(f8(a876,f888(a876,a876),a877),a337))),f334(f334(f7(a878,a881,f888(a877,f888(a877,a876))),f334(f334(f8(f888(a877,f888(a881,f888(a877,a876))),f888(a881,f888(a877,f888(a877,a876))),a878),f7(a877,a881,f888(a877,a876))),a204)),x102132))))))))),x102133))
% 160.93/160.65 [10215]P29(x102151,x102152,x102153)+~P1(f99(x102151,a876,f334(f334(f8(f888(a878,f888(f888(x102151,f888(a877,a876)),f888(x102151,a876))),f888(a878,f888(f888(x102151,f888(a877,a876)),a876)),f888(x102151,f888(a877,a876))),f334(f8(f888(f888(x102151,f888(a877,a876)),f888(x102151,a876)),f888(f888(x102151,f888(a877,a876)),a876),a878),f334(f8(f888(x102151,a876),a876,f888(x102151,f888(a877,a876))),f88(x102151)))),f334(f334(f8(f888(a878,f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876)))),f888(a878,f888(f888(x102151,f888(a877,a876)),f888(x102151,a876))),f888(x102151,f888(a877,a876))),f334(f8(f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876))),f888(f888(x102151,f888(a877,a876)),f888(x102151,a876)),a878),f334(f8(f888(x102151,f888(a877,a876)),f888(x102151,a876),f888(x102151,f888(a877,a876))),f334(f8(f888(a877,a876),a876,x102151),f88(a877))))),f334(f334(f7(f888(x102151,f888(a877,a876)),f888(a878,f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876)))),f888(a878,f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876))))),f334(f334(f8(f888(f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876))),f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876)))),f888(f888(a878,f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876)))),f888(a878,f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876))))),f888(x102151,f888(a877,a876))),f8(f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876))),f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876))),a878)),f334(f334(f8(f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876))),f888(f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876))),f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876)))),f888(x102151,f888(a877,a876))),f8(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876)))),f334(f334(f8(f888(x102151,f888(f888(a877,a876),f888(a877,a876))),f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876))),f888(x102151,f888(a877,a876))),f18(x102151,f888(a877,a876),f888(a877,a876))),f334(f334(f8(f888(x102151,f888(a877,f888(a876,a876))),f888(x102151,f888(f888(a877,a876),f888(a877,a876))),f888(x102151,f888(a877,a876))),f334(f8(f888(a877,f888(a876,a876)),f888(f888(a877,a876),f888(a877,a876)),x102151),f18(a877,a876,a876))),f334(f8(f888(a877,a876),f888(a877,f888(a876,a876)),x102151),f334(f8(a876,f888(a876,a876),a877),a337))))))),f334(f334(f8(f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,f888(a877,a876)))),f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876))),a878),f334(f8(f888(x102151,f888(a877,f888(a877,a876))),f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,a876))),f334(f8(f888(a877,f888(a877,a876)),f888(a877,a876),x102151),f334(f8(f888(a877,a876),a876,a877),f88(a877))))),f334(f334(f8(f888(f888(a877,a876),f888(a877,f888(a877,a876))),f888(f888(x102151,f888(a877,a876)),f888(x102151,f888(a877,f888(a877,a876)))),a878),f8(f888(a877,a876),f888(a877,f888(a877,a876)),x102151)),f334(f334(f8(f888(a877,f888(f888(a877,a876),f888(a877,a876))),f888(f888(a877,a876),f888(a877,f888(a877,a876))),a878),f7(a877,f888(a877,a876),f888(a877,a876))),f334(f334(f8(f888(a877,f888(a877,f888(a876,a876))),f888(a877,f888(f888(a877,a876),f888(a877,a876))),a878),f334(f8(f888(a877,f888(a876,a876)),f888(f888(a877,a876),f888(a877,a876)),a877),f18(a877,a876,a876))),f334(f334(f8(f888(a877,f888(a877,a876)),f888(a877,f888(a877,f888(a876,a876))),a878),f334(f8(f888(a877,a876),f888(a877,f888(a876,a876)),a877),f334(f8(a876,f888(a876,a876),a877),a337))),f334(f334(f7(a878,a881,f888(a877,f888(a877,a876))),f334(f334(f8(f888(a877,f888(a881,f888(a877,a876))),f888(a881,f888(a877,f888(a877,a876))),a878),f7(a877,a881,f888(a877,a876))),a204)),x102152))))))))),x102153))
% 160.93/160.65 [4683]E(x46831,x46832)+~E(f33(x46833,x46831),f33(x46834,x46832))
% 160.93/160.65 [4684]E(x46841,x46842)+~E(f33(x46841,x46843),f33(x46842,x46844))
% 160.93/160.65 [4685]E(x46851,x46852)+~E(f32(x46853,x46851),f32(x46854,x46852))
% 160.93/160.65 [4686]E(x46861,x46862)+~E(f32(x46861,x46863),f32(x46862,x46864))
% 160.93/160.65 [7754]P27(x77541,x77542,x77543,x77544)+~E(f548(x77544,x77543,x77542,x77541),f549(x77544,x77543,x77542,x77541))
% 160.93/160.65 [8044]P36(x80441,x80442,x80443,x80444,f117(x80442))+~E(x80444,f117(x80441))
% 160.93/160.65 [8045]P36(x80451,x80452,x80453,f117(x80451),x80454)+~E(x80454,f117(x80452))
% 160.93/160.65 [8270]~P27(x82701,f885(x82702),x82704,f186(x82701,x82702,x82704))+P27(x82701,f885(x82702),f187(x82701,x82702,x82703,x82704),f186(x82701,x82702,x82704))
% 160.93/160.65 [8476]~P27(x84761,f885(x84762),f187(x84761,x84762,x84764,x84763),f186(x84761,x84762,x84763))+P27(x84761,f885(x84762),x84763,f186(x84761,x84762,x84763))
% 160.93/160.65 [8600]~P36(x86002,x86003,x86004,x86001,f117(x86003))+E(x86001,f117(x86002))
% 160.93/160.65 [8601]~P36(x86013,x86012,x86014,f117(x86013),x86011)+E(x86011,f117(x86012))
% 160.93/160.65 [5057]~P19(x50573,x50571,x50574)+E(f334(f334(x50571,x50572),x50572),x50572)
% 160.93/160.65 [5345]~E(x53454,f196(f888(x53451,a876)))+E(f334(f313(x53451,x53452,x53453),x53454),f196(f888(x53452,a876)))
% 160.93/160.65 [5612]~E(f334(f313(x56122,x56123,x56124),x56121),f196(f888(x56123,a876)))+E(x56121,f196(f888(x56122,a876)))
% 160.93/160.65 [5895]~P108(x58952)+E(f334(f334(f150(x58951,x58952,x58953),x58954),f117(x58951)),f334(f334(f153(x58951),x58954),f117(x58951)))
% 160.93/160.65 [5932]E(f334(x59321,x59322),f210(x59323))+P1(f334(f334(f336(x59324),x59322),f186(x59324,x59323,x59321)))
% 160.93/160.65 [6255]~E(x62551,f196(f888(x62552,a876)))+~P1(f334(f62(x62552,x62553,x62551),x62554))
% 160.93/160.65 [6277]~P56(x62771,x62773,x62774,x62772)+P1(f334(f61(x62771),x62772))
% 160.93/160.65 [6278]~P56(x62781,x62783,x62782,x62784)+P1(f334(f61(x62781),x62782))
% 160.93/160.65 [6284]~P56(x62842,x62843,x62844,x62841)+~E(x62841,f196(f888(x62842,a876)))
% 160.93/160.65 [6315]~P109(x63151)+E(f334(f334(f105(f888(x63151,a876)),f334(f304(x63151,x63152),x63153)),f305(x63151,x63153,x63154)),f196(f888(x63151,a876)))
% 160.93/160.65 [6342]~P1(f334(f334(x63423,x63424),x63422))+P1(f334(f334(f336(x63421),x63422),f295(x63421,x63423,x63424)))
% 160.93/160.65 [6343]~P1(f334(f334(x63433,x63434),x63432))+P1(f334(f334(f336(x63431),x63432),f296(x63431,x63433,x63434)))
% 160.93/160.65 [6344]~P1(f334(f334(x63443,x63442),x63444))+P1(f334(f334(f336(x63441),x63442),f297(x63441,x63443,x63444)))
% 160.93/160.65 [6345]~P1(f334(f334(x63453,x63452),x63454))+P1(f334(f334(f336(x63451),x63452),f300(x63451,x63453,x63454)))
% 160.93/160.65 [6483]~P109(x64831)+E(f334(f334(f105(f888(x64831,a876)),f305(x64831,x64832,x64833)),f308(x64831,x64833,x64834)),f196(f888(x64831,a876)))
% 160.93/160.65 [6484]~P109(x64841)+E(f334(f334(f105(f888(x64841,a876)),f305(x64841,x64842,x64843)),f307(x64841,x64843,x64844)),f196(f888(x64841,a876)))
% 160.93/160.65 [6485]~P109(x64851)+E(f334(f334(f105(f888(x64851,a876)),f308(x64851,x64852,x64853)),f305(x64851,x64853,x64854)),f196(f888(x64851,a876)))
% 160.93/160.65 [6486]~P109(x64861)+E(f334(f334(f105(f888(x64861,a876)),f307(x64861,x64862,x64863)),f308(x64861,x64863,x64864)),f196(f888(x64861,a876)))
% 160.93/160.65 [6487]~P109(x64871)+E(f334(f334(f105(f888(x64871,a876)),f307(x64871,x64872,x64873)),f307(x64871,x64873,x64874)),f196(f888(x64871,a876)))
% 160.93/160.65 [6524]P1(f334(f334(x65241,x65242),f571(x65242,x65241)))+~P1(f334(f263(x65243,x65244,x65241),x65242))
% 160.93/160.65 [6572]~E(f334(x65721,x65722),f210(x65723))+~P1(f334(f334(f336(x65724),x65722),f186(x65724,x65723,x65721)))
% 160.93/160.65 [6601]~P108(x66012)+E(f334(f174(x66011),f152(x66011,x66012,x66013,x66014)),f334(f174(x66011),x66014))
% 160.93/160.65 [6654]~P142(x66541)+E(f198(x66541,x66542,f334(a116,x66543),x66544),f198(x66541,x66542,x66543,f334(x66542,x66544)))
% 160.93/160.65 [6714]~P1(f334(f334(f336(x67144),x67143),f295(x67144,x67141,x67142)))+P1(f334(f334(x67141,x67142),x67143))
% 160.93/160.65 [6715]~P1(f334(f334(f336(x67154),x67153),f296(x67154,x67151,x67152)))+P1(f334(f334(x67151,x67152),x67153))
% 160.93/160.65 [6716]~P1(f334(f334(f336(x67164),x67162),f297(x67164,x67161,x67163)))+P1(f334(f334(x67161,x67162),x67163))
% 160.93/160.65 [6717]~P1(f334(f334(f336(x67174),x67172),f300(x67174,x67171,x67173)))+P1(f334(f334(x67171,x67172),x67173))
% 160.93/160.65 [6794]E(f334(f37(f886(x67941,x67942)),f321(x67941,x67942,x67943,x67944)),f2(a881))+P1(f334(f61(x67942),x67944))
% 160.93/160.65 [6795]E(f334(f37(f886(x67951,x67952)),f321(x67951,x67952,x67953,x67954)),f2(a881))+P1(f334(f61(x67951),x67953))
% 160.93/160.65 [6996]~P17(x69964,x69961,x69962)+E(f334(f73(x69961,x69961,x69961,f334(x69962,x69963)),f334(x69962,x69963)),f334(x69962,x69963))
% 160.93/160.65 [7792]~P1(f334(x77921,x77924))+P1(f334(x77921,f96(x77922,a881,x77923,x77921)))
% 160.93/160.65 [7876]~E(x78762,x78763)+P1(f334(f334(f336(f887(x78761,x78761)),f334(f334(f269(x78761,x78761),x78762),x78763)),f310(x78761,x78764)))
% 160.93/160.65 [7905]~P27(x79051,x79052,x79053,f257(f888(x79051,a876)))+E(f334(f77(x79051,x79052,f257(f888(x79051,a876)),x79053),f334(x79053,x79054)),x79054)
% 160.93/160.65 [7995]~P1(f334(f334(f336(f882(x79951)),f334(f334(f153(x79951),x79954),x79952)),f163(x79951,x79953)))+P1(f334(f334(f336(f882(x79951)),x79952),f163(x79951,x79953)))
% 160.93/160.65 [7996]~P1(f334(f334(f336(f882(x79961)),f334(f334(f136(x79961),x79964),x79962)),f163(x79961,x79963)))+P1(f334(f334(f336(f882(x79961)),x79962),f163(x79961,x79963)))
% 160.93/160.65 [7997]~P1(f334(f334(f336(f882(x79971)),f334(f334(f136(x79971),x79972),x79974)),f163(x79971,x79973)))+P1(f334(f334(f336(f882(x79971)),x79972),f163(x79971,x79973)))
% 160.93/160.65 [8008]~P108(x80081)+P16(x80081,f334(f334(f156(x80082,x80081),x80083),f152(x80082,x80081,x80083,x80084)))
% 160.93/160.65 [8107]P27(x81074,x81073,x81071,x81072)+E(f334(x81071,f548(x81072,x81071,x81073,x81074)),f334(x81071,f549(x81072,x81071,x81073,x81074)))
% 160.93/160.65 [8120]E(f187(x81201,x81202,x81203,x81204),f187(x81201,x81202,x81204,x81203))+~E(f334(f334(f105(f888(x81201,a876)),f186(x81201,x81202,x81203)),f186(x81201,x81202,x81204)),f196(f888(x81201,a876)))
% 160.93/160.65 [8232]~P27(x82322,x82321,x82324,x82323)+P27(x82321,x82322,f77(x82322,x82321,x82323,x82324),f334(f313(x82322,x82321,x82324),x82323))
% 160.93/160.65 [8369]P39(f887(x83692,x83694),f286(x83692,x83694,x83691,x83693))+P1(f334(x83691,f563(x83692,x83693,x83694,x83691)))
% 160.93/160.65 [8484]E(x84841,x84842)+~P1(f334(f334(f336(f887(x84843,x84843)),f334(f334(f269(x84843,x84843),x84841),x84842)),f266(x84843,x84844)))
% 160.93/160.65 [8552]~P1(f334(f61(f886(x85523,x85521)),f321(x85523,x85521,x85524,x85522)))+P1(f334(f61(x85521),x85522))
% 160.93/160.65 [8553]~P1(f334(f61(f886(x85531,x85533)),f321(x85531,x85533,x85532,x85534)))+P1(f334(f61(x85531),x85532))
% 160.93/160.65 [8737]P39(f887(x87371,x87372),f286(x87371,x87372,x87373,x87374))+~P39(x87372,f334(x87374,f563(x87371,x87374,x87372,x87373)))
% 160.93/160.65 [9300]E(f334(f334(f161(x93001,x93002),f692(x93003,x93004,x93002,x93001)),f693(x93003,x93004,x93002,x93001)),x93004)+~P1(f334(f334(f336(f887(f882(x93001),f882(x93001))),f334(f334(f269(f882(x93001),f882(x93001)),x93002),x93004)),f159(x93001,x93003)))
% 160.93/160.65 [9301]~P1(f334(x93013,x93014))+P1(f334(f334(f248(a881),f334(x93011,f96(x93012,a881,x93011,x93013))),f334(x93011,x93014)))
% 160.93/160.65 [9307]~P1(f334(f334(f336(f887(f882(x93071),f882(x93071))),f334(f334(f269(f882(x93071),f882(x93071)),x93072),x93073)),f147(x93071,x93074)))+P1(f334(f334(f336(f887(f882(x93071),f882(x93071))),f334(f334(f269(f882(x93071),f882(x93071)),x93072),x93073)),f149(x93071,x93074)))
% 160.93/160.65 [9413]P1(f334(f61(x94131),x94132))+~P1(f334(f334(f336(f887(f888(x94131,a876),f888(x94131,a876))),f334(f334(f269(f888(x94131,a876),f888(x94131,a876)),x94133),x94132)),f325(x94131,x94134)))
% 160.93/160.65 [9414]P1(f334(f61(x94141),x94142))+~P1(f334(f334(f336(f887(f888(x94141,a876),f888(x94141,a876))),f334(f334(f269(f888(x94141,a876),f888(x94141,a876)),x94142),x94143)),f325(x94141,x94144)))
% 160.93/160.65 [9417]~E(x94171,f196(f888(x94172,a876)))+~P1(f334(f334(f336(f887(f888(x94172,a876),f888(x94172,a876))),f334(f334(f269(f888(x94172,a876),f888(x94172,a876)),x94173),x94171)),f325(x94172,x94174)))
% 160.93/160.65 [10060]P14(x100601,x100602,x100603,x100604)+~P1(f334(f334(f273(x100601,x100601,a876),f334(f334(f7(x100601,f888(x100601,x100602),f888(x100601,a876)),f334(f334(f8(f888(x100602,a876),f888(f888(x100601,x100602),f888(x100601,a876)),x100601),f8(x100602,a876,x100601)),f334(f334(f8(x100602,f888(x100602,a876),x100601),a331),x100604))),x100604)),f597(x100604,x100603,x100602,x100601)))
% 160.93/160.65 [4958]~E(x49582,f117(x49581))+E(f334(f334(f161(x49581,x49582),x49583),x49584),f117(x49581))
% 160.93/160.65 [4959]~E(x49594,f117(x49591))+E(f334(f334(f156(x49591,x49592),x49593),x49594),f117(x49592))
% 160.93/160.65 [4960]~E(x49604,f210(x49601))+E(f334(f334(f211(x49601,x49602),x49603),x49604),f210(x49602))
% 160.93/160.65 [5195]E(x51951,f117(x51952))+~E(f334(f334(f156(x51952,x51953),x51954),x51951),f117(x51953))
% 160.93/160.65 [5196]E(x51961,f210(x51962))+~E(f334(f334(f211(x51962,x51963),x51964),x51961),f210(x51963))
% 160.93/160.65 [5197]E(x51971,f117(x51972))+~E(f334(f334(f161(x51972,x51971),x51973),x51974),f117(x51972))
% 160.93/160.65 [5230]E(x52301,x52302)+~E(f334(f334(f136(x52303),x52304),x52301),f334(f334(f136(x52303),x52304),x52302))
% 160.93/160.65 [5231]E(x52311,x52312)+~E(f334(f334(f136(x52313),x52311),x52314),f334(f334(f136(x52313),x52312),x52314))
% 160.93/160.65 [5382]P1(f334(x53823,x53822))+E(f172(x53821,x53822,f334(f138(x53821,x53823),x53824)),f334(f138(x53821,x53823),x53824))
% 160.93/160.65 [5385]~P1(f334(x53852,x53853))+P35(x53851,x53852,f334(f334(f153(x53851),x53853),x53854))
% 160.93/160.65 [5394]E(x53941,x53942)+~E(f141(a881,f334(f304(a881,x53941),x53943)),f334(f334(f153(a881),x53942),x53944))
% 160.93/160.65 [5442]~P28(x54422,x54423)+P28(x54421,f334(f334(f74(x54422,x54421),x54423),x54424))
% 160.93/160.65 [5443]~P39(x54432,x54433)+P39(x54431,f334(f334(f290(x54432,x54431),x54433),x54434))
% 160.93/160.65 [5567]~P35(x55671,x55672,x55674)+P35(x55671,x55672,f334(f334(f153(x55671),x55673),x55674))
% 160.93/160.65 [5568]~P35(x55681,x55682,x55684)+P35(x55681,x55682,f334(f334(f136(x55681),x55683),x55684))
% 160.93/160.65 [5569]~P35(x55691,x55692,x55693)+P35(x55691,x55692,f334(f334(f136(x55691),x55693),x55694))
% 160.93/160.65 [5655]~E(x56551,f117(x56552))+~E(f334(f334(f136(x56552),x56553),f334(f334(f153(x56552),x56554),f117(x56552))),x56551)
% 160.93/160.65 [5680]~P33(x56803,x56801,f334(f334(f153(x56803),x56802),x56804))+P1(f334(x56801,x56802))
% 160.93/160.65 [5690]E(f118(x56901,x56902),x56903)+~E(f334(f334(f136(x56901),x56903),f334(f334(f153(x56901),x56904),f117(x56901))),x56902)
% 160.93/160.65 [5691]E(f146(x56911,x56912),x56913)+~E(f334(f334(f136(x56911),x56914),f334(f334(f153(x56911),x56913),f117(x56911))),x56912)
% 160.93/160.65 [5800]~E(f141(a881,f334(f304(a881,x58001),x58002)),f334(f334(f153(a881),x58003),x58004))+P1(f334(f334(f249(a881),x58001),x58002))
% 160.93/160.65 [5808]P33(x58081,x58082,x58083)+~P33(x58081,x58082,f334(f334(f153(x58081),x58084),x58083))
% 160.93/160.65 [5809]P33(x58091,x58092,x58093)+~P33(x58091,x58092,f334(f334(f136(x58091),x58094),x58093))
% 160.93/160.65 [5810]P33(x58101,x58102,x58103)+~P33(x58101,x58102,f334(f334(f136(x58101),x58103),x58104))
% 160.93/160.65 [5996]E(x59961,f334(f334(f136(x59962),f334(f171(x59962),x59963)),f334(f334(f153(x59962),x59964),f117(x59962))))+~E(f334(f171(x59962),x59961),f334(f334(f153(x59962),x59964),x59963))
% 160.93/160.65 [6173]~P109(x61731)+E(f334(f334(f105(f888(x61731,a876)),f334(f304(x61731,x61732),x61733)),f334(f304(x61731,x61733),x61734)),f196(f888(x61731,a876)))
% 160.93/160.65 [6213]~P68(x62131)+E(f334(f168(x62131),f334(f334(f156(a1,x62131),x62132),f181(x62133,x62134))),f334(f334(f6(a1,x62131),x62132),f334(f174(a1),f181(x62133,x62134))))
% 160.93/160.65 [6214]~P68(x62141)+E(f334(f334(f6(a1,x62141),x62142),f334(f174(a1),f181(x62143,x62144))),f334(f168(x62141),f334(f334(f156(a1,x62141),x62142),f181(x62143,x62144))))
% 160.93/160.65 [6355]~E(x63552,f334(f334(f136(x63551),f334(f171(x63551),x63554)),f334(f334(f153(x63551),x63553),f117(x63551))))+E(f334(f171(x63551),x63552),f334(f334(f153(x63551),x63553),x63554))
% 160.93/160.65 [6370]~P21(x63702,x63703,x63704,x63701)+E(f334(x63701,f196(f888(x63702,a876))),f34(x63703))
% 160.93/160.65 [6396]~P109(x63961)+E(f334(f334(f105(f888(x63961,a876)),f308(x63961,x63962,x63963)),f334(f304(x63961,x63963),x63964)),f196(f888(x63961,a876)))
% 160.93/160.65 [6602]E(x66021,f196(f888(x66022,a876)))+~E(f321(x66023,x66022,x66024,x66021),f196(f888(f886(x66023,x66022),a876)))
% 160.93/160.65 [6603]E(x66031,f196(f888(x66032,a876)))+~E(f321(x66032,x66033,x66031,x66034),f196(f888(f886(x66032,x66033),a876)))
% 160.93/160.65 [6673]~P108(x66732)+E(f334(f197(f882(x66731)),f152(x66731,x66732,x66733,x66734)),f334(f197(f882(x66731)),x66734))
% 160.93/160.65 [6685]~P1(f334(f264(x66853,x66854,x66851),x66852))+P1(f334(f334(x66851,f572(x66852,x66851)),x66852))
% 160.93/160.65 [6725]~P1(f334(f61(x67252),x67254))+P1(f334(f61(x67251),f334(f313(x67252,x67251,x67253),x67254)))
% 160.93/160.65 [6956]~P27(x69562,x69561,x69563,x69564)+E(f334(f37(x69561),f334(f313(x69562,x69561,x69563),x69564)),f334(f37(x69562),x69564))
% 160.93/160.65 [6975]E(f334(f313(x69751,x69752,x69753),f334(f314(x69751,x69752,x69753),x69754)),x69754)+~E(f334(f313(x69751,x69752,x69753),f257(f888(x69751,a876))),f257(f888(x69752,a876)))
% 160.93/160.65 [7385]~P27(x73851,x73852,x73853,f257(f888(x73851,a876)))+E(f334(f314(x73851,x73852,x73853),f334(f313(x73851,x73852,x73853),x73854)),x73854)
% 160.93/160.65 [7717]P1(f334(x77171,x77172))+~P1(f334(f334(f336(x77173),x77172),f334(f174(x77173),f179(x77173,x77171,x77174))))
% 160.93/160.65 [7823]~P1(f334(f334(f336(f882(x78231)),f334(f334(f153(x78231),x78232),x78234)),f163(x78231,x78233)))+P1(f334(f334(f336(x78231),x78232),x78233))
% 160.93/160.65 [7952]~P1(f334(f334(f336(x79521),x79522),f334(f174(x79521),f178(x79521,x79523,x79524))))+P1(f334(f334(f336(x79521),x79522),f334(f174(x79521),x79523)))
% 160.93/160.65 [7953]~P1(f334(f334(f336(x79531),x79532),f334(f174(x79531),f172(x79531,x79534,x79533))))+P1(f334(f334(f336(x79531),x79532),f334(f174(x79531),x79533)))
% 160.93/160.65 [7954]~P1(f334(f334(f336(x79541),x79542),f334(f174(x79541),f179(x79541,x79544,x79543))))+P1(f334(f334(f336(x79541),x79542),f334(f174(x79541),x79543)))
% 160.93/160.65 [7964]E(f334(f197(f882(x79641)),x79642),x79643)+~P1(f334(f334(f336(f882(x79641)),x79642),f334(f174(f882(x79641)),f54(x79641,x79643,x79644))))
% 160.93/160.65 [8056]P1(f334(x80563,x80562))+E(f334(f138(x80561,f334(f334(f8(a876,a876,x80561),a329),f334(a331,x80562))),f334(f138(x80561,x80563),x80564)),f334(f138(x80561,x80563),x80564))
% 160.93/160.65 [8176]E(f334(f334(f167(x81761),f179(x81761,x81762,x81763)),x81764),f334(f334(f167(x81761),x81763),x81764))+~P1(f334(f334(f249(a881),x81764),f334(f197(f882(x81761)),f179(x81761,x81762,x81763))))
% 160.93/160.65 [8268]~P68(x82681)+E(f334(f334(f6(a881,x82681),f334(f334(f8(a881,x82681,a881),x82682),a116)),f334(f304(a881,x82683),x82684)),f334(f334(f6(a881,x82681),x82682),f334(f304(a881,f334(a116,x82683)),f334(a116,x82684))))
% 160.93/160.65 [8278]~P68(x82781)+E(f334(f334(f6(a881,x82781),f334(f334(f8(a881,x82781,a881),x82782),a116)),f305(a881,x82783,x82784)),f334(f334(f6(a881,x82781),x82782),f305(a881,f334(a116,x82783),f334(a116,x82784))))
% 160.93/160.65 [8406]~P27(x84061,x84063,x84064,f257(f888(x84061,a876)))+P27(x84061,f888(x84062,x84063),f334(f334(f8(x84063,f888(x84062,x84063),x84061),f16(x84063,x84062)),x84064),f257(f888(x84061,a876)))
% 160.93/160.65 [8489]~P27(x84892,x84891,x84894,x84893)+E(f334(f313(x84891,x84892,f77(x84892,x84891,x84893,x84894)),f334(f313(x84892,x84891,x84894),x84893)),x84893)
% 160.93/160.65 [8554]~P1(f334(f334(f336(f887(x85541,x85541)),f334(f334(f269(x85541,x85541),x85542),x85544)),f266(x85541,x85543)))+P1(f334(f334(f336(x85541),x85542),x85543))
% 160.93/160.65 [8650]E(f334(f334(f334(f72(x86501,f885(x86502)),f334(f16(f885(x86502),x86501),f210(x86502))),x86503),f334(f241(x86502),f726(x86503,x86504,x86502,x86501))),x86504)+~E(f186(x86501,x86502,x86504),f334(f334(f312(x86501),x86503),f196(f888(x86501,a876))))
% 160.93/160.65 [8772]~E(f334(f334(f6(x87721,a881),x87724),x87723),f334(a116,x87722))+P1(f334(f334(f336(x87721),f874(x87722,x87723,x87724,x87721)),x87723))
% 160.93/160.65 [8792]~E(f334(f334(f6(x87924,a881),x87921),x87923),f334(a116,x87922))+P1(f334(f334(f249(a881),f2(a881)),f334(x87921,f874(x87922,x87923,x87921,x87924))))
% 160.93/160.65 [8803]~P1(f334(f61(x88032),x88034))+P1(f334(f334(f248(a881),f334(f37(x88031),f334(f313(x88032,x88031,x88033),x88034))),f334(f37(x88032),x88034)))
% 160.93/160.65 [8804]E(f334(f334(f269(x88041,x88042),f662(x88043,x88044,x88042,x88041)),f663(x88043,x88044,x88042,x88041)),x88044)+~P1(f334(f334(f336(f887(x88041,x88042)),x88044),f334(f289(x88042,x88041),x88043)))
% 160.93/160.65 [8812]P27(x88121,x88122,x88123,x88124)+P1(f334(f334(f336(x88121),f548(x88124,x88123,x88122,x88121)),x88124))
% 160.93/160.65 [8813]P27(x88131,x88132,x88133,x88134)+P1(f334(f334(f336(x88131),f549(x88134,x88133,x88132,x88131)),x88134))
% 160.93/160.65 [8874]P14(x88741,x88742,x88743,x88744)+P1(f334(f334(f336(f887(x88741,x88741)),f597(x88744,x88743,x88742,x88741)),x88743))
% 160.93/160.65 [8935]P1(f334(x89351,x89352))+~P1(f334(x89351,f334(f334(f269(x89353,x89354),f517(x89354,x89353,x89351)),f518(x89354,x89353,x89351))))
% 160.93/160.65 [8952]E(f334(f197(f882(x89521)),x89522),f334(f197(f882(x89521)),x89523))+~P1(f334(f334(f336(f887(f882(x89521),f882(x89521))),f334(f334(f269(f882(x89521),f882(x89521)),x89522),x89523)),f147(x89521,x89524)))
% 160.93/160.65 [8953]E(f334(f197(f882(x89531)),x89532),f334(f197(f882(x89531)),x89533))+~P1(f334(f334(f336(f887(f882(x89531),f882(x89531))),f334(f334(f269(f882(x89531),f882(x89531)),x89532),x89533)),f159(x89531,x89534)))
% 160.93/160.65 [8956]E(f334(f197(f882(x89561)),x89562),f334(f197(f882(x89561)),x89563))+~P1(f334(f334(f336(f887(f882(x89561),f882(x89561))),f334(f334(f269(f882(x89561),f882(x89561)),x89562),x89563)),f160(x89561,x89564)))
% 160.93/160.65 [9031]P1(f334(f334(f248(a881),f157(x90311,x90312,x90313)),f157(x90311,x90314,x90313)))+P1(f334(f334(f336(x90311),f691(x90314,x90312,x90313,x90311)),f334(f174(x90311),x90313)))
% 160.93/160.65 [9034]E(f334(f197(f882(x90341)),x90342),f334(f197(f882(x90341)),x90343))+~P1(f334(f334(f336(f887(f882(x90341),f882(x90341))),f334(f334(f269(f882(x90341),f882(x90341)),x90342),x90343)),f310(f882(x90341),f159(x90341,x90344))))
% 160.93/160.65 [9272]~P27(x92721,x92722,x92723,x92724)+~P1(f334(f334(f249(a881),f334(f37(x92722),f334(f313(x92721,x92722,x92723),x92724))),f334(f37(x92721),x92724)))
% 160.93/160.65 [9318]~P1(f334(f334(f336(f887(f882(x93181),f882(x93181))),f334(f334(f269(f882(x93181),f882(x93181)),x93182),x93183)),f159(x93181,x93184)))+P1(f334(f334(f336(f887(f882(x93181),f882(x93181))),f334(f334(f269(f882(x93181),f882(x93181)),x93182),x93183)),f160(x93181,f310(x93181,x93184))))
% 160.93/160.65 [9322]~P1(f334(f334(f336(f887(f882(x93221),f882(x93221))),f334(f334(f269(f882(x93221),f882(x93221)),x93222),x93223)),f160(x93221,x93224)))+P1(f334(f334(f336(f887(f882(x93221),f882(x93221))),f334(f334(f269(f882(x93221),f882(x93221)),x93222),x93223)),f310(f882(x93221),f159(x93221,x93224))))
% 160.93/160.65 [9339]P1(f334(f334(f336(f887(x93391,x93391)),f334(f334(f269(x93391,x93391),x93392),x93393)),f310(x93391,x93394)))+~P1(f334(f334(f336(f887(x93391,x93391)),f334(f334(f269(x93391,x93391),x93392),x93393)),f334(f334(f291(x93391,x93391,x93391),x93394),f310(x93391,x93394))))
% 160.93/160.65 [9524]E(f334(f334(f136(x95241),f705(x95242,x95243,x95244,x95241)),f334(f334(f153(x95241),f704(x95242,x95243,x95244,x95241)),f707(x95242,x95243,x95244,x95241))),x95244)+~P1(f334(f334(f336(f887(f882(x95241),f882(x95241))),f334(f334(f269(f882(x95241),f882(x95241)),x95244),x95243)),f159(x95241,x95242)))
% 160.93/160.65 [9525]E(f334(f334(f136(x95251),f705(x95252,x95253,x95254,x95251)),f334(f334(f153(x95251),f706(x95252,x95253,x95254,x95251)),f707(x95252,x95253,x95254,x95251))),x95253)+~P1(f334(f334(f336(f887(f882(x95251),f882(x95251))),f334(f334(f269(f882(x95251),f882(x95251)),x95254),x95253)),f159(x95251,x95252)))
% 160.93/160.65 [9602]P1(f334(f334(f336(f887(x96021,x96021)),f334(f334(f269(x96021,x96021),x96022),f644(x96023,x96024,x96022,x96021))),f310(x96021,x96023)))+~P1(f334(f334(f336(f887(x96021,x96021)),f334(f334(f269(x96021,x96021),x96022),x96024)),f334(f334(f291(x96021,x96021,x96021),x96023),f310(x96021,x96023))))
% 160.93/160.65 [9673]P1(f334(f334(f248(a881),f157(x96731,x96732,x96733)),f157(x96731,x96734,x96733)))+~P1(f334(f334(f249(a881),f334(x96732,f691(x96734,x96732,x96733,x96731))),f334(x96734,f691(x96734,x96732,x96733,x96731))))
% 160.93/160.65 [9741]P1(f334(f334(f336(f887(x97411,x97411)),f334(f334(f269(x97411,x97411),f652(x97412,x97413,x97414,x97411)),x97413)),f310(x97411,x97412)))+~P1(f334(f334(f336(f887(x97411,x97411)),f334(f334(f269(x97411,x97411),x97414),x97413)),f334(f334(f291(x97411,x97411,x97411),x97412),f310(x97411,x97412))))
% 160.93/160.65 [5211]~E(x52112,x52113)+E(f172(x52111,x52112,f334(f334(f153(x52111),x52113),x52114)),x52114)
% 160.93/160.65 [5337]P1(f334(x53372,x53373))+E(f179(x53371,x53372,f334(f334(f153(x53371),x53373),x53374)),f117(x53371))
% 160.93/160.65 [5406]~P87(x54062)+E(f334(f334(f79(f888(x54061,x54062)),x54063),x54064),f334(f79(x54062),f334(x54063,x54064)))
% 160.93/160.65 [5418]~E(x54182,f2(a881))+E(f334(f334(f140(x54181),x54182),f334(f334(f153(x54181),x54183),x54184)),f334(f334(f153(x54181),x54183),x54184))
% 160.93/160.65 [5419]P1(f334(x54192,x54193))+E(f334(f138(x54191,x54192),f334(f334(f153(x54191),x54193),x54194)),f334(f138(x54191,x54192),x54194))
% 160.93/160.65 [5550]~E(x55502,x55504)+P1(f334(f334(f334(f312(x55501),x55502),x55503),x55504))
% 160.93/160.65 [5558]E(x55581,f117(x55582))+E(f146(x55583,f334(f334(f156(x55582,x55583),x55584),x55581)),f334(x55584,f146(x55582,x55581)))
% 160.93/160.65 [5572]~E(x55721,f63(x55722,x55724))+E(f334(x55721,f334(f334(f312(x55722),x55723),f196(f888(x55722,a876)))),x55723)
% 160.93/160.65 [5607]E(x56071,f117(x56072))+E(f334(f143(x56073),f334(f334(f156(x56072,x56073),x56074),x56071)),f334(x56074,f334(f143(x56072),x56071)))
% 160.93/160.65 [5709]~P1(f334(x57093,x57094))+P1(f334(f334(f334(f312(x57091),x57092),x57093),x57094))
% 160.93/160.65 [5825]~P20(x58252,x58254,x58251)+E(f334(x58251,f334(f334(f312(x58252),x58253),f196(f888(x58252,a876)))),x58253)
% 160.93/160.65 [5849]~E(x58492,x58493)+P1(f334(f334(f336(x58491),x58492),f334(f334(f312(x58491),x58493),x58494)))
% 160.93/160.65 [5853]~P2(x58531)+E(f334(f334(f114(x58531),x58532),f334(f334(f114(x58531),x58533),x58534)),f334(f334(f114(x58531),x58533),f334(f334(f114(x58531),x58532),x58534)))
% 160.93/160.65 [5855]~P99(x58551)+E(f334(f334(f114(x58551),x58552),f334(f334(f114(x58551),x58553),x58554)),f334(f334(f114(x58551),x58553),f334(f334(f114(x58551),x58552),x58554)))
% 160.93/160.65 [5856]~P2(x58561)+E(f334(f334(f105(x58561),x58562),f334(f334(f105(x58561),x58563),x58564)),f334(f334(f105(x58561),x58563),f334(f334(f105(x58561),x58562),x58564)))
% 160.93/160.65 [5858]~P100(x58581)+E(f334(f334(f105(x58581),x58582),f334(f334(f105(x58581),x58583),x58584)),f334(f334(f105(x58581),x58583),f334(f334(f105(x58581),x58582),x58584)))
% 160.93/160.65 [5859]~P118(x58591)+E(f334(f334(f80(x58591),x58592),f334(f334(f80(x58591),x58593),x58594)),f334(f334(f80(x58591),x58593),f334(f334(f80(x58591),x58592),x58594)))
% 160.93/160.65 [5860]~P118(x58601)+E(f334(f334(f81(x58601),x58602),f334(f334(f81(x58601),x58603),x58604)),f334(f334(f81(x58601),x58603),f334(f334(f81(x58601),x58602),x58604)))
% 160.93/160.65 [5862]~P108(x58621)+E(f334(f334(f246(x58621),x58622),f334(f334(f246(x58621),x58623),x58624)),f334(f334(f246(x58621),x58623),f334(f334(f246(x58621),x58622),x58624)))
% 160.93/160.65 [5864]~P108(x58641)+E(f334(f334(f247(x58641),x58642),f334(f334(f247(x58641),x58643),x58644)),f334(f334(f247(x58641),x58643),f334(f334(f247(x58641),x58642),x58644)))
% 160.93/160.65 [5869]E(x58691,x58692)+E(f172(x58693,x58691,f334(f334(f153(x58693),x58692),x58694)),f334(f334(f153(x58693),x58692),f172(x58693,x58691,x58694)))
% 160.93/160.65 [5882]~P1(f334(x58822,x58823))+E(f334(f138(x58821,x58822),f334(f334(f153(x58821),x58823),x58824)),f334(f334(f153(x58821),x58823),f334(f138(x58821,x58822),x58824)))
% 160.93/160.65 [6016]~P1(f334(x60162,x60163))+E(f179(x60161,x60162,f334(f334(f153(x60161),x60163),x60164)),f334(f334(f153(x60161),x60163),f179(x60161,x60162,x60164)))
% 160.93/160.65 [6067]P26(x60671,x60672,x60673)+~P26(x60671,x60672,f334(f334(f312(f880(x60671)),x60674),x60673))
% 160.93/160.65 [6080]E(x60801,f196(f888(x60802,a876)))+E(f334(f334(f41(x60802,f888(x60803,a876)),x60801),f334(f16(f888(x60803,a876),x60802),x60804)),x60804)
% 160.93/160.65 [6081]E(x60811,f196(f888(x60812,a876)))+E(f334(f334(f42(x60812,f888(x60813,a876)),x60811),f334(f16(f888(x60813,a876),x60812),x60814)),x60814)
% 160.93/160.65 [6090]~E(x60904,f196(f888(x60902,a876)))+E(f334(f334(f271(x60901,x60902),x60903),f334(f16(f888(x60902,a876),x60901),x60904)),f196(f888(f887(x60901,x60902),a876)))
% 160.93/160.65 [6091]~E(x60913,f196(f888(x60911,a876)))+E(f334(f334(f271(x60911,x60912),x60913),f334(f16(f888(x60912,a876),x60911),x60914)),f196(f888(f887(x60911,x60912),a876)))
% 160.93/160.65 [6137]E(x61371,f2(a881))+E(f334(f334(f140(x61372),x61371),f334(f334(f153(x61372),x61373),x61374)),f334(f334(f140(x61372),f334(f334(f22(a881),x61371),f78(a881))),x61374))
% 160.93/160.65 [6167]E(x61671,f196(f888(x61672,a876)))+E(f334(f313(x61672,x61673,f334(f16(x61673,x61672),x61674)),x61671),f334(f334(f312(x61673),x61674),f196(f888(x61673,a876))))
% 160.93/160.65 [6170]E(f334(f314(x61701,x61702,f334(f16(x61702,x61701),x61703)),x61704),f196(f888(x61701,a876)))+P1(f334(f334(f336(x61702),x61703),x61704))
% 160.93/160.65 [6239]~E(x62393,f196(f888(x62391,a876)))+E(f334(f334(f41(x62391,f888(x62392,a876)),x62393),f334(f16(f888(x62392,a876),x62391),x62394)),f196(f888(x62392,a876)))
% 160.93/160.65 [6240]~E(x62403,f196(f888(x62401,a876)))+E(f334(f334(f42(x62401,f888(x62402,a876)),x62403),f334(f16(f888(x62402,a876),x62401),x62404)),f257(f888(x62402,a876)))
% 160.93/160.65 [6242]~P58(x62421)+E(f44(x62421,f334(f334(f81(x62421),x62422),x62423),f334(f334(f81(x62421),x62422),x62424)),f334(f334(f81(x62421),x62422),f44(x62421,x62423,x62424)))
% 160.93/160.65 [6406]E(f334(f314(x64061,x64062,f334(f16(x64062,x64061),x64063)),x64064),f257(f888(x64061,a876)))+~P1(f334(f334(f336(x64062),x64063),x64064))
% 160.93/160.65 [6429]~P1(f334(f334(f336(x64291),x64292),x64294))+P1(f334(f334(f336(x64291),x64292),f334(f334(f312(x64291),x64293),x64294)))
% 160.93/160.65 [6434]P1(f334(x64341,x64342))+~P1(f334(f162(x64343,x64341),f334(f334(f153(x64343),x64342),x64344)))
% 160.93/160.65 [6443]~E(x64433,f334(f334(f22(a881),f334(f197(f882(x64431)),x64432)),f78(a881)))+E(f118(x64431,f334(f334(f161(x64431,x64432),x64433),x64434)),f118(x64431,x64432))
% 160.93/160.65 [6462]~P108(x64621)+E(f334(f334(f105(f888(x64621,a876)),f334(f303(x64621),x64622)),f305(x64621,x64623,x64624)),f305(x64621,x64623,f334(f334(f246(x64621),x64622),x64624)))
% 160.93/160.65 [6463]~P108(x64631)+E(f334(f334(f105(f888(x64631,a876)),f334(f256(x64631),x64632)),f305(x64631,x64633,x64634)),f305(x64631,f334(f334(f247(x64631),x64632),x64633),x64634))
% 160.93/160.65 [6478]E(f334(f334(f105(f888(x64781,a876)),x64782),f334(f334(f312(x64781),x64783),x64784)),f334(f334(f105(f888(x64781,a876)),x64782),x64784))+P1(f334(f334(f336(x64781),x64783),x64782))
% 160.93/160.65 [6490]E(f172(x64901,x64902,f334(f334(f136(x64901),x64903),x64904)),f334(f334(f136(x64901),x64903),f172(x64901,x64902,x64904)))+P1(f334(f334(f336(x64901),x64902),f334(f174(x64901),x64903)))
% 160.93/160.65 [6494]~P80(x64941)+E(f334(f334(f81(x64941),f334(f334(f259(x64941),x64942),x64943)),f334(f334(f259(x64941),x64942),x64944)),f334(f334(f259(x64941),x64942),f334(f334(f80(a881),x64943),x64944)))
% 160.93/160.65 [6495]~P118(x64951)+E(f334(f334(f81(x64951),f334(f334(f259(x64951),x64952),x64953)),f334(f334(f259(x64951),x64952),x64954)),f334(f334(f259(x64951),x64952),f334(f334(f80(a881),x64953),x64954)))
% 160.93/160.65 [6531]~P97(x65311)+E(f334(f334(f105(x65311),f334(f334(f114(x65311),x65312),x65313)),f334(f334(f114(x65311),x65312),x65314)),f334(f334(f114(x65311),x65312),f334(f334(f105(x65311),x65313),x65314)))
% 160.93/160.65 [6532]~P97(x65321)+E(f334(f334(f114(x65321),f334(f334(f105(x65321),x65322),x65323)),f334(f334(f105(x65321),x65322),x65324)),f334(f334(f105(x65321),x65322),f334(f334(f114(x65321),x65323),x65324)))
% 160.93/160.65 [6533]~P118(x65331)+E(f334(f334(f80(x65331),f334(f334(f81(x65331),x65332),x65333)),f334(f334(f81(x65331),x65332),x65334)),f334(f334(f81(x65331),x65332),f334(f334(f80(x65331),x65333),x65334)))
% 160.93/160.65 [6534]~P108(x65341)+E(f334(f334(f247(x65341),f334(f334(f246(x65341),x65342),x65343)),f334(f334(f246(x65341),x65342),x65344)),f334(f334(f246(x65341),x65342),f334(f334(f247(x65341),x65343),x65344)))
% 160.93/160.65 [6535]~P108(x65351)+E(f334(f334(f246(x65351),f334(f334(f247(x65351),x65352),x65353)),f334(f334(f247(x65351),x65352),x65354)),f334(f334(f247(x65351),x65352),f334(f334(f246(x65351),x65353),x65354)))
% 160.93/160.65 [6566]~P58(x65661)+E(f44(x65661,f334(f334(f81(x65661),x65662),x65663),f334(f334(f81(x65661),x65664),x65663)),f334(f334(f81(x65661),f44(x65661,x65662,x65664)),x65663))
% 160.93/160.65 [6569]~E(f334(f197(f882(x65691)),x65693),f334(f197(f882(x65692)),x65694))+E(f334(f334(f156(f887(x65691,x65692),x65692),f272(x65691,x65692)),f334(f334(f184(x65691,x65692),x65693),x65694)),x65694)
% 160.93/160.65 [6570]~E(f334(f197(f882(x65701)),x65703),f334(f197(f882(x65702)),x65704))+E(f334(f334(f156(f887(x65701,x65702),x65701),f268(x65701,x65702)),f334(f334(f184(x65701,x65702),x65703),x65704)),x65703)
% 160.93/160.65 [6576]P1(f334(f162(x65761,x65762),x65763))+~P1(f334(f162(x65761,x65762),f334(f334(f153(x65761),x65764),x65763)))
% 160.93/160.65 [6577]P1(f334(f162(x65771,x65772),x65773))+~P1(f334(f162(x65771,x65772),f334(f334(f136(x65771),x65774),x65773)))
% 160.93/160.65 [6578]P1(f334(f162(x65781,x65782),x65783))+~P1(f334(f162(x65781,x65782),f334(f334(f136(x65781),x65783),x65784)))
% 160.93/160.65 [6583]~P59(x65831)+E(f44(x65831,f334(f334(f22(x65831),x65832),f44(x65831,x65833,x65834)),x65834),f44(x65831,f334(f334(f22(x65831),x65832),x65833),x65834))
% 160.93/160.65 [6585]~P58(x65851)+E(f44(x65851,f334(f334(f81(x65851),x65852),f44(x65851,x65853,x65854)),x65854),f44(x65851,f334(f334(f81(x65851),x65852),x65853),x65854))
% 160.93/160.65 [6586]~P58(x65861)+E(f44(x65861,f334(f334(f80(x65861),x65862),f44(x65861,x65863,x65864)),x65864),f44(x65861,f334(f334(f80(x65861),x65862),x65863),x65864))
% 160.93/160.65 [6667]~P108(x66671)+E(f334(f334(f105(f888(x66671,a876)),f305(x66671,x66672,x66673)),f334(f303(x66671),x66674)),f305(x66671,x66672,f334(f334(f246(x66671),x66673),x66674)))
% 160.93/160.65 [6668]~P108(x66681)+E(f334(f334(f105(f888(x66681,a876)),f305(x66681,x66682,x66683)),f334(f256(x66681),x66684)),f305(x66681,f334(f334(f247(x66681),x66682),x66684),x66683))
% 160.93/160.65 [6671]~E(f334(f197(f882(x66711)),x66713),f334(f197(f882(x66712)),x66714))+E(f334(f334(f184(x66711,x66712),f334(f171(x66711),x66713)),f334(f171(x66712),x66714)),f334(f171(f887(x66711,x66712)),f334(f334(f184(x66711,x66712),x66713),x66714)))
% 160.93/160.65 [6681]E(x66811,f334(f334(f22(a881),f334(f197(f882(x66812)),x66813)),f78(a881)))+E(f118(x66812,f334(f334(f161(x66812,x66813),x66811),x66814)),f334(f334(f161(x66812,f118(x66812,x66813)),x66811),x66814))
% 160.93/160.65 [6696]~P1(f334(f139(x66962),x66964))+P1(f334(f139(f887(x66961,x66962)),f334(f334(f184(x66961,x66962),x66963),x66964)))
% 160.93/160.65 [6697]~P1(f334(f139(x66971),x66973))+P1(f334(f139(f887(x66971,x66972)),f334(f334(f184(x66971,x66972),x66973),x66974)))
% 160.93/160.65 [6959]E(f334(f334(f38(a881),x69591),x69592),x69593)+~P1(f334(f47(x69591,x69592),f334(f334(f269(a881,a881),x69593),x69594)))
% 160.93/160.65 [6983]E(f44(a881,x69831,x69832),x69833)+~P1(f334(f47(x69831,x69832),f334(f334(f269(a881,a881),x69834),x69833)))
% 160.93/160.65 [6986]P1(f334(f139(x69861),x69862))+~P1(f334(f139(x69863),f334(f334(f156(x69861,x69863),x69864),x69862)))
% 160.93/160.65 [6994]~P26(x69941,x69942,f334(f334(f312(f880(x69941)),x69943),x69944))+P26(x69941,x69942,f334(f334(f312(f880(x69941)),x69943),f196(f888(f880(x69941),a876))))
% 160.93/160.65 [7070]E(f172(x70701,x70702,f334(f334(f136(x70701),x70703),x70704)),f334(f334(f136(x70701),f172(x70701,x70702,x70703)),x70704))+~P1(f334(f334(f336(x70701),x70702),f334(f174(x70701),x70703)))
% 160.93/160.65 [7160]~P59(x71601)+E(f44(x71601,f334(f334(f22(x71601),f44(x71601,x71602,x71603)),x71604),x71603),f44(x71601,f334(f334(f22(x71601),x71602),x71604),x71603))
% 160.93/160.65 [7163]~P58(x71631)+E(f44(x71631,f334(f334(f80(x71631),f44(x71631,x71632,x71633)),x71634),x71633),f44(x71631,f334(f334(f80(x71631),x71632),x71634),x71633))
% 160.93/160.65 [7164]~P58(x71641)+E(f44(x71641,f334(f334(f81(x71641),f44(x71641,x71642,x71643)),x71644),x71643),f44(x71641,f334(f334(f81(x71641),x71642),x71644),x71643))
% 160.93/160.65 [7181]P1(f334(f334(f334(a202,x71811),x71812),x71813))+~P1(f334(f334(f334(f334(a204,x71811),x71812),x71814),x71813))
% 160.93/160.65 [7356]~E(x73561,f334(f334(f153(x73562),x73563),x73564))+~P1(f334(f334(f248(a881),f334(f197(f882(x73562)),x73561)),f334(f197(f882(x73562)),x73564)))
% 160.93/160.65 [7431]~E(f334(f180(x74311,x74312),x74313),f334(f180(x74311,x74312),x74314))+E(f334(f313(f887(x74311,x74312),x74311,f268(x74311,x74312)),f334(f174(f887(x74311,x74312)),x74313)),f334(f313(f887(x74311,x74312),x74311,f268(x74311,x74312)),f334(f174(f887(x74311,x74312)),x74314)))
% 160.93/160.65 [7565]P27(x75651,x75652,x75653,f334(f174(x75651),x75654))+~P1(f334(f139(x75652),f334(f334(f156(x75651,x75652),x75653),x75654)))
% 160.93/160.65 [7641]~P1(f334(f334(f248(f888(x76411,a876)),x76412),x76414))+P1(f334(f334(f248(f888(x76411,a876)),x76412),f334(f334(f312(x76411),x76413),x76414)))
% 160.93/160.65 [7674]~P59(x76741)+E(f44(x76741,f334(f334(f22(x76741),f44(x76741,x76742,x76743)),f44(x76741,x76744,x76743)),x76743),f44(x76741,f334(f334(f22(x76741),x76742),x76744),x76743))
% 160.93/160.65 [7675]~P58(x76751)+E(f44(x76751,f334(f334(f80(x76751),f44(x76751,x76752,x76753)),f44(x76751,x76754,x76753)),x76753),f44(x76751,f334(f334(f80(x76751),x76752),x76754),x76753))
% 160.93/160.65 [7676]~P58(x76761)+E(f44(x76761,f334(f334(f81(x76761),f44(x76761,x76762,x76763)),f44(x76761,x76764,x76763)),x76763),f44(x76761,f334(f334(f81(x76761),x76762),x76764),x76763))
% 160.93/160.65 [7771]P1(f334(f334(f334(f334(a204,x77711),x77712),f334(a116,x77713)),x77714))+~P1(f334(f334(f334(f334(a204,x77711),x77712),x77713),x77714))
% 160.93/160.65 [7778]~E(f334(x77784,f833(x77784,x77783,x77781,x77782)),f196(f888(x77782,a876)))+E(f334(f334(f41(x77781,f888(x77782,a876)),x77783),x77784),f196(f888(x77782,a876)))
% 160.93/160.65 [7779]~E(f334(x77794,f486(x77794,x77793,x77791,x77792)),f257(f888(x77792,a876)))+E(f334(f334(f42(x77791,f888(x77792,a876)),x77793),x77794),f257(f888(x77792,a876)))
% 160.93/160.65 [7780]~E(f334(x77804,f841(x77804,x77803,x77802,x77801)),f196(f888(x77802,a876)))+E(f334(f334(f41(x77801,f888(x77802,a876)),x77803),x77804),f196(f888(x77802,a876)))
% 160.93/160.65 [7781]~E(f334(x77814,f489(x77814,x77813,x77812,x77811)),f257(f888(x77812,a876)))+E(f334(f334(f42(x77811,f888(x77812,a876)),x77813),x77814),f257(f888(x77812,a876)))
% 160.93/160.65 [8177]P1(f334(x81771,x81772))+~P1(f334(f334(f336(x81773),x81772),f334(f334(f105(f888(x81773,a876)),x81774),f334(f254(x81773),x81771))))
% 160.93/160.65 [8221]~P1(f334(f334(f248(f888(x82211,a876)),x82213),x82214))+P1(f334(f334(f248(f888(x82211,a876)),f334(f334(f312(x82211),x82212),x82213)),f334(f334(f312(x82211),x82212),x82214)))
% 160.93/160.65 [8396]P1(f334(x83962,x83963))+E(f334(f334(f140(x83961),f334(f197(f882(x83961)),f179(x83961,x83962,f334(f334(f153(x83961),x83963),x83964)))),f334(f334(f153(x83961),x83963),x83964)),f334(f334(f153(x83961),x83963),x83964))
% 160.93/160.65 [8503]P1(f334(f334(f334(a202,x85031),x85032),f495(x85033,x85032,x85034,x85031)))+~P1(f334(f334(f334(a202,f33(x85031,x85034)),x85032),x85033))
% 160.93/160.65 [8504]P1(f334(f334(f334(a202,x85041),x85042),f558(x85043,x85042,x85044,x85041)))+~P1(f334(f334(f334(a202,f33(x85041,x85044)),x85042),x85043))
% 160.93/160.65 [8505]~P1(f334(f334(f249(a881),f334(x85054,x85052)),f334(x85054,x85053)))+P1(f334(f334(f336(f887(x85051,x85051)),f334(f334(f269(x85051,x85051),x85052),x85053)),f334(f334(f290(a881,x85051),a253),x85054)))
% 160.93/160.65 [8603]~P1(f334(x86032,f787(x86034,x86032,x86033,x86031)))+E(f179(x86031,x86032,f334(f334(f136(x86031),x86033),x86034)),f334(f334(f136(x86031),x86033),f179(x86031,x86032,x86034)))
% 160.93/160.65 [8677]P27(f882(x86771),f882(x86772),f334(f156(x86771,x86772),x86773),x86774)+~P27(x86771,x86772,x86773,f39(f888(x86771,a876),f334(f313(f882(x86771),f888(x86771,a876),f174(x86771)),x86774)))
% 160.93/160.65 [8744]~P1(f334(x87442,x87443))+E(f334(f334(f140(x87441),f334(f197(f882(x87441)),f179(x87441,x87442,f334(f334(f153(x87441),x87443),x87444)))),f334(f334(f153(x87441),x87443),x87444)),f334(f334(f140(x87441),f334(f197(f882(x87441)),f179(x87441,x87442,x87444))),x87444))
% 160.93/160.65 [8783]~E(x87832,x87833)+E(f334(f138(x87831,f334(f334(f8(a876,a876,x87831),a329),f334(a331,x87832))),f334(f334(f153(x87831),x87833),x87834)),f334(f138(x87831,f334(f334(f8(a876,a876,x87831),a329),f334(a331,x87832))),x87834))
% 160.93/160.65 [8793]E(f334(f334(f41(x87931,f888(x87932,a876)),x87933),x87934),f196(f888(x87932,a876)))+P1(f334(f334(f336(x87931),f833(x87934,x87933,x87931,x87932)),x87933))
% 160.93/160.65 [8794]E(f334(f334(f42(x87941,f888(x87942,a876)),x87943),x87944),f257(f888(x87942,a876)))+P1(f334(f334(f336(x87941),f486(x87944,x87943,x87941,x87942)),x87943))
% 160.93/160.65 [8795]E(f334(f334(f41(x87951,f888(x87952,a876)),x87953),x87954),f196(f888(x87952,a876)))+P1(f334(f334(f336(x87951),f841(x87954,x87953,x87952,x87951)),x87953))
% 160.93/160.65 [8796]E(f334(f334(f42(x87961,f888(x87962,a876)),x87963),x87964),f257(f888(x87962,a876)))+P1(f334(f334(f336(x87961),f489(x87964,x87963,x87962,x87961)),x87963))
% 160.93/160.65 [8832]P1(f334(f334(f249(a881),f334(x88321,x88322)),f334(x88321,x88323)))+~P1(f334(f334(f336(f887(x88324,x88324)),f334(f334(f269(x88324,x88324),x88322),x88323)),f334(f334(f290(a881,x88324),a253),x88321)))
% 160.93/160.65 [8853]E(f179(x88531,x88532,f334(f334(f136(x88531),x88533),x88534)),f334(f334(f136(x88531),x88533),f179(x88531,x88532,x88534)))+P1(f334(f334(f336(x88531),f787(x88534,x88532,x88533,x88531)),f334(f174(x88531),x88533)))
% 160.93/160.65 [8969]P1(f334(f334(f334(a202,x89691),f495(x89692,x89693,x89691,x89694)),x89692))+~P1(f334(f334(f334(a202,f33(x89694,x89691)),x89693),x89692))
% 160.93/160.65 [8970]P1(f334(f334(f334(a202,x89701),f558(x89702,x89703,x89701,x89704)),x89702))+~P1(f334(f334(f334(a202,f33(x89704,x89701)),x89703),x89702))
% 160.93/160.65 [9020]P1(f334(f334(f336(x90201),f535(x90202,x90203,x90204,x90201)),x90203))+~P1(f334(f334(f336(f888(x90201,a876)),x90204),f334(f334(f60(x90201),x90203),x90202)))
% 160.93/160.65 [9023]E(x90231,x90232)+~P1(f334(f334(f336(f887(x90233,x90233)),f334(f334(f269(x90233,x90233),x90231),x90232)),f334(f334(f191(f887(x90233,x90233),a876),f2(a881)),x90234)))
% 160.93/160.65 [9105]E(f334(f288(x91051,x91051,x91052),f334(f334(f312(x91051),f535(x91052,x91053,x91054,x91051)),f196(f888(x91051,a876)))),x91054)+~P1(f334(f334(f336(f888(x91051,a876)),x91054),f334(f334(f60(x91051),x91053),x91052)))
% 160.93/160.65 [9111]~P1(f334(f334(f336(f887(x91111,x91111)),f334(f334(f269(x91111,x91111),x91113),x91112)),f310(x91111,x91114)))+P1(f334(f334(f336(f887(x91111,x91111)),f334(f334(f269(x91111,x91111),x91112),x91113)),f310(x91111,f334(f289(x91111,x91111),x91114))))
% 160.93/160.65 [9123]~P58(x91231)+E(f334(f334(f80(x91231),f334(f334(f80(x91231),f334(f334(f81(x91231),x91232),f334(f334(f38(x91231),x91233),x91232))),f44(x91231,x91233,x91232))),x91234),f334(f334(f80(x91231),x91233),x91234))
% 160.93/160.65 [9133]~P1(f334(f334(f336(x91331),x91333),x91334))+P1(f334(f334(f336(f888(x91331,a876)),f334(f288(x91331,x91331,x91332),f334(f334(f312(x91331),x91333),f196(f888(x91331,a876))))),f334(f334(f60(x91331),x91334),x91332)))
% 160.93/160.65 [9144]P1(f334(f334(f336(f887(x91441,x91441)),f334(f334(f269(x91441,x91441),x91442),x91443)),f310(x91441,x91444)))+~P1(f334(f334(f336(f887(x91441,x91441)),f334(f334(f269(x91441,x91441),x91443),x91442)),f310(x91441,f334(f289(x91441,x91441),x91444))))
% 160.93/160.65 [9236]E(f334(f334(f161(x92361,f334(f171(x92361),x92362)),f334(f334(f22(a881),f334(f334(f22(a881),f334(f197(f882(x92361)),x92362)),x92363)),f78(a881))),x92364),f334(f171(x92361),f334(f334(f161(x92361,x92362),x92363),x92364)))+~P1(f334(f334(f249(a881),x92363),f334(f197(f882(x92361)),x92362)))
% 160.93/160.65 [9239]~P1(f334(x92392,f778(x92394,x92392,x92393,x92391)))+E(f334(f334(f140(x92391),f334(f197(f882(x92391)),f179(x92391,x92392,f334(f334(f136(x92391),x92393),x92394)))),f334(f334(f136(x92391),x92393),x92394)),f334(f334(f140(x92391),f334(f197(f882(x92391)),f179(x92391,x92392,x92394))),x92394))
% 160.93/160.65 [9278]~P27(x92782,x92781,x92783,f257(f888(x92782,a876)))+P1(f334(f334(f248(f888(x92781,a876)),f334(f313(x92782,x92781,x92783),f334(f79(f888(x92782,a876)),x92784))),f334(f79(f888(x92781,a876)),f334(f313(x92782,x92781,x92783),x92784))))
% 160.93/160.65 [9291]~P5(x92911)+E(f334(f144(x92911,x92912,f334(f7(x92912,x92911,x92911),f334(f334(f8(x92911,f888(x92911,x92911),x92912),f114(x92911)),x92913)),f196(x92911)),x92914),f334(f334(f41(x92912,x92911),f334(f174(x92912),x92914)),x92913))
% 160.93/160.65 [9292]~P5(x92921)+E(f334(f144(x92921,x92922,f334(f7(x92922,x92921,x92921),f334(f334(f8(x92921,f888(x92921,x92921),x92922),f105(x92921)),x92923)),f257(x92921)),x92924),f334(f334(f42(x92922,x92921),f334(f174(x92922),x92924)),x92923))
% 160.93/160.65 [9304]E(f334(f334(f140(x93041),f334(f197(f882(x93041)),f179(x93041,x93042,f334(f334(f136(x93041),x93043),x93044)))),f334(f334(f136(x93041),x93043),x93044)),f334(f334(f140(x93041),f334(f197(f882(x93041)),f179(x93041,x93042,x93044))),x93044))+P1(f334(f334(f336(x93041),f778(x93044,x93042,x93043,x93041)),f334(f174(x93041),x93043)))
% 160.93/160.65 [9372]~P1(f334(f334(f336(f887(f882(x93724),f882(x93724))),f334(f334(f269(f882(x93724),f882(x93724)),x93723),x93722)),f159(x93724,x93721)))+P1(f334(f334(f249(a881),f692(x93721,x93722,x93723,x93724)),f334(f197(f882(x93724)),x93723)))
% 160.93/160.65 [9373]~P58(x93731)+E(f334(f334(f80(x93731),f334(f334(f80(x93731),f334(f334(f81(x93731),f334(f334(f38(x93731),x93732),x93733)),x93733)),f44(x93731,x93732,x93733))),x93734),f334(f334(f80(x93731),x93732),x93734))
% 160.93/160.65 [9400]~P1(f334(f334(f336(f887(f882(x94001),f882(x94001))),f334(f334(f269(f882(x94001),f882(x94001)),x94002),x94003)),f334(f289(f882(x94001),f882(x94001)),f159(x94001,x94004))))+P1(f334(f334(f336(f887(f882(x94001),f882(x94001))),f334(f334(f269(f882(x94001),f882(x94001)),x94002),x94003)),f159(x94001,f334(f289(x94001,x94001),x94004))))
% 160.93/160.65 [9401]P1(f334(f334(f336(f887(f882(x94011),f882(x94011))),f334(f334(f269(f882(x94011),f882(x94011)),x94012),x94013)),f334(f289(f882(x94011),f882(x94011)),f159(x94011,x94014))))+~P1(f334(f334(f336(f887(f882(x94011),f882(x94011))),f334(f334(f269(f882(x94011),f882(x94011)),x94012),x94013)),f159(x94011,f334(f289(x94011,x94011),x94014))))
% 160.93/160.65 [9436]~P1(f334(f334(f336(x94361),x94363),f334(f267(x94361,x94362),x94364)))+P1(f334(f334(f336(f887(x94361,x94362)),f334(f334(f269(x94361,x94362),x94363),f579(x94364,x94362,x94363,x94361))),x94364))
% 160.93/160.65 [9437]~P1(f334(f334(f336(x94371),x94373),f334(f267(x94371,x94372),x94374)))+P1(f334(f334(f336(f887(x94371,x94372)),f334(f334(f269(x94371,x94372),x94373),f583(x94374,x94372,x94373,x94371))),x94374))
% 160.93/160.65 [9550]~P1(f334(f61(f885(x95501)),f334(f313(x95502,f885(x95501),x95503),f257(f888(x95502,a876)))))+P1(f334(f61(f885(x95501)),f334(f313(x95502,f885(x95501),f187(x95502,x95501,x95503,f334(f180(x95502,x95501),x95504))),f257(f888(x95502,a876)))))
% 160.93/160.65 [9597]~P1(f334(f334(f336(f887(x95971,x95971)),f334(f334(f269(x95971,x95971),x95972),x95974)),f334(f334(f291(x95971,x95971,x95971),x95973),f310(x95971,x95973))))+P1(f334(f334(f336(f887(x95971,x95971)),f334(f334(f269(x95971,x95971),x95972),f652(x95973,x95974,x95972,x95971))),x95973))
% 160.93/160.65 [9768]~P1(f334(f334(f336(f887(x97682,x97681)),x97684),f334(f289(x97681,x97682),x97683)))+P1(f334(f334(f336(f887(x97681,x97682)),f334(f334(f269(x97681,x97682),f663(x97683,x97684,x97681,x97682)),f662(x97683,x97684,x97681,x97682))),x97683))
% 160.93/160.65 [9796]~P1(f334(f334(f336(f887(f882(x97961),f882(x97961))),f334(f334(f269(f882(x97961),f882(x97961)),x97964),x97963)),f159(x97961,x97962)))+P1(f334(f334(f336(f887(x97961,x97961)),f334(f334(f269(x97961,x97961),f704(x97962,x97963,x97964,x97961)),f706(x97962,x97963,x97964,x97961))),x97962))
% 160.93/160.65 [9893]~P1(f334(f334(f336(f887(f882(x98931),f882(x98931))),f334(f334(f269(f882(x98931),f882(x98931)),x98932),x98934)),f159(x98931,x98933)))+P1(f334(f334(f336(f887(x98931,x98931)),f334(f334(f269(x98931,x98931),f334(f334(f167(x98931),x98932),f692(x98933,x98934,x98932,x98931))),f693(x98933,x98934,x98932,x98931))),x98933))
% 160.93/160.65 [9915]~P1(f334(f61(x99152),x99154))+E(f334(f334(f334(f65(f888(x99151,a876),x99152,f114(f888(x99151,a876))),f334(f334(f7(x99152,f888(x99151,a876),f888(x99151,a876)),f334(f334(f8(x99151,f888(f888(x99151,a876),f888(x99151,a876)),x99152),f312(x99151)),x99153)),f196(f888(x99151,a876)))),f196(f888(x99151,a876))),x99154),f334(f313(x99152,x99151,x99153),x99154))
% 160.93/160.65 [10010]~P27(x100101,x100102,x100103,f257(f888(x100101,a876)))+P1(f334(f334(f248(f888(x100101,a876)),f334(f314(x100101,x100102,x100103),f334(f334(f312(x100102),x100104),f196(f888(x100102,a876))))),f334(f334(f312(x100101),f85(x100101,f334(f334(f7(x100101,x100102,a876),f334(f334(f8(x100102,f888(x100102,a876),x100101),a331),x100103)),x100104))),f196(f888(x100101,a876)))))
% 160.93/160.65 [5616]~E(f334(f334(f136(x56161),x56162),x56164),x56163)+E(f334(f334(f177(x56161),f334(f197(f882(x56161)),x56162)),x56163),x56162)
% 160.93/160.65 [5617]~E(f334(f334(f136(x56172),x56173),x56171),x56174)+E(x56171,f334(f334(f140(x56172),f334(f197(f882(x56172)),x56173)),x56174))
% 160.93/160.65 [5628]~E(x56284,f2(a881))+E(f334(f334(f167(x56281),f334(f334(f153(x56281),x56282),x56283)),x56284),x56282)
% 160.93/160.65 [6150]~P118(x61501)+E(f334(f334(f259(x61501),f334(f334(f259(x61501),x61502),x61503)),x61504),f334(f334(f259(x61501),x61502),f334(f334(f81(a881),x61503),x61504)))
% 160.93/160.65 [6151]~P80(x61511)+E(f334(f334(f259(x61511),f334(f334(f259(x61511),x61512),x61513)),x61514),f334(f334(f259(x61511),x61512),f334(f334(f81(a881),x61513),x61514)))
% 160.93/160.65 [6168]E(x61681,f2(a881))+E(f334(f334(f167(x61682),f334(f334(f153(x61682),x61683),x61684)),x61681),f334(f334(f167(x61682),x61684),f334(f334(f22(a881),x61681),f78(a881))))
% 160.93/160.65 [6197]~P120(x61971)+E(f334(f334(f292(x61971),f334(f334(f81(x61971),x61972),x61973)),x61974),f334(f334(f81(x61971),x61972),f334(f334(f292(x61971),x61973),x61974)))
% 160.93/160.65 [6198]~P2(x61981)+E(f334(f334(f114(x61981),f334(f334(f114(x61981),x61982),x61983)),x61984),f334(f334(f114(x61981),x61982),f334(f334(f114(x61981),x61983),x61984)))
% 160.93/160.65 [6200]~P99(x62001)+E(f334(f334(f114(x62001),f334(f334(f114(x62001),x62002),x62003)),x62004),f334(f334(f114(x62001),x62002),f334(f334(f114(x62001),x62003),x62004)))
% 160.93/160.65 [6201]~P2(x62011)+E(f334(f334(f105(x62011),f334(f334(f105(x62011),x62012),x62013)),x62014),f334(f334(f105(x62011),x62012),f334(f334(f105(x62011),x62013),x62014)))
% 160.93/160.65 [6203]~P100(x62031)+E(f334(f334(f105(x62031),f334(f334(f105(x62031),x62032),x62033)),x62034),f334(f334(f105(x62031),x62032),f334(f334(f105(x62031),x62033),x62034)))
% 160.93/160.65 [6204]~P69(x62041)+E(f334(f334(f80(x62041),f334(f334(f80(x62041),x62042),x62043)),x62044),f334(f334(f80(x62041),x62042),f334(f334(f80(x62041),x62043),x62044)))
% 160.93/160.65 [6205]~P118(x62051)+E(f334(f334(f80(x62051),f334(f334(f80(x62051),x62052),x62053)),x62054),f334(f334(f80(x62051),x62052),f334(f334(f80(x62051),x62053),x62054)))
% 160.93/160.65 [6206]~P70(x62061)+E(f334(f334(f81(x62061),f334(f334(f81(x62061),x62062),x62063)),x62064),f334(f334(f81(x62061),x62062),f334(f334(f81(x62061),x62063),x62064)))
% 160.93/160.65 [6207]~P118(x62071)+E(f334(f334(f81(x62071),f334(f334(f81(x62071),x62072),x62073)),x62074),f334(f334(f81(x62071),x62072),f334(f334(f81(x62071),x62073),x62074)))
% 160.93/160.65 [6210]~P108(x62101)+E(f334(f334(f246(x62101),f334(f334(f246(x62101),x62102),x62103)),x62104),f334(f334(f246(x62101),x62102),f334(f334(f246(x62101),x62103),x62104)))
% 160.93/160.65 [6212]~P108(x62121)+E(f334(f334(f247(x62121),f334(f334(f247(x62121),x62122),x62123)),x62124),f334(f334(f247(x62121),x62122),f334(f334(f247(x62121),x62123),x62124)))
% 160.93/160.65 [6223]~P58(x62231)+E(f44(x62231,f334(f334(f80(x62231),x62232),f334(f334(f81(x62231),x62233),x62234)),x62234),f44(x62231,x62232,x62234))
% 160.93/160.65 [6224]~P58(x62241)+E(f44(x62241,f334(f334(f80(x62241),x62242),f334(f334(f81(x62241),x62243),x62244)),x62243),f44(x62241,x62242,x62243))
% 160.93/160.65 [6356]E(f334(f334(f167(x63561),f334(f334(f177(x63561),x63562),x63563)),x63564),f334(f334(f167(x63561),x63563),x63564))+~P1(f334(f334(f249(a881),x63564),x63562))
% 160.93/160.65 [6529]~P118(x65291)+E(f334(f334(f80(x65291),f334(f334(f80(x65291),x65292),x65293)),x65294),f334(f334(f80(x65291),f334(f334(f80(x65291),x65292),x65294)),x65293))
% 160.93/160.65 [6530]~P118(x65301)+E(f334(f334(f81(x65301),f334(f334(f81(x65301),x65302),x65303)),x65304),f334(f334(f81(x65301),f334(f334(f81(x65301),x65302),x65304)),x65303))
% 160.93/160.65 [6589]~P142(x65892)+E(f334(f334(f6(x65891,x65892),f334(f16(x65892,x65891),x65893)),x65894),f334(f334(f81(x65892),f334(f104(x65892),f334(f37(x65891),x65894))),x65893))
% 160.93/160.65 [6759]E(f334(f334(f105(f888(x67591,a876)),f334(f334(f312(x67591),x67592),x67593)),x67594),f334(f334(f105(f888(x67591,a876)),x67593),x67594))+P1(f334(f334(f336(x67591),x67592),x67594))
% 160.93/160.65 [6828]~P97(x68281)+E(f334(f334(f105(x68281),f334(f334(f114(x68281),x68282),x68283)),f334(f334(f114(x68281),x68284),x68283)),f334(f334(f114(x68281),f334(f334(f105(x68281),x68282),x68284)),x68283))
% 160.93/160.65 [6829]~P83(x68291)+E(f334(f334(f246(x68291),f334(f334(f22(x68291),x68292),x68293)),f334(f334(f22(x68291),x68294),x68293)),f334(f334(f22(x68291),f334(f334(f246(x68291),x68292),x68294)),x68293))
% 160.93/160.65 [6830]~P83(x68301)+E(f334(f334(f247(x68301),f334(f334(f22(x68301),x68302),x68303)),f334(f334(f22(x68301),x68304),x68303)),f334(f334(f22(x68301),f334(f334(f247(x68301),x68302),x68304)),x68303))
% 160.93/160.65 [6831]~P97(x68311)+E(f334(f334(f114(x68311),f334(f334(f105(x68311),x68312),x68313)),f334(f334(f105(x68311),x68314),x68313)),f334(f334(f105(x68311),f334(f334(f114(x68311),x68312),x68314)),x68313))
% 160.93/160.65 [6832]~P82(x68321)+E(f334(f334(f246(x68321),f334(f334(f80(x68321),x68322),x68323)),f334(f334(f80(x68321),x68324),x68323)),f334(f334(f80(x68321),f334(f334(f246(x68321),x68322),x68324)),x68323))
% 160.93/160.65 [6833]~P82(x68331)+E(f334(f334(f247(x68331),f334(f334(f80(x68331),x68332),x68333)),f334(f334(f80(x68331),x68334),x68333)),f334(f334(f80(x68331),f334(f334(f247(x68331),x68332),x68334)),x68333))
% 160.93/160.65 [6834]~P112(x68341)+E(f334(f334(f80(x68341),f334(f334(f81(x68341),x68342),x68343)),f334(f334(f81(x68341),x68344),x68343)),f334(f334(f81(x68341),f334(f334(f80(x68341),x68342),x68344)),x68343))
% 160.93/160.65 [6836]~P74(x68361)+E(f334(f334(f81(x68361),f334(f334(f259(x68361),x68362),x68363)),f334(f334(f259(x68361),x68364),x68363)),f334(f334(f259(x68361),f334(f334(f81(x68361),x68362),x68364)),x68363))
% 160.93/160.65 [6837]~P118(x68371)+E(f334(f334(f81(x68371),f334(f334(f259(x68371),x68372),x68373)),f334(f334(f259(x68371),x68374),x68373)),f334(f334(f259(x68371),f334(f334(f81(x68371),x68372),x68374)),x68373))
% 160.93/160.65 [6838]~P61(x68381)+E(f334(f334(f292(x68381),f334(f334(f259(x68381),x68382),x68383)),f334(f334(f259(x68381),x68384),x68383)),f334(f334(f259(x68381),f334(f334(f292(x68381),x68382),x68384)),x68383))
% 160.93/160.65 [6839]~P120(x68391)+E(f334(f334(f22(x68391),f334(f334(f292(x68391),x68392),x68393)),f334(f334(f292(x68391),x68394),x68393)),f334(f334(f292(x68391),f334(f334(f22(x68391),x68392),x68394)),x68393))
% 160.93/160.65 [6840]~P120(x68401)+E(f334(f334(f80(x68401),f334(f334(f292(x68401),x68402),x68403)),f334(f334(f292(x68401),x68404),x68403)),f334(f334(f292(x68401),f334(f334(f80(x68401),x68402),x68404)),x68403))
% 160.93/160.65 [6841]~P108(x68411)+E(f334(f334(f247(x68411),f334(f334(f246(x68411),x68412),x68413)),f334(f334(f246(x68411),x68414),x68413)),f334(f334(f246(x68411),f334(f334(f247(x68411),x68412),x68414)),x68413))
% 160.93/160.65 [6842]~P108(x68421)+E(f334(f334(f246(x68421),f334(f334(f247(x68421),x68422),x68423)),f334(f334(f247(x68421),x68424),x68423)),f334(f334(f247(x68421),f334(f334(f246(x68421),x68422),x68424)),x68423))
% 160.93/160.65 [6843]~P118(x68431)+E(f334(f334(f80(x68431),f334(f334(f81(x68431),x68432),x68433)),f334(f334(f81(x68431),x68434),x68433)),f334(f334(f81(x68431),f334(f334(f80(x68431),x68432),x68434)),x68433))
% 160.93/160.65 [6876]E(f334(f334(f161(x68761,x68762),x68763),x68764),x68762)+~P1(f334(f334(f248(a881),f334(f197(f882(x68761)),x68762)),x68763))
% 160.93/160.65 [6901]~P1(f334(x69013,x69014))+P1(f334(f334(f334(f114(f888(x69011,a876)),x69012),x69013),x69014))
% 160.93/160.65 [6903]~P1(f334(x69032,x69034))+P1(f334(f334(f334(f114(f888(x69031,a876)),x69032),x69033),x69034))
% 160.93/160.65 [6922]E(f334(f334(f167(x69221),f334(f334(f136(x69221),x69222),x69223)),x69224),f334(f334(f167(x69221),x69222),x69224))+~P1(f334(f334(f249(a881),x69224),f334(f197(f882(x69221)),x69222)))
% 160.93/160.65 [6932]E(f334(f334(f22(f888(x69321,a876)),f334(f334(f312(x69321),x69322),x69323)),x69324),f334(f334(f22(f888(x69321,a876)),x69323),x69324))+~P1(f334(f334(f336(x69321),x69322),x69324))
% 160.93/160.65 [6973]~E(f141(a881,f334(f304(a881,x69731),x69732)),f334(f334(f153(a881),x69734),x69733))+E(f141(a881,f334(f304(a881,f334(f334(f80(a881),x69731),f78(a881))),x69732)),x69733)
% 160.93/160.65 [7044]E(x70441,f2(a881))+E(f334(f334(f153(x70442),x70443),f334(f334(f177(x70442),f334(f334(f22(a881),x70441),f78(a881))),x70444)),f334(f334(f177(x70442),x70441),f334(f334(f153(x70442),x70443),x70444)))
% 160.93/160.65 [7144]E(f334(f334(f167(x71441),x71442),f334(f334(f22(a881),x71443),f334(f197(f882(x71441)),x71444))),f334(f334(f167(x71441),f334(f334(f136(x71441),x71444),x71442)),x71443))+P1(f334(f334(f249(a881),x71443),f334(f197(f882(x71441)),x71444)))
% 160.93/160.65 [7174]E(f334(f334(f105(f888(x71741,a876)),x71742),f334(f334(f312(x71741),x71743),x71744)),f334(f334(f312(x71741),x71743),f334(f334(f105(f888(x71741,a876)),x71742),x71744)))+~P1(f334(f334(f336(x71741),x71743),x71742))
% 160.93/160.65 [7211]E(f334(f334(f167(x72111),f334(f334(f161(x72111,x72112),x72113),x72114)),x72113),x72114)+~P1(f334(f334(f249(a881),x72113),f334(f197(f882(x72111)),x72112)))
% 160.93/160.65 [7232]E(x72321,f196(f888(x72322,a876)))+E(f334(f313(f887(x72323,x72322),x72323,f268(x72323,x72322)),f334(f334(f271(x72323,x72322),x72324),f334(f16(f888(x72322,a876),x72323),x72321))),x72324)
% 160.93/160.65 [7233]E(x72331,f196(f888(x72332,a876)))+E(f334(f313(f887(x72332,x72333),x72333,f272(x72332,x72333)),f334(f334(f271(x72332,x72333),x72331),f334(f16(f888(x72333,a876),x72332),x72334))),x72334)
% 160.93/160.65 [7300]E(f334(f334(f22(f888(x73001,a876)),f334(f334(f312(x73001),x73002),x73003)),x73004),f334(f334(f312(x73001),x73002),f334(f334(f22(f888(x73001,a876)),x73003),x73004)))+P1(f334(f334(f336(x73001),x73002),x73004))
% 160.93/160.65 [7332]P1(f334(x73321,x73322))+P1(f334(f334(f334(f334(a204,f32(x73321,x73323)),x73322),x73324),x73322))
% 160.93/160.65 [7339]~E(x73394,f196(f888(x73392,a876)))+E(f334(f313(f887(x73391,x73392),x73391,f268(x73391,x73392)),f334(f334(f271(x73391,x73392),x73393),f334(f16(f888(x73392,a876),x73391),x73394))),f196(f888(x73391,a876)))
% 160.93/160.65 [7340]~E(x73403,f196(f888(x73401,a876)))+E(f334(f313(f887(x73401,x73402),x73402,f272(x73401,x73402)),f334(f334(f271(x73401,x73402),x73403),f334(f16(f888(x73402,a876),x73401),x73404))),f196(f888(x73402,a876)))
% 160.93/160.65 [7396]~P1(f334(f334(f336(x73961),x73962),x73964))+P1(f334(f334(f336(x73961),x73962),f334(f334(f114(f888(x73961,a876)),x73963),x73964)))
% 160.93/160.65 [7399]~P1(f334(f334(f336(x73991),x73992),x73993))+P1(f334(f334(f336(x73991),x73992),f334(f334(f114(f888(x73991,a876)),x73993),x73994)))
% 160.93/160.65 [7418]E(f334(f334(f105(f888(x74181,a876)),f334(f334(f312(x74181),x74182),x74183)),x74184),f334(f334(f312(x74181),x74182),f334(f334(f105(f888(x74181,a876)),x74183),x74184)))+~P1(f334(f334(f336(x74181),x74182),x74184))
% 160.93/160.65 [7696]P1(f334(x76961,x76962))+~P1(f334(f334(f334(f105(f888(x76963,a876)),x76964),x76961),x76962))
% 160.93/160.65 [7697]P1(f334(x76971,x76972))+~P1(f334(f334(f334(f105(f888(x76973,a876)),x76971),x76974),x76972))
% 160.93/160.65 [7700]E(f334(f334(f6(x77001,a881),x77002),f334(f334(f22(f888(x77001,a876)),x77003),f334(f334(f312(x77001),x77004),f196(f888(x77001,a876))))),f334(f334(f6(x77001,a881),x77002),x77003))+P1(f334(f334(f336(x77001),x77004),x77003))
% 160.93/160.65 [7705]~P68(x77051)+E(f334(f168(x77051),f334(f334(f156(a881,x77051),x77052),f141(a881,f334(f304(a881,x77053),x77054)))),f334(f334(f6(a881,x77051),x77052),f334(f174(a881),f141(a881,f334(f304(a881,x77053),x77054)))))
% 160.93/160.65 [7706]~P68(x77061)+E(f334(f334(f6(a881,x77061),x77062),f334(f174(a881),f141(a881,f334(f304(a881,x77063),x77064)))),f334(f168(x77061),f334(f334(f156(a881,x77061),x77062),f141(a881,f334(f304(a881,x77063),x77064)))))
% 160.93/160.65 [7816]~E(x78163,x78164)+P1(f334(f62(x78161,x78162,f334(f334(f312(x78161),x78163),f196(f888(x78161,a876)))),x78164))
% 160.93/160.65 [7913]P1(f334(f334(f336(x79131),x79132),f334(f174(x79131),x79133)))+~P1(f334(f334(f336(x79131),x79132),f334(f174(x79131),f334(f334(f177(x79131),x79134),x79133))))
% 160.93/160.65 [7914]P1(f334(f334(f336(x79141),x79142),f334(f174(x79141),x79143)))+~P1(f334(f334(f336(x79141),x79142),f334(f174(x79141),f334(f334(f140(x79141),x79144),x79143))))
% 160.93/160.65 [7985]P1(f334(f334(f336(x79851),x79852),x79853))+~P1(f334(f334(f336(x79851),x79852),f334(f334(f22(f888(x79851,a876)),x79853),x79854)))
% 160.93/160.65 [7987]P1(f334(f334(f336(x79871),x79872),x79873))+~P1(f334(f334(f336(x79871),x79872),f334(f334(f105(f888(x79871,a876)),x79874),x79873)))
% 160.93/160.65 [7990]P1(f334(f334(f336(x79901),x79902),x79903))+~P1(f334(f334(f336(x79901),x79902),f334(f334(f105(f888(x79901,a876)),x79903),x79904)))
% 160.93/160.65 [8005]E(f334(f334(f136(x80051),f334(f334(f177(x80051),x80052),x80053)),f334(f334(f153(x80051),x80054),f334(f334(f140(x80051),f334(a116,x80052)),x80053))),f334(f334(f161(x80051,x80053),x80052),x80054))+~P1(f334(f334(f249(a881),x80052),f334(f197(f882(x80051)),x80053)))
% 160.93/160.65 [8028]P1(f334(f334(f336(x80281),x80282),x80283))+~P1(f334(f334(f248(f888(x80281,a876)),f334(f334(f312(x80281),x80282),x80284)),x80283))
% 160.93/160.65 [8061]~P1(f334(f334(f336(x80611),x80612),x80613))+~P1(f334(f334(f336(x80611),x80612),f334(f334(f22(f888(x80611,a876)),x80614),x80613)))
% 160.93/160.65 [8095]~P1(f334(f334(f249(a881),x80954),f334(f197(f882(x80951)),x80953)))+P1(f334(f334(f336(x80951),x80952),f334(f174(x80951),f334(f334(f161(x80951,x80953),x80954),x80952))))
% 160.93/160.65 [8151]E(f334(f334(f167(x81511),f334(f334(f140(x81511),x81512),x81513)),x81514),f334(f334(f167(x81511),x81513),f334(f334(f80(a881),x81512),x81514)))+~P1(f334(f334(f248(a881),f334(f334(f80(a881),x81512),x81514)),f334(f197(f882(x81511)),x81513)))
% 160.93/160.65 [8161]~P142(x81612)+E(f334(f334(f6(x81611,x81612),f334(f334(f8(a881,x81612,x81611),f104(x81612)),x81613)),x81614),f334(f104(x81612),f334(f334(f6(x81611,a881),x81613),x81614)))
% 160.93/160.65 [8162]~P139(x81622)+E(f334(f334(f6(x81621,x81622),f334(f334(f8(a1,x81622,x81621),f106(x81622)),x81623)),x81624),f334(f106(x81622),f334(f334(f6(x81621,a1),x81623),x81624)))
% 160.93/160.65 [8223]~P64(x82232)+E(f334(f334(f9(x82231,x82232),f334(f334(f8(x82232,x82232,x82231),f75(x82232)),x82233)),x82234),f334(f75(x82232),f334(f334(f9(x82231,x82232),x82233),x82234)))
% 160.93/160.65 [8224]~P67(x82242)+E(f334(f334(f6(x82241,x82242),f334(f334(f8(x82242,x82242,x82241),f79(x82242)),x82243)),x82244),f334(f79(x82242),f334(f334(f6(x82241,x82242),x82243),x82244)))
% 160.93/160.65 [8226]E(f334(f334(f6(x82261,a881),x82262),f334(f334(f22(f888(x82261,a876)),x82263),f334(f334(f312(x82261),x82264),f196(f888(x82261,a876))))),f334(f334(f22(a881),f334(f334(f6(x82261,a881),x82262),x82263)),f334(x82262,x82264)))+~P1(f334(f334(f336(x82261),x82264),x82263))
% 160.93/160.65 [8247]P1(f334(f334(f248(f888(x82471,a876)),x82472),x82473))+~P1(f334(f334(f248(f888(x82471,a876)),f334(f334(f312(x82471),x82474),x82472)),x82473))
% 160.93/160.65 [8449]E(f334(a116,f538(x84491,x84492,x84493,x84494)),x84492)+~P1(f334(f334(f334(f334(a204,f334(a26,x84494)),x84493),x84492),x84491))
% 160.93/160.65 [8451]E(f334(f334(f180(x84511,x84512),x84513),x84514),f210(x84512))+P1(f334(f334(f336(x84511),x84514),f334(f313(f887(x84511,x84512),x84511,f268(x84511,x84512)),f334(f174(f887(x84511,x84512)),x84513))))
% 160.93/160.65 [8452]P39(x84521,x84522)+~P39(x84521,f334(f334(f312(f887(x84521,x84521)),f334(f334(f269(x84521,x84521),x84523),x84524)),x84522))
% 160.93/160.65 [8453]P55(x84531,x84532)+~P55(x84531,f334(f334(f312(f887(x84531,x84531)),f334(f334(f269(x84531,x84531),x84533),x84534)),x84532))
% 160.93/160.65 [8459]~P108(x84591)+E(f334(f334(f150(x84591,x84591,f5(x84591)),x84592),f334(f334(f150(x84591,x84591,f5(x84591)),x84593),x84594)),f334(f334(f150(x84591,x84591,f5(x84591)),x84593),f334(f334(f150(x84591,x84591,f5(x84591)),x84592),x84594)))
% 160.93/160.65 [8469]E(x84691,x84692)+~P1(f334(f62(x84693,x84694,f334(f334(f312(x84693),x84691),f196(f888(x84693,a876)))),x84692))
% 160.93/160.65 [8480]E(f334(f334(f136(x84801),f334(f334(f177(x84801),x84802),x84803)),f334(f334(f177(x84801),x84804),f334(f334(f140(x84801),x84802),x84803))),f334(f334(f177(x84801),f334(f334(f80(a881),x84802),x84804)),x84803))+~P1(f334(f334(f248(a881),f334(f334(f80(a881),x84802),x84804)),f334(f197(f882(x84801)),x84803)))
% 160.93/160.65 [8520]P1(f334(f61(x85201),x85202))+~E(x85202,f334(f313(a881,x85201,x85203),f334(f254(a881),f334(f334(f7(a881,a881,a876),f249(a881)),x85204))))
% 160.93/160.65 [8541]~P89(x85411)+E(f334(f144(x85411,x85411,f80(x85411),f334(f334(f80(x85411),x85412),x85413)),x85414),f334(f334(f80(x85411),x85412),f334(f144(x85411,x85411,f80(x85411),x85413),x85414)))
% 160.93/160.65 [8581]P1(f334(f334(f248(f888(x85811,a876)),f334(f267(x85811,x85812),x85813)),f334(f267(x85811,x85812),x85814)))+~P1(f334(f334(f248(f888(f887(x85811,x85812),a876)),x85813),x85814))
% 160.93/160.65 [8594]~P1(f334(f334(f248(a881),x85942),x85944))+P1(f334(f334(f248(f888(x85941,a876)),f334(f174(x85941),f334(f334(f177(x85941),x85942),x85943))),f334(f174(x85941),f334(f334(f177(x85941),x85944),x85943))))
% 160.93/160.65 [8595]~P1(f334(f334(f248(a881),x85954),x85952))+P1(f334(f334(f248(f888(x85951,a876)),f334(f174(x85951),f334(f334(f140(x85951),x85952),x85953))),f334(f174(x85951),f334(f334(f140(x85951),x85954),x85953))))
% 160.93/160.65 [8652]~P1(f334(f61(x86521),f334(f334(f22(f888(x86521,a876)),x86522),x86524)))+P1(f334(f61(x86521),f334(f334(f22(f888(x86521,a876)),x86522),f334(f334(f312(x86521),x86523),x86524))))
% 160.93/160.65 [8688]P1(f334(f334(f336(f887(x86881,x86881)),x86882),f310(x86881,x86883)))+~P1(f334(f334(f336(f887(x86881,x86881)),x86882),f334(f334(f191(f887(x86881,x86881),a876),x86884),x86883)))
% 160.93/160.65 [8765]~P1(f334(f61(x87651),f334(f334(f22(f888(x87651,a876)),x87652),f334(f334(f312(x87651),x87654),x87653))))+P1(f334(f61(x87651),f334(f334(f22(f888(x87651,a876)),x87652),x87653)))
% 160.93/160.65 [8912]~E(f334(f334(f180(x89121,x89122),x89123),x89124),f210(x89122))+~P1(f334(f334(f336(x89121),x89124),f334(f313(f887(x89121,x89122),x89121,f268(x89121,x89122)),f334(f174(f887(x89121,x89122)),x89123))))
% 160.93/160.65 [8981]~P2(x89811)+P1(f334(f334(f248(x89811),f334(f334(f114(x89811),x89812),f334(f334(f105(x89811),x89813),x89814))),f334(f334(f105(x89811),f334(f334(f114(x89811),x89812),x89813)),f334(f334(f114(x89811),x89812),x89814))))
% 160.93/160.65 [8982]~P108(x89821)+P1(f334(f334(f248(x89821),f334(f334(f247(x89821),x89822),f334(f334(f246(x89821),x89823),x89824))),f334(f334(f246(x89821),f334(f334(f247(x89821),x89822),x89823)),f334(f334(f247(x89821),x89822),x89824))))
% 160.93/160.65 [9129]E(x91291,x91292)+~P1(f334(f334(f336(f887(x91293,x91293)),f334(f334(f269(x91293,x91293),x91291),x91292)),f334(f174(f887(x91293,x91293)),f334(f334(f184(x91293,x91293),x91294),x91294))))
% 160.93/160.65 [9162]~P1(f334(f334(f336(f887(x91621,x91621)),f334(f334(f269(x91621,x91621),x91623),x91622)),f310(x91621,x91624)))+~P39(x91621,f334(f334(f312(f887(x91621,x91621)),f334(f334(f269(x91621,x91621),x91622),x91623)),x91624))
% 160.93/160.65 [9163]~P1(f334(f334(f336(f887(x91631,x91631)),f334(f334(f269(x91631,x91631),x91633),x91632)),f310(x91631,x91634)))+~P55(x91631,f334(f334(f312(f887(x91631,x91631)),f334(f334(f269(x91631,x91631),x91632),x91633)),x91634))
% 160.93/160.65 [9168]E(x91681,x91682)+E(f334(f138(x91683,f334(f334(f8(a876,a876,x91683),a329),f334(a331,x91681))),f334(f334(f153(x91683),x91682),x91684)),f334(f334(f153(x91683),x91682),f334(f138(x91683,f334(f334(f8(a876,a876,x91683),a329),f334(a331,x91681))),x91684)))
% 160.93/160.65 [9212]~P2(x92121)+P1(f334(f334(f248(x92121),f334(f334(f114(x92121),f334(f334(f105(x92121),x92122),x92123)),f334(f334(f105(x92121),x92122),x92124))),f334(f334(f105(x92121),x92122),f334(f334(f114(x92121),x92123),x92124))))
% 160.93/160.65 [9213]~P108(x92131)+P1(f334(f334(f248(x92131),f334(f334(f247(x92131),f334(f334(f246(x92131),x92132),x92133)),f334(f334(f246(x92131),x92132),x92134))),f334(f334(f246(x92131),x92132),f334(f334(f247(x92131),x92133),x92134))))
% 160.93/160.65 [9287]~E(f334(f313(x92872,x92871,x92873),f257(f888(x92872,a876))),f257(f888(x92871,a876)))+P1(f334(f334(f248(f888(x92871,a876)),f334(f79(f888(x92871,a876)),f334(f313(x92872,x92871,x92873),x92874))),f334(f313(x92872,x92871,x92873),f334(f79(f888(x92872,a876)),x92874))))
% 160.93/160.65 [9365]P1(f334(f334(f334(f334(a204,f334(f245(a878),f334(a28,x93651))),x93652),f538(x93653,x93654,x93652,x93651)),x93653))+~P1(f334(f334(f334(f334(a204,f334(a26,x93651)),x93652),x93654),x93653))
% 160.93/160.65 [9611]P1(f334(f334(f336(f887(x96111,x96111)),f334(f334(f269(x96111,x96111),x96112),x96113)),f334(f289(x96111,x96111),f334(f334(f291(x96111,x96111,x96111),x96114),f310(x96111,x96114)))))+~P1(f334(f334(f336(f887(x96111,x96111)),f334(f334(f269(x96111,x96111),x96112),x96113)),f334(f334(f291(x96111,x96111,x96111),f334(f289(x96111,x96111),x96114)),f310(x96111,f334(f289(x96111,x96111),x96114)))))
% 160.93/160.65 [9612]~P1(f334(f334(f336(f887(x96121,x96121)),f334(f334(f269(x96121,x96121),x96122),x96123)),f334(f289(x96121,x96121),f334(f334(f291(x96121,x96121,x96121),x96124),f310(x96121,x96124)))))+P1(f334(f334(f336(f887(x96121,x96121)),f334(f334(f269(x96121,x96121),x96122),x96123)),f334(f334(f291(x96121,x96121,x96121),f334(f289(x96121,x96121),x96124)),f310(x96121,f334(f289(x96121,x96121),x96124)))))
% 160.93/160.65 [9633]~P1(f334(f334(f336(x96332),x96334),f334(f265(x96331,x96332),x96333)))+P1(f334(f334(f336(f887(x96331,x96332)),f334(f334(f269(x96331,x96332),f569(x96333,x96331,x96334,x96332)),x96334)),x96333))
% 160.93/160.65 [9634]~P1(f334(f334(f336(x96342),x96344),f334(f265(x96341,x96342),x96343)))+P1(f334(f334(f336(f887(x96341,x96342)),f334(f334(f269(x96341,x96342),f581(x96343,x96341,x96344,x96342)),x96344)),x96343))
% 160.93/160.65 [9661]~P1(f334(f334(f336(x96611),x96614),f334(f334(f114(f888(x96611,a876)),x96612),x96613)))+P1(f334(f334(f334(f114(f888(x96611,a876)),f334(f334(f7(x96611,f888(x96611,a876),a876),f336(x96611)),x96612)),f334(f334(f7(x96611,f888(x96611,a876),a876),f336(x96611)),x96613)),x96614))
% 160.93/160.65 [9662]~P1(f334(f334(f336(x96621),x96624),f334(f334(f105(f888(x96621,a876)),x96622),x96623)))+P1(f334(f334(f334(f105(f888(x96621,a876)),f334(f334(f7(x96621,f888(x96621,a876),a876),f336(x96621)),x96622)),f334(f334(f7(x96621,f888(x96621,a876),a876),f336(x96621)),x96623)),x96624))
% 160.93/160.65 [9739]~P1(f334(f334(f336(f887(x97391,x97391)),f334(f334(f269(x97391,x97391),x97394),x97393)),f334(f334(f291(x97391,x97391,x97391),x97392),f310(x97391,x97392))))+P1(f334(f334(f336(f887(x97391,x97391)),f334(f334(f269(x97391,x97391),f644(x97392,x97393,x97394,x97391)),x97393)),x97392))
% 160.93/160.65 [9784]P1(f334(f334(f336(x97841),x97842),f334(f334(f114(f888(x97841,a876)),x97843),x97844)))+~P1(f334(f334(f334(f114(f888(x97841,a876)),f334(f334(f7(x97841,f888(x97841,a876),a876),f336(x97841)),x97843)),f334(f334(f7(x97841,f888(x97841,a876),a876),f336(x97841)),x97844)),x97842))
% 160.93/160.65 [9785]P1(f334(f334(f336(x97851),x97852),f334(f334(f105(f888(x97851,a876)),x97853),x97854)))+~P1(f334(f334(f334(f105(f888(x97851,a876)),f334(f334(f7(x97851,f888(x97851,a876),a876),f336(x97851)),x97853)),f334(f334(f7(x97851,f888(x97851,a876),a876),f336(x97851)),x97854)),x97852))
% 160.93/160.65 [10065]P34(x100651,f334(f334(f7(x100651,f888(f887(x100651,x100651),a876),f888(x100651,a876)),f334(f334(f8(f888(x100651,f888(f888(f887(x100651,x100651),a876),a876)),f888(f888(f887(x100651,x100651),a876),f888(x100651,a876)),x100651),f7(x100651,f888(f887(x100651,x100651),a876),a876)),f334(f334(f8(f888(x100651,f887(x100651,x100651)),f888(x100651,f888(f888(f887(x100651,x100651),a876),a876)),x100651),f334(f8(f887(x100651,x100651),f888(f888(f887(x100651,x100651),a876),a876),x100651),f336(f887(x100651,x100651)))),f269(x100651,x100651)))),x100652),x100653,x100654)+~P1(f334(f334(f336(f887(f882(x100651),f882(x100651))),f334(f334(f269(f882(x100651),f882(x100651)),x100653),x100654)),f160(x100651,x100652)))
% 160.93/160.65 [10069]P56(x100691,f334(f334(f7(x100691,f888(f887(x100691,x100691),a876),f888(x100691,a876)),f334(f334(f8(f888(x100691,f888(f888(f887(x100691,x100691),a876),a876)),f888(f888(f887(x100691,x100691),a876),f888(x100691,a876)),x100691),f7(x100691,f888(f887(x100691,x100691),a876),a876)),f334(f334(f8(f888(x100691,f887(x100691,x100691)),f888(x100691,f888(f888(f887(x100691,x100691),a876),a876)),x100691),f334(f8(f887(x100691,x100691),f888(f888(f887(x100691,x100691),a876),a876),x100691),f336(f887(x100691,x100691)))),f269(x100691,x100691)))),x100692),x100693,x100694)+~P1(f334(f334(f336(f887(f888(x100691,a876),f888(x100691,a876))),f334(f334(f269(f888(x100691,a876),f888(x100691,a876)),x100693),x100694)),f325(x100691,x100692)))
% 160.93/160.65 [10098]E(x100981,x100982)+~E(f334(f334(f7(x100983,f888(f887(x100983,x100984),a876),f888(x100984,a876)),f334(f334(f8(f888(x100984,f888(f888(f887(x100983,x100984),a876),a876)),f888(f888(f887(x100983,x100984),a876),f888(x100984,a876)),x100983),f7(x100984,f888(f887(x100983,x100984),a876),a876)),f334(f334(f8(f888(x100984,f887(x100983,x100984)),f888(x100984,f888(f888(f887(x100983,x100984),a876),a876)),x100983),f334(f8(f887(x100983,x100984),f888(f888(f887(x100983,x100984),a876),a876),x100984),f336(f887(x100983,x100984)))),f269(x100983,x100984)))),x100981),f334(f334(f7(x100983,f888(f887(x100983,x100984),a876),f888(x100984,a876)),f334(f334(f8(f888(x100984,f888(f888(f887(x100983,x100984),a876),a876)),f888(f888(f887(x100983,x100984),a876),f888(x100984,a876)),x100983),f7(x100984,f888(f887(x100983,x100984),a876),a876)),f334(f334(f8(f888(x100984,f887(x100983,x100984)),f888(x100984,f888(f888(f887(x100983,x100984),a876),a876)),x100983),f334(f8(f887(x100983,x100984),f888(f888(f887(x100983,x100984),a876),a876),x100984),f336(f887(x100983,x100984)))),f269(x100983,x100984)))),x100982))
% 160.93/160.65 [10102]~P34(x101021,f334(f334(f7(x101021,f888(f887(x101021,x101021),a876),f888(x101021,a876)),f334(f334(f8(f888(x101021,f888(f888(f887(x101021,x101021),a876),a876)),f888(f888(f887(x101021,x101021),a876),f888(x101021,a876)),x101021),f7(x101021,f888(f887(x101021,x101021),a876),a876)),f334(f334(f8(f888(x101021,f887(x101021,x101021)),f888(x101021,f888(f888(f887(x101021,x101021),a876),a876)),x101021),f334(f8(f887(x101021,x101021),f888(f888(f887(x101021,x101021),a876),a876),x101021),f336(f887(x101021,x101021)))),f269(x101021,x101021)))),x101024),x101022,x101023)+P1(f334(f334(f336(f887(f882(x101021),f882(x101021))),f334(f334(f269(f882(x101021),f882(x101021)),x101022),x101023)),f160(x101021,x101024)))
% 160.93/160.65 [10103]~P56(x101031,f334(f334(f7(x101031,f888(f887(x101031,x101031),a876),f888(x101031,a876)),f334(f334(f8(f888(x101031,f888(f888(f887(x101031,x101031),a876),a876)),f888(f888(f887(x101031,x101031),a876),f888(x101031,a876)),x101031),f7(x101031,f888(f887(x101031,x101031),a876),a876)),f334(f334(f8(f888(x101031,f887(x101031,x101031)),f888(x101031,f888(f888(f887(x101031,x101031),a876),a876)),x101031),f334(f8(f887(x101031,x101031),f888(f888(f887(x101031,x101031),a876),a876),x101031),f336(f887(x101031,x101031)))),f269(x101031,x101031)))),x101034),x101032,x101033)+P1(f334(f334(f336(f887(f888(x101031,a876),f888(x101031,a876))),f334(f334(f269(f888(x101031,a876),f888(x101031,a876)),x101032),x101033)),f325(x101031,x101034)))
% 160.93/160.65 [7469]~P93(x74691)+E(f334(f334(f80(x74691),f334(f107(x74691),x74692)),f334(f334(f22(x74691),f334(f107(x74691),x74693)),x74694)),f334(f334(f22(x74691),f334(f107(x74691),f334(f334(f80(a1),x74692),x74693))),x74694))
% 160.93/160.65 [7470]~P93(x74701)+E(f334(f334(f80(x74701),f334(f107(x74701),x74702)),f334(f334(f80(x74701),f334(f107(x74701),x74703)),x74704)),f334(f334(f80(x74701),f334(f107(x74701),f334(f334(f80(a1),x74702),x74703))),x74704))
% 160.93/160.65 [7471]~P93(x74711)+E(f334(f334(f81(x74711),f334(f107(x74711),x74712)),f334(f334(f81(x74711),f334(f107(x74711),x74713)),x74714)),f334(f334(f81(x74711),f334(f107(x74711),f334(f334(f81(a1),x74712),x74713))),x74714))
% 160.93/160.65 [7516]~P142(x75161)+E(f334(f168(x75161),f334(f334(f156(x75162,x75161),f334(f16(x75161,x75162),x75163)),x75164)),f334(f334(f81(x75161),f334(f104(x75161),f334(f197(f882(x75162)),x75164))),x75163))
% 160.93/160.65 [7750]E(f334(f280(x77501,f334(f334(f153(f887(a103,x77501)),x77502),x77503)),x77504),f334(f272(a103,x77501),x77502))+~P1(f334(f334(f249(a103),x77504),f334(f268(a103,x77501),x77502)))
% 160.93/160.65 [7794]~P93(x77941)+E(f334(f334(f80(x77941),f334(f107(x77941),x77942)),f334(f334(f22(x77941),x77943),f334(f107(x77941),x77944))),f334(f334(f80(x77941),f334(f107(x77941),f334(f334(f80(a1),x77942),f334(f79(a1),x77944)))),x77943))
% 160.93/160.65 [7926]E(f334(f280(x79261,x79262),f334(f334(f22(a103),x79263),f334(f268(a103,x79261),x79264))),f334(f280(x79261,f334(f334(f153(f887(a103,x79261)),x79264),x79262)),x79263))+P1(f334(f334(f249(a103),x79263),f334(f268(a103,x79261),x79264)))
% 160.93/160.65 [8373]~P1(f334(f334(f336(x83731),x83732),f334(f174(x83731),f118(x83731,x83734))))+P1(f334(f334(f336(x83731),x83732),f334(f174(x83731),f118(x83731,f334(f334(f136(x83731),x83733),x83734)))))
% 160.93/160.65 [8374]~P1(f334(f334(f336(x83741),x83742),f334(f174(x83741),f118(x83741,x83743))))+P1(f334(f334(f336(x83741),x83742),f334(f174(x83741),f118(x83741,f334(f334(f136(x83741),x83743),x83744)))))
% 160.93/160.65 [8391]E(f334(f334(f114(f888(x83911,a876)),f334(f334(f105(f888(x83911,a876)),x83912),x83913)),x83914),f334(f334(f105(f888(x83911,a876)),x83912),f334(f334(f114(f888(x83911,a876)),x83913),x83914)))+~P1(f334(f334(f248(f888(x83911,a876)),x83914),x83912))
% 160.93/160.65 [8701]~E(f334(f334(f114(f888(x87011,a876)),f334(f334(f105(f888(x87011,a876)),x87013),x87014)),x87012),f334(f334(f105(f888(x87011,a876)),x87013),f334(f334(f114(f888(x87011,a876)),x87014),x87012)))+P1(f334(f334(f248(f888(x87011,a876)),x87012),x87013))
% 160.93/160.65 [8986]~P1(f334(f334(f248(f888(x89861,a876)),x89862),f334(f334(f114(f888(x89861,a876)),x89863),x89864)))+P1(f334(f334(f248(f888(x89861,a876)),f334(f334(f22(f888(x89861,a876)),x89862),x89863)),x89864))
% 160.93/160.65 [9044]~P1(f334(f334(f334(f334(a204,f334(a26,x90441)),x90442),f334(a116,x90443)),x90444))+P1(f334(f334(f334(f334(a204,f334(f245(a878),f334(a28,x90441))),x90442),x90443),x90444))
% 160.93/160.65 [9107]P1(f334(f334(f248(f888(x91071,a876)),x91072),f334(f334(f114(f888(x91071,a876)),x91073),x91074)))+~P1(f334(f334(f248(f888(x91071,a876)),f334(f334(f22(f888(x91071,a876)),x91072),x91073)),x91074))
% 160.93/160.65 [9161]P1(f334(f334(f334(f334(a204,f334(a26,x91611)),x91612),f334(a116,x91613)),x91614))+~P1(f334(f334(f334(f334(a204,f334(f245(a878),f334(a28,x91611))),x91612),x91613),x91614))
% 160.93/160.65 [9193]~P85(x91931)+E(f334(f75(x91931),f334(f334(f6(x91932,x91931),f334(f334(f8(x91931,x91931,x91932),f75(x91931)),x91933)),x91934)),f334(f334(f6(x91932,x91931),f334(f334(f8(x91931,x91931,x91932),f75(x91931)),x91933)),x91934))
% 160.93/160.65 [9363]~P85(x93631)+P1(f334(f334(f248(x93631),f2(x93631)),f334(f334(f6(x93632,x93631),f334(f334(f8(x93631,x93631,x93632),f75(x93631)),x93633)),x93634)))
% 160.93/160.65 [9368]~P67(x93681)+E(f334(f168(x93681),f334(f334(f156(x93682,x93681),f334(f73(x93681,x93681,x93682,f79(x93681)),x93683)),x93684)),f334(f79(x93681),f334(f168(x93681),f334(f334(f156(x93682,x93681),x93683),x93684))))
% 160.93/160.65 [9502]~P85(x95021)+P1(f334(f334(f248(x95021),f334(f75(x95021),f334(f334(f6(x95022,x95021),x95023),x95024))),f334(f334(f6(x95022,x95021),f334(f334(f8(x95021,x95021,x95022),f75(x95021)),x95023)),x95024)))
% 160.93/160.65 [9535]~E(f334(f334(f80(a881),x95351),x95354),f334(f334(f80(a881),x95353),x95352))+P1(f334(f334(f336(f887(f887(a881,a881),f887(a881,a881))),f334(f334(f269(f887(a881,a881),f887(a881,a881)),f334(f334(f269(a881,a881),x95351),x95352)),f334(f334(f269(a881,a881),x95353),x95354))),a112))
% 160.93/160.65 [9536]~P1(f334(f334(f249(a881),x95361),x95363))+P1(f334(f334(f336(f887(f887(a881,a881),f887(a881,a881))),f334(f334(f269(f887(a881,a881),f887(a881,a881)),f334(f334(f269(a881,a881),x95361),x95362)),f334(f334(f269(a881,a881),x95363),x95364))),a35))
% 160.93/160.65 [9537]~P1(f334(f334(f249(a881),x95371),x95373))+P1(f334(f334(f336(f887(f887(a881,a881),f887(a881,a881))),f334(f334(f269(f887(a881,a881),f887(a881,a881)),f334(f334(f269(a881,a881),x95371),x95372)),f334(f334(f269(a881,a881),x95373),x95374))),a70))
% 160.93/160.65 [9686]E(f334(f334(f80(a881),x96861),x96862),f334(f334(f80(a881),x96863),x96864))+~P1(f334(f334(f336(f887(f887(a881,a881),f887(a881,a881))),f334(f334(f269(f887(a881,a881),f887(a881,a881)),f334(f334(f269(a881,a881),x96861),x96864)),f334(f334(f269(a881,a881),x96863),x96862))),a112))
% 160.93/160.65 [9713]E(f334(f334(f167(x97131),f334(f334(f140(x97131),f334(f197(f882(x97131)),f179(x97131,x97132,x97133))),x97133)),x97134),f334(f334(f167(x97131),x97133),f334(f334(f80(a881),x97134),f334(f197(f882(x97131)),f179(x97131,x97132,x97133)))))+~P1(f334(f334(f249(a881),x97134),f334(f197(f882(x97131)),f334(f334(f140(x97131),f334(f197(f882(x97131)),f179(x97131,x97132,x97133))),x97133))))
% 160.93/160.65 [9730]~P1(f334(f334(f336(x97302),x97304),f334(f334(f41(x97301,f888(x97302,a876)),f257(f888(x97301,a876))),x97303)))+P1(f334(f334(f334(f41(x97301,f888(x97302,a876)),f257(f888(x97301,a876))),f334(f334(f8(f888(x97302,a876),f888(x97302,a876),x97301),f334(f7(x97302,f888(x97302,a876),a876),f336(x97302))),x97303)),x97304))
% 160.93/160.65 [9731]~P1(f334(f334(f336(x97312),x97314),f334(f334(f42(x97311,f888(x97312,a876)),f257(f888(x97311,a876))),x97313)))+P1(f334(f334(f334(f42(x97311,f888(x97312,a876)),f257(f888(x97311,a876))),f334(f334(f8(f888(x97312,a876),f888(x97312,a876),x97311),f334(f7(x97312,f888(x97312,a876),a876),f336(x97312))),x97313)),x97314))
% 160.93/160.65 [9812]~P1(f334(f48(x98121,x98122),f334(f334(f269(a1,a1),x98124),x98123)))+P1(f334(f48(f334(f79(a1),x98121),x98122),f334(f334(f269(a1,a1),f334(f334(f334(f100(a1),f334(f334(a331,x98123),f2(a1))),f334(f79(a1),x98124)),f334(f334(f22(a1),f334(f79(a1),x98124)),f78(a1)))),f334(f334(f334(f100(a1),f334(f334(a331,x98123),f2(a1))),f2(a1)),f334(f334(f22(a1),x98122),x98123)))))
% 160.93/160.65 [9821]P1(f334(f334(f336(x98211),x98212),f334(f334(f41(x98213,f888(x98211,a876)),f257(f888(x98213,a876))),x98214)))+~P1(f334(f334(f334(f41(x98213,f888(x98211,a876)),f257(f888(x98213,a876))),f334(f334(f8(f888(x98211,a876),f888(x98211,a876),x98213),f334(f7(x98211,f888(x98211,a876),a876),f336(x98211))),x98214)),x98212))
% 160.93/160.65 [9822]P1(f334(f334(f336(x98221),x98222),f334(f334(f42(x98223,f888(x98221,a876)),f257(f888(x98223,a876))),x98224)))+~P1(f334(f334(f334(f42(x98223,f888(x98221,a876)),f257(f888(x98223,a876))),f334(f334(f8(f888(x98221,a876),f888(x98221,a876),x98223),f334(f7(x98221,f888(x98221,a876),a876),f336(x98221))),x98224)),x98222))
% 160.93/160.65 [9834]E(f334(f334(f41(a881,f888(x98341,a876)),f257(f888(a881,a876))),x98342),f334(f334(f41(a881,f888(x98341,a876)),f257(f888(a881,a876))),x98343))+~E(f334(f334(f41(a881,f888(x98341,a876)),f334(f304(a881,f2(a881)),f481(x98342,x98344,x98343,x98341))),x98343),f334(f334(f41(a881,f888(x98341,a876)),f334(f304(a881,f2(a881)),f334(f334(f80(a881),f481(x98342,x98344,x98343,x98341)),x98344))),x98342))
% 160.93/160.65 [10156]~P1(f334(f334(f248(f888(f887(x101561,x101562),a876)),x101563),x101564))+P1(f334(f334(f248(f888(x101561,f888(x101562,a876))),f334(f334(f7(x101561,f888(f887(x101561,x101562),a876),f888(x101562,a876)),f334(f334(f8(f888(x101562,f888(f888(f887(x101561,x101562),a876),a876)),f888(f888(f887(x101561,x101562),a876),f888(x101562,a876)),x101561),f7(x101562,f888(f887(x101561,x101562),a876),a876)),f334(f334(f8(f888(x101562,f887(x101561,x101562)),f888(x101562,f888(f888(f887(x101561,x101562),a876),a876)),x101561),f334(f8(f887(x101561,x101562),f888(f888(f887(x101561,x101562),a876),a876),x101562),f336(f887(x101561,x101562)))),f269(x101561,x101562)))),x101563)),f334(f334(f7(x101561,f888(f887(x101561,x101562),a876),f888(x101562,a876)),f334(f334(f8(f888(x101562,f888(f888(f887(x101561,x101562),a876),a876)),f888(f888(f887(x101561,x101562),a876),f888(x101562,a876)),x101561),f7(x101562,f888(f887(x101561,x101562),a876),a876)),f334(f334(f8(f888(x101562,f887(x101561,x101562)),f888(x101562,f888(f888(f887(x101561,x101562),a876),a876)),x101561),f334(f8(f887(x101561,x101562),f888(f888(f887(x101561,x101562),a876),a876),x101562),f336(f887(x101561,x101562)))),f269(x101561,x101562)))),x101564)))
% 160.93/160.65 [10173]P1(f334(f334(f248(f888(f887(x101731,x101732),a876)),x101733),x101734))+~P1(f334(f334(f248(f888(x101731,f888(x101732,a876))),f334(f334(f7(x101731,f888(f887(x101731,x101732),a876),f888(x101732,a876)),f334(f334(f8(f888(x101732,f888(f888(f887(x101731,x101732),a876),a876)),f888(f888(f887(x101731,x101732),a876),f888(x101732,a876)),x101731),f7(x101732,f888(f887(x101731,x101732),a876),a876)),f334(f334(f8(f888(x101732,f887(x101731,x101732)),f888(x101732,f888(f888(f887(x101731,x101732),a876),a876)),x101731),f334(f8(f887(x101731,x101732),f888(f888(f887(x101731,x101732),a876),a876),x101732),f336(f887(x101731,x101732)))),f269(x101731,x101732)))),x101733)),f334(f334(f7(x101731,f888(f887(x101731,x101732),a876),f888(x101732,a876)),f334(f334(f8(f888(x101732,f888(f888(f887(x101731,x101732),a876),a876)),f888(f888(f887(x101731,x101732),a876),f888(x101732,a876)),x101731),f7(x101732,f888(f887(x101731,x101732),a876),a876)),f334(f334(f8(f888(x101732,f887(x101731,x101732)),f888(x101732,f888(f888(f887(x101731,x101732),a876),a876)),x101731),f334(f8(f887(x101731,x101732),f888(f888(f887(x101731,x101732),a876),a876),x101732),f336(f887(x101731,x101732)))),f269(x101731,x101732)))),x101734)))
% 160.93/160.65 [9242]~P1(f334(f334(f336(f887(x92421,x92421)),x92422),f310(x92421,x92424)))+P1(f334(f334(f336(f887(x92421,x92421)),x92422),f310(x92421,f334(f334(f114(f888(f887(x92421,x92421),a876)),x92423),x92424))))
% 160.93/160.65 [9243]~P1(f334(f334(f336(f887(x92431,x92431)),x92432),f310(x92431,x92433)))+P1(f334(f334(f336(f887(x92431,x92431)),x92432),f310(x92431,f334(f334(f114(f888(f887(x92431,x92431),a876)),x92433),x92434))))
% 160.93/160.65 [9603]~E(f334(f174(x96031),x96034),f186(x96031,x96032,x96033))+E(f334(f180(x96031,x96032),f334(f334(f156(x96031,f887(x96031,x96032)),f334(f334(f18(x96031,x96032,f887(x96031,x96032)),f269(x96031,x96032)),f334(f334(f8(f885(x96032),x96032,x96031),f245(x96032)),x96033))),x96034)),x96033)
% 160.93/160.65 [9929]~P1(f334(f334(f249(a881),f334(f334(f80(a881),x99291),x99294)),f334(f334(f80(a881),x99293),x99292)))+P1(f334(f334(f249(a1),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x99291),x99292)),f196(f888(f887(a881,a881),a876)))))),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x99293),x99294)),f196(f888(f887(a881,a881),a876)))))))
% 160.93/160.65 [9930]~P1(f334(f334(f248(a881),f334(f334(f80(a881),x99301),x99304)),f334(f334(f80(a881),x99303),x99302)))+P1(f334(f334(f248(a1),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x99301),x99302)),f196(f888(f887(a881,a881),a876)))))),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x99303),x99304)),f196(f888(f887(a881,a881),a876)))))))
% 160.93/160.65 [10007]P1(f334(f334(f249(a881),f334(f334(f80(a881),x100071),x100072)),f334(f334(f80(a881),x100073),x100074)))+~P1(f334(f334(f249(a1),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x100071),x100074)),f196(f888(f887(a881,a881),a876)))))),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x100073),x100072)),f196(f888(f887(a881,a881),a876)))))))
% 160.93/160.65 [10008]P1(f334(f334(f248(a881),f334(f334(f80(a881),x100081),x100082)),f334(f334(f80(a881),x100083),x100084)))+~P1(f334(f334(f248(a1),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x100081),x100084)),f196(f888(f887(a881,a881),a876)))))),f334(a89,f334(f288(f887(a881,a881),f887(a881,a881),a112),f334(f334(f312(f887(a881,a881)),f334(f334(f269(a881,a881),x100083),x100082)),f196(f888(f887(a881,a881),a876)))))))
% 160.93/160.65 [10050]P1(f334(f334(f248(f888(x100501,a876)),f334(f334(f41(a881,f888(x100501,a876)),f257(f888(a881,a876))),x100502)),f334(f334(f41(a881,f888(x100501,a876)),f257(f888(a881,a876))),x100503)))+~P1(f334(f334(f248(f888(x100501,a876)),f334(f334(f41(a881,f888(x100501,a876)),f334(f304(a881,f2(a881)),f471(x100503,x100504,x100502,x100501))),x100502)),f334(f334(f41(a881,f888(x100501,a876)),f334(f304(a881,f2(a881)),f334(f334(f80(a881),f471(x100503,x100504,x100502,x100501)),x100504))),x100503)))
% 160.93/160.65 [10147]~P1(f334(f334(f336(x101472),x101474),f334(f265(x101471,x101472),x101473)))+P1(f334(f264(x101471,x101472,f334(f334(f7(x101471,f888(f887(x101471,x101472),a876),f888(x101472,a876)),f334(f334(f8(f888(x101472,f888(f888(f887(x101471,x101472),a876),a876)),f888(f888(f887(x101471,x101472),a876),f888(x101472,a876)),x101471),f7(x101472,f888(f887(x101471,x101472),a876),a876)),f334(f334(f8(f888(x101472,f887(x101471,x101472)),f888(x101472,f888(f888(f887(x101471,x101472),a876),a876)),x101471),f334(f8(f887(x101471,x101472),f888(f888(f887(x101471,x101472),a876),a876),x101472),f336(f887(x101471,x101472)))),f269(x101471,x101472)))),x101473)),x101474))
% 160.93/160.65 [10148]~P1(f334(f334(f336(x101481),x101484),f334(f267(x101481,x101482),x101483)))+P1(f334(f263(x101481,x101482,f334(f334(f7(x101481,f888(f887(x101481,x101482),a876),f888(x101482,a876)),f334(f334(f8(f888(x101482,f888(f888(f887(x101481,x101482),a876),a876)),f888(f888(f887(x101481,x101482),a876),f888(x101482,a876)),x101481),f7(x101482,f888(f887(x101481,x101482),a876),a876)),f334(f334(f8(f888(x101482,f887(x101481,x101482)),f888(x101482,f888(f888(f887(x101481,x101482),a876),a876)),x101481),f334(f8(f887(x101481,x101482),f888(f888(f887(x101481,x101482),a876),a876),x101482),f336(f887(x101481,x101482)))),f269(x101481,x101482)))),x101483)),x101484))
% 160.93/160.65 [10159]P1(f334(f334(f336(x101591),x101592),f334(f265(x101593,x101591),x101594)))+~P1(f334(f264(x101593,x101591,f334(f334(f7(x101593,f888(f887(x101593,x101591),a876),f888(x101591,a876)),f334(f334(f8(f888(x101591,f888(f888(f887(x101593,x101591),a876),a876)),f888(f888(f887(x101593,x101591),a876),f888(x101591,a876)),x101593),f7(x101591,f888(f887(x101593,x101591),a876),a876)),f334(f334(f8(f888(x101591,f887(x101593,x101591)),f888(x101591,f888(f888(f887(x101593,x101591),a876),a876)),x101593),f334(f8(f887(x101593,x101591),f888(f888(f887(x101593,x101591),a876),a876),x101591),f336(f887(x101593,x101591)))),f269(x101593,x101591)))),x101594)),x101592))
% 160.93/160.65 [10160]P1(f334(f334(f336(x101601),x101602),f334(f267(x101601,x101603),x101604)))+~P1(f334(f263(x101601,x101603,f334(f334(f7(x101601,f888(f887(x101601,x101603),a876),f888(x101603,a876)),f334(f334(f8(f888(x101603,f888(f888(f887(x101601,x101603),a876),a876)),f888(f888(f887(x101601,x101603),a876),f888(x101603,a876)),x101601),f7(x101603,f888(f887(x101601,x101603),a876),a876)),f334(f334(f8(f888(x101603,f887(x101601,x101603)),f888(x101603,f888(f888(f887(x101601,x101603),a876),a876)),x101601),f334(f8(f887(x101601,x101603),f888(f888(f887(x101601,x101603),a876),a876),x101603),f336(f887(x101601,x101603)))),f269(x101601,x101603)))),x101604)),x101602))
% 160.93/160.65 [9844]P1(f334(f162(x98441,x98442),x98443))+~P1(f334(f162(x98441,f334(f334(f18(x98441,a876,a876),f334(f334(f8(a876,f888(a876,a876),x98441),a332),x98444)),x98442)),x98443))
% 160.93/160.65 [9845]P1(f334(f162(x98451,x98452),x98453))+~P1(f334(f162(x98451,f334(f334(f18(x98451,a876,a876),f334(f334(f8(a876,f888(a876,a876),x98451),a332),x98452)),x98454)),x98453))
% 160.93/160.65 [9931]~P118(x99311)+E(f334(f334(f81(x99311),f334(f334(f80(x99311),f78(x99311)),f78(x99311))),f334(f334(f6(a881,x99311),f334(f334(f8(x99311,x99311,a881),f334(f80(x99311),x99312)),f334(f334(f7(a881,x99311,x99311),f334(f334(f8(x99311,f888(x99311,x99311),a881),f81(x99311)),f104(x99311))),x99313))),f334(f255(a881),x99314))),f334(f334(f81(x99311),f334(f104(x99311),x99314)),f334(f334(f80(x99311),x99312),f334(f334(f80(x99311),x99312),f334(f334(f81(x99311),f334(f104(x99311),f334(f334(f22(a881),x99314),f78(a881)))),x99313)))))
% 160.93/160.65 [10072]P1(f334(x100721,f567(x100722,x100723,x100724,x100721)))+P39(x100722,f334(f254(f887(x100722,x100722)),f334(f273(x100722,x100722,a876),f334(f334(f8(f888(x100722,a876),f888(x100722,a876),x100722),f334(f18(x100722,a876,a876),f334(f334(f8(a876,f888(a876,a876),x100722),a332),x100721))),f334(f334(f7(x100722,f888(x100722,x100722),f888(x100722,a876)),f334(f334(f8(f888(x100722,a876),f888(f888(x100722,x100722),f888(x100722,a876)),x100722),f8(x100722,a876,x100722)),a331)),x100723)))))
% 160.93/160.65 [10086]~P1(f334(f334(f249(a881),f334(x100864,f334(x100863,f567(x100861,x100863,x100864,x100862)))),f334(x100864,f567(x100861,x100863,x100864,x100862))))+P39(x100861,f334(f254(f887(x100861,x100861)),f334(f273(x100861,x100861,a876),f334(f334(f8(f888(x100861,a876),f888(x100861,a876),x100861),f334(f18(x100861,a876,a876),f334(f334(f8(a876,f888(a876,a876),x100861),a332),x100862))),f334(f334(f7(x100861,f888(x100861,x100861),f888(x100861,a876)),f334(f334(f8(f888(x100861,a876),f888(f888(x100861,x100861),f888(x100861,a876)),x100861),f8(x100861,a876,x100861)),a331)),x100863)))))
% 160.93/160.65 [10186]~P1(f334(f334(f336(f887(x101861,x101861)),f334(f334(f269(x101861,x101861),x101863),x101864)),f334(f334(f114(f888(f887(x101861,x101861),a876)),x101862),f310(x101861,f196(f888(f887(x101861,x101861),a876))))))+P1(f334(f334(f334(f334(f114(f888(x101861,f888(x101861,a876))),f334(f334(f7(x101861,f888(f887(x101861,x101861),a876),f888(x101861,a876)),f334(f334(f8(f888(x101861,f888(f888(f887(x101861,x101861),a876),a876)),f888(f888(f887(x101861,x101861),a876),f888(x101861,a876)),x101861),f7(x101861,f888(f887(x101861,x101861),a876),a876)),f334(f334(f8(f888(x101861,f887(x101861,x101861)),f888(x101861,f888(f888(f887(x101861,x101861),a876),a876)),x101861),f334(f8(f887(x101861,x101861),f888(f888(f887(x101861,x101861),a876),a876),x101861),f336(f887(x101861,x101861)))),f269(x101861,x101861)))),x101862)),a331),x101863),x101864))
% 160.93/160.65 [10196]P1(f334(f334(f336(f887(x101961,x101961)),f334(f334(f269(x101961,x101961),x101962),x101963)),f334(f334(f114(f888(f887(x101961,x101961),a876)),x101964),f310(x101961,f196(f888(f887(x101961,x101961),a876))))))+~P1(f334(f334(f334(f334(f114(f888(x101961,f888(x101961,a876))),f334(f334(f7(x101961,f888(f887(x101961,x101961),a876),f888(x101961,a876)),f334(f334(f8(f888(x101961,f888(f888(f887(x101961,x101961),a876),a876)),f888(f888(f887(x101961,x101961),a876),f888(x101961,a876)),x101961),f7(x101961,f888(f887(x101961,x101961),a876),a876)),f334(f334(f8(f888(x101961,f887(x101961,x101961)),f888(x101961,f888(f888(f887(x101961,x101961),a876),a876)),x101961),f334(f8(f887(x101961,x101961),f888(f888(f887(x101961,x101961),a876),a876),x101961),f336(f887(x101961,x101961)))),f269(x101961,x101961)))),x101964)),a331),x101962),x101963))
% 160.93/160.65 [10058]~P110(x100583)+E(f90(x100581,f334(f334(f18(x100581,a876,a876),f334(f334(f8(a876,f888(a876,a876),x100581),a332),x100582)),f334(f334(f8(f888(x100581,a876),a876,x100581),f88(x100581)),f334(f334(f8(f888(x100581,a876),f888(x100581,a876),x100581),f334(f18(x100581,a876,a876),f334(f334(f8(a876,f888(a876,a876),x100581),a337),x100582))),f334(f334(f8(x100583,f888(x100581,a876),x100581),f334(f7(x100581,x100583,a876),f334(f334(f8(x100583,f888(x100583,a876),x100581),f248(x100583)),x100584))),x100584))))),f334(f93(x100581,x100583,x100584),x100582))
% 160.93/160.65 [10101]~P110(x101013)+E(f90(x101011,f334(f334(f18(x101011,a876,a876),f334(f334(f8(a876,f888(a876,a876),x101011),a332),x101012)),f334(f334(f8(f888(x101011,a876),a876,x101011),f88(x101011)),f334(f334(f8(f888(x101011,a876),f888(x101011,a876),x101011),f334(f18(x101011,a876,a876),f334(f334(f8(a876,f888(a876,a876),x101011),a337),x101012))),f334(f334(f7(x101011,f888(x101011,x101013),f888(x101011,a876)),f334(f334(f8(f888(x101013,a876),f888(f888(x101011,x101013),f888(x101011,a876)),x101011),f8(x101013,a876,x101011)),f334(f334(f8(x101013,f888(x101013,a876),x101011),f248(x101013)),x101014))),x101014))))),f96(x101011,x101013,x101014,x101012))
% 160.93/160.65 [10145]E(f334(f334(f153(f882(x101451)),f334(f334(f153(x101451),x101452),f334(f144(f882(x101451),f882(x101451),f136(x101451),f117(x101451)),f334(f334(f156(f882(x101451),f882(x101451)),f158(f882(x101451),x101451,f117(x101451),f334(f334(f8(f882(x101451),f888(f882(x101451),f882(x101451)),x101451),f16(f882(x101451),f882(x101451))),f334(f334(f7(x101451,f882(x101451),f882(x101451)),f153(x101451)),f117(x101451))))),x101453)))),f182(x101451,f334(f334(f153(f882(x101451)),x101454),f334(f144(f882(f882(x101451)),f882(f882(x101451)),f136(f882(x101451)),f117(f882(x101451))),f334(f334(f156(f882(x101451),f882(f882(x101451))),f158(f882(f882(x101451)),x101451,f117(f882(x101451)),f334(f16(f888(f882(x101451),f882(f882(x101451))),x101451),f334(f334(f7(f882(x101451),f882(f882(x101451)),f882(f882(x101451))),f153(f882(x101451))),f117(f882(x101451)))))),x101453))))),f182(x101451,f334(f334(f153(f882(x101451)),f334(f334(f153(x101451),x101452),x101454)),x101453)))+~P1(f334(f322(f882(f882(x101451)),f183(x101451)),f334(f334(f153(f882(x101451)),f334(f334(f153(x101451),x101452),x101454)),x101453)))
% 160.93/160.65 [10185]~P1(f334(f61(x101852),f334(f254(x101852),x101854)))+P1(f334(f61(x101851),f334(f254(x101851),f334(f334(f8(f888(x101852,a876),a876,x101851),f87(x101852)),f334(f334(f7(x101851,f888(x101852,a876),f888(x101852,a876)),f334(f334(f8(f888(x101852,f888(a876,a876)),f888(f888(x101852,a876),f888(x101852,a876)),x101851),f18(x101852,a876,a876)),f334(f334(f8(f888(x101852,a876),f888(x101852,f888(a876,a876)),x101851),f334(f8(a876,f888(a876,a876),x101852),a332)),f334(f334(f7(x101851,f888(x101852,x101851),f888(x101852,a876)),f334(f334(f8(f888(x101851,a876),f888(f888(x101852,x101851),f888(x101852,a876)),x101851),f8(x101851,a876,x101852)),a331)),x101853)))),x101854)))))
% 160.93/160.65 [5266]E(x52661,x52662)+~E(f129(x52663,x52664,x52661),f129(x52663,x52665,x52662))
% 160.93/160.65 [5267]E(x52671,x52672)+~E(f129(x52673,x52671,x52674),f129(x52673,x52672,x52675))
% 160.93/160.65 [5641]E(f334(f334(f312(x56411),x56412),f186(x56411,x56413,x56414)),f186(x56411,x56413,x56414))+~E(f334(x56414,x56412),f334(f241(x56413),x56415))
% 160.93/160.65 [6046]P1(f334(f264(x60461,x60462,x60463),x60464))+~P1(f334(f334(x60463,x60465),x60464))
% 160.93/160.65 [6048]P1(f334(f263(x60481,x60482,x60483),x60484))+~P1(f334(f334(x60483,x60484),x60485))
% 160.93/160.65 [6051]~E(f334(x60514,x60512),f334(f241(x60513),x60515))+P1(f334(f334(f336(x60511),x60512),f186(x60511,x60513,x60514)))
% 160.93/160.65 [6052]~E(f334(x60524,x60525),f334(f241(x60521),x60522))+P1(f334(f334(f336(x60521),x60522),f188(x60523,x60521,x60524)))
% 160.93/160.65 [6519]~E(x65195,f2(a103))+E(f334(f209(x65191,x65192,x65193,x65194),x65195),f119(x65192))
% 160.93/160.65 [6520]~E(x65205,f2(a103))+E(f334(f206(x65201,x65202,x65203,x65204),x65205),f130(x65202))
% 160.93/160.65 [6656]~E(x66563,f2(a103))+E(f334(f283(x66561,x66562,x66563,x66564),x66565),f334(f269(x66561,x66562),x66565))
% 160.93/160.65 [6728]~E(f334(x67284,x67285),f210(x67282))+E(f334(f243(f885(x67281),x67282,f210(x67281),x67283),f334(x67284,x67285)),f210(x67281))
% 160.93/160.65 [7351]E(f334(x73511,x73512),f210(x73513))+~E(f334(f187(x73514,x73513,x73515,x73511),x73512),f210(x73513))
% 160.93/160.65 [7352]E(f334(x73521,x73522),f210(x73523))+~E(f334(f187(x73524,x73523,x73521,x73525),x73522),f210(x73523))
% 160.93/160.65 [7388]E(f334(f187(x73881,x73882,x73883,x73884),x73885),f334(x73883,x73885))+P1(f334(f334(f336(x73881),x73885),f186(x73881,x73882,x73884)))
% 160.93/160.65 [7389]E(f334(f187(x73891,x73892,x73893,x73894),x73895),f334(x73894,x73895))+P1(f334(f334(f336(x73891),x73895),f186(x73891,x73892,x73893)))
% 160.93/160.65 [7710]~P22(x77104,x77101,x77102,x77105)+E(f334(f73(x77101,x77101,x77101,f334(x77102,x77103)),f334(x77102,x77103)),f334(x77102,x77103))
% 160.93/160.65 [7752]E(f334(f187(x77521,x77522,x77523,x77524),x77525),f334(x77524,x77525))+~P1(f334(f334(f336(x77521),x77525),f186(x77521,x77522,x77524)))
% 160.93/160.65 [8096]~P18(x80965,x80961,x80962)+E(f334(f73(x80961,x80961,x80961,f334(x80962,x80963)),f334(x80962,x80964)),f334(f73(x80961,x80961,x80961,f334(x80962,x80964)),f334(x80962,x80963)))
% 160.93/160.65 [8433]P1(f334(f334(f336(f887(x84331,x84331)),f334(f334(f269(x84331,x84331),x84332),x84333)),f328(x84331,x84334,x84335)))+~P1(f334(f334(f249(a881),f334(x84334,x84332)),f334(x84334,x84333)))
% 160.93/160.65 [8526]~P1(f334(f334(f336(x85264),x85263),f298(x85264,x85261,x85262,x85265)))+P1(f334(f334(x85261,x85262),x85263))
% 160.93/160.65 [8527]~P1(f334(f334(f336(x85274),x85273),f301(x85274,x85271,x85272,x85275)))+P1(f334(f334(x85271,x85272),x85273))
% 160.93/160.65 [8528]~P1(f334(f334(f336(x85284),x85282),f298(x85284,x85281,x85285,x85283)))+P1(f334(f334(x85281,x85282),x85283))
% 160.93/160.65 [8529]~P1(f334(f334(f336(x85294),x85292),f301(x85294,x85291,x85295,x85293)))+P1(f334(f334(x85291,x85292),x85293))
% 160.93/160.65 [8678]~P54(x86782,x86781,x86785,x86783,x86784)+E(f334(f313(x86781,x86782,x86783),x86784),f257(f888(x86782,a876)))
% 160.93/160.65 [9119]~P36(x91191,x91192,x91193,x91194,x91195)+P36(x91191,x91192,x91193,f334(f171(x91191),x91194),f334(f171(x91192),x91195))
% 160.93/160.65 [9121]~P36(x91211,x91212,x91213,f334(f171(x91211),x91214),x91215)+P36(x91211,x91212,x91213,x91214,f334(f171(x91212),x91215))
% 160.93/160.65 [9122]~P36(x91221,x91222,x91223,x91224,f334(f171(x91222),x91225))+P36(x91221,x91222,x91223,f334(f171(x91221),x91224),x91225)
% 160.93/160.65 [9128]P36(x91281,x91282,x91283,x91284,x91285)+~P36(x91281,x91282,x91283,f334(f171(x91281),x91284),f334(f171(x91282),x91285))
% 160.93/160.65 [9526]P1(f334(f334(f336(f887(f882(x95261),f882(x95261))),f334(f334(f269(f882(x95261),f882(x95261)),f334(f334(f153(x95261),x95262),x95263)),f334(f334(f153(x95261),x95262),x95264))),f159(x95261,x95265)))+~P1(f334(f334(f336(f887(f882(x95261),f882(x95261))),f334(f334(f269(f882(x95261),f882(x95261)),x95263),x95264)),f159(x95261,x95265)))
% 160.93/160.65 [9527]P1(f334(f334(f336(f887(f882(x95271),f882(x95271))),f334(f334(f269(f882(x95271),f882(x95271)),f334(f334(f136(x95271),x95272),x95273)),f334(f334(f136(x95271),x95272),x95274))),f149(x95271,x95275)))+~P1(f334(f334(f336(f887(f882(x95271),f882(x95271))),f334(f334(f269(f882(x95271),f882(x95271)),x95273),x95274)),f149(x95271,x95275)))
% 160.93/160.65 [9720]E(f334(f334(f153(x97201),f675(x97202,x97203,x97204,x97205,x97201)),f678(x97202,x97203,x97204,x97205,x97201)),x97205)+~P1(f334(f334(f336(f887(f882(x97201),f882(x97201))),f334(f334(f269(f882(x97201),f882(x97201)),x97205),f334(f334(f153(x97201),x97204),x97203))),f160(x97201,x97202)))
% 160.93/160.65 [9742]E(f334(f334(f153(x97421),f676(x97422,x97423,x97424,x97425,x97421)),f677(x97422,x97423,x97424,x97425,x97421)),x97423)+~P1(f334(f334(f336(f887(f882(x97421),f882(x97421))),f334(f334(f269(f882(x97421),f882(x97421)),f334(f334(f153(x97421),x97425),x97424)),x97423)),f160(x97421,x97422)))
% 160.93/160.65 [9905]~P1(f334(f334(f336(f887(f882(x99051),f882(x99051))),f334(f334(f269(f882(x99051),f882(x99051)),f334(f334(f153(x99051),x99055),x99052)),x99054)),f160(x99051,x99053)))+P1(f334(f334(f336(f887(f882(x99051),f882(x99051))),f334(f334(f269(f882(x99051),f882(x99051)),x99052),f677(x99053,x99054,x99052,x99055,x99051))),f160(x99051,x99053)))
% 160.93/160.65 [9975]~P1(f334(f334(f336(f887(f882(x99751),f882(x99751))),f334(f334(f269(f882(x99751),f882(x99751)),x99755),f334(f334(f153(x99751),x99754),x99753))),f160(x99751,x99752)))+P1(f334(f334(f336(f887(f882(x99751),f882(x99751))),f334(f334(f269(f882(x99751),f882(x99751)),f678(x99752,x99753,x99754,x99755,x99751)),x99753)),f160(x99751,x99752)))
% 160.93/160.65 [10140]P1(f334(f334(f336(f887(x101401,x101401)),f334(f334(f269(x101401,x101401),f334(x101402,f334(f334(f80(a881),x101403),x101404))),f334(x101402,x101403))),f310(x101401,x101405)))+~P1(f334(f334(f336(f887(x101401,x101401)),f334(f334(f269(x101401,x101401),f334(x101402,f334(a116,f628(x101404,x101403,x101405,x101402,x101401)))),f334(x101402,f628(x101404,x101403,x101405,x101402,x101401)))),f310(x101401,x101405)))
% 160.93/160.65 [5232]E(x52321,x52322)+~E(f334(f334(f153(x52323),x52324),x52321),f334(f334(f153(x52323),x52325),x52322))
% 160.93/160.65 [5233]E(x52331,x52332)+~E(f334(f334(f153(x52333),x52331),x52334),f334(f334(f153(x52333),x52332),x52335))
% 160.93/160.65 [5283]P1(f334(x52831,x52832))+~E(f334(f138(x52833,x52831),x52834),f334(f334(f153(x52833),x52832),x52835))
% 160.93/160.65 [5284]P1(f334(x52841,x52842))+~E(f334(f334(f153(x52843),x52842),x52844),f334(f138(x52843,x52841),x52845))
% 160.93/160.65 [5439]~E(f334(f334(f140(x54391),x54393),x54392),f334(f334(f153(x54391),x54394),x54395))+E(f334(f334(f167(x54391),x54392),x54393),x54394)
% 160.93/160.65 [5571]~P17(x55714,x55715,x55711)+E(f334(f334(x55711,x55712),f334(f334(x55711,x55712),x55713)),f334(f334(x55711,x55712),x55713))
% 160.93/160.65 [6104]~E(x61044,f2(a103))+E(f334(f334(f121(x61041,x61042,x61043),x61044),x61045),f334(f334(f269(f882(x61042),x61041),f117(x61042)),x61045))
% 160.93/160.65 [6179]~P108(x61792)+~E(f334(f334(f150(x61791,x61792,x61793),x61794),x61795),f117(x61791))
% 160.93/160.65 [6556]E(x65561,x65562)+~E(f334(f334(f136(x65563),x65564),f334(f334(f153(x65563),x65561),f117(x65563))),f334(f334(f136(x65563),x65565),f334(f334(f153(x65563),x65562),f117(x65563))))
% 160.93/160.65 [6557]E(x65571,x65572)+~E(f334(f334(f136(x65573),x65571),f334(f334(f153(x65573),x65574),f117(x65573))),f334(f334(f136(x65573),x65572),f334(f334(f153(x65573),x65575),f117(x65573))))
% 160.93/160.65 [6811]E(f334(f190(x68111,x68112,x68113,x68114),x68115),f210(x68112))+P1(f334(f334(f336(x68111),x68115),x68114))
% 160.93/160.65 [6874]E(f334(f334(f312(x68741),f334(x68742,x68743)),f334(f313(x68744,x68741,x68742),x68745)),f334(f313(x68744,x68741,x68742),x68745))+~P1(f334(f334(f336(x68744),x68743),x68745))
% 160.93/160.65 [6881]~P1(f334(x68814,f334(x68813,x68815)))+P1(f334(f334(f314(x68811,x68812,x68813),x68814),x68815))
% 160.93/160.65 [6884]~P1(f334(f334(x68843,x68845),x68844))+P1(f334(f334(f258(x68841,x68842,x68843),x68844),x68845))
% 160.93/160.65 [6977]~E(f334(f313(x69771,x69772,x69773),x69774),x69775)+E(f334(f313(f888(x69771,a876),f888(x69772,a876),f313(x69771,x69772,x69773)),f334(f311(x69771),x69774)),f334(f311(x69772),x69775))
% 160.93/160.65 [7007]E(f334(f190(x70071,x70072,x70073,x70074),x70075),f334(x70073,x70075))+~P1(f334(f334(f336(x70071),x70075),x70074))
% 160.93/160.65 [7308]P27(x73081,x73082,x73083,x73084)+~P27(x73081,x73082,x73083,f334(f334(f312(x73081),x73085),x73084))
% 160.93/160.65 [7378]P1(f334(x73781,x73782))+~P1(f334(f334(f95(x73783,x73784,x73781),x73785),x73782))
% 160.93/160.65 [7422]~P1(f334(f334(f336(x74224),x74223),x74225))+P1(f334(f334(f336(x74221),f334(x74222,x74223)),f334(f313(x74224,x74221,x74222),x74225)))
% 160.93/160.65 [7445]~P108(x74452)+E(f152(x74451,x74452,x74453,f334(f138(x74451,x74454),x74455)),f334(f138(x74451,x74454),f152(x74451,x74452,x74453,x74455)))
% 160.93/160.65 [7478]P1(f334(x74781,f334(x74782,x74783)))+~P1(f334(f334(f314(x74784,x74785,x74782),x74781),x74783))
% 160.93/160.65 [7481]P1(f334(f334(x74811,x74812),x74813))+~P1(f334(f334(f258(x74814,x74815,x74811),x74813),x74812))
% 160.93/160.65 [7482]P1(f334(f334(x74821,x74822),x74823))+~P1(f334(f334(f95(x74824,x74821,x74825),x74822),x74823))
% 160.93/160.65 [7546]~P1(f334(f334(f336(x75463),f334(x75464,x75462)),x75465))+P1(f334(f334(f336(x75461),x75462),f334(f314(x75461,x75463,x75464),x75465)))
% 160.93/160.65 [7940]~P1(f334(f334(f336(x79405),x79403),f334(f314(x79405,x79401,x79402),x79404)))+P1(f334(f334(f336(x79401),f334(x79402,x79403)),x79404))
% 160.93/160.65 [8163]~E(x81633,f334(f334(f334(f72(x81631,f885(x81632)),f334(f16(f885(x81632),x81631),f210(x81632))),x81634),f334(f241(x81632),x81635)))+E(f186(x81631,x81632,x81633),f334(f334(f312(x81631),x81634),f196(f888(x81631,a876))))
% 160.93/160.65 [8252]~P18(x82522,x82521,x82523)+E(f334(f144(x82521,x82522,f334(f7(x82522,x82521,x82521),x82523),x82524),f154(x82522,x82525)),f334(f334(f64(x82522,x82521,x82523),x82524),f334(f174(x82522),x82525)))
% 160.93/160.65 [8271]E(f334(x82711,f360(x82712,x82711,x82713,x82714)),x82714)+~P1(f334(f334(f336(x82715),x82714),f334(f313(x82713,x82715,x82711),x82712)))
% 160.93/160.65 [8272]E(f334(x82721,f550(x82722,x82721,x82723,x82724)),x82724)+~P1(f334(f334(f336(x82725),x82724),f334(f313(x82723,x82725,x82721),x82722)))
% 160.93/160.65 [8579]~E(x85792,f334(f334(f153(x85791),x85794),x85795))+P1(f334(f334(f336(f887(f882(x85791),f882(x85791))),f334(f334(f269(f882(x85791),f882(x85791)),f117(x85791)),x85792)),f149(x85791,x85793)))
% 160.93/160.65 [8632]~P36(x86321,x86323,x86325,x86322,x86324)+E(f334(f197(f882(x86321)),x86322),f334(f197(f882(x86323)),x86324))
% 160.93/160.65 [8646]P1(f334(f334(f248(f888(x86461,a876)),f334(f334(f42(x86462,f888(x86461,a876)),x86463),x86464)),f334(x86464,x86465)))+~P1(f334(f334(f336(x86462),x86465),x86463))
% 160.93/160.65 [8694]~P54(x86941,x86942,x86943,x86945,x86944)+E(f334(f313(x86941,x86942,x86943),f257(f888(x86941,a876))),x86944)
% 160.93/160.65 [8898]E(f334(f334(f334(f72(x88981,f885(x88982)),f190(x88981,x88982,x88983,x88984)),x88985),f210(x88982)),f190(x88981,x88982,x88983,x88984))+P1(f334(f334(f336(x88981),x88985),x88984))
% 160.93/160.65 [8903]E(f334(f138(x89031,x89032),f789(x89033,x89034,x89035,x89032,x89031)),x89033)+~E(f334(f138(x89031,x89032),x89035),f334(f334(f153(x89031),x89034),x89033))
% 160.93/160.65 [8904]E(f334(f138(x89041,x89042),f790(x89043,x89042,x89044,x89045,x89041)),x89044)+~E(f334(f334(f153(x89041),x89045),x89044),f334(f138(x89041,x89042),x89043))
% 160.93/160.65 [8905]E(f334(x89051,f716(x89052,x89053,x89051,x89054,x89055)),x89052)+~E(f334(f334(f211(x89055,x89054),x89051),x89053),f334(f241(x89054),x89052))
% 160.93/160.65 [8909]E(f334(f241(x89091),f716(x89092,x89093,x89094,x89095,x89091)),x89093)+~E(f334(f334(f211(x89091,x89095),x89094),x89093),f334(f241(x89095),x89092))
% 160.93/160.65 [9007]E(f334(f197(f882(x90071)),x90072),x90073)+~P1(f334(f334(f336(f887(f882(x90071),f882(x90071))),f334(f334(f269(f882(x90071),f882(x90071)),x90074),x90072)),f334(f145(x90071,x90075),x90073)))
% 160.93/160.65 [9008]E(f334(f197(f882(x90081)),x90082),x90083)+~P1(f334(f334(f336(f887(f882(x90081),f882(x90081))),f334(f334(f269(f882(x90081),f882(x90081)),x90082),x90084)),f334(f145(x90081,x90085),x90083)))
% 160.93/160.65 [9076]P1(f334(f334(f336(x90761),f360(x90762,x90763,x90761,x90764)),x90762))+~P1(f334(f334(f336(x90765),x90764),f334(f313(x90761,x90765,x90763),x90762)))
% 160.93/160.65 [9077]P1(f334(f334(f336(x90771),f550(x90772,x90773,x90771,x90774)),x90772))+~P1(f334(f334(f336(x90775),x90774),f334(f313(x90771,x90775,x90773),x90772)))
% 160.93/160.65 [9240]E(f334(f313(x92401,x92402,x92403),f352(x92404,x92403,x92401,x92405,x92402)),x92405)+~P1(f334(f334(f248(f888(x92402,a876)),x92405),f334(f313(x92401,x92402,x92403),x92404)))
% 160.93/160.65 [9493]E(f334(x94931,f776(x94932,x94931,x94933,x94934,x94935)),f334(f241(x94935),x94934))+~P1(f334(f334(f336(x94935),x94934),f188(x94933,x94935,f190(x94933,x94935,x94931,x94932))))
% 160.93/160.65 [9543]P1(f334(f334(f336(f887(f882(x95431),f882(x95431))),f334(f334(f269(f882(x95431),f882(x95431)),f334(f334(f153(x95431),x95432),x95433)),f334(f334(f153(x95431),x95432),x95434))),f310(f882(x95431),f159(x95431,x95435))))+~P1(f334(f334(f336(f887(f882(x95431),f882(x95431))),f334(f334(f269(f882(x95431),f882(x95431)),x95433),x95434)),f310(f882(x95431),f159(x95431,x95435))))
% 160.93/160.65 [9574]~E(f334(x95743,f718(x95745,x95744,x95743,x95742,x95741)),f334(x95745,f718(x95745,x95744,x95743,x95742,x95741)))+E(f334(f334(f156(x95741,x95742),x95743),x95744),f334(f334(f156(x95741,x95742),x95745),x95744))
% 160.93/160.65 [9652]~E(f334(f138(x96521,x96525),x96524),f334(f334(f153(x96521),x96523),x96522))+E(f334(f334(f136(x96521),f793(x96522,x96523,x96524,x96525,x96521)),f334(f334(f153(x96521),x96523),f789(x96522,x96523,x96524,x96525,x96521))),x96524)
% 160.93/160.65 [9653]~E(f334(f334(f153(x96531),x96535),x96534),f334(f138(x96531,x96533),x96532))+E(f334(f334(f136(x96531),f791(x96532,x96533,x96534,x96535,x96531)),f334(f334(f153(x96531),x96535),f790(x96532,x96533,x96534,x96535,x96531))),x96532)
% 160.93/160.65 [9657]E(f334(f334(f156(x96571,x96572),x96573),x96574),f334(f334(f156(x96571,x96572),x96575),x96574))+P1(f334(f334(f336(x96571),f718(x96573,x96574,x96575,x96572,x96571)),f334(f174(x96571),x96574)))
% 160.93/160.65 [9687]~P1(f334(f334(f336(x96875),x96874),f334(f288(x96871,x96875,x96873),x96872)))+P1(f334(f334(f336(x96871),f530(x96872,x96873,x96871,x96874,x96875)),x96872))
% 160.93/160.65 [9688]~P1(f334(f334(f336(x96885),x96884),f334(f288(x96881,x96885,x96883),x96882)))+P1(f334(f334(f336(x96881),f536(x96882,x96883,x96881,x96884,x96885)),x96882))
% 160.93/160.65 [9714]~P1(f334(f334(f248(f888(x97145,a876)),x97144),f334(f313(x97141,x97145,x97143),x97142)))+P1(f334(f334(f248(f888(x97141,a876)),f352(x97142,x97143,x97141,x97144,x97145)),x97142))
% 160.93/160.65 [9765]~P1(f334(f334(f336(x97655),x97654),f188(x97651,x97655,f190(x97651,x97655,x97653,x97652))))+P1(f334(f334(f336(x97651),f776(x97652,x97653,x97651,x97654,x97655)),x97652))
% 160.93/160.65 [10162]E(x101621,f2(a103))+E(f334(f243(f887(f882(x101622),x101623),f887(x101622,x101623),f334(f334(f269(f882(x101622),x101623),f117(x101622)),x101624),f334(f273(x101622,x101623,f887(f882(x101622),x101623)),f334(f334(f7(x101622,f888(x101623,f887(f882(x101622),x101623)),f888(x101623,f887(f882(x101622),x101623))),f334(f334(f8(f888(f887(f882(x101622),x101623),f887(f882(x101622),x101623)),f888(f888(x101623,f887(f882(x101622),x101623)),f888(x101623,f887(f882(x101622),x101623))),x101622),f8(f887(f882(x101622),x101623),f887(f882(x101622),x101623),x101623)),f334(f334(f8(f888(f882(x101622),f888(x101623,f887(f882(x101622),x101623))),f888(f887(f882(x101622),x101623),f887(f882(x101622),x101623)),x101622),f273(f882(x101622),x101623,f887(f882(x101622),x101623))),f334(f334(f8(f888(f882(x101622),f882(x101622)),f888(f882(x101622),f888(x101623,f887(f882(x101622),x101623))),x101622),f334(f8(f882(x101622),f888(x101623,f887(f882(x101622),x101623)),f882(x101622)),f269(f882(x101622),x101623))),f153(x101622))))),f334(f121(x101623,x101622,x101625),f334(f334(f22(a103),x101621),f78(a103)))))),f334(x101625,x101624)),f334(f334(f121(x101623,x101622,x101625),x101621),x101624))
% 160.93/160.65 [5452]~E(f334(x54523,x54524),x54525)+E(f334(f334(f334(f72(x54521,x54522),x54523),x54524),x54525),x54523)
% 160.93/160.65 [5893]E(f334(x58931,x58932),x58933)+~E(f334(f334(f334(f72(x58934,x58935),x58931),x58932),x58933),x58931)
% 160.93/160.65 [5985]E(x59851,x59852)+~E(f334(f272(x59853,x59854),f334(f334(f269(x59853,x59854),x59855),x59851)),x59852)
% 160.93/160.65 [5986]E(x59861,x59862)+~E(f334(f268(x59863,x59864),f334(f334(f269(x59863,x59864),x59861),x59865)),x59862)
% 160.93/160.65 [6254]~E(x62543,f334(f334(f136(x62541),x62544),f334(f334(f153(x62541),x62542),x62545)))+P1(f334(f334(f336(x62541),x62542),f334(f174(x62541),x62543)))
% 160.93/160.65 [6642]E(f334(f313(x66421,x66422,f334(f16(x66422,x66421),x66423)),x66424),f334(f334(f312(x66422),x66423),f196(f888(x66422,a876))))+~P1(f334(f334(f336(x66421),x66425),x66424))
% 160.93/160.65 [6713]E(f334(f334(f114(f888(x67131,a876)),f334(f174(x67131),x67132)),f334(f174(x67131),x67133)),f334(f174(x67131),x67134))+~E(f169(x67131,x67135,x67134),f334(f334(f269(f882(x67131),f882(x67131)),x67132),x67133))
% 160.93/160.65 [6815]~P108(x68152)+E(f334(f197(f882(x68151)),f334(f334(f150(x68151,x68152,x68153),x68154),x68155)),f334(a116,f334(f197(f882(x68151)),x68155)))
% 160.93/160.65 [6827]~P108(x68272)+E(f334(f174(x68271),f334(f334(f150(x68271,x68272,x68273),x68274),x68275)),f334(f334(f312(x68271),x68274),f334(f174(x68271),x68275)))
% 160.93/160.65 [7098]~P118(x70981)+E(f334(f334(f80(x70981),f334(f334(f80(x70981),x70982),x70983)),f334(f334(f80(x70981),x70984),x70985)),f334(f334(f80(x70981),f334(f334(f80(x70981),x70982),x70984)),f334(f334(f80(x70981),x70983),x70985)))
% 160.93/160.65 [7099]~P118(x70991)+E(f334(f334(f81(x70991),f334(f334(f81(x70991),x70992),x70993)),f334(f334(f81(x70991),x70994),x70995)),f334(f334(f81(x70991),f334(f334(f81(x70991),x70992),x70994)),f334(f334(f81(x70991),x70993),x70995)))
% 160.93/160.65 [7100]~P61(x71001)+E(f334(f334(f292(x71001),f334(f334(f81(x71001),x71002),x71003)),f334(f334(f81(x71001),x71004),x71005)),f334(f334(f81(x71001),f334(f334(f292(x71001),x71002),x71004)),f334(f334(f292(x71001),x71003),x71005)))
% 160.93/160.65 [7114]~P108(x71141)+E(f305(x71141,f334(f334(f247(x71141),x71142),x71143),f334(f334(f246(x71141),x71144),x71145)),f334(f334(f105(f888(x71141,a876)),f305(x71141,x71142,x71144)),f305(x71141,x71143,x71145)))
% 160.93/160.65 [7115]~P108(x71151)+E(f308(x71151,f334(f334(f247(x71151),x71152),x71153),f334(f334(f246(x71151),x71154),x71155)),f334(f334(f105(f888(x71151,a876)),f308(x71151,x71152,x71154)),f308(x71151,x71153,x71155)))
% 160.93/160.65 [7116]~P108(x71161)+E(f307(x71161,f334(f334(f247(x71161),x71162),x71163),f334(f334(f246(x71161),x71164),x71165)),f334(f334(f105(f888(x71161,a876)),f307(x71161,x71162,x71164)),f307(x71161,x71163,x71165)))
% 160.93/160.65 [7117]~P108(x71171)+E(f334(f334(f105(f888(x71171,a876)),f334(f304(x71171,x71172),x71173)),f334(f304(x71171,x71174),x71175)),f334(f304(x71171,f334(f334(f247(x71171),x71172),x71174)),f334(f334(f246(x71171),x71173),x71175)))
% 160.93/160.65 [7234]~P1(f334(x72341,f510(x72343,x72342,x72341)))+P1(f334(x72341,f334(f334(f269(x72342,x72343),x72344),x72345)))
% 160.93/160.65 [7321]~E(f334(x73213,x73214),f210(x73212))+E(f188(x73211,x73212,f334(f334(f334(f72(x73211,f885(x73212)),x73213),x73214),f334(f241(x73212),x73215))),f334(f334(f312(x73212),x73215),f188(x73211,x73212,x73213)))
% 160.93/160.65 [7342]~E(x73422,f334(x73424,x73425))+P1(f334(f334(f336(x73421),x73422),f334(f313(x73423,x73421,x73424),f257(f888(x73423,a876)))))
% 160.93/160.65 [7400]~E(f334(x74003,x74004),f210(x74002))+E(f334(f334(f22(f888(x74001,a876)),f186(x74001,x74002,x74003)),f334(f334(f312(x74001),x74004),x74005)),f334(f334(f22(f888(x74001,a876)),f186(x74001,x74002,x74003)),x74005))
% 160.93/160.65 [7419]~P17(x74193,x74192,x74194)+P17(x74191,x74192,f334(f334(f8(x74193,f888(x74192,x74192),x74191),x74194),x74195))
% 160.93/160.65 [7420]~P18(x74203,x74202,x74204)+P18(x74201,x74202,f334(f334(f8(x74203,f888(x74202,x74202),x74201),x74204),x74205))
% 160.93/160.65 [7562]~P27(x75621,x75622,x75623,x75624)+P27(x75621,x75622,x75623,f334(f334(f22(f888(x75621,a876)),x75624),x75625))
% 160.93/160.65 [7719]~P1(f334(f334(x77193,x77194),x77195))+P1(f334(f334(f273(x77191,x77192,a876),x77193),f334(f334(f269(x77191,x77192),x77194),x77195)))
% 160.93/160.65 [7829]~P1(f334(x78292,x78294))+~E(f334(f334(f140(x78291),f334(f197(f882(x78291)),f179(x78291,x78292,x78293))),x78293),f334(f334(f153(x78291),x78294),x78295))
% 160.93/160.65 [7849]P27(x78491,x78492,x78493,x78494)+~P27(x78491,x78492,x78493,f334(f334(f114(f888(x78491,a876)),x78495),x78494))
% 160.93/160.65 [7850]P27(x78501,x78502,x78503,x78504)+~P27(x78501,x78502,x78503,f334(f334(f114(f888(x78501,a876)),x78504),x78505))
% 160.93/160.65 [7897]~P108(x78972)+E(f334(f334(f150(x78971,x78972,x78973),x78974),f152(x78971,x78972,x78973,x78975)),f152(x78971,x78972,x78973,f334(f334(f153(x78971),x78974),x78975)))
% 160.93/160.65 [8054]~P29(x80541,f334(a116,x80542),f334(f334(f334(f92(x80541),x80543),f334(a26,x80544)),x80545))+P29(x80541,x80542,f334(f334(f334(f92(x80541),x80543),f334(f245(a878),f334(a28,x80544))),x80545))
% 160.93/160.65 [8193]P29(x81931,f334(a116,x81932),f334(f334(f334(f92(x81931),x81933),f334(a26,x81934)),x81935))+~P29(x81931,x81932,f334(f334(f334(f92(x81931),x81933),f334(f245(a878),f334(a28,x81934))),x81935))
% 160.93/160.65 [8227]~P17(x82272,x82271,x82273)+E(f334(f144(x82271,x82272,f334(f7(x82272,x82271,x82271),x82273),x82274),x82275),f334(f334(f64(x82272,x82271,x82273),x82274),f334(f174(x82272),x82275)))
% 160.93/160.65 [8257]~E(f334(f334(f140(x82571),f334(f197(f882(x82571)),f179(x82571,x82572,x82573))),x82573),f334(f334(f153(x82571),x82574),x82575))+E(f334(f334(f136(x82571),f179(x82571,x82572,x82573)),f334(f334(f153(x82571),x82574),x82575)),x82573)
% 160.93/160.65 [8282]P1(f334(f334(x82821,x82822),x82823))+~P1(f334(f334(f273(x82824,x82825,a876),x82821),f334(f334(f269(x82824,x82825),x82822),x82823)))
% 160.93/160.65 [8344]~E(f334(f334(f180(x83441,x83442),x83445),x83443),f334(f241(x83442),x83444))+P1(f334(f334(f336(f887(x83441,x83442)),f334(f334(f269(x83441,x83442),x83443),x83444)),f334(f174(f887(x83441,x83442)),x83445)))
% 160.93/160.65 [8749]P1(f334(f334(f248(f888(x87491,a876)),f334(f313(x87492,x87491,x87493),x87494)),f334(f313(x87492,x87491,x87493),x87495)))+~P1(f334(f334(f248(f888(x87492,a876)),x87494),x87495))
% 160.93/160.65 [8750]P1(f334(f334(f248(f888(x87501,a876)),f334(f314(x87501,x87502,x87503),x87504)),f334(f314(x87501,x87502,x87503),x87505)))+~P1(f334(f334(f248(f888(x87502,a876)),x87504),x87505))
% 160.93/160.65 [8825]E(x88251,f2(a103))+E(f334(f334(f275(x88252,x88253,x88252,f887(x88253,x88252)),f334(x88254,x88255)),f283(x88253,x88252,f334(f334(f22(a103),x88251),f78(a103)),x88254)),f334(f283(x88253,x88252,x88251,x88254),x88255))
% 160.93/160.65 [9149]P29(x91491,x91492,f334(f334(f334(f92(x91491),x91493),x91494),x91495))+P1(f334(f334(x91493,f507(x91495,x91494,x91493,x91492)),f519(x91495,x91494,x91493,x91492)))
% 160.93/160.65 [9349]E(f334(f241(x93491),f720(x93492,x93493,x93494,x93491,x93495)),f334(f334(f180(x93495,x93491),x93492),x93494))+~P1(f334(f334(f336(f887(x93495,x93491)),f334(f334(f269(x93495,x93491),x93494),x93493)),f334(f174(f887(x93495,x93491)),x93492)))
% 160.93/160.65 [9393]P29(x93931,x93932,f334(f334(f334(f92(x93931),x93933),x93934),x93935))+~P1(f334(f334(x93935,f507(x93935,x93934,x93933,x93932)),f529(x93935,x93934,x93933,x93932)))
% 160.93/160.65 [9453]P29(x94531,x94532,f334(f334(f334(f92(x94531),x94533),x94534),x94535))+P1(f334(f334(f334(f334(a204,x94534),f519(x94535,x94534,x94533,x94532)),x94532),f529(x94535,x94534,x94533,x94532)))
% 160.93/160.65 [9456]~P26(x94561,x94562,f334(f334(f312(f880(x94561)),f334(f334(f334(f92(x94561),x94563),f334(f245(a878),f334(a28,x94564))),x94565)),f196(f888(f880(x94561),a876))))+P26(x94561,x94562,f334(f334(f312(f880(x94561)),f334(f334(f334(f92(x94561),x94563),f334(a26,x94564)),x94565)),f196(f888(f880(x94561),a876))))
% 160.93/160.65 [9484]~P1(f334(f61(x94843),f334(f313(x94842,x94843,x94845),f257(f888(x94842,a876)))))+P1(f334(f61(x94841),f334(f313(x94842,x94841,f334(f334(f8(x94843,x94841,x94842),x94844),x94845)),f257(f888(x94842,a876)))))
% 160.93/160.65 [9508]P1(f334(f334(f248(f888(f888(x95081,a876),a876)),f334(f313(f888(x95082,a876),f888(x95081,a876),f313(x95082,x95081,x95083)),f334(f311(x95082),x95084))),f334(f311(x95081),x95085)))+~P1(f334(f334(f248(f888(x95081,a876)),f334(f313(x95082,x95081,x95083),x95084)),x95085))
% 160.93/160.65 [9522]~P1(f334(f61(f885(x95221)),f334(f313(x95222,f885(x95221),x95223),f257(f888(x95222,a876)))))+P1(f334(f61(f885(x95221)),f334(f313(x95222,f885(x95221),f334(f334(f334(f72(x95222,f885(x95221)),x95223),x95224),f334(f241(x95221),x95225))),f257(f888(x95222,a876)))))
% 160.93/160.65 [9583]E(x95831,x95832)+~P1(f334(f66(x95833,x95834,x95835,x95831,f196(f888(x95833,a876))),x95832))
% 160.93/160.65 [9598]E(f334(f334(f269(x95981,x95982),f580(x95983,x95984,x95985,x95982,x95981)),f582(x95983,x95984,x95985,x95982,x95981)),x95985)+~P1(f334(f334(f336(f887(x95981,x95982)),x95985),f334(f334(f271(x95981,x95982),x95984),x95983)))
% 160.93/160.65 [9693]P1(f334(f334(f336(x96931),f580(x96932,x96933,x96934,x96935,x96931)),x96933))+~P1(f334(f334(f336(f887(x96931,x96935)),x96934),f334(f334(f271(x96931,x96935),x96933),x96932)))
% 160.93/160.65 [9801]P26(x98015,x98014,f334(f334(f312(f880(x98015)),f334(f334(f334(f92(x98015),x98011),x98013),x98012)),f196(f888(f880(x98015),a876))))+P1(f334(f334(x98011,f369(x98012,x98013,x98014,x98015,x98011)),f381(x98012,x98013,x98014,x98015,x98011)))
% 160.93/160.65 [9852]P1(f334(f334(f336(x98521),f582(x98522,x98523,x98524,x98521,x98525)),f334(x98522,f580(x98522,x98523,x98524,x98521,x98525))))+~P1(f334(f334(f336(f887(x98525,x98521)),x98524),f334(f334(f271(x98525,x98521),x98523),x98522)))
% 160.93/160.65 [9881]P1(f334(f334(f336(f887(x98811,x98811)),f334(f334(f269(x98811,x98811),x98812),f649(x98813,x98814,x98815,x98812,x98811))),x98813))+~P1(f334(f334(f336(f887(x98811,x98811)),f334(f334(f269(x98811,x98811),x98812),x98815)),f334(f334(f191(f887(x98811,x98811),a876),f334(a116,x98814)),x98813)))
% 160.93/160.65 [9882]P1(f334(f334(f336(f887(x98821,x98821)),f334(f334(f269(x98821,x98821),x98822),f650(x98823,x98824,x98825,x98822,x98821))),x98823))+~P1(f334(f334(f336(f887(x98821,x98821)),f334(f334(f269(x98821,x98821),x98822),x98825)),f334(f334(f191(f887(x98821,x98821),a876),f334(a116,x98824)),x98823)))
% 160.93/160.65 [9900]~P1(f334(f334(f336(f887(f882(x99001),f882(x99001))),f334(f334(f269(f882(x99001),f882(x99001)),f334(f334(f153(x99001),x99002),x99005)),x99004)),f160(x99001,x99003)))+P1(f334(f334(f336(f887(x99001,x99001)),f334(f334(f269(x99001,x99001),x99002),f676(x99003,x99004,x99005,x99002,x99001))),x99003))
% 160.93/160.65 [9902]~P26(x99021,x99022,f334(f334(f312(f880(x99021)),f334(f334(f334(f92(x99021),f95(x99021,x99023,x99024)),x99025),x99023)),f196(f888(f880(x99021),a876))))+P26(x99021,x99022,f334(f334(f312(f880(x99021)),f334(f334(f334(f92(x99021),x99023),f32(x99024,x99025)),f95(x99021,x99023,f334(f73(a876,a876,a877,a329),x99024)))),f196(f888(f880(x99021),a876))))
% 160.93/160.65 [9903]~P30(x99031,x99032,f334(f334(f312(f880(x99031)),f334(f334(f334(f92(x99031),f95(x99031,x99033,x99034)),x99035),x99033)),f196(f888(f880(x99031),a876))))+P30(x99031,x99032,f334(f334(f312(f880(x99031)),f334(f334(f334(f92(x99031),x99033),f32(x99034,x99035)),f95(x99031,x99033,f334(f73(a876,a876,a877,a329),x99034)))),f196(f888(f880(x99031),a876))))
% 160.93/160.65 [10163]P26(x101631,x101632,f334(f334(f312(f880(x101631)),f334(f334(f334(f92(x101631),x101633),x101634),x101635)),f196(f888(f880(x101631),a876))))+~P26(x101631,x101632,f334(f334(f312(f880(x101631)),f334(f334(f334(f92(x101631),f334(f16(f888(a877,a876),x101631),f334(f334(f7(a877,a877,a876),a331),f381(x101635,x101634,x101632,x101631,x101633)))),x101634),f334(f16(f888(a877,a876),x101631),f334(x101635,f369(x101635,x101634,x101632,x101631,x101633))))),f196(f888(f880(x101631),a876))))
% 160.93/160.65 [6328]P1(f334(x63282,x63284))+E(f179(x63281,x63282,f334(f334(f136(x63281),x63283),f334(f334(f153(x63281),x63284),x63285))),f179(x63281,x63282,x63283))
% 160.93/160.65 [6375]~P2(x63752)+E(f334(f334(f334(f114(f888(x63751,x63752)),x63753),x63754),x63755),f334(f334(f114(x63752),f334(x63753,x63755)),f334(x63754,x63755)))
% 160.93/160.65 [6377]~P65(x63772)+E(f334(f334(f334(f22(f888(x63771,x63772)),x63773),x63774),x63775),f334(f334(f22(x63772),f334(x63773,x63775)),f334(x63774,x63775)))
% 160.93/160.65 [6379]~P2(x63792)+E(f334(f334(f334(f105(f888(x63791,x63792)),x63793),x63794),x63795),f334(f334(f105(x63792),f334(x63793,x63795)),f334(x63794,x63795)))
% 160.93/160.65 [6397]E(x63971,x63972)+E(f334(f334(f167(x63973),f334(f334(f161(x63973,x63974),x63971),x63975)),x63972),f334(f334(f167(x63973),x63974),x63972))
% 160.93/160.65 [6661]~E(x66614,f196(f888(x66613,a876)))+E(f334(f334(f114(f888(x66611,a876)),x66612),f334(f334(f41(x66613,f888(x66611,a876)),x66614),x66615)),x66612)
% 160.93/160.65 [6662]~E(x66624,f196(f888(x66623,a876)))+E(f334(f334(f22(f888(x66621,a876)),x66622),f334(f334(f41(x66623,f888(x66621,a876)),x66624),x66625)),x66622)
% 160.93/160.65 [6663]~E(x66634,f196(f888(x66633,a876)))+E(f334(f334(f105(f888(x66631,a876)),x66632),f334(f334(f42(x66633,f888(x66631,a876)),x66634),x66635)),x66632)
% 160.93/160.65 [6677]~E(x66774,f196(f888(x66773,a876)))+E(f334(f334(f312(x66771),x66772),f334(f334(f41(x66773,f888(x66771,a876)),x66774),x66775)),f334(f334(f312(x66771),x66772),f196(f888(x66771,a876))))
% 160.93/160.65 [7467]E(f334(f334(f167(x74671),f334(f334(f156(x74672,x74671),x74673),x74674)),x74675),f334(x74673,f334(f334(f167(x74672),x74674),x74675)))+~P1(f334(f334(f249(a881),x74675),f334(f197(f882(x74672)),x74674)))
% 160.93/160.65 [7534]E(f334(f334(f114(f888(x75341,a876)),f334(x75342,x75343)),f334(f334(f41(x75344,f888(x75341,a876)),x75345),x75342)),f334(f334(f41(x75344,f888(x75341,a876)),x75345),x75342))+~P1(f334(f334(f336(x75344),x75343),x75345))
% 160.93/160.65 [7535]E(f334(f334(f105(f888(x75351,a876)),f334(x75352,x75353)),f334(f334(f42(x75354,f888(x75351,a876)),x75355),x75352)),f334(f334(f42(x75354,f888(x75351,a876)),x75355),x75352))+~P1(f334(f334(f336(x75354),x75353),x75355))
% 160.93/160.65 [8134]~E(x81343,f196(f888(x81341,a876)))+E(f334(f334(f41(x81341,f888(x81342,a876)),x81343),f334(f334(f8(f888(x81342,a876),f888(x81342,a876),x81341),f334(f312(x81342),x81344)),x81345)),f196(f888(x81342,a876)))
% 160.93/160.65 [8139]~P1(f334(f334(f336(x81394),x81393),x81395))+P1(f334(f334(f248(f888(x81391,a876)),f334(x81392,x81393)),f334(f334(f41(x81394,f888(x81391,a876)),x81395),x81392)))
% 160.93/160.65 [8281]~E(f334(x82814,x82812),x82815)+P1(f334(f334(f336(x82811),x82812),f334(f314(x82811,x82813,x82814),f334(f334(f312(x82813),x82815),f196(f888(x82813,a876))))))
% 160.93/160.65 [8326]~P52(x83261,x83262,f334(f289(x83262,x83261),x83263))+E(f334(f334(f105(f888(x83261,a876)),f334(f288(x83262,x83261,x83263),x83264)),f334(f288(x83262,x83261,x83263),x83265)),f334(f288(x83262,x83261,x83263),f334(f334(f105(f888(x83262,a876)),x83264),x83265)))
% 160.93/160.65 [8402]E(x84021,f2(a103))+E(f334(f122(x84022,x84023,f334(x84024,f334(f334(f22(a103),x84021),f78(a103)))),f334(f334(f7(x84022,a103,f883(x84023)),x84025),x84021)),f334(f209(x84022,x84023,x84024,x84025),x84021))
% 160.93/160.65 [8440]E(x84401,f196(f888(x84402,a876)))+E(f334(f334(f41(x84402,f888(x84403,a876)),x84401),f334(f334(f8(f888(x84403,a876),f888(x84403,a876),x84402),f334(f312(x84403),x84404)),x84405)),f334(f334(f312(x84403),x84404),f334(f334(f41(x84402,f888(x84403,a876)),x84401),x84405)))
% 160.93/160.65 [8490]~P27(x84902,x84901,x84903,f257(f888(x84902,a876)))+E(f334(f334(f22(f888(x84901,a876)),f334(f313(x84902,x84901,x84903),x84904)),f334(f313(x84902,x84901,x84903),x84905)),f334(f313(x84902,x84901,x84903),f334(f334(f22(f888(x84902,a876)),x84904),x84905)))
% 160.93/160.65 [8491]~P27(x84912,x84911,x84913,f257(f888(x84912,a876)))+E(f334(f334(f105(f888(x84911,a876)),f334(f313(x84912,x84911,x84913),x84914)),f334(f313(x84912,x84911,x84913),x84915)),f334(f313(x84912,x84911,x84913),f334(f334(f105(f888(x84912,a876)),x84914),x84915)))
% 160.93/160.65 [8565]~P1(f334(f334(f67(x85651,x85652,x85655),x85653),x85654))+P1(f334(f334(f336(f887(x85651,x85652)),f334(f334(f269(x85651,x85652),x85653),x85654)),x85655))
% 160.93/160.65 [8597]P1(f334(f334(f336(x85971),x85972),f334(f265(x85973,x85971),x85974)))+~P1(f334(f334(f336(f887(x85973,x85971)),f334(f334(f269(x85973,x85971),x85975),x85972)),x85974))
% 160.93/160.65 [8599]P1(f334(f334(f336(x85991),x85992),f334(f267(x85991,x85993),x85994)))+~P1(f334(f334(f336(f887(x85991,x85993)),f334(f334(f269(x85991,x85993),x85992),x85995)),x85994))
% 160.93/160.65 [8736]P1(f334(f334(f67(x87361,x87362,x87363),x87364),x87365))+~P1(f334(f334(f336(f887(x87361,x87362)),f334(f334(f269(x87361,x87362),x87364),x87365)),x87363))
% 160.93/160.65 [8771]E(f334(x87711,x87712),x87713)+~P1(f334(f334(f336(x87714),x87712),f334(f314(x87714,x87715,x87711),f334(f334(f312(x87715),x87713),f196(f888(x87715,a876))))))
% 160.93/160.65 [8980]E(x89801,f2(a103))+E(f125(x89802,f124(x89803,f883(f885(x89802)),f334(f334(f7(x89803,a103,f883(f885(x89802))),x89804),x89801),f334(x89805,f334(f334(f22(a103),x89801),f78(a103))))),f334(f206(x89803,x89802,x89805,x89804),x89801))
% 160.93/160.65 [9004]P1(f334(f334(f336(f887(x90041,x90042)),f334(f334(f269(x90041,x90042),x90043),x90044)),f334(f289(x90042,x90041),x90045)))+~P1(f334(f334(f336(f887(x90042,x90041)),f334(f334(f269(x90042,x90041),x90044),x90043)),x90045))
% 160.93/160.65 [9022]~P1(f334(f334(x90221,x90225),x90224))+P1(f334(f334(x90221,f334(f272(x90222,x90223),f334(f334(f269(x90222,x90223),x90224),x90225))),f334(f268(x90222,x90223),f334(f334(f269(x90222,x90223),x90224),x90225))))
% 160.93/160.65 [9052]~P1(f334(f334(f336(f887(x90522,x90521)),f334(f334(f269(x90522,x90521),x90524),x90523)),f334(f289(x90521,x90522),x90525)))+P1(f334(f334(f336(f887(x90521,x90522)),f334(f334(f269(x90521,x90522),x90523),x90524)),x90525))
% 160.93/160.65 [9085]~P1(f334(f334(f336(f887(x90853,x90851)),f334(f334(f269(x90853,x90851),x90855),x90852)),x90854))+P1(f334(f334(f336(x90851),x90852),f334(f288(x90853,x90851,x90854),f334(f334(f312(x90853),x90855),f196(f888(x90853,a876))))))
% 160.93/160.65 [9131]P1(f334(f334(f336(f887(x91311,x91312)),f334(f334(f269(x91311,x91312),x91313),x91314)),x91315))+~P1(f334(f334(f336(x91312),x91314),f334(f288(x91311,x91312,x91315),f334(f334(f312(x91311),x91313),f196(f888(x91311,a876))))))
% 160.93/160.65 [9152]E(f334(f334(f334(f72(x91521,f885(x91522)),f190(x91521,x91522,x91523,x91524)),x91525),f210(x91522)),f190(x91521,x91522,x91523,f334(f334(f22(f888(x91521,a876)),x91524),f334(f334(f312(x91521),x91525),f196(f888(x91521,a876))))))+~P1(f334(f334(f336(x91521),x91525),x91524))
% 160.93/160.65 [9220]~P68(x92201)+E(f334(f334(f6(a881,x92201),x92202),f305(a881,f334(f334(f80(a881),x92203),x92204),f334(f334(f80(a881),x92205),x92204))),f334(f334(f6(a881,x92201),f334(f334(f8(a881,x92201,a881),x92202),f334(f334(f7(a881,a881,a881),f80(a881)),x92204))),f305(a881,x92203,x92205)))
% 160.93/160.65 [9244]~P68(x92441)+E(f334(f334(f6(a881,x92441),x92442),f334(f304(a881,f334(f334(f80(a881),x92443),x92444)),f334(f334(f80(a881),x92445),x92444))),f334(f334(f6(a881,x92441),f334(f334(f8(a881,x92441,a881),x92442),f334(f334(f7(a881,a881,a881),f80(a881)),x92444))),f334(f304(a881,x92443),x92445)))
% 160.93/160.65 [9297]~P27(x92971,x92972,x92973,f257(f888(x92971,a876)))+E(f334(f334(f156(x92971,x92972),x92973),f334(f138(x92971,f334(f334(f8(a876,a876,x92971),a329),f334(a331,x92974))),x92975)),f334(f138(x92972,f334(f334(f8(a876,a876,x92972),a329),f334(a331,f334(x92973,x92974)))),f334(f334(f156(x92971,x92972),x92973),x92975)))
% 160.93/160.65 [9315]~P27(x93151,x93152,x93153,f334(f334(f312(x93151),x93154),f334(f174(x93151),x93155)))+E(f334(f334(f156(x93151,x93152),x93153),f334(f138(x93151,f334(f334(f8(a876,a876,x93151),a329),f334(a331,x93154))),x93155)),f334(f138(x93152,f334(f334(f8(a876,a876,x93152),a329),f334(a331,f334(x93153,x93154)))),f334(f334(f156(x93151,x93152),x93153),x93155)))
% 160.93/160.65 [9471]P1(f334(f334(f336(f887(f882(x94711),f882(x94711))),f334(f334(f269(f882(x94711),f882(x94711)),f334(f334(f153(x94711),x94712),x94713)),f334(f334(f153(x94711),x94714),x94713))),f159(x94711,x94715)))+~P1(f334(f334(f336(f887(x94711,x94711)),f334(f334(f269(x94711,x94711),x94712),x94714)),x94715))
% 160.93/160.65 [9509]P1(f334(f334(f334(f334(a204,x95091),x95092),x95093),f449(x95094,x95093,x95092,x95095,x95091)))+~P1(f334(f334(f334(f334(a204,f33(x95091,x95095)),x95092),x95093),x95094))
% 160.93/160.65 [9510]P1(f334(f334(f334(f334(a204,x95101),x95102),x95103),f573(x95104,x95103,x95102,x95105,x95101)))+~P1(f334(f334(f334(f334(a204,f33(x95101,x95105)),x95102),x95103),x95104))
% 160.93/160.65 [9581]P26(x95811,x95812,f334(f334(f312(f880(x95811)),f334(f334(f334(f92(x95811),x95813),f334(a26,x95814)),x95815)),f196(f888(f880(x95811),a876))))+~P26(x95811,f334(f334(f312(f880(x95811)),f334(f334(f334(f92(x95811),x95813),f334(a26,x95814)),x95815)),x95812),f334(f334(f312(f880(x95811)),f334(f334(f334(f92(x95811),x95813),f334(f245(a878),f334(a28,x95814))),x95815)),f196(f888(f880(x95811),a876))))
% 160.93/160.65 [9593]E(f334(f334(f312(x95931),f868(x95932,x95933,x95934,x95935,x95931)),f869(x95932,x95933,x95934,x95935,x95931)),f334(f334(f312(x95931),x95934),x95933))+~P1(f334(f62(x95931,x95935,f334(f334(f312(x95931),x95934),x95933)),x95932))
% 160.93/160.65 [9594]E(f334(f334(f312(x95941),f870(x95942,x95943,x95944,x95945,x95941)),f871(x95942,x95943,x95944,x95945,x95941)),f334(f334(f312(x95941),x95944),x95943))+~P1(f334(f62(x95941,x95945,f334(f334(f312(x95941),x95944),x95943)),x95942))
% 160.93/160.65 [9678]P1(f334(f334(f336(x96781),f497(x96782,x96783,x96784,x96785,x96781)),x96784))+P1(f334(f334(f334(f42(x96781,f888(x96785,a876)),x96784),x96783),x96782))
% 160.93/160.65 [9683]P1(f334(f334(f336(x96831),f491(x96832,x96833,x96831,x96834,x96835)),x96833))+P1(f334(f334(f336(x96835),x96834),f334(f334(f42(x96831,f888(x96835,a876)),x96833),x96832)))
% 160.93/160.65 [9691]P1(f334(f334(f336(x96911),f492(x96912,x96913,x96911,x96914,x96915)),x96913))+P1(f334(f334(f248(f888(x96915,a876)),x96914),f334(f334(f42(x96911,f888(x96915,a876)),x96913),x96912)))
% 160.93/160.65 [9694]P1(f334(f334(x96941,f838(x96942,x96941,x96943,x96944,x96945)),x96942))+~P1(f334(f334(f334(f41(x96945,f888(x96944,a876)),x96943),x96941),x96942))
% 160.93/160.65 [9697]P1(f334(f334(f336(x96971),f838(x96972,x96973,x96974,x96975,x96971)),x96974))+~P1(f334(f334(f334(f41(x96971,f888(x96975,a876)),x96974),x96973),x96972))
% 160.93/160.65 [9707]P1(f334(f334(f336(x97071),f839(x97072,x97073,x97071,x97074,x97075)),x97073))+~P1(f334(f334(f336(x97075),x97074),f334(f334(f41(x97071,f888(x97075,a876)),x97073),x97072)))
% 160.93/160.65 [9712]P1(f334(f334(f336(x97121),x97122),f334(x97123,f839(x97123,x97124,x97125,x97122,x97121))))+~P1(f334(f334(f336(x97121),x97122),f334(f334(f41(x97125,f888(x97121,a876)),x97124),x97123)))
% 160.93/160.65 [9806]~P1(f334(f334(x98064,f497(x98065,x98064,x98063,x98062,x98061)),x98065))+P1(f334(f334(f334(f42(x98061,f888(x98062,a876)),x98063),x98064),x98065))
% 160.93/160.65 [9809]~P1(f334(f334(f336(x98091),x98092),f334(x98095,f491(x98095,x98094,x98093,x98092,x98091))))+P1(f334(f334(f336(x98091),x98092),f334(f334(f42(x98093,f888(x98091,a876)),x98094),x98095)))
% 160.93/160.65 [9813]~P1(f334(f334(f248(f888(x98131,a876)),x98132),f334(x98135,f492(x98135,x98134,x98133,x98132,x98131))))+P1(f334(f334(f248(f888(x98131,a876)),x98132),f334(f334(f42(x98133,f888(x98131,a876)),x98134),x98135)))
% 160.93/160.65 [9858]P1(f334(f334(f334(f334(a204,x98581),f449(x98582,x98583,x98584,x98581,x98585)),x98583),x98582))+~P1(f334(f334(f334(f334(a204,f33(x98585,x98581)),x98584),x98583),x98582))
% 160.93/160.65 [9859]P1(f334(f334(f334(f334(a204,x98591),f573(x98592,x98593,x98594,x98591,x98595)),x98593),x98592))+~P1(f334(f334(f334(f334(a204,f33(x98595,x98591)),x98594),x98593),x98592))
% 160.93/160.65 [9885]~P1(f334(f334(f336(x98851),f868(x98855,x98854,x98853,x98852,x98851)),f869(x98855,x98854,x98853,x98852,x98851)))+~P1(f334(f62(x98851,x98852,f334(f334(f312(x98851),x98853),x98854)),x98855))
% 160.93/160.65 [9886]~P1(f334(f334(f336(x98861),f870(x98865,x98864,x98863,x98862,x98861)),f871(x98865,x98864,x98863,x98862,x98861)))+~P1(f334(f62(x98861,x98862,f334(f334(f312(x98861),x98863),x98864)),x98865))
% 160.93/160.65 [9887]~P1(f334(f334(f336(f887(x98871,x98871)),f334(f334(f269(x98871,x98871),x98872),x98875)),f334(f334(f191(f887(x98871,x98871),a876),f334(a116,x98874)),x98873)))+P1(f334(f334(f336(f887(x98871,x98871)),f334(f334(f269(x98871,x98871),x98872),f651(x98873,x98874,x98875,x98872,x98871))),f334(f334(f191(f887(x98871,x98871),a876),x98874),x98873)))
% 160.93/160.65 [9894]P1(f334(f66(x98941,x98941,x98942,f868(x98943,x98944,x98945,x98942,x98941),f869(x98943,x98944,x98945,x98942,x98941)),x98943))+~P1(f334(f62(x98941,x98942,f334(f334(f312(x98941),x98945),x98944)),x98943))
% 160.93/160.65 [9895]P1(f334(f66(x98951,x98951,x98952,f870(x98953,x98954,x98955,x98952,x98951),f871(x98953,x98954,x98955,x98952,x98951)),x98953))+~P1(f334(f62(x98951,x98952,f334(f334(f312(x98951),x98955),x98954)),x98953))
% 160.93/160.65 [9907]~P108(x99071)+P16(x99071,f334(f334(f156(x99072,x99071),x99073),f334(f138(x99072,f334(f334(f7(x99072,x99071,a876),f334(f334(f8(x99071,f888(x99071,a876),x99072),a331),x99073)),f334(x99074,x99075))),x99075)))
% 160.93/160.65 [9947]~P1(f334(f334(f336(x99472),x99475),f334(f288(x99471,x99472,x99474),x99473)))+P1(f334(f334(f336(f887(x99471,x99472)),f334(f334(f269(x99471,x99472),f530(x99473,x99474,x99471,x99475,x99472)),x99475)),x99474))
% 160.93/160.65 [9948]~P1(f334(f334(f336(x99482),x99485),f334(f288(x99481,x99482,x99484),x99483)))+P1(f334(f334(f336(f887(x99481,x99482)),f334(f334(f269(x99481,x99482),f536(x99483,x99484,x99481,x99485,x99482)),x99485)),x99484))
% 160.93/160.65 [9968]~P1(f334(f334(f336(f887(x99681,x99681)),f334(f334(f269(x99681,x99681),x99685),x99684)),f334(f334(f191(f887(x99681,x99681),a876),f334(a116,x99683)),x99682)))+P1(f334(f334(f336(f887(x99681,x99681)),f334(f334(f269(x99681,x99681),f651(x99682,x99683,x99684,x99685,x99681)),x99684)),x99682))
% 160.93/160.65 [9971]~P1(f334(f334(f336(f887(x99711,x99711)),f334(f334(f269(x99711,x99711),x99715),x99714)),f334(f334(f191(f887(x99711,x99711),a876),f334(a116,x99713)),x99712)))+P1(f334(f334(f336(f887(x99711,x99711)),f334(f334(f269(x99711,x99711),f649(x99712,x99713,x99714,x99715,x99711)),x99714)),f334(f334(f191(f887(x99711,x99711),a876),x99713),x99712)))
% 160.93/160.65 [9972]~P1(f334(f334(f336(f887(x99721,x99721)),f334(f334(f269(x99721,x99721),x99725),x99724)),f334(f334(f191(f887(x99721,x99721),a876),f334(a116,x99723)),x99722)))+P1(f334(f334(f336(f887(x99721,x99721)),f334(f334(f269(x99721,x99721),f650(x99722,x99723,x99724,x99725,x99721)),x99724)),f334(f334(f191(f887(x99721,x99721),a876),x99723),x99722)))
% 160.93/160.65 [9973]~P1(f334(f334(f336(f887(f882(x99731),f882(x99731))),f334(f334(f269(f882(x99731),f882(x99731)),x99735),f334(f334(f153(x99731),x99734),x99733))),f160(x99731,x99732)))+P1(f334(f334(f336(f887(x99731,x99731)),f334(f334(f269(x99731,x99731),f675(x99732,x99733,x99734,x99735,x99731)),x99734)),x99732))
% 160.93/160.65 [7060]E(x70601,f210(x70602))+E(f186(x70603,x70602,f334(f334(f334(f72(x70603,f885(x70602)),x70604),x70605),x70601)),f334(f334(f312(x70603),x70605),f186(x70603,x70602,x70604)))
% 160.93/160.65 [7555]~E(x75553,f196(f888(x75552,a876)))+E(f334(f334(f114(f888(x75551,a876)),f334(f334(f41(x75552,f888(x75551,a876)),x75553),x75554)),x75555),x75555)
% 160.93/160.65 [7556]~E(x75563,f196(f888(x75562,a876)))+E(f334(f334(f105(f888(x75561,a876)),f334(f334(f42(x75562,f888(x75561,a876)),x75563),x75564)),x75565),x75565)
% 160.93/160.65 [7912]~E(x79125,f210(x79122))+E(f186(x79121,x79122,f334(f334(f334(f72(x79121,f885(x79122)),x79123),x79124),x79125)),f334(f334(f22(f888(x79121,a876)),f186(x79121,x79122,x79123)),f334(f334(f312(x79121),x79124),f196(f888(x79121,a876)))))
% 160.93/160.65 [7979]~E(x79793,f196(f888(x79792,a876)))+E(f334(f334(f22(f888(x79791,a876)),f334(f334(f42(x79792,f888(x79791,a876)),x79793),x79794)),x79795),f334(f334(f22(f888(x79791,a876)),f257(f888(x79791,a876))),x79795))
% 160.93/160.65 [8106]E(f334(f334(f161(x81061,f334(f334(f136(x81061),x81062),x81063)),x81064),x81065),f334(f334(f136(x81061),f334(f334(f161(x81061,x81062),x81064),x81065)),x81063))+~P1(f334(f334(f249(a881),x81064),f334(f197(f882(x81061)),x81062)))
% 160.93/160.65 [8231]P1(f334(f334(f336(x82311),x82315),f334(f174(x82311),x82313)))+E(f334(f334(f180(x82311,x82312),f334(f334(f184(x82311,x82312),x82313),f334(f334(f156(x82311,x82312),x82314),x82313))),x82315),f210(x82312))
% 160.93/160.65 [8353]~P1(f334(f334(f336(x83531),x83535),f334(f174(x83531),x83533)))+E(f334(f334(f180(x83531,x83532),f334(f334(f184(x83531,x83532),x83533),f334(f334(f156(x83531,x83532),x83534),x83533))),x83535),f334(f241(x83532),f334(x83534,x83535)))
% 160.93/160.65 [8390]E(f334(f334(f167(x83901),f334(f334(f156(a881,x83901),x83902),f141(a881,f334(f304(a881,x83903),x83904)))),x83905),f334(x83902,f334(f334(f80(a881),x83903),x83905)))+~P1(f334(f334(f249(a881),x83905),f334(f334(f22(a881),x83904),x83903)))
% 160.93/160.65 [8430]~E(x84303,f196(f888(x84301,a876)))+E(f334(f334(f41(x84301,f888(x84302,a876)),x84303),f334(f334(f8(f888(x84302,a876),f888(x84302,a876),x84301),f334(f114(f888(x84302,a876)),x84304)),x84305)),f196(f888(x84302,a876)))
% 160.93/160.65 [8431]~E(x84313,f196(f888(x84311,a876)))+E(f334(f334(f42(x84311,f888(x84312,a876)),x84313),f334(f334(f8(f888(x84312,a876),f888(x84312,a876),x84311),f334(f22(f888(x84312,a876)),x84314)),x84315)),f257(f888(x84312,a876)))
% 160.93/160.65 [8432]~E(x84323,f196(f888(x84321,a876)))+E(f334(f334(f42(x84321,f888(x84322,a876)),x84323),f334(f334(f8(f888(x84322,a876),f888(x84322,a876),x84321),f334(f105(f888(x84322,a876)),x84324)),x84325)),f257(f888(x84322,a876)))
% 160.93/160.65 [8434]~P141(x84342)+E(f334(f334(f6(x84341,x84342),f334(f334(f8(x84342,x84342,x84341),f334(f81(x84342),x84343)),x84344)),x84345),f334(f334(f81(x84342),x84343),f334(f334(f6(x84341,x84342),x84344),x84345)))
% 160.93/160.65 [8721]E(x87211,f196(f888(x87212,a876)))+E(f334(f334(f41(x87212,f888(x87213,a876)),x87211),f334(f334(f8(f888(x87213,a876),f888(x87213,a876),x87212),f334(f114(f888(x87213,a876)),x87214)),x87215)),f334(f334(f114(f888(x87213,a876)),x87214),f334(f334(f41(x87212,f888(x87213,a876)),x87211),x87215)))
% 160.93/160.65 [8722]E(x87221,f196(f888(x87222,a876)))+E(f334(f334(f42(x87222,f888(x87223,a876)),x87221),f334(f334(f8(f888(x87223,a876),f888(x87223,a876),x87222),f334(f22(f888(x87223,a876)),x87224)),x87225)),f334(f334(f22(f888(x87223,a876)),x87224),f334(f334(f41(x87222,f888(x87223,a876)),x87221),x87225)))
% 160.93/160.65 [8723]E(x87231,f196(f888(x87232,a876)))+E(f334(f334(f42(x87232,f888(x87233,a876)),x87231),f334(f334(f8(f888(x87233,a876),f888(x87233,a876),x87232),f334(f105(f888(x87233,a876)),x87234)),x87235)),f334(f334(f105(f888(x87233,a876)),x87234),f334(f334(f42(x87232,f888(x87233,a876)),x87231),x87235)))
% 160.93/160.65 [8917]~P1(f334(f334(f249(a881),f334(x89174,x89172)),f334(x89174,x89173)))+P1(f334(f334(f336(f887(x89171,x89171)),f334(f334(f269(x89171,x89171),x89172),x89173)),f155(x89171,f334(f334(f153(f888(x89171,a881)),x89174),x89175))))
% 160.93/160.65 [9187]~P27(x91872,x91871,x91873,f334(f334(f114(f888(x91872,a876)),x91874),x91875))+E(f334(f334(f105(f888(x91871,a876)),f334(f313(x91872,x91871,x91873),f334(f334(f22(f888(x91872,a876)),x91874),x91875))),f334(f313(x91872,x91871,x91873),f334(f334(f22(f888(x91872,a876)),x91875),x91874))),f196(f888(x91871,a876)))
% 160.93/160.65 [9467]~P1(f334(f334(f248(f888(x94673,a876)),f334(f288(x94671,x94673,x94674),x94672)),x94675))+P1(f334(f334(f248(f888(x94671,a876)),x94672),f334(f79(f888(x94671,a876)),f334(f288(x94673,x94671,f334(f289(x94671,x94673),x94674)),f334(f79(f888(x94673,a876)),x94675)))))
% 160.93/160.65 [9492]~P27(x94921,x94922,x94923,f334(f334(f312(x94921),x94924),x94925))+~P1(f334(f334(f336(x94922),f334(x94923,x94924)),f334(f313(x94921,x94922,x94923),f334(f334(f22(f888(x94921,a876)),x94925),f334(f334(f312(x94921),x94924),f196(f888(x94921,a876)))))))
% 160.93/160.65 [9547]P1(f334(f334(f248(f888(x95471,a876)),f334(f288(x95472,x95471,x95473),x95474)),x95475))+~P1(f334(f334(f248(f888(x95472,a876)),x95474),f334(f79(f888(x95472,a876)),f334(f288(x95471,x95472,f334(f289(x95472,x95471),x95473)),f334(f79(f888(x95471,a876)),x95475)))))
% 160.93/160.65 [9621]~P85(x96211)+P1(f334(f334(f248(x96211),f334(f75(x96211),f334(f334(f22(x96211),f334(f334(f80(x96211),x96212),x96213)),f334(f334(f80(x96211),x96214),x96215)))),f334(f334(f80(x96211),f334(f75(x96211),f334(f334(f22(x96211),x96212),x96214))),f334(f75(x96211),f334(f334(f22(x96211),x96213),x96215)))))
% 160.93/160.65 [9727]P1(f334(f334(f336(x97271),f354(x97272,x97273,x97274,x97271,x97275)),x97274))+P1(f334(f334(f248(f888(x97275,a876)),f334(f334(f41(x97271,f888(x97275,a876)),x97274),x97273)),x97272))
% 160.93/160.65 [9925]~P1(f334(f334(f248(f888(x99251,a876)),f334(x99254,f354(x99255,x99254,x99253,x99252,x99251))),x99255))+P1(f334(f334(f248(f888(x99251,a876)),f334(f334(f41(x99252,f888(x99251,a876)),x99253),x99254)),x99255))
% 160.93/160.65 [8540]E(f334(f334(f136(x85401),x85402),f334(f334(f161(x85401,x85403),f334(f334(f22(a881),x85404),f334(f197(f882(x85401)),x85402))),x85405)),f334(f334(f161(x85401,f334(f334(f136(x85401),x85402),x85403)),x85404),x85405))+P1(f334(f334(f249(a881),x85404),f334(f197(f882(x85401)),x85402)))
% 160.93/160.65 [8573]~P137(x85731)+E(f334(f334(f80(x85731),f334(f334(f81(x85731),x85732),x85733)),f334(f334(f80(x85731),f334(f334(f81(x85731),x85734),x85733)),x85735)),f334(f334(f80(x85731),f334(f334(f81(x85731),f334(f334(f80(x85731),x85732),x85734)),x85733)),x85735))
% 160.93/160.65 [9141]~P141(x91411)+E(f334(f168(x91411),f334(f334(f156(x91412,x91411),f334(f334(f8(x91411,x91411,x91412),f334(f81(x91411),x91413)),x91414)),x91415)),f334(f334(f81(x91411),x91413),f334(f168(x91411),f334(f334(f156(x91412,x91411),x91414),x91415))))
% 160.93/160.65 [9314]E(f334(f197(f882(x93141)),f334(f334(f177(x93141),f334(f334(f246(a881),f334(f197(f882(x93141)),x93142)),f334(f197(f882(x93143)),x93144))),x93142)),f334(f197(f882(x93143)),f334(f334(f177(x93143),f334(f334(f246(a881),f334(f197(f882(x93141)),x93142)),f334(f197(f882(x93143)),x93144))),x93144)))+P1(f334(x93145,f334(f334(f184(x93141,x93143),x93142),x93144)))
% 160.93/160.65 [9558]~P141(x95582)+E(f334(f334(f6(x95581,x95582),f334(f334(f7(x95581,x95582,x95582),f334(f334(f8(x95582,f888(x95582,x95582),x95581),f81(x95582)),x95583)),x95584)),x95585),f334(f334(f81(x95582),f334(f334(f6(x95581,x95582),x95583),x95585)),x95584))
% 160.93/160.65 [9559]~P62(x95592)+E(f334(f334(f6(x95591,x95592),f334(f334(f7(x95591,x95592,x95592),f334(f334(f8(x95592,f888(x95592,x95592),x95591),f292(x95592)),x95593)),x95594)),x95595),f334(f334(f292(x95592),f334(f334(f6(x95591,x95592),x95593),x95595)),x95594))
% 160.93/160.65 [9566]~P67(x95662)+E(f334(f334(f6(x95661,x95662),f334(f334(f18(x95661,x95662,x95662),f334(f334(f8(x95662,f888(x95662,x95662),x95661),f22(x95662)),x95663)),x95664)),x95665),f334(f334(f22(x95662),f334(f334(f6(x95661,x95662),x95663),x95665)),f334(f334(f6(x95661,x95662),x95664),x95665)))
% 160.93/160.65 [9567]~P68(x95672)+E(f334(f334(f6(x95671,x95672),f334(f334(f18(x95671,x95672,x95672),f334(f334(f8(x95672,f888(x95672,x95672),x95671),f80(x95672)),x95673)),x95674)),x95675),f334(f334(f80(x95672),f334(f334(f6(x95671,x95672),x95673),x95675)),f334(f334(f6(x95671,x95672),x95674),x95675)))
% 160.93/160.65 [9568]~P74(x95682)+E(f334(f334(f9(x95681,x95682),f334(f334(f18(x95681,x95682,x95682),f334(f334(f8(x95682,f888(x95682,x95682),x95681),f81(x95682)),x95683)),x95684)),x95685),f334(f334(f81(x95682),f334(f334(f9(x95681,x95682),x95683),x95685)),f334(f334(f9(x95681,x95682),x95684),x95685)))
% 160.93/160.65 [9606]~E(x96063,f196(f888(x96061,a876)))+E(f334(f334(f41(x96061,f888(x96062,a876)),x96063),f334(f334(f7(x96061,f888(x96062,a876),f888(x96062,a876)),f334(f334(f8(f888(x96062,a876),f888(f888(x96062,a876),f888(x96062,a876)),x96061),f114(f888(x96062,a876))),x96064)),x96065)),f196(f888(x96062,a876)))
% 160.93/160.65 [9607]~E(x96073,f196(f888(x96071,a876)))+E(f334(f334(f42(x96071,f888(x96072,a876)),x96073),f334(f334(f7(x96071,f888(x96072,a876),f888(x96072,a876)),f334(f334(f8(f888(x96072,a876),f888(f888(x96072,a876),f888(x96072,a876)),x96071),f22(f888(x96072,a876))),x96074)),x96075)),f257(f888(x96072,a876)))
% 160.93/160.65 [9608]~E(x96083,f196(f888(x96081,a876)))+E(f334(f334(f42(x96081,f888(x96082,a876)),x96083),f334(f334(f7(x96081,f888(x96082,a876),f888(x96082,a876)),f334(f334(f8(f888(x96082,a876),f888(f888(x96082,a876),f888(x96082,a876)),x96081),f105(f888(x96082,a876))),x96084)),x96085)),f257(f888(x96082,a876)))
% 160.93/160.65 [9629]E(x96291,f196(f888(x96292,a876)))+E(f334(f334(f41(x96292,f888(x96293,a876)),x96291),f334(f334(f7(x96292,f888(x96293,a876),f888(x96293,a876)),f334(f334(f8(f888(x96293,a876),f888(f888(x96293,a876),f888(x96293,a876)),x96292),f114(f888(x96293,a876))),x96294)),x96295)),f334(f334(f114(f888(x96293,a876)),f334(f334(f41(x96292,f888(x96293,a876)),x96291),x96294)),x96295))
% 160.93/160.65 [9630]E(x96301,f196(f888(x96302,a876)))+E(f334(f334(f42(x96302,f888(x96303,a876)),x96301),f334(f334(f7(x96302,f888(x96303,a876),f888(x96303,a876)),f334(f334(f8(f888(x96303,a876),f888(f888(x96303,a876),f888(x96303,a876)),x96302),f22(f888(x96303,a876))),x96304)),x96305)),f334(f334(f22(f888(x96303,a876)),f334(f334(f42(x96302,f888(x96303,a876)),x96301),x96304)),x96305))
% 160.93/160.65 [9631]E(x96311,f196(f888(x96312,a876)))+E(f334(f334(f42(x96312,f888(x96313,a876)),x96311),f334(f334(f7(x96312,f888(x96313,a876),f888(x96313,a876)),f334(f334(f8(f888(x96313,a876),f888(f888(x96313,a876),f888(x96313,a876)),x96312),f105(f888(x96313,a876))),x96314)),x96315)),f334(f334(f105(f888(x96313,a876)),f334(f334(f42(x96312,f888(x96313,a876)),x96311),x96314)),x96315))
% 160.93/160.65 [9194]~P1(f334(f334(f248(a881),x91941),x91944))+E(f334(f334(f22(a881),f334(f334(f80(a881),f334(f334(f81(a881),x91941),x91942)),x91943)),f334(f334(f80(a881),f334(f334(f81(a881),x91944),x91942)),x91945)),f334(f334(f22(a881),x91943),f334(f334(f80(a881),f334(f334(f81(a881),f334(f334(f22(a881),x91944),x91941)),x91942)),x91945)))
% 160.93/160.65 [9787]~P141(x97871)+E(f334(f168(x97871),f334(f334(f156(x97872,x97871),f334(f334(f7(x97872,x97871,x97871),f334(f334(f8(x97871,f888(x97871,x97871),x97872),f81(x97871)),x97873)),x97874)),x97875)),f334(f334(f81(x97871),f334(f168(x97871),f334(f334(f156(x97872,x97871),x97873),x97875))),x97874))
% 160.93/160.65 [9793]~P67(x97931)+E(f334(f168(x97931),f334(f334(f156(x97932,x97931),f334(f334(f18(x97932,x97931,x97931),f334(f334(f8(x97931,f888(x97931,x97931),x97932),f22(x97931)),x97933)),x97934)),x97935)),f334(f334(f22(x97931),f334(f168(x97931),f334(f334(f156(x97932,x97931),x97933),x97935))),f334(f168(x97931),f334(f334(f156(x97932,x97931),x97934),x97935))))
% 160.93/160.65 [9794]~P68(x97941)+E(f334(f168(x97941),f334(f334(f156(x97942,x97941),f334(f334(f18(x97942,x97941,x97941),f334(f334(f8(x97941,f888(x97941,x97941),x97942),f80(x97941)),x97943)),x97944)),x97945)),f334(f334(f80(x97941),f334(f168(x97941),f334(f334(f156(x97942,x97941),x97943),x97945))),f334(f168(x97941),f334(f334(f156(x97942,x97941),x97944),x97945))))
% 160.93/160.65 [9938]P1(f334(x99381,f334(f334(f184(x99382,x99383),x99384),x99385)))+~P1(f334(x99381,f334(f334(f184(x99382,x99383),f334(f334(f177(x99382),f334(f334(f246(a881),f334(f197(f882(x99382)),x99384)),f334(f197(f882(x99383)),x99385))),x99384)),f334(f334(f177(x99383),f334(f334(f246(a881),f334(f197(f882(x99382)),x99384)),f334(f197(f882(x99383)),x99385))),x99385))))
% 160.93/160.65 [10172]~P1(f334(f334(f336(f887(x101722,x101721)),f334(f334(f269(x101722,x101721),x101724),x101725)),f334(f289(x101721,x101722),x101723)))+P1(f334(f334(f258(x101721,x101722,f334(f334(f7(x101721,f888(f887(x101721,x101722),a876),f888(x101722,a876)),f334(f334(f8(f888(x101722,f888(f888(f887(x101721,x101722),a876),a876)),f888(f888(f887(x101721,x101722),a876),f888(x101722,a876)),x101721),f7(x101722,f888(f887(x101721,x101722),a876),a876)),f334(f334(f8(f888(x101722,f887(x101721,x101722)),f888(x101722,f888(f888(f887(x101721,x101722),a876),a876)),x101721),f334(f8(f887(x101721,x101722),f888(f888(f887(x101721,x101722),a876),a876),x101722),f336(f887(x101721,x101722)))),f269(x101721,x101722)))),x101723)),x101724),x101725))
% 160.93/160.65 [10181]P1(f334(f334(f336(f887(x101811,x101812)),f334(f334(f269(x101811,x101812),x101813),x101814)),f334(f289(x101812,x101811),x101815)))+~P1(f334(f334(f258(x101812,x101811,f334(f334(f7(x101812,f888(f887(x101812,x101811),a876),f888(x101811,a876)),f334(f334(f8(f888(x101811,f888(f888(f887(x101812,x101811),a876),a876)),f888(f888(f887(x101812,x101811),a876),f888(x101811,a876)),x101812),f7(x101811,f888(f887(x101812,x101811),a876),a876)),f334(f334(f8(f888(x101811,f887(x101812,x101811)),f888(x101811,f888(f888(f887(x101812,x101811),a876),a876)),x101812),f334(f8(f887(x101812,x101811),f888(f888(f887(x101812,x101811),a876),a876),x101811),f336(f887(x101812,x101811)))),f269(x101812,x101811)))),x101815)),x101813),x101814))
% 160.93/160.65 [9435]~P1(f334(f334(f248(a881),x94354),x94351))+E(f334(f334(f22(a881),f334(f334(f80(a881),f334(f334(f81(a881),x94351),x94352)),x94353)),f334(f334(f80(a881),f334(f334(f81(a881),x94354),x94352)),x94355)),f334(f334(f22(a881),f334(f334(f80(a881),f334(f334(f81(a881),f334(f334(f22(a881),x94351),x94354)),x94352)),x94353)),x94355))
% 160.93/160.65 [10190]P26(x101901,x101902,f334(f313(a879,f880(x101901),f334(f334(f18(a879,f888(x101901,f888(a877,a876)),f880(x101901)),f334(f334(f18(a879,a878,f888(f888(x101901,f888(a877,a876)),f880(x101901))),f334(f334(f8(f888(x101901,f888(a877,a876)),f888(a878,f888(f888(x101901,f888(a877,a876)),f880(x101901))),a879),f92(x101901)),x101903)),a26)),x101904)),x101905))+~P26(x101901,f334(f334(f114(f888(f880(x101901),a876)),x101902),f334(f313(a879,f880(x101901),f334(f334(f18(a879,f888(x101901,f888(a877,a876)),f880(x101901)),f334(f334(f18(a879,a878,f888(f888(x101901,f888(a877,a876)),f880(x101901))),f334(f334(f8(f888(x101901,f888(a877,a876)),f888(a878,f888(f888(x101901,f888(a877,a876)),f880(x101901))),a879),f92(x101901)),x101903)),a26)),x101904)),x101905)),f334(f313(a879,f880(x101901),f334(f334(f18(a879,f888(x101901,f888(a877,a876)),f880(x101901)),f334(f334(f18(a879,a878,f888(f888(x101901,f888(a877,a876)),f880(x101901))),f334(f334(f8(f888(x101901,f888(a877,a876)),f888(a878,f888(f888(x101901,f888(a877,a876)),f880(x101901))),a879),f92(x101901)),x101903)),f334(f334(f8(f885(a878),a878,a879),f245(a878)),a28))),x101904)),x101905))
% 160.93/160.65 [10191]P30(x101911,x101912,f334(f313(a879,f880(x101911),f334(f334(f18(a879,f888(x101911,f888(a877,a876)),f880(x101911)),f334(f334(f18(a879,a878,f888(f888(x101911,f888(a877,a876)),f880(x101911))),f334(f334(f8(f888(x101911,f888(a877,a876)),f888(a878,f888(f888(x101911,f888(a877,a876)),f880(x101911))),a879),f92(x101911)),x101913)),a26)),x101914)),x101915))+~P30(x101911,f334(f334(f114(f888(f880(x101911),a876)),x101912),f334(f313(a879,f880(x101911),f334(f334(f18(a879,f888(x101911,f888(a877,a876)),f880(x101911)),f334(f334(f18(a879,a878,f888(f888(x101911,f888(a877,a876)),f880(x101911))),f334(f334(f8(f888(x101911,f888(a877,a876)),f888(a878,f888(f888(x101911,f888(a877,a876)),f880(x101911))),a879),f92(x101911)),x101913)),a26)),x101914)),x101915)),f334(f313(a879,f880(x101911),f334(f334(f18(a879,f888(x101911,f888(a877,a876)),f880(x101911)),f334(f334(f18(a879,a878,f888(f888(x101911,f888(a877,a876)),f880(x101911))),f334(f334(f8(f888(x101911,f888(a877,a876)),f888(a878,f888(f888(x101911,f888(a877,a876)),f880(x101911))),a879),f92(x101911)),x101913)),f334(f334(f8(f885(a878),a878,a879),f245(a878)),a28))),x101914)),x101915))
% 160.93/160.65 [5260]E(x52601,x52602)+~E(f30(x52603,x52604,x52601),f30(x52605,x52606,x52602))
% 160.93/160.65 [5261]E(x52611,x52612)+~E(f30(x52613,x52611,x52614),f30(x52615,x52612,x52616))
% 160.93/160.65 [5262]E(x52621,x52622)+~E(f30(x52621,x52623,x52624),f30(x52622,x52625,x52626))
% 160.93/160.65 [5263]E(x52631,x52632)+~E(f29(x52633,x52634,x52631),f29(x52635,x52636,x52632))
% 160.93/160.65 [5264]E(x52641,x52642)+~E(f29(x52643,x52641,x52644),f29(x52645,x52642,x52646))
% 160.93/160.65 [5265]E(x52651,x52652)+~E(f29(x52651,x52653,x52654),f29(x52652,x52655,x52656))
% 160.93/160.65 [6704]E(f334(f187(x67041,x67042,x67043,x67044),x67045),f334(f241(x67042),x67046))+~E(f334(x67044,x67045),f334(f241(x67042),x67046))
% 160.93/160.65 [6847]E(f334(f243(f885(x68471),x68472,f210(x68471),x68473),f334(x68474,x68475)),f334(x68473,x68476))+~E(f334(x68474,x68475),f334(f241(x68472),x68476))
% 160.93/160.65 [8376]~P21(x83765,x83761,x83762,x83766)+E(f334(f73(x83761,x83761,x83761,f334(x83762,x83763)),f334(x83762,x83764)),f334(f73(x83761,x83761,x83761,f334(x83762,x83764)),f334(x83762,x83763)))
% 160.93/160.65 [8614]~P54(x86144,x86145,x86142,x86141,x86146)+E(f334(x86141,f334(x86142,x86143)),x86143)
% 160.93/160.65 [8769]P27(x87691,x87692,x87693,x87694)+~P27(x87691,x87695,f334(f73(x87692,x87695,x87691,x87696),x87693),x87694)
% 160.93/160.65 [8852]~P27(x88524,x88522,f334(f73(x88521,x88522,x88524,x88523),x88525),x88526)+P27(x88521,x88522,x88523,f334(f313(x88524,x88521,x88525),x88526))
% 160.93/160.65 [9505]P51(x95051,x95052,x95053,x95054,x95055,x95056)+~P1(f334(f334(x95053,f334(x95054,x95055)),f334(x95054,x95056)))
% 160.93/160.65 [9569]P1(f334(f61(x95691),x95692))+~P1(f334(f66(x95691,x95693,x95694,x95695,x95692),x95696))
% 160.93/160.65 [9577]~P1(f334(f334(f336(x95774),x95773),f299(x95774,x95771,x95775,x95772,x95776)))+P1(f334(f334(x95771,x95772),x95773))
% 160.93/160.65 [9578]~P1(f334(f334(f336(x95784),x95783),f302(x95784,x95785,x95781,x95782,x95786)))+P1(f334(f334(x95781,x95782),x95783))
% 160.93/160.65 [9579]~P1(f334(f334(f336(x95794),x95792),f299(x95794,x95795,x95791,x95796,x95793)))+P1(f334(f334(x95791,x95792),x95793))
% 160.93/160.65 [9580]~P1(f334(f334(f336(x95804),x95802),f302(x95804,x95801,x95805,x95806,x95803)))+P1(f334(f334(x95801,x95802),x95803))
% 160.93/160.65 [9643]~P51(x96435,x96436,x96431,x96432,x96433,x96434)+P1(f334(f334(x96431,f334(x96432,x96433)),f334(x96432,x96434)))
% 160.93/160.65 [5761]E(x57611,x57612)+~E(f334(f334(f269(x57613,x57614),x57615),x57611),f334(f334(f269(x57613,x57614),x57616),x57612))
% 160.93/160.65 [5763]E(x57631,x57632)+~E(f334(f334(f269(x57633,x57634),x57631),x57635),f334(f334(f269(x57633,x57634),x57632),x57636))
% 160.93/160.65 [5887]~P18(x58875,x58876,x58871)+E(f334(f334(x58871,x58872),f334(f334(x58871,x58873),x58874)),f334(f334(x58871,x58873),f334(f334(x58871,x58872),x58874)))
% 160.93/160.65 [7302]~P34(x73024,x73021,f334(f334(f153(x73024),x73022),x73025),f334(f334(f153(x73024),x73023),x73026))+P1(f334(f334(x73021,x73022),x73023))
% 160.93/160.65 [7671]P34(x76711,x76712,x76713,x76714)+~P34(x76711,x76712,f334(f334(f153(x76711),x76715),x76713),f334(f334(f153(x76711),x76716),x76714))
% 160.93/160.65 [8712]~P54(x87125,x87121,x87122,x87126,x87124)+P1(f334(f334(f336(x87121),f334(x87122,x87123)),x87124))
% 160.93/160.65 [8880]E(f334(f76(x88801,x88802,x88803,x88804,x88805),x88806),f334(x88803,x88806))+P1(f334(f334(f336(x88801),x88806),x88805))
% 160.93/160.65 [8901]~E(x89013,f334(f334(f153(x89011),x89015),x89016))+P1(f334(f334(f336(f887(f882(x89011),f882(x89011))),f334(f334(f269(f882(x89011),f882(x89011)),x89012),f334(f334(f136(x89011),x89012),x89013))),f149(x89011,x89014)))
% 160.93/160.65 [8908]E(f334(f76(x89081,x89082,x89083,x89084,x89085),x89086),f334(x89084,x89086))+~P1(f334(f334(f336(x89081),x89086),x89085))
% 160.93/160.65 [8913]E(f334(f189(x89131,x89132,x89133,x89134,x89135),x89136),f334(x89133,x89136))+P1(f334(f334(f336(x89131),x89136),f334(f174(x89131),x89134)))
% 160.93/160.65 [9145]~P36(x91451,x91452,x91453,x91455,x91456)+P36(x91451,x91452,x91453,f334(f334(f177(x91451),x91454),x91455),f334(f334(f177(x91452),x91454),x91456))
% 160.93/160.65 [9146]~P36(x91461,x91462,x91463,x91465,x91466)+P36(x91461,x91462,x91463,f334(f334(f140(x91461),x91464),x91465),f334(f334(f140(x91462),x91464),x91466))
% 160.93/160.65 [9641]~P25(x96414,x96412,x96415,x96413,x96416,x96411)+E(f334(x96411,f196(f888(x96412,a876))),x96413)
% 160.93/160.65 [9888]~E(f334(x98884,f334(f268(x98881,x98883),x98885)),f334(x98886,f334(f268(x98881,x98883),x98885)))+E(f334(f274(x98881,x98882,x98883,x98883,x98884,f34(x98883)),x98885),f334(f274(x98881,x98882,x98883,x98883,x98886,f34(x98883)),x98885))
% 160.93/160.65 [9889]~E(f334(x98894,f334(f272(x98891,x98892),x98895)),f334(x98896,f334(f272(x98891,x98892),x98895)))+E(f334(f274(x98891,x98891,x98892,x98893,f34(x98891),x98894),x98895),f334(f274(x98891,x98891,x98892,x98893,f34(x98891),x98896),x98895))
% 160.93/160.65 [9934]~E(f334(f274(x99342,x99346,x99343,x99343,x99341,f34(x99343)),x99344),f334(f274(x99342,x99346,x99343,x99343,x99345,f34(x99343)),x99344))+E(f334(x99341,f334(f268(x99342,x99343),x99344)),f334(x99345,f334(f268(x99342,x99343),x99344)))
% 160.93/160.65 [9935]~E(f334(f274(x99352,x99352,x99353,x99356,f34(x99352),x99351),x99354),f334(f274(x99352,x99352,x99353,x99356,f34(x99352),x99355),x99354))+E(f334(x99351,f334(f272(x99352,x99353),x99354)),f334(x99355,f334(f272(x99352,x99353),x99354)))
% 160.93/160.65 [8808]P1(f334(f334(f336(x88081),x88082),x88083))+~P1(f334(f334(f336(f887(x88081,x88084)),f334(f334(f269(x88081,x88084),x88082),x88085)),f334(f334(f271(x88081,x88084),x88083),x88086)))
% 160.93/160.65 [8822]P1(f334(f334(f336(x88221),x88222),f334(x88223,x88224)))+~P1(f334(f334(f336(f887(x88225,x88221)),f334(f334(f269(x88225,x88221),x88224),x88222)),f334(f334(f271(x88225,x88221),x88226),x88223)))
% 160.93/160.65 [8910]~E(f334(f197(f882(x89101)),x89104),f334(f197(f882(x89102)),x89105))+E(f189(x89101,x89102,x89103,x89104,f334(f334(f136(x89102),x89105),x89106)),f189(x89101,x89102,x89103,x89104,x89105))
% 160.93/160.65 [8911]~E(f334(f197(f882(x89111)),x89114),f334(f197(f882(x89112)),x89116))+E(f189(x89111,x89112,x89113,f334(f334(f136(x89111),x89114),x89115),x89116),f189(x89111,x89112,x89113,x89114,x89116))
% 160.93/160.65 [9166]P1(f334(f334(f336(x91661),x91664),f186(x91661,x91662,x91666)))+E(f187(x91661,x91662,f334(f334(f334(f72(x91661,f885(x91662)),x91663),x91664),f334(f241(x91662),x91665)),x91666),f334(f334(f334(f72(x91661,f885(x91662)),f187(x91661,x91662,x91663,x91666)),x91664),f334(f241(x91662),x91665)))
% 160.93/160.65 [9265]P1(f334(f334(f336(f887(x92651,x92651)),f334(f334(f269(x92651,x92651),f334(x92652,x92653)),f334(x92652,x92654))),x92655))+~P1(f334(f334(f336(f887(x92656,x92656)),f334(f334(f269(x92656,x92656),x92653),x92654)),f334(f334(f290(x92651,x92656),x92655),x92652)))
% 160.93/160.65 [9285]~P1(f334(f334(f336(f887(x92854,x92854)),f334(f334(f269(x92854,x92854),f334(x92856,x92852)),f334(x92856,x92853))),x92855))+P1(f334(f334(f336(f887(x92851,x92851)),f334(f334(f269(x92851,x92851),x92852),x92853)),f334(f334(f290(x92854,x92851),x92855),x92856)))
% 160.93/160.65 [9937]E(f334(f334(f269(x99371,x99372),f665(x99373,x99374,x99375,x99376,x99372,x99371)),f666(x99373,x99374,x99375,x99376,x99372,x99371)),x99376)+~P1(f334(f334(f336(f887(x99371,x99372)),x99376),f334(f334(f291(x99371,x99375,x99372),x99374),x99373)))
% 160.93/160.65 [10138]~P1(f334(f334(f336(f887(x101381,x101386)),x101385),f334(f334(f291(x101381,x101382,x101386),x101384),x101383)))+P1(f334(f334(f336(f887(x101381,x101382)),f334(f334(f269(x101381,x101382),f665(x101383,x101384,x101382,x101385,x101386,x101381)),f667(x101383,x101384,x101382,x101385,x101386,x101381))),x101384))
% 160.93/160.65 [10139]~P1(f334(f334(f336(f887(x101396,x101392)),x101395),f334(f334(f291(x101396,x101391,x101392),x101394),x101393)))+P1(f334(f334(f336(f887(x101391,x101392)),f334(f334(f269(x101391,x101392),f667(x101393,x101394,x101391,x101395,x101392,x101396)),f666(x101393,x101394,x101391,x101395,x101392,x101396))),x101393))
% 160.93/160.65 [6165]~E(x61656,x61654)+E(f334(f334(f334(f334(f72(x61651,x61652),x61653),x61654),x61655),x61656),x61655)
% 160.93/160.65 [6217]E(x62171,x62172)+E(f334(f334(f334(f334(f72(x62173,x62174),x62175),x62172),x62176),x62171),f334(x62175,x62171))
% 160.93/160.65 [7739]~P5(x77392)+E(f334(f334(f41(x77391,x77392),x77393),f334(f334(f7(x77391,x77394,x77392),x77395),x77396)),f334(f334(f334(f41(x77391,f888(x77394,x77392)),x77393),x77395),x77396))
% 160.93/160.65 [7740]~P5(x77402)+E(f334(f334(f42(x77401,x77402),x77403),f334(f334(f7(x77401,x77404,x77402),x77405),x77406)),f334(f334(f334(f42(x77401,f888(x77404,x77402)),x77403),x77405),x77406))
% 160.93/160.65 [8521]E(f334(f334(f41(x85211,f888(x85212,a876)),x85213),f334(f334(f8(f888(x85212,a876),f888(x85212,a876),x85211),f334(f312(x85212),x85214)),x85215)),f334(f334(f312(x85212),x85214),f334(f334(f41(x85211,f888(x85212,a876)),x85213),x85215)))+~P1(f334(f334(f336(x85211),x85216),x85213))
% 160.93/160.65 [8963]~P5(x89632)+E(f334(f334(f41(x89631,x89632),x89633),f334(f334(f8(f888(x89634,x89632),x89632,x89631),f334(f41(x89634,x89632),x89635)),f334(f7(x89634,x89631,x89632),x89636))),f334(f334(f41(x89634,x89632),x89635),f334(f334(f8(f888(x89631,x89632),x89632,x89634),f334(f41(x89631,x89632),x89633)),x89636)))
% 160.93/160.65 [8964]~P5(x89642)+E(f334(f334(f42(x89641,x89642),x89643),f334(f334(f8(f888(x89644,x89642),x89642,x89641),f334(f42(x89644,x89642),x89645)),f334(f7(x89644,x89641,x89642),x89646))),f334(f334(f42(x89644,x89642),x89645),f334(f334(f8(f888(x89641,x89642),x89642,x89644),f334(f42(x89641,x89642),x89643)),x89646)))
% 160.93/160.65 [9175]P1(f334(f334(f336(x91751),x91752),f334(f174(x91751),x91753)))+~P1(f334(f334(f336(f887(x91754,x91751)),f334(f334(f269(x91754,x91751),x91755),x91752)),f334(f174(f887(x91754,x91751)),f334(f334(f184(x91754,x91751),x91756),x91753))))
% 160.93/160.65 [9176]P1(f334(f334(f336(x91761),x91762),f334(f174(x91761),x91763)))+~P1(f334(f334(f336(f887(x91761,x91764)),f334(f334(f269(x91761,x91764),x91762),x91765)),f334(f174(f887(x91761,x91764)),f334(f334(f184(x91761,x91764),x91763),x91766))))
% 160.93/160.65 [9279]P1(f334(f334(f248(f888(x92791,a876)),f334(f288(x92792,x92791,x92793),x92794)),x92795))+~P1(f334(f334(f248(f888(f887(x92792,x92791),a876)),x92793),f334(f334(f271(x92792,x92791),x92796),f334(f16(f888(x92791,a876),x92792),x92795))))
% 160.93/160.65 [9470]P1(f334(f334(f336(f887(f882(x94701),f882(x94701))),f334(f334(f269(f882(x94701),f882(x94701)),f334(f334(f153(x94701),x94702),x94703)),f334(f334(f153(x94701),x94704),x94705))),f149(x94701,x94706)))+~P1(f334(f334(f336(f887(x94701,x94701)),f334(f334(f269(x94701,x94701),x94702),x94704)),x94706))
% 160.93/160.65 [9933]E(f334(f334(f269(x99331,x99332),f610(x99333,x99334,x99335,x99332,x99331,x99336)),f611(x99333,x99334,x99335,x99332,x99331,x99336)),x99336)+P1(f334(f334(f336(x99335),x99334),f334(f334(f273(x99331,x99332,f888(x99335,a876)),x99333),x99336)))
% 160.93/160.65 [9939]E(f334(f334(f269(x99391,x99392),f612(x99393,x99394,x99392,x99391,x99395,x99396)),f613(x99393,x99394,x99392,x99391,x99395,x99396)),x99393)+~P1(f334(f334(f336(x99396),x99395),f334(f334(f273(x99391,x99392,f888(x99396,a876)),x99394),x99393)))
% 160.93/160.65 [10097]P1(f334(f334(f336(x100971),x100972),f334(f334(x100973,f612(x100974,x100973,x100975,x100976,x100972,x100971)),f613(x100974,x100973,x100975,x100976,x100972,x100971))))+~P1(f334(f334(f336(x100971),x100972),f334(f334(f273(x100976,x100975,f888(x100971,a876)),x100973),x100974)))
% 160.93/160.65 [10116]~P1(f334(f334(f336(x101161),x101162),f334(f334(x101165,f610(x101165,x101162,x101161,x101164,x101163,x101166)),f611(x101165,x101162,x101161,x101164,x101163,x101166))))+P1(f334(f334(f336(x101161),x101162),f334(f334(f273(x101163,x101164,f888(x101161,a876)),x101165),x101166)))
% 160.93/160.65 [7858]P1(f334(f334(f336(x78581),x78584),x78586))+E(f190(x78581,x78582,f334(f334(f334(f72(x78581,f885(x78582)),x78583),x78584),x78585),x78586),f190(x78581,x78582,x78583,x78586))
% 160.93/160.65 [7935]P1(f334(f334(f336(x79351),x79354),x79356))+E(f334(f313(x79351,x79352,f334(f334(f334(f72(x79351,x79352),x79353),x79354),x79355)),x79356),f334(f313(x79351,x79352,x79353),x79356))
% 160.93/160.65 [7962]P1(f334(f334(f336(x79621),x79624),f334(f174(x79621),x79626)))+E(f334(f334(f156(x79621,x79622),f334(f334(f334(f72(x79621,x79622),x79623),x79624),x79625)),x79626),f334(f334(f156(x79621,x79622),x79623),x79626))
% 160.93/160.65 [8422]E(x84221,x84222)+E(f334(f334(f161(x84223,f334(f334(f161(x84223,x84224),x84221),x84225)),x84222),x84226),f334(f334(f161(x84223,f334(f334(f161(x84223,x84224),x84222),x84226)),x84221),x84225))
% 160.93/160.65 [8971]~P1(f334(f334(f336(x89713),x89716),x89715))+E(f334(f334(f312(x89711),x89712),f334(f313(x89713,x89711,x89714),f334(f334(f22(f888(x89713,a876)),x89715),f334(f334(f312(x89713),x89716),f196(f888(x89713,a876)))))),f334(f313(x89713,x89711,f334(f334(f334(f72(x89713,x89711),x89714),x89716),x89712)),x89715))
% 160.93/160.65 [9749]E(f189(x97491,x97492,x97493,f334(f334(f136(x97491),x97494),f334(f334(f153(x97491),x97495),f117(x97491))),x97496),f334(f334(f334(f72(x97491,f885(x97492)),f189(x97491,x97492,x97493,x97494,x97496)),x97495),f334(f241(x97492),f334(f334(f167(x97492),x97496),f334(f197(f882(x97491)),x97494)))))+~P1(f334(f334(f249(a881),f334(f197(f882(x97491)),x97494)),f334(f197(f882(x97492)),x97496)))
% 160.93/160.65 [8751]~E(x87513,x87516)+E(f334(f334(f180(x87511,x87512),f334(f334(f153(f887(x87511,x87512)),f334(f334(f269(x87511,x87512),x87513),x87514)),x87515)),x87516),f334(f241(x87512),x87514))
% 160.93/160.65 [8778]E(x87781,x87782)+E(f334(f334(f180(x87783,x87784),f334(f334(f153(f887(x87783,x87784)),f334(f334(f269(x87783,x87784),x87781),x87785)),x87786)),x87782),f334(f334(f180(x87783,x87784),x87786),x87782))
% 160.93/160.65 [9046]~P1(f334(f334(x90464,x90465),x90466))+P1(f334(f334(f334(f334(f114(f888(x90461,f888(x90462,a876))),x90463),x90464),x90465),x90466))
% 160.93/160.65 [9048]~P1(f334(f334(x90483,x90485),x90486))+P1(f334(f334(f334(f334(f114(f888(x90481,f888(x90482,a876))),x90483),x90484),x90485),x90486))
% 160.93/160.65 [9336]P1(f334(f334(x93361,x93362),x93363))+~P1(f334(f334(f334(f334(f105(f888(x93364,f888(x93365,a876))),x93366),x93361),x93362),x93363))
% 160.93/160.65 [9337]P1(f334(f334(x93371,x93372),x93373))+~P1(f334(f334(f334(f334(f105(f888(x93374,f888(x93375,a876))),x93371),x93376),x93372),x93373))
% 160.93/160.65 [9771]~P68(x97712)+E(f334(f334(f6(x97711,x97712),f334(f334(f7(x97711,f888(x97713,a876),x97712),f334(f334(f8(f888(x97713,x97712),f888(f888(x97713,a876),x97712),x97711),f6(x97713,x97712)),x97714)),x97715)),x97716),f334(f334(f6(f887(x97711,x97713),x97712),f334(f273(x97711,x97713,x97712),x97714)),f334(f334(f271(x97711,x97713),x97716),f334(f16(f888(x97713,a876),x97711),x97715))))
% 160.93/160.65 [9772]~P74(x97722)+E(f334(f334(f9(x97721,x97722),f334(f334(f7(x97721,f888(x97723,a876),x97722),f334(f334(f8(f888(x97723,x97722),f888(f888(x97723,a876),x97722),x97721),f9(x97723,x97722)),x97724)),x97725)),x97726),f334(f334(f9(f887(x97721,x97723),x97722),f334(f273(x97721,x97723,x97722),x97724)),f334(f334(f271(x97721,x97723),x97726),f334(f16(f888(x97723,a876),x97721),x97725))))
% 160.93/160.65 [9916]~P68(x99162)+E(f334(f334(f6(x99161,x99162),f334(f334(f7(x99161,f888(x99163,a876),x99162),f334(f334(f8(f888(x99163,x99162),f888(f888(x99163,a876),x99162),x99161),f6(x99163,x99162)),f334(f7(x99163,x99161,x99162),x99164))),x99165)),x99166),f334(f334(f6(x99163,x99162),f334(f334(f7(x99163,f888(x99161,a876),x99162),f334(f334(f8(f888(x99161,x99162),f888(f888(x99161,a876),x99162),x99163),f6(x99161,x99162)),x99164)),x99166)),x99165))
% 160.93/160.65 [9610]~P1(f334(f334(f336(x96101),x96105),x96104))+E(f334(f334(f334(f72(x96101,f885(x96102)),f190(x96101,x96102,x96103,f334(f334(f22(f888(x96101,a876)),x96104),f334(f334(f312(x96101),x96105),f196(f888(x96101,a876)))))),x96105),x96106),f190(x96101,x96102,f334(f334(f334(f72(x96101,f885(x96102)),x96103),x96105),x96106),x96104))
% 160.93/160.65 [10194]~P1(f334(f334(f336(f887(x101941,x101942)),f334(f334(f269(x101941,x101942),x101945),x101946)),f334(f334(f114(f888(f887(x101941,x101942),a876)),x101943),x101944)))+P1(f334(f334(f334(f334(f114(f888(x101941,f888(x101942,a876))),f334(f334(f7(x101941,f888(f887(x101941,x101942),a876),f888(x101942,a876)),f334(f334(f8(f888(x101942,f888(f888(f887(x101941,x101942),a876),a876)),f888(f888(f887(x101941,x101942),a876),f888(x101942,a876)),x101941),f7(x101942,f888(f887(x101941,x101942),a876),a876)),f334(f334(f8(f888(x101942,f887(x101941,x101942)),f888(x101942,f888(f888(f887(x101941,x101942),a876),a876)),x101941),f334(f8(f887(x101941,x101942),f888(f888(f887(x101941,x101942),a876),a876),x101942),f336(f887(x101941,x101942)))),f269(x101941,x101942)))),x101943)),f334(f334(f7(x101941,f888(f887(x101941,x101942),a876),f888(x101942,a876)),f334(f334(f8(f888(x101942,f888(f888(f887(x101941,x101942),a876),a876)),f888(f888(f887(x101941,x101942),a876),f888(x101942,a876)),x101941),f7(x101942,f888(f887(x101941,x101942),a876),a876)),f334(f334(f8(f888(x101942,f887(x101941,x101942)),f888(x101942,f888(f888(f887(x101941,x101942),a876),a876)),x101941),f334(f8(f887(x101941,x101942),f888(f888(f887(x101941,x101942),a876),a876),x101942),f336(f887(x101941,x101942)))),f269(x101941,x101942)))),x101944)),x101945),x101946))
% 160.93/160.65 [10195]~P1(f334(f334(f336(f887(x101951,x101952)),f334(f334(f269(x101951,x101952),x101955),x101956)),f334(f334(f105(f888(f887(x101951,x101952),a876)),x101953),x101954)))+P1(f334(f334(f334(f334(f105(f888(x101951,f888(x101952,a876))),f334(f334(f7(x101951,f888(f887(x101951,x101952),a876),f888(x101952,a876)),f334(f334(f8(f888(x101952,f888(f888(f887(x101951,x101952),a876),a876)),f888(f888(f887(x101951,x101952),a876),f888(x101952,a876)),x101951),f7(x101952,f888(f887(x101951,x101952),a876),a876)),f334(f334(f8(f888(x101952,f887(x101951,x101952)),f888(x101952,f888(f888(f887(x101951,x101952),a876),a876)),x101951),f334(f8(f887(x101951,x101952),f888(f888(f887(x101951,x101952),a876),a876),x101952),f336(f887(x101951,x101952)))),f269(x101951,x101952)))),x101953)),f334(f334(f7(x101951,f888(f887(x101951,x101952),a876),f888(x101952,a876)),f334(f334(f8(f888(x101952,f888(f888(f887(x101951,x101952),a876),a876)),f888(f888(f887(x101951,x101952),a876),f888(x101952,a876)),x101951),f7(x101952,f888(f887(x101951,x101952),a876),a876)),f334(f334(f8(f888(x101952,f887(x101951,x101952)),f888(x101952,f888(f888(f887(x101951,x101952),a876),a876)),x101951),f334(f8(f887(x101951,x101952),f888(f888(f887(x101951,x101952),a876),a876),x101952),f336(f887(x101951,x101952)))),f269(x101951,x101952)))),x101954)),x101955),x101956))
% 160.93/160.65 [10201]P1(f334(f334(f336(f887(x102011,x102012)),f334(f334(f269(x102011,x102012),x102013),x102014)),f334(f334(f114(f888(f887(x102011,x102012),a876)),x102015),x102016)))+~P1(f334(f334(f334(f334(f114(f888(x102011,f888(x102012,a876))),f334(f334(f7(x102011,f888(f887(x102011,x102012),a876),f888(x102012,a876)),f334(f334(f8(f888(x102012,f888(f888(f887(x102011,x102012),a876),a876)),f888(f888(f887(x102011,x102012),a876),f888(x102012,a876)),x102011),f7(x102012,f888(f887(x102011,x102012),a876),a876)),f334(f334(f8(f888(x102012,f887(x102011,x102012)),f888(x102012,f888(f888(f887(x102011,x102012),a876),a876)),x102011),f334(f8(f887(x102011,x102012),f888(f888(f887(x102011,x102012),a876),a876),x102012),f336(f887(x102011,x102012)))),f269(x102011,x102012)))),x102015)),f334(f334(f7(x102011,f888(f887(x102011,x102012),a876),f888(x102012,a876)),f334(f334(f8(f888(x102012,f888(f888(f887(x102011,x102012),a876),a876)),f888(f888(f887(x102011,x102012),a876),f888(x102012,a876)),x102011),f7(x102012,f888(f887(x102011,x102012),a876),a876)),f334(f334(f8(f888(x102012,f887(x102011,x102012)),f888(x102012,f888(f888(f887(x102011,x102012),a876),a876)),x102011),f334(f8(f887(x102011,x102012),f888(f888(f887(x102011,x102012),a876),a876),x102012),f336(f887(x102011,x102012)))),f269(x102011,x102012)))),x102016)),x102013),x102014))
% 160.93/160.65 [10202]P1(f334(f334(f336(f887(x102021,x102022)),f334(f334(f269(x102021,x102022),x102023),x102024)),f334(f334(f105(f888(f887(x102021,x102022),a876)),x102025),x102026)))+~P1(f334(f334(f334(f334(f105(f888(x102021,f888(x102022,a876))),f334(f334(f7(x102021,f888(f887(x102021,x102022),a876),f888(x102022,a876)),f334(f334(f8(f888(x102022,f888(f888(f887(x102021,x102022),a876),a876)),f888(f888(f887(x102021,x102022),a876),f888(x102022,a876)),x102021),f7(x102022,f888(f887(x102021,x102022),a876),a876)),f334(f334(f8(f888(x102022,f887(x102021,x102022)),f888(x102022,f888(f888(f887(x102021,x102022),a876),a876)),x102021),f334(f8(f887(x102021,x102022),f888(f888(f887(x102021,x102022),a876),a876),x102022),f336(f887(x102021,x102022)))),f269(x102021,x102022)))),x102025)),f334(f334(f7(x102021,f888(f887(x102021,x102022),a876),f888(x102022,a876)),f334(f334(f8(f888(x102022,f888(f888(f887(x102021,x102022),a876),a876)),f888(f888(f887(x102021,x102022),a876),f888(x102022,a876)),x102021),f7(x102022,f888(f887(x102021,x102022),a876),a876)),f334(f334(f8(f888(x102022,f887(x102021,x102022)),f888(x102022,f888(f888(f887(x102021,x102022),a876),a876)),x102021),f334(f8(f887(x102021,x102022),f888(f888(f887(x102021,x102022),a876),a876),x102022),f336(f887(x102021,x102022)))),f269(x102021,x102022)))),x102026)),x102023),x102024))
% 160.93/160.65 [10188]~P1(f334(f334(f336(f887(x101882,x101883)),f334(f334(f269(x101882,x101883),x101885),x101886)),f334(f334(f41(x101881,f888(f887(x101882,x101883),a876)),f257(f888(x101881,a876))),x101884)))+P1(f334(f334(f334(f334(f41(x101881,f888(x101882,f888(x101883,a876))),f257(f888(x101881,a876))),f334(f334(f8(f888(f887(x101882,x101883),a876),f888(x101882,f888(x101883,a876)),x101881),f334(f7(x101882,f888(f887(x101882,x101883),a876),f888(x101883,a876)),f334(f334(f8(f888(x101883,f888(f888(f887(x101882,x101883),a876),a876)),f888(f888(f887(x101882,x101883),a876),f888(x101883,a876)),x101882),f7(x101883,f888(f887(x101882,x101883),a876),a876)),f334(f334(f8(f888(x101883,f887(x101882,x101883)),f888(x101883,f888(f888(f887(x101882,x101883),a876),a876)),x101882),f334(f8(f887(x101882,x101883),f888(f888(f887(x101882,x101883),a876),a876),x101883),f336(f887(x101882,x101883)))),f269(x101882,x101883))))),x101884)),x101885),x101886))
% 160.93/160.65 [10189]~P1(f334(f334(f336(f887(x101892,x101893)),f334(f334(f269(x101892,x101893),x101895),x101896)),f334(f334(f42(x101891,f888(f887(x101892,x101893),a876)),f257(f888(x101891,a876))),x101894)))+P1(f334(f334(f334(f334(f42(x101891,f888(x101892,f888(x101893,a876))),f257(f888(x101891,a876))),f334(f334(f8(f888(f887(x101892,x101893),a876),f888(x101892,f888(x101893,a876)),x101891),f334(f7(x101892,f888(f887(x101892,x101893),a876),f888(x101893,a876)),f334(f334(f8(f888(x101893,f888(f888(f887(x101892,x101893),a876),a876)),f888(f888(f887(x101892,x101893),a876),f888(x101893,a876)),x101892),f7(x101893,f888(f887(x101892,x101893),a876),a876)),f334(f334(f8(f888(x101893,f887(x101892,x101893)),f888(x101893,f888(f888(f887(x101892,x101893),a876),a876)),x101892),f334(f8(f887(x101892,x101893),f888(f888(f887(x101892,x101893),a876),a876),x101893),f336(f887(x101892,x101893)))),f269(x101892,x101893))))),x101894)),x101895),x101896))
% 160.93/160.65 [10198]P1(f334(f334(f336(f887(x101981,x101982)),f334(f334(f269(x101981,x101982),x101983),x101984)),f334(f334(f41(x101985,f888(f887(x101981,x101982),a876)),f257(f888(x101985,a876))),x101986)))+~P1(f334(f334(f334(f334(f41(x101985,f888(x101981,f888(x101982,a876))),f257(f888(x101985,a876))),f334(f334(f8(f888(f887(x101981,x101982),a876),f888(x101981,f888(x101982,a876)),x101985),f334(f7(x101981,f888(f887(x101981,x101982),a876),f888(x101982,a876)),f334(f334(f8(f888(x101982,f888(f888(f887(x101981,x101982),a876),a876)),f888(f888(f887(x101981,x101982),a876),f888(x101982,a876)),x101981),f7(x101982,f888(f887(x101981,x101982),a876),a876)),f334(f334(f8(f888(x101982,f887(x101981,x101982)),f888(x101982,f888(f888(f887(x101981,x101982),a876),a876)),x101981),f334(f8(f887(x101981,x101982),f888(f888(f887(x101981,x101982),a876),a876),x101982),f336(f887(x101981,x101982)))),f269(x101981,x101982))))),x101986)),x101983),x101984))
% 160.93/160.65 [10199]P1(f334(f334(f336(f887(x101991,x101992)),f334(f334(f269(x101991,x101992),x101993),x101994)),f334(f334(f42(x101995,f888(f887(x101991,x101992),a876)),f257(f888(x101995,a876))),x101996)))+~P1(f334(f334(f334(f334(f42(x101995,f888(x101991,f888(x101992,a876))),f257(f888(x101995,a876))),f334(f334(f8(f888(f887(x101991,x101992),a876),f888(x101991,f888(x101992,a876)),x101995),f334(f7(x101991,f888(f887(x101991,x101992),a876),f888(x101992,a876)),f334(f334(f8(f888(x101992,f888(f888(f887(x101991,x101992),a876),a876)),f888(f888(f887(x101991,x101992),a876),f888(x101992,a876)),x101991),f7(x101992,f888(f887(x101991,x101992),a876),a876)),f334(f334(f8(f888(x101992,f887(x101991,x101992)),f888(x101992,f888(f888(f887(x101991,x101992),a876),a876)),x101991),f334(f8(f887(x101991,x101992),f888(f888(f887(x101991,x101992),a876),a876),x101992),f336(f887(x101991,x101992)))),f269(x101991,x101992))))),x101996)),x101993),x101994))
% 160.93/160.65 [7415]E(f334(x74151,f334(x74152,x74153)),f334(x74154,x74153))+~E(f334(f73(x74155,x74156,x74157,x74151),x74152),x74154)
% 160.93/160.65 [9640]~P24(x96403,x96404,x96401,x96405,x96406,x96407)+E(f334(f334(x96401,x96402),x96402),x96402)
% 160.93/160.65 [10013]~E(f334(f243(f885(x100137),x100131,f210(x100137),x100135),f334(x100134,x100133)),f334(f241(x100137),x100132))+E(f334(f241(x100131),f773(x100132,x100133,x100134,x100135,x100136,x100137,x100131)),f334(x100134,x100133))
% 160.93/160.65 [10014]~E(f334(f243(f885(x100146),x100147,f210(x100146),x100141),f334(x100144,x100143)),f334(f241(x100146),x100142))+E(f334(x100141,f773(x100142,x100143,x100144,x100141,x100145,x100146,x100147)),f334(f241(x100146),x100142))
% 160.93/160.65 [5987]~E(f334(f334(f156(x59871,x59875),x59876),x59872),f334(f334(f156(x59873,x59875),x59877),x59874))+E(f334(f197(f882(x59871)),x59872),f334(f197(f882(x59873)),x59874))
% 160.93/160.65 [7492]E(x74921,x74922)+~E(f334(f334(f334(f72(x74923,f885(x74924)),x74925),x74926),f334(f241(x74924),x74921)),f334(f334(f334(f72(x74923,f885(x74924)),x74927),x74926),f334(f241(x74924),x74922)))
% 160.93/160.65 [8455]E(f334(x84551,f334(x84552,x84553)),f334(x84554,x84553))+~E(f334(f73(x84555,x84556,x84557,x84551),x84552),f334(f73(x84556,x84556,x84557,f34(x84556)),x84554))
% 160.93/160.65 [8797]~P36(x87974,x87975,x87971,f334(f334(f153(x87974),x87972),x87976),f334(f334(f153(x87975),x87973),x87977))+P1(f334(f334(x87971,x87972),x87973))
% 160.93/160.65 [9182]P36(x91821,x91822,x91823,x91824,x91825)+~P36(x91821,x91822,x91823,f334(f334(f153(x91821),x91826),x91824),f334(f334(f153(x91822),x91827),x91825))
% 160.93/160.65 [9810]P1(f334(f334(x98101,x98102),f561(x98103,x98102,x98104,x98101)))+~P1(f334(f334(f270(x98105,x98106,x98107,x98101,x98104),x98102),x98103))
% 160.93/160.65 [9831]P1(f334(f334(x98311,f561(x98312,x98313,x98311,x98314)),x98312))+~P1(f334(f334(f270(x98315,x98316,x98317,x98314,x98311),x98313),x98312))
% 160.93/160.65 [6031]E(x60311,x60312)+~E(f334(f334(f334(f92(x60313),x60314),x60315),x60311),f334(f334(f334(f92(x60313),x60316),x60317),x60312))
% 160.93/160.65 [6032]E(x60321,x60322)+~E(f334(f334(f334(f92(x60323),x60324),x60321),x60325),f334(f334(f334(f92(x60323),x60326),x60322),x60327))
% 160.93/160.65 [6033]E(x60331,x60332)+~E(f334(f334(f334(f92(x60333),x60331),x60334),x60335),f334(f334(f334(f92(x60333),x60332),x60336),x60337))
% 160.93/160.65 [8915]~P22(x89156,x89151,x89153,x89157)+E(f334(f73(x89151,x89151,x89152,f334(x89153,x89154)),f334(f73(x89151,x89151,x89152,f334(x89153,x89154)),x89155)),f334(f73(x89151,x89151,x89152,f334(x89153,x89154)),x89155))
% 160.93/160.65 [9288]~P36(x92883,x92882,x92884,f334(f334(f156(x92881,x92883),x92885),x92886),x92887)+P36(x92881,x92882,f334(f334(f8(x92883,f888(x92882,a876),x92881),x92884),x92885),x92886,x92887)
% 160.93/160.65 [9311]P36(x93111,x93112,x93113,f334(f334(f156(x93114,x93111),x93115),x93116),x93117)+~P36(x93114,x93112,f334(f334(f8(x93111,f888(x93112,a876),x93114),x93113),x93115),x93116,x93117)
% 160.93/160.65 [9729]E(f189(x97291,x97292,f334(f334(f334(f72(x97291,f885(x97292)),x97293),x97294),f334(f241(x97292),x97295)),x97296,x97297),f334(f334(f334(f72(x97291,f885(x97292)),f189(x97291,x97292,x97293,x97296,x97297)),x97294),f334(f241(x97292),x97295)))+P1(f334(f334(f336(x97291),x97294),f334(f174(x97291),x97296)))
% 160.93/160.65 [8914]~P1(f334(f334(f336(x89141),x89142),f334(f334(x89145,x89146),x89147)))+P1(f334(f334(f336(x89141),x89142),f334(f334(f273(x89143,x89144,f888(x89141,a876)),x89145),f334(f334(f269(x89143,x89144),x89146),x89147))))
% 160.93/160.65 [9208]P1(f334(f334(f334(x92081,x92082),x92083),x92084))+~P1(f334(f334(f334(f273(x92085,x92086,f888(x92087,a876)),x92081),f334(f334(f269(x92085,x92086),x92082),x92083)),x92084))
% 160.93/160.65 [9350]P1(f334(f334(f336(x93501),f334(f334(x93502,x93503),x93504)),f334(f313(f887(x93505,x93506),x93501,f334(f273(x93505,x93506,x93501),x93502)),x93507)))+~P1(f334(f334(f336(f887(x93505,x93506)),f334(f334(f269(x93505,x93506),x93503),x93504)),x93507))
% 160.93/160.65 [9689]P1(f334(f334(f336(f887(f882(x96891),f882(x96891))),f334(f334(f269(f882(x96891),f882(x96891)),f334(f334(f136(x96891),x96892),f334(f334(f153(x96891),x96893),x96894))),f334(f334(f136(x96891),x96892),f334(f334(f153(x96891),x96895),x96896)))),f149(x96891,x96897)))+~P1(f334(f334(f336(f887(x96891,x96891)),f334(f334(f269(x96891,x96891),x96893),x96895)),x96897))
% 160.93/160.65 [9751]~P36(x97511,x97513,x97514,x97516,f334(f334(f156(x97512,x97513),x97515),x97517))+P36(x97511,x97512,f334(f334(f7(x97511,f888(x97512,x97513),f888(x97512,a876)),f334(f334(f8(f888(x97513,a876),f888(f888(x97512,x97513),f888(x97512,a876)),x97511),f8(x97513,a876,x97512)),x97514)),x97515),x97516,x97517)
% 160.93/160.65 [9835]P36(x98351,x98352,x98353,x98354,f334(f334(f156(x98355,x98352),x98356),x98357))+~P36(x98351,x98355,f334(f334(f7(x98351,f888(x98355,x98352),f888(x98355,a876)),f334(f334(f8(f888(x98352,a876),f888(f888(x98355,x98352),f888(x98355,a876)),x98351),f8(x98352,a876,x98355)),x98353)),x98356),x98354,x98357)
% 160.93/160.65 [9200]E(x92001,x92002)+E(f334(f334(f334(f72(x92003,x92004),f334(f334(f334(f72(x92003,x92004),x92005),x92001),x92006)),x92002),x92007),f334(f334(f334(f72(x92003,x92004),f334(f334(f334(f72(x92003,x92004),x92005),x92002),x92007)),x92001),x92006))
% 160.93/160.65 [9444]E(f189(x94441,x94442,f334(f334(f334(f72(x94441,f885(x94442)),x94443),x94444),f334(f241(x94442),x94445)),x94446,x94447),f189(x94441,x94442,x94443,x94446,x94447))+~P1(f334(f334(f336(x94441),x94444),f334(f174(x94441),f334(f334(f177(x94441),f334(f197(f882(x94442)),x94447)),x94446))))
% 160.93/160.65 [9762]E(f189(x97621,x97622,f334(f334(f334(f72(x97621,f885(x97622)),x97623),x97624),f334(f241(x97622),x97625)),x97626,x97627),f334(f334(f334(f72(x97621,f885(x97622)),f189(x97621,x97622,x97623,x97626,x97627)),x97624),f334(f241(x97622),x97625)))+P1(f334(f334(f336(x97621),x97624),f334(f174(x97621),f334(f334(f177(x97621),f334(f197(f882(x97622)),x97627)),x97626))))
% 160.93/160.65 [10127]P1(f334(f334(f336(x101271),f496(x101272,x101273,x101274,x101275,x101276,x101277,x101271)),x101275))+P1(f334(f334(f334(f334(f42(x101271,f888(x101277,f888(x101276,a876))),x101275),x101274),x101273),x101272))
% 160.93/160.65 [10128]P1(f334(f334(f336(x101281),f840(x101282,x101283,x101284,x101285,x101286,x101287,x101281)),x101285))+~P1(f334(f334(f334(f334(f41(x101281,f888(x101287,f888(x101286,a876))),x101285),x101284),x101283),x101282))
% 160.93/160.65 [10153]P1(f334(f334(f334(x101531,f840(x101532,x101533,x101531,x101534,x101535,x101536,x101537)),x101533),x101532))+~P1(f334(f334(f334(f334(f41(x101537,f888(x101536,f888(x101535,a876))),x101534),x101531),x101533),x101532))
% 160.93/160.65 [10170]~P1(f334(f334(f334(x101705,f496(x101707,x101706,x101705,x101704,x101703,x101702,x101701)),x101706),x101707))+P1(f334(f334(f334(f334(f42(x101701,f888(x101702,f888(x101703,a876))),x101704),x101705),x101706),x101707))
% 160.93/160.65 [10187]~P1(f334(f334(f336(f887(x101871,x101873)),f334(f334(f269(x101871,x101873),x101876),x101877)),f334(f334(f291(x101871,x101872,x101873),x101874),x101875)))+P1(f334(f334(f270(x101871,x101872,x101873,f334(f334(f7(x101871,f888(f887(x101871,x101872),a876),f888(x101872,a876)),f334(f334(f8(f888(x101872,f888(f888(f887(x101871,x101872),a876),a876)),f888(f888(f887(x101871,x101872),a876),f888(x101872,a876)),x101871),f7(x101872,f888(f887(x101871,x101872),a876),a876)),f334(f334(f8(f888(x101872,f887(x101871,x101872)),f888(x101872,f888(f888(f887(x101871,x101872),a876),a876)),x101871),f334(f8(f887(x101871,x101872),f888(f888(f887(x101871,x101872),a876),a876),x101872),f336(f887(x101871,x101872)))),f269(x101871,x101872)))),x101874),f334(f334(f7(x101872,f888(f887(x101872,x101873),a876),f888(x101873,a876)),f334(f334(f8(f888(x101873,f888(f888(f887(x101872,x101873),a876),a876)),f888(f888(f887(x101872,x101873),a876),f888(x101873,a876)),x101872),f7(x101873,f888(f887(x101872,x101873),a876),a876)),f334(f334(f8(f888(x101873,f887(x101872,x101873)),f888(x101873,f888(f888(f887(x101872,x101873),a876),a876)),x101872),f334(f8(f887(x101872,x101873),f888(f888(f887(x101872,x101873),a876),a876),x101873),f336(f887(x101872,x101873)))),f269(x101872,x101873)))),x101875)),x101876),x101877))
% 160.93/160.65 [10197]P1(f334(f334(f336(f887(x101971,x101972)),f334(f334(f269(x101971,x101972),x101973),x101974)),f334(f334(f291(x101971,x101975,x101972),x101976),x101977)))+~P1(f334(f334(f270(x101971,x101975,x101972,f334(f334(f7(x101971,f888(f887(x101971,x101975),a876),f888(x101975,a876)),f334(f334(f8(f888(x101975,f888(f888(f887(x101971,x101975),a876),a876)),f888(f888(f887(x101971,x101975),a876),f888(x101975,a876)),x101971),f7(x101975,f888(f887(x101971,x101975),a876),a876)),f334(f334(f8(f888(x101975,f887(x101971,x101975)),f888(x101975,f888(f888(f887(x101971,x101975),a876),a876)),x101971),f334(f8(f887(x101971,x101975),f888(f888(f887(x101971,x101975),a876),a876),x101975),f336(f887(x101971,x101975)))),f269(x101971,x101975)))),x101976),f334(f334(f7(x101975,f888(f887(x101975,x101972),a876),f888(x101972,a876)),f334(f334(f8(f888(x101972,f888(f888(f887(x101975,x101972),a876),a876)),f888(f888(f887(x101975,x101972),a876),f888(x101972,a876)),x101975),f7(x101972,f888(f887(x101975,x101972),a876),a876)),f334(f334(f8(f888(x101972,f887(x101975,x101972)),f888(x101972,f888(f888(f887(x101975,x101972),a876),a876)),x101975),f334(f8(f887(x101975,x101972),f888(f888(f887(x101975,x101972),a876),a876),x101972),f336(f887(x101975,x101972)))),f269(x101975,x101972)))),x101977)),x101973),x101974))
% 160.93/160.65 [10137]~P141(x101372)+E(f334(f334(f6(x101371,x101372),f334(f334(f7(x101371,f888(x101373,a876),x101372),f334(f334(f8(f888(x101373,x101372),f888(f888(x101373,a876),x101372),x101371),f6(x101373,x101372)),f334(f334(f7(x101371,f888(x101373,x101372),f888(x101373,x101372)),f334(f334(f8(f888(x101372,x101372),f888(f888(x101373,x101372),f888(x101373,x101372)),x101371),f8(x101372,x101372,x101373)),f334(f334(f8(x101372,f888(x101372,x101372),x101371),f81(x101372)),x101374))),x101375))),x101376)),x101377),f334(f334(f81(x101372),f334(f334(f6(x101371,x101372),x101374),x101377)),f334(f334(f6(x101373,x101372),x101375),x101376)))
% 160.93/160.65 [9241]~P21(x92417,x92411,x92413,x92418)+E(f334(f73(x92411,x92411,x92412,f334(x92413,x92414)),f334(f73(x92411,x92411,x92412,f334(x92413,x92415)),x92416)),f334(f73(x92411,x92411,x92412,f334(x92413,x92415)),f334(f73(x92411,x92411,x92412,f334(x92413,x92414)),x92416)))
% 160.93/160.65 [10192]E(f334(f334(f269(x101921,x101922),f334(x101923,f588(x101924,x101925,x101923,x101926,x101927,x101928,x101922,x101921))),f334(x101925,f589(x101924,x101925,x101923,x101926,x101927,x101928,x101922,x101921))),x101928)+~P1(f334(f334(f336(f887(x101921,x101922)),x101928),f334(f313(f887(x101927,x101926),f887(x101921,x101922),f274(x101927,x101921,x101926,x101922,x101923,x101925)),x101924)))
% 160.93/160.65 [10208]~P1(f334(f334(f336(f887(x102088,x102087)),x102086),f334(f313(f887(x102081,x102082),f887(x102088,x102087),f274(x102081,x102088,x102082,x102087,x102085,x102084)),x102083)))+P1(f334(f334(f336(f887(x102081,x102082)),f334(f334(f269(x102081,x102082),f588(x102083,x102084,x102085,x102082,x102081,x102086,x102087,x102088)),f589(x102083,x102084,x102085,x102082,x102081,x102086,x102087,x102088))),x102083))
% 160.93/160.65 [9679]P1(f334(f334(f336(f887(f887(x96791,x96792),f887(x96791,x96792))),f334(f334(f269(f887(x96791,x96792),f887(x96791,x96792)),f334(f334(f269(x96791,x96792),x96793),x96794)),f334(f334(f269(x96791,x96792),x96795),x96796))),f326(x96791,x96792,x96797,x96798)))+~P1(f334(f334(f336(f887(x96791,x96791)),f334(f334(f269(x96791,x96791),x96793),x96795)),x96797))
% 160.93/160.65 [10180]E(f334(f144(x101801,x101802,f334(f7(x101802,x101801,x101801),x101803),f334(x101804,x101805)),x101806),f334(x101804,f334(f144(x101807,x101802,f334(f7(x101802,x101807,x101807),x101808),x101805),x101806)))+P1(f334(f334(f336(x101802),f777(x101805,x101808,x101804,x101803,x101807,x101801,x101806,x101802)),f334(f174(x101802),x101806)))
% 160.93/160.65 [10200]~E(f334(f73(x102001,x102001,x102007,f334(x102003,f777(x102005,x102008,x102004,x102003,x102007,x102001,x102006,x102002))),x102004),f334(f73(x102007,x102001,x102007,x102004),f334(x102008,f777(x102005,x102008,x102004,x102003,x102007,x102001,x102006,x102002))))+E(f334(f144(x102001,x102002,f334(f7(x102002,x102001,x102001),x102003),f334(x102004,x102005)),x102006),f334(x102004,f334(f144(x102007,x102002,f334(f7(x102002,x102007,x102007),x102008),x102005),x102006)))
% 160.93/160.65 [8461]E(f334(x84611,f334(x84612,x84613)),f334(x84614,f334(x84615,x84613)))+~E(f334(f73(x84616,x84617,x84618,x84611),x84612),f334(f73(x84619,x84617,x84618,x84614),x84615))
% 160.93/160.65 [10066]P1(f334(f334(f336(f887(x100661,x100662)),f334(f334(f269(x100661,x100662),f334(x100663,x100664)),f334(x100665,x100666))),f334(f313(f887(x100667,x100668),f887(x100661,x100662),f274(x100667,x100661,x100668,x100662,x100663,x100665)),x100669)))+~P1(f334(f334(f336(f887(x100667,x100668)),f334(f334(f269(x100667,x100668),x100664),x100666)),x100669))
% 160.93/160.65 [8745]~E(f334(x87454,f334(x87455,x87456)),f334(x87459,f334(x874510,x874511)))+E(f334(f334(f73(x87451,x87452,x87453,x87454),x87455),x87456),f334(f334(f73(x87457,x87452,x87458,x87459),x874510),x874511))
% 160.93/160.65 [4591]~P100(x45911)+~P108(x45911)+E(f105(x45911),f246(x45911))
% 160.93/160.65 [4592]~P99(x45921)+~P108(x45921)+E(f114(x45921),f247(x45921))
% 160.93/160.65 [4835]~P111(x48351)+~P93(x48351)+E(f334(f75(x48351),f334(f107(x48351),a101)),f78(x48351))
% 160.93/160.65 [5110]E(x51101,f2(a1))+E(f82(a1,x51101),f334(f79(a1),f78(a1)))+P1(f334(f334(f249(a1),f2(a1)),x51101))
% 160.93/160.65 [5323]E(x53231,f2(a1))+E(f82(a1,x53231),f78(a1))+~P1(f334(f334(f249(a1),f2(a1)),x53231))
% 160.93/160.65 [7306]~P40(x73061)+P1(f334(f61(a1),x73061))+~P1(f334(f61(a881),f334(f313(a1,a881,a108),x73061)))
% 160.93/160.65 [8570]~P9(a5000)+~P1(f334(f334(f336(f887(a879,a878)),x85701),f334(f174(f887(a879,a878)),a27)))+P1(f334(f334(f273(a879,a878,a876),f334(f16(f888(a878,a876),a879),a25)),x85701))
% 160.93/160.65 [9639]E(x96391,f196(f888(f887(a881,a881),a876)))+~P1(f334(f61(f887(a881,a881)),x96391))+P1(f334(f334(f336(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f334(f334(f269(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),f196(f888(f887(a881,a881),a876))),x96391)),a36))
% 160.93/160.65 [9811]E(x98111,f2(a881))+E(x98111,f334(a116,f2(a881)))+~P1(f334(f334(f249(a881),x98111),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))
% 160.93/160.65 [10094]E(x100941,f2(a103))+E(f334(f334(f80(a1),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f334(a20,f334(f334(f38(a103),x100941),f334(f107(a103),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))))),f78(a1)),f334(a20,x100941))+E(f44(a103,x100941,f334(f107(a103),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f2(a103))
% 160.93/160.65 [9944]E(x99441,f2(a103))+~E(f44(a103,x99441,f334(f107(a103),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f2(a103))+E(f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f334(a20,f334(f334(f38(a103),x99441),f334(f107(a103),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))),f334(a20,x99441))
% 160.93/160.65 [4664]~P55(x46641,x46642)+P45(x46641,x46642)+~P46(a876)
% 160.93/160.65 [4601]~P142(x46011)+P32(x46011,x46012)+~E(x46012,f2(x46011))
% 160.93/160.65 [4602]~P108(x46021)+P16(x46021,x46022)+~E(x46022,f117(x46021))
% 160.93/160.65 [4611]~P111(x46111)+~E(x46112,f2(x46111))+E(f82(x46111,x46112),f2(x46111))
% 160.93/160.65 [4612]~P88(x46121)+~E(x46122,f2(x46121))+E(f82(x46121,x46122),f2(x46121))
% 160.93/160.65 [4620]~P142(x46202)+~P32(x46202,x46201)+E(x46201,f2(x46202))
% 160.93/160.65 [4654]~P111(x46542)+~E(f82(x46542,x46541),f2(x46542))+E(x46541,f2(x46542))
% 160.93/160.65 [4671]~P4(x46712)+~P4(x46711)+P4(f888(x46711,x46712))
% 160.93/160.65 [4672]~P4(x46722)+~P4(x46721)+P4(f886(x46721,x46722))
% 160.93/160.65 [4673]~P4(x46732)+~P4(x46731)+P4(f887(x46731,x46732))
% 160.93/160.65 [4674]~P6(x46742)+~P6(x46741)+P6(f203(x46741,x46742))
% 160.93/160.65 [4675]~P144(x46752)+~P144(x46751)+P144(f887(x46751,x46752))
% 160.93/160.65 [4676]~P60(x46762)+~P60(x46761)+P60(f888(x46761,x46762))
% 160.93/160.65 [4677]~P60(x46772)+~P60(x46771)+P60(f886(x46771,x46772))
% 160.93/160.65 [4678]~P60(x46782)+~P60(x46781)+P60(f887(x46781,x46782))
% 160.93/160.65 [4679]~P60(x46791)+~P92(x46792)+P92(f888(x46791,x46792))
% 160.93/160.65 [4680]~P103(x46802)+~P103(x46801)+P103(f887(x46801,x46802))
% 160.93/160.65 [4806]~P108(x48061)+~P16(x48061,x48062)+P16(x48061,f154(x48061,x48062))
% 160.93/160.65 [5043]~P6(x50432)+~P6(x50431)+P6(f44(a1,x50431,x50432))
% 160.93/160.65 [4622]~P75(x46221)+~E(x46222,f2(x46221))+E(f334(f79(x46221),x46222),x46222)
% 160.93/160.65 [4626]~P139(x46261)+~E(x46262,f2(a1))+E(f334(f106(x46261),x46262),f2(x46261))
% 160.93/160.65 [4627]~P90(x46271)+~E(x46272,f2(a1))+E(f334(f106(x46271),x46272),f2(x46271))
% 160.93/160.65 [4651]~P66(x46511)+~E(f2(x46511),x46512)+E(f334(f79(x46511),x46512),f2(x46511))
% 160.93/160.65 [4652]~P85(x46521)+~E(x46522,f2(x46521))+E(f334(f75(x46521),x46522),f2(x46521))
% 160.93/160.65 [4653]~P66(x46531)+~E(x46532,f2(x46531))+E(f334(f79(x46531),x46532),f2(x46531))
% 160.93/160.65 [4682]~P75(x46822)+E(x46821,f2(x46822))+~E(f334(f79(x46822),x46821),x46821)
% 160.93/160.65 [4688]E(x46881,f334(a108,x46882))+~E(x46881,f2(a881))+~E(x46882,f334(f104(a1),x46881))
% 160.93/160.65 [4689]E(f334(a108,x46891),x46892)+~E(x46892,f2(a881))+~E(x46891,f334(f104(a1),x46892))
% 160.93/160.65 [4693]~P90(x46932)+E(x46931,f2(a1))+~E(f334(f106(x46932),x46931),f2(x46932))
% 160.93/160.65 [4698]~P85(x46982)+E(x46981,f2(x46982))+~E(f334(f75(x46982),x46981),f2(x46982))
% 160.93/160.65 [4699]~P66(x46992)+E(x46991,f2(x46992))+~E(f334(f79(x46992),x46991),f2(x46992))
% 160.93/160.65 [4700]~P66(x47001)+E(f2(x47001),x47002)+~E(f334(f79(x47001),x47002),f2(x47001))
% 160.93/160.65 [4840]~P9(a5000)+~E(f334(a28,x48402),f334(f241(a878),x48401))+P1(f334(a25,x48401))
% 160.93/160.65 [4882]~P108(x48821)+~P16(x48821,x48822)+P16(x48821,f334(f173(x48821),x48822))
% 160.93/160.65 [4908]~P1(x49082)+~P1(x49081)+P1(f334(f334(a332,x49081),x49082))
% 160.93/160.65 [4940]~E(f78(a881),f2(a881))+E(f334(f37(x49401),x49402),f2(a881))+~P1(f334(f61(x49401),x49402))
% 160.93/160.65 [4973]~P141(x49731)+~P113(x49731)+E(f334(f334(f259(x49731),f2(x49731)),f334(a116,x49732)),f2(x49731))
% 160.93/160.65 [5011]~P108(x50111)+P16(x50111,f141(x50111,x50112))+~P1(f334(f61(x50111),x50112))
% 160.93/160.65 [5012]~P108(x50121)+P16(x50121,f765(x50122,x50121))+~P1(f334(f61(x50121),x50122))
% 160.93/160.65 [5033]~P108(x50331)+E(f334(f174(x50331),f141(x50331,x50332)),x50332)+~P1(f334(f61(x50331),x50332))
% 160.93/160.65 [5034]~P108(x50341)+E(f334(f174(x50341),f765(x50342,x50341)),x50342)+~P1(f334(f61(x50341),x50342))
% 160.93/160.65 [5063]P1(x50631)+P1(x50632)+~P1(f334(f334(a333,x50632),x50631))
% 160.93/160.65 [5075]E(x50751,f196(f888(x50752,a876)))+~E(f334(f37(x50752),x50751),f2(a881))+~P1(f334(f61(x50752),x50751))
% 160.93/160.65 [5080]P1(x50801)+~P1(x50802)+~P1(f334(f334(a337,x50802),x50801))
% 160.93/160.65 [5128]~P73(x51281)+E(f334(f75(x51281),x51282),x51282)+P1(f334(f334(f249(x51281),x51282),f2(x51281)))
% 160.93/160.65 [5198]~P60(x51982)+~P1(f334(f57(x51982),x51981))+P1(f334(x51981,f723(x51981,x51982)))
% 160.93/160.65 [5199]~P60(x51992)+~P1(f334(f57(x51992),x51991))+P1(f334(x51991,f732(x51991,x51992)))
% 160.93/160.65 [5227]~P1(f334(a25,x52272))+~P1(f334(a25,x52271))+P1(f334(a25,f33(x52271,x52272)))
% 160.93/160.65 [5236]E(x52361,f117(x52362))+P1(f334(f139(x52362),f118(x52362,x52361)))+~P1(f334(f139(x52362),x52361))
% 160.93/160.65 [5241]~P108(x52411)+~P1(f334(f61(x52411),x52412))+P1(f334(f139(x52411),f141(x52411,x52412)))
% 160.93/160.65 [5242]~P108(x52421)+~P1(f334(f61(x52421),x52422))+P1(f334(f139(x52421),f765(x52422,x52421)))
% 160.93/160.65 [5248]~P139(x52481)+E(f334(f104(x52481),f334(a108,x52482)),f334(f106(x52481),x52482))+P1(f334(f334(f249(a1),x52482),f2(a1)))
% 160.93/160.65 [5275]P7(x52752,x52751)+E(f334(x52751,f534(x52751)),f334(x52751,f537(x52751)))+P1(f334(f334(x52751,f534(x52751)),f537(x52751)))
% 160.93/160.65 [5289]E(f334(f104(a1),f411(x52891,x52892)),x52891)+P1(f334(x52892,f334(a108,x52891)))+~P1(f334(x52892,f2(a881)))
% 160.93/160.65 [5301]~P60(x53011)+~P1(f334(x53012,f733(x53012,x53011)))+P1(f334(f58(x53011),x53012))
% 160.93/160.65 [5302]~P60(x53021)+~P1(f334(x53022,f734(x53022,x53021)))+P1(f334(f58(x53021),x53022))
% 160.93/160.65 [5316]~P60(x53162)+~P37(x53162,x53161,f55(x53162))+P1(f334(x53161,f783(x53161,x53162)))
% 160.93/160.65 [5332]~P111(x53321)+~E(f82(x53321,x53322),f334(f79(x53321),f78(x53321)))+P1(f334(f334(f249(x53321),x53322),f2(x53321)))
% 160.93/160.65 [5408]~E(x54082,f2(a1))+E(f228(x54081,x54082),f334(f334(f269(a1,a1),f2(a1)),f78(a1)))+P1(f334(f334(f249(a1),x54082),f2(a1)))
% 160.93/160.65 [5409]~E(x54091,f2(a1))+E(f228(x54091,x54092),f334(f334(f269(a1,a1),f2(a1)),f78(a1)))+P1(f334(f334(f249(a1),x54092),f2(a1)))
% 160.93/160.65 [5461]E(f334(f104(a1),f411(x54611,x54612)),x54611)+P1(f334(x54612,f334(a108,x54611)))+P1(f334(f334(f249(a1),x54611),f2(a1)))
% 160.93/160.65 [5524]~P111(x55241)+E(f82(x55241,x55242),f334(f79(x55241),f78(x55241)))+~P1(f334(f334(f249(x55241),x55242),f2(x55241)))
% 160.93/160.65 [5525]~P85(x55251)+E(f334(f75(x55251),x55252),f334(f79(x55251),x55252))+~P1(f334(f334(f249(x55251),x55252),f2(x55251)))
% 160.93/160.65 [5526]~P85(x55261)+E(f334(f75(x55261),x55262),f334(f79(x55261),x55262))+~P1(f334(f334(f248(x55261),x55262),f2(x55261)))
% 160.93/160.65 [5527]~P73(x55271)+E(f334(f75(x55271),x55272),f334(f79(x55271),x55272))+~P1(f334(f334(f249(x55271),x55272),f2(x55271)))
% 160.93/160.65 [5622]~P1(f334(x56221,f411(x56222,x56221)))+P1(f334(x56221,f334(a108,x56222)))+~P1(f334(x56221,f2(a881)))
% 160.93/160.65 [5629]E(x56291,f2(a881))+E(f334(a116,f848(x56292,x56291)),x56291)+~P1(f334(f334(f249(a881),x56291),f334(a116,x56292)))
% 160.93/160.65 [5633]P7(x56331,x56332)+~E(f334(x56332,f534(x56332)),f334(x56332,f537(x56332)))+~P1(f334(f334(x56332,f534(x56332)),f537(x56332)))
% 160.93/160.65 [5653]~P108(x56531)+P16(x56531,x56532)+P1(f334(f334(f248(a881),f749(x56532,x56531)),f750(x56532,x56531)))
% 160.93/160.65 [5654]~P108(x56541)+P16(x56541,x56542)+P1(f334(f334(f248(a881),f756(x56542,x56541)),f761(x56542,x56541)))
% 160.93/160.65 [5741]~P85(x57411)+~E(x57412,f2(x57411))+P1(f334(f334(f248(x57411),f334(f75(x57411),x57412)),f2(x57411)))
% 160.93/160.65 [5820]~P60(x58202)+~P60(x58201)+E(f59(x58201,x58202,f55(x58201),f55(x58202)),f55(f887(x58201,x58202)))
% 160.93/160.65 [5824]~P1(f334(x58241,f411(x58242,x58241)))+P1(f334(x58241,f334(a108,x58242)))+P1(f334(f334(f249(a1),x58242),f2(a1)))
% 160.93/160.65 [5847]~P1(f334(x58471,f334(a108,x58472)))+P1(f334(x58471,f2(a881)))+~P1(f334(f334(f249(a1),x58472),f2(a1)))
% 160.93/160.65 [6189]~P111(x61891)+~P1(f334(f334(f249(x61891),x61892),f2(x61891)))+P1(f334(f334(f249(x61891),f82(x61891,x61892)),f2(x61891)))
% 160.93/160.65 [6303]~P111(x63031)+P1(f334(f334(f249(x63031),f334(f106(x63031),x63032)),f2(x63031)))+~P1(f334(f334(f249(a1),x63032),f2(a1)))
% 160.93/160.65 [6304]~P111(x63041)+P1(f334(f334(f248(x63041),f334(f106(x63041),x63042)),f2(x63041)))+~P1(f334(f334(f248(a1),x63042),f2(a1)))
% 160.93/160.65 [6311]~P85(x63112)+E(x63111,f2(x63112))+~P1(f334(f334(f248(x63112),f334(f75(x63112),x63111)),f2(x63112)))
% 160.93/160.65 [6386]~P139(x63861)+~P1(f334(f334(f336(x63861),x63862),f113(x63861)))+P1(f334(f334(f336(x63861),f334(f79(x63861),x63862)),f113(x63861)))
% 160.93/160.65 [6418]~P111(x64181)+~P1(f334(f334(f249(x64181),f82(x64181,x64182)),f2(x64181)))+P1(f334(f334(f249(x64181),x64182),f2(x64181)))
% 160.93/160.65 [6587]~P111(x65872)+~P1(f334(f334(f249(x65872),f334(f106(x65872),x65871)),f2(x65872)))+P1(f334(f334(f249(a1),x65871),f2(a1)))
% 160.93/160.65 [6588]~P111(x65882)+~P1(f334(f334(f248(x65882),f334(f106(x65882),x65881)),f2(x65882)))+P1(f334(f334(f248(a1),x65881),f2(a1)))
% 160.93/160.65 [7091]~P111(x70911)+~P1(f334(f334(f249(x70911),x70912),f2(x70911)))+P1(f334(f334(f249(x70911),f334(f334(f80(x70911),x70912),x70912)),f2(x70911)))
% 160.93/160.65 [7092]~P75(x70921)+~P1(f334(f334(f249(x70921),x70922),f2(x70921)))+P1(f334(f334(f249(x70921),f334(f334(f80(x70921),x70922),x70922)),f2(x70921)))
% 160.93/160.65 [7093]~P75(x70931)+~P1(f334(f334(f248(x70931),x70932),f2(x70931)))+P1(f334(f334(f248(x70931),f334(f334(f80(x70931),x70932),x70932)),f2(x70931)))
% 160.93/160.65 [7665]~P111(x76651)+~P1(f334(f334(f249(x76651),f334(f334(f80(x76651),x76652),x76652)),f2(x76651)))+P1(f334(f334(f249(x76651),x76652),f2(x76651)))
% 160.93/160.65 [7666]~P75(x76661)+~P1(f334(f334(f249(x76661),f334(f334(f80(x76661),x76662),x76662)),f2(x76661)))+P1(f334(f334(f249(x76661),x76662),f2(x76661)))
% 160.93/160.65 [7667]~P75(x76671)+~P1(f334(f334(f248(x76671),f334(f334(f80(x76671),x76672),x76672)),f2(x76671)))+P1(f334(f334(f248(x76671),x76672),f2(x76671)))
% 160.93/160.65 [4738]~E(x47382,f2(a881))+~E(x47381,f2(a881))+E(f334(f334(f80(a881),x47381),x47382),f2(a881))
% 160.93/160.65 [4739]~E(x47392,f78(a881))+~E(x47391,f78(a881))+E(f334(f334(f81(a881),x47391),x47392),f78(a881))
% 160.93/160.65 [4740]~E(x47402,f78(a1))+~E(x47401,f78(a1))+E(f334(f334(f81(a1),x47401),x47402),f78(a1))
% 160.93/160.65 [4792]~P58(x47922)+E(x47921,f2(x47922))+E(f334(f334(f38(x47922),x47921),x47921),f78(x47922))
% 160.93/160.65 [4793]~P120(x47932)+E(x47931,f2(x47932))+E(f334(f334(f292(x47932),x47931),x47931),f78(x47932))
% 160.93/160.65 [4794]~P121(x47942)+E(x47941,f2(x47942))+E(f334(f334(f292(x47942),x47941),x47941),f78(x47942))
% 160.93/160.65 [4811]~P75(x48111)+~E(x48112,f2(x48111))+E(f334(f334(f80(x48111),x48112),x48112),f2(x48111))
% 160.93/160.65 [4814]~P140(x48141)+~E(x48142,f78(x48141))+E(f334(f334(f81(x48141),x48142),x48142),f78(x48141))
% 160.93/160.65 [4815]~P121(x48151)+~E(x48152,f2(x48151))+E(f334(f334(f292(x48151),x48152),x48152),f2(x48151))
% 160.93/160.65 [4861]~E(x48612,f2(a881))+~E(x48611,f2(a881))+E(f334(f79(a1),f334(f104(a1),x48611)),f334(f104(a1),x48612))
% 160.93/160.65 [4879]E(x48791,f78(a881))+E(x48792,f2(a881))+~E(f334(f334(f81(a881),x48792),x48791),x48792)
% 160.93/160.65 [4889]E(x48891,f2(a881))+E(x48892,f2(a881))+~E(f334(f334(f81(a881),x48892),x48891),f2(a881))
% 160.93/160.65 [4917]~E(x49172,f2(a881))+~E(x49171,f334(a116,f2(a881)))+E(f334(f334(f80(a881),x49171),x49172),f334(a116,f2(a881)))
% 160.93/160.65 [4918]~E(x49181,f2(a881))+~E(x49182,f334(a116,f2(a881)))+E(f334(f334(f80(a881),x49181),x49182),f334(a116,f2(a881)))
% 160.93/160.65 [4923]E(x49231,f78(a1))+E(x49232,f334(f107(a1),a101))+~E(f334(f334(f81(a1),x49231),x49232),f78(a1))
% 160.93/160.65 [4924]E(x49241,f78(a1))+E(x49242,f334(f107(a1),a101))+~E(f334(f334(f81(a1),x49242),x49241),f78(a1))
% 160.93/160.65 [4925]E(x49251,f78(a1))+E(x49251,f334(f107(a1),a101))+~E(f334(f334(f81(a1),x49252),x49251),f78(a1))
% 160.93/160.65 [4927]E(x49271,f78(a1))+E(x49271,f334(f107(a1),a101))+~E(f334(f334(f81(a1),x49271),x49272),f78(a1))
% 160.93/160.65 [4944]~P75(x49442)+E(x49441,f2(x49442))+~E(f334(f334(f80(x49442),x49441),x49441),f2(x49442))
% 160.93/160.65 [4950]~E(x49501,f334(f107(a1),a101))+~E(x49502,f334(f107(a1),a101))+E(f334(f334(f81(a1),x49501),x49502),f78(a1))
% 160.93/160.65 [4962]E(x49621,f2(a881))+E(x49622,f2(a881))+~E(f334(f334(f80(a881),x49622),x49621),f334(a116,f2(a881)))
% 160.93/160.65 [4972]~P61(x49721)+~P93(x49721)+E(f334(f334(f292(x49721),x49722),f334(f107(x49721),a83)),f2(x49721))
% 160.93/160.65 [4978]~P140(x49781)+~E(x49782,f334(f79(x49781),f78(x49781)))+E(f334(f334(f81(x49781),x49782),x49782),f78(x49781))
% 160.93/160.65 [4983]~P6(x49832)+~P6(x49831)+P6(f334(f334(f80(a1),x49831),x49832))
% 160.93/160.65 [4984]~P6(x49842)+~P6(x49841)+P6(f334(f334(f81(a1),x49841),x49842))
% 160.93/160.65 [4985]~P6(x49852)+~P6(x49851)+P6(f334(f334(f38(a1),x49851),x49852))
% 160.93/160.65 [4987]~E(x49872,f2(a1))+E(x49871,f2(a1))+E(f45(x49871,x49872),f334(f334(f269(a1,a1),f2(a1)),x49871))
% 160.93/160.65 [5009]~E(x50092,f334(a116,f2(a881)))+~E(x50091,f334(a116,f2(a881)))+E(f334(f334(f81(a881),x50091),x50092),f334(a116,f2(a881)))
% 160.93/160.65 [5024]E(x50241,f2(a881))+E(x50242,f334(a116,f2(a881)))+~E(f334(f334(f259(a881),x50242),x50241),f334(a116,f2(a881)))
% 160.93/160.65 [5025]E(x50251,f2(a881))+E(x50251,f334(a116,f2(a881)))+~E(f334(f334(f80(a881),x50252),x50251),f334(a116,f2(a881)))
% 160.93/160.65 [5026]E(x50261,f2(a881))+E(x50261,f334(a116,f2(a881)))+~E(f334(f334(f80(a881),x50261),x50262),f334(a116,f2(a881)))
% 160.93/160.65 [5035]~P61(x50351)+~P93(x50351)+E(f334(f334(f292(x50351),x50352),f334(f107(x50351),a101)),f334(f79(x50351),x50352))
% 160.93/160.65 [5055]E(x50551,f334(a108,x50552))+~E(x50551,f2(a881))+P1(f334(f334(f248(a1),f2(a1)),x50552))
% 160.93/160.65 [5056]E(f334(a108,x50561),x50562)+~E(x50562,f2(a881))+P1(f334(f334(f248(a1),f2(a1)),x50561))
% 160.93/160.65 [5071]E(x50711,f334(a116,f2(a881)))+E(x50712,f334(a116,f2(a881)))+~E(f334(f334(f80(a881),x50711),x50712),f334(a116,f2(a881)))
% 160.93/160.65 [5081]~E(x50811,f334(a108,x50812))+E(x50811,f2(a881))+P1(f334(f334(f248(a1),f2(a1)),x50812))
% 160.93/160.65 [5082]~E(f334(a108,x50822),x50821)+E(x50821,f2(a881))+P1(f334(f334(f248(a1),f2(a1)),x50822))
% 160.93/160.65 [5104]~P2(x51041)+E(f334(f63(x51041,f114(x51041)),x51042),f10(x51041,x51042))+~P1(f334(f61(x51041),x51042))
% 160.93/160.65 [5105]~P2(x51051)+E(f334(f63(x51051,f105(x51051)),x51052),f11(x51051,x51052))+~P1(f334(f61(x51051),x51052))
% 160.93/160.65 [5106]~P108(x51061)+E(f334(f63(x51061,f246(x51061)),x51062),f14(x51061,x51062))+~P1(f334(f61(x51061),x51062))
% 160.93/160.65 [5107]~P108(x51071)+E(f334(f63(x51071,f247(x51071)),x51072),f15(x51071,x51072))+~P1(f334(f61(x51071),x51072))
% 160.93/160.65 [5109]~P60(x51091)+~P1(f334(x51092,f210(x51091)))+P1(f334(f57(f885(x51091)),x51092))
% 160.93/160.65 [5191]~P60(x51912)+P1(f334(x51911,f210(x51912)))+~P1(f334(f58(f885(x51912)),x51911))
% 160.93/160.65 [5192]E(x51921,x51922)+~E(f334(f334(f22(a881),x51922),x51921),f2(a881))+~E(f334(f334(f22(a881),x51921),x51922),f2(a881))
% 160.93/160.65 [5206]P6(x52061)+~P40(x52062)+~P1(f334(f334(f336(a1),x52061),x52062))
% 160.93/160.65 [5237]~P111(x52371)+~E(f82(x52371,x52372),f78(x52371))+P1(f334(f334(f249(x52371),f2(x52371)),x52372))
% 160.93/160.65 [5249]~P93(x52491)+E(f334(f104(x52491),f334(f107(a881),x52492)),f334(f107(x52491),x52492))+P1(f334(a201,f334(f107(a1),x52492)))
% 160.93/160.65 [5255]~P45(x52551,x52552)+P46(a876)+P1(f334(f61(f887(x52551,x52551)),x52552))
% 160.93/160.65 [5325]~P108(x53251)+E(f334(f63(x53251,f247(x53251)),x53252),f12(x53251,f247(x53251),x53252))+~P1(f334(f61(x53251),x53252))
% 160.93/160.65 [5326]~P108(x53261)+E(f334(f63(x53261,f246(x53261)),x53262),f13(x53261,f246(x53261),x53262))+~P1(f334(f61(x53261),x53262))
% 160.93/160.65 [5339]E(x53391,x53392)+P1(f334(f334(f249(a881),x53392),x53391))+P1(f334(f334(f249(a881),x53391),x53392))
% 160.93/160.65 [5340]E(x53401,x53402)+P1(f334(f334(f249(a1),x53402),x53401))+P1(f334(f334(f249(a1),x53401),x53402))
% 160.93/160.65 [5395]~P93(x53951)+E(f334(f104(x53951),f334(f107(a881),x53952)),f2(x53951))+~P1(f334(a201,f334(f107(a1),x53952)))
% 160.93/160.65 [5398]~E(x53982,f334(a108,x53981))+E(x53981,f334(f104(a1),x53982))+~P1(f334(f334(f248(a1),f2(a1)),x53981))
% 160.93/160.65 [5399]~E(f334(a108,x53991),x53992)+E(x53991,f334(f104(a1),x53992))+~P1(f334(f334(f248(a1),f2(a1)),x53991))
% 160.93/160.65 [5400]~E(x54001,f334(a108,x54002))+E(f334(f104(a1),x54001),x54002)+~P1(f334(f334(f248(a1),f2(a1)),x54002))
% 160.93/160.65 [5410]E(x54101,f334(a108,x54102))+~E(x54102,f334(f104(a1),x54101))+~P1(f334(f334(f248(a1),f2(a1)),x54102))
% 160.93/160.65 [5411]E(f334(a108,x54111),x54112)+~E(x54111,f334(f104(a1),x54112))+~P1(f334(f334(f248(a1),f2(a1)),x54111))
% 160.93/160.65 [5450]~P85(x54502)+E(x54501,f2(x54502))+P1(f334(f334(f249(x54502),f2(x54502)),f334(f75(x54502),x54501)))
% 160.93/160.65 [5517]~P111(x55171)+E(f82(x55171,x55172),f78(x55171))+~P1(f334(f334(f249(x55171),f2(x55171)),x55172))
% 160.93/160.65 [5521]~P93(x55211)+E(f334(f104(x55211),f334(f107(a881),x55212)),f2(x55211))+P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),x55212)))
% 160.93/160.65 [5528]~P85(x55281)+E(f334(f75(x55281),x55282),x55282)+~P1(f334(f334(f249(x55281),f2(x55281)),x55282))
% 160.93/160.65 [5529]~P85(x55291)+E(f334(f75(x55291),x55292),x55292)+~P1(f334(f334(f248(x55291),f2(x55291)),x55292))
% 160.93/160.65 [5536]E(x55361,f2(a881))+~E(f141(a881,f334(f304(a881,x55362),x55361)),f117(a881))+P1(f334(f334(f248(a881),x55361),x55362))
% 160.93/160.65 [5546]~P68(x55461)+E(f334(f334(f6(x55461,x55461),f5(x55461)),f334(f174(x55461),x55462)),f334(f168(x55461),x55462))+~P1(f334(f139(x55461),x55462))
% 160.93/160.65 [5549]~P139(x55491)+E(f334(f104(x55491),f334(a108,x55492)),f334(f106(x55491),x55492))+~P1(f334(f334(f248(a1),f2(a1)),x55492))
% 160.93/160.65 [5576]E(x55761,x55762)+P1(f334(f334(f249(a881),x55761),x55762))+~P1(f334(f334(f248(a881),x55761),x55762))
% 160.93/160.65 [5577]E(x55771,x55772)+P1(f334(f334(f249(a1),x55771),x55772))+~P1(f334(f334(f248(a1),x55771),x55772))
% 160.93/160.65 [5580]E(x55801,f78(a1))+~E(f334(f334(f81(a1),x55802),x55801),f78(a1))+~P1(f334(f334(f249(a1),f2(a1)),x55802))
% 160.93/160.65 [5581]E(x55811,f78(a1))+~E(f334(f334(f81(a1),x55811),x55812),f78(a1))+~P1(f334(f334(f249(a1),f2(a1)),x55811))
% 160.93/160.65 [5619]~P40(x56192)+P1(f334(f334(f248(a1),f2(a1)),x56191))+~P1(f334(f334(f336(a1),x56191),x56192))
% 160.93/160.65 [5638]~P55(x56381,x56382)+P39(x56381,x56382)+~P1(f334(f61(f887(x56381,x56381)),x56382))
% 160.93/160.65 [5640]~P55(x56401,x56402)+P45(x56401,x56402)+~P1(f334(f61(f887(x56401,x56401)),x56402))
% 160.93/160.65 [5684]E(x56841,f196(f888(x56842,a876)))+~P1(f334(f61(x56842),x56841))+P1(f334(f334(f249(a881),f2(a881)),f334(f37(x56842),x56841)))
% 160.93/160.65 [5710]~P1(f334(x57101,x57102))+P1(f334(x57101,f2(a881)))+P1(f334(f334(f249(a881),f418(x57102,x57101)),x57102))
% 160.93/160.65 [5735]E(x57351,f2(a881))+~E(f334(f168(a881),x57352),f2(a881))+~P1(f334(f334(f336(a881),x57351),f334(f174(a881),x57352)))
% 160.93/160.65 [5801]E(x58011,x58012)+~P1(f334(f334(f248(a881),x58012),x58011))+~P1(f334(f334(f248(a881),x58011),x58012))
% 160.93/160.65 [5802]E(x58021,x58022)+~P1(f334(f334(f248(a1),x58022),x58021))+~P1(f334(f334(f248(a1),x58021),x58022))
% 160.93/160.65 [5803]E(f334(f37(x58031),x58032),f2(a881))+~P1(f334(f61(x58031),x58032))+P1(f334(f334(f336(x58031),f499(x58032,x58031)),x58032))
% 160.93/160.65 [5812]E(f49(x58121,x58122),f45(x58121,x58122))+P1(f334(f334(f248(a1),f2(a1)),x58121))+~P1(f334(f334(f249(a1),f2(a1)),x58122))
% 160.93/160.65 [5836]~P1(f334(x58361,f372(x58361)))+P1(f334(x58361,f334(a108,x58362)))+~P1(f334(f334(f248(a1),f2(a1)),x58362))
% 160.93/160.65 [5838]P1(f334(f334(f249(a881),x58381),f866(x58382)))+~P1(f334(f61(a881),x58382))+~P1(f334(f334(f336(a881),x58381),x58382))
% 160.93/160.65 [5839]P1(f334(f334(f248(a881),x58391),f364(x58392)))+~P1(f334(f61(a881),x58392))+~P1(f334(f334(f336(a881),x58391),x58392))
% 160.93/160.65 [5868]E(x58681,x58682)+~P1(f334(f334(f249(a881),x58681),f334(a116,x58682)))+P1(f334(f334(f249(a881),x58681),x58682))
% 160.93/160.65 [5902]E(x59021,f334(a116,x59022))+~P1(f334(f334(f248(a881),x59021),f334(a116,x59022)))+P1(f334(f334(f248(a881),x59021),x59022))
% 160.93/160.65 [5915]P1(f334(x59151,f412(x59151)))+~P1(f334(x59151,f334(a108,x59152)))+~P1(f334(f334(f248(a1),f2(a1)),x59152))
% 160.93/160.65 [5929]~P1(f334(x59291,x59292))+~P1(f334(f334(f248(a1),f2(a1)),x59292))+P1(f334(x59291,f334(f104(a1),f362(x59291))))
% 160.93/160.65 [5943]~P85(x59432)+~E(x59431,f2(x59432))+~P1(f334(f334(f249(x59432),f2(x59432)),f334(f75(x59432),x59431)))
% 160.93/160.65 [5968]~P55(x59681,x59682)+P39(x59681,f334(f289(x59681,x59681),x59682))+~P1(f334(f61(f887(x59681,x59681)),x59682))
% 160.93/160.65 [5976]~P93(x59761)+E(f334(f104(x59761),f334(f107(a881),x59762)),f334(f107(x59761),x59762))+~P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),x59762)))
% 160.93/160.65 [5979]E(f334(a116,x59791),x59792)+~P1(f334(f334(f249(a881),x59791),x59792))+P1(f334(f334(f249(a881),f334(a116,x59791)),x59792))
% 160.93/160.65 [5993]E(f334(f334(f38(a1),x59931),x59932),f2(a1))+~P1(f334(f334(f248(a1),x59931),f2(a1)))+~P1(f334(f334(f249(a1),x59932),x59931))
% 160.93/160.65 [6004]E(f44(a1,x60041,x60042),x60041)+~P1(f334(f334(f248(a1),x60041),f2(a1)))+~P1(f334(f334(f249(a1),x60042),x60041))
% 160.93/160.65 [6017]E(f46(x60171,x60172),f45(x60171,x60172))+~P1(f334(f334(f248(a1),f2(a1)),x60171))+~P1(f334(f334(f248(a1),f2(a1)),x60172))
% 160.93/160.65 [6025]E(f334(f334(f38(a1),x60251),x60252),f2(a1))+~P1(f334(f334(f248(a1),f2(a1)),x60251))+~P1(f334(f334(f249(a1),x60251),x60252))
% 160.93/160.65 [6037]E(f44(a881,f334(f107(a881),x60371),f334(f107(a881),x60372)),f334(f107(a881),x60371))+P1(f334(a201,f334(f107(a1),x60371)))+~P1(f334(a201,f334(f107(a1),x60372)))
% 160.93/160.65 [6039]E(f44(a1,x60391,x60392),x60391)+~P1(f334(f334(f248(a1),f2(a1)),x60391))+~P1(f334(f334(f249(a1),x60391),x60392))
% 160.93/160.65 [6040]E(x60401,x60402)+~P1(f334(f334(f249(a881),x60401),f334(a116,x60402)))+~P1(f334(f334(f248(a881),x60402),x60401))
% 160.93/160.65 [6057]~P111(x60571)+~P1(f334(f334(f249(x60571),x60572),f2(x60571)))+P1(f334(f334(f249(x60571),x60572),f334(f79(x60571),x60572)))
% 160.93/160.65 [6058]~P75(x60581)+~P1(f334(f334(f248(x60581),x60582),f2(x60581)))+P1(f334(f334(f248(x60581),x60582),f334(f79(x60581),x60582)))
% 160.93/160.65 [6068]~P5(x60681)+E(f334(f334(f64(x60681,x60681,f114(x60681)),f196(x60681)),x60682),f39(x60681,x60682))+~P1(f334(f61(x60681),x60682))
% 160.93/160.65 [6069]~P5(x60691)+E(f334(f334(f64(x60691,x60691,f105(x60691)),f257(x60691)),x60692),f40(x60691,x60692))+~P1(f334(f61(x60691),x60692))
% 160.93/160.65 [6083]~P106(x60831)+~P1(f334(f334(f249(a881),f2(a881)),x60832))+P1(f334(f334(f249(x60831),f2(x60831)),f334(f104(x60831),x60832)))
% 160.93/160.65 [6084]~P111(x60841)+~P1(f334(f334(f249(a1),f2(a1)),x60842))+P1(f334(f334(f249(x60841),f2(x60841)),f334(f106(x60841),x60842)))
% 160.93/160.65 [6085]~P111(x60851)+~P1(f334(f334(f248(a1),f2(a1)),x60852))+P1(f334(f334(f248(x60851),f2(x60851)),f334(f106(x60851),x60852)))
% 160.93/160.65 [6088]~P6(x60882)+~P6(x60881)+E(f334(f313(a881,a1,f104(a1)),f305(a881,f334(a108,x60881),f334(a108,x60882))),f305(a1,x60881,x60882))
% 160.93/160.65 [6094]P1(f334(x60941,x60942))+~P1(f334(f334(f248(a1),f2(a1)),x60942))+~P1(f334(x60941,f334(f104(a1),f365(x60941))))
% 160.93/160.65 [6119]E(f334(f334(f80(a881),f334(f107(a881),x61191)),f334(f107(a881),x61192)),f334(f107(a881),x61191))+P1(f334(f334(f249(a1),x61191),a83))+~P1(f334(f334(f249(a1),x61192),a83))
% 160.93/160.65 [6123]~P111(x61231)+P1(f334(f334(f249(x61231),f2(x61231)),f82(x61231,x61232)))+~P1(f334(f334(f249(x61231),f2(x61231)),x61232))
% 160.93/160.65 [6134]~P83(x61341)+~P1(f334(f334(f249(x61341),x61342),f2(x61341)))+P1(f334(f334(f249(x61341),f2(x61341)),f334(f79(x61341),x61342)))
% 160.93/160.65 [6135]~P83(x61351)+~P1(f334(f334(f248(x61351),x61352),f2(x61351)))+P1(f334(f334(f248(x61351),f2(x61351)),f334(f79(x61351),x61352)))
% 160.93/160.65 [6138]E(x61381,f257(f888(x61382,a876)))+~E(f334(f37(x61382),x61381),f334(f37(x61382),f257(f888(x61382,a876))))+~P1(f334(f61(x61382),f257(f888(x61382,a876))))
% 160.93/160.65 [6181]~P111(x61811)+P1(f334(f334(f249(x61811),x61812),f2(x61811)))+~P1(f334(f334(f249(x61811),x61812),f334(f79(x61811),x61812)))
% 160.93/160.65 [6182]~P75(x61821)+P1(f334(f334(f248(x61821),x61822),f2(x61821)))+~P1(f334(f334(f248(x61821),x61822),f334(f79(x61821),x61822)))
% 160.93/160.65 [6191]~P93(x61911)+P1(f334(f334(f336(x61911),f334(f107(x61911),x61912)),f194(x61911)))+~P1(f334(f334(f248(a1),a83),x61912))
% 160.93/160.65 [6222]E(x62221,f2(a881))+~P1(f334(f334(f249(a881),x62221),f334(a116,x62222)))+P1(f334(f334(f249(a881),f848(x62222,x62221)),x62222))
% 160.93/160.65 [6244]~P111(x62441)+~P1(f334(f334(f249(x62441),f2(x62441)),f82(x62441,x62442)))+P1(f334(f334(f249(x62441),f2(x62441)),x62442))
% 160.93/160.65 [6246]~E(f334(f107(a881),x62462),f334(f107(a881),x62461))+P1(f334(f334(f248(a1),f334(f107(a1),x62461)),f2(a1)))+~P1(f334(a201,f334(f107(a1),x62462)))
% 160.93/160.65 [6276]E(f334(f268(a1,a1),f49(x62761,x62762)),f334(f334(f38(a1),x62761),x62762))+~P1(f334(f334(f249(a1),x62761),f2(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x62762))
% 160.93/160.65 [6309]E(f334(f272(a1,a1),f49(x63091,x63092)),f44(a1,x63091,x63092))+~P1(f334(f334(f249(a1),x63091),f2(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x63092))
% 160.93/160.65 [6312]~P106(x63122)+~P1(f334(f334(f249(x63122),f2(x63122)),f334(f104(x63122),x63121)))+P1(f334(f334(f249(a881),f2(a881)),x63121))
% 160.93/160.65 [6313]~P111(x63132)+~P1(f334(f334(f249(x63132),f2(x63132)),f334(f106(x63132),x63131)))+P1(f334(f334(f249(a1),f2(a1)),x63131))
% 160.93/160.65 [6314]~P111(x63142)+~P1(f334(f334(f248(x63142),f2(x63142)),f334(f106(x63142),x63141)))+P1(f334(f334(f248(a1),f2(a1)),x63141))
% 160.93/160.65 [6317]E(f334(f268(a1,a1),f46(x63171,x63172)),f334(f334(f38(a1),x63171),x63172))+~P1(f334(f334(f249(a1),f2(a1)),x63171))+~P1(f334(f334(f248(a1),f2(a1)),x63172))
% 160.93/160.65 [6332]E(f334(f272(a1,a1),f46(x63321,x63322)),f44(a1,x63321,x63322))+~P1(f334(f334(f249(a1),f2(a1)),x63321))+~P1(f334(f334(f248(a1),f2(a1)),x63322))
% 160.93/160.65 [6347]~P83(x63471)+P1(f334(f334(f249(x63471),x63472),f2(x63471)))+~P1(f334(f334(f249(x63471),f2(x63471)),f334(f79(x63471),x63472)))
% 160.93/160.65 [6348]~P83(x63481)+P1(f334(f334(f248(x63481),x63482),f2(x63481)))+~P1(f334(f334(f248(x63481),f2(x63481)),f334(f79(x63481),x63482)))
% 160.93/160.65 [6373]P1(f334(f48(x63731,x63732),f49(x63731,x63732)))+~P1(f334(f334(f249(a1),x63731),f2(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x63732))
% 160.93/160.65 [6398]P1(f334(f48(x63981,x63982),f46(x63981,x63982)))+~P1(f334(f334(f249(a1),f2(a1)),x63982))+~P1(f334(f334(f248(a1),f2(a1)),x63981))
% 160.93/160.65 [6441]~P83(x64411)+P1(f334(f334(f249(x64411),f334(f79(x64411),x64412)),f2(x64411)))+~P1(f334(f334(f249(x64411),f2(x64411)),x64412))
% 160.93/160.65 [6442]~P83(x64421)+P1(f334(f334(f248(x64421),f334(f79(x64421),x64422)),f2(x64421)))+~P1(f334(f334(f248(x64421),f2(x64421)),x64422))
% 160.93/160.65 [6459]E(f334(f334(f22(a881),f334(a108,x64591)),f334(a108,x64592)),f334(a108,f203(x64591,x64592)))+~P1(f334(f334(f248(a1),f2(a1)),x64592))+~P1(f334(f334(f248(a1),f2(a1)),x64591))
% 160.93/160.65 [6476]P1(f334(f334(f248(a1),f2(a1)),f203(x64761,x64762)))+~P1(f334(f334(f248(a1),f2(a1)),x64762))+~P1(f334(f334(f248(a1),f2(a1)),x64761))
% 160.93/160.65 [6513]~P1(f334(x65131,x65132))+P1(f334(x65131,f2(a881)))+P1(f334(x65131,f334(f334(f80(a881),f418(x65132,x65131)),f78(a881))))
% 160.93/160.65 [6594]E(f334(f107(a881),x65941),f334(f107(a881),x65942))+~P1(f334(f334(f248(a1),f334(f107(a1),x65942)),f2(a1)))+~P1(f334(a201,f334(f107(a1),x65941)))
% 160.93/160.65 [6604]~E(x66041,f2(a881))+~E(f710(x66042,x66041),f2(a881))+E(f334(f144(a881,a881,f80(a881),x66041),x66042),f2(a881))
% 160.93/160.65 [6630]~P1(f334(f61(x66301),f849(x66302,x66301)))+~P1(f334(f61(f888(x66301,a876)),x66302))+P1(f334(f61(x66301),f39(f888(x66301,a876),x66302)))
% 160.93/160.65 [6636]E(x66361,x66362)+P1(f334(f334(f249(a1),x66361),x66362))+~P1(f334(f334(f249(a1),x66361),f334(f334(f80(a1),x66362),f78(a1))))
% 160.93/160.65 [6638]P1(f334(f334(f249(a881),f334(a108,x66381)),f334(a108,x66382)))+~P1(f334(f334(f249(a1),f2(a1)),x66382))+~P1(f334(f334(f249(a1),x66381),x66382))
% 160.93/160.65 [6639]P1(f334(f334(f249(a881),f334(a108,x66391)),f334(a108,x66392)))+~P1(f334(f334(f248(a1),f2(a1)),x66391))+~P1(f334(f334(f249(a1),x66391),x66392))
% 160.93/160.65 [6640]P1(f334(f334(f248(a881),f334(a108,x66401)),f334(a108,x66402)))+~P1(f334(f334(f249(a1),f2(a1)),x66401))+~P1(f334(f334(f248(a1),x66401),x66402))
% 160.93/160.65 [6641]P1(f334(f334(f248(a881),f334(a108,x66411)),f334(a108,x66412)))+~P1(f334(f334(f248(a1),f2(a1)),x66412))+~P1(f334(f334(f248(a1),x66411),x66412))
% 160.93/160.65 [6653]E(f44(a881,f334(a108,x66531),f334(a108,x66532)),f334(a108,f44(a1,x66531,x66532)))+~P1(f334(f334(f248(a1),f2(a1)),x66532))+~P1(f334(f334(f248(a1),f2(a1)),x66531))
% 160.93/160.65 [6675]~P83(x66751)+~P1(f334(f334(f249(x66751),f334(f79(x66751),x66752)),f2(x66751)))+P1(f334(f334(f249(x66751),f2(x66751)),x66752))
% 160.93/160.65 [6676]~P83(x66761)+~P1(f334(f334(f248(x66761),f334(f79(x66761),x66762)),f2(x66761)))+P1(f334(f334(f248(x66761),f2(x66761)),x66762))
% 160.93/160.65 [6691]~P1(f334(f334(f249(a1),a83),x66912))+~P1(f334(f334(f249(a1),x66911),x66912))+P1(f334(f334(f249(a881),f334(f107(a881),x66911)),f334(f107(a881),x66912)))
% 160.93/160.65 [6782]~P1(f334(f334(f248(a1),f2(a1)),x67821))+P1(f334(f334(f249(a881),f334(a108,x67821)),x67822))+~P1(f334(f334(f249(a1),x67821),f334(f104(a1),x67822)))
% 160.93/160.65 [6799]E(x67991,f2(a1))+E(f44(a1,x67992,x67991),f2(a1))+E(f334(f334(f22(a1),f334(f79(a1),f334(f334(f38(a1),x67992),x67991))),f78(a1)),f334(f334(f38(a1),x67992),f334(f79(a1),x67991)))
% 160.93/160.65 [6814]~P1(f334(f334(f248(a1),f2(a1)),x68141))+~P1(f334(f334(f249(a881),f334(a108,x68141)),x68142))+P1(f334(f334(f249(a1),x68141),f334(f104(a1),x68142)))
% 160.93/160.65 [6851]~P1(f334(f334(f248(a881),f334(a108,x68511)),f334(a108,x68512)))+~P1(f334(f334(f249(a1),f2(a1)),x68511))+P1(f334(f334(f248(a1),x68511),x68512))
% 160.93/160.65 [6852]~P1(f334(f334(f248(a881),f334(a108,x68521)),f334(a108,x68522)))+~P1(f334(f334(f248(a1),f2(a1)),x68522))+P1(f334(f334(f248(a1),x68521),x68522))
% 160.93/160.65 [6879]P1(f334(f334(f248(a1),x68791),x68792))+~P1(f334(f334(f248(a881),f334(f107(a881),x68791)),f334(f107(a881),x68792)))+P1(f334(f334(f248(a1),x68791),a83))
% 160.93/160.65 [6904]P1(f334(f334(f248(a1),f2(a1)),f44(a1,x69041,x69042)))+~P1(f334(f334(f248(a1),f2(a1)),x69042))+~P1(f334(f334(f248(a1),f2(a1)),x69041))
% 160.93/160.65 [7002]P1(f334(f334(f249(a1),a83),x70021))+~P1(f334(f334(f249(a1),x70022),x70021))+~P1(f334(f334(f249(a881),f334(f107(a881),x70022)),f334(f107(a881),x70021)))
% 160.93/160.65 [7053]E(f334(f334(f269(a1,a1),f334(f334(f38(a1),x70531),x70532)),f44(a1,x70531,x70532)),f49(x70531,x70532))+~P1(f334(f334(f249(a1),x70531),f2(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x70532))
% 160.93/160.65 [7074]E(f334(f334(f269(a1,a1),f334(f334(f38(a1),x70741),x70742)),f44(a1,x70741,x70742)),f46(x70741,x70742))+~P1(f334(f334(f248(a1),f2(a1)),x70742))+~P1(f334(f334(f248(a1),f2(a1)),x70741))
% 160.93/160.65 [7125]~P95(x71252)+E(x71251,f117(x71252))+E(f334(f144(x71252,x71252,f81(x71252),f334(f143(x71252),x71251)),f334(f173(x71252),x71251)),f334(f63(x71252,f81(x71252)),f334(f174(x71252),x71251)))
% 160.93/160.65 [7239]~E(x72391,f2(a881))+E(f334(f144(a881,a881,f80(a881),x72391),x72392),f2(a881))+P1(f334(f334(f336(a881),f710(x72392,x72391)),f334(f174(a881),x72392)))
% 160.93/160.65 [7286]~P1(f334(f334(f249(a1),x72862),f2(a1)))+P1(f334(f334(f249(a1),f334(f334(f38(a1),x72861),x72862)),f2(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x72861))
% 160.93/160.65 [7288]~P1(f334(f334(f249(a1),x72881),f2(a1)))+P1(f334(f334(f249(a1),f334(f334(f38(a1),x72881),x72882)),f2(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x72882))
% 160.93/160.65 [7289]~P1(f334(f334(f249(a1),x72892),f2(a1)))+P1(f334(f334(f248(a1),f334(f334(f38(a1),x72891),x72892)),f2(a1)))+~P1(f334(f334(f248(a1),f2(a1)),x72891))
% 160.93/160.65 [7290]~P1(f334(f334(f248(a1),x72901),f2(a1)))+P1(f334(f334(f248(a1),f334(f334(f38(a1),x72901),x72902)),f2(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x72902))
% 160.93/160.65 [7296]P1(f334(f334(f336(f888(x72961,a876)),f849(x72962,x72961)),x72962))+~P1(f334(f61(f888(x72961,a876)),x72962))+P1(f334(f61(x72961),f39(f888(x72961,a876),x72962)))
% 160.93/160.65 [7393]P27(x73931,x73931,x73932,f257(f888(x73931,a876)))+~E(f334(f313(x73931,x73931,x73932),f257(f888(x73931,a876))),f257(f888(x73931,a876)))+~P1(f334(f61(x73931),f257(f888(x73931,a876))))
% 160.93/160.65 [7520]~P27(x75201,x75201,x75202,f257(f888(x75201,a876)))+E(f334(f313(x75201,x75201,x75202),f257(f888(x75201,a876))),f257(f888(x75201,a876)))+~P1(f334(f61(x75201),f257(f888(x75201,a876))))
% 160.93/160.65 [7659]E(f334(f334(f38(a1),x76591),x76592),f334(f107(a1),a101))+~P1(f334(f334(f248(a1),f334(f334(f80(a1),x76591),x76592)),f2(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x76591))
% 160.93/160.65 [7716]~P1(f334(f334(f249(a1),x77162),f2(a1)))+~P1(f334(f334(f249(a1),f334(f334(f38(a1),x77161),x77162)),f2(a1)))+P1(f334(f334(f249(a1),f2(a1)),x77161))
% 160.93/160.65 [7721]E(f334(f334(f80(a1),x77211),x77212),f44(a1,x77211,x77212))+~P1(f334(f334(f248(a1),f334(f334(f80(a1),x77211),x77212)),f2(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x77211))
% 160.93/160.65 [7724]P1(f334(f334(f249(a1),x77241),f2(a1)))+~P1(f334(f334(f249(a1),f334(f334(f38(a1),x77241),x77242)),f2(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x77242))
% 160.93/160.65 [8109]~P60(x81091)+~P1(f334(f58(f885(x81091)),x81092))+P1(f334(f58(x81091),f334(f334(f8(f885(x81091),a876,x81091),x81092),f241(x81091))))
% 160.93/160.65 [8427]~P108(x84271)+P16(x84271,x84272)+~P1(f334(f334(f248(x84271),f334(f334(f167(x84271),x84272),f749(x84272,x84271))),f334(f334(f167(x84271),x84272),f750(x84272,x84271))))
% 160.93/160.65 [8428]~P108(x84281)+P16(x84281,x84282)+~P1(f334(f334(f248(x84281),f334(f334(f167(x84281),x84282),f756(x84282,x84281))),f334(f334(f167(x84281),x84282),f761(x84282,x84281))))
% 160.93/160.65 [8584]~P60(x85841)+P1(f334(f57(f885(x85841)),x85842))+~P1(f334(f57(x85841),f334(f334(f8(f885(x85841),a876,x85841),x85842),f241(x85841))))
% 160.93/160.65 [9759]~P60(x97591)+~P60(x97592)+E(f334(f334(f156(f882(x97591),f888(x97592,x97591)),f334(f334(f8(f888(x97592,f885(x97591)),f888(x97592,x97591),f882(x97591)),f73(f885(x97591),x97591,x97592,f245(x97591))),f334(f334(f8(f882(f887(x97592,x97591)),f888(x97592,f885(x97591)),f882(x97591)),f180(x97592,x97591)),f334(f184(x97592,x97591),f55(x97592))))),f54(x97591,f334(f197(f882(x97592)),f55(x97592)),f55(x97591))),f55(f888(x97592,x97591)))
% 160.93/160.65 [5677]E(x56771,f2(a1))+~E(f44(a1,x56772,x56771),f2(a1))+E(f334(f334(f38(a1),x56772),f334(f79(a1),x56771)),f334(f79(a1),f334(f334(f38(a1),x56772),x56771)))
% 160.93/160.65 [5695]~P40(x56952)+~P40(x56951)+P40(f334(f334(f114(f888(a1,a876)),x56951),x56952))
% 160.93/160.65 [5696]~P40(x56962)+~P40(x56961)+P40(f334(f334(f105(f888(a1,a876)),x56961),x56962))
% 160.93/160.65 [5713]~P61(x57131)+~P93(x57131)+E(f334(f79(x57131),f334(f334(f292(x57131),f78(x57131)),x57132)),f334(f334(f292(x57131),f334(f107(x57131),a101)),x57132))
% 160.93/160.65 [5828]E(x58281,f2(a1))+~E(f44(a1,x58282,x58281),f2(a1))+E(f334(f334(f38(a1),f334(f79(a1),x58282)),x58281),f334(f79(a1),f334(f334(f38(a1),x58282),x58281)))
% 160.93/160.65 [5962]~P108(x59621)+P16(x59621,x59622)+P1(f334(f334(f249(a881),f750(x59622,x59621)),f334(f197(f882(x59621)),x59622)))
% 160.93/160.65 [5963]~P108(x59631)+P16(x59631,x59632)+P1(f334(f334(f249(a881),f761(x59632,x59631)),f334(f197(f882(x59631)),x59632)))
% 160.93/160.65 [6115]~P93(x61151)+~E(f334(f107(x61151),x61152),f2(x61151))+P32(x61151,f334(f107(x61151),f334(f334(f80(a1),x61152),f334(f79(a1),a83))))
% 160.93/160.65 [6116]~P93(x61161)+~E(f334(f107(x61161),x61162),f2(x61161))+P32(x61161,f334(f107(x61161),f334(f334(f80(a1),a83),f334(f79(a1),x61162))))
% 160.93/160.65 [6118]E(f334(a50,f46(f334(f79(a1),x61181),f334(f79(a1),x61182))),f45(x61181,x61182))+P1(f334(f334(f249(a1),f2(a1)),x61182))+P1(f334(f334(f248(a1),f2(a1)),x61181))
% 160.93/160.65 [6252]~E(x62522,f2(a881))+~E(x62521,f2(a881))+P1(f334(f334(f248(a1),f334(f104(a1),x62521)),f334(f79(a1),f334(f104(a1),x62522))))
% 160.93/160.65 [6280]E(f334(f334(f80(a881),f334(f107(a881),x62801)),f334(f107(a881),x62802)),f334(f107(a881),f334(f334(f80(a1),x62801),x62802)))+P1(f334(f334(f249(a1),x62801),a83))+P1(f334(f334(f249(a1),x62802),a83))
% 160.93/160.65 [6407]~P75(x64071)+~P1(f334(f334(f249(x64071),f2(x64071)),x64072))+P1(f334(f334(f249(x64071),f334(f79(x64071),x64072)),x64072))
% 160.93/160.65 [6408]~P75(x64081)+~P1(f334(f334(f248(x64081),f2(x64081)),x64082))+P1(f334(f334(f248(x64081),f334(f79(x64081),x64082)),x64082))
% 160.93/160.65 [6580]E(f334(f334(f22(a881),f334(a108,x65801)),f334(a108,x65802)),f334(a108,f334(f334(f22(a1),x65801),x65802)))+~P1(f334(f334(f248(a1),f2(a1)),x65802))+~P1(f334(f334(f248(a1),x65802),x65801))
% 160.93/160.65 [6613]E(f334(a108,f44(a1,f334(f107(a1),x66131),f334(f107(a1),x66132))),f44(a881,f334(f107(a881),x66131),f334(f107(a881),x66132)))+P1(f334(a201,f334(f107(a1),x66131)))+P1(f334(a201,f334(f107(a1),x66132)))
% 160.93/160.65 [6631]~P75(x66311)+P1(f334(f334(f249(x66311),f2(x66311)),x66312))+~P1(f334(f334(f249(x66311),f334(f79(x66311),x66312)),x66312))
% 160.93/160.65 [6632]~P75(x66321)+P1(f334(f334(f248(x66321),f2(x66321)),x66322))+~P1(f334(f334(f248(x66321),f334(f79(x66321),x66322)),x66322))
% 160.93/160.65 [6644]~P75(x66441)+~P1(f334(f334(f249(x66441),f2(x66441)),x66442))+P1(f334(f334(f249(x66441),f2(x66441)),f334(f334(f80(x66441),x66442),x66442)))
% 160.93/160.65 [6646]~P75(x66461)+~P1(f334(f334(f248(x66461),f2(x66461)),x66462))+P1(f334(f334(f248(x66461),f2(x66461)),f334(f334(f80(x66461),x66462),x66462)))
% 160.93/160.65 [6658]E(f334(f334(f80(a881),f334(a108,x66581)),f334(a108,x66582)),f334(a108,f334(f334(f80(a1),x66581),x66582)))+~P1(f334(f334(f248(a1),f2(a1)),x66582))+~P1(f334(f334(f248(a1),f2(a1)),x66581))
% 160.93/160.65 [6670]E(x66701,f2(a881))+P1(f334(f334(f249(a881),f2(a881)),x66702))+~P1(f334(f334(f249(a881),f2(a881)),f334(f334(f259(a881),x66702),x66701)))
% 160.93/160.65 [6700]~P93(x67001)+E(f334(f107(x67001),x67002),f2(x67001))+~P32(x67001,f334(f107(x67001),f334(f334(f80(a1),a83),f334(f79(a1),x67002))))
% 160.93/160.65 [6701]~P93(x67011)+E(f334(f107(x67011),x67012),f2(x67011))+~P32(x67011,f334(f107(x67011),f334(f334(f80(a1),x67012),f334(f79(a1),a83))))
% 160.93/160.65 [6760]~P1(f334(f61(x67601),x67602))+~P1(f334(f61(x67601),f257(f888(x67601,a876))))+P1(f334(f61(x67601),f334(f79(f888(x67601,a876)),x67602)))
% 160.93/160.65 [6783]~P1(f334(f334(f249(a1),f2(a1)),x67832))+~P1(f334(f334(f248(a1),x67832),x67831))+P1(f334(f334(f249(a1),f2(a1)),f334(f334(f38(a1),x67831),x67832)))
% 160.93/160.65 [6784]~P1(f334(f334(f249(a1),x67842),f2(a1)))+~P1(f334(f334(f248(a1),x67841),f2(a1)))+P1(f334(f334(f248(a1),f2(a1)),f334(f334(f38(a1),x67841),x67842)))
% 160.93/160.65 [6822]~P1(f334(f334(f249(a881),f2(a881)),x68222))+~P1(f334(f334(f249(a881),f2(a881)),x68221))+P1(f334(f334(f249(a881),f2(a881)),f334(f334(f81(a881),x68221),x68222)))
% 160.93/160.65 [6823]~P1(f334(f334(f248(a1),f2(a1)),x68232))+~P1(f334(f334(f248(a1),f2(a1)),x68231))+P1(f334(f334(f248(a1),f2(a1)),f334(f334(f80(a1),x68231),x68232)))
% 160.93/160.65 [6824]~P1(f334(f334(f248(a1),f2(a1)),x68242))+~P1(f334(f334(f248(a1),f2(a1)),x68241))+P1(f334(f334(f248(a1),f2(a1)),f334(f334(f81(a1),x68241),x68242)))
% 160.93/160.65 [6825]~P1(f334(f334(f249(a1),f2(a1)),x68252))+~P1(f334(f334(f248(a1),f2(a1)),x68251))+P1(f334(f334(f248(a1),f2(a1)),f334(f334(f38(a1),x68251),x68252)))
% 160.93/160.65 [6826]~P1(f334(f334(f248(a1),f2(a1)),x68262))+~P1(f334(f334(f248(a1),f2(a1)),x68261))+P1(f334(f334(f248(a1),f2(a1)),f334(f334(f38(a1),x68261),x68262)))
% 160.93/160.65 [6892]E(x68921,f2(a1))+E(f44(a1,x68922,x68921),f2(a1))+E(f334(f334(f22(a1),f334(f79(a1),f334(f334(f38(a1),x68922),x68921))),f78(a1)),f334(f334(f38(a1),f334(f79(a1),x68922)),x68921))
% 160.93/160.65 [6945]P1(f334(f334(f249(a881),f2(a881)),x69451))+P1(f334(f334(f249(a881),f2(a881)),x69452))+~P1(f334(f334(f249(a881),f2(a881)),f334(f334(f80(a881),x69452),x69451)))
% 160.93/160.65 [6949]~P75(x69491)+P1(f334(f334(f249(x69491),f2(x69491)),x69492))+~P1(f334(f334(f249(x69491),f2(x69491)),f334(f334(f80(x69491),x69492),x69492)))
% 160.93/160.65 [6950]~P75(x69501)+P1(f334(f334(f248(x69501),f2(x69501)),x69502))+~P1(f334(f334(f248(x69501),f2(x69501)),f334(f334(f80(x69501),x69502),x69502)))
% 160.93/160.65 [7003]~P1(f334(f61(x70031),x70032))+P1(f334(f61(x70031),f257(f888(x70031,a876))))+~P1(f334(f61(x70031),f334(f79(f888(x70031,a876)),x70032)))
% 160.93/160.65 [7066]P1(f334(f334(f248(a1),x70661),f2(a1)))+~P1(f334(f334(f249(a1),x70662),f2(a1)))+~P1(f334(f334(f248(a1),f2(a1)),f334(f334(f38(a1),x70661),x70662)))
% 160.93/160.65 [7072]~P1(f334(f334(f249(a1),f2(a1)),x70721))+P1(f334(f334(f248(a1),x70721),x70722))+~P1(f334(f334(f249(a1),f2(a1)),f334(f334(f38(a1),x70722),x70721)))
% 160.93/160.65 [7073]~P1(f334(f334(f248(a1),f2(a1)),x70732))+P1(f334(f334(f248(a1),x70731),x70732))+~P1(f334(f334(f249(a1),f2(a1)),f334(f334(f38(a1),x70732),x70731)))
% 160.93/160.65 [7102]P1(f334(f334(f249(a1),f2(a1)),x71021))+~P1(f334(f334(f248(a1),f2(a1)),x71022))+~P1(f334(f334(f249(a1),f2(a1)),f334(f334(f38(a1),x71022),x71021)))
% 160.93/160.65 [7103]P1(f334(f334(f248(a1),f2(a1)),x71031))+~P1(f334(f334(f249(a1),f2(a1)),x71032))+~P1(f334(f334(f248(a1),f2(a1)),f334(f334(f38(a1),x71031),x71032)))
% 160.93/160.65 [7551]~P1(f334(f61(x75512),f257(f888(x75512,a876))))+~P1(f334(f61(x75511),f257(f888(x75511,a876))))+P1(f334(f61(f886(x75511,x75512)),f257(f888(f886(x75511,x75512),a876))))
% 160.93/160.65 [7552]~P1(f334(f61(x75522),f257(f888(x75522,a876))))+~P1(f334(f61(x75521),f257(f888(x75521,a876))))+P1(f334(f61(f887(x75521,x75522)),f257(f888(f887(x75521,x75522),a876))))
% 160.93/160.65 [7623]~P1(f334(f334(f249(a881),f334(a116,f2(a881))),x76231))+~P1(f334(f334(f249(a881),f334(a116,f2(a881))),x76232))+P1(f334(f334(f249(a881),x76231),f334(f334(f81(a881),x76232),x76231)))
% 160.93/160.65 [7624]~P1(f334(f334(f249(a881),f334(a116,f2(a881))),x76241))+~P1(f334(f334(f249(a881),f334(a116,f2(a881))),x76242))+P1(f334(f334(f249(a881),x76241),f334(f334(f81(a881),x76241),x76242)))
% 160.93/160.65 [7658]E(f334(f37(x76581),f257(f888(x76581,a876))),f334(a116,f2(a881)))+P1(f334(f61(x76582),f257(f888(x76582,a876))))+~P1(f334(f61(f888(x76582,x76581)),f257(f888(f888(x76582,x76581),a876))))
% 160.93/160.65 [7782]~P1(f334(f334(f249(a881),f334(a116,f2(a881))),x77822))+~P1(f334(f334(f249(a881),f334(a116,f2(a881))),x77821))+P1(f334(f334(f249(a881),f334(a116,f2(a881))),f334(f334(f81(a881),x77821),x77822)))
% 160.93/160.65 [7783]~P1(f334(f334(f248(a881),f334(a116,f2(a881))),x77831))+~P1(f334(f334(f248(a881),f334(a116,f2(a881))),x77832))+P1(f334(f334(f248(a881),f334(a116,f2(a881))),f334(f334(f81(a881),x77831),x77832)))
% 160.93/160.65 [8472]E(x84721,f117(x84722))+~P1(f334(f139(x84722),x84721))+E(f179(x84722,f334(f334(f8(a876,a876,x84722),a329),f334(f334(f7(x84722,x84722,a876),a331),f146(x84722,x84721))),x84721),f118(x84722,x84721))
% 160.93/160.65 [8575]~P40(x85752)+~P40(x85751)+E(f334(f313(a881,a1,f104(a1)),f334(f334(f114(f888(a881,a876)),f334(f313(a1,a881,a108),x85751)),f334(f313(a1,a881,a108),x85752))),f334(f334(f114(f888(a1,a876)),x85751),x85752))
% 160.93/160.65 [8576]~P40(x85762)+~P40(x85761)+E(f334(f313(a881,a1,f104(a1)),f334(f334(f105(f888(a881,a876)),f334(f313(a1,a881,a108),x85761)),f334(f313(a1,a881,a108),x85762))),f334(f334(f105(f888(a1,a876)),x85761),x85762))
% 160.93/160.65 [9235]~P93(x92351)+~E(f334(f107(x92351),x92352),f78(x92351))+P32(x92351,f334(f107(x92351),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f79(a1),x92352))))
% 160.93/160.65 [9468]~P93(x94681)+E(f334(f107(x94681),x94682),f78(x94681))+~P32(x94681,f334(f107(x94681),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f79(a1),x94682))))
% 160.93/160.65 [10205]E(x102051,f2(a1))+E(x102052,f2(a1))+E(f334(f274(a1,a1,a1,a1,f34(a1),f334(f81(a1),f82(a1,x102052))),f334(f334(f334(f100(f887(a1,a1)),f334(f334(a331,f82(a1,x102051)),f82(a1,x102052))),f52(x102051,x102052)),f334(f334(f273(a1,a1,f887(a1,a1)),f334(f334(f18(a1,f888(a1,f887(a1,a1)),f888(a1,f887(a1,a1))),f334(f334(f8(f888(a1,f888(f887(a1,a1),f887(a1,a1))),f888(f888(a1,f887(a1,a1)),f888(a1,f887(a1,a1))),a1),f18(a1,f887(a1,a1),f887(a1,a1))),f334(f334(f8(f887(a1,a1),f888(a1,f888(f887(a1,a1),f887(a1,a1))),a1),f334(f7(a1,f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),f334(f334(f8(a876,f888(f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),a1),f100(f887(a1,a1))),f334(f334(f7(a1,a1,a876),a331),f2(a1))))),f334(f334(f7(a1,a1,f887(a1,a1)),f334(f334(f8(a1,f888(a1,f887(a1,a1)),a1),f269(a1,a1)),f79(a1))),f2(a1))))),f334(f334(f7(a1,f888(a1,a1),f888(a1,f887(a1,a1))),f334(f334(f8(f888(a1,f887(a1,a1)),f888(f888(a1,a1),f888(a1,f887(a1,a1))),a1),f8(a1,f887(a1,a1),a1)),f334(f334(f8(a1,f888(a1,f887(a1,a1)),a1),f269(a1,a1)),f334(f334(f7(a1,a1,a1),f334(f334(f8(a1,f888(a1,a1),a1),f22(a1)),f79(a1))),f78(a1))))),f334(f22(a1),f334(f75(a1),x102052))))),f52(x102051,x102052)))),f45(x102051,x102052))
% 160.93/160.65 [10206]E(x102061,f2(a1))+E(x102062,f2(a1))+E(f334(f274(a1,a1,a1,a1,f34(a1),f334(f81(a1),f82(a1,x102062))),f334(f334(f334(f100(f887(a1,a1)),f334(f334(a333,f334(f334(a332,f334(f334(f249(a1),f2(a1)),x102062)),f334(f334(f248(a1),f2(a1)),x102061))),f334(f334(a332,f334(f334(f249(a1),x102062),f2(a1))),f334(f334(f249(a1),x102061),f2(a1))))),f52(x102061,x102062)),f334(f334(f273(a1,a1,f887(a1,a1)),f334(f334(f18(a1,f888(a1,f887(a1,a1)),f888(a1,f887(a1,a1))),f334(f334(f8(f888(a1,f888(f887(a1,a1),f887(a1,a1))),f888(f888(a1,f887(a1,a1)),f888(a1,f887(a1,a1))),a1),f18(a1,f887(a1,a1),f887(a1,a1))),f334(f334(f8(f887(a1,a1),f888(a1,f888(f887(a1,a1),f887(a1,a1))),a1),f334(f7(a1,f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),f334(f334(f8(a876,f888(f887(a1,a1),f888(f887(a1,a1),f887(a1,a1))),a1),f100(f887(a1,a1))),f334(f334(f7(a1,a1,a876),a331),f2(a1))))),f334(f334(f7(a1,a1,f887(a1,a1)),f334(f334(f8(a1,f888(a1,f887(a1,a1)),a1),f269(a1,a1)),f79(a1))),f2(a1))))),f334(f334(f7(a1,f888(a1,a1),f888(a1,f887(a1,a1))),f334(f334(f8(f888(a1,f887(a1,a1)),f888(f888(a1,a1),f888(a1,f887(a1,a1))),a1),f8(a1,f887(a1,a1),a1)),f334(f334(f8(a1,f888(a1,f887(a1,a1)),a1),f269(a1,a1)),f334(f334(f7(a1,a1,a1),f334(f334(f8(a1,f888(a1,a1),a1),f22(a1)),f79(a1))),f78(a1))))),f334(f22(a1),f334(f75(a1),x102062))))),f52(x102061,x102062)))),f45(x102061,x102062))
% 160.93/160.65 [10207]~P31(a5000)+P26(a877,x102071,f334(f334(f312(f880(a877)),f334(f334(f334(f92(a877),a331),x102072),f334(a202,x102072))),f196(f888(f880(a877),a876))))+~P26(a877,x102071,f334(f334(f312(f880(a877)),f334(f334(f334(f92(a877),f334(f334(f8(f888(a877,f888(a877,a876)),f888(a877,a876),a877),f334(f8(f888(a877,a876),a876,a877),f88(a877))),f334(f334(f8(f888(a877,a876),f888(a877,f888(a877,a876)),a877),f334(f7(a877,f888(a877,a876),f888(a877,a876)),f334(f334(f8(f888(a877,f888(a876,a876)),f888(f888(a877,a876),f888(a877,a876)),a877),f18(a877,a876,a876)),f334(f334(f8(f888(a877,a876),f888(a877,f888(a876,a876)),a877),f334(f8(a876,f888(a876,a876),a877),a337)),f334(a202,x102072))))),a331))),x102072),a331)),f196(f888(f880(a877),a876))))
% 160.93/160.65 [5703]~P111(x57031)+~P93(x57031)+E(f334(f75(x57031),f334(f334(f259(x57031),f334(f107(x57031),a101)),x57032)),f78(x57031))
% 160.93/160.65 [6192]~P139(x61921)+~P1(f334(f334(f249(a1),x61922),f2(a1)))+E(f334(f79(x61921),f334(f104(x61921),f334(a108,f334(f79(a1),x61922)))),f334(f106(x61921),x61922))
% 160.93/160.65 [6391]P1(f334(f334(f248(a103),x63911),f78(a103)))+E(f334(f334(f80(a103),f78(a103)),f282(x63911,f334(f334(f38(a103),x63912),x63911))),f282(x63911,x63912))+P1(f334(f334(f249(a103),x63912),x63911))
% 160.93/160.65 [6990]~P90(x69901)+~P1(f334(f334(f336(x69901),x69902),f113(x69901)))+~E(f334(f334(f80(x69901),f334(f334(f80(x69901),f78(x69901)),x69902)),x69902),f2(x69901))
% 160.93/160.65 [7104]~P1(f334(f334(f249(a1),x71041),f2(a1)))+~P1(f334(f334(f248(a1),x71042),f2(a1)))+E(f334(f268(a1,a1),f334(a50,f46(f334(f79(a1),x71041),f334(f79(a1),x71042)))),f334(f334(f38(a1),x71041),x71042))
% 160.93/160.65 [7121]~P1(f334(f334(f249(a1),x71211),f2(a1)))+~P1(f334(f334(f248(a1),x71212),f2(a1)))+E(f334(f272(a1,a1),f334(a50,f46(f334(f79(a1),x71211),f334(f79(a1),x71212)))),f44(a1,x71211,x71212))
% 160.93/160.65 [7127]~P1(f334(f334(f249(a1),x71272),f2(a1)))+E(f334(f268(a1,a1),f334(a50,f49(f334(f79(a1),x71271),f334(f79(a1),x71272)))),f334(f334(f38(a1),x71271),x71272))+~P1(f334(f334(f249(a1),f2(a1)),x71271))
% 160.93/160.65 [7145]~P1(f334(f334(f249(a1),x71452),f2(a1)))+E(f334(f272(a1,a1),f334(a50,f49(f334(f79(a1),x71451),f334(f79(a1),x71452)))),f44(a1,x71451,x71452))+~P1(f334(f334(f249(a1),f2(a1)),x71451))
% 160.93/160.65 [7200]E(f334(f334(f38(a1),f334(f334(f259(a1),x72001),x72002)),x72001),f334(f334(f259(a1),x72001),f334(f334(f22(a881),x72002),f334(a116,f2(a881)))))+~P1(f334(f334(f249(a881),f2(a881)),x72002))+~P1(f334(f334(f249(a1),f2(a1)),x72001))
% 160.93/160.65 [7293]~P1(f334(f334(f249(a881),f2(a881)),x72931))+~P1(f334(f334(f249(a881),f2(a881)),x72932))+P1(f334(f334(f249(a881),f334(f334(f22(a881),x72931),x72932)),x72931))
% 160.93/160.65 [7294]~P1(f334(f334(f249(a881),f2(a881)),x72941))+~P1(f334(f334(f249(a881),f78(a881)),x72942))+P1(f334(f334(f249(a881),f334(f334(f38(a881),x72941),x72942)),x72941))
% 160.93/160.65 [7295]~P1(f334(f334(f249(a1),f2(a1)),x72951))+~P1(f334(f334(f249(a1),f78(a1)),x72952))+P1(f334(f334(f249(a1),f334(f334(f38(a1),x72951),x72952)),x72951))
% 160.93/160.65 [7442]E(x74421,f2(a881))+~E(x74422,f2(a1))+~P1(f334(f334(f249(a1),f2(a1)),f334(f334(f259(a1),f334(f75(a1),x74422)),x74421)))
% 160.93/160.65 [7861]~E(x78612,f117(f882(x78611)))+E(f334(f197(f882(f882(x78611))),f182(x78611,x78612)),f2(a881))+~P16(a881,f334(f171(a881),f334(f334(f156(f882(x78611),a881),f197(f882(x78611))),x78612)))
% 160.93/160.65 [8108]P1(f334(x81081,x81082))+~P1(f334(x81081,f334(a110,f586(x81081,x81082))))+~P1(f334(f334(f336(f888(f887(a881,a881),a876)),x81082),a102))
% 160.93/160.65 [8127]E(x81271,f117(f882(x81272)))+E(f334(f197(f882(x81272)),f334(f334(f167(f882(x81272)),x81271),f2(a881))),f334(f197(f882(f882(x81272))),f182(x81272,x81271)))+~P16(a881,f334(f171(a881),f334(f334(f156(f882(x81272),a881),f197(f882(x81272))),x81271)))
% 160.93/160.65 [8840]~P1(f334(f61(x88401),f334(f254(x88401),x88402)))+~P1(f334(f61(x88401),f257(f888(x88401,a876))))+P1(f334(f61(x88401),f334(f254(x88401),f334(f334(f8(a876,a876,x88401),a329),x88402))))
% 160.93/160.65 [8902]E(f334(f334(f269(a881,a881),f334(a116,f334(f334(f38(a881),f334(f334(f22(a881),x89021),x89022)),x89022))),f44(a881,f334(f334(f22(a881),x89021),x89022),x89022)),f85(f887(a881,a881),f47(x89021,x89022)))+~P1(f334(f334(f249(a881),f2(a881)),x89022))+~P1(f334(f334(f248(a881),x89022),x89021))
% 160.93/160.65 [9198]~P1(f334(f61(x91981),f334(f254(x91981),x91982)))+P1(f334(f61(x91981),f257(f888(x91981,a876))))+~P1(f334(f61(x91981),f334(f254(x91981),f334(f334(f8(a876,a876,x91981),a329),x91982))))
% 160.93/160.65 [9927]P28(x99271,x99272)+~P39(x99271,f334(f268(f888(f887(x99271,x99271),a876),f888(f887(x99271,x99271),a876)),x99272))+~P1(f334(f334(f248(f888(f887(x99271,x99271),a876)),f334(f334(f291(x99271,x99271,x99271),f334(f268(f888(f887(x99271,x99271),a876),f888(f887(x99271,x99271),a876)),x99272)),f334(f272(f888(f887(x99271,x99271),a876),f888(f887(x99271,x99271),a876)),x99272))),f334(f268(f888(f887(x99271,x99271),a876),f888(f887(x99271,x99271),a876)),x99272)))
% 160.93/160.65 [7226]~P1(f334(f334(f249(a881),f2(a881)),x72262))+P1(f334(f334(f249(a881),x72261),x72262))+E(f334(a116,f334(f334(f38(a881),f334(f334(f22(a881),x72261),x72262)),x72262)),f334(f334(f38(a881),x72261),x72262))
% 160.93/160.65 [7363]~P1(f334(f334(f249(a881),f2(a881)),x73632))+~P1(f334(f334(f248(a881),x73632),x73631))+E(f334(a116,f334(f334(f38(a881),f334(f334(f22(a881),x73631),x73632)),x73632)),f334(f334(f38(a881),x73631),x73632))
% 160.93/160.65 [8346]~P93(x83461)+~P90(x83461)+~P32(x83461,f334(f107(x83461),f334(f334(f22(a1),f334(f334(f80(a1),x83462),x83462)),a101)))
% 160.93/160.65 [9104]E(x91041,f2(a881))+E(f334(f334(f273(a881,a881,f887(a881,a881)),f334(f334(f8(a881,f888(a881,f887(a881,a881)),a881),f269(a881,a881)),a116)),f85(f887(a881,a881),f47(f334(f334(f22(a881),x91042),x91041),x91041))),f85(f887(a881,a881),f47(x91042,x91041)))+P1(f334(f334(f249(a881),x91042),x91041))
% 160.93/160.65 [9534]P1(f334(x95342,f660(x95342,x95341)))+P1(f334(x95341,f660(x95342,x95341)))+E(f334(f254(a1),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f248(a1),f2(a1)))),x95341)),f334(f254(a1),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f248(a1),f2(a1)))),x95342)))
% 160.93/160.65 [9538]~P1(f334(x95382,f660(x95382,x95381)))+~P1(f334(x95381,f660(x95382,x95381)))+E(f334(f254(a1),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f248(a1),f2(a1)))),x95381)),f334(f254(a1),f334(f334(f18(a1,a876,a876),f334(f334(f8(a876,f888(a876,a876),a1),a332),f334(f248(a1),f2(a1)))),x95382)))
% 160.93/160.65 [7579]~P62(x75791)+~P93(x75791)+E(f334(f334(f292(x75791),x75792),f334(f107(x75791),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))),x75792)
% 160.93/160.65 [9234]~P93(x92341)+~E(f334(f107(x92341),x92342),f78(x92341))+P32(x92341,f334(f107(x92341),f334(f334(f80(a1),x92342),f334(f79(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))
% 160.93/160.65 [9411]~P140(x94111)+~E(x94112,f2(x94111))+E(f334(f334(f259(x94111),x94112),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f2(x94111))
% 160.93/160.65 [9412]~P140(x94121)+~E(x94122,f78(x94121))+E(f334(f334(f259(x94121),x94122),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f78(x94121))
% 160.93/160.65 [9425]~P140(x94251)+~E(x94252,f334(f79(x94251),f78(x94251)))+E(f334(f334(f259(x94251),x94252),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f78(x94251))
% 160.93/160.65 [9469]~P93(x94691)+E(f334(f107(x94691),x94692),f78(x94691))+~P32(x94691,f334(f107(x94691),f334(f334(f80(a1),x94692),f334(f79(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))
% 160.93/160.65 [9861]~P111(x98612)+E(x98611,f2(x98612))+P1(f334(f334(f249(x98612),f2(x98612)),f334(f334(f259(x98612),x98611),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))))
% 160.93/160.65 [9926]~P111(x99262)+~E(x99261,f2(x99262))+~P1(f334(f334(f249(x99262),f2(x99262)),f334(f334(f259(x99262),x99261),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))))
% 160.93/160.65 [9952]P1(f334(f334(f248(a1),x99521),f2(a1)))+P1(f334(f334(f249(a1),x99522),x99521))+E(f334(f43(x99521),f46(x99522,f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x99521))),f46(x99522,x99521))
% 160.93/160.65 [9953]~P1(f334(f334(f249(a1),f2(a1)),x99531))+P1(f334(f334(f249(a1),x99532),x99531))+E(f334(f43(x99531),f46(x99532,f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x99531))),f46(x99532,x99531))
% 160.93/160.65 [9954]P1(f334(f334(f248(a1),x99541),f2(a1)))+P1(f334(f334(f248(a1),f2(a1)),f334(f334(f80(a1),x99542),x99541)))+E(f334(f43(x99541),f49(x99542,f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x99541))),f49(x99542,x99541))
% 160.93/160.65 [9955]~P1(f334(f334(f249(a1),f2(a1)),x99551))+P1(f334(f334(f248(a1),f2(a1)),f334(f334(f80(a1),x99552),x99551)))+E(f334(f43(x99551),f49(x99552,f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x99551))),f49(x99552,x99551))
% 160.93/160.65 [9956]~P142(x99561)+~P1(f334(f334(f248(a1),f2(a1)),x99562))+E(f334(f104(x99561),f334(a108,f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x99562))),f334(f334(f80(x99561),f334(f104(x99561),f334(a108,x99562))),f334(f104(x99561),f334(a108,x99562))))
% 160.93/160.65 [5044]~P145(x50441,x50442,x50443)+~E(x50443,f2(a1))+P1(f334(x50441,x50442))
% 160.93/160.65 [5164]~P108(x51641)+~P16(x51641,x51643)+P16(x51641,f172(x51641,x51642,x51643))
% 160.93/160.65 [5165]~P108(x51651)+~P16(x51651,x51653)+P16(x51651,f179(x51651,x51652,x51653))
% 160.93/160.65 [4749]~P66(x47492)+~E(x47493,f334(f79(x47492),x47491))+E(x47491,f334(f79(x47492),x47493))
% 160.93/160.65 [4751]~P66(x47511)+~E(f334(f79(x47511),x47513),x47512)+E(f334(f79(x47511),x47512),x47513)
% 160.93/160.65 [4825]~P108(x48253)+E(x48251,x48252)+~E(f334(f255(x48253),x48251),f334(f255(x48253),x48252))
% 160.93/160.65 [4826]~P102(x48263)+E(x48261,x48262)+~E(f334(f104(x48263),x48261),f334(f104(x48263),x48262))
% 160.93/160.65 [4827]~P108(x48273)+E(x48271,x48272)+~E(f334(f303(x48273),x48271),f334(f303(x48273),x48272))
% 160.93/160.65 [4828]~P108(x48283)+E(x48281,x48282)+~E(f334(f256(x48283),x48281),f334(f256(x48283),x48282))
% 160.93/160.65 [4829]~P108(x48293)+E(x48291,x48292)+~E(f334(f306(x48293),x48291),f334(f306(x48293),x48292))
% 160.93/160.65 [4830]~P66(x48303)+E(x48301,x48302)+~E(f334(f79(x48303),x48301),f334(f79(x48303),x48302))
% 160.93/160.65 [4831]~P94(x48313)+E(x48311,x48312)+~E(f334(f79(x48313),x48311),f334(f79(x48313),x48312))
% 160.93/160.65 [4832]~P90(x48323)+E(x48321,x48322)+~E(f334(f106(x48323),x48321),f334(f106(x48323),x48322))
% 160.93/160.65 [4931]~P60(x49311)+~P1(f334(x49312,x49313))+P1(f334(f57(x49311),x49312))
% 160.93/160.65 [4964]~P60(x49643)+P1(f334(x49641,x49642))+~P1(f334(f58(x49643),x49641))
% 160.93/160.65 [5062]~P146(x50621,x50623,x50622)+~E(x50622,f2(a1))+P1(f334(x50621,f2(a1)))
% 160.93/160.65 [5099]~E(x50991,f2(a881))+E(f782(x50991,x50992,x50993),f196(f888(x50993,a876)))+~E(f334(f37(x50993),x50992),f334(a116,x50991))
% 160.93/160.65 [5254]~E(x52542,f2(a881))+E(f334(f268(a881,a881),x52541),f2(a881))+~P1(f334(f47(x52543,x52542),x52541))
% 160.93/160.65 [5298]P1(f334(x52981,x52982))+~E(x52983,f334(f104(a1),x52982))+~P1(f334(x52981,f334(a108,x52983)))
% 160.93/160.65 [5767]~E(x57673,f2(a881))+~P1(f334(x57671,x57672))+P1(f334(x57671,f44(a881,x57672,x57673)))
% 160.93/160.65 [5898]~P1(f334(a25,x58983))+~P1(f334(a25,x58982))+P1(f334(a25,f30(x58981,x58982,x58983)))
% 160.93/160.65 [5930]~P60(x59303)+~P12(x59303,x59301,x59302)+P1(f334(x59301,f724(x59302,x59301,x59303)))
% 160.93/160.65 [5988]~P103(x59882)+~P103(x59881)+E(f133(x59881,x59882,f134(x59881,x59883),f134(x59882,x59883)),f134(f887(x59881,x59882),x59883))
% 160.93/160.65 [6172]~E(x61723,f2(a881))+P1(f334(x61721,x61722))+~P1(f334(x61721,f44(a881,x61722,x61723)))
% 160.93/160.65 [6323]~P60(x63231)+P13(x63231,x63232,x63233)+~P1(f334(x63232,f731(x63233,x63232,x63231)))
% 160.93/160.65 [6848]E(x68481,f2(a881))+~P1(f334(x68482,f447(x68481,x68483,x68482)))+P1(f334(x68482,f44(a881,x68483,x68481)))
% 160.93/160.65 [6955]~P5(x69551)+~P1(f334(f334(f248(x69551),x69552),f494(x69553,x69552,x69551)))+P1(f334(f334(f248(x69551),x69552),f40(x69551,x69553)))
% 160.93/160.65 [6957]~P1(f334(x69571,x69572))+~P1(f334(x69571,f447(x69573,x69572,x69571)))+P1(f334(x69571,f44(a881,x69572,x69573)))
% 160.93/160.65 [7059]E(x70591,f117(x70592))+E(f334(f334(f153(x70592),f711(x70593,x70591,x70592)),f714(x70593,x70591,x70592)),x70591)+~P1(f334(f334(f336(f882(x70592)),x70591),f163(x70592,x70593)))
% 160.93/160.65 [7090]~P139(x70901)+~P1(f334(f334(f336(x70901),x70902),f113(x70901)))+P1(f334(f334(f336(x70901),f334(f334(f259(x70901),x70902),x70903)),f113(x70901)))
% 160.93/160.65 [7412]P39(x74121,x74122)+~P1(f334(f334(f336(x74121),x74123),f632(x74122,x74121)))+P1(f334(f334(f336(x74121),f658(x74122,x74121,x74123)),f632(x74122,x74121)))
% 160.93/160.65 [7683]E(x76831,f117(x76832))+~P1(f334(f334(f336(f882(x76832)),x76831),f163(x76832,x76833)))+P1(f334(f334(f336(f882(x76832)),f714(x76833,x76831,x76832)),f163(x76832,x76833)))
% 160.93/160.65 [7735]E(x77351,f2(a881))+E(f334(f334(f80(a881),f334(f334(f81(a881),x77351),f448(x77351,x77352,x77353))),f447(x77351,x77352,x77353)),x77352)+P1(f334(x77353,f44(a881,x77352,x77351)))
% 160.93/160.65 [7777]~P1(f334(x77773,x77772))+E(f334(f334(f80(a881),f334(f334(f81(a881),x77771),f448(x77771,x77772,x77773))),f447(x77771,x77772,x77773)),x77772)+P1(f334(x77773,f44(a881,x77772,x77771)))
% 160.93/160.65 [7917]P1(f334(f334(f249(a1),x79171),f437(x79172,x79173,x79171)))+P1(f334(f334(x79173,f334(f334(f38(a1),x79172),x79171)),f44(a1,x79172,x79171)))+~P1(f334(f334(f249(a1),x79171),f2(a1)))
% 160.93/160.65 [8192]P1(f334(f334(x81922,f334(f334(f38(a1),x81921),x81923)),f44(a1,x81921,x81923)))+~P1(f334(f334(f249(a1),x81923),f2(a1)))+P1(f334(f334(f248(a1),f437(x81921,x81922,x81923)),f2(a1)))
% 160.93/160.65 [8379]E(f334(f334(f80(a1),f334(f334(f81(a1),x83791),f438(x83792,x83793,x83791))),f437(x83792,x83793,x83791)),x83792)+P1(f334(f334(x83793,f334(f334(f38(a1),x83792),x83791)),f44(a1,x83792,x83791)))+~P1(f334(f334(f249(a1),x83791),f2(a1)))
% 160.93/160.65 [8621]~P1(f334(f334(x86211,f438(x86212,x86211,x86213)),f437(x86212,x86211,x86213)))+P1(f334(f334(x86211,f334(f334(f38(a1),x86212),x86213)),f44(a1,x86212,x86213)))+~P1(f334(f334(f249(a1),x86213),f2(a1)))
% 160.93/160.65 [8850]~P108(x88501)+~P16(x88501,x88503)+P16(x88501,f151(x88501,x88501,f5(x88501),x88502,x88503))
% 160.93/160.65 [9360]~P124(x93602)+E(x93601,f2(x93602))+~P1(f334(f334(f248(x93602),f334(f334(f80(x93602),f334(f334(f81(x93602),x93603),x93603)),f334(f334(f81(x93602),x93601),x93601))),f2(x93602)))
% 160.93/160.65 [9361]~P124(x93612)+E(x93611,f2(x93612))+~P1(f334(f334(f248(x93612),f334(f334(f80(x93612),f334(f334(f81(x93612),x93611),x93611)),f334(f334(f81(x93612),x93613),x93613))),f2(x93612)))
% 160.93/160.65 [10143]~P111(x101431)+~P1(f334(f334(f249(x101431),x101432),f2(x101431)))+P1(f334(f334(f249(x101431),f334(f334(f259(x101431),x101432),f334(a116,f334(f334(f81(a881),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x101433)))),f2(x101431)))
% 160.93/160.65 [10151]~P111(x101512)+E(x101511,f2(x101512))+~P1(f334(f334(f248(x101512),f334(f334(f80(x101512),f334(f334(f259(x101512),x101513),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x101512),x101511),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))),f2(x101512)))
% 160.93/160.65 [10152]~P111(x101522)+E(x101521,f2(x101522))+~P1(f334(f334(f248(x101522),f334(f334(f80(x101522),f334(f334(f259(x101522),x101521),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x101522),x101523),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))),f2(x101522)))
% 160.93/160.65 [4781]~E(x47812,x47813)+~P66(x47811)+E(f334(f334(f22(x47811),x47812),x47813),f2(x47811))
% 160.93/160.65 [4782]~E(x47822,x47823)+~P67(x47821)+E(f334(f334(f22(x47821),x47822),x47823),f2(x47821))
% 160.93/160.65 [4795]~P143(x47951)+~E(x47953,f2(x47951))+E(f334(f334(f80(x47951),x47952),x47953),x47952)
% 160.93/160.65 [4812]~P138(x48121)+~E(x48123,f2(x48121))+E(f334(f334(f81(x48121),x48122),x48123),f2(x48121))
% 160.93/160.65 [4813]~P138(x48131)+~E(x48132,f2(x48131))+E(f334(f334(f81(x48131),x48132),x48133),f2(x48131))
% 160.93/160.65 [4834]~E(x48343,f117(x48341))+~E(x48342,f117(x48341))+E(f334(f334(f136(x48341),x48342),x48343),f117(x48341))
% 160.93/160.65 [4921]~P143(x49212)+E(x49211,f2(x49212))+~E(f334(f334(f80(x49212),x49213),x49211),x49213)
% 160.93/160.65 [4922]~P66(x49221)+~E(x49222,f334(f79(x49221),x49223))+E(f334(f334(f80(x49221),x49222),x49223),f2(x49221))
% 160.93/160.65 [4929]E(x49291,f117(x49292))+E(x49293,f2(a881))+~E(f334(f334(f177(x49292),x49293),x49291),f117(x49292))
% 160.93/160.65 [4935]~P66(x49353)+E(x49351,x49352)+~E(f334(f334(f22(x49353),x49351),x49352),f2(x49353))
% 160.93/160.65 [4936]~P67(x49363)+E(x49361,x49362)+~E(f334(f334(f22(x49363),x49361),x49362),f2(x49363))
% 160.93/160.65 [4945]~P140(x49452)+E(x49451,f2(x49452))+~E(f334(f334(f259(x49452),x49451),x49453),f2(x49452))
% 160.93/160.65 [4946]~P3(x49462)+E(x49461,f196(x49462))+~E(f334(f334(f114(x49462),x49463),x49461),f196(x49462))
% 160.93/160.65 [4947]~P3(x49472)+E(x49471,f196(x49472))+~E(f334(f334(f114(x49472),x49471),x49473),f196(x49472))
% 160.93/160.65 [4948]~P98(x49482)+E(x49481,f257(x49482))+~E(f334(f334(f105(x49482),x49483),x49481),f257(x49482))
% 160.93/160.65 [4949]~P98(x49492)+E(x49491,f257(x49492))+~E(f334(f334(f105(x49492),x49491),x49493),f257(x49492))
% 160.93/160.65 [5015]~P66(x50152)+E(x50151,f334(f79(x50152),x50153))+~E(f334(f334(f80(x50152),x50151),x50153),f2(x50152))
% 160.93/160.65 [5016]~P66(x50161)+E(f334(f79(x50161),x50162),x50163)+~E(f334(f334(f80(x50161),x50162),x50163),f2(x50161))
% 160.93/160.65 [5018]~E(x50182,x50183)+~P107(x50181)+P1(f334(f334(f248(x50181),x50182),x50183))
% 160.93/160.65 [5020]~E(x50202,x50203)+~P109(x50201)+P1(f334(f334(f248(x50201),x50202),x50203))
% 160.93/160.65 [5021]~E(x50212,x50213)+~P92(x50211)+P1(f334(f334(f91(x50211),x50212),x50213))
% 160.93/160.65 [5115]~P119(x51151)+~E(x51152,f334(f79(x51151),x51153))+E(f334(f334(f81(x51151),x51152),x51152),f334(f334(f81(x51151),x51153),x51153))
% 160.93/160.65 [5123]~P108(x51231)+~P16(x51231,x51233)+P16(x51231,f334(f334(f177(x51231),x51232),x51233))
% 160.93/160.65 [5124]~P108(x51241)+~P16(x51241,x51243)+P16(x51241,f334(f334(f140(x51241),x51242),x51243))
% 160.93/160.65 [5162]E(x51621,x51622)+E(x51623,f2(a881))+~E(f334(f334(f81(a881),x51623),x51621),f334(f334(f81(a881),x51623),x51622))
% 160.93/160.65 [5163]E(x51631,x51632)+E(x51633,f2(a881))+~E(f334(f334(f81(a881),x51631),x51633),f334(f334(f81(a881),x51632),x51633))
% 160.93/160.65 [5245]~E(x52452,x52453)+~P109(x52451)+E(f305(x52451,x52452,x52453),f334(f334(f312(x52451),x52452),f196(f888(x52451,a876))))
% 160.93/160.65 [5286]E(x52861,x52862)+~P92(x52863)+~P1(f334(f334(f91(x52863),x52861),x52862))
% 160.93/160.65 [5296]~E(x52961,x52962)+~P108(x52963)+~P1(f334(f334(f249(x52963),x52961),x52962))
% 160.93/160.65 [5297]~E(x52971,x52972)+~P109(x52973)+~P1(f334(f334(f249(x52973),x52971),x52972))
% 160.93/160.65 [5307]~P109(x53071)+E(f334(f304(x53071,x53072),x53073),f196(f888(x53071,a876)))+P1(f334(f334(f249(x53071),x53072),x53073))
% 160.93/160.65 [5353]~P109(x53531)+E(f305(x53531,x53532,x53533),f196(f888(x53531,a876)))+P1(f334(f334(f248(x53531),x53532),x53533))
% 160.93/160.65 [5354]~P109(x53541)+E(f307(x53541,x53542,x53543),f196(f888(x53541,a876)))+P1(f334(f334(f249(x53541),x53542),x53543))
% 160.93/160.65 [5355]~P109(x53551)+E(f196(f888(x53551,a876)),f305(x53551,x53552,x53553))+P1(f334(f334(f248(x53551),x53552),x53553))
% 160.93/160.65 [5356]~P109(x53561)+E(f196(f888(x53561,a876)),f307(x53561,x53562,x53563))+P1(f334(f334(f249(x53561),x53562),x53563))
% 160.93/160.65 [5364]~P99(x53641)+~E(f334(f334(f114(x53641),x53642),x53643),x53643)+P1(f334(f334(f248(x53641),x53642),x53643))
% 160.93/160.65 [5365]~P100(x53651)+~E(f334(f334(f105(x53651),x53652),x53653),x53652)+P1(f334(f334(f248(x53651),x53652),x53653))
% 160.93/160.65 [5366]~P108(x53661)+~E(f334(f334(f246(x53661),x53662),x53663),x53662)+P1(f334(f334(f248(x53661),x53662),x53663))
% 160.93/160.65 [5367]~P108(x53671)+~E(f334(f334(f247(x53671),x53672),x53673),x53673)+P1(f334(f334(f248(x53671),x53672),x53673))
% 160.93/160.65 [5387]~P108(x53871)+P16(x53871,x53872)+~P16(x53871,f334(f334(f153(x53871),x53873),x53872))
% 160.93/160.65 [5388]~P108(x53881)+P16(x53881,x53882)+~P16(x53881,f334(f334(f136(x53881),x53883),x53882))
% 160.93/160.65 [5389]~P108(x53891)+P16(x53891,x53892)+~P16(x53891,f334(f334(f136(x53891),x53892),x53893))
% 160.93/160.65 [5457]~P108(x54571)+P1(f334(f334(f248(x54571),x54573),x54572))+P1(f334(f334(f249(x54571),x54572),x54573))
% 160.93/160.65 [5459]~P108(x54591)+P1(f334(f334(f248(x54591),x54593),x54592))+P1(f334(f334(f248(x54591),x54592),x54593))
% 160.93/160.65 [5497]~P99(x54971)+E(f334(f334(f114(x54971),x54972),x54973),x54972)+~P1(f334(f334(f248(x54971),x54973),x54972))
% 160.93/160.65 [5499]~P99(x54991)+E(f334(f334(f114(x54991),x54992),x54993),x54993)+~P1(f334(f334(f248(x54991),x54992),x54993))
% 160.93/160.65 [5500]~P100(x55001)+E(f334(f334(f105(x55001),x55002),x55003),x55003)+~P1(f334(f334(f248(x55001),x55003),x55002))
% 160.93/160.65 [5502]~P100(x55021)+E(f334(f334(f105(x55021),x55022),x55023),x55022)+~P1(f334(f334(f248(x55021),x55022),x55023))
% 160.93/160.65 [5503]~P108(x55031)+E(f334(f334(f246(x55031),x55032),x55033),x55033)+~P1(f334(f334(f248(x55031),x55033),x55032))
% 160.93/160.65 [5505]~P108(x55051)+E(f334(f334(f246(x55051),x55052),x55053),x55052)+~P1(f334(f334(f248(x55051),x55052),x55053))
% 160.93/160.65 [5506]~P108(x55061)+E(f334(f334(f247(x55061),x55062),x55063),x55062)+~P1(f334(f334(f248(x55061),x55063),x55062))
% 160.93/160.65 [5508]~P108(x55081)+E(f334(f334(f247(x55081),x55082),x55083),x55083)+~P1(f334(f334(f248(x55081),x55082),x55083))
% 160.93/160.65 [5515]~P120(x55152)+E(x55151,f2(x55152))+E(f334(f334(f292(x55152),f334(f79(x55152),x55153)),f334(f79(x55152),x55151)),f334(f334(f292(x55152),x55153),x55151))
% 160.93/160.65 [5560]~P109(x55601)+E(f334(f304(x55601,x55602),x55603),f196(f888(x55601,a876)))+~P1(f334(f334(f248(x55601),x55603),x55602))
% 160.93/160.65 [5592]~P109(x55921)+E(f305(x55921,x55922,x55923),f196(f888(x55921,a876)))+~P1(f334(f334(f249(x55921),x55923),x55922))
% 160.93/160.65 [5593]~P109(x55931)+E(f308(x55931,x55932,x55933),f196(f888(x55931,a876)))+~P1(f334(f334(f248(x55931),x55933),x55932))
% 160.93/160.65 [5594]~P109(x55941)+E(f307(x55941,x55942,x55943),f196(f888(x55941,a876)))+~P1(f334(f334(f248(x55941),x55943),x55942))
% 160.93/160.65 [5645]~E(f334(f334(f22(a881),x56451),x56453),x56452)+E(x56451,f334(f334(f80(a881),x56452),x56453))+~P1(f334(f334(f248(a881),x56453),x56451))
% 160.93/160.65 [5646]~E(x56461,f334(f334(f80(a881),x56463),x56462))+E(f334(f334(f22(a881),x56461),x56462),x56463)+~P1(f334(f334(f248(a881),x56462),x56461))
% 160.93/160.65 [5692]~P1(f334(x56921,x56923))+P1(f334(x56921,f348(x56921,x56922)))+~P1(f334(f334(f249(a881),x56923),x56922))
% 160.93/160.65 [5693]~P1(f334(x56931,x56933))+P1(f334(x56931,f366(x56931,x56932)))+~P1(f334(f334(f248(a881),x56933),x56932))
% 160.93/160.65 [5701]~P109(x57011)+~E(f334(f304(x57011,x57012),x57013),f196(f888(x57011,a876)))+~P1(f334(f334(f249(x57011),x57012),x57013))
% 160.93/160.65 [5705]~P107(x57051)+~P1(f334(f334(f249(x57051),x57052),x57053))+P1(f334(f334(f248(x57051),x57052),x57053))
% 160.93/160.65 [5707]~P109(x57071)+~P1(f334(f334(f249(x57071),x57072),x57073))+P1(f334(f334(f248(x57071),x57072),x57073))
% 160.93/160.65 [5815]~P109(x58151)+~E(f305(x58151,x58152,x58153),f196(f888(x58151,a876)))+~P1(f334(f334(f248(x58151),x58152),x58153))
% 160.93/160.65 [5816]~P109(x58161)+~E(f307(x58161,x58162,x58163),f196(f888(x58161,a876)))+~P1(f334(f334(f249(x58161),x58162),x58163))
% 160.93/160.65 [5817]~P109(x58171)+~E(f196(f888(x58171,a876)),f305(x58171,x58172,x58173))+~P1(f334(f334(f248(x58171),x58172),x58173))
% 160.93/160.65 [5818]~P109(x58181)+~E(f196(f888(x58181,a876)),f307(x58181,x58182,x58183))+~P1(f334(f334(f249(x58181),x58182),x58183))
% 160.93/160.65 [5826]P1(f334(x58261,x58262))+~P1(f334(x58261,f357(x58261,x58263)))+~P1(f334(f334(f249(a881),x58262),x58263))
% 160.93/160.65 [5827]P1(f334(x58271,x58272))+~P1(f334(x58271,f367(x58271,x58273)))+~P1(f334(f334(f248(a881),x58272),x58273))
% 160.93/160.65 [5835]~E(x58351,f334(a116,x58353))+P1(f334(f334(f249(a881),x58351),f334(a116,x58352)))+~P1(f334(f334(f249(a881),x58353),x58352))
% 160.93/160.65 [5851]E(x58511,x58512)+~E(f334(f334(f81(a881),x58513),x58511),f334(f334(f81(a881),x58513),x58512))+~P1(f334(f334(f249(a881),f2(a881)),x58513))
% 160.93/160.65 [5909]E(f334(x59091,f828(x59091,x59092,x59093)),f78(a881))+~E(f334(f334(f6(x59093,a881),x59091),x59092),f78(a881))+~P1(f334(f61(x59093),x59092))
% 160.93/160.65 [5921]~P5(x59211)+P1(f334(f334(f248(x59211),x59212),f39(x59211,x59213)))+~P1(f334(f334(f336(x59211),x59212),x59213))
% 160.93/160.65 [5950]~P107(x59501)+~P1(f334(f334(f249(x59501),x59503),x59502))+~P1(f334(f334(f249(x59501),x59502),x59503))
% 160.93/160.65 [5951]~P107(x59511)+~P1(f334(f334(f248(x59511),x59513),x59512))+~P1(f334(f334(f249(x59511),x59512),x59513))
% 160.93/160.65 [5952]~P108(x59521)+~P1(f334(f334(f249(x59521),x59523),x59522))+~P1(f334(f334(f249(x59521),x59522),x59523))
% 160.93/160.65 [5955]~P108(x59551)+~P1(f334(f334(f248(x59551),x59553),x59552))+~P1(f334(f334(f249(x59551),x59552),x59553))
% 160.93/160.65 [5956]~P109(x59561)+~P1(f334(f334(f249(x59561),x59563),x59562))+~P1(f334(f334(f249(x59561),x59562),x59563))
% 160.93/160.65 [5982]~E(f334(x59822,f786(x59822,x59823,x59821)),f2(a881))+E(f334(f334(f6(x59821,a881),x59822),x59823),f2(a881))+~P1(f334(f61(x59821),x59823))
% 160.93/160.65 [5983]~E(f334(x59832,f349(x59832,x59833,x59831)),f78(a881))+E(f334(f334(f9(x59831,a881),x59832),x59833),f78(a881))+~P1(f334(f61(x59831),x59833))
% 160.93/160.65 [5997]~P110(x59971)+~P1(f334(f334(f248(x59971),x59973),x59972))+P1(f334(f334(f336(x59971),x59972),f334(f256(x59971),x59973)))
% 160.93/160.65 [5998]~P110(x59981)+~P1(f334(f334(f249(x59981),x59983),x59982))+P1(f334(f334(f336(x59981),x59982),f334(f306(x59981),x59983)))
% 160.93/160.65 [5999]~P110(x59991)+~P1(f334(f334(f249(x59991),x59992),x59993))+P1(f334(f334(f336(x59991),x59992),f334(f255(x59991),x59993)))
% 160.93/160.65 [6000]~P110(x60001)+~P1(f334(f334(f248(x60001),x60002),x60003))+P1(f334(f334(f336(x60001),x60002),f334(f303(x60001),x60003)))
% 160.93/160.65 [6012]E(f334(x60121,f800(x60121,x60122,x60123)),f334(a116,f2(a881)))+~E(f334(f334(f6(x60123,a881),x60121),x60122),f334(a116,f2(a881)))+~P1(f334(f61(x60123),x60122))
% 160.93/160.65 [6095]~P5(x60951)+~P1(f334(f334(f336(x60951),x60953),x60952))+P1(f334(f334(f248(x60951),f40(x60951,x60952)),x60953))
% 160.93/160.65 [6112]~P1(f334(f334(f248(a881),x61121),x61123))+P1(f334(f334(f248(a881),x61121),x61122))+~P1(f334(f334(f248(a881),x61123),x61122))
% 160.93/160.65 [6113]~P1(f334(f334(f248(a1),x61131),x61133))+P1(f334(f334(f248(a1),x61131),x61132))+~P1(f334(f334(f248(a1),x61133),x61132))
% 160.93/160.65 [6130]~P110(x61301)+~P1(f334(f334(f336(x61301),x61303),f334(f306(x61301),x61302)))+P1(f334(f334(f249(x61301),x61302),x61303))
% 160.93/160.65 [6131]~P110(x61311)+~P1(f334(f334(f336(x61311),x61312),f334(f255(x61311),x61313)))+P1(f334(f334(f249(x61311),x61312),x61313))
% 160.93/160.65 [6132]~P110(x61321)+~P1(f334(f334(f336(x61321),x61323),f334(f256(x61321),x61322)))+P1(f334(f334(f248(x61321),x61322),x61323))
% 160.93/160.65 [6133]~P110(x61331)+~P1(f334(f334(f336(x61331),x61332),f334(f303(x61331),x61333)))+P1(f334(f334(f248(x61331),x61332),x61333))
% 160.93/160.65 [6258]P1(f334(x62581,x62582))+~P1(f334(x62581,f595(x62581)))+~P1(f334(f334(f336(x62583),x62582),f257(f888(x62583,a876))))
% 160.93/160.65 [6357]~P63(x63571)+P1(f334(f334(f249(x63571),f2(x63571)),f428(x63573,x63572,x63571)))+P1(f334(f334(f248(x63571),x63572),x63573))
% 160.93/160.65 [6424]~P83(x64241)+~P1(f334(f334(f249(x64241),x64243),f334(f79(x64241),x64242)))+P1(f334(f334(f249(x64241),x64242),f334(f79(x64241),x64243)))
% 160.93/160.65 [6426]~P83(x64261)+~P1(f334(f334(f248(x64261),x64263),f334(f79(x64261),x64262)))+P1(f334(f334(f248(x64261),x64262),f334(f79(x64261),x64263)))
% 160.93/160.65 [6438]~P1(f334(f334(f249(a881),x64381),x64383))+~P1(f334(f334(f249(a881),x64383),x64382))+P1(f334(f334(f249(a881),f334(a116,x64381)),x64382))
% 160.93/160.65 [6465]~P111(x64651)+P1(f334(f334(f249(x64651),f334(f106(x64651),x64652)),f334(f106(x64651),x64653)))+~P1(f334(f334(f249(a1),x64652),x64653))
% 160.93/160.65 [6466]~P106(x64661)+P1(f334(f334(f249(x64661),f334(f104(x64661),x64662)),f334(f104(x64661),x64663)))+~P1(f334(f334(f249(a881),x64662),x64663))
% 160.93/160.65 [6467]~P106(x64671)+P1(f334(f334(f248(x64671),f334(f104(x64671),x64672)),f334(f104(x64671),x64673)))+~P1(f334(f334(f248(a881),x64672),x64673))
% 160.93/160.65 [6468]~P111(x64681)+P1(f334(f334(f248(x64681),f334(f106(x64681),x64682)),f334(f106(x64681),x64683)))+~P1(f334(f334(f248(a1),x64682),x64683))
% 160.93/160.65 [6474]~P108(x64741)+E(f334(f334(f114(f888(x64741,a876)),f334(f255(x64741),x64742)),f334(f304(x64741,x64742),x64743)),f334(f255(x64741),x64743))+~P1(f334(f334(f248(x64741),x64742),x64743))
% 160.93/160.65 [6503]~P83(x65031)+~P1(f334(f334(f249(x65031),x65033),x65032))+P1(f334(f334(f249(x65031),f334(f79(x65031),x65032)),f334(f79(x65031),x65033)))
% 160.93/160.65 [6505]~P83(x65051)+~P1(f334(f334(f248(x65051),x65053),x65052))+P1(f334(f334(f248(x65051),f334(f79(x65051),x65052)),f334(f79(x65051),x65053)))
% 160.93/160.65 [6507]~P94(x65071)+~P1(f334(f334(f248(x65071),x65073),x65072))+P1(f334(f334(f248(x65071),f334(f79(x65071),x65072)),f334(f79(x65071),x65073)))
% 160.93/160.65 [6539]~P108(x65391)+E(f334(f334(f114(f888(x65391,a876)),f334(f255(x65391),x65392)),f305(x65391,x65392,x65393)),f334(f303(x65391),x65393))+~P1(f334(f334(f248(x65391),x65392),x65393))
% 160.93/160.65 [6540]~P108(x65401)+E(f334(f334(f114(f888(x65401,a876)),f334(f303(x65401),x65402)),f308(x65401,x65402,x65403)),f334(f255(x65401),x65403))+~P1(f334(f334(f249(x65401),x65402),x65403))
% 160.93/160.65 [6541]~P108(x65411)+E(f334(f334(f114(f888(x65411,a876)),f334(f303(x65411),x65412)),f307(x65411,x65412,x65413)),f334(f303(x65411),x65413))+~P1(f334(f334(f248(x65411),x65412),x65413))
% 160.93/160.65 [6575]~P108(x65751)+E(f334(f334(f114(f888(x65751,a876)),f334(f304(x65751,x65752),x65753)),f334(f256(x65751),x65753)),f334(f256(x65751),x65752))+~P1(f334(f334(f248(x65751),x65752),x65753))
% 160.93/160.65 [6731]~P108(x67311)+E(f334(f334(f114(f888(x67311,a876)),f305(x67311,x67312,x67313)),f334(f306(x67311),x67313)),f334(f256(x67311),x67312))+~P1(f334(f334(f248(x67311),x67312),x67313))
% 160.93/160.65 [6732]~P108(x67321)+E(f334(f334(f114(f888(x67321,a876)),f308(x67321,x67322,x67323)),f334(f256(x67321),x67323)),f334(f306(x67321),x67322))+~P1(f334(f334(f249(x67321),x67322),x67323))
% 160.93/160.65 [6733]~P108(x67331)+E(f334(f334(f114(f888(x67331,a876)),f307(x67331,x67332,x67333)),f334(f306(x67331),x67333)),f334(f306(x67331),x67332))+~P1(f334(f334(f248(x67331),x67332),x67333))
% 160.93/160.65 [6751]P1(f334(x67511,x67512))+~P1(f334(f334(f248(a881),x67512),x67513))+P1(f334(f334(f336(a881),f367(x67511,x67513)),f305(a881,f2(a881),x67513)))
% 160.93/160.65 [6785]E(x67851,x67852)+~E(f334(f334(f167(x67853),x67851),f656(x67853,x67852,x67851)),f334(f334(f167(x67853),x67852),f656(x67853,x67852,x67851)))+~E(f334(f197(f882(x67853)),x67851),f334(f197(f882(x67853)),x67852))
% 160.93/160.65 [6790]~E(x67903,f334(f334(f38(a881),x67901),x67902))+~P1(f334(f334(f249(a881),f2(a881)),x67902))+P1(f334(f334(f249(a881),x67901),f334(f334(f81(a881),x67902),f334(a116,x67903))))
% 160.93/160.65 [6807]~P1(f334(x68071,x68073))+~P1(f334(f334(f248(a881),x68073),x68072))+P1(f334(f334(f336(a881),f366(x68071,x68072)),f305(a881,f2(a881),x68072)))
% 160.93/160.65 [6845]~P1(f334(x68451,x68453))+P1(f334(x68451,f371(x68451,x68452)))+~P1(f334(f334(f336(a881),x68453),f305(a881,f2(a881),x68452)))
% 160.93/160.65 [6865]~P106(x68653)+~P1(f334(f334(f249(x68653),f334(f104(x68653),x68651)),f334(f104(x68653),x68652)))+P1(f334(f334(f249(a881),x68651),x68652))
% 160.93/160.65 [6866]~P111(x68663)+~P1(f334(f334(f249(x68663),f334(f106(x68663),x68661)),f334(f106(x68663),x68662)))+P1(f334(f334(f249(a1),x68661),x68662))
% 160.93/160.65 [6867]~P106(x68673)+~P1(f334(f334(f248(x68673),f334(f104(x68673),x68671)),f334(f104(x68673),x68672)))+P1(f334(f334(f248(a881),x68671),x68672))
% 160.93/160.65 [6868]~P111(x68683)+~P1(f334(f334(f248(x68683),f334(f106(x68683),x68681)),f334(f106(x68683),x68682)))+P1(f334(f334(f248(a1),x68681),x68682))
% 160.93/160.65 [6886]~P106(x68861)+~P1(f334(f334(f249(x68861),f78(x68861)),x68862))+P1(f334(f334(f249(x68861),f78(x68861)),f334(f334(f259(x68861),x68862),f334(a116,x68863))))
% 160.93/160.65 [6888]~P83(x68881)+~P1(f334(f334(f249(x68881),f334(f79(x68881),x68883)),f334(f79(x68881),x68882)))+P1(f334(f334(f249(x68881),x68882),x68883))
% 160.93/160.65 [6889]~P83(x68891)+~P1(f334(f334(f248(x68891),f334(f79(x68891),x68893)),f334(f79(x68891),x68892)))+P1(f334(f334(f248(x68891),x68892),x68893))
% 160.93/160.65 [6890]~P94(x68901)+~P1(f334(f334(f248(x68901),f334(f79(x68901),x68903)),f334(f79(x68901),x68902)))+P1(f334(f334(f248(x68901),x68902),x68903))
% 160.93/160.65 [6914]P1(f334(x69141,x69142))+~P1(f334(x69141,f368(x69141,x69143)))+~P1(f334(f334(f336(a881),x69142),f305(a881,f2(a881),x69143)))
% 160.93/160.65 [6933]~P63(x69331)+P1(f334(f334(f249(x69331),f428(x69333,x69332,x69331)),f78(x69331)))+P1(f334(f334(f248(x69331),x69332),x69333))
% 160.93/160.65 [6952]~E(f44(a881,x69523,x69522),f44(a881,x69521,x69522))+E(f334(f334(f80(a881),x69521),f334(f334(f81(a881),x69522),f452(x69521,x69522,x69523))),x69523)+~P1(f334(f334(f248(a881),x69521),x69523))
% 160.93/160.65 [6971]E(f334(x69711,f767(x69711,x69712,x69713)),f210(x69712))+~P1(f334(f61(x69713),f186(x69713,x69712,x69711)))+P1(f334(f61(x69713),f257(f888(x69713,a876))))
% 160.93/160.65 [7010]E(f334(f334(f6(x70101,a881),x70102),x70103),f2(a881))+~P1(f334(f61(x70101),x70103))+P1(f334(f334(f336(x70101),f786(x70102,x70103,x70101)),x70103))
% 160.93/160.65 [7011]E(f334(f334(f9(x70111,a881),x70112),x70113),f78(a881))+~P1(f334(f61(x70111),x70113))+P1(f334(f334(f336(x70111),f349(x70112,x70113,x70111)),x70113))
% 160.93/160.65 [7033]~P108(x70331)+~P1(f334(f334(f249(x70331),x70332),x70333))+P1(f334(f334(f249(f888(x70331,a876)),f334(f255(x70331),x70332)),f334(f255(x70331),x70333)))
% 160.93/160.65 [7034]~P108(x70341)+~P1(f334(f334(f248(x70341),x70342),x70343))+P1(f334(f334(f248(f888(x70341,a876)),f334(f255(x70341),x70342)),f334(f255(x70341),x70343)))
% 160.93/160.65 [7035]~P109(x70351)+~P1(f334(f334(f248(x70351),x70352),x70353))+P1(f334(f334(f248(f888(x70351,a876)),f334(f303(x70351),x70352)),f334(f303(x70351),x70353)))
% 160.93/160.65 [7036]~P109(x70361)+~P1(f334(f334(f248(x70361),x70363),x70362))+P1(f334(f334(f248(f888(x70361,a876)),f334(f256(x70361),x70362)),f334(f256(x70361),x70363)))
% 160.93/160.65 [7037]~P108(x70371)+~P1(f334(f334(f248(x70371),x70373),x70372))+P1(f334(f334(f248(f888(x70371,a876)),f334(f306(x70371),x70372)),f334(f306(x70371),x70373)))
% 160.93/160.65 [7045]~P5(x70451)+P1(f334(f334(f248(x70451),x70452),f40(x70451,x70453)))+P1(f334(f334(f336(x70451),f494(x70453,x70452,x70451)),x70453))
% 160.93/160.65 [7051]~P83(x70511)+P1(f334(f334(f249(x70511),f334(f334(f22(x70511),x70512),x70513)),f2(x70511)))+~P1(f334(f334(f249(x70511),x70512),x70513))
% 160.93/160.65 [7052]~P83(x70521)+P1(f334(f334(f248(x70521),f334(f334(f22(x70521),x70522),x70523)),f2(x70521)))+~P1(f334(f334(f248(x70521),x70522),x70523))
% 160.93/160.65 [7094]P1(f334(x70941,x70942))+P1(f334(f334(f248(a881),f368(x70941,x70943)),x70943))+~P1(f334(f334(f336(a881),x70942),f305(a881,f2(a881),x70943)))
% 160.93/160.65 [7134]~E(f334(f334(f6(x71341,a881),x71342),x71343),f78(a881))+~P1(f334(f61(x71341),x71343))+P1(f334(f334(f336(x71341),f828(x71342,x71343,x71341)),x71343))
% 160.93/160.65 [7135]~P1(f334(x71351,x71353))+P1(f334(f334(f248(a881),f371(x71351,x71352)),x71352))+~P1(f334(f334(f336(a881),x71353),f305(a881,f2(a881),x71352)))
% 160.93/160.65 [7175]~P5(x71751)+P1(f334(f334(f336(x71751),f351(x71753,x71752,x71751)),x71752))+P1(f334(f334(f248(x71751),f39(x71751,x71752)),x71753))
% 160.93/160.65 [7208]~E(f334(f334(f6(x72081,a881),x72082),x72083),f334(a116,f2(a881)))+~P1(f334(f61(x72081),x72083))+P1(f334(f334(f336(x72081),f800(x72082,x72083,x72081)),x72083))
% 160.93/160.65 [7219]E(x72191,f2(a881))+P1(f334(x72192,f44(a881,x72193,x72191)))+P1(f334(f334(f249(a881),f447(x72191,x72193,x72192)),x72191))
% 160.93/160.65 [7324]~P1(f334(x73241,x73242))+P1(f334(x73241,f44(a881,x73242,x73243)))+P1(f334(f334(f249(a881),f447(x73243,x73242,x73241)),x73243))
% 160.93/160.65 [7446]E(x74461,f117(x74462))+~P1(f334(f334(f336(f882(x74462)),x74461),f163(x74462,x74463)))+P1(f334(f334(f336(x74462),f711(x74463,x74461,x74462)),x74463))
% 160.93/160.65 [7468]~P108(x74681)+E(f334(f334(f114(f888(x74681,a876)),f334(f334(f312(x74681),x74682),f196(f888(x74681,a876)))),f308(x74681,x74682,x74683)),f334(f304(x74681,x74682),x74683))+~P1(f334(f334(f249(x74681),x74682),x74683))
% 160.93/160.65 [7494]~P108(x74941)+E(f334(f334(f114(f888(x74941,a876)),f334(f334(f312(x74941),x74942),f196(f888(x74941,a876)))),f307(x74941,x74942,x74943)),f305(x74941,x74942,x74943))+~P1(f334(f334(f248(x74941),x74942),x74943))
% 160.93/160.65 [7603]~P108(x76031)+P1(f334(f334(f249(x76031),x76032),x76033))+~P1(f334(f334(f249(f888(x76031,a876)),f334(f255(x76031),x76032)),f334(f255(x76031),x76033)))
% 160.93/160.65 [7604]~P108(x76041)+P1(f334(f334(f248(x76041),x76042),x76043))+~P1(f334(f334(f248(f888(x76041,a876)),f334(f306(x76041),x76043)),f334(f306(x76041),x76042)))
% 160.93/160.65 [7605]~P109(x76051)+P1(f334(f334(f248(x76051),x76052),x76053))+~P1(f334(f334(f248(f888(x76051,a876)),f334(f256(x76051),x76053)),f334(f256(x76051),x76052)))
% 160.93/160.65 [7606]~P108(x76061)+P1(f334(f334(f248(x76061),x76062),x76063))+~P1(f334(f334(f248(f888(x76061,a876)),f334(f255(x76061),x76062)),f334(f255(x76061),x76063)))
% 160.93/160.65 [7607]~P109(x76071)+P1(f334(f334(f248(x76071),x76072),x76073))+~P1(f334(f334(f248(f888(x76071,a876)),f334(f303(x76071),x76072)),f334(f303(x76071),x76073)))
% 160.93/160.65 [7630]~P83(x76301)+~P1(f334(f334(f249(x76301),f334(f334(f22(x76301),x76302),x76303)),f2(x76301)))+P1(f334(f334(f249(x76301),x76302),x76303))
% 160.93/160.65 [7631]~P83(x76311)+~P1(f334(f334(f248(x76311),f334(f334(f22(x76311),x76312),x76313)),f2(x76311)))+P1(f334(f334(f248(x76311),x76312),x76313))
% 160.93/160.65 [7784]E(x77841,f2(a881))+~E(f334(f144(a881,a881,f80(a881),x77842),x77843),f2(a881))+~P1(f334(f334(f336(a881),x77841),f334(f174(a881),x77843)))
% 160.93/160.65 [7788]~P5(x77881)+~P1(f334(f334(f248(x77881),f351(x77883,x77882,x77881)),x77883))+P1(f334(f334(f248(x77881),f39(x77881,x77882)),x77883))
% 160.93/160.65 [7943]P1(f334(f334(f248(a1),f2(a1)),f440(x79431,x79432,x79433)))+P1(f334(f334(x79432,f334(f334(f38(a1),x79431),x79433)),f44(a1,x79431,x79433)))+~P1(f334(f334(f249(a1),f2(a1)),x79433))
% 160.93/160.65 [8030]E(x80301,x80302)+~E(f334(f197(f882(x80303)),x80301),f334(f197(f882(x80303)),x80302))+~P1(f334(f334(f273(x80303,x80303,a876),a331),f686(x80303,x80301,x80302)))
% 160.93/160.65 [8099]~P39(x80992,x80993)+E(x80991,f196(f888(x80992,a876)))+~P1(f334(f334(f248(f888(x80992,a876)),x80991),f334(f288(x80992,x80992,x80993),x80991)))
% 160.93/160.65 [8170]P41(x81701,x81702,x81703)+P1(f334(f334(f336(x81701),f591(x81703,x81702,x81701)),x81702))+P1(f334(f334(f336(f887(x81701,x81701)),f592(x81703,x81702,x81701)),x81703))
% 160.93/160.65 [8196]P1(f334(f334(x81962,f334(f334(f38(a1),x81961),x81963)),f44(a1,x81961,x81963)))+~P1(f334(f334(f249(a1),f2(a1)),x81963))+P1(f334(f334(f249(a1),f440(x81961,x81962,x81963)),x81963))
% 160.93/160.65 [8225]E(f334(f313(a881,a881,f334(f334(f7(a881,a881,a881),f22(a881)),x82251)),f334(f304(a881,x82252),x82253)),f196(f888(a881,a876)))+P1(f334(f334(f249(a881),x82251),x82253))+P1(f334(f334(f249(a881),x82252),x82253))
% 160.93/160.65 [8332]E(f334(f313(a881,a881,f334(f334(f7(a881,a881,a881),f22(a881)),x83321)),f334(f304(a881,x83322),x83323)),f334(f334(f312(a881),f2(a881)),f196(f888(a881,a876))))+P1(f334(f334(f249(a881),x83321),x83323))+~P1(f334(f334(f249(a881),x83322),x83323))
% 160.93/160.65 [8349]~P108(x83491)+E(f151(x83491,x83491,f5(x83491),x83492,x83493),x83493)+~P1(f334(f334(f336(x83491),x83492),f334(f174(x83491),x83493)))
% 160.93/160.65 [8363]P27(x83631,x83631,x83632,x83633)+~P1(f334(f61(x83631),x83633))+~P1(f334(f334(f248(f888(x83631,a876)),x83633),f334(f313(x83631,x83631,x83632),x83633)))
% 160.93/160.65 [8386]E(f334(f334(f80(a1),f334(f334(f81(a1),x83861),f441(x83862,x83863,x83861))),f440(x83862,x83863,x83861)),x83862)+P1(f334(f334(x83863,f334(f334(f38(a1),x83862),x83861)),f44(a1,x83862,x83861)))+~P1(f334(f334(f249(a1),f2(a1)),x83861))
% 160.93/160.65 [8627]~P1(f334(f334(x86271,f441(x86272,x86271,x86273)),f440(x86272,x86271,x86273)))+P1(f334(f334(x86271,f334(f334(f38(a1),x86272),x86273)),f44(a1,x86272,x86273)))+~P1(f334(f334(f249(a1),f2(a1)),x86273))
% 160.93/160.65 [9498]~P1(f334(f61(x94981),x94982))+~P1(f334(f334(f336(x94981),x94983),x94982))+P1(f334(f334(f249(a881),f334(f37(x94981),f334(f334(f22(f888(x94981,a876)),x94982),f334(f334(f312(x94981),x94983),f196(f888(x94981,a876)))))),f334(f37(x94981),x94982)))
% 160.93/160.65 [10104]P41(x101041,x101042,x101043)+~P1(f334(f334(f273(x101041,x101041,a876),f334(f334(f7(x101041,f888(x101041,a876),f888(x101041,a876)),f334(f334(f8(f888(a876,a876),f888(f888(x101041,a876),f888(x101041,a876)),x101041),f8(a876,a876,x101041)),f334(f334(f8(a876,f888(a876,a876),x101041),a332),f334(f334(f7(x101041,f888(x101041,a876),a876),f336(x101041)),x101042)))),f334(f334(f7(x101041,f888(x101041,a876),a876),f336(x101041)),x101042))),f592(x101043,x101042,x101041)))+P1(f334(f334(f336(x101041),f591(x101043,x101042,x101041)),x101042))
% 160.93/160.65 [5476]~P120(x54762)+E(x54761,f2(x54762))+E(f334(f334(f292(x54762),x54763),f334(f79(x54762),x54761)),f334(f79(x54762),f334(f334(f292(x54762),x54763),x54761)))
% 160.93/160.65 [5608]~E(x56083,f196(f888(x56081,a876)))+~E(x56082,f196(f888(x56081,a876)))+E(f334(f334(f114(f888(x56081,a876)),x56082),x56083),f196(f888(x56081,a876)))
% 160.93/160.65 [5666]~E(x56663,f2(a881))+~P1(f334(x56661,f2(a881)))+P1(f334(x56661,f334(f334(f38(a881),x56662),x56663)))
% 160.93/160.65 [5807]~P64(x58072)+E(x58071,f2(x58072))+E(f334(f334(f292(x58072),f334(f75(x58072),x58073)),f334(f75(x58072),x58071)),f334(f75(x58072),f334(f334(f292(x58072),x58073),x58071)))
% 160.93/160.65 [5972]~P1(f334(f61(x59721),x59723))+E(f334(f37(x59721),f334(f334(f312(x59721),x59722),x59723)),f334(a116,f334(f37(x59721),x59723)))+P1(f334(f334(f336(x59721),x59722),x59723))
% 160.93/160.65 [6044]~E(x60442,f2(a881))+P1(f334(x60441,f2(a881)))+~P1(f334(x60441,f334(f334(f38(a881),x60443),x60442)))
% 160.93/160.65 [6063]~P1(f334(f61(x60631),x60633))+E(f334(f37(x60631),f334(f334(f312(x60631),x60632),x60633)),f334(f37(x60631),x60633))+~P1(f334(f334(f336(x60631),x60632),x60633))
% 160.93/160.65 [6097]~P1(f334(f61(x60971),x60973))+E(f334(f37(x60971),f334(f334(f312(x60971),x60972),x60973)),f334(f334(f80(a881),f78(a881)),f334(f37(x60971),x60973)))+P1(f334(f334(f336(x60971),x60972),x60973))
% 160.93/160.65 [6220]E(f334(f334(f80(a881),x62201),f842(x62201,x62202,x62203)),x62202)+~P1(f334(x62203,f2(a881)))+P1(f334(x62203,f334(f334(f22(a881),x62202),x62201)))
% 160.93/160.65 [6221]E(f334(f334(f80(a881),x62211),f843(x62211,x62212,x62213)),x62212)+~P1(f334(x62213,f2(a881)))+P1(f334(x62213,f334(f334(f22(a881),x62212),x62211)))
% 160.93/160.65 [6268]~P5(x62681)+~P1(f334(f61(x62681),x62683))+E(f334(f334(f64(x62681,x62681,f114(x62681)),x62682),x62683),f334(f334(f114(x62681),x62682),f39(x62681,x62683)))
% 160.93/160.65 [6269]~P5(x62691)+~P1(f334(f61(x62691),x62693))+E(f334(f334(f64(x62691,x62691,f105(x62691)),x62692),x62693),f334(f334(f105(x62691),x62692),f40(x62691,x62693)))
% 160.93/160.65 [6275]~P93(x62751)+~E(f334(f107(x62751),x62752),f334(f107(x62751),x62753))+P32(x62751,f334(f107(x62751),f334(f334(f80(a1),x62752),f334(f79(a1),x62753))))
% 160.93/160.65 [6282]~P139(x62821)+E(f334(f334(f22(x62821),f334(f104(x62821),x62822)),f334(f104(x62821),x62823)),f334(f104(x62821),f334(f334(f22(a881),x62822),x62823)))+~P1(f334(f334(f248(a881),x62823),x62822))
% 160.93/160.65 [6367]E(f334(f334(f80(a881),x63671),f842(x63671,x63672,x63673)),x63672)+P1(f334(f334(f249(a881),x63672),x63671))+P1(f334(x63673,f334(f334(f22(a881),x63672),x63671)))
% 160.93/160.65 [6368]E(f334(f334(f80(a881),x63681),f843(x63681,x63682,x63683)),x63682)+P1(f334(f334(f249(a881),x63682),x63681))+P1(f334(x63683,f334(f334(f22(a881),x63682),x63681)))
% 160.93/160.65 [6383]~P111(x63831)+E(f334(f334(f81(x63831),f334(f75(x63831),x63832)),x63833),f334(f75(x63831),f334(f334(f81(x63831),x63832),x63833)))+~P1(f334(f334(f248(x63831),f2(x63831)),x63833))
% 160.93/160.65 [6384]~P63(x63841)+E(f334(f334(f292(x63841),f334(f75(x63841),x63842)),x63843),f334(f75(x63841),f334(f334(f292(x63841),x63842),x63843)))+~P1(f334(f334(f249(x63841),f2(x63841)),x63843))
% 160.93/160.65 [6392]~P2(x63921)+~P1(f334(f61(x63921),x63923))+E(f334(f334(f64(x63921,x63921,f114(x63921)),x63922),x63923),f10(x63921,f334(f334(f312(x63921),x63922),x63923)))
% 160.93/160.65 [6393]~P2(x63931)+~P1(f334(f61(x63931),x63933))+E(f334(f334(f64(x63931,x63931,f105(x63931)),x63932),x63933),f11(x63931,f334(f334(f312(x63931),x63932),x63933)))
% 160.93/160.65 [6394]~P108(x63941)+~P1(f334(f61(x63941),x63943))+E(f334(f334(f64(x63941,x63941,f246(x63941)),x63942),x63943),f14(x63941,f334(f334(f312(x63941),x63942),x63943)))
% 160.93/160.65 [6395]~P108(x63951)+~P1(f334(f61(x63951),x63953))+E(f334(f334(f64(x63951,x63951,f247(x63951)),x63952),x63953),f15(x63951,f334(f334(f312(x63951),x63952),x63953)))
% 160.93/160.65 [6440]E(x64401,f117(x64402))+~E(f182(x64402,x64403),f117(f882(x64402)))+~P1(f334(f334(f336(f882(x64402)),x64401),f334(f174(f882(x64402)),x64403)))
% 160.93/160.65 [6482]~P1(f334(f139(x64821),x64823))+P1(f334(f334(f336(x64821),x64822),f334(f174(x64821),x64823)))+P1(f334(f139(x64821),f334(f334(f153(x64821),x64822),x64823)))
% 160.93/160.65 [6493]~P95(x64931)+~P1(f334(f61(x64931),x64933))+E(f334(f63(x64931,f81(x64931)),f334(f334(f312(x64931),x64932),x64933)),f334(f334(f64(x64931,x64931,f81(x64931)),x64932),x64933))
% 160.93/160.65 [6515]~P108(x65151)+~P1(f334(f61(x65151),x65153))+E(f12(x65151,f247(x65151),f334(f334(f312(x65151),x65152),x65153)),f334(f334(f64(x65151,x65151,f247(x65151)),x65152),x65153))
% 160.93/160.65 [6516]~P108(x65161)+~P1(f334(f61(x65161),x65163))+E(f13(x65161,f246(x65161),f334(f334(f312(x65161),x65162),x65163)),f334(f334(f64(x65161,x65161,f246(x65161)),x65162),x65163))
% 160.93/160.65 [6518]P1(f334(x65181,f2(a881)))+~P1(f334(f334(f249(a881),x65182),x65183))+~P1(f334(x65181,f334(f334(f22(a881),x65182),x65183)))
% 160.93/160.65 [6536]~P111(x65361)+P1(f334(f334(f249(x65361),x65362),x65363))+~P1(f334(f334(f249(x65361),f334(f75(x65361),x65362)),x65363))
% 160.93/160.65 [6538]~P85(x65381)+P1(f334(f334(f248(x65381),x65382),x65383))+~P1(f334(f334(f248(x65381),f334(f75(x65381),x65382)),x65383))
% 160.93/160.65 [6555]E(x65551,f117(x65552))+E(f334(f143(x65552),f334(f334(f140(x65552),x65553),x65551)),f334(f334(f167(x65552),x65551),x65553))+~P1(f334(f334(f249(a881),x65553),f334(f197(f882(x65552)),x65551)))
% 160.93/160.65 [6606]~P1(f334(x66061,x66063))+P1(f334(x66061,f358(x66061,x66062)))+~P1(f334(f334(f336(a881),x66063),f334(f304(a881,f2(a881)),x66062)))
% 160.93/160.65 [6628]P1(f334(x66281,x66282))+~P1(f334(f334(f249(a881),x66282),x66283))+P1(f334(f334(f336(a881),f357(x66281,x66283)),f334(f304(a881,f2(a881)),x66283)))
% 160.93/160.65 [6645]~P106(x66451)+~P1(f334(f334(f249(x66451),f2(x66451)),x66452))+P1(f334(f334(f249(x66451),f2(x66451)),f334(f334(f259(x66451),x66452),x66453)))
% 160.93/160.65 [6647]~P106(x66471)+~P1(f334(f334(f248(x66471),f2(x66471)),x66472))+P1(f334(f334(f248(x66471),f2(x66471)),f334(f334(f259(x66471),x66472),x66473)))
% 160.93/160.65 [6648]~P106(x66481)+~P1(f334(f334(f248(x66481),f78(x66481)),x66482))+P1(f334(f334(f248(x66481),f78(x66481)),f334(f334(f259(x66481),x66482),x66483)))
% 160.93/160.65 [6672]~P1(f334(x66721,x66723))+~P1(f334(f334(f249(a881),x66723),x66722))+P1(f334(f334(f336(a881),f348(x66721,x66722)),f334(f304(a881,f2(a881)),x66722)))
% 160.93/160.65 [6679]P1(f334(f61(x66791),x66792))+~P1(f334(f61(x66791),x66793))+~P1(f334(f334(f248(f888(x66791,a876)),x66792),x66793))
% 160.93/160.65 [6687]P1(f334(x66871,x66872))+~P1(f334(x66871,f359(x66871,x66873)))+~P1(f334(f334(f336(a881),x66872),f334(f304(a881,f2(a881)),x66873)))
% 160.93/160.65 [6698]E(x66981,f2(a881))+P1(f334(x66982,f413(x66981,x66983,x66982)))+~P1(f334(x66982,f334(f334(f38(a881),x66983),x66981)))
% 160.93/160.65 [6706]~P124(x67062)+E(x67061,f2(x67062))+~E(f334(f334(f80(x67062),f334(f334(f81(x67062),x67063),x67063)),f334(f334(f81(x67062),x67061),x67061)),f2(x67062))
% 160.93/160.65 [6707]~P124(x67072)+E(x67071,f2(x67072))+~E(f334(f334(f80(x67072),f334(f334(f81(x67072),x67071),x67071)),f334(f334(f81(x67072),x67073),x67073)),f2(x67072))
% 160.93/160.65 [6752]E(x67521,f2(a881))+~P1(f334(x67522,f414(x67521,x67523,x67522)))+P1(f334(x67522,f334(f334(f38(a881),x67523),x67521)))
% 160.93/160.65 [6757]~P108(x67571)+~P16(x67571,x67573)+P16(x67571,f334(f334(f150(x67571,x67571,f5(x67571)),x67572),x67573))
% 160.93/160.65 [6800]P1(f334(x68001,f413(x68002,x68003,x68001)))+P1(f334(x68001,f2(a881)))+~P1(f334(x68001,f334(f334(f38(a881),x68003),x68002)))
% 160.93/160.65 [6806]~P93(x68061)+E(f334(f107(x68061),x68062),f334(f107(x68061),x68063))+~P32(x68061,f334(f107(x68061),f334(f334(f80(a1),x68062),f334(f79(a1),x68063))))
% 160.93/160.65 [6871]E(x68711,f2(a1))+E(x68712,f2(a1))+~P1(f334(f48(x68712,x68712),f334(f334(f269(a1,a1),x68713),x68711)))
% 160.93/160.65 [6872]E(x68721,f78(a1))+E(x68722,f2(a1))+~P1(f334(f48(x68722,x68722),f334(f334(f269(a1,a1),x68721),x68723)))
% 160.93/160.65 [6887]P1(f334(x68871,x68872))+P1(f334(f334(f249(a881),f359(x68871,x68873)),x68873))+~P1(f334(f334(f336(a881),x68872),f334(f304(a881,f2(a881)),x68873)))
% 160.93/160.65 [6909]~P1(f334(x69091,f842(x69093,x69092,x69091)))+~P1(f334(x69091,f2(a881)))+P1(f334(x69091,f334(f334(f22(a881),x69092),x69093)))
% 160.93/160.65 [6910]~P1(f334(x69101,f843(x69103,x69102,x69101)))+~P1(f334(x69101,f2(a881)))+P1(f334(x69101,f334(f334(f22(a881),x69102),x69103)))
% 160.93/160.65 [6911]~P1(f334(x69111,f414(x69113,x69112,x69111)))+~P1(f334(x69111,f2(a881)))+P1(f334(x69111,f334(f334(f38(a881),x69112),x69113)))
% 160.93/160.65 [6929]~P1(f334(x69291,x69293))+P1(f334(f334(f249(a881),f358(x69291,x69292)),x69292))+~P1(f334(f334(f336(a881),x69293),f334(f304(a881,f2(a881)),x69292)))
% 160.93/160.65 [6930]E(f334(f334(f22(a881),f334(f334(f22(a881),x69301),x69302)),f334(f334(f22(a881),x69303),x69302)),f334(f334(f22(a881),x69301),x69303))+~P1(f334(f334(f248(a881),x69302),x69301))+~P1(f334(f334(f248(a881),x69302),x69303))
% 160.93/160.65 [6965]~P83(x69651)+~P1(f334(f334(f249(x69651),f334(f79(x69651),x69653)),x69652))+P1(f334(f334(f249(x69651),f334(f79(x69651),x69652)),x69653))
% 160.93/160.65 [6966]~P111(x69661)+~P1(f334(f334(f249(x69661),f334(f75(x69661),x69662)),x69663))+P1(f334(f334(f249(x69661),f334(f79(x69661),x69662)),x69663))
% 160.93/160.65 [6968]~P83(x69681)+~P1(f334(f334(f248(x69681),f334(f79(x69681),x69683)),x69682))+P1(f334(f334(f248(x69681),f334(f79(x69681),x69682)),x69683))
% 160.93/160.65 [6970]~P85(x69701)+~P1(f334(f334(f248(x69701),f334(f75(x69701),x69702)),x69703))+P1(f334(f334(f248(x69701),f334(f79(x69701),x69702)),x69703))
% 160.93/160.65 [7004]~P1(f334(x70043,f842(x70042,x70041,x70043)))+P1(f334(f334(f249(a881),x70041),x70042))+P1(f334(x70043,f334(f334(f22(a881),x70041),x70042)))
% 160.93/160.65 [7005]~P1(f334(x70053,f843(x70052,x70051,x70053)))+P1(f334(f334(f249(a881),x70051),x70052))+P1(f334(x70053,f334(f334(f22(a881),x70051),x70052)))
% 160.93/160.65 [7055]~E(f863(x70553,x70552,x70551),f864(x70553,x70552,x70551))+E(f334(f334(f105(f888(x70551,a876)),x70552),f39(f888(x70551,a876),x70553)),f196(f888(x70551,a876)))+P1(f334(f334(f336(f888(x70551,a876)),x70552),x70553))
% 160.93/160.65 [7064]~P1(f334(f61(x70641),x70643))+P1(f334(f61(x70641),f40(f888(x70641,a876),x70642)))+~P1(f334(f334(f336(f888(x70641,a876)),x70643),x70642))
% 160.93/160.65 [7123]~P108(x71231)+E(f334(f334(f114(f888(x71231,a876)),f334(f304(x71231,x71232),x71233)),f334(f334(f312(x71231),x71233),f196(f888(x71231,a876)))),f305(x71231,x71232,x71233))+~P1(f334(f334(f248(x71231),x71232),x71233))
% 160.93/160.65 [7124]E(x71241,f2(a881))+P1(f334(f334(f249(a881),f415(x71241,x71243,x71242)),x71241))+P1(f334(x71242,f334(f334(f38(a881),x71243),x71241)))
% 160.93/160.65 [7159]E(x71591,x71592)+~P1(f334(f334(f248(f888(x71593,a876)),x71591),x71592))+P1(f334(f334(f249(f888(x71593,a876)),x71591),x71592))
% 160.93/160.65 [7172]E(x71721,x71722)+~E(f334(f197(f882(x71723)),x71721),f334(f197(f882(x71723)),x71722))+P1(f334(f334(f249(a881),f656(x71723,x71721,x71722)),f334(f197(f882(x71723)),x71722)))
% 160.93/160.65 [7220]P8(x72201,x72202,x72203)+~E(f334(f267(x72201,x72201),x72203),x72202)+~E(f334(f334(f291(x72201,x72201,x72201),f334(f289(x72201,x72201),x72203)),x72203),x72203)
% 160.93/160.65 [7292]~P1(f334(x72921,f2(a881)))+P1(f334(f334(f249(a881),f415(x72923,x72922,x72921)),x72923))+P1(f334(x72921,f334(f334(f38(a881),x72922),x72923)))
% 160.93/160.65 [7301]~P108(x73011)+E(f334(f334(f114(f888(x73011,a876)),f308(x73011,x73012,x73013)),f334(f334(f312(x73011),x73013),f196(f888(x73011,a876)))),f307(x73011,x73012,x73013))+~P1(f334(f334(f249(x73011),x73012),x73013))
% 160.93/160.65 [7401]~P1(f334(f61(x74011),x74013))+P1(f334(f334(f249(a881),f334(f37(x74011),x74012)),f334(f37(x74011),x74013)))+~P1(f334(f334(f249(f888(x74011,a876)),x74012),x74013))
% 160.93/160.65 [7402]~P1(f334(f61(x74021),x74023))+P1(f334(f334(f248(a881),f334(f37(x74021),x74022)),f334(f37(x74021),x74023)))+~P1(f334(f334(f248(f888(x74021,a876)),x74022),x74023))
% 160.93/160.65 [7539]E(x75391,x75392)+~P1(f334(f334(f248(f888(x75393,a876)),x75392),x75391))+~P1(f334(f334(f248(f888(x75393,a876)),x75391),x75392))
% 160.93/160.65 [7542]~P108(x75421)+P16(x75421,x75422)+~P16(x75421,f334(f334(f150(x75421,x75421,f5(x75421)),x75423),x75422))
% 160.93/160.65 [7610]~P1(f334(f334(f249(a881),x76103),x76102))+~P1(f334(f334(f249(a881),x76103),x76101))+P1(f334(f334(f249(a881),f334(f334(f22(a881),x76101),x76102)),f334(f334(f22(a881),x76101),x76103)))
% 160.93/160.65 [7611]~P1(f334(f334(f249(a881),x76111),x76113))+~P1(f334(f334(f248(a881),x76112),x76111))+P1(f334(f334(f249(a881),f334(f334(f22(a881),x76111),x76112)),f334(f334(f22(a881),x76113),x76112)))
% 160.93/160.65 [7628]~P1(f334(f334(f249(a1),x76282),f2(a1)))+~P1(f334(f334(f248(a1),x76283),x76281))+P1(f334(f334(f248(a1),f334(f334(f38(a1),x76281),x76282)),f334(f334(f38(a1),x76283),x76282)))
% 160.93/160.65 [7648]~P1(f334(f334(f249(a881),f2(a881)),x76482))+~P1(f334(f334(f249(a881),x76481),x76483))+P1(f334(f334(f249(a881),f334(f334(f81(a881),x76481),x76482)),f334(f334(f81(a881),x76483),x76482)))
% 160.93/160.65 [7649]~P1(f334(f334(f249(a881),f2(a881)),x76491))+~P1(f334(f334(f249(a881),x76492),x76493))+P1(f334(f334(f249(a881),f334(f334(f81(a881),x76491),x76492)),f334(f334(f81(a881),x76491),x76493)))
% 160.93/160.65 [7650]~P1(f334(f334(f249(a1),f2(a1)),x76501))+~P1(f334(f334(f249(a1),x76502),x76503))+P1(f334(f334(f249(a1),f334(f334(f81(a1),x76501),x76502)),f334(f334(f81(a1),x76501),x76503)))
% 160.93/160.65 [7652]~P1(f334(f334(f249(a881),f2(a881)),x76523))+~P1(f334(f334(f248(a881),x76523),x76522))+P1(f334(f334(f248(a881),f334(f334(f38(a881),x76521),x76522)),f334(f334(f38(a881),x76521),x76523)))
% 160.93/160.65 [7653]~P1(f334(f334(f249(a1),f2(a1)),x76532))+~P1(f334(f334(f248(a1),x76531),x76533))+P1(f334(f334(f248(a1),f334(f334(f38(a1),x76531),x76532)),f334(f334(f38(a1),x76533),x76532)))
% 160.93/160.65 [7701]E(x77011,f2(a881))+E(f334(f334(f80(a881),f334(f334(f81(a881),x77011),f414(x77011,x77012,x77013))),f415(x77011,x77012,x77013)),x77012)+P1(f334(x77013,f334(f334(f38(a881),x77012),x77011)))
% 160.93/160.65 [7757]E(f334(f334(f80(a881),f334(f334(f81(a881),x77571),f414(x77571,x77572,x77573))),f415(x77571,x77572,x77573)),x77572)+~P1(f334(x77573,f2(a881)))+P1(f334(x77573,f334(f334(f38(a881),x77572),x77571)))
% 160.93/160.65 [7766]~P1(f334(x77663,x77662))+P1(f334(f334(f334(a202,x77661),x77662),f467(x77662,x77661,x77663)))+~P1(f334(f334(f334(a202,f32(x77663,x77661)),x77662),x77662))
% 160.93/160.65 [7775]~P1(f334(f61(x77751),x77753))+P1(f334(f334(f336(x77751),f356(x77752,x77753,x77751)),x77753))+P1(f334(f334(f249(a881),f2(a881)),f334(f334(f9(x77751,a881),x77752),x77753)))
% 160.93/160.65 [7776]~P1(f334(f61(x77761),x77763))+P1(f334(f334(f336(x77761),f443(x77762,x77763,x77761)),x77763))+P1(f334(f334(f249(a881),f2(a881)),f334(f334(f9(x77761,a881),x77762),x77763)))
% 160.93/160.65 [8063]E(x80631,f196(f888(x80632,a876)))+E(x80631,f334(f334(f312(x80632),x80633),f196(f888(x80632,a876))))+~P1(f334(f334(f248(f888(x80632,a876)),x80631),f334(f334(f312(x80632),x80633),f196(f888(x80632,a876)))))
% 160.93/160.65 [8081]~P60(x80811)+P13(x80811,x80812,x80813)+P1(f334(f334(f336(f882(x80811)),f731(x80813,x80812,x80811)),f334(f174(f882(x80811)),f54(x80811,x80813,f55(x80811)))))
% 160.93/160.65 [8101]~P1(f334(f334(f249(a881),f2(a881)),x81013))+P1(f334(f334(f249(a881),x81011),x81012))+~P1(f334(f334(f249(a881),f334(f334(f259(a881),x81013),x81011)),f334(f334(f259(a881),x81013),x81012)))
% 160.93/160.65 [8103]~P1(f334(f334(f249(a881),f2(a881)),x81033))+P1(f334(f334(f248(a881),x81031),x81032))+~P1(f334(f334(f248(a881),f334(f334(f81(a881),x81033),x81031)),f334(f334(f81(a881),x81033),x81032)))
% 160.93/160.65 [8104]~P1(f334(f334(f249(a881),f2(a881)),x81043))+P1(f334(f334(f248(a881),x81041),x81042))+~P1(f334(f334(f248(a881),f334(f334(f81(a881),x81041),x81043)),f334(f334(f81(a881),x81042),x81043)))
% 160.93/160.65 [8130]~P60(x81301)+~P12(x81301,x81303,x81302)+P1(f334(f334(f336(f882(x81301)),f724(x81302,x81303,x81301)),f334(f174(f882(x81301)),f54(x81301,x81302,f55(x81301)))))
% 160.93/160.65 [8148]~E(f334(f334(f105(f888(x81481,a876)),f864(x81483,x81482,x81481)),f863(x81483,x81482,x81481)),f196(f888(x81481,a876)))+E(f334(f334(f105(f888(x81481,a876)),x81482),f39(f888(x81481,a876),x81483)),f196(f888(x81481,a876)))+P1(f334(f334(f336(f888(x81481,a876)),x81482),x81483))
% 160.93/160.65 [8165]E(x81651,f117(x81652))+~E(f334(f144(f882(x81652),f882(x81652),f136(x81652),f117(x81652)),x81653),f117(x81652))+~P1(f334(f334(f336(f882(x81652)),x81651),f334(f174(f882(x81652)),x81653)))
% 160.93/160.65 [8230]E(x82301,f196(f888(f888(x82302,a876),a876)))+P1(f334(f334(f336(f888(x82302,a876)),f500(x82303,x82301,x82302)),x82301))+P1(f334(f334(f248(f888(x82302,a876)),f40(f888(x82302,a876),x82301)),x82303))
% 160.93/160.65 [8238]~P68(x82381)+~P74(x82381)+E(f334(f334(f6(a1,x82381),f334(f334(f8(a881,x82381,a1),x82382),a108)),f334(f313(a881,a1,f104(a1)),x82383)),f334(f334(f6(a881,x82381),x82382),x82383))
% 160.93/160.65 [8239]~P68(x82391)+~P74(x82391)+E(f334(f334(f9(a1,x82391),f334(f334(f8(a881,x82391,a1),x82392),a108)),f334(f313(a881,a1,f104(a1)),x82393)),f334(f334(f9(a881,x82391),x82392),x82393))
% 160.93/160.65 [8279]~P1(f334(f61(x82791),x82793))+~P1(f334(f334(f249(a881),f2(a881)),f334(x82792,f356(x82792,x82793,x82791))))+P1(f334(f334(f249(a881),f2(a881)),f334(f334(f9(x82791,a881),x82792),x82793)))
% 160.93/160.65 [8280]~P1(f334(f61(x82801),x82803))+~P1(f334(f334(f249(a881),f2(a881)),f334(x82802,f443(x82802,x82803,x82801))))+P1(f334(f334(f249(a881),f2(a881)),f334(f334(f9(x82801,a881),x82802),x82803)))
% 160.93/160.65 [8310]~P1(f334(x83101,x83103))+P1(f334(f334(f334(a202,f32(x83101,x83102)),f467(x83103,x83102,x83101)),x83103))+~P1(f334(f334(f334(a202,f32(x83101,x83102)),x83103),x83103))
% 160.93/160.65 [8314]~P62(x83142)+E(x83141,f78(x83142))+E(f334(f334(f292(x83142),f334(f334(f22(x83142),f334(f334(f259(x83142),x83141),x83143)),f78(x83142))),f334(f334(f22(x83142),x83141),f78(x83142))),f334(f334(f6(a881,x83142),f334(f259(x83142),x83141)),f334(f304(a881,f2(a881)),x83143)))
% 160.93/160.65 [8372]E(x83721,f2(a881))+~P1(f334(x83723,f334(f334(f38(a881),x83722),x83721)))+P1(f334(f334(f249(a881),x83722),f334(f334(f81(a881),x83721),f334(a116,f413(x83721,x83722,x83723)))))
% 160.93/160.65 [8389]P1(f334(x83891,f2(a881)))+~P1(f334(x83891,f334(f334(f38(a881),x83892),x83893)))+P1(f334(f334(f249(a881),x83892),f334(f334(f81(a881),x83893),f334(a116,f413(x83893,x83892,x83891)))))
% 160.93/160.65 [8429]E(x84291,f2(a881))+~P1(f334(x84293,f334(f334(f38(a881),x84292),x84291)))+P1(f334(f334(f248(a881),f334(f334(f81(a881),x84291),f413(x84291,x84292,x84293))),x84292))
% 160.93/160.65 [8463]P1(f334(x84631,f2(a881)))+~P1(f334(x84631,f334(f334(f38(a881),x84633),x84632)))+P1(f334(f334(f248(a881),f334(f334(f81(a881),x84632),f413(x84632,x84633,x84631))),x84633))
% 160.93/160.65 [8466]~P108(x84661)+E(f334(f334(f150(x84661,x84661,f5(x84661)),x84662),x84663),f151(x84661,x84661,f5(x84661),x84662,x84663))+P1(f334(f334(f336(x84661),x84662),f334(f174(x84661),x84663)))
% 160.93/160.65 [8502]~E(f334(x85023,f607(x85022,x85023,x85021)),f334(x85023,f609(x85022,x85023,x85021)))+~P57(x85021,f334(x85023,f608(x85022,x85023,x85021)))+P57(x85021,f334(f334(f41(x85022,f888(x85021,f888(x85021,a876))),f257(f888(x85022,a876))),x85023))
% 160.93/160.65 [8513]E(x85131,f196(f888(f888(x85132,a876),a876)))+~P1(f334(f334(f248(f888(x85132,a876)),f500(x85133,x85131,x85132)),x85133))+P1(f334(f334(f248(f888(x85132,a876)),f40(f888(x85132,a876),x85131)),x85133))
% 160.93/160.65 [8578]~P64(x85781)+~P1(f334(f334(f249(x85781),x85782),x85783))+P1(f334(f334(f249(x85781),x85782),f334(f334(f292(x85781),f334(f334(f80(x85781),x85782),x85783)),f334(f334(f80(x85781),f78(x85781)),f78(x85781)))))
% 160.93/160.65 [8633]~P1(f334(f334(x86331,f515(x86331,x86333,x86332)),f520(x86331,x86333,x86332)))+P1(f334(f334(x86331,x86332),x86333))+~P1(f334(f322(f887(a1,a1),a51),f334(f334(f269(a1,a1),x86332),x86333)))
% 160.93/160.65 [8634]~P1(f334(f334(x86341,f521(x86341,x86343,x86342)),f522(x86341,x86343,x86342)))+P1(f334(f334(x86341,x86342),x86343))+~P1(f334(f322(f887(a1,a1),a56),f334(f334(f269(a1,a1),x86342),x86343)))
% 160.93/160.65 [8635]~P1(f334(f334(x86351,f523(x86351,x86353,x86352)),f524(x86351,x86353,x86352)))+P1(f334(f334(x86351,x86352),x86353))+~P1(f334(f322(f887(a1,a1),a237),f334(f334(f269(a1,a1),x86352),x86353)))
% 160.93/160.65 [8636]~P1(f334(f334(x86361,f527(x86361,x86363,x86362)),f528(x86361,x86363,x86362)))+P1(f334(f334(x86361,x86362),x86363))+~P1(f334(f322(f887(a881,a881),a232),f334(f334(f269(a881,a881),x86362),x86363)))
% 160.93/160.65 [8637]~P1(f334(f334(x86371,f697(x86371,x86373,x86372)),f699(x86371,x86373,x86372)))+P1(f334(f334(x86371,x86372),x86373))+~P1(f334(f322(f887(a1,a1),a185),f334(f334(f269(a1,a1),x86372),x86373)))
% 160.93/160.65 [8638]~P1(f334(f334(x86381,f819(x86381,x86383,x86382)),f820(x86381,x86383,x86382)))+P1(f334(f334(x86381,x86382),x86383))+~P1(f334(f322(f887(a1,a1),a135),f334(f334(f269(a1,a1),x86382),x86383)))
% 160.93/160.65 [8891]P1(f334(f334(x88911,x88912),x88913))+P1(f334(f322(f887(a881,a881),a232),f334(f334(f269(a881,a881),f527(x88911,x88913,x88912)),f528(x88911,x88913,x88912))))+~P1(f334(f322(f887(a881,a881),a232),f334(f334(f269(a881,a881),x88912),x88913)))
% 160.93/160.65 [8892]P1(f334(f334(x88921,x88922),x88923))+P1(f334(f322(f887(a1,a1),a51),f334(f334(f269(a1,a1),f515(x88921,x88923,x88922)),f520(x88921,x88923,x88922))))+~P1(f334(f322(f887(a1,a1),a51),f334(f334(f269(a1,a1),x88922),x88923)))
% 160.93/160.65 [8893]P1(f334(f334(x88931,x88932),x88933))+P1(f334(f322(f887(a1,a1),a56),f334(f334(f269(a1,a1),f521(x88931,x88933,x88932)),f522(x88931,x88933,x88932))))+~P1(f334(f322(f887(a1,a1),a56),f334(f334(f269(a1,a1),x88932),x88933)))
% 160.93/160.65 [8894]P1(f334(f334(x88941,x88942),x88943))+P1(f334(f322(f887(a1,a1),a237),f334(f334(f269(a1,a1),f523(x88941,x88943,x88942)),f524(x88941,x88943,x88942))))+~P1(f334(f322(f887(a1,a1),a237),f334(f334(f269(a1,a1),x88942),x88943)))
% 160.93/160.65 [8895]P1(f334(f334(x88951,x88952),x88953))+P1(f334(f322(f887(a1,a1),a185),f334(f334(f269(a1,a1),f697(x88951,x88953,x88952)),f699(x88951,x88953,x88952))))+~P1(f334(f322(f887(a1,a1),a185),f334(f334(f269(a1,a1),x88952),x88953)))
% 160.93/160.65 [8896]P1(f334(f334(x88961,x88962),x88963))+P1(f334(f322(f887(a1,a1),a135),f334(f334(f269(a1,a1),f819(x88961,x88963,x88962)),f820(x88961,x88963,x88962))))+~P1(f334(f322(f887(a1,a1),a135),f334(f334(f269(a1,a1),x88962),x88963)))
% 160.93/160.65 [9245]~P1(f334(f61(x92451),x92453))+P1(f334(f334(f336(f887(f888(x92451,a876),f888(x92451,a876))),f334(f334(f269(f888(x92451,a876),f888(x92451,a876)),x92452),x92453)),f309(x92451)))+~P1(f334(f334(f249(f888(x92451,a876)),x92452),x92453))
% 160.93/160.65 [9316]~P57(x93161,f334(x93163,f608(x93162,x93163,x93161)))+P57(x93161,f334(f334(f41(x93162,f888(x93161,f888(x93161,a876))),f257(f888(x93162,a876))),x93163))+~E(f334(f334(f105(f888(x93161,a876)),f263(x93161,x93161,f334(x93163,f607(x93162,x93163,x93161)))),f264(x93161,x93161,f334(x93163,f609(x93162,x93163,x93161)))),f196(f888(x93161,a876)))
% 160.93/160.65 [9405]~P30(a877,f196(f888(f880(a877),a876)),f334(f334(f312(f880(a877)),f334(f334(f334(f92(a877),x94051),x94052),x94053)),f196(f888(f880(a877),a876))))+P26(a877,f196(f888(f880(a877),a876)),f334(f334(f312(f880(a877)),f334(f334(f334(f92(a877),x94051),x94052),x94053)),f196(f888(f880(a877),a876))))+~P26(a877,f196(f888(f880(a877),a876)),f334(f334(f312(f880(a877)),f334(f334(f334(f92(a877),a331),x94052),f334(a202,x94052))),f196(f888(f880(a877),a876))))
% 160.93/160.65 [9516]P41(x95161,x95162,x95163)+P1(f334(f334(f336(f887(x95161,x95161)),f592(x95163,x95162,x95161)),x95163))+~P1(f334(f334(f336(f887(x95161,x95161)),f334(f334(f269(x95161,x95161),f591(x95163,x95162,x95161)),f591(x95163,x95162,x95161))),x95163))
% 160.93/160.65 [10105]P41(x101051,x101052,x101053)+~P1(f334(f334(f273(x101051,x101051,a876),f334(f334(f7(x101051,f888(x101051,a876),f888(x101051,a876)),f334(f334(f8(f888(a876,a876),f888(f888(x101051,a876),f888(x101051,a876)),x101051),f8(a876,a876,x101051)),f334(f334(f8(a876,f888(a876,a876),x101051),a332),f334(f334(f7(x101051,f888(x101051,a876),a876),f336(x101051)),x101052)))),f334(f334(f7(x101051,f888(x101051,a876),a876),f336(x101051)),x101052))),f592(x101053,x101052,x101051)))+~P1(f334(f334(f336(f887(x101051,x101051)),f334(f334(f269(x101051,x101051),f591(x101053,x101052,x101051)),f591(x101053,x101052,x101051))),x101053))
% 160.93/160.65 [5647]~P58(x56472)+E(x56471,f2(x56472))+E(f334(f334(f38(x56472),f334(f334(f81(x56472),x56473),x56471)),x56471),x56473)
% 160.93/160.65 [5648]~P58(x56482)+E(x56481,f2(x56482))+E(f334(f334(f38(x56482),f334(f334(f81(x56482),x56481),x56483)),x56481),x56483)
% 160.93/160.65 [6439]~P68(x64391)+~E(f334(x64392,f2(a881)),f2(x64391))+E(f334(f334(f6(a881,x64391),x64392),f334(f304(a881,f334(a116,f2(a881))),x64393)),f334(f334(f6(a881,x64391),x64392),f334(f304(a881,f2(a881)),x64393)))
% 160.93/160.65 [6567]~P58(x65672)+E(x65671,f2(x65672))+E(f334(f334(f38(x65672),f334(f334(f80(x65672),x65673),x65671)),x65671),f334(f334(f80(x65672),f334(f334(f38(x65672),x65673),x65671)),f78(x65672)))
% 160.93/160.65 [6568]~P58(x65682)+E(x65681,f2(x65682))+E(f334(f334(f38(x65682),f334(f334(f80(x65682),x65681),x65683)),x65681),f334(f334(f80(x65682),f334(f334(f38(x65682),x65683),x65681)),f78(x65682)))
% 160.93/160.65 [6788]~P1(f334(x67883,f2(a1)))+P1(f334(f334(f248(a881),x67881),x67882))+P1(f334(x67883,f334(f104(a1),f334(f334(f22(a881),x67882),x67881))))
% 160.93/160.65 [6893]P1(f334(f334(f248(a881),x68932),x68931))+P1(f334(f334(f249(a881),x68931),x68932))+P1(f334(x68933,f334(f104(a1),f334(f334(f22(a881),x68931),x68932))))
% 160.93/160.65 [6963]E(f334(f334(f80(a881),f334(f107(a881),x69631)),f334(f334(f80(a881),f334(f107(a881),x69632)),x69633)),f334(f334(f80(a881),f334(f107(a881),x69631)),x69633))+P1(f334(a201,f334(f107(a1),x69631)))+~P1(f334(a201,f334(f107(a1),x69632)))
% 160.93/160.65 [7042]~E(x70422,f334(f334(f38(a881),x70423),x70421))+~P1(f334(f334(f249(a881),f2(a881)),x70421))+P1(f334(f334(f248(a881),f334(f334(f81(a881),x70421),x70422)),x70423))
% 160.93/160.65 [7156]~P1(f334(f61(x71561),x71563))+~P1(f334(f61(x71561),x71562))+P1(f334(f61(x71561),f334(f334(f114(f888(x71561,a876)),x71562),x71563)))
% 160.93/160.65 [7452]~P108(x74521)+~P1(f334(f61(x74521),x74522))+E(f141(x74521,f334(f334(f22(f888(x74521,a876)),x74522),f334(f334(f312(x74521),x74523),f196(f888(x74521,a876))))),f172(x74521,x74523,f141(x74521,x74522)))
% 160.93/160.65 [7518]P1(f334(x75181,f2(a1)))+~P1(f334(f334(f249(a881),x75182),x75183))+~P1(f334(x75181,f334(f104(a1),f334(f334(f22(a881),x75182),x75183))))
% 160.93/160.65 [7536]~P1(f334(f61(x75361),x75362))+E(f334(f37(x75361),f334(f334(f22(f888(x75361,a876)),x75362),f334(f334(f312(x75361),x75363),f196(f888(x75361,a876))))),f334(f37(x75361),x75362))+P1(f334(f334(f336(x75361),x75363),x75362))
% 160.93/160.65 [7668]~P106(x76681)+~P1(f334(f334(f249(x76681),f78(x76681)),x76682))+P1(f334(f334(f249(x76681),f78(x76681)),f334(f334(f81(x76681),x76682),f334(f334(f259(x76681),x76682),x76683))))
% 160.93/160.65 [7711]~P1(f334(f61(x77111),x77113))+E(f334(f334(f22(a881),f334(f37(x77111),x77112)),f334(f37(x77111),x77113)),f334(f37(x77111),f334(f334(f22(f888(x77111,a876)),x77112),x77113)))+~P1(f334(f334(f248(f888(x77111,a876)),x77113),x77112))
% 160.93/160.65 [7767]~P1(f334(f334(f248(a881),x77672),x77673))+~P1(f334(f334(f248(a881),x77671),f334(f334(f22(a881),x77673),x77672)))+P1(f334(f334(f248(a881),f334(f334(f80(a881),x77671),x77672)),x77673))
% 160.93/160.65 [7819]P1(f334(f61(x78191),x78192))+~P1(f334(f61(x78191),x78193))+~P1(f334(f61(x78191),f334(f334(f22(f888(x78191,a876)),x78192),x78193)))
% 160.93/160.65 [7825]~P1(f334(f61(x78251),x78252))+E(f334(f37(x78251),f334(f334(f22(f888(x78251,a876)),x78252),f334(f334(f312(x78251),x78253),f196(f888(x78251,a876))))),f334(f334(f22(a881),f334(f37(x78251),x78252)),f78(a881)))+~P1(f334(f334(f336(x78251),x78253),x78252))
% 160.93/160.65 [7901]P57(x79011,x79012)+~P57(x79011,x79013)+~P1(f334(f334(f248(f888(x79011,f888(x79011,a876))),x79012),x79013))
% 160.93/160.65 [7942]~P1(f334(f334(f248(a881),x79423),x79422))+P1(f334(f334(f248(a881),x79421),f334(f334(f22(a881),x79422),x79423)))+~P1(f334(f334(f248(a881),f334(f334(f80(a881),x79421),x79423)),x79422))
% 160.93/160.65 [7960]P39(x79601,x79602)+~P39(x79601,x79603)+~P1(f334(f334(f248(f888(f887(x79601,x79601),a876)),x79602),x79603))
% 160.93/160.65 [7961]P55(x79611,x79612)+~P55(x79611,x79613)+~P1(f334(f334(f248(f888(f887(x79611,x79611),a876)),x79612),x79613))
% 160.93/160.65 [8203]~P106(x82031)+~P1(f334(f334(f249(x82031),f78(x82031)),x82032))+P1(f334(f334(f249(x82031),f334(f334(f259(x82031),x82032),x82033)),f334(f334(f81(x82031),x82032),f334(f334(f259(x82031),x82032),x82033))))
% 160.93/160.65 [8297]~P1(f334(x82971,f2(a1)))+~P1(f334(x82971,f334(f334(f22(a1),f334(f104(a1),x82972)),f334(f104(a1),x82973))))+P1(f334(x82971,f334(f104(a1),f334(f334(f22(a881),x82972),x82973))))
% 160.93/160.65 [8311]~P1(f334(f334(f248(a881),x83113),x83112))+P1(f334(x83111,f334(f334(f22(a1),f334(f104(a1),x83112)),f334(f104(a1),x83113))))+~P1(f334(x83111,f334(f104(a1),f334(f334(f22(a881),x83112),x83113))))
% 160.93/160.65 [8329]P1(f334(f334(f249(a881),x83291),x83292))+~P1(f334(x83293,f334(f334(f22(a1),f334(f104(a1),x83291)),f334(f104(a1),x83292))))+P1(f334(x83293,f334(f104(a1),f334(f334(f22(a881),x83291),x83292))))
% 160.93/160.65 [8383]~P124(x83832)+E(x83831,f2(x83832))+P1(f334(f334(f249(x83832),f2(x83832)),f334(f334(f80(x83832),f334(f334(f81(x83832),x83833),x83833)),f334(f334(f81(x83832),x83831),x83831))))
% 160.93/160.65 [8384]~P124(x83842)+E(x83841,f2(x83842))+P1(f334(f334(f249(x83842),f2(x83842)),f334(f334(f80(x83842),f334(f334(f81(x83842),x83841),x83841)),f334(f334(f81(x83842),x83843),x83843))))
% 160.93/160.65 [8485]~P1(f334(f334(f249(a881),f2(a881)),x84851))+~P1(f334(f334(f249(a1),x84852),x84853))+P1(f334(f334(f249(a1),f334(f334(f81(a1),f334(f104(a1),x84851)),x84852)),f334(f334(f81(a1),f334(f104(a1),x84851)),x84853)))
% 160.93/160.65 [8542]E(f334(f334(f105(f888(x85421,a876)),x85422),f39(f888(x85421,a876),x85423)),f196(f888(x85421,a876)))+P1(f334(f334(f336(f888(x85421,a876)),x85422),x85423))+P1(f334(f334(f336(f888(x85421,a876)),f864(x85423,x85422,x85421)),f334(f334(f312(f888(x85421,a876)),x85422),x85423)))
% 160.93/160.65 [8543]E(f334(f334(f105(f888(x85431,a876)),x85432),f39(f888(x85431,a876),x85433)),f196(f888(x85431,a876)))+P1(f334(f334(f336(f888(x85431,a876)),x85432),x85433))+P1(f334(f334(f336(f888(x85431,a876)),f863(x85433,x85432,x85431)),f334(f334(f312(f888(x85431,a876)),x85432),x85433)))
% 160.93/160.65 [8577]E(x85771,x85772)+~E(f334(f197(f882(x85773)),x85771),f334(f197(f882(x85773)),x85772))+P1(f334(f334(f336(f887(x85773,x85773)),f686(x85773,x85771,x85772)),f334(f174(f887(x85773,x85773)),f334(f334(f184(x85773,x85773),x85772),x85771))))
% 160.93/160.65 [8811]E(f310(x88111,x88112),f310(x88111,x88113))+~P1(f334(f334(f248(f888(f887(x88111,x88111),a876)),x88113),f310(x88111,x88112)))+~P1(f334(f334(f248(f888(f887(x88111,x88111),a876)),x88112),x88113))
% 160.93/160.65 [8871]~P41(x88711,f257(f888(x88711,a876)),x88713)+P1(f334(f334(f248(f888(f887(f882(x88711),f882(x88711)),a876)),f159(x88711,x88712)),f160(x88711,x88713)))+~P1(f334(f334(f248(f888(f887(x88711,x88711),a876)),x88712),x88713))
% 160.93/160.65 [9080]P39(x90801,x90802)+~P1(f334(f334(f336(x90801),x90803),f632(x90802,x90801)))+P1(f334(f334(f336(f887(x90801,x90801)),f334(f334(f269(x90801,x90801),f658(x90802,x90801,x90803)),x90803)),x90802))
% 160.93/160.65 [9115]~P1(f334(f61(x91151),x91152))+P1(f334(f61(f888(x91151,a876)),f334(f334(f60(x91151),x91152),x91153)))+~P1(f334(f334(f248(f888(f887(x91151,x91151),a876)),x91153),f334(f334(f271(x91151,x91151),x91152),f334(f16(f888(x91151,a876),x91151),x91152))))
% 160.93/160.65 [9150]P41(x91501,x91502,x91503)+P1(f334(f334(f336(x91501),f587(x91503,x91502,x91501)),x91502))+~P1(f334(f334(f248(f888(f887(x91501,x91501),a876)),x91503),f334(f334(f271(x91501,x91501),x91502),f334(f16(f888(x91501,a876),x91501),x91502))))
% 160.93/160.65 [9151]P41(x91511,x91512,x91513)+P1(f334(f334(f336(x91511),f590(x91512,x91513,x91511)),x91512))+~P1(f334(f334(f248(f888(f887(x91511,x91511),a876)),x91513),f334(f334(f271(x91511,x91511),x91512),f334(f16(f888(x91511,a876),x91511),x91512))))
% 160.93/160.65 [9186]~P64(x91861)+~P1(f334(f334(f249(x91861),x91862),x91863))+P1(f334(f334(f249(x91861),f334(f334(f292(x91861),f334(f334(f80(x91861),x91862),x91863)),f334(f334(f80(x91861),f78(x91861)),f78(x91861)))),x91863))
% 160.93/160.65 [9215]~P63(x92151)+P1(f334(f334(f248(x92151),x92152),x92153))+~P1(f334(f334(f248(x92151),f334(f334(f81(x92151),f428(x92153,x92152,x92151)),x92152)),x92153))
% 160.93/160.65 [9351]E(f334(f197(f882(f882(x93511))),f334(f138(f882(x93511),f334(f334(f8(a881,a876,f882(x93511)),f334(f249(a881),x93512)),f197(f882(x93511)))),f182(x93511,x93513))),f334(f197(f882(x93511)),f334(f334(f167(f882(x93511)),x93513),x93512)))+~P16(a881,f334(f171(a881),f334(f334(f156(f882(x93511),a881),f197(f882(x93511))),x93513)))+~P1(f334(f334(f249(a881),x93512),f334(f197(f882(f882(x93511))),x93513)))
% 160.93/160.65 [9459]~P39(x94591,x94592)+P28(x94591,f334(f334(f269(f888(f887(x94591,x94591),a876),f888(f887(x94591,x94591),a876)),x94592),x94593))+~P1(f334(f334(f248(f888(f887(x94591,x94591),a876)),f334(f334(f291(x94591,x94591,x94591),x94592),x94593)),x94592))
% 160.93/160.65 [9466]E(f334(f334(f156(f882(x94661),x94661),f334(f334(f7(f882(x94661),a881,x94661),f167(x94661)),x94662)),f334(f138(f882(x94661),f334(f334(f8(a881,a876,f882(x94661)),f334(f249(a881),x94662)),f197(f882(x94661)))),f182(x94661,x94663))),f334(f334(f167(f882(x94661)),x94663),x94662))+~P16(a881,f334(f171(a881),f334(f334(f156(f882(x94661),a881),f197(f882(x94661))),x94663)))+~P1(f334(f334(f249(a881),x94662),f334(f197(f882(f882(x94661))),x94663)))
% 160.93/160.65 [9604]P41(x96041,x96042,x96043)+~P1(f334(f334(f336(f887(x96041,x96041)),f334(f334(f269(x96041,x96041),f587(x96043,x96042,x96041)),f587(x96043,x96042,x96041))),x96043))+~P1(f334(f334(f248(f888(f887(x96041,x96041),a876)),x96043),f334(f334(f271(x96041,x96041),x96042),f334(f16(f888(x96041,a876),x96041),x96042))))
% 160.93/160.65 [9605]P41(x96051,x96052,x96053)+~P1(f334(f334(f336(f887(x96051,x96051)),f334(f334(f269(x96051,x96051),f590(x96052,x96053,x96051)),f590(x96052,x96053,x96051))),x96053))+~P1(f334(f334(f248(f888(f887(x96051,x96051),a876)),x96053),f334(f334(f271(x96051,x96051),x96052),f334(f16(f888(x96051,a876),x96051),x96052))))
% 160.93/160.65 [9782]~P139(x97821)+~P122(x97821)+E(f334(f334(f292(x97821),f334(f106(x97821),f334(f334(f73(f887(a1,a1),a1,x97822,f268(a1,a1)),f225(x97822)),x97823))),f334(f106(x97821),f334(f334(f73(f887(a1,a1),a1,x97822,f272(a1,a1)),f225(x97822)),x97823))),f238(x97822,x97821,x97823))
% 160.93/160.65 [9984]~E(x99843,f2(a881))+~E(f334(f197(f882(x99841)),f334(f334(f167(f882(x99841)),x99842),f752(x99843,x99841,x99842))),x99843)+E(f334(f334(f156(a881,f882(x99841)),f334(f334(f7(a881,f882(a881),f882(x99841)),f334(f334(f8(f888(a881,x99841),f888(f882(a881),f882(x99841)),a881),f156(a881,x99841)),f334(f7(a881,a881,x99841),f334(f334(f8(f882(x99841),f888(a881,x99841),a881),f167(x99841)),f334(f167(f882(x99841)),x99842))))),f141(a881,f334(f304(a881,f2(a881)),f334(f197(f882(f882(x99841))),x99842))))),f141(a881,f334(f304(a881,f2(a881)),x99843))),f182(x99841,x99842))
% 160.93/160.65 [9985]E(x99851,f117(f882(x99852)))+~E(f334(f197(f882(x99852)),f334(f334(f167(f882(x99852)),x99851),f752(x99853,x99852,x99851))),x99853)+E(f334(f334(f156(a881,f882(x99852)),f334(f334(f7(a881,f882(a881),f882(x99852)),f334(f334(f8(f888(a881,x99852),f888(f882(a881),f882(x99852)),a881),f156(a881,x99852)),f334(f7(a881,a881,x99852),f334(f334(f8(f882(x99852),f888(a881,x99852),a881),f167(x99852)),f334(f167(f882(x99852)),x99851))))),f141(a881,f334(f304(a881,f2(a881)),f334(f197(f882(f882(x99852))),x99851))))),f141(a881,f334(f304(a881,f2(a881)),x99853))),f182(x99852,x99851))
% 160.93/160.65 [9986]~E(x99863,f2(a881))+E(f334(f334(f156(a881,f882(x99861)),f334(f334(f7(a881,f882(a881),f882(x99861)),f334(f334(f8(f888(a881,x99861),f888(f882(a881),f882(x99861)),a881),f156(a881,x99861)),f334(f7(a881,a881,x99861),f334(f334(f8(f882(x99861),f888(a881,x99861),a881),f167(x99861)),f334(f167(f882(x99861)),x99862))))),f141(a881,f334(f304(a881,f2(a881)),f334(f197(f882(f882(x99861))),x99862))))),f141(a881,f334(f304(a881,f2(a881)),x99863))),f182(x99861,x99862))+P1(f334(f334(f249(a881),f752(x99863,x99861,x99862)),f334(f197(f882(f882(x99861))),x99862)))
% 160.93/160.65 [9987]E(x99871,f117(f882(x99872)))+E(f334(f334(f156(a881,f882(x99872)),f334(f334(f7(a881,f882(a881),f882(x99872)),f334(f334(f8(f888(a881,x99872),f888(f882(a881),f882(x99872)),a881),f156(a881,x99872)),f334(f7(a881,a881,x99872),f334(f334(f8(f882(x99872),f888(a881,x99872),a881),f167(x99872)),f334(f167(f882(x99872)),x99871))))),f141(a881,f334(f304(a881,f2(a881)),f334(f197(f882(f882(x99872))),x99871))))),f141(a881,f334(f304(a881,f2(a881)),x99873))),f182(x99872,x99871))+P1(f334(f334(f249(a881),f752(x99873,x99872,x99871)),f334(f197(f882(f882(x99872))),x99871)))
% 160.93/160.65 [7708]E(f334(f334(f80(a881),f334(f107(a881),x77081)),f334(f334(f80(a881),f334(f107(a881),x77082)),x77083)),f334(f334(f80(a881),f334(f107(a881),f334(f334(f80(a1),x77081),x77082))),x77083))+P1(f334(a201,f334(f107(a1),x77081)))+P1(f334(a201,f334(f107(a1),x77082)))
% 160.93/160.65 [8475]~P1(f334(f61(x84751),x84752))+~P1(f334(f334(f336(x84751),x84753),x84752))+E(f334(a116,f334(f37(x84751),f334(f334(f22(f888(x84751,a876)),x84752),f334(f334(f312(x84751),x84753),f196(f888(x84751,a876)))))),f334(f37(x84751),x84752))
% 160.93/160.65 [8492]~P1(f334(f61(x84921),x84922))+~P1(f334(f334(f336(x84921),x84923),x84922))+E(f334(f334(f80(a881),f78(a881)),f334(f37(x84921),f334(f334(f22(f888(x84921,a876)),x84922),f334(f334(f312(x84921),x84923),f196(f888(x84921,a876)))))),f334(f37(x84921),x84922))
% 160.93/160.65 [8586]~P108(x85861)+~P1(f334(f61(x85861),x85863))+E(f334(f334(f150(x85861,x85861,f5(x85861)),x85862),f141(x85861,f334(f334(f22(f888(x85861,a876)),x85863),f334(f334(f312(x85861),x85862),f196(f888(x85861,a876)))))),f141(x85861,f334(f334(f312(x85861),x85862),x85863)))
% 160.93/160.65 [8741]~P1(f334(f61(x87411),x87413))+~P1(f334(f61(x87411),x87412))+E(f334(f334(f80(a881),f334(f37(x87411),f334(f334(f114(f888(x87411,a876)),x87412),x87413))),f334(f37(x87411),f334(f334(f105(f888(x87411,a876)),x87412),x87413))),f334(f334(f80(a881),f334(f37(x87411),x87412)),f334(f37(x87411),x87413)))
% 160.93/160.65 [9932]~P27(x99321,f888(f888(x99321,a876),a876),f334(f334(f7(x99321,f888(f887(x99321,x99321),a876),f888(f888(x99321,a876),a876)),f334(f334(f8(f888(x99321,a876),f888(f888(f887(x99321,x99321),a876),f888(f888(x99321,a876),a876)),x99321),f60(x99321)),f334(f334(f7(x99321,f888(x99321,a876),f888(x99321,a876)),f312(x99321)),f196(f888(x99321,a876))))),x99323),x99322)+~P1(f334(f61(x99321),x99322))+E(f334(f37(f888(x99321,a876)),f334(f334(f60(x99321),x99322),x99323)),f334(f37(x99321),x99322))
% 160.93/160.65 [7974]~P93(x79741)+P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),x79743)))+E(f334(f334(f259(x79741),x79742),f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),x79743),x79743)),a101))),f78(x79741))
% 160.93/160.65 [9442]~P93(x94421)+~P1(f334(f334(f248(a1),f2(a1)),f334(f107(a1),x94423)))+E(f334(f334(f259(x94421),x94422),f334(f107(a881),f334(f334(f22(a1),f334(f334(f80(a1),x94423),x94423)),a101))),f334(f334(f86(x94421,x94421),f334(f334(f259(x94421),x94422),f334(f107(a881),x94423))),f334(f334(f18(x94421,x94421,x94421),f334(f334(f8(x94421,f888(x94421,x94421),x94421),f81(x94421)),f334(f81(x94421),x94422))),f5(x94421))))
% 160.93/160.65 [9841]~P1(f334(f139(x98411),x98413))+~P1(f334(f334(f336(x98411),x98412),f334(f174(x98411),x98413)))+E(f334(f334(f140(x98411),f334(f197(f882(x98411)),f179(x98411,f334(f334(f8(a876,a876,x98411),a329),f334(f334(f7(x98411,x98411,a876),a331),x98412)),f334(f171(x98411),x98413)))),f334(f171(x98411),x98413)),f334(f334(f153(x98411),x98412),f334(f171(x98411),f179(x98411,f334(f334(f8(a876,a876,x98411),a329),f334(f334(f7(x98411,x98411,a876),a331),x98412)),x98413))))
% 160.93/160.65 [9913]P1(f334(f334(f248(f888(f887(x99131,x99131),a876)),f310(x99131,x99132)),x99133))+~P1(f334(f334(f248(f888(f887(x99131,x99131),a876)),f310(x99131,f196(f888(f887(x99131,x99131),a876)))),x99133))+~P1(f334(f334(f248(f888(f887(x99131,x99131),a876)),f334(f334(f291(x99131,x99131,x99131),f334(f334(f105(f888(f887(x99131,x99131),a876)),f310(x99131,x99132)),x99133)),x99132)),x99133))
% 160.93/160.65 [9753]~P1(f334(f61(x97531),f334(f254(x97531),x97533)))+~P1(f334(f61(x97531),f334(f254(x97531),x97532)))+P1(f334(f61(x97531),f334(f254(x97531),f334(f334(f18(x97531,a876,a876),f334(f334(f8(a876,f888(a876,a876),x97531),a333),x97532)),x97533))))
% 160.93/160.65 [10047]P1(f334(f334(f248(f888(f887(x100471,x100471),a876)),f334(f334(f291(x100471,x100471,x100471),x100472),f310(x100471,x100472))),x100473))+~P1(f334(f334(f248(f888(f887(x100471,x100471),a876)),x100472),x100473))+~P1(f334(f334(f248(f888(f887(x100471,x100471),a876)),f334(f334(f291(x100471,x100471,x100471),f334(f334(f105(f888(f887(x100471,x100471),a876)),f334(f334(f291(x100471,x100471,x100471),x100472),f310(x100471,x100472))),x100473)),x100472)),x100473))
% 160.93/160.65 [10000]~P111(x100002)+E(x100001,f2(x100002))+~E(f334(f334(f80(x100002),f334(f334(f259(x100002),x100003),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x100002),x100001),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f2(x100002))
% 160.93/160.65 [10001]~P111(x100012)+E(x100011,f2(x100012))+~E(f334(f334(f80(x100012),f334(f334(f259(x100012),x100011),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x100012),x100013),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f2(x100012))
% 160.93/160.65 [10006]~P1(f334(f139(x100061),x100063))+~P1(f334(f334(f336(x100061),x100062),f334(f174(x100061),x100063)))+E(f334(f171(x100061),f334(f173(x100061),f334(f334(f140(x100061),f334(f197(f882(x100061)),f179(x100061,f334(f334(f8(a876,a876,x100061),a329),f334(f334(f7(x100061,x100061,a876),a331),x100062)),x100063))),x100063))),f179(x100061,f334(f334(f8(a876,a876,x100061),a329),f334(f334(f7(x100061,x100061,a876),a331),x100062)),f334(f171(x100061),x100063)))
% 160.93/160.65 [10092]~P111(x100922)+E(x100921,f2(x100922))+P1(f334(f334(f249(x100922),f2(x100922)),f334(f334(f80(x100922),f334(f334(f259(x100922),x100923),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x100922),x100921),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))))
% 160.93/160.65 [10093]~P111(x100932)+E(x100931,f2(x100932))+P1(f334(f334(f249(x100932),f2(x100932)),f334(f334(f80(x100932),f334(f334(f259(x100932),x100931),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x100932),x100933),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))))
% 160.93/160.65 [10135]~P111(x101351)+P1(f334(f334(f248(x101351),f2(x101351)),x101352))+~P1(f334(f334(f248(x101351),f2(x101351)),f334(f334(f259(x101351),x101352),f334(a116,f334(f334(f81(a881),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),x101353)))))
% 160.93/160.65 [5489]~P26(x54891,x54894,x54893)+P26(x54891,x54892,x54893)+~P26(x54891,x54892,x54894)
% 160.93/160.65 [4955]~E(x49552,f90(x49553,x49551))+P1(f334(x49551,x49552))+~P1(f334(x49551,x49554))
% 160.93/160.65 [6699]~P39(x66992,x66994)+~P39(x66991,x66993)+P39(f887(x66991,x66992),f326(x66991,x66992,x66993,x66994))
% 160.93/160.65 [5134]~P7(x51344,x51341)+~E(f334(x51341,x51342),f334(x51341,x51343))+P1(f334(f334(x51341,x51342),x51343))
% 160.93/160.65 [5305]~P7(x53054,x53051)+E(f334(x53051,x53052),f334(x53051,x53053))+~P1(f334(f334(x53051,x53052),x53053))
% 160.93/160.65 [5396]~P20(x53963,x53964,x53961)+E(f334(x53961,x53962),f334(f63(x53963,x53964),x53962))+~P1(f334(f61(x53963),x53962))
% 160.93/160.65 [5397]~P10(x53973,x53974,x53971)+E(f334(x53971,x53972),f334(f63(x53973,x53974),x53972))+~P1(f334(f61(x53973),x53972))
% 160.93/160.65 [5522]~P7(x55224,x55221)+~P1(f334(f334(x55221,x55223),x55222))+P1(f334(f334(x55221,x55222),x55223))
% 160.93/160.65 [5589]E(x55891,x55892)+~E(f334(f268(x55893,x55894),x55891),f334(f268(x55893,x55894),x55892))+~E(f334(f272(x55893,x55894),x55891),f334(f272(x55893,x55894),x55892))
% 160.93/160.65 [5615]E(x56151,x56152)+~P1(f334(f47(x56153,x56154),x56152))+~P1(f334(f47(x56153,x56154),x56151))
% 160.93/160.65 [5806]~P68(x58062)+E(f239(x58061,x58062,x58063,x58064),f2(x58062))+P1(f334(f61(x58061),x58064))
% 160.93/160.65 [5942]~P1(f334(f322(x59421,x59422),x59424))+P1(f334(f322(x59421,x59422),x59423))+~P1(f334(f334(x59422,x59423),x59424))
% 160.93/160.65 [7896]~P108(x78962)+~P1(f334(f139(x78961),x78964))+P1(f334(f139(x78961),f152(x78961,x78962,x78963,x78964)))
% 160.93/160.65 [8118]~P1(f334(f61(x81182),x81184))+~P1(f334(f61(x81181),x81183))+P1(f334(f61(f886(x81181,x81182)),f321(x81181,x81182,x81183,x81184)))
% 160.93/160.65 [8119]~P1(f334(f139(x81192),x81194))+~P1(f334(f139(x81191),x81193))+P1(f334(f139(f887(x81191,x81192)),f59(x81191,x81192,x81193,x81194)))
% 160.93/160.65 [8123]P1(f334(f334(f336(f882(x81231)),f334(f334(f136(x81231),x81232),x81233)),f163(x81231,x81234)))+~P1(f334(f334(f336(f882(x81231)),x81233),f163(x81231,x81234)))+~P1(f334(f334(f336(f882(x81231)),x81232),f163(x81231,x81234)))
% 160.93/160.65 [8454]~P108(x84543)+~P1(f334(f139(x84541),f152(x84541,x84543,x84544,x84542)))+P1(f334(f139(x84541),x84542))
% 160.93/160.65 [8732]~P1(f334(f334(f336(f887(x87321,x87321)),f334(f334(f269(x87321,x87321),x87322),x87324)),f310(x87321,x87323)))+P1(f334(f334(f336(x87321),x87322),f323(x87321,x87323)))+~P1(f334(f334(f336(x87321),x87324),f323(x87321,x87323)))
% 160.93/160.65 [5118]~P68(x51182)+E(f334(f334(f6(x51181,x51182),x51183),x51184),f2(x51182))+P1(f334(f61(x51181),x51184))
% 160.93/160.65 [5121]~P74(x51212)+E(f334(f334(f9(x51211,x51212),x51213),x51214),f78(x51212))+P1(f334(f61(x51211),x51214))
% 160.93/160.65 [5269]~P71(x52693)+E(x52691,x52692)+~E(f334(f334(f80(x52693),x52694),x52691),f334(f334(f80(x52693),x52694),x52692))
% 160.93/160.65 [5270]~P72(x52703)+E(x52701,x52702)+~E(f334(f334(f80(x52703),x52704),x52701),f334(f334(f80(x52703),x52704),x52702))
% 160.93/160.65 [5272]~P71(x52723)+E(x52721,x52722)+~E(f334(f334(f80(x52723),x52721),x52724),f334(f334(f80(x52723),x52722),x52724))
% 160.93/160.65 [5392]~P5(x53923)+E(x53921,f196(f888(x53922,a876)))+E(f334(f334(f41(x53922,x53923),x53921),f334(f16(x53923,x53922),x53924)),x53924)
% 160.93/160.65 [5393]~P5(x53933)+E(x53931,f196(f888(x53932,a876)))+E(f334(f334(f42(x53932,x53933),x53931),f334(f16(x53933,x53932),x53934)),x53934)
% 160.93/160.65 [5603]~P109(x56033)+E(x56031,x56032)+~E(f305(x56033,x56034,x56031),f334(f334(f312(x56033),x56032),f196(f888(x56033,a876))))
% 160.93/160.65 [5604]~P109(x56043)+E(x56041,x56042)+~E(f305(x56043,x56041,x56042),f334(f334(f312(x56043),x56044),f196(f888(x56043,a876))))
% 160.93/160.65 [5664]~P37(x56643,x56641,x56644)+P37(x56643,x56641,f334(f334(f153(x56643),x56642),x56644))+P1(f334(x56641,x56642))
% 160.93/160.65 [5766]~P33(x57661,x57662,x57664)+~P1(f334(x57662,x57663))+P33(x57661,x57662,f334(f334(f153(x57661),x57663),x57664))
% 160.93/160.65 [5899]P1(f334(x58991,x58992))+~P1(f334(f262(x58993,x58991),x58994))+~P1(f334(f334(f336(x58993),x58992),x58994))
% 160.93/160.65 [5908]~P33(x59081,x59082,x59084)+~P33(x59081,x59082,x59083)+P33(x59081,x59082,f334(f334(f136(x59081),x59083),x59084))
% 160.93/160.65 [5918]P35(x59181,x59182,x59183)+~P35(x59181,x59182,f334(f334(f153(x59181),x59184),x59183))+P1(f334(x59182,x59184))
% 160.93/160.65 [5919]P37(x59191,x59192,x59193)+~P37(x59191,x59192,f334(f334(f153(x59191),x59194),x59193))+P1(f334(x59192,x59194))
% 160.93/160.65 [5994]P35(x59941,x59942,x59943)+P35(x59941,x59942,x59944)+~P35(x59941,x59942,f334(f334(f136(x59941),x59944),x59943))
% 160.93/160.65 [6013]~P68(x60131)+E(f334(f334(f6(a881,x60131),x60132),f334(f304(a881,x60133),f334(a116,x60134))),f2(x60131))+~P1(f334(f334(f249(a881),x60134),x60133))
% 160.93/160.65 [6018]~P59(x60181)+~E(f44(x60181,x60182,x60183),f44(x60181,x60184,x60183))+E(f44(x60181,f334(f79(x60181),x60182),x60183),f44(x60181,f334(f79(x60181),x60184),x60183))
% 160.93/160.65 [6086]P1(f334(x60861,x60862))+~E(f334(f138(x60863,x60861),x60864),x60864)+~P1(f334(f334(f336(x60863),x60862),f334(f174(x60863),x60864)))
% 160.93/160.65 [6105]~E(f334(f334(f80(a881),x61053),x61052),f334(f334(f80(a881),x61051),x61054))+~P1(f334(f334(f249(a881),x61053),x61054))+P1(f334(f334(f249(a881),x61051),x61052))
% 160.93/160.65 [6109]P35(x61091,x61092,x61093)+~P1(f334(x61092,x61094))+~P1(f334(f334(f336(x61091),x61094),f334(f174(x61091),x61093)))
% 160.93/160.65 [6145]~P33(x61453,x61451,x61454)+P1(f334(x61451,x61452))+~P1(f334(f334(f336(x61453),x61452),f334(f174(x61453),x61454)))
% 160.93/160.65 [6147]~E(f334(f138(x61471,x61472),x61473),f117(x61471))+~P1(f334(x61472,x61474))+~P1(f334(f334(f336(x61471),x61474),f334(f174(x61471),x61473)))
% 160.93/160.65 [6148]~E(f179(x61483,x61481,x61484),x61484)+P1(f334(x61481,x61482))+~P1(f334(f334(f336(x61483),x61482),f334(f174(x61483),x61484)))
% 160.93/160.65 [6185]~E(x61854,f196(f888(x61852,a876)))+~E(x61853,f196(f888(x61851,a876)))+E(f321(x61851,x61852,x61853,x61854),f196(f888(f886(x61851,x61852),a876)))
% 160.93/160.65 [6330]P1(f334(x63301,x63302))+~P1(f334(f162(x63303,x63301),x63304))+~P1(f334(f334(f336(x63303),x63302),f334(f174(x63303),x63304)))
% 160.93/160.65 [6596]~P68(x65961)+E(f334(f334(f6(a881,x65961),x65962),f305(a881,x65963,f334(a116,x65964))),f2(x65961))+~P1(f334(f334(f249(a881),f334(a116,x65964)),x65963))
% 160.93/160.65 [6643]E(x66431,x66432)+~P1(f334(f334(f334(a202,x66433),x66434),x66431))+~P1(f334(f334(f334(a202,x66433),x66434),x66432))
% 160.93/160.65 [6738]~P108(x67381)+E(f334(f334(f22(f888(x67381,a876)),f334(f304(x67381,x67382),x67383)),f334(f304(x67381,x67382),x67384)),f334(f304(x67381,x67384),x67383))+~P1(f334(f334(f248(x67381),x67382),x67384))
% 160.93/160.65 [7088]~P1(f334(f334(f336(f882(x70881)),x70884),f163(x70881,x70883)))+P1(f334(f334(f336(x70881),x70882),x70883))+~P1(f334(f334(f336(x70881),x70882),f334(f174(x70881),x70884)))
% 160.93/160.65 [7095]~P39(x70951,x70952)+P1(f334(f334(f336(x70951),f633(x70952,x70951,x70953)),x70953))+~P1(f334(f334(f336(x70951),x70954),x70953))
% 160.93/160.65 [7151]~P68(x71511)+E(f334(f334(f334(f65(x71511,x71512,f80(x71511)),x71513),f2(x71511)),x71514),f334(f334(f6(x71512,x71511),x71513),x71514))+~P1(f334(f61(x71512),x71514))
% 160.93/160.65 [7153]~P74(x71531)+E(f334(f334(f334(f65(x71531,x71532,f81(x71531)),x71533),f78(x71531)),x71534),f334(f334(f9(x71532,x71531),x71533),x71534))+~P1(f334(f61(x71532),x71534))
% 160.93/160.65 [7183]P27(x71831,x71832,x71833,x71834)+~E(f334(f37(x71832),f334(f313(x71831,x71832,x71833),x71834)),f334(f37(x71831),x71834))+~P1(f334(f61(x71831),x71834))
% 160.93/160.65 [7369]~P68(x73691)+E(f334(f334(f80(x73691),f334(x73692,x73693)),f334(f334(f6(a881,x73691),x73692),f307(a881,x73693,x73694))),f334(f334(f6(a881,x73691),x73692),f305(a881,x73693,x73694)))+~P1(f334(f334(f248(a881),x73693),x73694))
% 160.93/160.65 [7379]~P68(x73791)+~P27(x73792,x73791,x73793,x73794)+E(f334(f334(f6(x73791,x73791),f34(x73791)),f334(f313(x73792,x73791,x73793),x73794)),f334(f334(f6(x73792,x73791),x73793),x73794))
% 160.93/160.65 [7380]~P74(x73801)+~P27(x73802,x73801,x73803,x73804)+E(f334(f334(f9(x73801,x73801),f34(x73801)),f334(f313(x73802,x73801,x73803),x73804)),f334(f334(f9(x73802,x73801),x73803),x73804))
% 160.93/160.65 [7433]E(f334(f37(f886(x74331,x74332)),f321(x74331,x74332,x74333,x74334)),f334(f334(f80(a881),f334(f37(x74331),x74333)),f334(f37(x74332),x74334)))+~P1(f334(f61(x74332),x74334))+~P1(f334(f61(x74331),x74333))
% 160.93/160.65 [7519]E(x75191,x75192)+P1(f334(f334(f336(x75193),x75191),f334(f174(x75193),f172(x75193,x75192,x75194))))+~P1(f334(f334(f336(x75193),x75191),f334(f174(x75193),x75194)))
% 160.93/160.65 [7744]~P68(x77441)+E(f334(f334(f80(x77441),f334(f334(f6(a881,x77441),x77442),f334(f304(a881,x77443),x77444))),f334(x77442,x77444)),f334(f334(f6(a881,x77441),x77442),f334(f304(a881,x77443),f334(a116,x77444))))+P1(f334(f334(f249(a881),x77444),x77443))
% 160.93/160.65 [7796]~P27(x77961,x77962,x77963,f257(f888(x77961,a876)))+~P1(f334(f61(x77962),x77964))+P1(f334(f61(x77961),f334(f314(x77961,x77962,x77963),x77964)))
% 160.93/160.65 [7909]P1(f334(f334(f336(f882(x79091)),f334(f334(f153(x79091),x79092),x79093)),f163(x79091,x79094)))+~P1(f334(f334(f336(f882(x79091)),x79093),f163(x79091,x79094)))+~P1(f334(f334(f336(x79091),x79092),x79094))
% 160.93/160.65 [7998]~E(f334(f313(x79983,x79981,x79984),f257(f888(x79983,a876))),f257(f888(x79981,a876)))+P1(f334(f61(x79981),x79982))+~P1(f334(f61(x79983),f334(f314(x79983,x79981,x79984),x79982)))
% 160.93/160.65 [8089]~P27(x80891,x80893,x80894,x80892)+P1(f334(f61(x80891),x80892))+~P1(f334(f61(x80893),f334(f313(x80891,x80893,x80894),x80892)))
% 160.93/160.65 [8111]~E(x81112,x81113)+P1(f334(f334(f336(f887(x81111,x81111)),f334(f334(f269(x81111,x81111),x81112),x81113)),f266(x81111,x81114)))+~P1(f334(f334(f336(x81111),x81112),x81114))
% 160.93/160.65 [8150]~P68(x81501)+E(f334(f334(f80(x81501),f334(f334(f6(a881,x81501),x81502),f305(a881,x81503,x81504))),f334(x81502,f334(a116,x81504))),f334(f334(f6(a881,x81501),x81502),f305(a881,x81503,f334(a116,x81504))))+P1(f334(f334(f249(a881),f334(a116,x81504)),x81503))
% 160.93/160.65 [8222]P1(f334(x82221,x82222))+~P1(f334(x82221,f334(f334(f167(x82223),x82224),f683(x82221,x82224,x82223))))+~P1(f334(f334(f336(x82223),x82222),f334(f174(x82223),x82224)))
% 160.93/160.65 [8362]~P1(f334(f334(f336(x83621),x83622),f323(x83621,x83624)))+P1(f334(f334(f336(f882(x83621)),f334(f334(f153(x83621),x83622),x83623)),f323(f882(x83621),f159(x83621,x83624))))+~P1(f334(f334(f336(f882(x83621)),x83623),f323(f882(x83621),f159(x83621,x83624))))
% 160.93/160.65 [8375]~P27(x83752,x83753,x83754,f568(x83754,x83753,x83752,x83751))+P27(x83752,x83753,x83754,f40(f888(x83752,a876),x83751))+E(x83751,f196(f888(f888(x83752,a876),a876)))
% 160.93/160.65 [8651]E(x86511,x86512)+~P1(f334(f334(f336(f887(x86513,x86513)),f334(f334(f269(x86513,x86513),x86511),x86512)),f310(x86513,x86514)))+P1(f334(f334(f336(x86513),x86511),f334(f267(x86513,x86513),x86514)))
% 160.93/160.65 [8930]P27(x89302,x89303,x89304,f40(f888(x89302,a876),x89301))+E(x89301,f196(f888(f888(x89302,a876),a876)))+P1(f334(f334(f336(f888(x89302,a876)),f568(x89304,x89303,x89302,x89301)),x89301))
% 160.93/160.65 [9068]P1(f334(f61(x90681),x90682))+~P1(f334(f61(x90684),f334(f313(x90681,x90684,x90683),x90682)))+P1(f334(f334(f336(x90681),f463(x90683,x90684,x90682,x90681)),x90682))
% 160.93/160.65 [9164]~P5(x91642)+E(f334(f334(f64(x91641,x91642,f334(f334(f8(x91642,f888(x91642,x91642),x91641),f114(x91642)),x91643)),f196(x91642)),x91644),f334(f334(f41(x91641,x91642),x91644),x91643))+~P1(f334(f61(x91641),x91644))
% 160.93/160.65 [9165]~P5(x91652)+E(f334(f334(f64(x91651,x91652,f334(f334(f8(x91652,f888(x91652,x91652),x91651),f105(x91652)),x91653)),f257(x91652)),x91654),f334(f334(f42(x91651,x91652),x91654),x91653))+~P1(f334(f61(x91651),x91654))
% 160.93/160.65 [9248]P1(f334(x92481,x92482))+~P1(f334(x92481,f334(f334(f167(x92483),x92484),f740(x92482,x92481,x92484,x92483))))+~P1(f334(f334(f336(x92483),x92482),f334(f174(x92483),x92484)))
% 160.93/160.65 [9268]E(x92681,x92682)+~P1(f334(f334(f336(f887(x92683,x92683)),f334(f334(f269(x92683,x92683),x92681),x92682)),f310(x92683,x92684)))+P1(f334(f334(f336(f887(x92683,x92683)),f334(f334(f269(x92683,x92683),x92681),x92682)),f334(f334(f291(x92683,x92683,x92683),x92684),f310(x92683,x92684))))
% 160.93/160.65 [9317]~E(f334(f197(f882(x93171)),x93172),f334(f197(f882(x93171)),x93173))+~P1(f334(f334(f336(f887(f882(x93171),f882(x93171))),f334(f334(f269(f882(x93171),f882(x93171)),x93172),x93173)),f149(x93171,x93174)))+P1(f334(f334(f336(f887(f882(x93171),f882(x93171))),f334(f334(f269(f882(x93171),f882(x93171)),x93172),x93173)),f147(x93171,x93174)))
% 160.93/160.65 [9551]P33(x95511,f334(f334(f18(x95511,a876,a876),f334(f334(f8(a876,f888(a876,a876),x95511),a333),f334(f334(f8(a876,a876,x95511),a329),x95512))),f334(a331,x95513)),x95514)+~P1(f334(x95512,x95513))+~P37(x95511,x95512,f334(f334(f153(x95511),x95513),x95514))
% 160.93/160.65 [9715]~P33(x97151,f334(f334(f18(x97151,a876,a876),f334(f334(f8(a876,f888(a876,a876),x97151),a333),f334(f334(f8(a876,a876,x97151),a329),x97152))),f334(a331,x97153)),x97154)+~P1(f334(x97152,x97153))+P37(x97151,x97152,f334(f334(f153(x97151),x97153),x97154))
% 160.93/160.65 [9719]~P37(x97191,x97192,x97194)+~P33(x97191,f334(f334(f18(x97191,a876,a876),f334(f334(f8(a876,f888(a876,a876),x97191),a333),f334(f334(f8(a876,a876,x97191),a329),x97192))),f334(a331,x97193)),x97194)+P37(x97191,x97192,f334(f334(f153(x97191),x97193),x97194))
% 160.93/160.65 [9756]~P67(x97561)+E(f334(f334(f6(a881,x97561),f334(f334(f18(a881,x97561,x97561),f334(f334(f8(x97561,f888(x97561,x97561),a881),f22(x97561)),x97562)),f334(f334(f8(a881,x97561,a881),x97562),f334(f334(f7(a881,a881,a881),f80(a881)),f78(a881))))),f305(a881,x97563,x97564)),f2(x97561))+P1(f334(f334(f248(a881),x97563),x97564))
% 160.93/160.65 [9999]~P39(x99992,x99994)+~P27(x99992,x99991,x99993,f257(f888(x99992,a876)))+P39(x99991,f334(f313(f887(x99992,x99992),f887(x99991,x99991),f274(x99992,x99991,x99992,x99991,x99993,x99993)),x99994))
% 160.93/160.65 [10161]~E(f334(f197(f882(x101611)),x101613),f334(f197(f882(x101611)),x101612))+P1(f334(f334(f336(f887(f882(x101611),f882(x101611))),f334(f334(f269(f882(x101611),f882(x101611)),x101612),x101613)),f160(x101611,x101614)))+~P1(f334(f334(f273(x101611,x101611,a876),f334(f334(f7(x101611,f888(f887(x101611,x101611),a876),f888(x101611,a876)),f334(f334(f8(f888(x101611,f888(f888(f887(x101611,x101611),a876),a876)),f888(f888(f887(x101611,x101611),a876),f888(x101611,a876)),x101611),f7(x101611,f888(f887(x101611,x101611),a876),a876)),f334(f334(f8(f888(x101611,f887(x101611,x101611)),f888(x101611,f888(f888(f887(x101611,x101611),a876),a876)),x101611),f334(f8(f887(x101611,x101611),f888(f888(f887(x101611,x101611),a876),a876),x101611),f336(f887(x101611,x101611)))),f269(x101611,x101611)))),x101614)),f687(x101614,x101613,x101612,x101611)))
% 160.93/160.65 [6070]~P58(x60701)+~E(x60702,f2(x60701))+E(f334(f334(f38(x60701),f334(f334(f81(x60701),x60702),x60703)),f334(f334(f81(x60701),x60702),x60704)),f2(x60701))
% 160.93/160.65 [6108]E(x61081,f117(x61082))+E(x61083,f334(f334(f22(a881),f334(f197(f882(x61082)),x61081)),f78(a881)))+E(f146(x61082,f334(f334(f161(x61082,x61081),x61083),x61084)),f146(x61082,x61081))
% 160.93/160.65 [6136]E(x61361,x61362)+P1(f334(x61363,x61362))+~P1(f334(f334(f334(f312(x61364),x61361),x61363),x61362))
% 160.93/160.65 [6152]~P68(x61521)+~P1(f334(f139(x61522),x61524))+E(f334(f168(x61521),f334(f334(f156(x61522,x61521),x61523),x61524)),f334(f334(f6(x61522,x61521),x61523),f334(f174(x61522),x61524)))
% 160.93/160.65 [6178]~P74(x61782)+~P1(f334(f61(x61781),x61784))+E(f334(f334(f9(x61781,x61782),f334(f16(x61782,x61781),x61783)),x61784),f334(f334(f259(x61782),x61783),f334(f37(x61781),x61784)))
% 160.93/160.65 [6186]~E(x61864,x61862)+P1(f334(x61861,x61862))+P1(f334(f334(f334(a202,f32(x61861,x61863)),x61862),x61864))
% 160.93/160.65 [6233]~P58(x62332)+E(x62331,f2(x62332))+E(f334(f334(f38(x62332),f334(f334(f81(x62332),x62333),x62331)),f334(f334(f81(x62332),x62334),x62331)),f334(f334(f38(x62332),x62333),x62334))
% 160.93/160.65 [6235]~P61(x62352)+E(x62351,f2(x62352))+E(f334(f334(f292(x62352),f334(f334(f81(x62352),x62353),x62351)),f334(f334(f81(x62352),x62354),x62351)),f334(f334(f292(x62352),x62353),x62354))
% 160.93/160.65 [6236]~P61(x62362)+E(x62361,f2(x62362))+E(f334(f334(f292(x62362),f334(f334(f81(x62362),x62361),x62363)),f334(f334(f81(x62362),x62361),x62364)),f334(f334(f292(x62362),x62363),x62364))
% 160.93/160.65 [6237]~P58(x62372)+E(x62371,f2(x62372))+E(f334(f334(f38(x62372),f334(f334(f81(x62372),x62371),x62373)),f334(f334(f81(x62372),x62371),x62374)),f334(f334(f38(x62372),x62373),x62374))
% 160.93/160.65 [6300]P1(f334(x63001,x63002))+~E(x63003,f334(f334(f80(a881),x63004),x63002))+~P1(f334(x63001,f334(f334(f22(a881),x63003),x63004)))
% 160.93/160.65 [6380]P30(x63801,x63802,x63803)+P29(x63801,f601(x63803,x63802,x63801),x63804)+~P1(f334(f334(f336(f880(x63801)),x63804),x63802))
% 160.93/160.65 [6382]~P1(f334(x63822,x63823))+~P1(f334(f162(x63821,x63822),x63824))+P1(f334(f162(x63821,x63822),f334(f334(f153(x63821),x63823),x63824)))
% 160.93/160.65 [6422]E(x64221,f117(x64222))+~E(x64223,f334(f334(f22(a881),f334(f197(f882(x64222)),x64221)),f78(a881)))+E(f146(x64222,f334(f334(f161(x64222,x64221),x64223),x64224)),x64224)
% 160.93/160.65 [6445]~P99(x64451)+~P1(f334(f334(f249(x64451),x64452),x64454))+P1(f334(f334(f249(x64451),x64452),f334(f334(f114(x64451),x64453),x64454)))
% 160.93/160.65 [6446]~P99(x64461)+~P1(f334(f334(f249(x64461),x64462),x64463))+P1(f334(f334(f249(x64461),x64462),f334(f334(f114(x64461),x64463),x64464)))
% 160.93/160.65 [6448]~P108(x64481)+~P1(f334(f334(f249(x64481),x64482),x64484))+P1(f334(f334(f249(x64481),x64482),f334(f334(f247(x64481),x64483),x64484)))
% 160.93/160.65 [6450]~P108(x64501)+~P1(f334(f334(f249(x64501),x64502),x64503))+P1(f334(f334(f249(x64501),x64502),f334(f334(f247(x64501),x64503),x64504)))
% 160.93/160.65 [6451]~P99(x64511)+~P1(f334(f334(f248(x64511),x64512),x64514))+P1(f334(f334(f248(x64511),x64512),f334(f334(f114(x64511),x64513),x64514)))
% 160.93/160.65 [6452]~P99(x64521)+~P1(f334(f334(f248(x64521),x64522),x64523))+P1(f334(f334(f248(x64521),x64522),f334(f334(f114(x64521),x64523),x64524)))
% 160.93/160.65 [6454]~P108(x64541)+~P1(f334(f334(f248(x64541),x64542),x64544))+P1(f334(f334(f248(x64541),x64542),f334(f334(f247(x64541),x64543),x64544)))
% 160.93/160.65 [6456]~P108(x64561)+~P1(f334(f334(f248(x64561),x64562),x64563))+P1(f334(f334(f248(x64561),x64562),f334(f334(f247(x64561),x64563),x64564)))
% 160.93/160.65 [6542]~E(f334(f334(f167(x65421),x65422),x65423),x65424)+E(f334(f334(f161(x65421,x65422),x65423),x65424),x65422)+~P1(f334(f334(f249(a881),x65423),f334(f197(f882(x65421)),x65422)))
% 160.93/160.65 [6582]P1(f334(x65821,x65822))+~P1(f334(x65823,x65822))+~P1(f334(f334(f248(f888(x65824,a876)),x65823),x65821))
% 160.93/160.65 [6614]~E(f334(f334(f161(x66141,x66142),x66143),x66144),x66142)+E(f334(f334(f167(x66141),x66142),x66143),x66144)+~P1(f334(f334(f249(a881),x66143),f334(f197(f882(x66141)),x66142)))
% 160.93/160.65 [6629]~P1(f334(f162(x66291,x66292),x66294))+~P1(f334(f162(x66291,x66292),x66293))+P1(f334(f162(x66291,x66292),f334(f334(f136(x66291),x66293),x66294)))
% 160.93/160.65 [6726]P29(x67261,x67262,x67263)+~P29(x67261,f334(a116,x67262),f602(x67262,x67264,x67261))+~P1(f334(f334(f336(f880(x67261)),x67263),x67264))
% 160.93/160.65 [6735]E(x67351,f196(f888(x67352,a876)))+E(x67353,f196(f888(x67354,a876)))+~E(f334(f334(f271(x67354,x67352),x67353),f334(f16(f888(x67352,a876),x67354),x67351)),f196(f888(f887(x67354,x67352),a876)))
% 160.93/160.65 [6754]E(x67541,x67542)+P1(f334(f334(f336(x67543),x67541),x67544))+~P1(f334(f334(f336(x67543),x67541),f334(f334(f312(x67543),x67542),x67544)))
% 160.93/160.65 [6770]~P108(x67701)+P1(f334(f334(f249(x67701),x67702),x67703))+~P1(f334(f334(f249(x67701),x67702),f334(f334(f246(x67701),x67704),x67703)))
% 160.93/160.65 [6771]~P108(x67711)+P1(f334(f334(f249(x67711),x67712),x67713))+~P1(f334(f334(f249(x67711),x67712),f334(f334(f246(x67711),x67713),x67714)))
% 160.93/160.65 [6773]~P100(x67731)+P1(f334(f334(f248(x67731),x67732),x67733))+~P1(f334(f334(f248(x67731),x67732),f334(f334(f105(x67731),x67734),x67733)))
% 160.93/160.65 [6775]~P100(x67751)+P1(f334(f334(f248(x67751),x67752),x67753))+~P1(f334(f334(f248(x67751),x67752),f334(f334(f105(x67751),x67753),x67754)))
% 160.93/160.65 [6777]~P108(x67771)+P1(f334(f334(f248(x67771),x67772),x67773))+~P1(f334(f334(f248(x67771),x67772),f334(f334(f246(x67771),x67774),x67773)))
% 160.93/160.65 [6779]~P108(x67791)+P1(f334(f334(f248(x67791),x67792),x67793))+~P1(f334(f334(f248(x67791),x67792),f334(f334(f246(x67791),x67793),x67794)))
% 160.93/160.65 [6801]~E(f334(f334(f167(x68011),x68013),x68014),x68012)+P1(f334(f334(f336(x68011),x68012),f334(f174(x68011),x68013)))+~P1(f334(f334(f249(a881),x68014),f334(f197(f882(x68011)),x68013)))
% 160.93/160.65 [6812]~P108(x68121)+~P16(x68121,f334(f334(f153(x68121),x68122),f334(f334(f153(x68121),x68123),x68124)))+P1(f334(f334(f248(x68121),x68122),x68123))
% 160.93/160.65 [6873]E(x68731,x68732)+P1(f334(x68733,x68731))+~P1(f334(f334(f334(a202,f32(x68733,x68734)),x68731),x68732))
% 160.93/160.65 [6953]~P33(x69532,x69531,x69533)+P1(f334(x69531,f334(f334(f167(x69532),x69533),x69534)))+~P1(f334(f334(f249(a881),x69534),f334(f197(f882(x69532)),x69533)))
% 160.93/160.65 [6972]E(x69721,f2(a1))+E(f334(f334(f38(a1),x69722),x69721),x69723)+~P1(f334(f48(x69722,x69721),f334(f334(f269(a1,a1),x69723),x69724)))
% 160.93/160.65 [6993]E(f44(a1,x69932,x69931),x69933)+E(x69931,f2(a1))+~P1(f334(f48(x69932,x69931),f334(f334(f269(a1,a1),x69934),x69933)))
% 160.93/160.65 [7109]P1(f334(f334(f336(x71091),x71092),x71093))+~P1(f334(f334(f336(x71091),x71092),x71094))+~P1(f334(f334(f249(f888(x71091,a876)),x71094),x71093))
% 160.93/160.65 [7113]P1(f334(f334(f336(x71131),x71132),x71133))+~P1(f334(f334(f336(x71131),x71132),x71134))+~P1(f334(f334(f248(f888(x71131,a876)),x71134),x71133))
% 160.93/160.65 [7223]P35(x72231,x72232,x72233)+~P1(f334(x72232,f334(f334(f167(x72231),x72233),x72234)))+~P1(f334(f334(f249(a881),x72234),f334(f197(f882(x72231)),x72233)))
% 160.93/160.65 [7334]~P110(x73342)+~P1(f334(f334(f249(f888(x73341,x73342)),x73343),x73344))+P1(f334(f334(f248(f888(x73341,x73342)),x73343),x73344))
% 160.93/160.65 [7421]~P26(x74211,x74212,x74214)+P26(x74211,x74212,f334(f334(f312(f880(x74211)),x74213),x74214))+~P26(x74211,x74212,f334(f334(f312(f880(x74211)),x74213),f196(f888(f880(x74211),a876))))
% 160.93/160.65 [7465]~P1(f334(f334(f336(x74651),x74652),x74654))+P1(f334(f334(f336(x74651),x74652),f39(f888(x74651,a876),x74653)))+~P1(f334(f334(f336(f888(x74651,a876)),x74654),x74653))
% 160.93/160.65 [7477]P29(x74771,x74772,x74773)+P1(f334(f334(f336(f880(x74771)),f602(x74772,x74774,x74771)),x74774))+~P1(f334(f334(f336(f880(x74771)),x74773),x74774))
% 160.93/160.65 [7497]~P82(x74971)+~P1(f334(f334(f249(x74971),x74973),x74974))+P1(f334(f334(f249(x74971),f334(f334(f80(x74971),x74972),x74973)),f334(f334(f80(x74971),x74972),x74974)))
% 160.93/160.65 [7498]~P86(x74981)+~P1(f334(f334(f249(x74981),x74983),x74984))+P1(f334(f334(f249(x74981),f334(f334(f80(x74981),x74982),x74983)),f334(f334(f80(x74981),x74982),x74984)))
% 160.93/160.65 [7499]~P82(x74991)+~P1(f334(f334(f249(x74991),x74992),x74994))+P1(f334(f334(f249(x74991),f334(f334(f80(x74991),x74992),x74993)),f334(f334(f80(x74991),x74994),x74993)))
% 160.93/160.65 [7500]~P86(x75001)+~P1(f334(f334(f249(x75001),x75002),x75004))+P1(f334(f334(f249(x75001),f334(f334(f80(x75001),x75002),x75003)),f334(f334(f80(x75001),x75004),x75003)))
% 160.93/160.65 [7501]~P82(x75011)+~P1(f334(f334(f248(x75011),x75013),x75014))+P1(f334(f334(f248(x75011),f334(f334(f80(x75011),x75012),x75013)),f334(f334(f80(x75011),x75012),x75014)))
% 160.93/160.65 [7502]~P84(x75021)+~P1(f334(f334(f248(x75021),x75023),x75024))+P1(f334(f334(f248(x75021),f334(f334(f80(x75021),x75022),x75023)),f334(f334(f80(x75021),x75022),x75024)))
% 160.93/160.65 [7503]~P82(x75031)+~P1(f334(f334(f248(x75031),x75032),x75034))+P1(f334(f334(f248(x75031),f334(f334(f80(x75031),x75032),x75033)),f334(f334(f80(x75031),x75034),x75033)))
% 160.93/160.65 [7504]~P84(x75041)+~P1(f334(f334(f248(x75041),x75042),x75044))+P1(f334(f334(f248(x75041),f334(f334(f80(x75041),x75042),x75043)),f334(f334(f80(x75041),x75044),x75043)))
% 160.93/160.65 [7513]~P105(x75131)+~P91(x75131)+E(f334(f334(f22(x75131),f334(f334(f81(x75131),x75132),f334(f107(x75131),x75133))),f334(f334(f81(x75131),x75134),f334(f107(x75131),x75133))),f334(f334(f81(x75131),f334(f334(f22(x75131),x75132),x75134)),f334(f107(x75131),x75133)))
% 160.93/160.65 [7514]~P137(x75141)+~P91(x75141)+E(f334(f334(f80(x75141),f334(f334(f81(x75141),x75142),f334(f107(x75141),x75143))),f334(f334(f81(x75141),x75144),f334(f107(x75141),x75143))),f334(f334(f81(x75141),f334(f334(f80(x75141),x75142),x75144)),f334(f107(x75141),x75143)))
% 160.93/160.65 [7550]~P68(x75501)+E(f334(f334(f80(x75501),f334(x75502,x75503)),f334(f334(f6(a881,x75501),x75502),f305(a881,f334(a116,x75503),x75504))),f334(f334(f6(a881,x75501),x75502),f305(a881,x75503,x75504)))+~P1(f334(f334(f248(a881),x75503),x75504))
% 160.93/160.65 [7561]~P27(x75612,x75611,x75613,f334(f174(x75612),x75614))+~P1(f334(f139(x75612),x75614))+P1(f334(f139(x75611),f334(f334(f156(x75612,x75611),x75613),x75614)))
% 160.93/160.65 [7612]~P1(f334(f334(f249(a881),x76122),x76124))+~P1(f334(f334(f249(a881),x76121),x76123))+P1(f334(f334(f249(a881),f334(f334(f80(a881),x76121),x76122)),f334(f334(f80(a881),x76123),x76124)))
% 160.93/160.65 [7613]~P1(f334(f334(f249(a1),x76131),x76133))+~P1(f334(f334(f248(a1),x76132),x76134))+P1(f334(f334(f249(a1),f334(f334(f80(a1),x76131),x76132)),f334(f334(f80(a1),x76133),x76134)))
% 160.93/160.65 [7614]~P1(f334(f334(f248(a881),x76142),x76144))+~P1(f334(f334(f248(a881),x76141),x76143))+P1(f334(f334(f248(a881),f334(f334(f80(a881),x76141),x76142)),f334(f334(f80(a881),x76143),x76144)))
% 160.93/160.65 [7615]~P1(f334(f334(f248(a881),x76152),x76154))+~P1(f334(f334(f248(a881),x76151),x76153))+P1(f334(f334(f248(a881),f334(f334(f81(a881),x76151),x76152)),f334(f334(f81(a881),x76153),x76154)))
% 160.93/160.65 [7663]P1(f334(f334(f336(x76631),x76632),x76633))+~P1(f334(f334(f336(x76631),x76632),f40(f888(x76631,a876),x76634)))+~P1(f334(f334(f336(f888(x76631,a876)),x76633),x76634))
% 160.93/160.65 [7678]~P1(f334(x76781,f681(x76781,x76783,x76782)))+P1(f334(x76781,f334(f334(f167(x76782),x76783),x76784)))+~P1(f334(f334(f249(a881),x76784),f334(f197(f882(x76782)),x76783)))
% 160.93/160.65 [7682]P1(f334(x76821,x76822))+~P1(f334(f334(f336(x76824),x76822),f334(f174(x76824),x76823)))+P1(f334(f334(f249(a881),f683(x76821,x76823,x76824)),f334(f197(f882(x76824)),x76823)))
% 160.93/160.65 [7730]~P110(x77301)+~P1(f334(f334(f248(f888(x77302,x77301)),x77304),x77303))+~P1(f334(f334(f249(f888(x77302,x77301)),x77303),x77304))
% 160.93/160.65 [7773]~P1(f334(x77734,x77732))+~P1(f334(f334(f336(x77731),x77732),x77733))+P1(f334(f334(f336(x77731),x77732),f334(f334(f105(f888(x77731,a876)),x77733),f334(f254(x77731),x77734))))
% 160.93/160.65 [7918]~P1(f334(f334(f336(x79181),x79183),x79184))+~P1(f334(f334(f249(f888(x79181,a876)),x79182),x79184))+P1(f334(f334(f249(f888(x79181,a876)),x79182),f334(f334(f312(x79181),x79183),x79184)))
% 160.93/160.65 [7920]E(f334(f334(f105(f888(x79201,a876)),x79202),x79203),f196(f888(x79201,a876)))+~E(f334(f334(f105(f888(x79201,a876)),f39(f888(x79201,a876),x79204)),x79203),f196(f888(x79201,a876)))+~P1(f334(f334(f336(f888(x79201,a876)),x79202),x79204))
% 160.93/160.65 [7994]P1(f334(f334(f336(x79941),x79942),x79943))+~P1(f334(f334(f248(f888(x79941,a876)),x79943),f334(f334(f312(x79941),x79942),x79944)))+P1(f334(f334(f248(f888(x79941,a876)),x79943),x79944))
% 160.93/160.65 [8011]P1(f334(f334(f336(x80112),f681(x80111,x80113,x80112)),f334(f174(x80112),x80113)))+P1(f334(x80111,f334(f334(f167(x80112),x80113),x80114)))+~P1(f334(f334(f249(a881),x80114),f334(f197(f882(x80112)),x80113)))
% 160.93/160.65 [8019]~P1(f334(f334(f249(f888(x80191,a876)),x80192),x80194))+P1(f334(f334(f249(f888(x80191,a876)),x80192),x80193))+~P1(f334(f334(f249(f888(x80191,a876)),x80194),x80193))
% 160.93/160.65 [8020]~P1(f334(f334(f248(f888(x80201,a876)),x80202),x80204))+P1(f334(f334(f249(f888(x80201,a876)),x80202),x80203))+~P1(f334(f334(f249(f888(x80201,a876)),x80204),x80203))
% 160.93/160.65 [8021]~P1(f334(f334(f248(f888(x80211,a876)),x80214),x80213))+~P1(f334(f334(f249(f888(x80211,a876)),x80212),x80214))+P1(f334(f334(f249(f888(x80211,a876)),x80212),x80213))
% 160.93/160.65 [8022]~P1(f334(f334(f248(f888(x80221,a876)),x80222),x80224))+P1(f334(f334(f248(f888(x80221,a876)),x80222),x80223))+~P1(f334(f334(f248(f888(x80221,a876)),x80224),x80223))
% 160.93/160.65 [8062]~P1(f334(f334(f336(x80621),x80624),x80623))+~P1(f334(f334(f249(f888(x80621,a876)),x80622),f334(f334(f312(x80621),x80624),x80623)))+P1(f334(f334(f249(f888(x80621,a876)),x80622),x80623))
% 160.93/160.65 [8074]~P82(x80741)+P1(f334(f334(f249(x80741),x80742),x80743))+~P1(f334(f334(f249(x80741),f334(f334(f80(x80741),x80744),x80742)),f334(f334(f80(x80741),x80744),x80743)))
% 160.93/160.65 [8076]~P82(x80761)+P1(f334(f334(f249(x80761),x80762),x80763))+~P1(f334(f334(f249(x80761),f334(f334(f80(x80761),x80762),x80764)),f334(f334(f80(x80761),x80763),x80764)))
% 160.93/160.65 [8078]~P82(x80781)+P1(f334(f334(f248(x80781),x80782),x80783))+~P1(f334(f334(f248(x80781),f334(f334(f80(x80781),x80784),x80782)),f334(f334(f80(x80781),x80784),x80783)))
% 160.93/160.65 [8080]~P82(x80801)+P1(f334(f334(f248(x80801),x80802),x80803))+~P1(f334(f334(f248(x80801),f334(f334(f80(x80801),x80802),x80804)),f334(f334(f80(x80801),x80803),x80804)))
% 160.93/160.65 [8094]~P1(f334(f334(f334(a202,x80942),x80943),x80944))+~P1(f334(f334(f334(a202,f32(x80941,x80942)),x80944),x80943))+P1(f334(f334(f334(a202,f32(x80941,x80942)),x80943),x80943))
% 160.93/160.65 [8129]P1(f334(x81291,x81292))+~E(f334(f334(f140(x81293),f334(f197(f882(x81293)),f179(x81293,x81291,x81294))),x81294),f117(x81293))+~P1(f334(f334(f336(x81293),x81292),f334(f174(x81293),x81294)))
% 160.93/160.65 [8265]P1(f334(x82651,x82652))+~P1(f334(f334(f336(x82653),x82652),f334(f174(x82653),x82654)))+P1(f334(f334(f249(a881),f334(f197(f882(x82653)),f334(f138(x82653,x82651),x82654))),f334(f197(f882(x82653)),x82654)))
% 160.93/160.65 [8506]E(x85061,x85062)+P1(f334(f334(f334(a202,x85063),x85061),f468(x85062,x85061,x85063,x85064)))+~P1(f334(f334(f334(a202,f32(x85064,x85063)),x85061),x85062))
% 160.93/160.65 [8535]~P1(f334(x85354,x85352))+P1(f334(f334(f334(a202,x85351),x85352),f468(x85353,x85352,x85351,x85354)))+~P1(f334(f334(f334(a202,f32(x85354,x85351)),x85352),x85353))
% 160.93/160.65 [8743]~P1(f334(x87431,f788(x87431,x87433,x87432,x87434)))+P1(f334(x87431,f334(f334(f167(x87432),x87433),x87434)))+~P1(f334(f334(f249(a881),x87434),f334(f197(f882(x87432)),x87433)))
% 160.93/160.65 [8766]~P27(x87664,x87663,x87661,f257(f888(x87664,a876)))+E(f334(x87661,f551(x87662,x87661,x87663,x87664)),x87662)+~P1(f334(f334(f336(x87663),x87662),f334(f313(x87664,x87663,x87661),f257(f888(x87664,a876)))))
% 160.93/160.65 [8831]E(f179(x88311,x88312,x88313),f334(f334(f177(x88311),x88314),x88313))+P1(f334(f334(f249(a881),f763(x88312,x88313,x88311,x88314)),x88314))+P1(f334(f334(f249(a881),x88314),f334(f197(f882(x88311)),x88313)))
% 160.93/160.65 [8834]E(f179(x88341,x88342,x88343),f334(f334(f177(x88341),x88344),x88343))+P1(f334(f334(f249(a881),f763(x88342,x88343,x88341,x88344)),x88344))+P1(f334(x88342,f334(f334(f167(x88341),x88343),x88344)))
% 160.93/160.65 [8863]P1(f334(x88631,x88632))+~P1(f334(f334(f336(x88634),x88632),f334(f174(x88634),x88633)))+P1(f334(f334(f249(a881),f740(x88632,x88631,x88633,x88634)),f334(f197(f882(x88634)),x88633)))
% 160.93/160.65 [8866]E(f179(x88661,x88662,x88663),f334(f334(f177(x88661),x88664),x88663))+P1(f334(f334(f249(a881),x88664),f334(f197(f882(x88661)),x88663)))+P1(f334(f334(f249(a881),f763(x88662,x88663,x88661,x88664)),f334(f197(f882(x88661)),x88663)))
% 160.93/160.65 [8873]E(f179(x88731,x88732,x88733),f334(f334(f177(x88731),x88734),x88733))+P1(f334(x88732,f334(f334(f167(x88731),x88733),x88734)))+P1(f334(f334(f249(a881),f763(x88732,x88733,x88731,x88734)),f334(f197(f882(x88731)),x88733)))
% 160.93/160.65 [8899]~P106(x88994)+P1(f334(f334(f336(x88991),f664(x88992,x88993,x88991,x88994)),x88993))+P1(f334(f334(f249(x88994),f2(x88994)),f334(f334(f9(x88991,x88994),x88992),x88993)))
% 160.93/160.65 [8900]~P106(x89004)+P1(f334(f334(f336(x89001),f668(x89002,x89003,x89001,x89004)),x89003))+P1(f334(f334(f248(x89004),f2(x89004)),f334(f334(f9(x89001,x89004),x89002),x89003)))
% 160.93/160.65 [8932]~P1(f334(f61(x89321),x89324))+P1(f334(f334(f336(x89321),f574(x89322,x89323,x89324,x89321)),x89324))+P1(f334(f61(f887(x89321,x89323)),f334(f334(f271(x89321,x89323),x89324),x89322)))
% 160.93/160.65 [8966]P1(f334(f334(f336(x89662),f788(x89661,x89663,x89662,x89664)),f334(f174(x89662),x89663)))+P1(f334(x89661,f334(f334(f167(x89662),x89663),x89664)))+~P1(f334(f334(f249(a881),x89664),f334(f197(f882(x89662)),x89663)))
% 160.93/160.65 [9073]E(x90731,x90732)+P1(f334(f334(f334(a202,f32(x90733,x90734)),f468(x90731,x90732,x90734,x90733)),x90731))+~P1(f334(f334(f334(a202,f32(x90733,x90734)),x90732),x90731))
% 160.93/160.65 [9078]~P1(f334(x90781,x90784))+P1(f334(f334(f334(a202,f32(x90781,x90782)),f468(x90783,x90784,x90782,x90781)),x90783))+~P1(f334(f334(f334(a202,f32(x90781,x90782)),x90784),x90783))
% 160.93/160.65 [9100]P1(f334(f334(f248(a881),x91004),f334(f197(f882(x91002)),f179(x91002,x91003,x91001))))+P1(f334(f334(f249(a881),f764(x91001,x91002,x91003,x91004)),x91004))+~P1(f334(f334(f248(a881),x91004),f334(f197(f882(x91002)),x91001)))
% 160.93/160.65 [9205]~E(f334(f334(f180(x92051,x92052),x92053),f775(x92054,x92053,x92052,x92051)),f334(f334(f180(x92051,x92052),x92054),f775(x92054,x92053,x92052,x92051)))+E(f334(f180(x92051,x92052),x92053),f334(f180(x92051,x92052),x92054))+~E(f334(f174(x92051),f334(f334(f156(f887(x92051,x92052),x92051),f268(x92051,x92052)),x92053)),f334(f174(x92051),f334(f334(f156(f887(x92051,x92052),x92051),f268(x92051,x92052)),x92054)))
% 160.93/160.65 [9251]E(f179(x92511,x92512,x92513),f334(f334(f177(x92511),x92514),x92513))+~P1(f334(x92512,f334(f334(f167(x92511),x92513),f763(x92512,x92513,x92511,x92514))))+P1(f334(f334(f249(a881),x92514),f334(f197(f882(x92511)),x92513)))
% 160.93/160.65 [9255]E(f179(x92551,x92552,x92553),f334(f334(f177(x92551),x92554),x92553))+~P1(f334(x92552,f334(f334(f167(x92551),x92553),f763(x92552,x92553,x92551,x92554))))+P1(f334(x92552,f334(f334(f167(x92551),x92553),x92554)))
% 160.93/160.65 [9262]~P1(f334(f61(x92621),x92623))+~P1(f334(f61(x92622),f334(x92624,f574(x92624,x92622,x92623,x92621))))+P1(f334(f61(f887(x92621,x92622)),f334(f334(f271(x92621,x92622),x92623),x92624)))
% 160.93/160.65 [9270]~P106(x92701)+~P1(f334(f334(f249(x92701),f2(x92701)),f334(x92703,f664(x92703,x92704,x92702,x92701))))+P1(f334(f334(f249(x92701),f2(x92701)),f334(f334(f9(x92702,x92701),x92703),x92704)))
% 160.93/160.65 [9271]~P106(x92711)+~P1(f334(f334(f248(x92711),f2(x92711)),f334(x92713,f668(x92713,x92714,x92712,x92711))))+P1(f334(f334(f248(x92711),f2(x92711)),f334(f334(f9(x92712,x92711),x92713),x92714)))
% 160.93/160.65 [9277]~E(f334(f197(f882(x92774)),x92772),f334(f197(f882(x92774)),x92773))+P1(f334(f334(f336(f887(f882(x92774),f882(x92774))),f334(f334(f269(f882(x92774),f882(x92774)),x92773),x92772)),f160(x92774,x92771)))+P1(f334(f334(f249(a881),f669(x92771,x92772,x92773,x92774)),f334(f197(f882(x92774)),x92773)))
% 160.93/160.65 [9331]~P1(f334(x93313,f334(f334(f167(x93312),x93314),f764(x93314,x93312,x93313,x93311))))+P1(f334(f334(f248(a881),x93311),f334(f197(f882(x93312)),f179(x93312,x93313,x93314))))+~P1(f334(f334(f248(a881),x93311),f334(f197(f882(x93312)),x93314)))
% 160.93/160.65 [9408]E(f334(f334(f177(x94081),f682(x94082,x94083,x94084,x94081)),x94083),f334(f334(f177(x94081),f682(x94082,x94083,x94084,x94081)),x94084))+~P1(f334(f334(f336(f887(f882(x94081),f882(x94081))),f334(f334(f269(f882(x94081),f882(x94081)),x94084),x94083)),f149(x94081,x94082)))+P1(f334(f334(f249(a881),f334(f197(f882(x94081)),x94084)),f334(f197(f882(x94081)),x94083)))
% 160.93/160.65 [9462]~P1(f334(f334(f249(a881),f2(a881)),x94623))+~P1(f334(f334(f249(a881),x94624),x94621))+P1(f334(f334(f249(a881),f334(f334(f80(a881),f334(f334(f81(a881),x94621),f44(a881,x94622,x94623))),x94624)),f334(f334(f81(a881),x94621),x94623)))
% 160.93/160.65 [9659]~P110(x96592)+~P1(f334(f334(f248(x96592),f334(x96593,f875(x96594,x96593,x96591,x96592))),f334(x96594,f875(x96594,x96593,x96591,x96592))))+P1(f334(f334(f248(f888(x96591,x96592)),x96593),x96594))
% 160.93/160.65 [9763]~P67(x97631)+E(f334(f334(f6(a881,x97631),f334(f334(f18(a881,x97631,x97631),f334(f334(f8(x97631,f888(x97631,x97631),a881),f22(x97631)),x97632)),f334(f334(f8(a881,x97631,a881),x97632),f334(f334(f7(a881,a881,a881),f80(a881)),f78(a881))))),f305(a881,x97633,x97634)),f334(f334(f22(x97631),f334(x97632,x97633)),f334(x97632,f334(f334(f80(a881),x97634),f78(a881)))))+~P1(f334(f334(f248(a881),x97633),x97634))
% 160.93/160.65 [6805]E(f334(f334(f136(x68051),x68052),x68053),x68054)+~E(x68053,f334(f334(f140(x68051),f334(f197(f882(x68051)),x68052)),x68054))+~E(f334(f334(f177(x68051),f334(f197(f882(x68051)),x68052)),x68054),x68052)
% 160.93/160.65 [6860]~P62(x68602)+E(x68601,f2(x68602))+E(f334(f334(f292(x68602),f334(f334(f259(x68602),x68603),x68604)),f334(f334(f259(x68602),x68601),x68604)),f334(f334(f259(x68602),f334(f334(f292(x68602),x68603),x68601)),x68604))
% 160.93/160.65 [6995]~E(f334(f197(f882(x69951)),x69953),f334(f197(f882(x69952)),x69954))+~P1(f334(f139(x69951),x69953))+E(f186(x69951,x69952,f334(f180(x69951,x69952),f334(f334(f184(x69951,x69952),x69953),x69954))),f334(f174(x69951),x69953))
% 160.93/160.65 [7012]~P100(x70121)+~P1(f334(f334(f249(x70121),x70123),x70124))+P1(f334(f334(f249(x70121),f334(f334(f105(x70121),x70122),x70123)),x70124))
% 160.93/160.65 [7013]~P100(x70131)+~P1(f334(f334(f249(x70131),x70132),x70134))+P1(f334(f334(f249(x70131),f334(f334(f105(x70131),x70132),x70133)),x70134))
% 160.93/160.65 [7015]~P108(x70151)+~P1(f334(f334(f249(x70151),x70153),x70154))+P1(f334(f334(f249(x70151),f334(f334(f246(x70151),x70152),x70153)),x70154))
% 160.93/160.65 [7017]~P108(x70171)+~P1(f334(f334(f249(x70171),x70172),x70174))+P1(f334(f334(f249(x70171),f334(f334(f246(x70171),x70172),x70173)),x70174))
% 160.93/160.65 [7018]~P100(x70181)+~P1(f334(f334(f248(x70181),x70183),x70184))+P1(f334(f334(f248(x70181),f334(f334(f105(x70181),x70182),x70183)),x70184))
% 160.93/160.65 [7019]~P100(x70191)+~P1(f334(f334(f248(x70191),x70192),x70194))+P1(f334(f334(f248(x70191),f334(f334(f105(x70191),x70192),x70193)),x70194))
% 160.93/160.65 [7021]~P108(x70211)+~P1(f334(f334(f248(x70211),x70213),x70214))+P1(f334(f334(f248(x70211),f334(f334(f246(x70211),x70212),x70213)),x70214))
% 160.93/160.65 [7023]~P108(x70231)+~P1(f334(f334(f248(x70231),x70232),x70234))+P1(f334(f334(f248(x70231),f334(f334(f246(x70231),x70232),x70233)),x70234))
% 160.93/160.65 [7043]~P1(f334(x70433,x70434))+~P1(f334(x70432,x70434))+P1(f334(f334(f334(f105(f888(x70431,a876)),x70432),x70433),x70434))
% 160.93/160.65 [7167]P26(x71671,x71672,x71673)+~P26(x71671,x71674,x71673)+~P1(f334(f334(f248(f888(f880(x71671),a876)),x71674),x71672))
% 160.93/160.65 [7168]P26(x71681,x71682,x71683)+~P26(x71681,x71682,x71684)+~P1(f334(f334(f248(f888(f880(x71681),a876)),x71683),x71684))
% 160.93/160.65 [7540]~P68(x75401)+E(f334(f334(f80(x75401),f334(x75402,x75403)),f334(f334(f6(a881,x75401),x75402),f334(f304(a881,f334(a116,x75403)),x75404))),f334(f334(f6(a881,x75401),x75402),f334(f304(a881,x75403),x75404)))+~P1(f334(f334(f249(a881),x75403),x75404))
% 160.93/160.65 [7568]~P108(x75681)+P1(f334(f334(f249(x75681),x75682),x75683))+~P1(f334(f334(f249(x75681),f334(f334(f247(x75681),x75684),x75682)),x75683))
% 160.93/160.65 [7569]~P108(x75691)+P1(f334(f334(f249(x75691),x75692),x75693))+~P1(f334(f334(f249(x75691),f334(f334(f247(x75691),x75692),x75694)),x75693))
% 160.93/160.65 [7571]~P99(x75711)+P1(f334(f334(f248(x75711),x75712),x75713))+~P1(f334(f334(f248(x75711),f334(f334(f114(x75711),x75714),x75712)),x75713))
% 160.93/160.65 [7573]~P99(x75731)+P1(f334(f334(f248(x75731),x75732),x75733))+~P1(f334(f334(f248(x75731),f334(f334(f114(x75731),x75732),x75734)),x75733))
% 160.93/160.65 [7575]~P108(x75751)+P1(f334(f334(f248(x75751),x75752),x75753))+~P1(f334(f334(f248(x75751),f334(f334(f247(x75751),x75754),x75752)),x75753))
% 160.93/160.65 [7577]~P108(x75771)+P1(f334(f334(f248(x75771),x75772),x75773))+~P1(f334(f334(f248(x75771),f334(f334(f247(x75771),x75772),x75774)),x75773))
% 160.93/160.65 [7655]~P1(f334(f334(f336(x76551),x76552),x76554))+P1(f334(f334(f336(x76551),x76552),x76553))+P1(f334(f334(f336(x76551),x76552),f334(f334(f22(f888(x76551,a876)),x76554),x76553)))
% 160.93/160.65 [7736]P1(f334(x77361,x77362))+P1(f334(x77363,x77362))+~P1(f334(f334(f334(f114(f888(x77364,a876)),x77363),x77361),x77362))
% 160.93/160.65 [7746]~P1(f334(f334(f336(x77461),x77462),x77464))+~P1(f334(f334(f336(x77461),x77462),x77463))+P1(f334(f334(f336(x77461),x77462),f334(f334(f105(f888(x77461,a876)),x77463),x77464)))
% 160.93/160.65 [7797]~P99(x77971)+~P1(f334(f61(x77971),x77974))+E(f334(f334(f64(x77971,x77971,f114(x77971)),x77972),f334(f334(f312(x77971),x77973),x77974)),f334(f334(f114(x77971),x77973),f334(f334(f64(x77971,x77971,f114(x77971)),x77972),x77974)))
% 160.93/160.65 [7798]~P100(x77981)+~P1(f334(f61(x77981),x77984))+E(f334(f334(f64(x77981,x77981,f105(x77981)),x77982),f334(f334(f312(x77981),x77983),x77984)),f334(f334(f105(x77981),x77983),f334(f334(f64(x77981,x77981,f105(x77981)),x77982),x77984)))
% 160.93/160.65 [7799]~P108(x77991)+~P1(f334(f61(x77991),x77994))+E(f334(f334(f64(x77991,x77991,f246(x77991)),x77992),f334(f334(f312(x77991),x77993),x77994)),f334(f334(f246(x77991),x77993),f334(f334(f64(x77991,x77991,f246(x77991)),x77992),x77994)))
% 160.93/160.65 [7800]~P108(x78001)+~P1(f334(f61(x78001),x78004))+E(f334(f334(f64(x78001,x78001,f247(x78001)),x78002),f334(f334(f312(x78001),x78003),x78004)),f334(f334(f247(x78001),x78003),f334(f334(f64(x78001,x78001,f247(x78001)),x78002),x78004)))
% 160.93/160.65 [7801]~P105(x78011)+~P91(x78011)+E(f334(f334(f22(x78011),f334(f334(f81(x78011),f334(f107(x78011),x78012)),x78013)),f334(f334(f81(x78011),f334(f107(x78011),x78012)),x78014)),f334(f334(f81(x78011),f334(f107(x78011),x78012)),f334(f334(f22(x78011),x78013),x78014)))
% 160.93/160.65 [7802]~P137(x78021)+~P91(x78021)+E(f334(f334(f80(x78021),f334(f334(f81(x78021),f334(f107(x78021),x78022)),x78023)),f334(f334(f81(x78021),f334(f107(x78021),x78022)),x78024)),f334(f334(f81(x78021),f334(f107(x78021),x78022)),f334(f334(f80(x78021),x78023),x78024)))
% 160.93/160.65 [7916]E(x79161,x79162)+P1(f334(f334(f336(x79163),x79161),f334(f174(x79163),x79164)))+~P1(f334(f334(f336(x79163),x79161),f334(f174(x79163),f334(f334(f153(x79163),x79162),x79164))))
% 160.93/160.65 [7941]~P60(x79411)+~E(f334(f197(f882(x79412)),x79413),f334(f197(f882(x79411)),f55(x79411)))+E(f334(f334(f180(x79411,x79412),f334(f334(f184(x79411,x79412),f55(x79411)),x79413)),x79414),f334(f241(x79412),f739(x79414,x79413,x79412,x79411)))
% 160.93/160.65 [8087]P52(x80871,x80872,x80873)+~P52(x80871,x80872,x80874)+~P1(f334(f334(f248(f888(f887(x80871,x80872),a876)),x80873),x80874))
% 160.93/160.65 [8132]P1(f334(f334(f336(x81321),x81322),x81323))+P1(f334(f334(f336(x81321),x81322),x81324))+~P1(f334(f334(f336(x81321),x81322),f334(f334(f114(f888(x81321,a876)),x81324),x81323)))
% 160.93/160.65 [8142]~P41(x81421,x81424,x81423)+~P1(f334(f334(f336(x81421),x81422),x81424))+P1(f334(f334(f336(f887(x81421,x81421)),f334(f334(f269(x81421,x81421),x81422),x81422)),x81423))
% 160.93/160.65 [8159]~P1(f334(f61(x81592),x81594))+~P1(f334(f61(x81591),x81593))+P1(f334(f61(f887(x81591,x81592)),f334(f334(f271(x81591,x81592),x81593),f334(f16(f888(x81592,a876),x81591),x81594))))
% 160.93/160.65 [8160]~P1(f334(f334(f336(x81601),x81602),x81604))+~P1(f334(f334(f248(f888(x81601,a876)),x81603),x81604))+P1(f334(f334(f248(f888(x81601,a876)),f334(f334(f312(x81601),x81602),x81603)),x81604))
% 160.93/160.65 [8168]~P74(x81682)+~P142(x81682)+E(f334(f334(f9(x81681,x81682),f334(f334(f8(a881,x81682,x81681),f104(x81682)),x81683)),x81684),f334(f104(x81682),f334(f334(f9(x81681,a881),x81683),x81684)))
% 160.93/160.65 [8169]~P74(x81692)+~P139(x81692)+E(f334(f334(f9(x81691,x81692),f334(f334(f8(a1,x81692,x81691),f106(x81692)),x81693)),x81694),f334(f106(x81692),f334(f334(f9(x81691,a1),x81693),x81694)))
% 160.93/160.65 [8198]E(f334(f334(f22(f888(x81981,a876)),x81982),f334(f334(f22(f888(x81981,a876)),x81983),x81984)),x81984)+~P1(f334(f334(f248(f888(x81981,a876)),x81982),x81983))+~P1(f334(f334(f248(f888(x81981,a876)),x81984),x81982))
% 160.93/160.65 [8298]~P1(f334(f61(x82981),x82984))+E(f334(f334(f22(a881),f334(f334(f6(x82981,a881),x82982),x82983)),f334(f334(f6(x82981,a881),x82982),x82984)),f334(f334(f6(x82981,a881),x82982),f334(f334(f22(f888(x82981,a876)),x82983),x82984)))+~P1(f334(f334(f248(f888(x82981,a876)),x82984),x82983))
% 160.93/160.65 [8450]~P8(x84501,x84504,x84503)+~P1(f334(f334(f336(x84501),x84502),x84504))+P1(f334(f334(f336(x84501),x84502),f334(f288(x84501,x84501,x84503),f334(f334(f312(x84501),x84502),f196(f888(x84501,a876))))))
% 160.93/160.65 [8511]~P1(f334(f334(f248(f888(x85111,a876)),x85112),x85113))+~P1(f334(f334(f248(f888(x85111,a876)),x85112),x85114))+P1(f334(f334(f248(f888(x85111,a876)),x85112),f334(f334(f105(f888(x85111,a876)),x85113),x85114)))
% 160.93/160.65 [8615]E(x86151,f196(f888(x86152,a876)))+P1(f334(f61(x86153),x86154))+~P1(f334(f61(f887(x86153,x86152)),f334(f334(f271(x86153,x86152),x86154),f334(f16(f888(x86152,a876),x86153),x86151))))
% 160.93/160.65 [8616]E(x86161,f196(f888(x86162,a876)))+P1(f334(f61(x86163),x86164))+~P1(f334(f61(f887(x86162,x86163)),f334(f334(f271(x86162,x86163),x86161),f334(f16(f888(x86163,a876),x86162),x86164))))
% 160.93/160.65 [8686]P1(f334(f334(f336(x86861),x86862),f323(x86861,x86863)))+~P1(f334(f334(f336(x86861),x86864),f323(x86861,x86863)))+~P1(f334(f334(f336(f887(x86861,x86861)),f334(f334(f269(x86861,x86861),x86862),x86864)),x86863))
% 160.93/160.65 [8738]~P39(x87381,x87384)+P1(f334(f334(f336(f887(x87381,x87381)),f334(f334(f269(x87381,x87381),x87383),x87382)),f310(x87381,x87384)))+P39(x87381,f334(f334(f312(f887(x87381,x87381)),f334(f334(f269(x87381,x87381),x87382),x87383)),x87384))
% 160.93/160.65 [8739]~P55(x87391,x87394)+P1(f334(f334(f336(f887(x87391,x87391)),f334(f334(f269(x87391,x87391),x87393),x87392)),f310(x87391,x87394)))+P55(x87391,f334(f334(f312(f887(x87391,x87391)),f334(f334(f269(x87391,x87391),x87392),x87393)),x87394))
% 160.93/160.65 [8816]~E(x88162,x88163)+~P1(f334(f334(f336(x88161),x88162),f334(f174(x88161),x88164)))+P1(f334(f334(f336(f887(x88161,x88161)),f334(f334(f269(x88161,x88161),x88162),x88163)),f334(f174(f887(x88161,x88161)),f334(f334(f184(x88161,x88161),x88164),x88164))))
% 160.93/160.65 [8897]~E(x88973,x88974)+P1(f334(f334(f273(x88971,x88971,a876),a331),x88972))+~P1(f334(f334(f336(f887(x88971,x88971)),x88972),f334(f174(f887(x88971,x88971)),f334(f334(f184(x88971,x88971),x88973),x88974))))
% 160.93/160.65 [8923]~P1(f334(x89234,x89232))+P1(f334(f334(f334(f334(a204,x89231),x89232),x89233),f442(x89233,x89232,x89231,x89234)))+~P1(f334(f334(f334(f334(a204,f32(x89234,x89231)),x89232),x89233),x89232))
% 160.93/160.65 [8950]P1(f334(f334(f336(f887(f882(x89501),f882(x89501))),f334(f334(f269(f882(x89501),f882(x89501)),x89502),x89503)),f149(x89501,x89504)))+~E(f334(f334(f177(x89501),f334(f197(f882(x89501)),x89502)),x89503),x89502)+~P1(f334(f334(f249(a881),f334(f197(f882(x89501)),x89502)),f334(f197(f882(x89501)),x89503)))
% 160.93/160.65 [9049]~P1(f334(f61(x90491),x90494))+P1(f334(f334(f336(x90491),f829(x90492,x90493,x90494,x90491)),x90494))+P1(f334(f61(x90493),f334(f334(f41(x90491,f888(x90493,a876)),x90494),x90492)))
% 160.93/160.65 [9050]~P1(f334(f61(x90501),x90504))+P1(f334(f334(f336(x90501),f858(x90502,x90503,x90504,x90501)),x90504))+P1(f334(f61(x90503),f334(f334(f41(x90501,f888(x90503,a876)),x90504),x90502)))
% 160.93/160.65 [9135]P1(f334(f334(f336(f887(x91351,x91351)),x91352),f334(f334(f291(x91351,x91351,x91351),x91353),f310(x91351,x91353))))+~P1(f334(f334(f249(a881),f2(a881)),x91354))+~P1(f334(f334(f336(f887(x91351,x91351)),x91352),f334(f334(f191(f887(x91351,x91351),a876),x91354),x91353)))
% 160.93/160.65 [9143]~P39(x91431,x91432)+~P1(f334(f334(f336(f887(x91431,x91431)),f334(f334(f269(x91431,x91431),x91434),x91433)),x91432))+~P1(f334(f334(f336(f887(x91431,x91431)),f334(f334(f269(x91431,x91431),x91433),x91434)),x91432))
% 160.93/160.65 [9269]~P1(f334(f61(x92691),x92694))+E(f334(f334(f6(x92691,a881),f334(f334(f8(f888(x92692,a876),a881,x92691),f37(x92692)),x92693)),x92694),f334(f37(f887(x92691,x92692)),f334(f334(f271(x92691,x92692),x92694),x92693)))+P1(f334(f334(f336(x92691),f575(x92693,x92692,x92694,x92691)),x92694))
% 160.93/160.65 [9273]~P1(f334(f139(x92731),x92732))+P1(f334(f139(x92731),f334(f334(f161(x92731,x92732),x92733),x92734)))+P1(f334(f334(f336(x92731),x92734),f334(f334(f22(f888(x92731,a876)),f334(f174(x92731),x92732)),f334(f334(f312(x92731),f334(f334(f167(x92731),x92732),x92733)),f196(f888(x92731,a876))))))
% 160.93/160.65 [9289]~P1(f334(f61(x92892),x92893))+~P1(f334(f61(x92891),f334(x92894,f829(x92894,x92891,x92893,x92892))))+P1(f334(f61(x92891),f334(f334(f41(x92892,f888(x92891,a876)),x92893),x92894)))
% 160.93/160.65 [9290]~P1(f334(f61(x92902),x92903))+~P1(f334(f61(x92901),f334(x92904,f858(x92904,x92901,x92903,x92902))))+P1(f334(f61(x92901),f334(f334(f41(x92902,f888(x92901,a876)),x92903),x92904)))
% 160.93/160.65 [9369]~P1(f334(f334(f336(f887(x93691,x93691)),x93692),f334(f334(f291(x93691,x93691,x93691),x93694),f310(x93691,x93694))))+P1(f334(f334(f336(f887(x93691,x93691)),x93692),f334(f334(f291(x93691,x93691,x93691),x93693),f310(x93691,x93693))))+~P1(f334(f334(f248(f888(f887(x93691,x93691),a876)),x93694),x93693))
% 160.93/160.65 [9376]E(f334(f334(f177(x93761),f682(x93764,x93763,x93762,x93761)),x93763),f334(f334(f177(x93761),f682(x93764,x93763,x93762,x93761)),x93762))+~P1(f334(f334(f336(f887(f882(x93761),f882(x93761))),f334(f334(f269(f882(x93761),f882(x93761)),x93762),x93763)),f149(x93761,x93764)))+E(f334(f334(f177(x93761),f334(f197(f882(x93761)),x93762)),x93763),x93762)
% 160.93/160.65 [9392]~P1(f334(f61(x93921),x93924))+E(f334(f334(f6(x93921,a881),f334(f334(f8(f888(x93922,a876),a881,x93921),f37(x93922)),x93923)),x93924),f334(f37(f887(x93921,x93922)),f334(f334(f271(x93921,x93922),x93924),x93923)))+~P1(f334(f61(x93922),f334(x93923,f575(x93923,x93922,x93924,x93921))))
% 160.93/160.65 [9396]~E(f334(f197(f882(x93961)),x93963),f334(f197(f882(x93961)),x93962))+P1(f334(f334(f336(f887(f882(x93961),f882(x93961))),f334(f334(f269(f882(x93961),f882(x93961)),x93962),x93963)),f160(x93961,x93964)))+P1(f334(f334(f336(f887(x93961,x93961)),f687(x93964,x93963,x93962,x93961)),f334(f174(f887(x93961,x93961)),f334(f334(f184(x93961,x93961),x93962),x93963))))
% 160.93/160.65 [9474]~P1(f334(f334(f336(f887(f882(x94741),f882(x94741))),f334(f334(f269(f882(x94741),f882(x94741)),x94742),x94743)),f149(x94741,x94744)))+E(f334(f334(f177(x94741),f334(f197(f882(x94741)),x94742)),x94743),x94742)+P1(f334(f334(f249(a881),f682(x94744,x94743,x94742,x94741)),f334(f334(f246(a881),f334(f197(f882(x94741)),x94742)),f334(f197(f882(x94741)),x94743))))
% 160.93/160.65 [9475]E(f334(f180(x94751,x94752),x94753),f334(f180(x94751,x94752),x94754))+~E(f334(f174(x94751),f334(f334(f156(f887(x94751,x94752),x94751),f268(x94751,x94752)),x94753)),f334(f174(x94751),f334(f334(f156(f887(x94751,x94752),x94751),f268(x94751,x94752)),x94754)))+P1(f334(f334(f336(x94751),f775(x94753,x94754,x94752,x94751)),f334(f174(x94751),f334(f334(f156(f887(x94751,x94752),x94751),f268(x94751,x94752)),x94754))))
% 160.93/160.65 [9491]~P1(f334(x94911,x94914))+P1(f334(f334(f334(f334(a204,f32(x94911,x94912)),f442(x94913,x94914,x94912,x94911)),x94913),x94914))+~P1(f334(f334(f334(f334(a204,f32(x94911,x94912)),x94914),x94913),x94914))
% 160.93/160.65 [9496]~P1(f334(f334(f336(f887(f882(x94961),f882(x94961))),f334(f334(f269(f882(x94961),f882(x94961)),x94962),x94963)),f149(x94961,x94964)))+P1(f334(f334(f249(a881),f334(f197(f882(x94961)),x94962)),f334(f197(f882(x94961)),x94963)))+P1(f334(f334(f249(a881),f682(x94964,x94963,x94962,x94961)),f334(f334(f246(a881),f334(f197(f882(x94961)),x94962)),f334(f197(f882(x94961)),x94963))))
% 160.93/160.65 [9800]~P1(f334(f334(f334(x98001,f728(x98001,x98004,x98003,x98002)),f729(x98001,x98004,x98003,x98002)),f730(x98001,x98004,x98003,x98002)))+P1(f334(f334(f334(x98001,x98002),x98003),x98004))+~P1(f334(f322(f887(f888(a1,f885(f882(a330))),f887(a1,a1)),a320),f334(f334(f269(f888(a1,f885(f882(a330))),f887(a1,a1)),x98002),f334(f334(f269(a1,a1),x98003),x98004))))
% 160.93/160.65 [9880]P1(f334(f334(f334(x98801,x98802),x98803),x98804))+P1(f334(f322(f887(f888(a1,f885(f882(a330))),f887(a1,a1)),a320),f334(f334(f269(f888(a1,f885(f882(a330))),f887(a1,a1)),f728(x98801,x98804,x98803,x98802)),f334(f334(f269(a1,a1),f729(x98801,x98804,x98803,x98802)),f730(x98801,x98804,x98803,x98802)))))+~P1(f334(f322(f887(f888(a1,f885(f882(a330))),f887(a1,a1)),a320),f334(f334(f269(f888(a1,f885(f882(a330))),f887(a1,a1)),x98802),f334(f334(f269(a1,a1),x98803),x98804))))
% 160.93/160.65 [9919]~P1(f334(f334(f336(f887(f882(x99191),f882(x99191))),f334(f334(f269(f882(x99191),f882(x99191)),x99192),x99193)),f149(x99191,x99194)))+E(f334(f334(f177(x99191),f334(f197(f882(x99191)),x99192)),x99193),x99192)+P1(f334(f334(f336(f887(x99191,x99191)),f334(f334(f269(x99191,x99191),f334(f334(f167(x99191),x99192),f682(x99194,x99193,x99192,x99191))),f334(f334(f167(x99191),x99193),f682(x99194,x99193,x99192,x99191)))),x99194))
% 160.93/160.65 [9920]~P1(f334(f334(f336(f887(f882(x99201),f882(x99201))),f334(f334(f269(f882(x99201),f882(x99201)),x99202),x99203)),f149(x99201,x99204)))+P1(f334(f334(f249(a881),f334(f197(f882(x99201)),x99202)),f334(f197(f882(x99201)),x99203)))+P1(f334(f334(f336(f887(x99201,x99201)),f334(f334(f269(x99201,x99201),f334(f334(f167(x99201),x99202),f682(x99204,x99203,x99202,x99201))),f334(f334(f167(x99201),x99203),f682(x99204,x99203,x99202,x99201)))),x99204))
% 160.93/160.65 [9977]~E(f334(f197(f882(x99771)),x99772),f334(f197(f882(x99771)),x99773))+P1(f334(f334(f336(f887(f882(x99771),f882(x99771))),f334(f334(f269(f882(x99771),f882(x99771)),x99772),x99773)),f160(x99771,x99774)))+~P1(f334(f334(f336(f887(x99771,x99771)),f334(f334(f269(x99771,x99771),f334(f334(f167(x99771),x99772),f669(x99774,x99773,x99772,x99771))),f334(f334(f167(x99771),x99773),f669(x99774,x99773,x99772,x99771)))),x99774))
% 160.93/160.65 [10113]~P68(x101131)+~P1(f334(f61(x101132),x101134))+E(f334(f168(x101131),f334(f334(f156(x101132,x101131),x101133),f90(f882(x101132),f334(f334(f18(f882(x101132),a876,a876),f334(f334(f8(a876,f888(a876,a876),f882(x101132)),a332),f334(f334(f7(f882(x101132),f888(x101132,a876),a876),f334(f334(f8(f888(x101132,a876),f888(f888(x101132,a876),a876),f882(x101132)),a331),f174(x101132))),x101134))),f139(x101132))))),f239(x101132,x101131,x101133,x101134))
% 160.93/160.65 [7381]~P61(x73812)+E(x73811,f2(x73812))+E(f334(f334(f292(x73812),f334(f334(f80(x73812),x73813),f334(f334(f81(x73812),x73814),x73811))),x73811),f334(f334(f80(x73812),x73814),f334(f334(f292(x73812),x73813),x73811)))
% 160.93/160.65 [7382]~P58(x73822)+E(x73821,f2(x73822))+E(f334(f334(f38(x73822),f334(f334(f80(x73822),x73823),f334(f334(f81(x73822),x73824),x73821))),x73821),f334(f334(f80(x73822),x73824),f334(f334(f38(x73822),x73823),x73821)))
% 160.93/160.65 [7383]~P58(x73832)+E(x73831,f2(x73832))+E(f334(f334(f38(x73832),f334(f334(f80(x73832),x73833),f334(f334(f81(x73832),x73831),x73834))),x73831),f334(f334(f80(x73832),x73834),f334(f334(f38(x73832),x73833),x73831)))
% 160.93/160.65 [7618]~P62(x76182)+E(x76181,f2(x76182))+E(f334(f334(f292(x76182),f334(f334(f22(x76182),x76183),f334(f334(f81(x76182),x76181),x76184))),x76181),f334(f334(f22(x76182),f334(f334(f292(x76182),x76183),x76181)),x76184))
% 160.93/160.65 [7619]~P61(x76192)+E(x76191,f2(x76192))+E(f334(f334(f292(x76192),f334(f334(f80(x76192),x76193),f334(f334(f81(x76192),x76194),x76191))),x76191),f334(f334(f80(x76192),f334(f334(f292(x76192),x76193),x76191)),x76194))
% 160.93/160.65 [7620]~P62(x76202)+E(x76201,f2(x76202))+E(f334(f334(f292(x76202),f334(f334(f80(x76202),x76203),f334(f334(f81(x76202),x76201),x76204))),x76201),f334(f334(f80(x76202),f334(f334(f292(x76202),x76203),x76201)),x76204))
% 160.93/160.65 [8327]~P1(f334(f162(x83271,x83273),x83274))+~P1(f334(f162(x83271,x83272),x83274))+P1(f334(f162(x83271,f334(f334(f105(f888(x83271,a876)),x83272),x83273)),x83274))
% 160.93/160.65 [8700]~E(f334(f334(f291(x87001,x87001,x87001),x87002),x87004),f196(f888(f887(x87001,x87001),a876)))+~E(f334(f334(f291(x87001,x87001,x87001),x87002),x87003),f196(f888(f887(x87001,x87001),a876)))+E(f334(f334(f291(x87001,x87001,x87001),x87002),f334(f334(f114(f888(f887(x87001,x87001),a876)),x87003),x87004)),f196(f888(f887(x87001,x87001),a876)))
% 160.93/160.65 [8817]~P1(f334(f334(f248(f888(x88171,a876)),x88173),x88174))+~P1(f334(f334(f248(f888(x88171,a876)),x88172),x88174))+P1(f334(f334(f248(f888(x88171,a876)),f334(f334(f114(f888(x88171,a876)),x88172),x88173)),x88174))
% 160.93/160.65 [9199]~P1(f334(f61(x91991),x91994))+~P1(f334(f61(x91991),x91993))+E(f334(f334(f22(a881),f334(f334(f80(a881),f334(f334(f6(x91991,a881),x91992),x91993)),f334(f334(f6(x91991,a881),x91992),x91994))),f334(f334(f6(x91991,a881),x91992),f334(f334(f105(f888(x91991,a876)),x91993),x91994))),f334(f334(f6(x91991,a881),x91992),f334(f334(f114(f888(x91991,a876)),x91993),x91994)))
% 160.93/160.65 [9286]~P1(f334(f334(f336(x92861),x92863),x92862))+~P1(f334(f334(f248(f888(x92861,a876)),x92862),f334(f334(f312(x92861),x92863),x92864)))+P1(f334(f334(f248(f888(x92861,a876)),f334(f334(f22(f888(x92861,a876)),x92862),f334(f334(f312(x92861),x92863),f196(f888(x92861,a876))))),x92864))
% 160.93/160.65 [9446]~P1(f334(f334(f336(x94461),x94463),x94462))+P1(f334(f334(f248(f888(x94461,a876)),x94462),f334(f334(f312(x94461),x94463),x94464)))+~P1(f334(f334(f248(f888(x94461,a876)),f334(f334(f22(f888(x94461,a876)),x94462),f334(f334(f312(x94461),x94463),f196(f888(x94461,a876))))),x94464))
% 160.93/160.65 [9539]~P1(f334(f334(f249(a881),x95392),x95394))+~P1(f334(f334(f248(a881),x95391),x95393))+P1(f334(f334(f336(f887(f887(a881,a881),f887(a881,a881))),f334(f334(f269(f887(a881,a881),f887(a881,a881)),f334(f334(f269(a881,a881),x95391),x95392)),f334(f334(f269(a881,a881),x95393),x95394))),a35))
% 160.93/160.65 [9540]~P1(f334(f334(f248(a881),x95402),x95404))+~P1(f334(f334(f248(a881),x95401),x95403))+P1(f334(f334(f336(f887(f887(a881,a881),f887(a881,a881))),f334(f334(f269(f887(a881,a881),f887(a881,a881)),f334(f334(f269(a881,a881),x95401),x95402)),f334(f334(f269(a881,a881),x95403),x95404))),a70))
% 160.93/160.65 [9839]~P1(f334(f334(f336(f882(x98391)),x98394),f163(x98391,x98393)))+~P1(f334(f334(f336(f882(x98391)),x98394),f163(x98391,x98392)))+P1(f334(f162(x98391,f334(f334(f105(f888(x98391,a876)),f334(f334(f7(x98391,f888(x98391,a876),a876),f336(x98391)),x98392)),f334(f334(f7(x98391,f888(x98391,a876),a876),f336(x98391)),x98393))),x98394))
% 160.93/160.65 [9942]~P27(x99421,f888(f888(x99421,a876),a876),f334(f334(f7(x99421,f888(f887(x99421,x99421),a876),f888(f888(x99421,a876),a876)),f334(f334(f8(f888(x99421,a876),f888(f888(f887(x99421,x99421),a876),f888(f888(x99421,a876),a876)),x99421),f60(x99421)),f334(f334(f7(x99421,f888(x99421,a876),f888(x99421,a876)),f312(x99421)),f196(f888(x99421,a876))))),x99423),x99422)+~P1(f334(f334(f336(x99421),x99424),x99422))+E(f334(f334(f22(f888(f888(x99421,a876),a876)),f334(f334(f60(x99421),x99422),x99423)),f334(f334(f60(x99421),f334(f334(f312(x99421),x99424),f196(f888(x99421,a876)))),x99423)),f334(f334(f60(x99421),f334(f334(f22(f888(x99421,a876)),x99422),f334(f334(f312(x99421),x99424),f196(f888(x99421,a876))))),x99423))
% 160.93/160.65 [10077]~P41(x100771,x100772,x100774)+~P1(f334(f334(f336(f887(x100771,x100771)),x100773),x100774))+P1(f334(f334(f273(x100771,x100771,a876),f334(f334(f7(x100771,f888(x100771,a876),f888(x100771,a876)),f334(f334(f8(f888(a876,a876),f888(f888(x100771,a876),f888(x100771,a876)),x100771),f8(a876,a876,x100771)),f334(f334(f8(a876,f888(a876,a876),x100771),a332),f334(f334(f7(x100771,f888(x100771,a876),a876),f336(x100771)),x100772)))),f334(f334(f7(x100771,f888(x100771,a876),a876),f336(x100771)),x100772))),x100773))
% 160.93/160.65 [10089]P1(f334(f61(x100891),x100892))+~P1(f334(f61(x100893),f334(f313(x100891,x100893,x100894),x100892)))+~P1(f334(f61(x100891),f334(f254(x100891),f334(f334(f18(x100891,a876,a876),f334(f334(f8(a876,f888(a876,a876),x100891),a332),f334(f334(f7(x100891,f888(x100891,a876),a876),f336(x100891)),x100892))),f334(f334(f7(x100891,x100893,a876),f334(f334(f8(x100893,f888(x100893,a876),x100891),a331),x100894)),f334(x100894,f463(x100894,x100893,x100892,x100891)))))))
% 160.93/160.65 [8069]~P62(x80692)+E(x80691,f2(x80692))+E(f334(f334(f292(x80692),f334(f334(f22(x80692),f334(f334(f81(x80692),x80691),x80693)),x80694)),x80691),f334(f334(f22(x80692),x80693),f334(f334(f292(x80692),x80694),x80691)))
% 160.93/160.65 [8070]~P62(x80702)+E(x80701,f2(x80702))+E(f334(f334(f292(x80702),f334(f334(f80(x80702),f334(f334(f81(x80702),x80701),x80703)),x80704)),x80701),f334(f334(f80(x80702),x80703),f334(f334(f292(x80702),x80704),x80701)))
% 160.93/160.65 [8983]~E(f334(f334(f291(x89831,x89831,x89831),x89833),x89834),f196(f888(f887(x89831,x89831),a876)))+~E(f334(f334(f291(x89831,x89831,x89831),x89832),x89834),f196(f888(f887(x89831,x89831),a876)))+E(f334(f334(f291(x89831,x89831,x89831),f334(f334(f114(f888(f887(x89831,x89831),a876)),x89832),x89833)),x89834),f196(f888(f887(x89831,x89831),a876)))
% 160.93/160.65 [10019]~P144(x100191)+~P144(x100192)+E(f334(f334(f319(x100191),f334(f334(f7(x100191,a103,f885(f882(a330))),f334(f334(f8(f888(x100192,f885(f882(a330))),f888(a103,f885(f882(a330))),x100191),f319(x100192)),f334(f334(f8(f888(x100192,f887(x100191,x100192)),f888(x100192,f885(f882(a330))),x100191),f334(f8(f887(x100191,x100192),f885(f882(a330)),x100192),x100193)),f269(x100191,x100192)))),x100194)),x100194),f334(f334(f319(f887(x100191,x100192)),x100193),x100194))
% 160.93/160.65 [9748]~P1(f334(f162(x97481,x97483),x97484))+~P1(f334(f162(x97481,x97482),x97484))+P1(f334(f162(x97481,f334(f334(f18(x97481,a876,a876),f334(f334(f8(a876,f888(a876,a876),x97481),a332),x97482)),x97483)),x97484))
% 160.93/160.65 [10011]P1(f334(x100111,f459(x100112,x100113,x100111,x100114)))+~P1(f334(f61(x100114),f334(f254(x100114),x100111)))+P1(f334(f61(x100113),f334(f254(x100113),f334(f334(f8(f888(x100114,a876),a876,x100113),f87(x100114)),f334(f334(f8(f888(x100114,a876),f888(x100114,a876),x100113),f334(f18(x100114,a876,a876),f334(f334(f8(a876,f888(a876,a876),x100114),a332),x100111))),x100112)))))
% 160.93/160.65 [10032]~P1(f334(f61(x100322),f334(f254(x100322),x100323)))+~P1(f334(f61(x100321),f334(f254(x100321),f334(f334(f7(x100321,x100322,a876),x100324),f459(x100324,x100321,x100323,x100322)))))+P1(f334(f61(x100321),f334(f254(x100321),f334(f334(f8(f888(x100322,a876),a876,x100321),f87(x100322)),f334(f334(f8(f888(x100322,a876),f888(x100322,a876),x100321),f334(f18(x100322,a876,a876),f334(f334(f8(a876,f888(a876,a876),x100322),a332),x100323))),x100324)))))
% 160.93/160.65 [6523]E(x65231,x65232)+~E(f334(x65233,x65231),f334(x65233,x65232))+~P27(x65234,x65235,x65233,f257(f888(x65234,a876)))
% 160.93/160.65 [6683]~E(f334(x66833,x66835),f210(x66832))+~E(f334(x66834,x66835),f210(x66832))+E(f334(f187(x66831,x66832,x66833,x66834),x66835),f210(x66832))
% 160.93/160.65 [7416]E(x74161,x74162)+~P27(x74163,x74164,x74165,f257(f888(x74163,a876)))+~E(f334(f313(x74163,x74164,x74165),x74161),f334(f313(x74163,x74164,x74165),x74162))
% 160.93/160.65 [7672]P27(x76722,x76723,f541(x76724,x76723,x76722,x76721),x76721)+~E(f334(f313(x76723,x76722,x76725),x76724),x76721)+E(x76721,f196(f888(x76722,a876)))
% 160.93/160.65 [8212]~P1(f334(f334(x82123,x82122),x82125))+~P1(f334(f334(x82123,x82124),x82122))+P1(f334(f334(f336(x82121),x82122),f298(x82121,x82123,x82124,x82125)))
% 160.93/160.65 [8213]~P1(f334(f334(x82133,x82132),x82135))+~P1(f334(f334(x82133,x82134),x82132))+P1(f334(f334(f336(x82131),x82132),f301(x82131,x82133,x82134,x82135)))
% 160.93/160.65 [8775]~P27(x87751,x87753,x87755,f257(f888(x87751,a876)))+~P27(x87753,x87752,x87754,f257(f888(x87753,a876)))+P27(x87751,x87752,f334(f73(x87753,x87752,x87751,x87754),x87755),f257(f888(x87751,a876)))
% 160.93/160.65 [9345]P1(f334(f334(f336(f887(x93451,x93451)),f334(f334(f269(x93451,x93451),x93452),x93453)),f310(x93451,x93454)))+~P1(f334(f334(f336(f887(x93451,x93451)),f334(f334(f269(x93451,x93451),x93452),x93455)),f310(x93451,x93454)))+~P1(f334(f334(f336(f887(x93451,x93451)),f334(f334(f269(x93451,x93451),x93455),x93453)),f310(x93451,x93454)))
% 160.93/160.65 [9383]~P108(x93832)+~P1(f334(f139(x93831),x93835))+P1(f334(f139(x93831),f151(x93831,x93832,x93833,x93834,x93835)))
% 160.93/160.65 [5358]~E(x53582,f117(x53581))+E(f334(f334(f136(x53581),x53582),x53583),f334(f334(f153(x53581),x53584),x53585))+~E(x53583,f334(f334(f153(x53581),x53584),x53585))
% 160.93/160.65 [5359]~E(x53592,f117(x53591))+E(f334(f334(f136(x53591),x53592),x53593),f334(f334(f153(x53591),x53594),x53595))+~E(f334(f334(f153(x53591),x53594),x53595),x53593)
% 160.93/160.65 [6480]~E(f334(f197(f882(x64801)),x64805),f334(f197(f882(x64802)),x64804))+E(f334(f334(f156(f887(x64801,x64802),x64802),f272(x64801,x64802)),x64803),x64804)+~E(f334(f334(f184(x64801,x64802),x64805),x64804),x64803)
% 160.93/160.65 [6481]~E(f334(f197(f882(x64811)),x64814),f334(f197(f882(x64812)),x64815))+E(f334(f334(f156(f887(x64811,x64812),x64811),f268(x64811,x64812)),x64813),x64814)+~E(f334(f334(f184(x64811,x64812),x64814),x64815),x64813)
% 160.93/160.65 [6954]~P108(x69541)+~P16(x69541,f334(f334(f156(x69542,x69541),x69543),x69545))+P16(x69541,f334(f334(f156(x69542,x69541),x69543),f334(f138(x69542,x69544),x69545)))
% 160.93/160.65 [6999]~P1(f334(x69993,x69995))+~P1(f334(f334(x69992,x69994),x69995))+P1(f334(f334(f95(x69991,x69992,x69993),x69994),x69995))
% 160.93/160.65 [7096]~P108(x70961)+P16(x70961,f334(f334(f156(x70962,x70961),x70963),f172(x70962,x70964,x70965)))+~P16(x70961,f334(f334(f156(x70962,x70961),x70963),x70965))
% 160.93/160.65 [7119]~P52(x71193,x71192,x71195)+~P52(x71191,x71193,x71194)+P52(x71191,x71192,f334(f334(f291(x71191,x71193,x71192),x71194),x71195))
% 160.93/160.65 [7213]E(x72131,x72132)+~P27(x72133,x72134,x72135,f257(f888(x72133,a876)))+~E(f334(f334(f156(x72133,x72134),x72135),x72131),f334(f334(f156(x72133,x72134),x72135),x72132))
% 160.93/160.65 [7367]~P1(f334(f334(f249(a881),x73671),f334(x73673,x73675)))+P1(f334(f334(f249(a881),x73671),f157(x73672,x73673,x73674)))+~P1(f334(f334(f336(x73672),x73675),f334(f174(x73672),x73674)))
% 160.93/160.65 [7368]~P1(f334(f334(f248(a881),x73681),f334(x73683,x73685)))+P1(f334(f334(f248(a881),x73681),f157(x73682,x73683,x73684)))+~P1(f334(f334(f336(x73682),x73685),f334(f174(x73682),x73684)))
% 160.93/160.65 [7772]~P109(x77721)+P1(f334(f334(f248(f888(x77721,a876)),f305(x77721,x77722,x77723)),f305(x77721,x77724,x77725)))+P1(f334(f334(f248(x77721),x77722),x77723))
% 160.93/160.65 [7795]~P5(x77951)+P1(f334(f334(f248(x77951),f334(f334(f42(x77952,x77951),x77953),x77954)),f334(x77954,x77955)))+~P1(f334(f334(f336(x77952),x77955),x77953))
% 160.93/160.65 [7862]~P27(x78621,x78622,x78624,x78623)+E(f334(f77(x78621,x78622,x78623,x78624),f334(x78624,x78625)),x78625)+~P1(f334(f334(f336(x78621),x78625),x78623))
% 160.93/160.65 [8057]~P1(f334(x80571,x80575))+P1(f334(x80571,f857(x80571,x80572,x80573,x80574)))+~P1(f334(f334(f336(x80574),x80575),x80573))
% 160.93/160.65 [8058]~P1(f334(x80581,x80585))+P1(f334(x80581,f857(x80581,x80582,x80583,x80584)))+~P1(f334(f334(f336(x80584),x80585),x80582))
% 160.93/160.65 [8157]P1(f334(f61(x81571),x81572))+~P1(f334(f61(x81573),x81574))+~P1(f334(f334(f248(f888(x81571,a876)),x81572),f334(f313(x81573,x81571,x81575),x81574)))
% 160.93/160.65 [8331]E(x83311,x83312)+~P27(x83313,x83314,x83315,f334(f334(f114(f888(x83313,a876)),f334(f174(x83313),x83311)),f334(f174(x83313),x83312)))+~E(f334(f334(f156(x83313,x83314),x83315),x83311),f334(f334(f156(x83313,x83314),x83315),x83312))
% 160.93/160.65 [8385]~P109(x83851)+~P1(f334(f334(f249(f888(x83851,a876)),f305(x83851,x83854,x83855)),f305(x83851,x83852,x83853)))+P1(f334(f334(f248(x83851),x83852),x83853))
% 160.93/160.65 [8448]~P27(x84481,x84484,x84485,f257(f888(x84481,a876)))+~P1(f334(f334(f336(x84484),f334(x84485,x84482)),f334(f313(x84481,x84484,x84485),x84483)))+P1(f334(f334(f336(x84481),x84482),x84483))
% 160.93/160.65 [8524]P1(f334(x85241,x85242))+~P1(f334(x85241,f562(x85241,x85243,x85244,x85245)))+~P1(f334(f334(f336(x85245),x85242),x85244))
% 160.93/160.65 [8525]P1(f334(x85251,x85252))+~P1(f334(x85251,f562(x85251,x85253,x85254,x85255)))+~P1(f334(f334(f336(x85255),x85252),x85253))
% 160.93/160.65 [8814]~P27(x88142,x88143,x88141,x88144)+E(f334(x88141,f334(f77(x88142,x88143,x88144,x88141),x88145)),x88145)+~P1(f334(f334(f336(x88143),x88145),f334(f313(x88142,x88143,x88141),x88144)))
% 160.93/160.65 [8918]E(x89181,f117(x89182))+E(f334(f334(f153(x89182),x89183),f700(x89184,x89183,x89185,x89181,x89182)),x89181)+~E(f334(f334(f136(x89182),x89181),x89185),f334(f334(f153(x89182),x89183),x89184))
% 160.93/160.65 [8919]E(x89191,f117(x89192))+E(f334(f334(f153(x89192),x89193),f701(x89194,x89191,x89195,x89193,x89192)),x89191)+~E(f334(f334(f136(x89192),x89191),x89194),f334(f334(f153(x89192),x89193),x89195))
% 160.93/160.65 [8936]E(f334(f334(f153(x89362),x89363),f700(x89364,x89363,x89361,x89365,x89362)),x89365)+~E(f334(f334(f136(x89362),x89365),x89361),f334(f334(f153(x89362),x89363),x89364))+E(x89361,f334(f334(f153(x89362),x89363),x89364))
% 160.93/160.65 [8937]E(f334(f334(f153(x89371),x89372),f701(x89374,x89375,x89373,x89372,x89371)),x89375)+~E(f334(f334(f136(x89371),x89375),x89374),f334(f334(f153(x89371),x89372),x89373))+E(f334(f334(f153(x89371),x89372),x89373),x89374)
% 160.93/160.65 [9019]~E(f334(f313(x90193,x90192,x90194),f257(f888(x90193,a876))),f257(f888(x90192,a876)))+~E(f334(f313(x90191,x90193,x90195),f257(f888(x90191,a876))),f257(f888(x90193,a876)))+E(f334(f313(x90191,x90192,f334(f73(x90193,x90192,x90191,x90194),x90195)),f257(f888(x90191,a876))),f257(f888(x90192,a876)))
% 160.93/160.65 [9389]E(x93891,f117(x93892))+~E(f334(f334(f136(x93892),x93891),x93893),f334(f334(f153(x93892),x93895),x93894))+E(f334(f334(f136(x93892),f701(x93893,x93891,x93894,x93895,x93892)),x93893),x93894)
% 160.93/160.65 [9390]E(x93901,f117(x93902))+~E(f334(f334(f136(x93902),x93901),x93905),f334(f334(f153(x93902),x93904),x93903))+E(f334(f334(f136(x93902),f700(x93903,x93904,x93905,x93901,x93902)),x93905),x93903)
% 160.93/160.65 [9397]E(f334(f334(f136(x93972),f700(x93974,x93973,x93971,x93975,x93972)),x93971),x93974)+~E(f334(f334(f136(x93972),x93975),x93971),f334(f334(f153(x93972),x93973),x93974))+E(x93971,f334(f334(f153(x93972),x93973),x93974))
% 160.93/160.65 [9398]~E(f334(f334(f136(x93981),x93985),x93984),f334(f334(f153(x93981),x93982),x93983))+E(f334(f334(f136(x93981),f701(x93984,x93985,x93983,x93982,x93981)),x93984),x93983)+E(f334(f334(f153(x93981),x93982),x93983),x93984)
% 160.93/160.65 [9399]E(f334(f334(f136(x93991),x93995),f703(x93993,x93992,x93994,x93995,x93991)),x93992)+E(f334(f334(f136(x93991),x93992),f702(x93993,x93992,x93994,x93995,x93991)),x93995)+~E(f334(f334(f136(x93991),x93995),x93994),f334(f334(f136(x93991),x93992),x93993))
% 160.93/160.65 [9432]~P108(x94321)+P16(x94321,f334(f334(f156(x94322,x94321),x94323),f151(x94322,x94321,x94323,x94324,x94325)))+~P16(x94321,f334(f334(f156(x94322,x94321),x94323),x94325))
% 160.93/160.65 [9443]~P56(x94435,x94431,x94434,x94433)+P1(f334(f334(x94431,x94432),f560(x94433,x94434,x94431,x94435,x94432)))+~P1(f334(f334(f336(x94435),x94432),x94434))
% 160.93/160.65 [9552]~P1(f334(f334(f336(f887(x95521,x95521)),f334(f334(f269(x95521,x95521),x95525),x95523)),f310(x95521,x95524)))+P1(f334(f334(f336(f887(x95521,x95521)),f334(f334(f269(x95521,x95521),x95522),x95523)),f334(f334(f291(x95521,x95521,x95521),x95524),f310(x95521,x95524))))+~P1(f334(f334(f336(f887(x95521,x95521)),f334(f334(f269(x95521,x95521),x95522),x95525)),f334(f334(f291(x95521,x95521,x95521),x95524),f310(x95521,x95524))))
% 160.93/160.65 [9553]~P1(f334(f334(f336(f887(x95531,x95531)),f334(f334(f269(x95531,x95531),x95532),x95535)),f310(x95531,x95534)))+P1(f334(f334(f336(f887(x95531,x95531)),f334(f334(f269(x95531,x95531),x95532),x95533)),f334(f334(f291(x95531,x95531,x95531),x95534),f310(x95531,x95534))))+~P1(f334(f334(f336(f887(x95531,x95531)),f334(f334(f269(x95531,x95531),x95535),x95533)),f334(f334(f291(x95531,x95531,x95531),x95534),f310(x95531,x95534))))
% 160.93/160.65 [9556]P1(f334(f334(f336(f887(f882(x95561),f882(x95561))),f334(f334(f269(f882(x95561),f882(x95561)),x95562),x95563)),f160(x95561,f310(x95561,x95564))))+~P1(f334(f334(f336(f887(f882(x95561),f882(x95561))),f334(f334(f269(f882(x95561),f882(x95561)),x95562),x95565)),f160(x95561,f310(x95561,x95564))))+~P1(f334(f334(f336(f887(f882(x95561),f882(x95561))),f334(f334(f269(f882(x95561),f882(x95561)),x95565),x95563)),f160(x95561,f310(x95561,x95564))))
% 160.93/160.65 [9560]E(f334(f334(f136(x95601),x95602),f702(x95603,x95602,x95604,x95605,x95601)),x95605)+E(f334(f334(f136(x95601),f703(x95603,x95602,x95604,x95605,x95601)),x95603),x95604)+~E(f334(f334(f136(x95601),x95602),x95603),f334(f334(f136(x95601),x95605),x95604))
% 160.93/160.65 [9561]E(f334(f334(f136(x95611),x95612),f703(x95613,x95614,x95615,x95612,x95611)),x95614)+E(f334(f334(f136(x95611),f702(x95613,x95614,x95615,x95612,x95611)),x95615),x95613)+~E(f334(f334(f136(x95611),x95612),x95615),f334(f334(f136(x95611),x95614),x95613))
% 160.93/160.65 [9615]P1(f334(f334(f336(f887(x96151,x96151)),f334(f334(f269(x96151,x96151),x96152),x96153)),f334(f334(f291(x96151,x96151,x96151),x96154),f310(x96151,x96154))))+~P1(f334(f334(f336(f887(x96151,x96151)),f334(f334(f269(x96151,x96151),x96152),x96155)),f334(f334(f291(x96151,x96151,x96151),x96154),f310(x96151,x96154))))+~P1(f334(f334(f336(f887(x96151,x96151)),f334(f334(f269(x96151,x96151),x96155),x96153)),f334(f334(f291(x96151,x96151,x96151),x96154),f310(x96151,x96154))))
% 160.93/160.65 [9644]P36(x96441,x96442,x96443,x96444,x96445)+~E(f334(f197(f882(x96441)),x96444),f334(f197(f882(x96442)),x96445))+~P1(f334(f334(f273(x96441,x96442,a876),x96443),f742(x96445,x96444,x96443,x96442,x96441)))
% 160.93/160.65 [9645]P36(x96451,x96452,x96453,x96454,x96455)+~E(f334(f197(f882(x96451)),x96454),f334(f197(f882(x96452)),x96455))+~P1(f334(f334(f273(x96451,x96452,a876),x96453),f743(x96453,x96455,x96454,x96452,x96451)))
% 160.93/160.65 [9650]E(f334(f334(f136(x96501),f702(x96502,x96503,x96504,x96505,x96501)),x96504),x96502)+~E(f334(f334(f136(x96501),x96503),x96502),f334(f334(f136(x96501),x96505),x96504))+E(f334(f334(f136(x96501),f703(x96502,x96503,x96504,x96505,x96501)),x96502),x96504)
% 160.93/160.65 [9665]~P108(x96652)+E(f334(f334(f150(x96651,x96652,x96653),x96654),x96655),f334(f334(f153(x96651),x96654),x96655))+P1(f334(f334(f336(x96651),f792(x96654,x96653,x96655,x96651,x96652)),f334(f174(x96651),x96655)))
% 160.93/160.65 [9670]~P56(x96701,x96704,x96703,x96702)+~P1(f334(f334(f336(x96701),x96705),x96703))+P1(f334(f334(f336(x96701),f560(x96702,x96703,x96704,x96701,x96705)),x96702))
% 160.93/160.65 [9791]~P1(f334(f334(f336(f887(f888(x97911,a876),f888(x97911,a876))),f334(f334(f269(f888(x97911,a876),f888(x97911,a876)),x97914),x97913)),f325(x97911,x97912)))+~P1(f334(f334(f336(x97911),x97915),x97914))+P1(f334(f334(f336(x97911),f623(x97912,x97913,x97914,x97911,x97915)),x97913))
% 160.93/160.65 [9803]~P108(x98032)+E(f334(f334(f150(x98031,x98032,x98033),x98034),x98035),f334(f334(f153(x98031),x98034),x98035))+~P1(f334(f334(f248(x98032),f334(x98033,x98034)),f334(x98033,f792(x98034,x98033,x98035,x98031,x98032))))
% 160.93/160.65 [9994]P36(x99941,x99942,x99943,x99944,x99945)+~E(f334(f197(f882(x99941)),x99944),f334(f197(f882(x99942)),x99945))+~P1(f334(f334(x99943,f334(f334(f167(x99941),x99944),f744(x99945,x99944,x99943,x99942,x99941))),f334(f334(f167(x99942),x99945),f744(x99945,x99944,x99943,x99942,x99941))))
% 160.93/160.65 [9995]P36(x99951,x99952,x99953,x99954,x99955)+~E(f334(f197(f882(x99951)),x99954),f334(f197(f882(x99952)),x99955))+~P1(f334(f334(x99953,f334(f334(f167(x99951),x99954),f779(x99953,x99955,x99952,x99954,x99951))),f334(f334(f167(x99952),x99955),f779(x99953,x99955,x99952,x99954,x99951))))
% 160.93/160.65 [6551]~P19(x65512,x65515,x65511)+~P1(f334(f61(x65512),x65514))+E(f334(x65511,f334(f334(f312(x65512),x65513),x65514)),f334(f334(f64(x65512,x65512,x65515),x65513),x65514))
% 160.93/160.65 [6552]~E(x65523,x65524)+~E(x65522,x65525)+E(f334(f334(f312(x65521),x65522),f334(f334(f312(x65521),x65523),f196(f888(x65521,a876)))),f334(f334(f312(x65521),x65524),f334(f334(f312(x65521),x65525),f196(f888(x65521,a876)))))
% 160.93/160.65 [6562]P1(f334(x65622,x65625))+E(f179(x65621,x65622,f334(f334(f136(x65621),x65623),x65624)),f179(x65621,x65622,x65623))+~P1(f334(f334(f336(x65621),x65625),f334(f174(x65621),x65623)))
% 160.93/160.65 [6599]E(f334(x65991,x65992),f196(f888(x65993,a876)))+~E(f334(f334(f41(x65994,f888(x65993,a876)),x65995),x65991),f196(f888(x65993,a876)))+~P1(f334(f334(f336(x65994),x65992),x65995))
% 160.93/160.65 [6600]E(f334(x66001,x66002),f257(f888(x66003,a876)))+~E(f334(f334(f42(x66004,f888(x66003,a876)),x66005),x66001),f257(f888(x66003,a876)))+~P1(f334(f334(f336(x66004),x66002),x66005))
% 160.93/160.65 [7106]~E(x71062,x71064)+~P143(x71061)+E(f334(f334(f80(x71061),f334(f334(f81(x71061),x71062),x71063)),f334(f334(f81(x71061),x71064),x71065)),f334(f334(f80(x71061),f334(f334(f81(x71061),x71062),x71065)),f334(f334(f81(x71061),x71064),x71063)))
% 160.93/160.65 [7166]~P5(x71661)+~P1(f334(f334(f336(x71664),x71663),x71665))+P1(f334(f334(f248(x71661),f334(x71662,x71663)),f334(f334(f41(x71664,x71661),x71665),x71662)))
% 160.93/160.65 [7218]~P110(x72181)+P1(f334(f334(f248(x72181),f334(x72182,x72183)),f334(x72184,x72183)))+~P1(f334(f334(f248(f888(x72185,x72181)),x72182),x72184))
% 160.93/160.65 [7335]E(x73351,x73352)+E(x73353,x73351)+~E(f334(f334(f312(x73354),x73351),f334(f334(f312(x73354),x73355),f196(f888(x73354,a876)))),f334(f334(f312(x73354),x73352),f334(f334(f312(x73354),x73353),f196(f888(x73354,a876)))))
% 160.93/160.65 [7336]E(x73361,x73362)+E(x73363,x73361)+~E(f334(f334(f312(x73364),x73363),f334(f334(f312(x73364),x73362),f196(f888(x73364,a876)))),f334(f334(f312(x73364),x73365),f334(f334(f312(x73364),x73361),f196(f888(x73364,a876)))))
% 160.93/160.65 [7337]E(x73371,x73372)+E(x73371,x73373)+~E(f334(f334(f312(x73374),x73373),f334(f334(f312(x73374),x73372),f196(f888(x73374,a876)))),f334(f334(f312(x73374),x73375),f334(f334(f312(x73374),x73371),f196(f888(x73374,a876)))))
% 160.93/160.65 [7338]E(x73381,x73382)+E(x73381,x73383)+~E(f334(f334(f312(x73384),x73381),f334(f334(f312(x73384),x73385),f196(f888(x73384,a876)))),f334(f334(f312(x73384),x73382),f334(f334(f312(x73384),x73383),f196(f888(x73384,a876)))))
% 160.93/160.65 [7583]~P1(f334(f334(f334(a202,x75831),x75833),x75835))+~P1(f334(f334(f334(a202,x75832),x75835),x75834))+P1(f334(f334(f334(a202,f33(x75831,x75832)),x75833),x75834))
% 160.93/160.65 [7872]P27(x78721,x78722,x78723,x78724)+~P27(x78721,x78722,x78723,x78725)+~P1(f334(f334(f248(f888(x78721,a876)),x78724),x78725))
% 160.93/160.65 [7879]~P1(f334(f334(f248(a881),x78795),x78793))+~P1(f334(f334(f334(f334(a204,x78791),x78792),x78795),x78794))+P1(f334(f334(f334(f334(a204,x78791),x78792),x78793),x78794))
% 160.93/160.65 [8047]E(x80471,x80472)+~E(f334(f313(x80473,x80474,x80475),x80471),f334(f313(x80473,x80474,x80475),x80472))+~P27(x80473,x80474,x80475,f334(f334(f114(f888(x80473,a876)),x80471),x80472))
% 160.93/160.65 [8122]P1(f334(x81222,x81224))+E(f334(f334(f140(x81221),f334(f197(f882(x81221)),f179(x81221,x81222,x81223))),x81223),f334(f334(f153(x81221),x81224),x81225))+~E(f334(f334(f136(x81221),f179(x81221,x81222,x81223)),f334(f334(f153(x81221),x81224),x81225)),x81223)
% 160.93/160.65 [8154]~P27(x81541,x81542,x81543,x81545)+~P27(x81541,x81542,x81543,x81544)+P27(x81541,x81542,x81543,f334(f334(f105(f888(x81541,a876)),x81544),x81545))
% 160.93/160.65 [8173]P1(f334(x81731,x81732))+~P1(f334(f334(f334(a202,x81734),x81732),x81735))+P1(f334(f334(f334(a202,f30(x81731,x81733,x81734)),x81732),x81735))
% 160.93/160.65 [8210]~P1(f334(x82101,x82104))+~P1(f334(f334(f334(a202,x82102),x82104),x82105))+P1(f334(f334(f334(a202,f30(x82101,x82102,x82103)),x82104),x82105))
% 160.93/160.65 [8273]~P68(x82731)+E(f334(f334(f80(x82731),f334(x82732,x82733)),f334(f168(x82731),f334(f334(f156(x82734,x82731),x82732),f172(x82734,x82733,x82735)))),f334(f168(x82731),f334(f334(f156(x82734,x82731),x82732),x82735)))+~P1(f334(f334(f336(x82734),x82733),f334(f174(x82734),x82735)))
% 160.93/160.65 [8361]~P108(x83611)+~P16(x83611,f334(f334(f156(x83612,x83611),x83613),x83615))+P16(x83611,f334(f334(f156(x83612,x83611),x83613),f334(f334(f150(x83612,x83611,x83613),x83614),x83615)))
% 160.93/160.65 [8444]~P5(x84441)+P1(f334(f334(f248(x84441),f334(f334(f41(x84442,x84441),x84443),x84444)),f334(f334(f41(x84442,x84441),x84445),x84444)))+~P1(f334(f334(f248(f888(x84442,a876)),x84443),x84445))
% 160.93/160.65 [8445]~P5(x84451)+P1(f334(f334(f248(x84451),f334(f334(f42(x84452,x84451),x84453),x84454)),f334(f334(f42(x84452,x84451),x84455),x84454)))+~P1(f334(f334(f248(f888(x84452,a876)),x84455),x84453))
% 160.93/160.65 [8477]~P108(x84773)+P1(f334(f139(x84771),x84772))+~P1(f334(f139(x84771),f334(f334(f150(x84771,x84773,x84774),x84775),x84772)))
% 160.93/160.65 [8546]P1(f334(x85461,x85462))+P1(f334(f334(f334(a202,x85463),x85462),x85464))+~P1(f334(f334(f334(a202,f30(x85461,x85465,x85463)),x85462),x85464))
% 160.93/160.65 [8564]~P1(f334(x85644,x85642))+P1(f334(f334(f334(a202,x85641),x85642),x85643))+~P1(f334(f334(f334(a202,f30(x85644,x85641,x85645)),x85642),x85643))
% 160.93/160.65 [8626]~P108(x86261)+~P1(f334(f334(f336(x86262),x86263),f334(f174(x86262),x86264)))+~P1(f334(f139(x86262),f334(f334(f150(x86262,x86261,x86265),x86263),x86264)))
% 160.93/160.65 [8644]P1(f334(f334(f334(a202,x86441),x86442),x86443))+P1(f334(f334(f334(a202,x86444),x86442),x86443))+~P1(f334(f334(f334(a202,f30(x86445,x86441,x86444)),x86442),x86443))
% 160.93/160.65 [8710]~P108(x87101)+P16(x87101,f334(f334(f156(x87102,x87101),x87103),x87104))+~P16(x87101,f334(f334(f156(x87102,x87101),x87103),f334(f334(f150(x87102,x87101,x87103),x87105),x87104)))
% 160.93/160.65 [8802]~P108(x88022)+E(f334(f334(f150(x88021,x88022,x88023),x88024),x88025),f151(x88021,x88022,x88023,x88024,x88025))+P1(f334(f334(f336(x88022),f334(x88023,x88024)),f334(f313(x88021,x88022,x88023),f334(f174(x88021),x88025))))
% 160.93/160.65 [8876]~P108(x88762)+E(f151(x88761,x88762,x88763,x88764,x88765),x88765)+~P1(f334(f334(f336(x88762),f334(x88763,x88764)),f334(f313(x88761,x88762,x88763),f334(f174(x88761),x88765))))
% 160.93/160.65 [8890]~P27(x88902,x88901,x88903,x88905)+P1(f334(f334(f249(f888(x88901,a876)),f334(f313(x88902,x88901,x88903),x88904)),f334(f313(x88902,x88901,x88903),x88905)))+~P1(f334(f334(f249(f888(x88902,a876)),x88904),x88905))
% 160.93/160.65 [9061]~P27(x90611,x90612,x90613,f257(f888(x90611,a876)))+~P1(f334(f334(f248(f888(x90612,a876)),x90614),f334(f313(x90611,x90612,x90613),x90615)))+P1(f334(f334(f248(f888(x90611,a876)),f334(f314(x90611,x90612,x90613),x90614)),x90615))
% 160.93/160.65 [9084]~E(f334(f313(x90843,x90841,x90844),f257(f888(x90843,a876))),f257(f888(x90841,a876)))+P1(f334(f334(f248(f888(x90841,a876)),x90842),f334(f313(x90843,x90841,x90844),x90845)))+~P1(f334(f334(f248(f888(x90843,a876)),f334(f314(x90843,x90841,x90844),x90842)),x90845))
% 160.93/160.65 [9109]~E(f334(f241(x91092),x91094),f334(f334(f180(x91091,x91092),x91095),x91093))+~P1(f334(f139(x91091),f334(f334(f156(f887(x91091,x91092),x91091),f268(x91091,x91092)),x91095)))+P1(f334(f334(f336(f887(x91091,x91092)),f334(f334(f269(x91091,x91092),x91093),x91094)),f334(f174(f887(x91091,x91092)),x91095)))
% 160.93/160.65 [9191]~P27(x91911,x91914,x91915,f257(f888(x91911,a876)))+~P1(f334(f334(f248(f888(x91914,a876)),f334(f313(x91911,x91914,x91915),x91912)),f334(f313(x91911,x91914,x91915),x91913)))+P1(f334(f334(f248(f888(x91911,a876)),x91912),x91913))
% 160.93/160.65 [9256]E(f334(f241(x92561),x92562),f334(f334(f180(x92563,x92561),x92564),x92565))+~P1(f334(f139(x92563),f334(f334(f156(f887(x92563,x92561),x92563),f268(x92563,x92561)),x92564)))+~P1(f334(f334(f336(f887(x92563,x92561)),f334(f334(f269(x92563,x92561),x92565),x92562)),f334(f174(f887(x92563,x92561)),x92564)))
% 160.93/160.65 [9258]E(f334(f334(f180(x92581,x92582),x92583),x92584),f334(f241(x92582),x92585))+~P1(f334(f139(x92581),f334(f334(f156(f887(x92581,x92582),x92581),f268(x92581,x92582)),x92583)))+~P1(f334(f334(f336(f887(x92581,x92582)),f334(f334(f269(x92581,x92582),x92584),x92585)),f334(f174(f887(x92581,x92582)),x92583)))
% 160.93/160.65 [9313]~P79(x93131)+~E(f334(x93133,f760(x93133,x93134,x93135,x93132,x93131)),f2(x93131))+E(f334(f168(x93131),f334(f334(f156(x93132,x93131),x93133),f334(f138(x93132,x93134),x93135))),f334(f168(x93131),f334(f334(f156(x93132,x93131),x93133),x93135)))
% 160.93/160.65 [9490]~P18(x94901,x94902,x94903)+~P1(f334(f61(x94901),x94905))+P1(f334(f66(x94901,x94902,x94903,x94904,x94905),f334(f334(f64(x94901,x94902,x94903),x94904),x94905)))
% 160.93/160.65 [9573]P1(f334(x95731,f661(x95732,x95731,x95733,x95734,x95735)))+~P1(f334(f334(f248(f888(x95735,a876)),x95734),x95733))+P1(f334(f334(f248(f888(x95735,a876)),f334(f334(f105(f888(x95735,a876)),x95734),f334(f254(x95735),x95731))),f334(f334(f105(f888(x95735,a876)),x95733),f334(f254(x95735),x95732))))
% 160.93/160.65 [9587]~P79(x95871)+~P1(f334(x95874,f760(x95873,x95874,x95875,x95872,x95871)))+E(f334(f168(x95871),f334(f334(f156(x95872,x95871),x95873),f334(f138(x95872,x95874),x95875))),f334(f168(x95871),f334(f334(f156(x95872,x95871),x95873),x95875)))
% 160.93/160.65 [9668]~P5(x96685)+P1(f334(f334(f336(x96681),f490(x96682,x96683,x96681,x96684,x96685)),x96683))+P1(f334(f334(f248(x96685),x96684),f334(f334(f42(x96681,x96685),x96683),x96682)))
% 160.93/160.65 [9671]~P79(x96711)+E(f334(f168(x96711),f334(f334(f156(x96712,x96711),x96713),f334(f138(x96712,x96714),x96715))),f334(f168(x96711),f334(f334(f156(x96712,x96711),x96713),x96715)))+P1(f334(f334(f336(x96712),f760(x96713,x96714,x96715,x96712,x96711)),f334(f174(x96712),x96715)))
% 160.93/160.65 [9681]~P1(f334(x96815,f661(x96815,x96813,x96814,x96812,x96811)))+~P1(f334(f334(f248(f888(x96811,a876)),x96812),x96814))+P1(f334(f334(f248(f888(x96811,a876)),f334(f334(f105(f888(x96811,a876)),x96812),f334(f254(x96811),x96813))),f334(f334(f105(f888(x96811,a876)),x96814),f334(f254(x96811),x96815))))
% 160.93/160.65 [9716]P36(x97161,x97162,x97163,x97164,x97165)+~E(f334(f197(f882(x97162)),x97165),f334(f197(f882(x97161)),x97164))+P1(f334(f334(f249(a881),f744(x97165,x97164,x97163,x97162,x97161)),f334(f197(f882(x97161)),x97164)))
% 160.93/160.65 [9717]P36(x97171,x97172,x97173,x97174,x97175)+~E(f334(f197(f882(x97172)),x97175),f334(f197(f882(x97171)),x97174))+P1(f334(f334(f249(a881),f779(x97173,x97175,x97172,x97174,x97171)),f334(f197(f882(x97171)),x97174)))
% 160.93/160.65 [9750]P1(f334(f334(f336(x97501),f661(x97502,x97503,x97504,x97505,x97501)),x97505))+~P1(f334(f334(f248(f888(x97501,a876)),x97505),x97504))+P1(f334(f334(f248(f888(x97501,a876)),f334(f334(f105(f888(x97501,a876)),x97505),f334(f254(x97501),x97503))),f334(f334(f105(f888(x97501,a876)),x97504),f334(f254(x97501),x97502))))
% 160.93/160.65 [9804]~P5(x98041)+~P1(f334(f334(f248(x98041),x98042),f334(x98045,f490(x98045,x98044,x98043,x98042,x98041))))+P1(f334(f334(f248(x98041),x98042),f334(f334(f42(x98043,x98041),x98044),x98045)))
% 160.93/160.65 [9837]~P74(x98371)+~P1(f334(f61(x98372),x98375))+E(f334(f334(f334(f65(x98371,x98372,f81(x98371)),f334(f334(f18(x98372,x98371,x98371),f334(f334(f8(x98371,f888(x98371,x98371),x98372),f81(x98371)),x98373)),x98374)),f78(x98371)),x98375),f334(f334(f81(x98371),f334(f334(f334(f65(x98371,x98372,f81(x98371)),x98373),f78(x98371)),x98375)),f334(f334(f334(f65(x98371,x98372,f81(x98371)),x98374),f78(x98371)),x98375)))
% 160.93/160.65 [9901]~P1(f334(f334(f336(f887(f888(x99011,a876),f888(x99011,a876))),f334(f334(f269(f888(x99011,a876),f888(x99011,a876)),x99015),x99014)),f325(x99011,x99013)))+~P1(f334(f334(f336(x99011),x99012),x99015))+P1(f334(f334(f336(f887(x99011,x99011)),f334(f334(f269(x99011,x99011),x99012),f623(x99013,x99014,x99015,x99011,x99012))),x99013))
% 160.93/160.65 [10029]~P1(f334(f334(f336(f887(f882(x100291),f882(x100291))),f334(f334(f269(f882(x100291),f882(x100291)),f334(f334(f136(x100291),x100295),x100292)),f334(f334(f136(x100291),x100295),x100293))),f149(x100291,x100294)))+P1(f334(f334(f336(f887(f882(x100291),f882(x100291))),f334(f334(f269(f882(x100291),f882(x100291)),x100292),x100293)),f149(x100291,x100294)))+P1(f334(f334(f336(f887(x100291,x100291)),f334(f334(f269(x100291,x100291),f708(x100294,x100293,x100292,x100295,x100291)),f708(x100294,x100293,x100292,x100295,x100291))),x100294))
% 160.93/160.65 [7146]~E(f334(f197(f882(x71461)),x71463),f334(f197(f882(x71462)),x71464))+E(f334(f334(f180(x71461,x71462),f334(f334(f184(x71461,x71462),x71463),x71464)),x71465),f210(x71462))+P1(f334(f334(f336(x71461),x71465),f334(f174(x71461),x71463)))
% 160.93/160.65 [7221]~E(x72213,x72215)+E(f334(f334(f167(x72211),f334(f334(f161(x72211,x72212),x72213),x72214)),x72215),x72214)+~P1(f334(f334(f249(a881),x72213),f334(f197(f882(x72211)),x72212)))
% 160.93/160.65 [7330]~E(f334(f334(f136(x73301),x73302),x73304),f334(f334(f136(x73301),x73303),x73305))+E(f334(f334(f177(x73301),f334(f197(f882(x73301)),x73302)),x73303),x73302)+P1(f334(f334(f248(a881),f334(f197(f882(x73301)),x73303)),f334(f197(f882(x73301)),x73302)))
% 160.93/160.65 [7347]~E(x73475,x73472)+P1(f334(x73471,x73472))+P1(f334(f334(f334(f334(a204,f32(x73471,x73473)),x73472),x73474),x73475))
% 160.93/160.65 [7833]~E(f334(f334(f136(x78331),x78332),x78334),f334(f334(f136(x78331),x78333),x78335))+E(f334(f334(f177(x78331),f334(f197(f882(x78331)),x78332)),x78333),x78332)+~P1(f334(f334(f248(a881),f334(f197(f882(x78331)),x78332)),f334(f197(f882(x78331)),x78333)))
% 160.93/160.65 [7857]~P1(f334(f61(x78571),f334(x78574,x78575)))+~P1(f334(f334(f336(x78572),x78575),x78573))+P1(f334(f61(x78571),f334(f334(f42(x78572,f888(x78571,a876)),x78573),x78574)))
% 160.93/160.65 [7910]~E(f334(f197(f882(x79101)),x79102),f334(f197(f882(x79103)),x79104))+~E(f334(f334(f180(x79101,x79103),f334(f334(f184(x79101,x79103),x79102),x79104)),x79105),f210(x79103))+~P1(f334(f334(f336(x79101),x79105),f334(f174(x79101),x79102)))
% 160.93/160.65 [8032]~P41(x80321,x80323,x80325)+~P41(x80321,x80322,x80324)+P41(x80321,f334(f334(f114(f888(x80321,a876)),x80322),x80323),f334(f334(f114(f888(f887(x80321,x80321),a876)),x80324),x80325))
% 160.93/160.65 [8033]~P41(x80331,x80333,x80335)+~P41(x80331,x80332,x80334)+P41(x80331,f334(f334(f105(f888(x80331,a876)),x80332),x80333),f334(f334(f105(f888(f887(x80331,x80331),a876)),x80334),x80335))
% 160.93/160.65 [8116]E(x81161,x81162)+P1(f334(x81163,x81161))+~P1(f334(f334(f334(f334(a204,f32(x81163,x81164)),x81161),x81165),x81162))
% 160.93/160.65 [8397]E(f334(f334(f269(x83971,x83972),f334(f334(f167(x83971),x83973),x83974)),f334(f334(f167(x83972),x83975),x83974)),f334(f334(f167(f887(x83971,x83972)),f334(f334(f184(x83971,x83972),x83973),x83975)),x83974))+~P1(f334(f334(f249(a881),x83974),f334(f197(f882(x83971)),x83973)))+~P1(f334(f334(f249(a881),x83974),f334(f197(f882(x83972)),x83975)))
% 160.93/160.65 [8556]~P41(x85561,x85563,x85564)+P1(f334(f334(f336(x85561),x85562),x85563))+~P1(f334(f334(f336(f887(x85561,x85561)),f334(f334(f269(x85561,x85561),x85565),x85562)),x85564))
% 160.93/160.65 [8557]~P41(x85571,x85573,x85574)+P1(f334(f334(f336(x85571),x85572),x85573))+~P1(f334(f334(f336(f887(x85571,x85571)),f334(f334(f269(x85571,x85571),x85572),x85575)),x85574))
% 160.93/160.65 [8558]~P8(x85581,x85583,x85584)+P1(f334(f334(f336(x85581),x85582),x85583))+~P1(f334(f334(f336(f887(x85581,x85581)),f334(f334(f269(x85581,x85581),x85585),x85582)),x85584))
% 160.93/160.65 [8559]~P8(x85591,x85593,x85594)+P1(f334(f334(f336(x85591),x85592),x85593))+~P1(f334(f334(f336(f887(x85591,x85591)),f334(f334(f269(x85591,x85591),x85592),x85595)),x85594))
% 160.93/160.65 [8824]~P8(x88241,x88245,x88242)+E(f334(f288(x88241,x88241,x88242),f334(f334(f312(x88241),x88243),f196(f888(x88241,a876)))),f334(f288(x88241,x88241,x88242),f334(f334(f312(x88241),x88244),f196(f888(x88241,a876)))))+~P1(f334(f334(f336(f887(x88241,x88241)),f334(f334(f269(x88241,x88241),x88243),x88244)),x88242))
% 160.93/160.65 [8906]~P1(f334(f334(f334(f334(a204,x89062),x89063),x89064),x89065))+~P1(f334(f334(f334(f334(a204,f32(x89061,x89062)),x89065),x89064),x89063))+P1(f334(f334(f334(f334(a204,f32(x89061,x89062)),x89063),x89064),x89063))
% 160.93/160.65 [9016]P1(f334(x90161,x90162))+~P1(f334(f334(f336(x90163),x90162),x90165))+P1(f334(f334(f336(x90163),f562(x90161,x90164,x90165,x90163)),f334(f334(f114(f888(x90163,a876)),x90165),x90164)))
% 160.93/160.65 [9017]P1(f334(x90171,x90172))+~P1(f334(f334(f336(x90173),x90172),x90174))+P1(f334(f334(f336(x90173),f562(x90171,x90174,x90175,x90173)),f334(f334(f114(f888(x90173,a876)),x90175),x90174)))
% 160.93/160.65 [9025]~P1(f334(x90252,x90255))+~P1(f334(f334(f336(x90251),x90255),x90254))+P1(f334(f334(f336(x90251),f857(x90252,x90253,x90254,x90251)),f334(f334(f114(f888(x90251,a876)),x90254),x90253)))
% 160.93/160.65 [9026]~P1(f334(x90262,x90265))+~P1(f334(f334(f336(x90261),x90265),x90263))+P1(f334(f334(f336(x90261),f857(x90262,x90263,x90264,x90261)),f334(f334(f114(f888(x90261,a876)),x90264),x90263)))
% 160.93/160.65 [9041]~P1(f334(f334(f248(f888(x90411,a876)),x90413),x90415))+~P1(f334(f334(f248(f888(x90411,a876)),x90412),x90414))+P1(f334(f334(f248(f888(x90411,a876)),f334(f334(f114(f888(x90411,a876)),x90412),x90413)),f334(f334(f114(f888(x90411,a876)),x90414),x90415)))
% 160.93/160.65 [9042]~P1(f334(f334(f248(f888(x90421,a876)),x90425),x90423))+~P1(f334(f334(f248(f888(x90421,a876)),x90422),x90424))+P1(f334(f334(f248(f888(x90421,a876)),f334(f334(f22(f888(x90421,a876)),x90422),x90423)),f334(f334(f22(f888(x90421,a876)),x90424),x90425)))
% 160.93/160.65 [9043]~P1(f334(f334(f248(f888(x90431,a876)),x90433),x90435))+~P1(f334(f334(f248(f888(x90431,a876)),x90432),x90434))+P1(f334(f334(f248(f888(x90431,a876)),f334(f334(f105(f888(x90431,a876)),x90432),x90433)),f334(f334(f105(f888(x90431,a876)),x90434),x90435)))
% 160.93/160.65 [9134]~E(f334(f197(f882(x91341)),x91343),f334(f197(f882(x91342)),x91344))+E(f334(f334(f180(x91341,x91342),f334(f334(f184(x91341,x91342),x91343),x91344)),x91345),f334(f241(x91342),f717(x91345,x91344,x91342,x91343,x91341)))+~P1(f334(f334(f336(x91341),x91345),f334(f174(x91341),x91343)))
% 160.93/160.65 [9138]P1(f334(f334(f336(f887(x91381,x91381)),f334(f334(f269(x91381,x91381),x91382),x91383)),f328(x91381,x91384,x91385)))+~P1(f334(f334(f248(a881),f334(x91384,x91382)),f334(x91384,x91383)))+~P1(f334(f334(f336(f887(x91381,x91381)),f334(f334(f269(x91381,x91381),x91382),x91383)),x91385))
% 160.93/160.65 [9323]P1(f334(f334(f336(f887(x93231,x93231)),f334(f334(f269(x93231,x93231),x93232),x93233)),f310(x93231,x93234)))+~P1(f334(f334(f336(f887(x93231,x93231)),f334(f334(f269(x93231,x93231),x93232),x93235)),f310(x93231,x93234)))+~P1(f334(f334(f336(f887(x93231,x93231)),f334(f334(f269(x93231,x93231),x93235),x93233)),x93234))
% 160.93/160.65 [9324]P1(f334(f334(f336(f887(x93241,x93241)),f334(f334(f269(x93241,x93241),x93242),x93243)),f310(x93241,x93244)))+~P1(f334(f334(f336(f887(x93241,x93241)),f334(f334(f269(x93241,x93241),x93245),x93243)),f310(x93241,x93244)))+~P1(f334(f334(f336(f887(x93241,x93241)),f334(f334(f269(x93241,x93241),x93242),x93245)),x93244))
% 160.93/160.65 [9421]E(x94211,x94212)+E(f334(a116,f639(x94213,x94214,x94211,x94212,x94215)),x94214)+~P1(f334(f334(f336(f887(x94215,x94215)),f334(f334(f269(x94215,x94215),x94212),x94211)),f334(f334(f191(f887(x94215,x94215),a876),x94214),x94213)))
% 160.93/160.65 [9422]E(x94221,x94222)+E(f334(a116,f641(x94223,x94224,x94221,x94222,x94225)),x94224)+~P1(f334(f334(f336(f887(x94225,x94225)),f334(f334(f269(x94225,x94225),x94222),x94221)),f334(f334(f191(f887(x94225,x94225),a876),x94224),x94223)))
% 160.93/160.65 [9423]E(x94231,f2(a881))+E(f334(a116,f639(x94232,x94231,x94233,x94234,x94235)),x94231)+~P1(f334(f334(f336(f887(x94235,x94235)),f334(f334(f269(x94235,x94235),x94234),x94233)),f334(f334(f191(f887(x94235,x94235),a876),x94231),x94232)))
% 160.93/160.65 [9424]E(x94241,f2(a881))+E(f334(a116,f641(x94242,x94241,x94243,x94244,x94245)),x94241)+~P1(f334(f334(f336(f887(x94245,x94245)),f334(f334(f269(x94245,x94245),x94244),x94243)),f334(f334(f191(f887(x94245,x94245),a876),x94241),x94242)))
% 160.93/160.65 [9440]P1(f334(f334(f336(f887(x94401,x94401)),f334(f334(f269(x94401,x94401),x94402),x94403)),f334(f334(f291(x94401,x94401,x94401),x94404),f310(x94401,x94404))))+~P1(f334(f334(f336(f887(x94401,x94401)),f334(f334(f269(x94401,x94401),x94402),x94405)),x94404))+~P1(f334(f334(f336(f887(x94401,x94401)),f334(f334(f269(x94401,x94401),x94405),x94403)),x94404))
% 160.93/160.65 [9447]~P1(f334(f334(f336(f887(x94471,x94471)),f334(f334(f269(x94471,x94471),x94472),x94475)),f310(x94471,x94474)))+P1(f334(f334(f336(f887(x94471,x94471)),f334(f334(f269(x94471,x94471),x94472),x94473)),f334(f334(f291(x94471,x94471,x94471),x94474),f310(x94471,x94474))))+~P1(f334(f334(f336(f887(x94471,x94471)),f334(f334(f269(x94471,x94471),x94475),x94473)),x94474))
% 160.93/160.65 [9486]~P8(x94861,x94865,x94862)+~P1(f334(f334(f336(f887(x94861,x94861)),f334(f334(f269(x94861,x94861),x94863),x94864)),x94862))+P1(f334(f334(f248(f888(x94861,a876)),f334(f288(x94861,x94861,x94862),f334(f334(f312(x94861),x94863),f196(f888(x94861,a876))))),f334(f288(x94861,x94861,x94862),f334(f334(f312(x94861),x94864),f196(f888(x94861,a876))))))
% 160.93/160.65 [9511]E(x95111,x95112)+P1(f334(f334(f334(f334(a204,x95113),x95111),x95114),f434(x95112,x95114,x95111,x95113,x95115)))+~P1(f334(f334(f334(f334(a204,f32(x95115,x95113)),x95111),x95114),x95112))
% 160.93/160.65 [9515]~P1(f334(x95155,x95152))+P1(f334(f334(f334(f334(a204,x95151),x95152),x95153),f434(x95154,x95153,x95152,x95151,x95155)))+~P1(f334(f334(f334(f334(a204,f32(x95155,x95151)),x95152),x95153),x95154))
% 160.93/160.65 [9545]P1(f334(f334(f336(f887(x95451,x95451)),f334(f334(f269(x95451,x95451),x95452),x95453)),f334(f334(f291(x95451,x95451,x95451),x95454),f310(x95451,x95454))))+~P1(f334(f334(f336(f887(x95451,x95451)),f334(f334(f269(x95451,x95451),x95452),x95455)),f334(f334(f291(x95451,x95451,x95451),x95454),f310(x95451,x95454))))+~P1(f334(f334(f336(f887(x95451,x95451)),f334(f334(f269(x95451,x95451),x95455),x95453)),x95454))
% 160.93/160.65 [9546]P1(f334(f334(f336(f887(x95461,x95461)),f334(f334(f269(x95461,x95461),x95462),x95463)),f334(f334(f291(x95461,x95461,x95461),x95464),f310(x95461,x95464))))+~P1(f334(f334(f336(f887(x95461,x95461)),f334(f334(f269(x95461,x95461),x95465),x95463)),f334(f334(f291(x95461,x95461,x95461),x95464),f310(x95461,x95464))))+~P1(f334(f334(f336(f887(x95461,x95461)),f334(f334(f269(x95461,x95461),x95462),x95465)),x95464))
% 160.93/160.65 [9596]~P1(f334(f66(x95961,x95961,x95964,x95962,x95963),x95965))+P1(f334(f334(f336(x95961),x95962),x95963))+P1(f334(f62(x95961,x95964,f334(f334(f312(x95961),x95962),x95963)),x95965))
% 160.93/160.65 [9635]~E(f334(f313(x96353,x96352,x96355),x96354),x96351)+E(x96351,f196(f888(x96352,a876)))+P1(f334(f334(f248(f888(x96353,a876)),f334(f313(x96352,x96353,f541(x96354,x96353,x96352,x96351)),x96351)),x96354))
% 160.93/160.65 [9684]~P5(x96845)+P1(f334(f334(f336(x96841),f353(x96842,x96843,x96844,x96841,x96845)),x96844))+P1(f334(f334(f248(x96845),f334(f334(f41(x96841,x96845),x96844),x96843)),x96842))
% 160.93/160.65 [9736]P36(x97361,x97362,x97363,x97364,x97365)+~E(f334(f197(f882(x97361)),x97364),f334(f197(f882(x97362)),x97365))+P1(f334(f334(f336(f887(x97361,x97362)),f742(x97365,x97364,x97363,x97362,x97361)),f334(f174(f887(x97361,x97362)),f334(f334(f184(x97361,x97362),x97364),x97365))))
% 160.93/160.65 [9737]P36(x97371,x97372,x97373,x97374,x97375)+~E(f334(f197(f882(x97371)),x97374),f334(f197(f882(x97372)),x97375))+P1(f334(f334(f336(f887(x97371,x97372)),f743(x97373,x97375,x97374,x97372,x97371)),f334(f174(f887(x97371,x97372)),f334(f334(f184(x97371,x97372),x97374),x97375))))
% 160.93/160.65 [9868]E(x98681,x98682)+P1(f334(f334(f334(f334(a204,f32(x98683,x98684)),f434(x98681,x98685,x98682,x98684,x98683)),x98685),x98681))+~P1(f334(f334(f334(f334(a204,f32(x98683,x98684)),x98682),x98685),x98681))
% 160.93/160.65 [9870]~P1(f334(x98701,x98705))+P1(f334(f334(f334(f334(a204,f32(x98701,x98702)),f434(x98703,x98704,x98705,x98702,x98701)),x98704),x98703))+~P1(f334(f334(f334(f334(a204,f32(x98701,x98702)),x98705),x98704),x98703))
% 160.93/160.65 [9878]E(x98781,x98782)+P1(f334(f334(f336(f887(x98783,x98783)),f334(f334(f269(x98783,x98783),x98781),f640(x98784,x98785,x98782,x98781,x98783))),x98784))+~P1(f334(f334(f336(f887(x98783,x98783)),f334(f334(f269(x98783,x98783),x98781),x98782)),f334(f334(f191(f887(x98783,x98783),a876),x98785),x98784)))
% 160.93/160.65 [9879]E(x98791,f2(a881))+P1(f334(f334(f336(f887(x98792,x98792)),f334(f334(f269(x98792,x98792),x98793),f640(x98794,x98791,x98795,x98793,x98792))),x98794))+~P1(f334(f334(f336(f887(x98792,x98792)),f334(f334(f269(x98792,x98792),x98793),x98795)),f334(f334(f191(f887(x98792,x98792),a876),x98791),x98794)))
% 160.93/160.65 [9922]~P5(x99221)+~P1(f334(f334(f248(x99221),f334(x99224,f353(x99225,x99224,x99223,x99222,x99221))),x99225))+P1(f334(f334(f248(x99221),f334(f334(f41(x99222,x99221),x99223),x99224)),x99225))
% 160.93/160.65 [9964]E(x99641,x99642)+P1(f334(f334(f336(f887(x99643,x99643)),f334(f334(f269(x99643,x99643),f643(x99644,x99645,x99641,x99642,x99643)),x99641)),x99644))+~P1(f334(f334(f336(f887(x99643,x99643)),f334(f334(f269(x99643,x99643),x99642),x99641)),f334(f334(f191(f887(x99643,x99643),a876),x99645),x99644)))
% 160.93/160.65 [9965]E(x99651,f2(a881))+P1(f334(f334(f336(f887(x99652,x99652)),f334(f334(f269(x99652,x99652),f643(x99653,x99651,x99654,x99655,x99652)),x99654)),x99653))+~P1(f334(f334(f336(f887(x99652,x99652)),f334(f334(f269(x99652,x99652),x99655),x99654)),f334(f334(f191(f887(x99652,x99652),a876),x99651),x99653)))
% 160.93/160.65 [9969]E(x99691,x99692)+P1(f334(f334(f336(f887(x99693,x99693)),f334(f334(f269(x99693,x99693),x99691),f643(x99694,x99695,x99692,x99691,x99693))),f334(f334(f191(f887(x99693,x99693),a876),f641(x99694,x99695,x99692,x99691,x99693)),x99694)))+~P1(f334(f334(f336(f887(x99693,x99693)),f334(f334(f269(x99693,x99693),x99691),x99692)),f334(f334(f191(f887(x99693,x99693),a876),x99695),x99694)))
% 160.93/160.65 [9970]E(x99701,f2(a881))+P1(f334(f334(f336(f887(x99702,x99702)),f334(f334(f269(x99702,x99702),x99703),f643(x99704,x99701,x99705,x99703,x99702))),f334(f334(f191(f887(x99702,x99702),a876),f641(x99704,x99701,x99705,x99703,x99702)),x99704)))+~P1(f334(f334(f336(f887(x99702,x99702)),f334(f334(f269(x99702,x99702),x99703),x99705)),f334(f334(f191(f887(x99702,x99702),a876),x99701),x99704)))
% 160.93/160.65 [10020]E(x100201,x100202)+P1(f334(f334(f336(f887(x100203,x100203)),f334(f334(f269(x100203,x100203),f640(x100204,x100205,x100201,x100202,x100203)),x100201)),f334(f334(f191(f887(x100203,x100203),a876),f639(x100204,x100205,x100201,x100202,x100203)),x100204)))+~P1(f334(f334(f336(f887(x100203,x100203)),f334(f334(f269(x100203,x100203),x100202),x100201)),f334(f334(f191(f887(x100203,x100203),a876),x100205),x100204)))
% 160.93/160.65 [10021]E(x100211,f2(a881))+P1(f334(f334(f336(f887(x100212,x100212)),f334(f334(f269(x100212,x100212),f640(x100213,x100211,x100214,x100215,x100212)),x100214)),f334(f334(f191(f887(x100212,x100212),a876),f639(x100213,x100211,x100214,x100215,x100212)),x100213)))+~P1(f334(f334(f336(f887(x100212,x100212)),f334(f334(f269(x100212,x100212),x100215),x100214)),f334(f334(f191(f887(x100212,x100212),a876),x100211),x100213)))
% 160.93/160.65 [10055]~P68(x100552)+~P1(f334(f61(x100551),x100555))+E(f334(f334(f6(x100551,x100552),f334(f334(f7(x100551,x100552,x100552),f334(f334(f18(x100551,x100552,f888(x100552,x100552)),f334(f334(f8(a876,f888(x100552,f888(x100552,x100552)),x100551),f100(x100552)),f334(f334(f7(x100551,f888(x100551,a876),a876),f336(x100551)),x100553))),x100554)),f2(x100552))),x100555),f334(f334(f6(x100551,x100552),x100554),f334(f334(f105(f888(x100551,a876)),x100555),x100553)))
% 160.93/160.65 [8623]~P68(x86231)+~P1(f334(f61(x86234),x86235))+E(f334(f334(f80(x86231),f334(x86232,x86233)),f334(f334(f6(x86234,x86231),x86232),f334(f334(f22(f888(x86234,a876)),x86235),f334(f334(f312(x86234),x86233),f196(f888(x86234,a876)))))),f334(f334(f6(x86234,x86231),x86232),f334(f334(f312(x86234),x86233),x86235)))
% 160.93/160.65 [8624]~P74(x86241)+~P1(f334(f61(x86244),x86245))+E(f334(f334(f81(x86241),f334(x86242,x86243)),f334(f334(f9(x86244,x86241),x86242),f334(f334(f22(f888(x86244,a876)),x86245),f334(f334(f312(x86244),x86243),f196(f888(x86244,a876)))))),f334(f334(f9(x86244,x86241),x86242),f334(f334(f312(x86244),x86243),x86245)))
% 160.93/160.65 [8945]~P108(x89452)+~P16(x89452,f334(f171(x89452),f334(f334(f156(x89451,x89452),x89454),x89455)))+E(f334(f138(x89451,f334(f334(f8(x89452,a876,x89451),f334(f249(x89452),x89453)),x89454)),x89455),f179(x89451,f334(f334(f8(x89452,a876,x89451),f334(f249(x89452),x89453)),x89454),x89455))
% 160.93/160.65 [8972]~P68(x89721)+E(f334(f334(f80(x89721),f334(f334(f6(a881,x89721),x89722),f305(a881,x89723,x89724))),f334(f334(f6(a881,x89721),x89722),f305(a881,f334(f334(f80(a881),x89724),f78(a881)),f334(f334(f80(a881),x89724),x89725)))),f334(f334(f6(a881,x89721),x89722),f305(a881,x89723,f334(f334(f80(a881),x89724),x89725))))+~P1(f334(f334(f248(a881),x89723),f334(f334(f80(a881),x89724),f78(a881))))
% 160.93/160.65 [8973]~P1(f334(f334(f336(x89731),x89734),x89735))+~P1(f334(f334(f248(f888(x89731,a876)),f334(f174(x89731),x89732)),x89735))+P1(f334(f334(f248(f888(x89731,a876)),f334(f174(x89731),f334(f334(f161(x89731,x89732),x89733),x89734))),x89735))
% 160.93/160.65 [9201]~P5(x92012)+~P1(f334(f61(x92011),x92015))+E(f334(f334(f64(x92011,x92012,f334(f334(f8(x92012,f888(x92012,x92012),x92011),f114(x92012)),x92013)),x92014),x92015),f334(f334(f114(x92012),x92014),f334(f334(f41(x92011,x92012),x92015),x92013)))
% 160.93/160.65 [9202]~P5(x92022)+~P1(f334(f61(x92021),x92025))+E(f334(f334(f64(x92021,x92022,f334(f334(f8(x92022,f888(x92022,x92022),x92021),f105(x92022)),x92023)),x92024),x92025),f334(f334(f105(x92022),x92024),f334(f334(f42(x92021,x92022),x92025),x92023)))
% 160.93/160.65 [9249]E(f334(x92491,x92492),f334(x92491,x92493))+P1(f334(f334(f249(a881),f334(x92491,x92492)),f334(x92491,x92493)))+~P1(f334(f334(f336(f887(x92494,x92494)),f334(f334(f269(x92494,x92494),x92492),x92493)),f155(x92494,f334(f334(f153(f888(x92494,a881)),x92491),x92495))))
% 160.93/160.65 [9280]~E(f334(x92804,x92802),f334(x92804,x92803))+~P1(f334(f334(f336(f887(x92801,x92801)),f334(f334(f269(x92801,x92801),x92802),x92803)),f155(x92801,x92805)))+P1(f334(f334(f336(f887(x92801,x92801)),f334(f334(f269(x92801,x92801),x92802),x92803)),f155(x92801,f334(f334(f153(f888(x92801,a881)),x92804),x92805))))
% 160.93/160.65 [9302]~P27(x93021,x93022,x93023,x93025)+P27(x93021,x93022,x93023,f334(f334(f312(x93021),x93024),x93025))+P1(f334(f334(f336(x93022),f334(x93023,x93024)),f334(f313(x93021,x93022,x93023),f334(f334(f22(f888(x93021,a876)),x93025),f334(f334(f312(x93021),x93024),f196(f888(x93021,a876)))))))
% 160.93/160.65 [9306]P1(f334(x93062,x93065))+~P1(f334(f334(f336(x93061),x93065),f334(f174(x93061),x93063)))+E(f334(f334(f140(x93061),f334(f197(f882(x93061)),f179(x93061,x93062,f334(f334(f136(x93061),x93063),x93064)))),f334(f334(f136(x93061),x93063),x93064)),f334(f334(f136(x93061),f334(f334(f140(x93061),f334(f197(f882(x93061)),f179(x93061,x93062,x93063))),x93063)),x93064))
% 160.93/160.65 [9309]~P1(f334(f334(f336(f887(x93091,x93091)),f334(f334(f269(x93091,x93091),x93092),x93093)),f155(x93091,x93095)))+~P1(f334(f334(f248(a881),f334(x93094,x93092)),f334(x93094,x93093)))+P1(f334(f334(f336(f887(x93091,x93091)),f334(f334(f269(x93091,x93091),x93092),x93093)),f155(x93091,f334(f334(f153(f888(x93091,a881)),x93094),x93095))))
% 160.93/160.65 [9374]P1(f334(f334(f336(f887(x93744,x93744)),f334(f334(f269(x93744,x93744),x93742),x93743)),f155(x93744,x93745)))+P1(f334(f334(f249(a881),f334(x93741,x93742)),f334(x93741,x93743)))+~P1(f334(f334(f336(f887(x93744,x93744)),f334(f334(f269(x93744,x93744),x93742),x93743)),f155(x93744,f334(f334(f153(f888(x93744,a881)),x93741),x93745))))
% 160.93/160.65 [9518]~P1(f334(f334(f336(f887(f882(x95181),f882(x95181))),f334(f334(f269(f882(x95181),f882(x95181)),x95182),x95184)),f160(x95181,x95185)))+~P1(f334(f334(f249(a881),x95183),f334(f197(f882(x95181)),x95182)))+P1(f334(f334(f336(f887(x95181,x95181)),f334(f334(f269(x95181,x95181),f334(f334(f167(x95181),x95182),x95183)),f334(f334(f167(x95181),x95184),x95183))),x95185))
% 160.93/160.65 [9764]E(x97641,f2(a1))+~P1(f334(f48(x97643,x97641),f334(f334(f269(a1,a1),x97644),x97645)))+P1(f334(f48(f334(f334(f81(a1),x97642),x97643),x97641),f334(f334(f269(a1,a1),f334(f334(f80(a1),f334(f334(f81(a1),x97642),x97644)),f334(f334(f38(a1),f334(f334(f81(a1),x97642),x97645)),x97641))),f44(a1,f334(f334(f81(a1),x97642),x97645),x97641))))
% 160.93/160.65 [9766]~P1(f334(f334(f249(a881),f2(a881)),x97663))+~P1(f334(f47(x97662,x97663),f334(f334(f269(a881,a881),x97664),x97665)))+P1(f334(f47(f334(f334(f81(a881),x97661),x97662),x97663),f334(f334(f269(a881,a881),f334(f334(f80(a881),f334(f334(f81(a881),x97661),x97664)),f334(f334(f38(a881),f334(f334(f81(a881),x97661),x97665)),x97663))),f44(a881,f334(f334(f81(a881),x97661),x97665),x97663))))
% 160.93/160.65 [10078]~P68(x100782)+~P1(f334(f61(x100781),x100784))+E(f334(f334(f6(x100781,x100782),x100783),f334(f254(x100781),f334(f334(f18(x100781,a876,a876),f334(f334(f8(a876,f888(a876,a876),x100781),a332),f334(f334(f7(x100781,f888(x100781,a876),a876),f336(x100781)),x100784))),f334(f334(f7(x100781,f888(x100781,a876),a876),f336(x100781)),x100785)))),f334(f334(f6(x100781,x100782),f334(f334(f7(x100781,x100782,x100782),f334(f334(f18(x100781,x100782,f888(x100782,x100782)),f334(f334(f8(a876,f888(x100782,f888(x100782,x100782)),x100781),f100(x100782)),f334(f334(f7(x100781,f888(x100781,a876),a876),f336(x100781)),x100785))),x100783)),f2(x100782))),x100784))
% 160.93/160.65 [8254]~E(f334(f334(f136(x82541),x82542),x82545),f334(f334(f136(x82541),x82543),x82544))+E(f334(f334(f136(x82541),f334(f334(f140(x82541),f334(f197(f882(x82541)),x82542)),x82543)),x82544),x82545)+P1(f334(f334(f248(a881),f334(f197(f882(x82541)),x82543)),f334(f197(f882(x82541)),x82542)))
% 160.93/160.65 [8447]~E(f334(f334(f136(x84472),x84473),x84471),f334(f334(f136(x84472),x84474),x84475))+E(x84471,f334(f334(f136(x84472),f334(f334(f140(x84472),f334(f197(f882(x84472)),x84473)),x84474)),x84475))+~P1(f334(f334(f248(a881),f334(f197(f882(x84472)),x84473)),f334(f197(f882(x84472)),x84474)))
% 160.93/160.65 [8536]~E(f334(f334(f80(a881),f334(f334(f81(a881),x85363),x85364)),x85361),f334(f334(f80(a881),f334(f334(f81(a881),x85362),x85364)),x85365))+~P1(f334(f334(f248(a881),x85363),x85362))+E(x85361,f334(f334(f80(a881),f334(f334(f81(a881),f334(f334(f22(a881),x85362),x85363)),x85364)),x85365))
% 160.93/160.65 [8537]~E(f334(f334(f80(a881),f334(f334(f81(a881),x85371),x85373)),x85374),f334(f334(f80(a881),f334(f334(f81(a881),x85372),x85373)),x85375))+~P1(f334(f334(f248(a881),x85372),x85371))+E(f334(f334(f80(a881),f334(f334(f81(a881),f334(f334(f22(a881),x85371),x85372)),x85373)),x85374),x85375)
% 160.93/160.65 [8703]E(f334(f334(f80(a881),f334(f334(f81(a881),x87031),x87032)),x87033),f334(f334(f80(a881),f334(f334(f81(a881),x87034),x87032)),x87035))+~P1(f334(f334(f248(a881),x87034),x87031))+~E(x87035,f334(f334(f80(a881),f334(f334(f81(a881),f334(f334(f22(a881),x87031),x87034)),x87032)),x87033))
% 160.93/160.65 [8704]E(f334(f334(f80(a881),f334(f334(f81(a881),x87041),x87042)),x87043),f334(f334(f80(a881),f334(f334(f81(a881),x87044),x87042)),x87045))+~P1(f334(f334(f248(a881),x87044),x87041))+~E(f334(f334(f80(a881),f334(f334(f81(a881),f334(f334(f22(a881),x87041),x87044)),x87042)),x87043),x87045)
% 160.93/160.65 [9572]~P61(x95722)+~P1(f334(f61(x95721),x95725))+E(f334(f334(f9(x95721,x95722),f334(f334(f18(x95721,x95722,x95722),f334(f334(f8(x95722,f888(x95722,x95722),x95721),f292(x95722)),x95723)),x95724)),x95725),f334(f334(f292(x95722),f334(f334(f9(x95721,x95722),x95723),x95725)),f334(f334(f9(x95721,x95722),x95724),x95725)))
% 160.93/160.65 [9700]~E(f645(x97005,x97004,x97003,x97002,x97001),f646(x97005,x97004,x97003,x97002,x97001))+P1(f334(f334(f336(f887(x97001,x97001)),f334(f334(f269(x97001,x97001),x97002),x97003)),f310(x97001,x97004)))+~P1(f334(f334(f336(f887(x97001,x97001)),f334(f334(f269(x97001,x97001),x97002),x97003)),f310(x97001,f334(f334(f114(f888(f887(x97001,x97001),a876)),x97004),x97005))))
% 160.93/160.65 [9701]~E(f647(x97015,x97014,x97013,x97012,x97011),f648(x97015,x97014,x97013,x97012,x97011))+P1(f334(f334(f336(f887(x97011,x97011)),f334(f334(f269(x97011,x97011),x97012),x97013)),f310(x97011,x97014)))+~P1(f334(f334(f336(f887(x97011,x97011)),f334(f334(f269(x97011,x97011),x97012),x97013)),f310(x97011,f334(f334(f114(f888(f887(x97011,x97011),a876)),x97014),x97015))))
% 160.93/160.65 [9912]P1(f334(f334(f336(f887(x99121,x99121)),f334(f334(f269(x99121,x99121),x99122),f648(x99125,x99124,x99123,x99122,x99121))),f310(x99121,x99124)))+P1(f334(f334(f336(f887(x99121,x99121)),f334(f334(f269(x99121,x99121),x99122),x99123)),f310(x99121,x99124)))+~P1(f334(f334(f336(f887(x99121,x99121)),f334(f334(f269(x99121,x99121),x99122),x99123)),f310(x99121,f334(f334(f114(f888(f887(x99121,x99121),a876)),x99124),x99125))))
% 160.93/160.65 [9991]P1(f334(f334(f336(f887(x99911,x99911)),f334(f334(f269(x99911,x99911),f646(x99915,x99914,x99913,x99912,x99911)),x99913)),f310(x99911,x99914)))+P1(f334(f334(f336(f887(x99911,x99911)),f334(f334(f269(x99911,x99911),x99912),x99913)),f310(x99911,x99914)))+~P1(f334(f334(f336(f887(x99911,x99911)),f334(f334(f269(x99911,x99911),x99912),x99913)),f310(x99911,f334(f334(f114(f888(f887(x99911,x99911),a876)),x99914),x99915))))
% 160.93/160.65 [10027]P1(f334(f334(f336(f887(x100271,x100271)),f334(f334(f269(x100271,x100271),x100272),x100273)),f310(x100271,x100274)))+P1(f334(f334(f336(f887(x100271,x100271)),f334(f334(f269(x100271,x100271),f645(x100275,x100274,x100273,x100272,x100271)),f646(x100275,x100274,x100273,x100272,x100271))),x100275))+~P1(f334(f334(f336(f887(x100271,x100271)),f334(f334(f269(x100271,x100271),x100272),x100273)),f310(x100271,f334(f334(f114(f888(f887(x100271,x100271),a876)),x100274),x100275))))
% 160.93/160.65 [10028]P1(f334(f334(f336(f887(x100281,x100281)),f334(f334(f269(x100281,x100281),x100282),x100283)),f310(x100281,x100284)))+P1(f334(f334(f336(f887(x100281,x100281)),f334(f334(f269(x100281,x100281),f648(x100285,x100284,x100283,x100282,x100281)),f647(x100285,x100284,x100283,x100282,x100281))),x100285))+~P1(f334(f334(f336(f887(x100281,x100281)),f334(f334(f269(x100281,x100281),x100282),x100283)),f310(x100281,f334(f334(f114(f888(f887(x100281,x100281),a876)),x100284),x100285))))
% 160.93/160.65 [10149]~P1(f334(f334(f336(f887(f882(x101491),f882(x101491))),f334(f334(f269(f882(x101491),f882(x101491)),x101494),x101495)),f160(x101491,x101492)))+~P1(f334(f334(f336(f887(x101491,x101491)),x101493),f334(f174(f887(x101491,x101491)),f334(f334(f184(x101491,x101491),x101494),x101495))))+P1(f334(f334(f273(x101491,x101491,a876),f334(f334(f7(x101491,f888(f887(x101491,x101491),a876),f888(x101491,a876)),f334(f334(f8(f888(x101491,f888(f888(f887(x101491,x101491),a876),a876)),f888(f888(f887(x101491,x101491),a876),f888(x101491,a876)),x101491),f7(x101491,f888(f887(x101491,x101491),a876),a876)),f334(f334(f8(f888(x101491,f887(x101491,x101491)),f888(x101491,f888(f888(f887(x101491,x101491),a876),a876)),x101491),f334(f8(f887(x101491,x101491),f888(f888(f887(x101491,x101491),a876),a876),x101491),f336(f887(x101491,x101491)))),f269(x101491,x101491)))),x101492)),x101493))
% 160.93/160.65 [9600]~P1(f334(f334(f248(a881),x96003),x96002))+~P1(f334(f334(f249(a881),f334(f334(f80(a881),f334(f334(f81(a881),x96003),x96004)),x96001)),f334(f334(f80(a881),f334(f334(f81(a881),x96002),x96004)),x96005)))+P1(f334(f334(f249(a881),x96001),f334(f334(f80(a881),f334(f334(f81(a881),f334(f334(f22(a881),x96002),x96003)),x96004)),x96005)))
% 160.93/160.65 [9601]~P1(f334(f334(f248(a881),x96013),x96012))+~P1(f334(f334(f248(a881),f334(f334(f80(a881),f334(f334(f81(a881),x96013),x96014)),x96011)),f334(f334(f80(a881),f334(f334(f81(a881),x96012),x96014)),x96015)))+P1(f334(f334(f248(a881),x96011),f334(f334(f80(a881),f334(f334(f81(a881),f334(f334(f22(a881),x96012),x96013)),x96014)),x96015)))
% 160.93/160.65 [9619]~P1(f334(f334(f248(a881),x96191),x96194))+P1(f334(f334(f249(a881),f334(f334(f80(a881),f334(f334(f81(a881),x96191),x96192)),x96193)),f334(f334(f80(a881),f334(f334(f81(a881),x96194),x96192)),x96195)))+~P1(f334(f334(f249(a881),x96193),f334(f334(f80(a881),f334(f334(f81(a881),f334(f334(f22(a881),x96194),x96191)),x96192)),x96195)))
% 160.93/160.65 [9620]~P1(f334(f334(f248(a881),x96201),x96204))+P1(f334(f334(f248(a881),f334(f334(f80(a881),f334(f334(f81(a881),x96201),x96202)),x96203)),f334(f334(f80(a881),f334(f334(f81(a881),x96204),x96202)),x96205)))+~P1(f334(f334(f248(a881),x96203),f334(f334(f80(a881),f334(f334(f81(a881),f334(f334(f22(a881),x96204),x96201)),x96202)),x96205)))
% 160.93/160.65 [9734]~P1(f334(f334(f248(a881),x97342),x97341))+~P1(f334(f334(f249(a881),f334(f334(f80(a881),f334(f334(f81(a881),x97341),x97343)),x97344)),f334(f334(f80(a881),f334(f334(f81(a881),x97342),x97343)),x97345)))+P1(f334(f334(f249(a881),f334(f334(f80(a881),f334(f334(f81(a881),f334(f334(f22(a881),x97341),x97342)),x97343)),x97344)),x97345))
% 160.93/160.65 [9735]~P1(f334(f334(f248(a881),x97352),x97351))+~P1(f334(f334(f248(a881),f334(f334(f80(a881),f334(f334(f81(a881),x97351),x97353)),x97354)),f334(f334(f80(a881),f334(f334(f81(a881),x97352),x97353)),x97355)))+P1(f334(f334(f248(a881),f334(f334(f80(a881),f334(f334(f81(a881),f334(f334(f22(a881),x97351),x97352)),x97353)),x97354)),x97355))
% 160.93/160.65 [9788]~P1(f334(f334(f248(a881),x97884),x97881))+P1(f334(f334(f249(a881),f334(f334(f80(a881),f334(f334(f81(a881),x97881),x97882)),x97883)),f334(f334(f80(a881),f334(f334(f81(a881),x97884),x97882)),x97885)))+~P1(f334(f334(f249(a881),f334(f334(f80(a881),f334(f334(f81(a881),f334(f334(f22(a881),x97881),x97884)),x97882)),x97883)),x97885))
% 160.93/160.65 [9789]~P1(f334(f334(f248(a881),x97894),x97891))+P1(f334(f334(f248(a881),f334(f334(f80(a881),f334(f334(f81(a881),x97891),x97892)),x97893)),f334(f334(f80(a881),f334(f334(f81(a881),x97894),x97892)),x97895)))+~P1(f334(f334(f248(a881),f334(f334(f80(a881),f334(f334(f81(a881),f334(f334(f22(a881),x97891),x97894)),x97892)),x97893)),x97895))
% 160.93/160.65 [10012]~P14(x100121,x100122,x100125,x100123)+~P1(f334(f334(f336(f887(x100121,x100121)),x100124),x100125))+P1(f334(f334(f273(x100121,x100121,a876),f334(f334(f7(x100121,f888(x100121,x100122),f888(x100121,a876)),f334(f334(f8(f888(x100122,a876),f888(f888(x100121,x100122),f888(x100121,a876)),x100121),f8(x100122,a876,x100121)),f334(f334(f8(x100122,f888(x100122,a876),x100121),a331),x100123))),x100123)),x100124))
% 160.93/160.65 [6793]~E(f334(x67934,x67935),f210(x67932))+E(f334(f187(x67931,x67932,x67933,x67934),x67935),f334(f241(x67932),x67936))+~E(f334(x67933,x67935),f334(f241(x67932),x67936))
% 160.93/160.65 [6894]~E(f334(x68943,x68946),f210(x68941))+E(f334(f243(f885(x68941),x68942,f210(x68941),x68943),f334(x68944,x68945)),f210(x68941))+~E(f334(x68944,x68945),f334(f241(x68942),x68946))
% 160.93/160.65 [7476]E(f334(x74761,x74762),f210(x74763))+~E(f334(f187(x74765,x74763,x74766,x74761),x74762),f334(f241(x74763),x74764))+E(f334(x74761,x74762),f334(f241(x74763),x74764))
% 160.93/160.65 [7512]~E(f334(f187(x75126,x75123,x75125,x75121),x75122),f334(f241(x75123),x75124))+E(f334(x75121,x75122),f334(f241(x75123),x75124))+E(f334(x75125,x75122),f334(f241(x75123),x75124))
% 160.93/160.65 [8411]~P21(x84116,x84111,x84112,x84114)+E(f334(f73(x84111,x84111,x84111,f334(x84112,x84113)),f334(x84114,x84115)),f334(f73(x84111,x84111,x84111,f334(x84114,x84115)),f334(x84112,x84113)))+~P1(f334(f61(x84116),x84115))
% 160.93/160.65 [8836]~P27(x88361,x88363,x88365,x88366)+~P27(x88363,x88362,x88364,f334(f313(x88361,x88363,x88365),x88366))+P27(x88361,x88362,f334(f73(x88363,x88362,x88361,x88364),x88365),x88366)
% 160.93/160.65 [9406]~P1(f334(f334(x94064,x94062),x94066))+~P1(f334(f334(x94063,x94065),x94062))+P1(f334(f334(f336(x94061),x94062),f299(x94061,x94063,x94064,x94065,x94066)))
% 160.93/160.65 [9407]~P1(f334(f334(x94073,x94072),x94076))+~P1(f334(f334(x94074,x94075),x94072))+P1(f334(f334(f336(x94071),x94072),f302(x94071,x94073,x94074,x94075,x94076)))
% 160.93/160.65 [9519]E(x95191,x95192)+E(x95193,x95194)+~P1(f334(f334(f336(f887(f882(x95195),f882(x95195))),f334(f334(f269(f882(x95195),f882(x95195)),f334(f334(f153(x95195),x95193),x95191)),f334(f334(f153(x95195),x95194),x95192))),f159(x95195,x95196)))
% 160.93/160.65 [9528]~E(x95282,x95284)+P1(f334(f334(f336(f887(f882(x95281),f882(x95281))),f334(f334(f269(f882(x95281),f882(x95281)),f334(f334(f153(x95281),x95282),x95283)),f334(f334(f153(x95281),x95284),x95285))),f147(x95281,x95286)))+~P1(f334(f334(f336(f887(f882(x95281),f882(x95281))),f334(f334(f269(f882(x95281),f882(x95281)),x95283),x95285)),f147(x95281,x95286)))
% 160.93/160.65 [9529]~E(x95292,x95294)+P1(f334(f334(f336(f887(f882(x95291),f882(x95291))),f334(f334(f269(f882(x95291),f882(x95291)),f334(f334(f153(x95291),x95292),x95293)),f334(f334(f153(x95291),x95294),x95295))),f149(x95291,x95296)))+~P1(f334(f334(f336(f887(f882(x95291),f882(x95291))),f334(f334(f269(f882(x95291),f882(x95291)),x95293),x95295)),f149(x95291,x95296)))
% 160.93/160.65 [9530]~E(x95302,x95304)+P1(f334(f334(f336(f887(f882(x95301),f882(x95301))),f334(f334(f269(f882(x95301),f882(x95301)),f334(f334(f153(x95301),x95302),x95303)),f334(f334(f153(x95301),x95304),x95305))),f159(x95301,x95306)))+~P1(f334(f334(f336(f887(f882(x95301),f882(x95301))),f334(f334(f269(f882(x95301),f882(x95301)),x95303),x95305)),f159(x95301,x95306)))
% 160.93/160.65 [9531]~E(x95312,x95314)+P1(f334(f334(f336(f887(f882(x95311),f882(x95311))),f334(f334(f269(f882(x95311),f882(x95311)),f334(f334(f136(x95311),x95312),x95313)),f334(f334(f136(x95311),x95314),x95315))),f159(x95311,x95316)))+~P1(f334(f334(f336(f887(f882(x95311),f882(x95311))),f334(f334(f269(f882(x95311),f882(x95311)),x95313),x95315)),f159(x95311,x95316)))
% 160.93/160.65 [9532]~E(x95323,x95325)+P1(f334(f334(f336(f887(f882(x95321),f882(x95321))),f334(f334(f269(f882(x95321),f882(x95321)),f334(f334(f136(x95321),x95322),x95323)),f334(f334(f136(x95321),x95324),x95325))),f159(x95321,x95326)))+~P1(f334(f334(f336(f887(f882(x95321),f882(x95321))),f334(f334(f269(f882(x95321),f882(x95321)),x95322),x95324)),f159(x95321,x95326)))
% 160.93/160.65 [9588]E(x95881,x95882)+P1(f334(f334(f336(f887(f882(x95883),f882(x95883))),f334(f334(f269(f882(x95883),f882(x95883)),x95881),x95882)),f159(x95883,x95884)))+~P1(f334(f334(f336(f887(f882(x95883),f882(x95883))),f334(f334(f269(f882(x95883),f882(x95883)),f334(f334(f153(x95883),x95885),x95881)),f334(f334(f153(x95883),x95886),x95882))),f159(x95883,x95884)))
% 160.93/160.65 [9738]~E(x97383,x97385)+P1(f334(f334(f336(f887(f882(x97381),f882(x97381))),f334(f334(f269(f882(x97381),f882(x97381)),f334(f334(f136(x97381),x97382),f334(f334(f153(x97381),x97383),f117(x97381)))),f334(f334(f136(x97381),x97384),f334(f334(f153(x97381),x97385),f117(x97381))))),f159(x97381,x97386)))+~P1(f334(f334(f336(f887(f882(x97381),f882(x97381))),f334(f334(f269(f882(x97381),f882(x97381)),x97382),x97384)),f159(x97381,x97386)))
% 160.93/160.65 [9754]E(f334(x97541,x97542),f210(x97543))+~E(f334(f243(f885(x97546),x97543,f210(x97546),x97544),f334(x97541,x97542)),f210(x97546))+E(f334(x97544,f774(x97542,x97541,x97544,x97545,x97546,x97543)),f210(x97546))
% 160.93/160.65 [9755]E(f334(x97551,x97552),f210(x97553))+~E(f334(f243(f885(x97556),x97553,f210(x97556),x97554),f334(x97551,x97552)),f210(x97556))+E(f334(f241(x97553),f774(x97552,x97551,x97554,x97555,x97556,x97553)),f334(x97551,x97552))
% 160.93/160.65 [9792]E(x97921,x97922)+E(x97923,x97924)+~P1(f334(f334(f336(f887(f882(x97925),f882(x97925))),f334(f334(f269(f882(x97925),f882(x97925)),f334(f334(f136(x97925),x97923),f334(f334(f153(x97925),x97921),f117(x97925)))),f334(f334(f136(x97925),x97924),f334(f334(f153(x97925),x97922),f117(x97925))))),f159(x97925,x97926)))
% 160.93/160.65 [9817]E(x98171,x98172)+~P1(f334(f334(f336(f887(f882(x98173),f882(x98173))),f334(f334(f269(f882(x98173),f882(x98173)),f334(f334(f136(x98173),x98171),f334(f334(f153(x98173),x98175),f117(x98173)))),f334(f334(f136(x98173),x98172),f334(f334(f153(x98173),x98176),f117(x98173))))),f159(x98173,x98174)))+P1(f334(f334(f336(f887(f882(x98173),f882(x98173))),f334(f334(f269(f882(x98173),f882(x98173)),x98171),x98172)),f159(x98173,x98174)))
% 160.93/160.65 [9853]~P1(f334(f334(f336(f887(f888(x98531,a876),f888(x98531,a876))),f334(f334(f269(f888(x98531,a876),f888(x98531,a876)),x98532),x98534)),f325(x98531,x98536)))+~P1(f334(f334(f336(f887(f888(x98531,a876),f888(x98531,a876))),f334(f334(f269(f888(x98531,a876),f888(x98531,a876)),x98533),x98535)),f325(x98531,x98536)))+P1(f334(f334(f336(f887(f888(x98531,a876),f888(x98531,a876))),f334(f334(f269(f888(x98531,a876),f888(x98531,a876)),f334(f334(f114(f888(x98531,a876)),x98532),x98533)),f334(f334(f114(f888(x98531,a876)),x98534),x98535))),f325(x98531,x98536)))
% 160.93/160.65 [5246]~E(f334(x52463,x52466),x52465)+~E(x52464,f334(f241(x52461),x52466))+E(f334(f334(f211(x52461,x52462),x52463),x52464),f334(f241(x52462),x52465))
% 160.93/160.65 [5656]~E(f334(f334(f136(x56561),x56566),x56563),x56565)+E(f334(f334(f136(x56561),x56562),x56563),f334(f334(f153(x56561),x56564),x56565))+~E(x56562,f334(f334(f153(x56561),x56564),x56566))
% 160.93/160.65 [5657]~E(f334(f334(f136(x56571),x56576),x56573),x56575)+E(f334(f334(f136(x56571),x56572),x56573),f334(f334(f136(x56571),x56574),x56575))+~E(x56572,f334(f334(f136(x56571),x56574),x56576))
% 160.93/160.65 [5659]E(f334(f334(f136(x56591),x56592),x56593),f334(f334(f153(x56591),x56594),x56595))+~E(f334(f334(f153(x56591),x56594),x56596),x56592)+~E(x56595,f334(f334(f136(x56591),x56596),x56593))
% 160.93/160.65 [5661]~E(f334(f334(f136(x56611),x56612),x56616),x56614)+E(f334(f334(f136(x56611),x56612),x56613),f334(f334(f136(x56611),x56614),x56615))+~E(x56613,f334(f334(f136(x56611),x56616),x56615))
% 160.93/160.65 [6787]E(f334(x67871,x67872),f334(x67873,x67872))+~E(f334(f334(f156(x67874,x67875),x67871),x67876),f334(f334(f156(x67874,x67875),x67873),x67876))+~P1(f334(f334(f336(x67874),x67872),f334(f174(x67874),x67876)))
% 160.93/160.65 [7169]~P21(x71694,x71695,x71696,x71691)+E(f334(f334(x71691,x71692),x71693),f334(f334(f64(x71694,x71695,x71696),x71693),x71692))+~P1(f334(f61(x71694),x71692))
% 160.93/160.65 [7237]~E(x72372,f334(x72374,x72376))+~P1(f334(f334(f336(x72373),x72376),x72375))+P1(f334(f334(f336(x72371),x72372),f334(f313(x72373,x72371,x72374),x72375)))
% 160.93/160.65 [7238]~E(f334(x72384,x72382),x72386)+~P1(f334(f334(f336(x72383),x72386),x72385))+P1(f334(f334(f336(x72381),x72382),f334(f314(x72381,x72383,x72384),x72385)))
% 160.93/160.65 [7692]~P34(x76921,x76922,x76924,x76926)+P34(x76921,x76922,f334(f334(f153(x76921),x76923),x76924),f334(f334(f153(x76921),x76925),x76926))+~P1(f334(f334(x76922,x76923),x76925))
% 160.93/160.65 [8711]~P54(x87114,x87115,x87111,x87112,x87116)+E(f334(x87111,f334(x87112,x87113)),x87113)+~P1(f334(f334(f336(x87115),x87113),x87116))
% 160.93/160.65 [9521]E(x95211,x95212)+E(f334(f197(f882(x95213)),x95214),f334(f197(f882(x95213)),x95215))+~P1(f334(f334(f336(f887(f882(x95213),f882(x95213))),f334(f334(f269(f882(x95213),f882(x95213)),f334(f334(f153(x95213),x95211),x95214)),f334(f334(f153(x95213),x95212),x95215))),f147(x95213,x95216)))
% 160.93/160.65 [9584]~P18(x95841,x95842,x95843)+E(f334(f334(f64(x95841,x95842,x95843),x95844),x95845),x95846)+~P1(f334(f66(x95841,x95842,x95843,x95844,x95845),x95846))
% 160.93/160.65 [9591]E(f334(f197(f882(x95911)),x95912),f334(f197(f882(x95911)),x95913))+P1(f334(f334(f336(f887(f882(x95911),f882(x95911))),f334(f334(f269(f882(x95911),f882(x95911)),x95912),x95913)),f147(x95911,x95914)))+~P1(f334(f334(f336(f887(f882(x95911),f882(x95911))),f334(f334(f269(f882(x95911),f882(x95911)),f334(f334(f153(x95911),x95915),x95912)),f334(f334(f153(x95911),x95916),x95913))),f147(x95911,x95914)))
% 160.93/160.65 [9613]~P1(f334(f334(f336(f887(x96131,x96131)),f334(f334(f269(x96131,x96131),x96132),x96134)),f310(x96131,x96136)))+P1(f334(f334(f336(f887(f882(x96131),f882(x96131))),f334(f334(f269(f882(x96131),f882(x96131)),f334(f334(f153(x96131),x96132),x96133)),f334(f334(f153(x96131),x96134),x96135))),f310(f882(x96131),f159(x96131,x96136))))+~P1(f334(f334(f336(f887(f882(x96131),f882(x96131))),f334(f334(f269(f882(x96131),f882(x96131)),x96133),x96135)),f310(f882(x96131),f159(x96131,x96136))))
% 160.93/160.65 [9798]~P1(f334(x97982,x97986))+~E(f334(f138(x97981,x97982),x97983),f334(f334(f153(x97981),x97984),x97985))+~P1(f334(f334(f336(x97981),x97986),f334(f174(x97981),f793(x97985,x97984,x97983,x97982,x97981))))
% 160.93/160.65 [9799]~P1(f334(x97994,x97996))+~E(f334(f334(f153(x97991),x97992),x97993),f334(f138(x97991,x97994),x97995))+~P1(f334(f334(f336(x97991),x97996),f334(f174(x97991),f791(x97995,x97994,x97993,x97992,x97991))))
% 160.93/160.65 [10106]~P68(x101062)+E(f334(f334(f6(x101061,x101062),f334(f334(f8(f888(x101063,a876),x101062,x101061),f334(f6(x101063,x101062),x101064)),f334(f334(f8(f888(x101063,a876),f888(x101063,a876),x101061),f254(x101063)),f334(f334(f8(f888(x101063,a876),f888(x101063,a876),x101061),f334(f18(x101063,a876,a876),f334(f334(f8(a876,f888(a876,a876),x101063),a332),f334(f334(f7(x101063,f888(x101063,a876),a876),f336(x101063)),x101065)))),f334(f7(x101063,x101061,a876),f334(f334(f8(x101061,f888(x101061,a876),x101063),a331),x101066)))))),f334(f313(x101063,x101061,x101066),x101065)),f334(f334(f6(x101063,x101062),x101064),x101065))+~P1(f334(f61(x101063),x101065))
% 160.93/160.65 [6844]~P108(x68443)+P1(f334(x68442,x68445))+E(f334(f138(x68441,x68442),f334(f334(f150(x68441,x68443,x68444),x68445),x68446)),f334(f138(x68441,x68442),x68446))
% 160.93/160.65 [6846]P1(f334(x68461,x68462))+~E(f169(x68463,x68461,x68464),f334(f334(f269(f882(x68463),f882(x68463)),x68465),x68466))+~P1(f334(f334(f336(x68463),x68462),f334(f174(x68463),x68465)))
% 160.93/160.65 [6891]~P1(f334(x68912,x68916))+~E(f169(x68911,x68912,x68913),f334(f334(f269(f882(x68911),f882(x68911)),x68914),x68915))+~P1(f334(f334(f336(x68911),x68916),f334(f174(x68911),x68915)))
% 160.93/160.65 [7557]~P17(x75571,x75572,x75573)+~P1(f334(f61(x75571),x75576))+E(f334(f334(f64(x75571,x75572,x75573),x75574),f334(f334(f312(x75571),x75575),x75576)),f334(f334(f64(x75571,x75572,x75573),f334(f334(x75573,x75575),x75574)),x75576))
% 160.93/160.65 [7609]~P108(x76092)+~P1(f334(f334(f248(x76092),f334(x76093,x76094)),f334(x76093,x76095)))+E(f334(f334(f150(x76091,x76092,x76093),x76094),f334(f334(f153(x76091),x76095),x76096)),f334(f334(f153(x76091),x76094),f334(f334(f153(x76091),x76095),x76096)))
% 160.93/160.65 [7722]E(x77221,x77222)+~E(f334(f334(f271(x77223,x77224),x77221),f334(f16(f888(x77224,a876),x77223),x77225)),f334(f334(f271(x77223,x77224),x77222),f334(f16(f888(x77224,a876),x77223),x77225)))+~P1(f334(f334(f336(x77224),x77226),x77225))
% 160.93/160.65 [7785]~P17(x77851,x77852,x77853)+~P1(f334(f61(x77851),x77856))+E(f334(f334(f64(x77851,x77852,x77853),x77854),f334(f334(f312(x77851),x77855),x77856)),f334(f334(x77853,x77855),f334(f334(f64(x77851,x77852,x77853),x77854),x77856)))
% 160.93/160.65 [7902]~P18(x79021,x79022,x79023)+~P1(f334(f61(x79021),x79026))+E(f334(f334(f64(x79021,x79022,x79023),f334(f334(x79023,x79024),x79025)),x79026),f334(f334(x79023,x79024),f334(f334(f64(x79021,x79022,x79023),x79025),x79026)))
% 160.93/160.65 [7972]~P22(x79722,x79725,x79726,x79721)+~P1(f334(f61(x79722),x79724))+E(f334(x79721,f334(f334(f312(x79722),x79723),x79724)),f334(f73(x79725,x79725,x79725,f334(x79721,x79724)),f334(x79726,x79723)))
% 160.93/160.65 [8004]~P108(x80042)+P1(f334(f334(f248(x80042),f334(x80043,x80044)),f334(x80043,x80045)))+E(f334(f334(f150(x80041,x80042,x80043),x80044),f334(f334(f153(x80041),x80045),x80046)),f334(f334(f153(x80041),x80045),f334(f334(f150(x80041,x80042,x80043),x80044),x80046)))
% 160.93/160.65 [8146]~E(f334(f197(f882(x81461)),x81465),f334(f197(f882(x81462)),x81466))+~E(f334(f197(f882(x81461)),x81463),f334(f197(f882(x81462)),x81464))+E(f334(f334(f136(f887(x81461,x81462)),f334(f334(f184(x81461,x81462),x81463),x81464)),f334(f334(f184(x81461,x81462),x81465),x81466)),f334(f334(f184(x81461,x81462),f334(f334(f136(x81461),x81463),x81465)),f334(f334(f136(x81462),x81464),x81466)))
% 160.93/160.65 [8269]~E(x82692,f334(f313(x82693,x82691,x82694),x82696))+P1(f334(f334(f248(f888(x82691,a876)),x82692),f334(f313(x82693,x82691,x82694),x82695)))+~P1(f334(f334(f248(f888(x82693,a876)),x82696),x82695))
% 160.93/160.65 [8370]~P108(x83705)+E(f334(x83701,x83702),f334(x83701,x83703))+E(f334(f334(f150(x83704,x83705,x83701),x83702),f334(f334(f150(x83704,x83705,x83701),x83703),x83706)),f334(f334(f150(x83704,x83705,x83701),x83703),f334(f334(f150(x83704,x83705,x83701),x83702),x83706)))
% 160.93/160.65 [8405]~P27(x84053,x84051,x84054,x84055)+P27(x84053,x84051,f334(f334(f334(f72(x84053,x84051),x84054),x84056),x84052),x84055)+P1(f334(f334(f336(x84051),x84052),f334(f313(x84053,x84051,x84054),x84055)))
% 160.93/160.65 [8548]~P1(f334(f334(f336(x85482),x85484),f334(x85486,x85483)))+~P1(f334(f334(f336(x85481),x85483),x85485))+P1(f334(f334(f336(f887(x85481,x85482)),f334(f334(f269(x85481,x85482),x85483),x85484)),f334(f334(f271(x85481,x85482),x85485),x85486)))
% 160.93/160.65 [9014]~P68(x90142)+~P27(x90144,x90141,x90145,x90146)+E(f334(f334(f6(x90141,x90142),x90143),f334(f313(x90144,x90141,x90145),x90146)),f334(f334(f6(x90144,x90142),f334(f73(x90141,x90142,x90144,x90143),x90145)),x90146))
% 160.93/160.65 [9015]~P74(x90152)+~P27(x90154,x90151,x90155,x90156)+E(f334(f334(f9(x90151,x90152),x90153),f334(f313(x90154,x90151,x90155),x90156)),f334(f334(f9(x90154,x90152),f334(f73(x90151,x90152,x90154,x90153),x90155)),x90156))
% 160.93/160.65 [9063]~P36(x90632,x90635,x90631,x90633,x90636)+P1(f334(f334(x90631,f334(f334(f167(x90632),x90633),x90634)),f334(f334(f167(x90635),x90636),x90634)))+~P1(f334(f334(f249(a881),x90634),f334(f197(f882(x90635)),x90636)))
% 160.93/160.65 [9064]~P36(x90642,x90645,x90641,x90643,x90646)+P1(f334(f334(x90641,f334(f334(f167(x90642),x90643),x90644)),f334(f334(f167(x90645),x90646),x90644)))+~P1(f334(f334(f249(a881),x90644),f334(f197(f882(x90642)),x90643)))
% 160.93/160.65 [9276]~P21(x92763,x92761,x92766,x92762)+~P1(f334(f61(x92763),x92764))+E(f334(f73(x92761,x92761,x92761,f334(x92762,f334(f334(f22(f888(x92763,a876)),x92764),f334(f334(f312(x92763),x92765),f196(f888(x92763,a876)))))),f334(x92766,x92765)),f334(x92762,f334(f334(f312(x92763),x92765),x92764)))
% 160.93/160.65 [9892]~E(f334(f313(x98922,x98924,x98926),f257(f888(x98922,a876))),f257(f888(x98924,a876)))+~E(f334(f313(x98921,x98923,x98925),f257(f888(x98921,a876))),f257(f888(x98923,a876)))+E(f334(f313(f887(x98921,x98922),f887(x98923,x98924),f274(x98921,x98923,x98922,x98924,x98925,x98926)),f257(f888(f887(x98921,x98922),a876))),f257(f888(f887(x98923,x98924),a876)))
% 160.93/160.65 [9940]~P27(x99403,x99404,x99405,f334(x99406,f593(x99406,x99405,x99404,x99403,x99402,x99401)))+P27(x99403,x99404,x99405,f334(f334(f42(x99402,f888(x99403,a876)),x99401),x99406))+E(x99401,f196(f888(x99402,a876)))
% 160.93/160.65 [9998]P27(x99986,x99985,x99984,f334(f334(f42(x99982,f888(x99986,a876)),x99981),x99983))+E(x99981,f196(f888(x99982,a876)))+P1(f334(f334(f336(x99982),f593(x99983,x99984,x99985,x99986,x99982,x99981)),x99981))
% 160.93/160.65 [10003]P1(f334(f334(f336(x100031),f619(x100032,x100033,x100034,x100035,x100036,x100031)),x100036))+P1(f334(f334(f248(f888(f887(x100031,x100034),a876)),f334(f334(f271(x100031,x100034),x100036),x100033)),f334(f334(f271(x100031,x100034),x100035),x100032)))+~P1(f334(f334(f248(f888(x100031,a876)),x100036),x100035))
% 160.93/160.65 [10041]P26(x100416,x100415,f334(f334(f312(f880(x100416)),f334(f334(f334(f92(x100416),x100414),x100413),x100412)),f196(f888(f880(x100416),a876))))+~P26(x100416,x100415,f334(f334(f312(f880(x100416)),f334(f334(f334(f92(x100416),x100414),x100413),x100411)),f196(f888(f880(x100416),a876))))+P1(f334(f334(x100411,f390(x100412,x100411,x100413,x100414,x100415,x100416)),f403(x100412,x100411,x100413,x100414,x100415,x100416)))
% 160.93/160.65 [10042]P26(x100426,x100425,f334(f334(f312(f880(x100426)),f334(f334(f334(f92(x100426),x100421),x100423),x100422)),f196(f888(f880(x100426),a876))))+~P26(x100426,x100425,f334(f334(f312(f880(x100426)),f334(f334(f334(f92(x100426),x100424),x100423),x100422)),f196(f888(f880(x100426),a876))))+P1(f334(f334(x100421,f410(x100421,x100422,x100423,x100424,x100425,x100426)),f422(x100421,x100422,x100423,x100424,x100425,x100426)))
% 160.93/160.65 [10081]~P26(x100811,x100812,f334(f334(f312(f880(x100811)),f334(f334(f334(f92(x100811),x100813),x100814),x100816)),f196(f888(f880(x100811),a876))))+P26(x100811,x100812,f334(f334(f312(f880(x100811)),f334(f334(f334(f92(x100811),x100813),x100814),x100815)),f196(f888(f880(x100811),a876))))+~P1(f334(f334(x100815,f390(x100815,x100816,x100814,x100813,x100812,x100811)),f403(x100815,x100816,x100814,x100813,x100812,x100811)))
% 160.93/160.65 [10082]~P26(x100821,x100822,f334(f334(f312(f880(x100821)),f334(f334(f334(f92(x100821),x100826),x100824),x100825)),f196(f888(f880(x100821),a876))))+P26(x100821,x100822,f334(f334(f312(f880(x100821)),f334(f334(f334(f92(x100821),x100823),x100824),x100825)),f196(f888(f880(x100821),a876))))+~P1(f334(f334(x100826,f410(x100823,x100825,x100824,x100826,x100822,x100821)),f422(x100823,x100825,x100824,x100826,x100822,x100821)))
% 160.93/160.65 [10117]~P1(f334(f334(f248(f888(x101172,a876)),f334(x101174,f619(x101176,x101174,x101172,x101175,x101173,x101171))),f334(x101176,f619(x101176,x101174,x101172,x101175,x101173,x101171))))+~P1(f334(f334(f248(f888(x101171,a876)),x101173),x101175))+P1(f334(f334(f248(f888(f887(x101171,x101172),a876)),f334(f334(f271(x101171,x101172),x101173),x101174)),f334(f334(f271(x101171,x101172),x101175),x101176)))
% 160.93/160.65 [7741]~P1(f334(x77411,x77415))+~P1(f334(x77416,x77414))+P1(f334(x77411,f334(f272(x77412,x77413),f334(f334(f269(x77412,x77413),x77414),x77415))))
% 160.93/160.65 [7742]~P1(f334(x77421,x77424))+~P1(f334(x77426,x77425))+P1(f334(x77421,f334(f268(x77422,x77423),f334(f334(f269(x77422,x77423),x77424),x77425))))
% 160.93/160.65 [7762]~E(f334(f197(f882(x77621)),x77623),f334(f197(f882(x77624)),x77625))+~E(f334(f334(f180(x77621,x77624),f334(f334(f184(x77621,x77624),x77623),x77625)),x77622),f334(f241(x77624),x77626))+P1(f334(f334(f336(x77621),x77622),f334(f174(x77621),x77623)))
% 160.93/160.65 [7790]~P1(f334(f334(x77904,x77906),x77905))+~P1(f334(f334(f336(x77901),x77906),x77903))+P1(f334(f334(f334(f41(x77901,f888(x77902,a876)),x77903),x77904),x77905))
% 160.93/160.65 [8093]~P1(f334(f334(f336(x80931),x80932),f334(x80935,x80936)))+~P1(f334(f334(f336(x80933),x80936),x80934))+P1(f334(f334(f336(x80931),x80932),f334(f334(f41(x80933,f888(x80931,a876)),x80934),x80935)))
% 160.93/160.65 [8137]P1(f334(f334(x81371,x81372),x81373))+~P1(f334(f334(x81374,x81372),x81373))+~P1(f334(f334(f248(f888(x81375,f888(x81376,a876))),x81374),x81371))
% 160.93/160.65 [8292]P1(f334(f334(x82921,x82922),x82923))+~P1(f334(f334(f336(x82924),x82922),x82925))+~P1(f334(f334(f334(f42(x82924,f888(x82926,a876)),x82925),x82921),x82923))
% 160.93/160.65 [8426]P1(f334(f334(f336(x84261),x84262),f334(x84263,x84264)))+~P1(f334(f334(f336(x84265),x84264),x84266))+~P1(f334(f334(f336(x84261),x84262),f334(f334(f42(x84265,f888(x84261,a876)),x84266),x84263)))
% 160.93/160.65 [8620]~P1(f334(f334(f334(f334(a204,x86201),x86203),x86204),x86206))+~P1(f334(f334(f334(f334(a204,x86202),x86206),x86204),x86205))+P1(f334(f334(f334(f334(a204,f33(x86201,x86202)),x86203),x86204),x86205))
% 160.93/160.65 [8693]~P14(x86934,x86935,x86936,x86931)+E(f334(x86931,x86932),f334(x86931,x86933))+~P1(f334(f334(f336(f887(x86934,x86934)),f334(f334(f269(x86934,x86934),x86932),x86933)),x86936))
% 160.93/160.65 [8724]P1(f334(f334(f248(f888(x87241,a876)),x87242),f334(x87243,x87244)))+~P1(f334(f334(f336(x87245),x87244),x87246))+~P1(f334(f334(f248(f888(x87241,a876)),x87242),f334(f334(f42(x87245,f888(x87241,a876)),x87246),x87243)))
% 160.93/160.65 [8752]~P52(x87523,x87524,f334(f289(x87524,x87523),x87525))+E(x87521,f196(f888(x87522,a876)))+E(f334(f334(f42(x87522,f888(x87523,a876)),x87521),f334(f334(f8(f888(x87524,a876),f888(x87523,a876),x87522),f288(x87524,x87523,x87525)),x87526)),f334(f288(x87524,x87523,x87525),f334(f334(f42(x87522,f888(x87524,a876)),x87521),x87526)))
% 160.93/160.65 [8827]P1(f334(f334(f336(x88271),x88272),f334(f288(x88273,x88271,x88274),x88275)))+~P1(f334(f334(f336(x88273),x88276),x88275))+~P1(f334(f334(f336(f887(x88273,x88271)),f334(f334(f269(x88273,x88271),x88276),x88272)),x88274))
% 160.93/160.65 [8944]P1(f334(x89441,x89442))+~P1(f334(f334(f334(f334(a204,x89444),x89442),x89445),x89446))+P1(f334(f334(f334(f334(a204,f30(x89441,x89443,x89444)),x89442),x89445),x89446))
% 160.93/160.65 [8961]~P1(f334(x89611,x89614))+~P1(f334(f334(f334(f334(a204,x89612),x89614),x89615),x89616))+P1(f334(f334(f334(f334(a204,f30(x89611,x89612,x89613)),x89614),x89615),x89616))
% 160.93/160.65 [9140]P1(f334(f334(f248(f888(x91401,a876)),f334(f288(x91402,x91401,x91403),x91404)),f334(f288(x91402,x91401,x91405),x91406)))+~P1(f334(f334(f248(f888(x91402,a876)),x91404),x91406))+~P1(f334(f334(f248(f888(f887(x91402,x91401),a876)),x91403),x91405))
% 160.93/160.65 [9228]P1(f334(x92281,x92282))+P1(f334(f334(f334(f334(a204,x92283),x92282),x92284),x92285))+~P1(f334(f334(f334(f334(a204,f30(x92281,x92286,x92283)),x92282),x92284),x92285))
% 160.93/160.65 [9233]~P1(f334(x92335,x92332))+P1(f334(f334(f334(f334(a204,x92331),x92332),x92333),x92334))+~P1(f334(f334(f334(f334(a204,f30(x92335,x92331,x92336)),x92332),x92333),x92334))
% 160.93/160.65 [9283]P1(f334(f334(f334(f334(a204,x92831),x92832),x92833),x92834))+P1(f334(f334(f334(f334(a204,x92835),x92832),x92833),x92834))+~P1(f334(f334(f334(f334(a204,f30(x92836,x92831,x92835)),x92832),x92833),x92834))
% 160.93/160.65 [9325]~P1(f334(f334(f336(x93252),x93256),x93254))+~P1(f334(f334(f248(f888(x93251,a876)),x93253),x93255))+P1(f334(f334(f248(f888(f887(x93251,x93252),a876)),f334(f334(f271(x93251,x93252),x93253),f334(f16(f888(x93252,a876),x93251),x93254))),f334(f334(f271(x93251,x93252),x93255),f334(f16(f888(x93252,a876),x93251),x93254))))
% 160.93/160.65 [9338]~P36(x93381,x93382,x93383,x93385,x93386)+P1(f334(f334(f273(x93381,x93382,a876),x93383),x93384))+~P1(f334(f334(f336(f887(x93381,x93382)),x93384),f334(f174(f887(x93381,x93382)),f334(f334(f184(x93381,x93382),x93385),x93386))))
% 160.93/160.65 [9472]~E(x94723,x94725)+P1(f334(f334(f336(f887(f882(x94721),f882(x94721))),f334(f334(f269(f882(x94721),f882(x94721)),f334(f334(f153(x94721),x94722),x94723)),f334(f334(f153(x94721),x94724),x94725))),f159(x94721,x94726)))+~P1(f334(f334(f336(f887(x94721,x94721)),f334(f334(f269(x94721,x94721),x94722),x94724)),x94726))
% 160.93/160.65 [9478]~E(f334(f197(f882(x94781)),x94785),f334(f197(f882(x94782)),x94786))+E(f189(x94781,x94782,f190(x94781,x94782,x94783,f334(f334(f22(f888(x94781,a876)),x94784),f334(f174(x94781),x94785))),x94785,x94786),f190(x94781,x94782,f189(x94781,x94782,x94783,x94785,x94786),x94784))+~P1(f334(f334(f248(f888(x94781,a876)),f334(f174(x94781),x94785)),x94784))
% 160.93/160.65 [9479]~E(f334(f197(f882(x94791)),x94793),f334(f197(f882(x94791)),x94795))+P1(f334(f334(f336(f887(f882(x94791),f882(x94791))),f334(f334(f269(f882(x94791),f882(x94791)),f334(f334(f153(x94791),x94792),x94793)),f334(f334(f153(x94791),x94794),x94795))),f147(x94791,x94796)))+~P1(f334(f334(f336(f887(x94791,x94791)),f334(f334(f269(x94791,x94791),x94792),x94794)),x94796))
% 160.93/160.65 [9512]P1(f334(f334(f336(f887(x95121,x95121)),f334(f334(f269(x95121,x95121),x95122),x95123)),f334(f334(f191(f887(x95121,x95121),a876),f334(a116,x95124)),x95125)))+~P1(f334(f334(f336(f887(x95121,x95121)),f334(f334(f269(x95121,x95121),x95126),x95123)),x95125))+~P1(f334(f334(f336(f887(x95121,x95121)),f334(f334(f269(x95121,x95121),x95122),x95126)),f334(f334(f191(f887(x95121,x95121),a876),x95124),x95125)))
% 160.93/160.65 [9513]P1(f334(f334(f336(f887(x95131,x95131)),f334(f334(f269(x95131,x95131),x95132),x95133)),f334(f334(f191(f887(x95131,x95131),a876),f334(a116,x95134)),x95135)))+~P1(f334(f334(f336(f887(x95131,x95131)),f334(f334(f269(x95131,x95131),x95132),x95136)),x95135))+~P1(f334(f334(f336(f887(x95131,x95131)),f334(f334(f269(x95131,x95131),x95136),x95133)),f334(f334(f191(f887(x95131,x95131),a876),x95134),x95135)))
% 160.93/160.65 [9517]~P1(f334(f334(f336(x95174),x95175),x95176))+P1(f334(f334(f248(f888(x95171,a876)),x95172),x95173))+~P1(f334(f334(f248(f888(f887(x95171,x95174),a876)),f334(f334(f271(x95171,x95174),x95172),f334(f16(f888(x95174,a876),x95171),x95176))),f334(f334(f271(x95171,x95174),x95173),f334(f16(f888(x95174,a876),x95171),x95176))))
% 160.93/160.65 [9562]E(x95621,x95622)+~P1(f334(f334(f336(f887(f882(x95623),f882(x95623))),f334(f334(f269(f882(x95623),f882(x95623)),f334(f334(f153(x95623),x95621),x95625)),f334(f334(f153(x95623),x95622),x95626))),f147(x95623,x95624)))+P1(f334(f334(f336(f887(x95623,x95623)),f334(f334(f269(x95623,x95623),x95621),x95622)),x95624))
% 160.93/160.65 [9563]E(x95631,x95632)+~P1(f334(f334(f336(f887(f882(x95633),f882(x95633))),f334(f334(f269(f882(x95633),f882(x95633)),f334(f334(f153(x95633),x95631),x95635)),f334(f334(f153(x95633),x95632),x95636))),f149(x95633,x95634)))+P1(f334(f334(f336(f887(x95633,x95633)),f334(f334(f269(x95633,x95633),x95631),x95632)),x95634))
% 160.93/160.65 [9564]E(x95641,x95642)+~P1(f334(f334(f336(f887(f882(x95643),f882(x95643))),f334(f334(f269(f882(x95643),f882(x95643)),f334(f334(f153(x95643),x95641),x95645)),f334(f334(f153(x95643),x95642),x95646))),f159(x95643,x95644)))+P1(f334(f334(f336(f887(x95643,x95643)),f334(f334(f269(x95643,x95643),x95641),x95642)),x95644))
% 160.93/160.65 [9599]P1(f334(f334(f336(f887(f882(x95991),f882(x95991))),f334(f334(f269(f882(x95991),f882(x95991)),f334(f334(f153(x95991),x95992),x95993)),f334(f334(f153(x95991),x95994),x95995))),f160(x95991,x95996)))+~P1(f334(f334(f336(f887(f882(x95991),f882(x95991))),f334(f334(f269(f882(x95991),f882(x95991)),x95993),x95995)),f160(x95991,x95996)))+~P1(f334(f334(f336(f887(x95991,x95991)),f334(f334(f269(x95991,x95991),x95992),x95994)),x95996))
% 160.93/160.65 [9617]P1(f334(x96171,x96172))+~P1(f334(x96171,f836(x96171,x96173,x96174,x96175,x96176)))+~P1(f334(f334(f336(x96176),x96172),f334(f334(f41(x96175,f888(x96176,a876)),x96174),x96173)))
% 160.93/160.65 [9622]~P1(f334(f334(f336(f887(f882(x96221),f882(x96221))),f334(f334(f269(f882(x96221),f882(x96221)),f334(f334(f153(x96221),x96222),x96225)),f334(f334(f153(x96221),x96223),x96226))),f147(x96221,x96224)))+P1(f334(f334(f336(f887(f882(x96221),f882(x96221))),f334(f334(f269(f882(x96221),f882(x96221)),x96225),x96226)),f147(x96221,x96224)))+P1(f334(f334(f336(f887(x96221,x96221)),f334(f334(f269(x96221,x96221),x96222),x96223)),x96224))
% 160.93/160.65 [9623]~P1(f334(f334(f336(f887(f882(x96231),f882(x96231))),f334(f334(f269(f882(x96231),f882(x96231)),f334(f334(f153(x96231),x96232),x96235)),f334(f334(f153(x96231),x96233),x96236))),f149(x96231,x96234)))+P1(f334(f334(f336(f887(f882(x96231),f882(x96231))),f334(f334(f269(f882(x96231),f882(x96231)),x96235),x96236)),f149(x96231,x96234)))+P1(f334(f334(f336(f887(x96231,x96231)),f334(f334(f269(x96231,x96231),x96232),x96233)),x96234))
% 160.93/160.65 [9624]~P1(f334(f334(f336(f887(f882(x96241),f882(x96241))),f334(f334(f269(f882(x96241),f882(x96241)),f334(f334(f153(x96241),x96242),x96245)),f334(f334(f153(x96241),x96243),x96246))),f159(x96241,x96244)))+P1(f334(f334(f336(f887(f882(x96241),f882(x96241))),f334(f334(f269(f882(x96241),f882(x96241)),x96245),x96246)),f159(x96241,x96244)))+P1(f334(f334(f336(f887(x96241,x96241)),f334(f334(f269(x96241,x96241),x96242),x96243)),x96244))
% 160.93/160.65 [9710]P1(f334(x97101,x97102))+P1(f334(f334(f336(x97103),f837(x97101,x97104,x97105,x97103,x97106)),x97105))+~P1(f334(f334(f336(x97106),x97102),f334(f334(f41(x97103,f888(x97106,a876)),x97105),x97104)))
% 160.93/160.65 [9721]~E(x97212,x97214)+P1(f334(f334(f336(f887(f882(x97211),f882(x97211))),f334(f334(f269(f882(x97211),f882(x97211)),f334(f334(f136(x97211),x97212),f334(f334(f153(x97211),x97213),f117(x97211)))),f334(f334(f136(x97211),x97214),f334(f334(f153(x97211),x97215),f117(x97211))))),f159(x97211,x97216)))+~P1(f334(f334(f336(f887(x97211,x97211)),f334(f334(f269(x97211,x97211),x97213),x97215)),x97216))
% 160.93/160.65 [9808]E(x98081,x98082)+~P1(f334(f334(f336(f887(f882(x98083),f882(x98083))),f334(f334(f269(f882(x98083),f882(x98083)),f334(f334(f136(x98083),x98085),f334(f334(f153(x98083),x98081),f117(x98083)))),f334(f334(f136(x98083),x98086),f334(f334(f153(x98083),x98082),f117(x98083))))),f159(x98083,x98084)))+P1(f334(f334(f336(f887(x98083,x98083)),f334(f334(f269(x98083,x98083),x98081),x98082)),x98084))
% 160.93/160.65 [9836]~P1(f334(f334(f336(f887(f882(x98361),f882(x98361))),f334(f334(f269(f882(x98361),f882(x98361)),f334(f334(f136(x98361),x98365),f334(f334(f153(x98361),x98362),f117(x98361)))),f334(f334(f136(x98361),x98366),f334(f334(f153(x98361),x98363),f117(x98361))))),f159(x98361,x98364)))+P1(f334(f334(f336(f887(f882(x98361),f882(x98361))),f334(f334(f269(f882(x98361),f882(x98361)),x98365),x98366)),f159(x98361,x98364)))+P1(f334(f334(f336(f887(x98361,x98361)),f334(f334(f269(x98361,x98361),x98362),x98363)),x98364))
% 160.93/160.65 [9854]P1(f334(x98541,x98542))+P1(f334(f334(f336(x98543),f836(x98541,x98544,x98545,x98546,x98543)),f334(x98544,f837(x98541,x98544,x98545,x98546,x98543))))+~P1(f334(f334(f336(x98543),x98542),f334(f334(f41(x98546,f888(x98543,a876)),x98545),x98544)))
% 160.93/160.65 [8842]~P18(x88423,x88424,x88421)+~P1(f334(f61(x88423),x88426))+E(f334(f334(x88421,x88422),f334(f334(f64(x88423,x88424,x88421),x88425),f334(f334(f22(f888(x88423,a876)),x88426),f334(f334(f312(x88423),x88422),f196(f888(x88423,a876)))))),f334(f334(f64(x88423,x88424,x88421),x88425),f334(f334(f312(x88423),x88422),x88426)))
% 160.93/160.65 [8927]~E(f334(f334(f180(x89271,x89272),x89274),x89275),f334(f241(x89272),x89276))+~P1(f334(f334(x89273,x89275),x89276))+E(f334(f334(f180(x89271,x89272),f334(f138(f887(x89271,x89272),f334(f273(x89271,x89272,a876),x89273)),x89274)),x89275),f334(f241(x89272),x89276))
% 160.93/160.65 [9147]~P1(f334(f334(f336(x91475),x91473),x91476))+P1(f334(f334(f248(f888(x91471,a876)),f334(x91472,x91473)),x91474))+~P1(f334(f334(f248(f888(x91471,a876)),f334(f334(f41(x91475,f888(x91471,a876)),x91476),x91472)),x91474))
% 160.93/160.65 [9781]~P8(x97811,x97815,x97814)+P1(f334(f334(f336(f887(x97811,x97811)),f334(f334(f269(x97811,x97811),x97812),x97813)),x97814))+~P1(f334(f334(f336(x97811),x97816),f334(f334(f105(f888(x97811,a876)),f334(f288(x97811,x97811,x97814),f334(f334(f312(x97811),x97812),f196(f888(x97811,a876))))),f334(f288(x97811,x97811,x97814),f334(f334(f312(x97811),x97813),f196(f888(x97811,a876)))))))
% 160.93/160.65 [8587]~P105(x85872)+~E(f334(f334(f80(x85872),f334(f334(f81(x85872),x85874),x85875)),x85871),f334(f334(f80(x85872),f334(f334(f81(x85872),x85873),x85875)),x85876))+E(x85871,f334(f334(f80(x85872),f334(f334(f81(x85872),f334(f334(f22(x85872),x85873),x85874)),x85875)),x85876))
% 160.93/160.65 [8588]~P105(x85881)+~E(f334(f334(f80(x85881),f334(f334(f81(x85881),x85882),x85884)),x85885),f334(f334(f80(x85881),f334(f334(f81(x85881),x85883),x85884)),x85886))+E(f334(f334(f80(x85881),f334(f334(f81(x85881),f334(f334(f22(x85881),x85882),x85883)),x85884)),x85885),x85886)
% 160.93/160.65 [8755]~P105(x87551)+E(f334(f334(f80(x87551),f334(f334(f81(x87551),x87552),x87553)),x87554),f334(f334(f80(x87551),f334(f334(f81(x87551),x87555),x87553)),x87556))+~E(x87556,f334(f334(f80(x87551),f334(f334(f81(x87551),f334(f334(f22(x87551),x87552),x87555)),x87553)),x87554))
% 160.93/160.65 [8756]~P105(x87561)+E(f334(f334(f80(x87561),f334(f334(f81(x87561),x87562),x87563)),x87564),f334(f334(f80(x87561),f334(f334(f81(x87561),x87565),x87563)),x87566))+~E(f334(f334(f80(x87561),f334(f334(f81(x87561),f334(f334(f22(x87561),x87562),x87565)),x87563)),x87564),x87566)
% 160.93/160.65 [9086]~P1(f334(f334(x90864,x90865),x90866))+~P1(f334(f334(x90863,x90865),x90866))+P1(f334(f334(f334(f334(f105(f888(x90861,f888(x90862,a876))),x90863),x90864),x90865),x90866))
% 160.93/160.65 [9346]P1(f334(f334(x93461,x93462),x93463))+P1(f334(f334(x93464,x93462),x93463))+~P1(f334(f334(f334(f334(f114(f888(x93465,f888(x93466,a876))),x93464),x93461),x93462),x93463))
% 160.93/160.65 [9637]~P125(x96371)+~P1(f334(f334(f249(x96371),f334(f334(f80(x96371),f334(f334(f81(x96371),x96374),x96375)),x96372)),f334(f334(f80(x96371),f334(f334(f81(x96371),x96373),x96375)),x96376)))+P1(f334(f334(f249(x96371),x96372),f334(f334(f80(x96371),f334(f334(f81(x96371),f334(f334(f22(x96371),x96373),x96374)),x96375)),x96376)))
% 160.93/160.65 [9638]~P125(x96381)+~P1(f334(f334(f248(x96381),f334(f334(f80(x96381),f334(f334(f81(x96381),x96384),x96385)),x96382)),f334(f334(f80(x96381),f334(f334(f81(x96381),x96383),x96385)),x96386)))+P1(f334(f334(f248(x96381),x96382),f334(f334(f80(x96381),f334(f334(f81(x96381),f334(f334(f22(x96381),x96383),x96384)),x96385)),x96386)))
% 160.93/160.65 [9663]~P125(x96631)+P1(f334(f334(f249(x96631),f334(f334(f80(x96631),f334(f334(f81(x96631),x96632),x96633)),x96634)),f334(f334(f80(x96631),f334(f334(f81(x96631),x96635),x96633)),x96636)))+~P1(f334(f334(f249(x96631),x96634),f334(f334(f80(x96631),f334(f334(f81(x96631),f334(f334(f22(x96631),x96635),x96632)),x96633)),x96636)))
% 160.93/160.65 [9664]~P125(x96641)+P1(f334(f334(f248(x96641),f334(f334(f80(x96641),f334(f334(f81(x96641),x96642),x96643)),x96644)),f334(f334(f80(x96641),f334(f334(f81(x96641),x96645),x96643)),x96646)))+~P1(f334(f334(f248(x96641),x96644),f334(f334(f80(x96641),f334(f334(f81(x96641),f334(f334(f22(x96641),x96645),x96642)),x96643)),x96646)))
% 160.93/160.65 [9769]~P125(x97691)+~P1(f334(f334(f249(x97691),f334(f334(f80(x97691),f334(f334(f81(x97691),x97692),x97694)),x97695)),f334(f334(f80(x97691),f334(f334(f81(x97691),x97693),x97694)),x97696)))+P1(f334(f334(f249(x97691),f334(f334(f80(x97691),f334(f334(f81(x97691),f334(f334(f22(x97691),x97692),x97693)),x97694)),x97695)),x97696))
% 160.93/160.65 [9770]~P125(x97701)+~P1(f334(f334(f248(x97701),f334(f334(f80(x97701),f334(f334(f81(x97701),x97702),x97704)),x97705)),f334(f334(f80(x97701),f334(f334(f81(x97701),x97703),x97704)),x97706)))+P1(f334(f334(f248(x97701),f334(f334(f80(x97701),f334(f334(f81(x97701),f334(f334(f22(x97701),x97702),x97703)),x97704)),x97705)),x97706))
% 160.93/160.65 [9819]~P125(x98191)+P1(f334(f334(f249(x98191),f334(f334(f80(x98191),f334(f334(f81(x98191),x98192),x98193)),x98194)),f334(f334(f80(x98191),f334(f334(f81(x98191),x98195),x98193)),x98196)))+~P1(f334(f334(f249(x98191),f334(f334(f80(x98191),f334(f334(f81(x98191),f334(f334(f22(x98191),x98192),x98195)),x98193)),x98194)),x98196))
% 160.93/160.65 [9820]~P125(x98201)+P1(f334(f334(f248(x98201),f334(f334(f80(x98201),f334(f334(f81(x98201),x98202),x98203)),x98204)),f334(f334(f80(x98201),f334(f334(f81(x98201),x98205),x98203)),x98206)))+~P1(f334(f334(f248(x98201),f334(f334(f80(x98201),f334(f334(f81(x98201),f334(f334(f22(x98201),x98202),x98205)),x98203)),x98204)),x98206))
% 160.93/160.65 [9992]~P68(x99922)+~P1(f334(f61(x99921),x99926))+E(f334(f334(f6(x99921,x99922),f334(f334(f18(x99921,x99922,x99922),f334(f334(f18(x99921,x99922,f888(x99922,x99922)),f334(f334(f8(a876,f888(x99922,f888(x99922,x99922)),x99921),f100(x99922)),x99923)),x99924)),x99925)),x99926),f334(f334(f80(x99922),f334(f334(f6(x99921,x99922),x99924),f334(f334(f105(f888(x99921,a876)),x99926),f334(f254(x99921),x99923)))),f334(f334(f6(x99921,x99922),x99925),f334(f334(f105(f888(x99921,a876)),x99926),f334(f79(f888(x99921,a876)),f334(f254(x99921),x99923))))))
% 160.93/160.65 [10051]P1(f334(f334(f336(x100512),x100514),x100516))+P1(f334(f334(f336(x100512),x100515),x100516))+E(f334(f314(x100511,x100512,f334(f334(f7(x100511,x100512,x100512),f334(f334(f7(x100511,x100512,f888(x100512,x100512)),f334(f334(f8(a876,f888(x100512,f888(x100512,x100512)),x100511),f100(x100512)),f334(f334(f7(x100511,f888(x100511,a876),a876),f336(x100511)),x100513))),x100514)),x100515)),x100516),f196(f888(x100511,a876)))
% 160.93/160.65 [10052]P1(f334(f334(f336(x100522),x100525),x100526))+~P1(f334(f334(f336(x100522),x100524),x100526))+E(f334(f314(x100521,x100522,f334(f334(f7(x100521,x100522,x100522),f334(f334(f7(x100521,x100522,f888(x100522,x100522)),f334(f334(f8(a876,f888(x100522,f888(x100522,x100522)),x100521),f100(x100522)),f334(f334(f7(x100521,f888(x100521,a876),a876),f336(x100521)),x100523))),x100524)),x100525)),x100526),x100523)
% 160.93/160.65 [10053]P1(f334(f334(f336(x100532),x100534),x100536))+~P1(f334(f334(f336(x100532),x100535),x100536))+E(f334(f314(x100531,x100532,f334(f334(f7(x100531,x100532,x100532),f334(f334(f7(x100531,x100532,f888(x100532,x100532)),f334(f334(f8(a876,f888(x100532,f888(x100532,x100532)),x100531),f100(x100532)),f334(f334(f7(x100531,f888(x100531,a876),a876),f336(x100531)),x100533))),x100534)),x100535)),x100536),f334(f79(f888(x100531,a876)),x100533))
% 160.93/160.65 [10054]~P1(f334(f334(f336(x100542),x100544),x100546))+~P1(f334(f334(f336(x100542),x100545),x100546))+E(f334(f314(x100541,x100542,f334(f334(f7(x100541,x100542,x100542),f334(f334(f7(x100541,x100542,f888(x100542,x100542)),f334(f334(f8(a876,f888(x100542,f888(x100542,x100542)),x100541),f100(x100542)),f334(f334(f7(x100541,f888(x100541,a876),a876),f336(x100541)),x100543))),x100544)),x100545)),x100546),f257(f888(x100541,a876)))
% 160.93/160.65 [10183]P26(x101831,x101832,f334(f334(f312(f880(x101831)),f334(f334(f334(f92(x101831),f334(x101833,x101834)),f334(a26,x101834)),f334(x101835,x101834))),f196(f888(f880(x101831),a876))))+~P1(f334(f334(f336(a879),x101834),x101836))+~P26(x101831,f334(f334(f114(f888(f880(x101831),a876)),x101832),f334(f313(a879,f880(x101831),f334(f334(f18(a879,f888(x101831,f888(a877,a876)),f880(x101831)),f334(f334(f18(a879,a878,f888(f888(x101831,f888(a877,a876)),f880(x101831))),f334(f334(f8(f888(x101831,f888(a877,a876)),f888(a878,f888(f888(x101831,f888(a877,a876)),f880(x101831))),a879),f92(x101831)),x101833)),a26)),x101835)),x101836)),f334(f313(a879,f880(x101831),f334(f334(f18(a879,f888(x101831,f888(a877,a876)),f880(x101831)),f334(f334(f18(a879,a878,f888(f888(x101831,f888(a877,a876)),f880(x101831))),f334(f334(f8(f888(x101831,f888(a877,a876)),f888(a878,f888(f888(x101831,f888(a877,a876)),f880(x101831))),a879),f92(x101831)),x101833)),f334(f334(f8(f885(a878),a878,a879),f245(a878)),a28))),x101835)),x101836))
% 160.93/160.65 [8617]E(x86171,x86172)+~P54(x86174,x86175,x86173,x86176,x86177)+~E(f334(x86173,x86171),f334(x86173,x86172))
% 160.93/160.65 [6997]E(f334(f243(f885(x69971),x69972,f210(x69971),x69973),f334(x69974,x69975)),f334(f241(x69971),x69976))+~E(f334(x69974,x69975),f334(f241(x69972),x69977))+~E(f334(x69973,x69977),f334(f241(x69971),x69976))
% 160.93/160.65 [8649]~P11(x86496,x86495,x86497,x86494,x86491)+E(f334(f334(x86491,x86492),x86493),x86494)+P1(f334(f61(x86495),x86493))
% 160.93/160.65 [9499]P44(x94991,x94992,x94993,x94994,x94995,f334(f334(x94993,x94996),x94997))+~E(f334(f334(x94993,x94996),x94997),x94994)+~E(x94995,f196(f888(x94991,a876)))
% 160.93/160.65 [9685]~P1(f334(x96856,x96853))+~P1(f334(f334(f336(f887(x96852,x96852)),f334(f334(f269(x96852,x96852),x96854),x96855)),f334(x96857,x96853)))+P1(f334(f334(f336(f887(f887(x96851,x96852),f887(x96851,x96852))),f334(f334(f269(f887(x96851,x96852),f887(x96851,x96852)),f334(f334(f269(x96851,x96852),x96853),x96854)),f334(f334(f269(x96851,x96852),x96853),x96855))),f286(x96851,x96852,x96856,x96857)))
% 160.93/160.65 [10108]~P44(x101082,x101087,x101083,x101086,x101081,f334(f334(x101083,x101085),x101084))+E(f334(f334(x101083,f531(x101084,x101085,x101081,x101086,x101083,x101087,x101082)),f532(x101084,x101085,x101081,x101086,x101083,x101087,x101082)),f334(f334(x101083,x101085),x101084))+E(x101081,f196(f888(x101082,a876)))
% 160.93/160.65 [10109]~P44(x101097,x101096,x101091,x101094,x101095,f334(f334(x101091,x101092),x101093))+E(f334(f334(x101091,f531(x101093,x101092,x101095,x101094,x101091,x101096,x101097)),f532(x101093,x101092,x101095,x101094,x101091,x101096,x101097)),f334(f334(x101091,x101092),x101093))+E(f334(f334(x101091,x101092),x101093),x101094)
% 160.93/160.65 [9185]~P36(x91851,x91852,x91853,x91855,x91857)+P36(x91851,x91852,x91853,f334(f334(f153(x91851),x91854),x91855),f334(f334(f153(x91852),x91856),x91857))+~P1(f334(f334(x91853,x91854),x91856))
% 160.93/160.65 [9203]P36(x92031,x92032,x92033,x92034,x92035)+~P36(x92031,x92032,x92033,f334(f334(f136(x92031),x92036),x92034),f334(f334(f136(x92032),x92037),x92035))+~E(f334(f197(f882(x92031)),x92036),f334(f197(f882(x92032)),x92037))
% 160.93/160.65 [9204]P36(x92041,x92042,x92043,x92044,x92045)+~P36(x92041,x92042,x92043,f334(f334(f136(x92041),x92044),x92046),f334(f334(f136(x92042),x92045),x92047))+~E(f334(f197(f882(x92041)),x92044),f334(f197(f882(x92042)),x92045))
% 160.93/160.65 [9409]~P36(x94091,x94092,x94093,x94095,x94097)+~P36(x94091,x94092,x94093,x94094,x94096)+P36(x94091,x94092,x94093,f334(f334(f136(x94091),x94094),x94095),f334(f334(f136(x94092),x94096),x94097))
% 160.93/160.65 [9758]~P1(f334(f66(x97581,x97584,x97585,x97586,x97583),x97587))+P1(f334(f66(x97581,x97584,x97585,x97586,f334(f334(f312(x97581),x97582),x97583)),f334(f334(x97585,x97582),x97587)))+P1(f334(f334(f336(x97581),x97582),x97583))
% 160.93/160.65 [9890]~P27(x98903,x98901,x98904,f257(f888(x98903,a876)))+E(f334(f334(f180(x98901,x98902),f334(f334(f156(f887(x98903,x98902),f887(x98901,x98902)),f334(f273(x98903,x98902,f887(x98901,x98902)),f334(f334(f8(x98901,f888(x98902,f887(x98901,x98902)),x98903),f269(x98901,x98902)),x98904))),x98905)),f334(x98904,x98906)),f334(f241(x98902),x98907))+~E(f334(f334(f180(x98903,x98902),x98905),x98906),f334(f241(x98902),x98907))
% 160.93/160.65 [10129]~P44(x101292,x101297,x101296,x101295,x101291,f334(f334(x101296,x101294),x101293))+E(x101291,f196(f888(x101292,a876)))+P1(f334(f334(f336(x101292),f531(x101293,x101294,x101291,x101295,x101296,x101297,x101292)),x101291))
% 160.93/160.65 [10130]~P44(x101305,x101307,x101301,x101304,x101306,f334(f334(x101301,x101302),x101303))+E(f334(f334(x101301,x101302),x101303),x101304)+P1(f334(f334(f336(x101305),f531(x101303,x101302,x101306,x101304,x101301,x101307,x101305)),x101306))
% 160.93/160.65 [6786]~E(x67865,x67867)+~E(x67866,x67864)+E(f334(f334(f334(f334(f72(x67861,f885(x67862)),x67863),x67864),f334(f241(x67862),x67865)),x67866),f334(f241(x67862),x67867))
% 160.93/160.65 [6913]E(x69131,x69132)+~E(f334(x69135,x69131),f334(f241(x69134),x69137))+E(f334(f334(f334(f334(f72(x69133,f885(x69134)),x69135),x69132),f334(f241(x69134),x69136)),x69131),f334(f241(x69134),x69137))
% 160.93/160.65 [7634]E(x76341,x76342)+~E(x76343,x76344)+~E(f334(f334(f334(f334(f72(x76345,f885(x76346)),x76347),x76344),f334(f241(x76346),x76341)),x76343),f334(f241(x76346),x76342))
% 160.93/160.65 [7698]E(x76981,x76982)+E(f334(x76983,x76984),f334(f241(x76985),x76981))+~E(f334(f334(f334(f334(f72(x76986,f885(x76985)),x76983),x76987),f334(f241(x76985),x76982)),x76984),f334(f241(x76985),x76981))
% 160.93/160.65 [7699]E(x76991,x76992)+E(f334(x76993,x76991),f334(f241(x76994),x76995))+~E(f334(f334(f334(f334(f72(x76996,f885(x76994)),x76993),x76992),f334(f241(x76994),x76997)),x76991),f334(f241(x76994),x76995))
% 160.93/160.65 [8867]~P23(x88674,x88675,x88676,x88677,x88671)+~P1(f334(f61(x88675),x88673))+E(f334(f334(x88671,x88672),x88673),f334(f334(f334(f65(x88674,x88675,x88676),x88672),x88677),x88673))
% 160.93/160.65 [8868]~P11(x88684,x88685,x88686,x88687,x88681)+~P1(f334(f61(x88685),x88683))+E(f334(f334(x88681,x88682),x88683),f334(f334(f334(f65(x88684,x88685,x88686),x88682),x88687),x88683))
% 160.93/160.65 [9465]~P26(x94651,x94652,f334(f334(f312(f880(x94651)),f334(f334(f334(f92(x94651),x94653),x94654),x94657)),f196(f888(f880(x94651),a876))))+P26(x94651,x94652,f334(f334(f312(f880(x94651)),f334(f334(f334(f92(x94651),x94653),f33(x94654,x94655)),x94656)),f196(f888(f880(x94651),a876))))+~P26(x94651,x94652,f334(f334(f312(f880(x94651)),f334(f334(f334(f92(x94651),x94657),x94655),x94656)),f196(f888(f880(x94651),a876))))
% 160.93/160.65 [9658]~P25(x96583,x96584,x96585,x96587,x96586,x96581)+~P1(f334(f61(x96584),x96582))+E(f334(x96581,x96582),f334(f334(f334(f65(x96583,x96584,x96585),x96586),x96587),x96582))
% 160.93/160.65 [9814]P44(x98141,x98142,x98143,x98144,x98145,f334(f334(x98143,x98146),x98147))+~P44(x98141,x98142,x98143,x98144,f334(f334(f22(f888(x98141,a876)),x98145),f334(f334(f312(x98141),x98146),f196(f888(x98141,a876)))),x98147)+~P1(f334(f334(f336(x98141),x98146),x98145))
% 160.93/160.65 [10083]~P26(x100831,x100832,f334(f334(f312(f880(x100831)),f334(f334(f334(f92(x100831),f95(x100831,x100833,x100834)),x100835),x100837)),f196(f888(f880(x100831),a876))))+P26(x100831,x100832,f334(f334(f312(f880(x100831)),f334(f334(f334(f92(x100831),x100833),f30(x100834,x100835,x100836)),x100837)),f196(f888(f880(x100831),a876))))+~P26(x100831,x100832,f334(f334(f312(f880(x100831)),f334(f334(f334(f92(x100831),f95(x100831,x100833,f334(f73(a876,a876,a877,a329),x100834))),x100836),x100837)),f196(f888(f880(x100831),a876))))
% 160.93/160.65 [10154]~P44(x101542,x101543,x101544,x101545,x101541,f334(f334(x101544,x101547),x101546))+P44(x101542,x101543,x101544,x101545,f334(f334(f22(f888(x101542,a876)),x101541),f334(f334(f312(x101542),f531(x101546,x101547,x101541,x101545,x101544,x101543,x101542)),f196(f888(x101542,a876)))),f532(x101546,x101547,x101541,x101545,x101544,x101543,x101542))+E(x101541,f196(f888(x101542,a876)))
% 160.93/160.65 [10155]~P44(x101555,x101556,x101551,x101554,x101557,f334(f334(x101551,x101552),x101553))+P44(x101555,x101556,x101551,x101554,f334(f334(f22(f888(x101555,a876)),x101557),f334(f334(f312(x101555),f531(x101553,x101552,x101557,x101554,x101551,x101556,x101555)),f196(f888(x101555,a876)))),f532(x101553,x101552,x101557,x101554,x101551,x101556,x101555))+E(f334(f334(x101551,x101552),x101553),x101554)
% 160.93/160.65 [9192]E(f189(x91921,x91922,x91923,x91924,f334(f334(f161(x91922,x91925),x91926),x91927)),f189(x91921,x91922,x91923,x91924,x91925))+~P1(f334(f334(f249(a881),x91926),f334(f197(f882(x91922)),x91925)))+~P1(f334(f334(f248(a881),f334(f197(f882(x91921)),x91924)),x91926))
% 160.93/160.65 [9487]P1(f334(f334(f248(f888(f887(x94871,x94872),a876)),f334(f334(f291(x94871,x94873,x94872),x94874),x94875)),f334(f334(f291(x94871,x94873,x94872),x94876),x94877)))+~P1(f334(f334(f248(f888(f887(x94873,x94872),a876)),x94875),x94877))+~P1(f334(f334(f248(f888(f887(x94871,x94873),a876)),x94874),x94876))
% 160.93/160.65 [9825]~P1(f334(f334(f336(x98251),x98256),x98255))+P1(f334(f66(x98251,x98252,x98253,x98254,x98255),f334(f334(x98253,x98256),x98257)))+~P1(f334(f66(x98251,x98252,x98253,x98254,f334(f334(f22(f888(x98251,a876)),x98255),f334(f334(f312(x98251),x98256),f196(f888(x98251,a876))))),x98257))
% 160.93/160.65 [10214]~P141(x102141)+~P27(f887(x102142,x102143),x102141,f334(f273(x102142,x102143,x102141),f334(f334(f7(x102142,f888(x102143,x102141),f888(x102143,x102141)),f334(f334(f8(f888(x102141,x102141),f888(f888(x102143,x102141),f888(x102143,x102141)),x102142),f8(x102141,x102141,x102143)),f334(f334(f8(x102141,f888(x102141,x102141),x102142),f81(x102141)),x102144))),x102145)),f334(f334(f271(x102142,x102143),x102146),f334(f16(f888(x102143,a876),x102142),x102147)))+E(f334(f334(f6(x102141,x102141),f34(x102141)),f334(f254(x102141),f334(f334(f8(f888(x102142,a876),a876,x102141),f87(x102142)),f334(f334(f8(f888(x102142,f888(x102143,a876)),f888(x102142,a876),x102141),f334(f8(f888(x102143,a876),a876,x102142),f87(x102143))),f334(f334(f7(x102141,f888(x102142,f888(x102143,a876)),f888(x102142,f888(x102143,a876))),f334(f334(f8(f888(x102142,f888(f888(x102143,a876),f888(x102143,a876))),f888(f888(x102142,f888(x102143,a876)),f888(x102142,f888(x102143,a876))),x102141),f18(x102142,f888(x102143,a876),f888(x102143,a876))),f334(f334(f8(f888(x102142,f888(x102143,f888(a876,a876))),f888(x102142,f888(f888(x102143,a876),f888(x102143,a876))),x102141),f334(f8(f888(x102143,f888(a876,a876)),f888(f888(x102143,a876),f888(x102143,a876)),x102142),f18(x102143,a876,a876))),f334(f334(f8(f888(x102142,f888(x102143,a876)),f888(x102142,f888(x102143,f888(a876,a876))),x102141),f334(f8(f888(x102143,a876),f888(x102143,f888(a876,a876)),x102142),f334(f8(a876,f888(a876,a876),x102143),a332))),f334(f334(f7(x102141,f888(x102142,f888(x102143,x102141)),f888(x102142,f888(x102143,a876))),f334(f334(f8(f888(f888(x102143,x102141),f888(x102143,a876)),f888(f888(x102142,f888(x102143,x102141)),f888(x102142,f888(x102143,a876))),x102141),f8(f888(x102143,x102141),f888(x102143,a876),x102142)),f334(f334(f8(f888(x102141,a876),f888(f888(x102143,x102141),f888(x102143,a876)),x102141),f8(x102141,a876,x102143)),a331))),f334(f334(f7(x102142,f888(x102143,x102141),f888(x102143,x102141)),f334(f334(f8(f888(x102141,x102141),f888(f888(x102143,x102141),f888(x102143,x102141)),x102142),f8(x102141,x102141,x102143)),f334(f334(f8(x102141,f888(x102141,x102141),x102142),f81(x102141)),x102144))),x102145)))))),f334(f334(f7(x102142,f888(x102143,a876),f888(x102143,a876)),f334(f334(f8(f888(a876,a876),f888(f888(x102143,a876),f888(x102143,a876)),x102142),f8(a876,a876,x102143)),f334(f334(f8(a876,f888(a876,a876),x102142),a332),f334(f334(f7(x102142,f888(x102142,a876),a876),f336(x102142)),x102146)))),f334(f334(f7(x102143,f888(x102143,a876),a876),f336(x102143)),x102147))))))),f334(f334(f81(x102141),f334(f334(f6(x102142,x102141),x102144),x102146)),f334(f334(f6(x102143,x102141),x102145),x102147)))
% 160.93/160.65 [9656]~P1(f334(f334(x96564,x96566),x96568))+~P1(f334(f334(x96565,x96568),x96567))+P1(f334(f334(f270(x96561,x96562,x96563,x96564,x96565),x96566),x96567))
% 160.93/160.65 [9253]~P21(x92538,x92531,x92533,x92535)+~P1(f334(f61(x92538),x92536))+E(f334(f73(x92531,x92531,x92532,f334(x92533,x92534)),f334(f73(x92531,x92531,x92532,f334(x92535,x92536)),x92537)),f334(f73(x92531,x92531,x92532,f334(x92535,x92536)),f334(f73(x92531,x92531,x92532,f334(x92533,x92534)),x92537)))
% 160.93/160.65 [9646]~P24(x96467,x96462,x96465,x96468,x96466,x96461)+~P1(f334(f61(x96462),x96464))+E(f334(x96461,f334(f334(f312(x96462),x96463),x96464)),f334(f334(x96465,f334(x96466,x96463)),f334(x96461,x96464)))
% 160.93/160.65 [9767]~P27(x97672,x97674,x97676,x97678)+~P27(x97671,x97673,x97675,x97677)+P27(f887(x97671,x97672),f887(x97673,x97674),f274(x97671,x97673,x97672,x97674,x97675,x97676),f334(f334(f271(x97671,x97672),x97677),f334(f16(f888(x97672,a876),x97671),x97678)))
% 160.93/160.65 [9433]P1(f334(f334(f336(f887(x94331,x94332)),f334(f334(f269(x94331,x94332),x94333),x94334)),f334(f334(f291(x94331,x94335,x94332),x94336),x94337)))+~P1(f334(f334(f336(f887(x94331,x94335)),f334(f334(f269(x94331,x94335),x94333),x94338)),x94336))+~P1(f334(f334(f336(f887(x94335,x94332)),f334(f334(f269(x94335,x94332),x94338),x94334)),x94337))
% 160.93/160.65 [9625]~P1(f334(f334(f248(f888(f887(x96253,x96252),a876)),x96255),f334(f334(f271(x96253,x96252),x96258),f334(f16(f888(x96252,a876),x96253),x96257))))+~P1(f334(f334(f248(f888(f887(x96251,x96253),a876)),x96254),f334(f334(f271(x96251,x96253),x96256),f334(f16(f888(x96253,a876),x96251),x96258))))+P1(f334(f334(f248(f888(f887(x96251,x96252),a876)),f334(f334(f291(x96251,x96253,x96252),x96254),x96255)),f334(f334(f271(x96251,x96252),x96256),f334(f16(f888(x96252,a876),x96251),x96257))))
% 160.93/160.65 [9680]~E(x96803,x96805)+P1(f334(f334(f336(f887(f887(x96801,x96802),f887(x96801,x96802))),f334(f334(f269(f887(x96801,x96802),f887(x96801,x96802)),f334(f334(f269(x96801,x96802),x96803),x96804)),f334(f334(f269(x96801,x96802),x96805),x96806))),f326(x96801,x96802,x96807,x96808)))+~P1(f334(f334(f336(f887(x96802,x96802)),f334(f334(f269(x96802,x96802),x96804),x96806)),x96808))
% 160.93/160.65 [9790]E(x97901,x97902)+~P1(f334(f334(f336(f887(f887(x97903,x97905),f887(x97903,x97905))),f334(f334(f269(f887(x97903,x97905),f887(x97903,x97905)),f334(f334(f269(x97903,x97905),x97901),x97906)),f334(f334(f269(x97903,x97905),x97902),x97907))),f326(x97903,x97905,x97904,x97908)))+P1(f334(f334(f336(f887(x97903,x97903)),f334(f334(f269(x97903,x97903),x97901),x97902)),x97904))
% 160.93/160.65 [9807]~P1(f334(f334(f336(f887(f887(x98071,x98075),f887(x98071,x98075))),f334(f334(f269(f887(x98071,x98075),f887(x98071,x98075)),f334(f334(f269(x98071,x98075),x98072),x98076)),f334(f334(f269(x98071,x98075),x98073),x98077))),f326(x98071,x98075,x98074,x98078)))+P1(f334(f334(f336(f887(x98071,x98071)),f334(f334(f269(x98071,x98071),x98072),x98073)),x98074))+P1(f334(f334(f336(f887(x98075,x98075)),f334(f334(f269(x98075,x98075),x98076),x98077)),x98078))
% 160.93/160.65 [9711]~P25(x97117,x97115,x97111,x97118,x97112,x97114)+~P1(f334(f61(x97115),x97116))+E(f334(f334(x97111,f334(x97112,x97113)),f334(x97114,f334(f334(f22(f888(x97115,a876)),x97116),f334(f334(f312(x97115),x97113),f196(f888(x97115,a876)))))),f334(x97114,f334(f334(f312(x97115),x97113),x97116)))
% 160.93/160.65 [9211]~P1(f334(f334(f334(x92115,x92118),x92116),x92117))+~P1(f334(f334(f336(x92111),x92118),x92114))+P1(f334(f334(f334(f334(f41(x92111,f888(x92112,f888(x92113,a876))),x92114),x92115),x92116),x92117))
% 160.93/160.65 [9420]P1(f334(f334(f334(x94201,x94202),x94203),x94204))+~P1(f334(f334(f336(x94205),x94202),x94206))+~P1(f334(f334(f334(f334(f42(x94205,f888(x94207,f888(x94208,a876))),x94206),x94201),x94203),x94204))
% 160.93/160.65 [9618]~P23(x96183,x96182,x96184,x96188,x96181)+~P1(f334(f61(x96182),x96187))+E(f334(f334(x96181,f334(f334(f18(x96182,x96183,x96183),f334(f334(f8(x96183,f888(x96183,x96183),x96182),x96184),x96185)),x96186)),x96187),f334(f334(x96184,f334(f334(x96181,x96185),x96187)),f334(f334(x96181,x96186),x96187)))
% 160.93/160.65 [9898]~E(f334(f313(x98982,x98984,x98986),x98988),x989810)+~E(f334(f313(x98981,x98983,x98985),x98987),x98989)+E(f334(f313(f887(x98981,x98982),f887(x98983,x98984),f274(x98981,x98983,x98982,x98984,x98985,x98986)),f334(f334(f271(x98981,x98982),x98987),f334(f16(f888(x98982,a876),x98981),x98988))),f334(f334(f271(x98983,x98984),x98989),f334(f16(f888(x98984,a876),x98983),x989810)))
% 160.93/160.65 [8233]~P31(a5000)+~P9(a5000)+~P1(f334(a25,x82331))+P26(a877,f196(f888(f880(a877),a876)),f334(f334(f312(f880(a877)),f334(f334(f334(f92(a877),a331),x82331),f334(a202,x82331))),f196(f888(f880(a877),a876))))
% 160.93/160.65 [4841]~P108(x48412)+~P16(x48412,x48411)+P16(x48412,f118(x48412,x48411))+E(x48411,f117(x48412))
% 160.93/160.65 [4842]~P108(x48422)+~P16(x48422,x48421)+P16(x48422,f748(x48421,x48422))+E(x48421,f117(x48422))
% 160.93/160.65 [5073]~P5(x50732)+E(f10(x50732,x50731),f39(x50732,x50731))+E(x50731,f196(f888(x50732,a876)))+~P1(f334(f61(x50732),x50731))
% 160.93/160.65 [5074]~P5(x50742)+E(f11(x50742,x50741),f40(x50742,x50741))+E(x50741,f196(f888(x50742,a876)))+~P1(f334(f61(x50742),x50741))
% 160.93/160.65 [5234]~P108(x52342)+~P16(x52342,x52341)+E(x52341,f117(x52342))+E(f334(f334(f153(x52342),f766(x52341,x52342)),f748(x52341,x52342)),x52341)
% 160.93/160.65 [6022]~P2(x60222)+E(x60221,f196(f888(x60222,a876)))+P1(f334(f334(f248(x60222),f11(x60222,x60221)),f10(x60222,x60221)))+~P1(f334(f61(x60222),x60221))
% 160.93/160.65 [6034]~P40(x60342)+~P40(x60341)+E(x60341,x60342)+~E(f334(f313(a1,a881,a108),x60341),f334(f313(a1,a881,a108),x60342))
% 160.93/160.65 [9065]~P111(x90651)+~P1(f334(f334(f336(x90651),x90652),f113(x90651)))+P1(f334(f334(f249(x90651),f334(f334(f80(x90651),f334(f334(f80(x90651),f78(x90651)),x90652)),x90652)),f2(x90651)))+~P1(f334(f334(f249(x90651),x90652),f2(x90651)))
% 160.93/160.65 [9308]~P111(x93081)+~P1(f334(f334(f336(x93081),x93082),f113(x93081)))+~P1(f334(f334(f249(x93081),f334(f334(f80(x93081),f334(f334(f80(x93081),f78(x93081)),x93082)),x93082)),f2(x93081)))+P1(f334(f334(f249(x93081),x93082),f2(x93081)))
% 160.93/160.65 [4897]~P141(x48972)+~P113(x48972)+E(x48971,f2(a881))+E(f334(f334(f259(x48972),f2(x48972)),x48971),f2(x48972))
% 160.93/160.65 [4901]~P141(x49011)+~P113(x49011)+~E(x49012,f2(a881))+E(f334(f334(f259(x49011),f2(x49011)),x49012),f78(x49011))
% 160.93/160.65 [5060]~P140(x50602)+E(x50601,f78(x50602))+E(x50601,f334(f79(x50602),f78(x50602)))+~E(f334(f334(f81(x50602),x50601),x50601),f78(x50602))
% 160.93/160.65 [5314]~P88(x53142)+E(x53141,f2(x53142))+E(f82(x53142,x53141),f334(f79(x53142),f78(x53142)))+P1(f334(f334(f249(x53142),f2(x53142)),x53141))
% 160.93/160.65 [5547]~P88(x55472)+E(f82(x55472,x55471),f78(x55472))+E(x55471,f2(x55472))+~P1(f334(f334(f249(x55472),f2(x55472)),x55471))
% 160.93/160.65 [5556]E(x55561,x55562)+~E(f334(f107(a881),x55561),f334(f107(a881),x55562))+P1(f334(a201,f334(f107(a1),x55562)))+P1(f334(a201,f334(f107(a1),x55561)))
% 160.93/160.65 [5606]~P90(x56061)+~E(x56062,f2(x56061))+E(f334(f334(f80(x56061),x56062),x56062),f2(x56061))+~P1(f334(f334(f336(x56061),x56062),f113(x56061)))
% 160.93/160.65 [5644]E(x56441,f2(a1))+~E(f334(f334(f38(a1),x56442),x56441),f2(a1))+P1(f334(f334(f249(a1),x56441),x56442))+P1(f334(f334(f249(a1),x56442),x56441))
% 160.93/160.65 [5675]E(x56751,f2(a1))+~E(f334(f334(f38(a1),x56752),x56751),f2(a1))+P1(f334(f334(f248(a1),x56752),f2(a1)))+P1(f334(f334(f249(a1),x56752),x56751))
% 160.93/160.65 [5708]E(x57081,f2(a1))+~E(f334(f334(f38(a1),x57082),x57081),f2(a1))+P1(f334(f334(f248(a1),f2(a1)),x57082))+P1(f334(f334(f249(a1),x57081),x57082))
% 160.93/160.65 [5744]~P90(x57442)+E(x57441,f2(x57442))+~E(f334(f334(f80(x57442),x57441),x57441),f2(x57442))+~P1(f334(f334(f336(x57442),x57441),f113(x57442)))
% 160.93/160.65 [5804]E(f334(f107(a881),x58041),f334(f107(a881),x58042))+~E(f334(f107(a1),x58042),f2(a1))+P1(f334(a201,f334(f107(a1),x58042)))+~P1(f334(a201,f334(f107(a1),x58041)))
% 160.93/160.65 [5831]~E(f334(f107(a881),x58312),f334(f107(a881),x58311))+E(f334(f107(a1),x58311),f2(a1))+P1(f334(a201,f334(f107(a1),x58311)))+~P1(f334(a201,f334(f107(a1),x58312)))
% 160.93/160.65 [5840]~P108(x58402)+E(x58401,f196(f888(x58402,a876)))+~P1(f334(f61(x58402),x58401))+P1(f334(f334(f336(x58402),f14(x58402,x58401)),x58401))
% 160.93/160.65 [5841]~P108(x58412)+E(x58411,f196(f888(x58412,a876)))+~P1(f334(f61(x58412),x58411))+P1(f334(f334(f336(x58412),f15(x58412,x58411)),x58411))
% 160.93/160.65 [6002]~P111(x60021)+~P93(x60021)+P1(f334(f334(f249(x60021),f2(x60021)),f334(f107(x60021),x60022)))+~P1(f334(f334(f249(a1),a83),x60022))
% 160.93/160.65 [6003]~P111(x60031)+~P93(x60031)+P1(f334(f334(f248(x60031),f2(x60031)),f334(f107(x60031),x60032)))+~P1(f334(f334(f248(a1),a83),x60032))
% 160.93/160.65 [6021]~P111(x60211)+~P93(x60211)+E(f334(f75(x60211),f334(f107(x60211),x60212)),f334(f107(x60211),x60212))+P1(f334(f334(f249(x60211),f334(f107(x60211),x60212)),f2(x60211)))
% 160.93/160.65 [6061]E(x60611,x60612)+~E(f334(a108,x60611),f334(a108,x60612))+~P1(f334(f334(f248(a1),f2(a1)),x60612))+~P1(f334(f334(f248(a1),f2(a1)),x60611))
% 160.93/160.65 [6260]~P93(x62602)+~P111(x62602)+~P1(f334(f334(f249(x62602),f2(x62602)),f334(f107(x62602),x62601)))+P1(f334(f334(f249(a1),a83),x62601))
% 160.93/160.65 [6261]~P93(x62612)+~P111(x62612)+~P1(f334(f334(f248(x62612),f2(x62612)),f334(f107(x62612),x62611)))+P1(f334(f334(f248(a1),a83),x62611))
% 160.93/160.65 [6266]~P111(x62661)+~P93(x62661)+P1(f334(f334(f249(x62661),f334(f107(x62661),x62662)),f2(x62661)))+~P1(f334(f334(f249(a1),x62662),a83))
% 160.93/160.65 [6267]~P111(x62671)+~P93(x62671)+P1(f334(f334(f248(x62671),f334(f107(x62671),x62672)),f2(x62671)))+~P1(f334(f334(f248(a1),x62672),a83))
% 160.93/160.65 [6573]~P93(x65732)+~P111(x65732)+~P1(f334(f334(f249(x65732),f334(f107(x65732),x65731)),f2(x65732)))+P1(f334(f334(f249(a1),x65731),a83))
% 160.93/160.65 [6574]~P93(x65742)+~P111(x65742)+~P1(f334(f334(f248(x65742),f334(f107(x65742),x65741)),f2(x65742)))+P1(f334(f334(f248(a1),x65741),a83))
% 160.93/160.65 [6666]~P111(x66661)+~P93(x66661)+E(f334(f75(x66661),f334(f107(x66661),x66662)),f334(f79(x66661),f334(f107(x66661),x66662)))+~P1(f334(f334(f249(x66661),f334(f107(x66661),x66662)),f2(x66661)))
% 160.93/160.65 [6684]E(f334(f107(a881),x66841),f334(f107(a881),x66842))+~E(f334(f107(a1),x66842),f2(a1))+~P1(f334(f334(f248(a1),f334(f107(a1),x66841)),f2(a1)))+~P1(f334(a201,f334(f107(a1),x66841)))
% 160.93/160.65 [7563]~P108(x75632)+E(x75631,f196(f888(x75632,a876)))+~P1(f334(f61(x75632),x75631))+P1(f334(f334(f248(x75632),f13(x75632,f246(x75632),x75631)),f12(x75632,f247(x75632),x75631)))
% 160.93/160.65 [7878]~P40(x78782)+~P6(x78781)+P1(f334(f334(f336(a1),x78781),x78782))+~P1(f334(f334(f336(a881),f334(a108,x78781)),f334(f313(a1,a881,a108),x78782)))
% 160.93/160.65 [8149]~P60(x81492)+P1(f334(x81491,f210(x81492)))+~P1(f334(f57(f885(x81492)),x81491))+P1(f334(f57(x81492),f334(f334(f8(f885(x81492),a876,x81492),x81491),f241(x81492))))
% 160.93/160.65 [8625]~P60(x86251)+~P1(f334(x86252,f210(x86251)))+P1(f334(f58(f885(x86251)),x86252))+~P1(f334(f58(x86251),f334(f334(f8(f885(x86251),a876,x86251),x86252),f241(x86251))))
% 160.93/160.65 [5837]~P139(x58372)+E(x58371,f2(a1))+E(f334(f79(x58372),f334(f106(x58372),f334(f79(a1),x58371))),f334(f106(x58372),x58371))+~P1(f334(f334(f249(a1),x58371),f2(a1)))
% 160.93/160.65 [5910]~P90(x59101)+~P93(x59101)+~P32(x59101,f334(f107(x59101),x59102))+P32(x59101,f334(f107(x59101),f334(f334(f80(a1),x59102),x59102)))
% 160.93/160.65 [6248]~P75(x62482)+E(x62481,f196(f888(x62482,a876)))+E(f15(x62482,f334(f313(x62482,x62482,f79(x62482)),x62481)),f334(f79(x62482),f14(x62482,x62481)))+~P1(f334(f61(x62482),x62481))
% 160.93/160.65 [6249]~P75(x62492)+E(x62491,f196(f888(x62492,a876)))+E(f14(x62492,f334(f313(x62492,x62492,f79(x62492)),x62491)),f334(f79(x62492),f15(x62492,x62491)))+~P1(f334(f61(x62492),x62491))
% 160.93/160.65 [6281]~P90(x62811)+~P93(x62811)+P32(x62811,f334(f107(x62811),x62812))+~P32(x62811,f334(f107(x62811),f334(f334(f80(a1),x62812),x62812)))
% 160.93/160.65 [6369]E(x63691,f2(a1))+E(f334(a50,f49(f334(f79(a1),x63691),f334(f79(a1),x63692))),f45(x63691,x63692))+P1(f334(f334(f248(a1),f2(a1)),x63692))+~P1(f334(f334(f248(a1),f2(a1)),x63691))
% 160.93/160.65 [8478]~P31(a5000)+~P1(f334(a25,x84781))+P26(a877,x84782,f334(f334(f312(f880(a877)),f334(f334(f334(f92(a877),a331),x84781),f334(a202,x84781))),f196(f888(f880(a877),a876))))+P1(f334(f334(f336(a879),f594(x84781,x84782)),f186(a879,a878,a28)))
% 160.93/160.65 [8672]~P40(x86722)+~P40(x86721)+P1(f334(f334(f249(f888(a881,a876)),f334(f313(a1,a881,a108),x86721)),f334(f313(a1,a881,a108),x86722)))+~P1(f334(f334(f249(f888(a1,a876)),x86721),x86722))
% 160.93/160.65 [8885]~E(f769(x88852,x88851),f770(x88852,x88851))+~P1(f334(f139(x88851),f771(x88852,x88851)))+~P1(f334(f139(f882(x88851)),x88852))+P1(f334(f139(x88851),f334(f144(f882(x88851),f882(x88851),f136(x88851),f117(x88851)),x88852)))
% 160.93/160.65 [8984]~P40(x89842)+~P40(x89841)+~P1(f334(f334(f249(f888(a881,a876)),f334(f313(a1,a881,a108),x89841)),f334(f313(a1,a881,a108),x89842)))+P1(f334(f334(f249(f888(a1,a876)),x89841),x89842))
% 160.93/160.65 [8985]~P40(x89852)+~P40(x89851)+~P1(f334(f334(f248(f888(a881,a876)),f334(f313(a1,a881,a108),x89851)),f334(f313(a1,a881,a108),x89852)))+P1(f334(f334(f248(f888(a1,a876)),x89851),x89852))
% 160.93/160.65 [8991]~E(f769(x89912,x89911),f770(x89912,x89911))+~P1(f334(f139(f882(x89911)),x89912))+P1(f334(f139(x89911),f334(f144(f882(x89911),f882(x89911),f136(x89911),f117(x89911)),x89912)))+P1(f334(f334(f336(f882(x89911)),f771(x89912,x89911)),f334(f174(f882(x89911)),x89912)))
% 160.93/160.65 [9032]~P1(f334(f139(x90321),f771(x90322,x90321)))+~P1(f334(f139(f882(x90321)),x90322))+P1(f334(f139(x90321),f334(f144(f882(x90321),f882(x90321),f136(x90321),f117(x90321)),x90322)))+P1(f334(f334(f336(f882(x90321)),f770(x90322,x90321)),f334(f174(f882(x90321)),x90322)))
% 160.93/160.65 [9033]~P1(f334(f139(x90331),f771(x90332,x90331)))+~P1(f334(f139(f882(x90331)),x90332))+P1(f334(f139(x90331),f334(f144(f882(x90331),f882(x90331),f136(x90331),f117(x90331)),x90332)))+P1(f334(f334(f336(f882(x90331)),f769(x90332,x90331)),f334(f174(f882(x90331)),x90332)))
% 160.93/160.65 [9112]~P1(f334(f139(f882(x91121)),x91122))+P1(f334(f139(x91121),f334(f144(f882(x91121),f882(x91121),f136(x91121),f117(x91121)),x91122)))+P1(f334(f334(f336(f882(x91121)),f770(x91122,x91121)),f334(f174(f882(x91121)),x91122)))+P1(f334(f334(f336(f882(x91121)),f771(x91122,x91121)),f334(f174(f882(x91121)),x91122)))
% 160.93/160.65 [9113]~P1(f334(f139(f882(x91131)),x91132))+P1(f334(f139(x91131),f334(f144(f882(x91131),f882(x91131),f136(x91131),f117(x91131)),x91132)))+P1(f334(f334(f336(f882(x91131)),f769(x91132,x91131)),f334(f174(f882(x91131)),x91132)))+P1(f334(f334(f336(f882(x91131)),f771(x91132,x91131)),f334(f174(f882(x91131)),x91132)))
% 160.93/160.65 [9126]~E(f334(f334(f105(f888(x91261,a876)),f334(f174(x91261),f770(x91262,x91261))),f334(f174(x91261),f769(x91262,x91261))),f196(f888(x91261,a876)))+~P1(f334(f139(x91261),f771(x91262,x91261)))+~P1(f334(f139(f882(x91261)),x91262))+P1(f334(f139(x91261),f334(f144(f882(x91261),f882(x91261),f136(x91261),f117(x91261)),x91262)))
% 160.93/160.65 [9188]~E(f334(f334(f105(f888(x91881,a876)),f334(f174(x91881),f770(x91882,x91881))),f334(f174(x91881),f769(x91882,x91881))),f196(f888(x91881,a876)))+~P1(f334(f139(f882(x91881)),x91882))+P1(f334(f139(x91881),f334(f144(f882(x91881),f882(x91881),f136(x91881),f117(x91881)),x91882)))+P1(f334(f334(f336(f882(x91881)),f771(x91882,x91881)),f334(f174(f882(x91881)),x91882)))
% 160.93/160.65 [9457]E(x94571,f2(a1))+E(x94572,f2(a1))+E(f334(f334(f86(a1,f887(a1,a1)),f334(f334(a230,x94572),x94571)),f334(f334(f18(a1,a1,f887(a1,a1)),f334(f334(f8(a1,f888(a1,f887(a1,a1)),a1),f269(a1,a1)),f334(f38(a1),x94572))),f334(f38(a1),x94571))),f228(x94572,x94571))+P1(f334(f334(f249(a1),x94571),f2(a1)))
% 160.93/160.65 [9542]~P31(a5000)+~P1(f334(a25,x95422))+P26(a877,x95421,f334(f334(f312(f880(a877)),f334(f334(f334(f92(a877),a331),x95422),f334(a202,x95422))),f196(f888(f880(a877),a876))))+~P26(a877,x95421,f334(f334(f312(f880(a877)),f334(f334(f334(f92(a877),a331),f334(a26,f594(x95422,x95421))),f334(a202,f334(a26,f594(x95422,x95421))))),f196(f888(f880(a877),a876))))
% 160.93/160.65 [8216]~P93(x82162)+~P111(x82162)+~P1(f334(f334(f249(x82162),f334(f107(x82162),x82161)),f78(x82162)))+P1(f334(f334(f249(a1),x82161),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))
% 160.93/160.65 [8217]~P93(x82172)+~P111(x82172)+~P1(f334(f334(f248(x82172),f334(f107(x82172),x82171)),f78(x82172)))+P1(f334(f334(f248(a1),x82171),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))
% 160.93/160.65 [8487]~P111(x84871)+~P93(x84871)+P1(f334(f334(f249(x84871),f334(f107(x84871),x84872)),f78(x84871)))+~P1(f334(f334(f249(a1),x84872),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))
% 160.93/160.65 [8488]~P111(x84881)+~P93(x84881)+P1(f334(f334(f248(x84881),f334(f107(x84881),x84882)),f78(x84881)))+~P1(f334(f334(f248(a1),x84882),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))
% 160.93/160.65 [8698]~P93(x86982)+~P111(x86982)+~P1(f334(f334(f249(x86982),f78(x86982)),f334(f107(x86982),x86981)))+P1(f334(f334(f249(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),x86981))
% 160.93/160.65 [8699]~P93(x86992)+~P111(x86992)+~P1(f334(f334(f248(x86992),f78(x86992)),f334(f107(x86992),x86991)))+P1(f334(f334(f248(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),x86991))
% 160.93/160.65 [9071]~P111(x90711)+~P93(x90711)+P1(f334(f334(f249(x90711),f78(x90711)),f334(f107(x90711),x90712)))+~P1(f334(f334(f249(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),x90712))
% 160.93/160.65 [9072]~P111(x90721)+~P93(x90721)+P1(f334(f334(f248(x90721),f78(x90721)),f334(f107(x90721),x90722)))+~P1(f334(f334(f248(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),x90722))
% 160.93/160.65 [9590]~P140(x95902)+E(x95901,f78(x95902))+E(x95901,f334(f79(x95902),f78(x95902)))+~E(f334(f334(f259(x95902),x95901),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f78(x95902))
% 160.93/160.65 [9866]~P63(x98661)+~P93(x98661)+~P1(f334(f334(f249(x98661),f2(x98661)),x98662))+P1(f334(f334(f249(x98661),f2(x98661)),f334(f334(f292(x98661),x98662),f334(f107(x98661),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))))
% 160.93/160.65 [9928]~P63(x99281)+~P93(x99281)+P1(f334(f334(f249(x99281),f2(x99281)),x99282))+~P1(f334(f334(f249(x99281),f2(x99281)),f334(f334(f292(x99281),x99282),f334(f107(x99281),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))))
% 160.93/160.65 [10182]~P139(x101822)+E(x101821,f2(a1))+P1(f334(f334(f249(a1),x101821),f2(a1)))+E(f334(f334(f273(a1,a1,x101822),f334(f334(f7(a1,f888(a1,f888(x101822,x101822)),f888(a1,x101822)),f334(f334(f8(f888(f888(x101822,x101822),x101822),f888(f888(a1,f888(x101822,x101822)),f888(a1,x101822)),a1),f8(f888(x101822,x101822),x101822,a1)),f334(f334(f8(x101822,f888(f888(x101822,x101822),x101822),a1),f86(x101822,x101822)),f106(x101822)))),f334(f334(f7(a1,f888(x101822,x101822),f888(x101822,x101822)),f334(f334(f8(f888(x101822,f888(x101822,x101822)),f888(f888(x101822,x101822),f888(x101822,x101822)),a1),f18(x101822,x101822,x101822)),f334(f334(f7(a1,f888(x101822,x101822),f888(x101822,f888(x101822,x101822))),f334(f334(f8(f888(x101822,f888(x101822,x101822)),f888(f888(x101822,x101822),f888(x101822,f888(x101822,x101822))),a1),f8(x101822,f888(x101822,x101822),x101822)),f334(f334(f8(a876,f888(x101822,f888(x101822,x101822)),a1),f100(x101822)),f334(f334(f7(a1,a1,a876),a331),f2(a1))))),f334(f334(f18(x101822,x101822,x101822),f80(x101822)),f5(x101822))))),f334(f334(f7(x101822,x101822,x101822),f334(f334(f8(x101822,f888(x101822,x101822),x101822),f80(x101822)),f334(f334(f18(x101822,x101822,x101822),f80(x101822)),f5(x101822)))),f78(x101822))))),f45(x101821,f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f106(x101822),x101821))
% 160.93/160.65 [5229]~P60(x52293)+~P37(x52293,x52292,f55(x52293))+E(x52291,f783(x52292,x52293))+~P1(f334(x52292,x52291))
% 160.93/160.65 [5384]~P60(x53841)+P37(x53841,x53842,f55(x53841))+~E(f784(x53842,x53841,x53843),x53843)+~P1(f334(x53842,x53843))
% 160.93/160.65 [4868]~P90(x48683)+~P93(x48683)+E(x48681,x48682)+~E(f334(f107(x48683),x48681),f334(f107(x48683),x48682))
% 160.93/160.65 [6001]~P60(x60011)+P37(x60011,x60012,f55(x60011))+~P1(f334(x60012,x60013))+P1(f334(x60012,f784(x60012,x60011,x60013)))
% 160.93/160.65 [6011]~P1(f334(x60111,x60112))+~P1(f334(x60111,x60113))+~P1(f334(f334(f248(a881),x60113),f418(x60112,x60111)))+P1(f334(x60111,f2(a881)))
% 160.93/160.65 [6432]P146(x64322,x64323,x64321)+E(x64321,f2(a1))+P1(f334(f334(f248(a1),f2(a1)),f814(x64321,x64323,x64322)))+P1(f334(f334(f249(a1),x64321),f2(a1)))
% 160.93/160.65 [6433]P145(x64332,x64333,x64331)+E(x64331,f2(a1))+P1(f334(f334(f248(a1),f2(a1)),f823(x64331,x64333,x64332)))+P1(f334(f334(f249(a1),x64331),f2(a1)))
% 160.93/160.65 [6553]P145(x65531,x65532,x65533)+~P1(f334(x65531,x65532))+P1(f334(f334(f248(a1),f2(a1)),f823(x65533,x65532,x65531)))+P1(f334(f334(f249(a1),x65533),f2(a1)))
% 160.93/160.65 [6579]P146(x65791,x65792,x65793)+P1(f334(f334(f248(a1),f2(a1)),f814(x65793,x65792,x65791)))+~P1(f334(x65791,f2(a1)))+P1(f334(f334(f249(a1),x65793),f2(a1)))
% 160.93/160.65 [6607]P146(x66072,x66073,x66071)+E(x66071,f2(a1))+~P1(f334(x66072,f815(x66071,x66073,x66072)))+P1(f334(f334(f249(a1),x66071),f2(a1)))
% 160.93/160.65 [6608]P145(x66082,x66083,x66081)+E(x66081,f2(a1))+~P1(f334(x66082,f823(x66081,x66083,x66082)))+P1(f334(f334(f249(a1),x66081),f2(a1)))
% 160.93/160.65 [6709]~P5(x67091)+~P108(x67091)+~P1(f334(f334(f249(x67091),x67092),f39(x67091,x67093)))+P1(f334(f334(f249(x67091),x67092),f850(x67093,x67092,x67091)))
% 160.93/160.65 [6718]P145(x67181,x67182,x67183)+~P1(f334(x67181,x67182))+~P1(f334(x67181,f823(x67183,x67182,x67181)))+P1(f334(f334(f249(a1),x67183),f2(a1)))
% 160.93/160.65 [6750]P146(x67501,x67502,x67503)+~P1(f334(x67501,f815(x67503,x67502,x67501)))+~P1(f334(x67501,f2(a1)))+P1(f334(f334(f249(a1),x67503),f2(a1)))
% 160.93/160.65 [7000]P146(x70002,x70003,x70001)+E(x70001,f2(a1))+P1(f334(f334(f248(a1),f2(a1)),f814(x70001,x70003,x70002)))+P1(f334(f334(f249(a1),x70001),f813(x70001,x70003,x70002)))
% 160.93/160.65 [7001]P145(x70012,x70013,x70011)+E(x70011,f2(a1))+P1(f334(f334(f248(a1),f2(a1)),f823(x70011,x70013,x70012)))+P1(f334(f334(f249(a1),x70011),f822(x70011,x70013,x70012)))
% 160.93/160.65 [7118]P145(x71181,x71182,x71183)+~P1(f334(x71181,x71182))+P1(f334(f334(f248(a1),f2(a1)),f823(x71183,x71182,x71181)))+P1(f334(f334(f249(a1),x71183),f822(x71183,x71182,x71181)))
% 160.93/160.65 [7137]P146(x71371,x71372,x71373)+P1(f334(f334(f248(a1),f2(a1)),f814(x71373,x71372,x71371)))+P1(f334(f334(f249(a1),x71373),f813(x71373,x71372,x71371)))+~P1(f334(x71371,f2(a1)))
% 160.93/160.65 [7170]P146(x71702,x71703,x71701)+E(x71701,f2(a1))+~P1(f334(x71702,f815(x71701,x71703,x71702)))+P1(f334(f334(f249(a1),x71701),f813(x71701,x71703,x71702)))
% 160.93/160.65 [7171]P145(x71712,x71713,x71711)+E(x71711,f2(a1))+~P1(f334(x71712,f823(x71711,x71713,x71712)))+P1(f334(f334(f249(a1),x71711),f822(x71711,x71713,x71712)))
% 160.93/160.65 [7214]P146(x72142,x72143,x72141)+E(x72141,f2(a1))+P1(f334(f334(f248(a1),f2(a1)),f814(x72141,x72143,x72142)))+~P1(f334(x72142,f821(x72141,x72143,x72142)))
% 160.93/160.65 [7215]P145(x72152,x72153,x72151)+E(x72151,f2(a1))+P1(f334(f334(f248(a1),f2(a1)),f823(x72151,x72153,x72152)))+~P1(f334(x72152,f822(x72151,x72153,x72152)))
% 160.93/160.65 [7303]P145(x73031,x73032,x73033)+~P1(f334(x73031,x73032))+~P1(f334(x73031,f823(x73033,x73032,x73031)))+P1(f334(f334(f249(a1),x73033),f822(x73033,x73032,x73031)))
% 160.93/160.65 [7319]P146(x73191,x73192,x73193)+~P1(f334(x73191,f815(x73193,x73192,x73191)))+P1(f334(f334(f249(a1),x73193),f813(x73193,x73192,x73191)))+~P1(f334(x73191,f2(a1)))
% 160.93/160.65 [7323]P145(x73231,x73232,x73233)+~P1(f334(x73231,x73232))+P1(f334(f334(f248(a1),f2(a1)),f823(x73233,x73232,x73231)))+~P1(f334(x73231,f822(x73233,x73232,x73231)))
% 160.93/160.65 [7341]P146(x73411,x73412,x73413)+P1(f334(f334(f248(a1),f2(a1)),f814(x73413,x73412,x73411)))+~P1(f334(x73411,f821(x73413,x73412,x73411)))+~P1(f334(x73411,f2(a1)))
% 160.93/160.65 [7365]P146(x73652,x73653,x73651)+E(x73651,f2(a1))+~P1(f334(x73652,f815(x73651,x73653,x73652)))+~P1(f334(x73652,f821(x73651,x73653,x73652)))
% 160.93/160.65 [7366]P145(x73662,x73663,x73661)+E(x73661,f2(a1))+~P1(f334(x73662,f823(x73661,x73663,x73662)))+~P1(f334(x73662,f822(x73661,x73663,x73662)))
% 160.93/160.65 [7457]P145(x74571,x74572,x74573)+~P1(f334(x74571,x74572))+~P1(f334(x74571,f823(x74573,x74572,x74571)))+~P1(f334(x74571,f822(x74573,x74572,x74571)))
% 160.93/160.65 [7474]P146(x74741,x74742,x74743)+~P1(f334(x74741,f815(x74743,x74742,x74741)))+~P1(f334(x74741,f821(x74743,x74742,x74741)))+~P1(f334(x74741,f2(a1)))
% 160.93/160.65 [7523]P146(x75232,x75233,x75231)+E(x75231,f2(a1))+P1(f334(f334(f248(a1),f2(a1)),f814(x75231,x75233,x75232)))+P1(f334(f334(f248(a1),f813(x75231,x75233,x75232)),f2(a1)))
% 160.93/160.65 [7524]P145(x75242,x75243,x75241)+E(x75241,f2(a1))+P1(f334(f334(f248(a1),f2(a1)),f823(x75241,x75243,x75242)))+P1(f334(f334(f248(a1),f822(x75241,x75243,x75242)),f2(a1)))
% 160.93/160.65 [7525]~P139(x75251)+~P1(f334(f334(f336(x75251),x75253),f113(x75251)))+~P1(f334(f334(f336(x75251),x75252),f113(x75251)))+P1(f334(f334(f336(x75251),f334(f334(f22(x75251),x75252),x75253)),f113(x75251)))
% 160.93/160.65 [7526]~P139(x75261)+~P1(f334(f334(f336(x75261),x75263),f113(x75261)))+~P1(f334(f334(f336(x75261),x75262),f113(x75261)))+P1(f334(f334(f336(x75261),f334(f334(f80(x75261),x75262),x75263)),f113(x75261)))
% 160.93/160.65 [7527]~P142(x75271)+~P1(f334(f334(f336(x75271),x75273),f194(x75271)))+~P1(f334(f334(f336(x75271),x75272),f194(x75271)))+P1(f334(f334(f336(x75271),f334(f334(f80(x75271),x75272),x75273)),f194(x75271)))
% 160.93/160.65 [7528]~P139(x75281)+~P1(f334(f334(f336(x75281),x75283),f113(x75281)))+~P1(f334(f334(f336(x75281),x75282),f113(x75281)))+P1(f334(f334(f336(x75281),f334(f334(f81(x75281),x75282),x75283)),f113(x75281)))
% 160.93/160.65 [7529]~P142(x75291)+~P1(f334(f334(f336(x75291),x75293),f194(x75291)))+~P1(f334(f334(f336(x75291),x75292),f194(x75291)))+P1(f334(f334(f336(x75291),f334(f334(f81(x75291),x75292),x75293)),f194(x75291)))
% 160.93/160.65 [7530]~P81(x75301)+~P1(f334(f334(f249(x75301),x75303),f2(x75301)))+~P1(f334(f334(f249(x75301),x75302),f2(x75301)))+P1(f334(f334(f249(x75301),f334(f334(f80(x75301),x75302),x75303)),f2(x75301)))
% 160.93/160.65 [7531]~P81(x75311)+~P1(f334(f334(f248(x75311),x75312),f2(x75311)))+~P1(f334(f334(f249(x75311),x75313),f2(x75311)))+P1(f334(f334(f249(x75311),f334(f334(f80(x75311),x75312),x75313)),f2(x75311)))
% 160.93/160.65 [7532]~P81(x75321)+~P1(f334(f334(f248(x75321),x75323),f2(x75321)))+~P1(f334(f334(f249(x75321),x75322),f2(x75321)))+P1(f334(f334(f249(x75321),f334(f334(f80(x75321),x75322),x75323)),f2(x75321)))
% 160.93/160.65 [7533]~P81(x75331)+~P1(f334(f334(f248(x75331),x75333),f2(x75331)))+~P1(f334(f334(f248(x75331),x75332),f2(x75331)))+P1(f334(f334(f248(x75331),f334(f334(f80(x75331),x75332),x75333)),f2(x75331)))
% 160.93/160.65 [7559]P146(x75593,x75592,x75591)+E(x75591,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x75591),f815(x75591,x75592,x75593))),f814(x75591,x75592,x75593)),x75592)+P1(f334(f334(f249(a1),x75591),f2(a1)))
% 160.93/160.65 [7560]P145(x75603,x75602,x75601)+E(x75601,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x75601),f824(x75601,x75602,x75603))),f823(x75601,x75602,x75603)),x75602)+P1(f334(f334(f249(a1),x75601),f2(a1)))
% 160.93/160.65 [7644]P145(x76441,x76442,x76443)+~P1(f334(x76441,x76442))+P1(f334(f334(f248(a1),f2(a1)),f823(x76443,x76442,x76441)))+P1(f334(f334(f248(a1),f822(x76443,x76442,x76441)),f2(a1)))
% 160.93/160.65 [7673]P146(x76731,x76732,x76733)+P1(f334(f334(f248(a1),f2(a1)),f814(x76733,x76732,x76731)))+~P1(f334(x76731,f2(a1)))+P1(f334(f334(f248(a1),f813(x76733,x76732,x76731)),f2(a1)))
% 160.93/160.65 [7681]P145(x76813,x76812,x76811)+~P1(f334(x76813,x76812))+E(f334(f334(f80(a1),f334(f334(f81(a1),x76811),f824(x76811,x76812,x76813))),f823(x76811,x76812,x76813)),x76812)+P1(f334(f334(f249(a1),x76811),f2(a1)))
% 160.93/160.65 [7687]P146(x76872,x76873,x76871)+E(x76871,f2(a1))+~P1(f334(x76872,f815(x76871,x76873,x76872)))+P1(f334(f334(f248(a1),f813(x76871,x76873,x76872)),f2(a1)))
% 160.93/160.65 [7688]P145(x76882,x76883,x76881)+E(x76881,f2(a1))+~P1(f334(x76882,f823(x76881,x76883,x76882)))+P1(f334(f334(f248(a1),f822(x76881,x76883,x76882)),f2(a1)))
% 160.93/160.65 [7693]P146(x76933,x76932,x76931)+E(f334(f334(f80(a1),f334(f334(f81(a1),x76931),f815(x76931,x76932,x76933))),f814(x76931,x76932,x76933)),x76932)+~P1(f334(x76933,f2(a1)))+P1(f334(f334(f249(a1),x76931),f2(a1)))
% 160.93/160.65 [7747]P145(x77471,x77472,x77473)+~P1(f334(x77471,x77472))+~P1(f334(x77471,f823(x77473,x77472,x77471)))+P1(f334(f334(f248(a1),f822(x77473,x77472,x77471)),f2(a1)))
% 160.93/160.65 [7751]P146(x77511,x77512,x77513)+~P1(f334(x77511,f815(x77513,x77512,x77511)))+~P1(f334(x77511,f2(a1)))+P1(f334(f334(f248(a1),f813(x77513,x77512,x77511)),f2(a1)))
% 160.93/160.65 [7820]~P63(x78201)+~P1(f334(f334(f249(x78201),f334(f334(f292(x78201),x78203),x78202)),f2(x78201)))+P1(f334(f334(f249(x78201),x78202),f2(x78201)))+P1(f334(f334(f249(x78201),x78203),f2(x78201)))
% 160.93/160.65 [7821]~P124(x78211)+~P1(f334(f334(f248(x78211),f334(f334(f81(x78211),x78213),x78212)),f2(x78211)))+P1(f334(f334(f248(x78211),x78212),f2(x78211)))+P1(f334(f334(f248(x78211),x78213),f2(x78211)))
% 160.93/160.65 [7822]~P63(x78221)+~P1(f334(f334(f248(x78221),f334(f334(f292(x78221),x78223),x78222)),f2(x78221)))+P1(f334(f334(f248(x78221),x78222),f2(x78221)))+P1(f334(f334(f248(x78221),x78223),f2(x78221)))
% 160.93/160.65 [7936]P146(x79363,x79362,x79361)+E(x79361,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x79361),f815(x79361,x79362,x79363))),f814(x79361,x79362,x79363)),x79362)+P1(f334(f334(f249(a1),x79361),f813(x79361,x79362,x79363)))
% 160.93/160.65 [7937]P145(x79373,x79372,x79371)+E(x79371,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x79371),f824(x79371,x79372,x79373))),f823(x79371,x79372,x79373)),x79372)+P1(f334(f334(f249(a1),x79371),f822(x79371,x79372,x79373)))
% 160.93/160.65 [7949]P146(x79493,x79492,x79491)+E(x79491,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x79491),f821(x79491,x79492,x79493))),f813(x79491,x79492,x79493)),x79492)+P1(f334(f334(f248(a1),f2(a1)),f814(x79491,x79492,x79493)))
% 160.93/160.65 [7950]P145(x79503,x79502,x79501)+E(x79501,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x79501),f825(x79501,x79502,x79503))),f822(x79501,x79502,x79503)),x79502)+P1(f334(f334(f248(a1),f2(a1)),f823(x79501,x79502,x79503)))
% 160.93/160.65 [7992]P145(x79923,x79922,x79921)+~P1(f334(x79923,x79922))+E(f334(f334(f80(a1),f334(f334(f81(a1),x79921),f824(x79921,x79922,x79923))),f823(x79921,x79922,x79923)),x79922)+P1(f334(f334(f249(a1),x79921),f822(x79921,x79922,x79923)))
% 160.93/160.65 [8001]P146(x80013,x80012,x80011)+E(f334(f334(f80(a1),f334(f334(f81(a1),x80011),f815(x80011,x80012,x80013))),f814(x80011,x80012,x80013)),x80012)+P1(f334(f334(f249(a1),x80011),f813(x80011,x80012,x80013)))+~P1(f334(x80013,f2(a1)))
% 160.93/160.65 [8007]P145(x80073,x80072,x80071)+~P1(f334(x80073,x80072))+E(f334(f334(f80(a1),f334(f334(f81(a1),x80071),f825(x80071,x80072,x80073))),f822(x80071,x80072,x80073)),x80072)+P1(f334(f334(f248(a1),f2(a1)),f823(x80071,x80072,x80073)))
% 160.93/160.65 [8013]P146(x80133,x80132,x80131)+E(f334(f334(f80(a1),f334(f334(f81(a1),x80131),f821(x80131,x80132,x80133))),f813(x80131,x80132,x80133)),x80132)+P1(f334(f334(f248(a1),f2(a1)),f814(x80131,x80132,x80133)))+~P1(f334(x80133,f2(a1)))
% 160.93/160.65 [8024]P146(x80243,x80242,x80241)+E(x80241,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x80241),f815(x80241,x80242,x80243))),f814(x80241,x80242,x80243)),x80242)+~P1(f334(x80243,f821(x80241,x80242,x80243)))
% 160.93/160.65 [8025]P145(x80253,x80252,x80251)+E(x80251,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x80251),f824(x80251,x80252,x80253))),f823(x80251,x80252,x80253)),x80252)+~P1(f334(x80253,f822(x80251,x80252,x80253)))
% 160.93/160.65 [8026]P146(x80263,x80262,x80261)+E(x80261,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x80261),f821(x80261,x80262,x80263))),f813(x80261,x80262,x80263)),x80262)+~P1(f334(x80263,f815(x80261,x80262,x80263)))
% 160.93/160.65 [8027]P145(x80273,x80272,x80271)+E(x80271,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x80271),f825(x80271,x80272,x80273))),f822(x80271,x80272,x80273)),x80272)+~P1(f334(x80273,f823(x80271,x80272,x80273)))
% 160.93/160.65 [8085]P145(x80853,x80852,x80851)+~P1(f334(x80853,x80852))+E(f334(f334(f80(a1),f334(f334(f81(a1),x80851),f824(x80851,x80852,x80853))),f823(x80851,x80852,x80853)),x80852)+~P1(f334(x80853,f822(x80851,x80852,x80853)))
% 160.93/160.65 [8086]P145(x80863,x80862,x80861)+~P1(f334(x80863,x80862))+E(f334(f334(f80(a1),f334(f334(f81(a1),x80861),f825(x80861,x80862,x80863))),f822(x80861,x80862,x80863)),x80862)+~P1(f334(x80863,f823(x80861,x80862,x80863)))
% 160.93/160.65 [8097]P146(x80973,x80972,x80971)+E(f334(f334(f80(a1),f334(f334(f81(a1),x80971),f815(x80971,x80972,x80973))),f814(x80971,x80972,x80973)),x80972)+~P1(f334(x80973,f821(x80971,x80972,x80973)))+~P1(f334(x80973,f2(a1)))
% 160.93/160.65 [8098]P146(x80983,x80982,x80981)+E(f334(f334(f80(a1),f334(f334(f81(a1),x80981),f821(x80981,x80982,x80983))),f813(x80981,x80982,x80983)),x80982)+~P1(f334(x80983,f815(x80981,x80982,x80983)))+~P1(f334(x80983,f2(a1)))
% 160.93/160.65 [8206]P146(x82063,x82062,x82061)+E(x82061,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x82061),f815(x82061,x82062,x82063))),f814(x82061,x82062,x82063)),x82062)+P1(f334(f334(f248(a1),f813(x82061,x82062,x82063)),f2(a1)))
% 160.93/160.65 [8207]P145(x82073,x82072,x82071)+E(x82071,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x82071),f824(x82071,x82072,x82073))),f823(x82071,x82072,x82073)),x82072)+P1(f334(f334(f248(a1),f822(x82071,x82072,x82073)),f2(a1)))
% 160.93/160.65 [8253]P145(x82533,x82532,x82531)+~P1(f334(x82533,x82532))+E(f334(f334(f80(a1),f334(f334(f81(a1),x82531),f824(x82531,x82532,x82533))),f823(x82531,x82532,x82533)),x82532)+P1(f334(f334(f248(a1),f822(x82531,x82532,x82533)),f2(a1)))
% 160.93/160.65 [8258]P146(x82583,x82582,x82581)+E(f334(f334(f80(a1),f334(f334(f81(a1),x82581),f815(x82581,x82582,x82583))),f814(x82581,x82582,x82583)),x82582)+~P1(f334(x82583,f2(a1)))+P1(f334(f334(f248(a1),f813(x82581,x82582,x82583)),f2(a1)))
% 160.93/160.65 [8387]P146(x83873,x83872,x83871)+E(x83871,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x83871),f821(x83871,x83872,x83873))),f813(x83871,x83872,x83873)),x83872)+E(f334(f334(f80(a1),f334(f334(f81(a1),x83871),f815(x83871,x83872,x83873))),f814(x83871,x83872,x83873)),x83872)
% 160.93/160.65 [8388]P145(x83883,x83882,x83881)+E(x83881,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x83881),f825(x83881,x83882,x83883))),f822(x83881,x83882,x83883)),x83882)+E(f334(f334(f80(a1),f334(f334(f81(a1),x83881),f824(x83881,x83882,x83883))),f823(x83881,x83882,x83883)),x83882)
% 160.93/160.65 [8410]P145(x84103,x84102,x84101)+~P1(f334(x84103,x84102))+E(f334(f334(f80(a1),f334(f334(f81(a1),x84101),f825(x84101,x84102,x84103))),f822(x84101,x84102,x84103)),x84102)+E(f334(f334(f80(a1),f334(f334(f81(a1),x84101),f824(x84101,x84102,x84103))),f823(x84101,x84102,x84103)),x84102)
% 160.93/160.65 [8421]P146(x84213,x84212,x84211)+E(f334(f334(f80(a1),f334(f334(f81(a1),x84211),f821(x84211,x84212,x84213))),f813(x84211,x84212,x84213)),x84212)+E(f334(f334(f80(a1),f334(f334(f81(a1),x84211),f815(x84211,x84212,x84213))),f814(x84211,x84212,x84213)),x84212)+~P1(f334(x84213,f2(a1)))
% 160.93/160.65 [9079]~P124(x90791)+~E(x90793,f2(x90791))+~E(x90792,f2(x90791))+P1(f334(f334(f248(x90791),f334(f334(f80(x90791),f334(f334(f81(x90791),x90792),x90792)),f334(f334(f81(x90791),x90793),x90793))),f2(x90791)))
% 160.93/160.65 [10132]~P111(x101321)+~E(x101323,f2(x101321))+~E(x101322,f2(x101321))+P1(f334(f334(f248(x101321),f334(f334(f80(x101321),f334(f334(f259(x101321),x101322),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x101321),x101323),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))),f2(x101321)))
% 160.93/160.65 [4816]~E(x48163,x48161)+~P120(x48162)+E(x48161,f2(x48162))+E(f334(f334(f292(x48162),x48163),x48161),f78(x48162))
% 160.93/160.65 [4869]~P3(x48691)+~E(x48693,f196(x48691))+~E(x48692,f196(x48691))+E(f334(f334(f114(x48691),x48692),x48693),f196(x48691))
% 160.93/160.65 [4870]~P98(x48701)+~E(x48703,f257(x48701))+~E(x48702,f257(x48701))+E(f334(f334(f105(x48701),x48702),x48703),f257(x48701))
% 160.93/160.65 [4956]~P120(x49563)+E(x49561,x49562)+E(x49562,f2(x49563))+~E(f334(f334(f292(x49563),x49561),x49562),f78(x49563))
% 160.93/160.65 [4975]~P130(x49752)+E(x49751,f2(x49752))+E(x49753,f2(x49752))+~E(f334(f334(f81(x49752),x49753),x49751),f2(x49752))
% 160.93/160.65 [4976]~P138(x49762)+E(x49761,f2(x49762))+E(x49763,f2(x49762))+~E(f334(f334(f81(x49762),x49763),x49761),f2(x49762))
% 160.93/160.65 [5351]~P119(x53513)+E(x53511,x53512)+E(x53511,f334(f79(x53513),x53512))+~E(f334(f334(f81(x53513),x53511),x53511),f334(f334(f81(x53513),x53512),x53512))
% 160.93/160.65 [5391]~P94(x53911)+E(f334(f79(x53911),x53912),x53913)+~E(f334(f334(f114(x53911),x53912),x53913),f257(x53911))+~E(f334(f334(f105(x53911),x53912),x53913),f196(x53911))
% 160.93/160.65 [5470]~P111(x54703)+E(x54701,x54702)+P1(f334(f334(f249(x54703),x54702),x54701))+P1(f334(f334(f249(x54703),x54701),x54702))
% 160.93/160.65 [5471]~P108(x54713)+E(x54711,x54712)+P1(f334(f334(f249(x54713),x54712),x54711))+P1(f334(f334(f249(x54713),x54711),x54712))
% 160.93/160.65 [5472]~E(x54722,x54723)+~P108(x54721)+P1(f334(f334(f248(x54721),x54722),x54723))+P1(f334(f334(f249(x54721),x54722),x54723))
% 160.93/160.65 [5724]~P109(x57243)+E(x57241,x57242)+~P1(f334(f334(f248(x57243),x57242),x57241))+P1(f334(f334(f249(x57243),x57242),x57241))
% 160.93/160.65 [5726]~P108(x57263)+E(x57261,x57262)+~P1(f334(f334(f248(x57263),x57261),x57262))+P1(f334(f334(f249(x57263),x57261),x57262))
% 160.93/160.65 [5732]~P109(x57323)+E(x57321,x57322)+~P1(f334(f334(f248(x57323),x57321),x57322))+P1(f334(f334(f249(x57323),x57321),x57322))
% 160.93/160.65 [5834]P145(x58341,x58342,x58343)+~P1(f334(x58341,x58342))+P1(f334(f334(f249(a1),x58343),f2(a1)))+P1(f334(f334(f249(a1),f2(a1)),x58343))
% 160.93/160.65 [5881]P146(x58811,x58812,x58813)+~P1(f334(x58811,f2(a1)))+P1(f334(f334(f249(a1),x58813),f2(a1)))+P1(f334(f334(f249(a1),f2(a1)),x58813))
% 160.93/160.65 [5885]~P2(x58851)+E(f334(f334(f114(x58851),x58852),f11(x58851,x58853)),x58852)+~P1(f334(f61(x58851),x58853))+~P1(f334(f334(f336(x58851),x58852),x58853))
% 160.93/160.65 [5886]~P2(x58861)+E(f334(f334(f105(x58861),x58862),f10(x58861,x58863)),x58862)+~P1(f334(f61(x58861),x58863))+~P1(f334(f334(f336(x58861),x58862),x58863))
% 160.93/160.65 [5922]~P2(x59221)+E(f334(f334(f114(x59221),x59222),f10(x59221,x59223)),f10(x59221,x59223))+~P1(f334(f61(x59221),x59223))+~P1(f334(f334(f336(x59221),x59222),x59223))
% 160.93/160.65 [5923]~P2(x59231)+E(f334(f334(f105(x59231),x59232),f11(x59231,x59233)),f11(x59231,x59233))+~P1(f334(f61(x59231),x59233))+~P1(f334(f334(f336(x59231),x59232),x59233))
% 160.93/160.65 [5924]~P108(x59241)+E(f334(f334(f246(x59241),x59242),f14(x59241,x59243)),f14(x59241,x59243))+~P1(f334(f61(x59241),x59243))+~P1(f334(f334(f336(x59241),x59242),x59243))
% 160.93/160.65 [5925]~P108(x59251)+E(f334(f334(f247(x59251),x59252),f15(x59251,x59253)),f15(x59251,x59253))+~P1(f334(f61(x59251),x59253))+~P1(f334(f334(f336(x59251),x59252),x59253))
% 160.93/160.65 [5967]E(x59671,x59672)+~P109(x59673)+~P1(f334(f334(f248(x59673),x59672),x59671))+~P1(f334(f334(f248(x59673),x59671),x59672))
% 160.93/160.65 [6106]~P107(x61061)+P1(f334(f334(f248(x61061),x61063),x61062))+~P1(f334(f334(f248(x61061),x61062),x61063))+P1(f334(f334(f249(x61061),x61062),x61063))
% 160.93/160.65 [6127]~P108(x61271)+~P1(f334(f61(x61271),x61273))+P1(f334(f334(f248(x61271),x61272),f15(x61271,x61273)))+~P1(f334(f334(f336(x61271),x61272),x61273))
% 160.93/160.65 [6183]~P108(x61831)+E(f334(f334(f246(x61831),x61832),f12(x61831,f247(x61831),x61833)),x61832)+~P1(f334(f61(x61831),x61833))+~P1(f334(f334(f336(x61831),x61832),x61833))
% 160.93/160.65 [6184]~P108(x61841)+E(f334(f334(f247(x61841),x61842),f13(x61841,f246(x61841),x61843)),x61842)+~P1(f334(f61(x61841),x61843))+~P1(f334(f334(f336(x61841),x61842),x61843))
% 160.93/160.65 [6322]E(x63221,x63222)+~E(f334(f334(f22(a881),x63221),x63223),f334(f334(f22(a881),x63222),x63223))+~P1(f334(f334(f248(a881),x63223),x63221))+~P1(f334(f334(f248(a881),x63223),x63222))
% 160.93/160.65 [6349]~P108(x63491)+~P1(f334(f61(x63491),x63492))+~P1(f334(f334(f336(x63491),x63493),x63492))+P1(f334(f334(f248(x63491),f14(x63491,x63492)),x63493))
% 160.93/160.65 [6411]P146(x64112,x64113,x64111)+E(x64111,f2(a1))+P1(f334(f334(f249(a1),x64111),f813(x64111,x64113,x64112)))+P1(f334(f334(f249(a1),f2(a1)),x64111))
% 160.93/160.65 [6412]P145(x64122,x64123,x64121)+E(x64121,f2(a1))+P1(f334(f334(f249(a1),x64121),f822(x64121,x64123,x64122)))+P1(f334(f334(f249(a1),f2(a1)),x64121))
% 160.93/160.65 [6413]~P108(x64131)+E(f334(f334(f246(x64131),x64132),f13(x64131,f246(x64131),x64133)),f13(x64131,f246(x64131),x64133))+~P1(f334(f61(x64131),x64133))+~P1(f334(f334(f336(x64131),x64132),x64133))
% 160.93/160.65 [6414]~P108(x64141)+E(f334(f334(f247(x64141),x64142),f12(x64141,f247(x64141),x64143)),f12(x64141,f247(x64141),x64143))+~P1(f334(f61(x64141),x64143))+~P1(f334(f334(f336(x64141),x64142),x64143))
% 160.93/160.65 [6420]~P1(f334(x64201,x64202))+P1(f334(x64201,f502(x64202,x64201,x64203)))+P1(f334(x64201,f2(a881)))+~P1(f334(f334(f249(a881),x64202),x64203))
% 160.93/160.65 [6475]~P1(f334(x64751,x64752))+~P1(f334(f61(x64753),x64752))+P1(f334(x64751,f727(x64751,x64752,x64753)))+P1(f334(x64751,f196(f888(x64753,a876))))
% 160.93/160.65 [6488]~P111(x64881)+~P93(x64881)+P1(f334(f334(f249(x64881),f334(f107(x64881),x64882)),f334(f107(x64881),x64883)))+~P1(f334(f334(f249(a1),x64882),x64883))
% 160.93/160.65 [6489]~P111(x64891)+~P93(x64891)+P1(f334(f334(f248(x64891),f334(f107(x64891),x64892)),f334(f107(x64891),x64893)))+~P1(f334(f334(f248(a1),x64892),x64893))
% 160.93/160.65 [6492]~P1(f334(x64921,x64923))+~P1(f334(f61(x64922),x64923))+P1(f334(f61(x64922),f727(x64921,x64923,x64922)))+P1(f334(x64921,f196(f888(x64922,a876))))
% 160.93/160.65 [6525]P145(x65251,x65252,x65253)+~P1(f334(x65251,x65252))+P1(f334(f334(f249(a1),x65253),f822(x65253,x65252,x65251)))+P1(f334(f334(f249(a1),f2(a1)),x65253))
% 160.93/160.65 [6559]P146(x65591,x65592,x65593)+P1(f334(f334(f249(a1),x65593),f813(x65593,x65592,x65591)))+~P1(f334(x65591,f2(a1)))+P1(f334(f334(f249(a1),f2(a1)),x65593))
% 160.93/160.65 [6590]~P110(x65901)+~P91(x65901)+E(f334(f334(f246(x65901),f334(f107(x65901),x65902)),f334(f107(x65901),x65903)),f334(f107(x65901),x65903))+P1(f334(f334(f248(x65901),f334(f107(x65901),x65902)),f334(f107(x65901),x65903)))
% 160.93/160.65 [6591]~P110(x65911)+~P91(x65911)+E(f334(f334(f247(x65911),f334(f107(x65911),x65912)),f334(f107(x65911),x65913)),f334(f107(x65911),x65912))+P1(f334(f334(f248(x65911),f334(f107(x65911),x65912)),f334(f107(x65911),x65913)))
% 160.93/160.65 [6650]P146(x66502,x66503,x66501)+E(x66501,f2(a1))+~P1(f334(x66502,f821(x66501,x66503,x66502)))+P1(f334(f334(f249(a1),f2(a1)),x66501))
% 160.93/160.65 [6651]P145(x66512,x66513,x66511)+E(x66511,f2(a1))+~P1(f334(x66512,f822(x66511,x66513,x66512)))+P1(f334(f334(f249(a1),f2(a1)),x66511))
% 160.93/160.65 [6655]P1(f334(x66551,x66552))+~P1(f334(f61(x66553),x66552))+P1(f334(x66551,f807(x66551,x66552,x66553)))+~P1(f334(x66551,f196(f888(x66553,a876))))
% 160.93/160.65 [6674]P1(f334(x66741,x66742))+P1(f334(f61(x66743),f807(x66741,x66742,x66743)))+~P1(f334(f61(x66743),x66742))+~P1(f334(x66741,f196(f888(x66743,a876))))
% 160.93/160.65 [6739]P145(x67391,x67392,x67393)+~P1(f334(x67391,x67392))+~P1(f334(x67391,f822(x67393,x67392,x67391)))+P1(f334(f334(f249(a1),f2(a1)),x67393))
% 160.93/160.65 [6769]P146(x67691,x67692,x67693)+~P1(f334(x67691,f821(x67693,x67692,x67691)))+~P1(f334(x67691,f2(a1)))+P1(f334(f334(f249(a1),f2(a1)),x67693))
% 160.93/160.65 [6877]~P93(x68773)+~P111(x68773)+~P1(f334(f334(f249(x68773),f334(f107(x68773),x68771)),f334(f107(x68773),x68772)))+P1(f334(f334(f249(a1),x68771),x68772))
% 160.93/160.65 [6878]~P93(x68783)+~P111(x68783)+~P1(f334(f334(f248(x68783),f334(f107(x68783),x68781)),f334(f107(x68783),x68782)))+P1(f334(f334(f248(a1),x68781),x68782))
% 160.93/160.65 [6905]~P108(x69051)+~P16(x69051,x69053)+P16(x69051,f334(f334(f153(x69051),x69052),x69053))+~P1(f334(f334(f248(x69051),x69052),f751(x69053,x69052,x69051)))
% 160.93/160.65 [6906]~P108(x69061)+~P16(x69061,x69063)+P16(x69061,f334(f334(f153(x69061),x69062),x69063))+~P1(f334(f334(f248(x69061),x69062),f753(x69063,x69062,x69061)))
% 160.93/160.65 [6907]~P108(x69071)+~P16(x69071,x69073)+P16(x69071,f334(f334(f153(x69071),x69072),x69073))+~P1(f334(f334(f248(x69071),x69072),f796(x69072,x69073,x69071)))
% 160.93/160.65 [6991]P146(x69912,x69913,x69911)+E(x69911,f2(a1))+P1(f334(f334(f249(a1),x69911),f2(a1)))+P1(f334(f334(f249(a1),f814(x69911,x69913,x69912)),x69911))
% 160.93/160.65 [6992]P145(x69922,x69923,x69921)+E(x69921,f2(a1))+P1(f334(f334(f249(a1),x69921),f2(a1)))+P1(f334(f334(f249(a1),f823(x69921,x69923,x69922)),x69921))
% 160.93/160.65 [7031]P146(x70312,x70313,x70311)+E(x70311,f2(a1))+P1(f334(f334(f248(a1),f813(x70311,x70313,x70312)),f2(a1)))+P1(f334(f334(f249(a1),f2(a1)),x70311))
% 160.93/160.65 [7032]P145(x70322,x70323,x70321)+E(x70321,f2(a1))+P1(f334(f334(f248(a1),f822(x70321,x70323,x70322)),f2(a1)))+P1(f334(f334(f249(a1),f2(a1)),x70321))
% 160.93/160.65 [7054]~P108(x70541)+~P16(x70541,x70543)+E(f334(f334(f150(x70541,x70541,f5(x70541)),x70542),f172(x70541,x70542,x70543)),x70543)+~P1(f334(f334(f336(x70541),x70542),f334(f174(x70541),x70543)))
% 160.93/160.65 [7101]P145(x71011,x71012,x71013)+~P1(f334(x71011,x71012))+P1(f334(f334(f249(a1),x71013),f2(a1)))+P1(f334(f334(f249(a1),f823(x71013,x71012,x71011)),x71013))
% 160.93/160.65 [7107]~P110(x71071)+~P91(x71071)+E(f334(f334(f246(x71071),f334(f107(x71071),x71072)),f334(f107(x71071),x71073)),f334(f107(x71071),x71072))+~P1(f334(f334(f248(x71071),f334(f107(x71071),x71072)),f334(f107(x71071),x71073)))
% 160.93/160.65 [7108]~P110(x71081)+~P91(x71081)+E(f334(f334(f247(x71081),f334(f107(x71081),x71082)),f334(f107(x71081),x71083)),f334(f107(x71081),x71083))+~P1(f334(f334(f248(x71081),f334(f107(x71081),x71082)),f334(f107(x71081),x71083)))
% 160.93/160.65 [7122]P146(x71221,x71222,x71223)+~P1(f334(x71221,f2(a1)))+P1(f334(f334(f249(a1),x71223),f2(a1)))+P1(f334(f334(f249(a1),f814(x71223,x71222,x71221)),x71223))
% 160.93/160.65 [7130]P145(x71301,x71302,x71303)+~P1(f334(x71301,x71302))+P1(f334(f334(f248(a1),f822(x71303,x71302,x71301)),f2(a1)))+P1(f334(f334(f249(a1),f2(a1)),x71303))
% 160.93/160.65 [7154]P146(x71541,x71542,x71543)+~P1(f334(x71541,f2(a1)))+P1(f334(f334(f248(a1),f813(x71543,x71542,x71541)),f2(a1)))+P1(f334(f334(f249(a1),f2(a1)),x71543))
% 160.93/160.65 [7184]~P1(f334(x71841,x71842))+P1(f334(x71841,f2(a881)))+~P1(f334(f334(f249(a881),x71842),x71843))+P1(f334(f334(f249(a881),f502(x71842,x71841,x71843)),x71843))
% 160.93/160.65 [7201]~P108(x72011)+~P16(x72011,x72013)+P16(x72011,f334(f334(f153(x72011),x72012),x72013))+P1(f334(f334(f336(x72011),f751(x72013,x72012,x72011)),f334(f174(x72011),x72013)))
% 160.93/160.65 [7202]~P108(x72021)+~P16(x72021,x72023)+P16(x72021,f334(f334(f153(x72021),x72022),x72023))+P1(f334(f334(f336(x72021),f753(x72023,x72022,x72021)),f334(f174(x72021),x72023)))
% 160.93/160.65 [7203]~P108(x72031)+~P16(x72031,x72033)+P16(x72031,f334(f334(f153(x72031),x72032),x72033))+P1(f334(f334(f336(x72031),f796(x72032,x72033,x72031)),f334(f174(x72031),x72033)))
% 160.93/160.65 [7307]~P5(x73071)+~P108(x73071)+~P1(f334(f334(f249(x73071),x73073),f39(x73071,x73072)))+P1(f334(f334(f336(x73071),f850(x73072,x73073,x73071)),x73072))
% 160.93/160.65 [7472]~P5(x74721)+~P108(x74721)+~P1(f334(f334(f249(x74721),f40(x74721,x74723)),x74722))+P1(f334(f334(f336(x74721),f498(x74722,x74723,x74721)),x74723))
% 160.93/160.65 [7473]~P5(x74731)+~P108(x74731)+~P1(f334(f334(f249(x74731),f40(x74731,x74733)),x74732))+P1(f334(f334(f249(x74731),f498(x74732,x74733,x74731)),x74732))
% 160.93/160.65 [7488]P146(x74882,x74883,x74881)+E(x74881,f2(a1))+P1(f334(f334(f249(a1),x74881),f813(x74881,x74883,x74882)))+P1(f334(f334(f249(a1),f814(x74881,x74883,x74882)),x74881))
% 160.93/160.65 [7489]P145(x74892,x74893,x74891)+E(x74891,f2(a1))+P1(f334(f334(f249(a1),x74891),f822(x74891,x74893,x74892)))+P1(f334(f334(f249(a1),f823(x74891,x74893,x74892)),x74891))
% 160.93/160.66 [7580]P146(x75803,x75802,x75801)+E(x75801,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x75801),f821(x75801,x75802,x75803))),f813(x75801,x75802,x75803)),x75802)+P1(f334(f334(f249(a1),f2(a1)),x75801))
% 160.93/160.66 [7581]P145(x75813,x75812,x75811)+E(x75811,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x75811),f825(x75811,x75812,x75813))),f822(x75811,x75812,x75813)),x75812)+P1(f334(f334(f249(a1),f2(a1)),x75811))
% 160.93/160.66 [7585]~P126(x75851)+~P1(f334(f334(f249(x75851),x75853),f2(x75851)))+P1(f334(f334(f249(x75851),f334(f334(f81(x75851),x75852),x75853)),f2(x75851)))+~P1(f334(f334(f249(x75851),f2(x75851)),x75852))
% 160.93/160.66 [7586]~P126(x75861)+~P1(f334(f334(f249(x75861),x75862),f2(x75861)))+P1(f334(f334(f249(x75861),f334(f334(f81(x75861),x75862),x75863)),f2(x75861)))+~P1(f334(f334(f249(x75861),f2(x75861)),x75863))
% 160.93/160.66 [7587]~P63(x75871)+~P1(f334(f334(f249(x75871),x75873),f2(x75871)))+P1(f334(f334(f249(x75871),f334(f334(f292(x75871),x75872),x75873)),f2(x75871)))+~P1(f334(f334(f249(x75871),f2(x75871)),x75872))
% 160.93/160.66 [7588]~P63(x75881)+~P1(f334(f334(f249(x75881),x75882),f2(x75881)))+P1(f334(f334(f249(x75881),f334(f334(f292(x75881),x75882),x75883)),f2(x75881)))+~P1(f334(f334(f249(x75881),f2(x75881)),x75883))
% 160.93/160.66 [7589]~P64(x75891)+~P1(f334(f334(f249(x75891),x75893),f2(x75891)))+P1(f334(f334(f249(x75891),f334(f334(f292(x75891),x75892),x75893)),f2(x75891)))+~P1(f334(f334(f249(x75891),f2(x75891)),x75892))
% 160.93/160.66 [7590]~P64(x75901)+~P1(f334(f334(f249(x75901),x75902),f2(x75901)))+P1(f334(f334(f249(x75901),f334(f334(f292(x75901),x75902),x75903)),f2(x75901)))+~P1(f334(f334(f249(x75901),f2(x75901)),x75903))
% 160.93/160.66 [7592]~P124(x75921)+~P1(f334(f334(f248(x75921),x75923),f2(x75921)))+P1(f334(f334(f248(x75921),f334(f334(f81(x75921),x75922),x75923)),f2(x75921)))+~P1(f334(f334(f248(x75921),f2(x75921)),x75922))
% 160.93/160.66 [7593]~P124(x75931)+~P1(f334(f334(f248(x75931),x75932),f2(x75931)))+P1(f334(f334(f248(x75931),f334(f334(f81(x75931),x75932),x75933)),f2(x75931)))+~P1(f334(f334(f248(x75931),f2(x75931)),x75933))
% 160.93/160.66 [7595]~P132(x75951)+~P1(f334(f334(f248(x75951),x75953),f2(x75951)))+P1(f334(f334(f248(x75951),f334(f334(f81(x75951),x75952),x75953)),f2(x75951)))+~P1(f334(f334(f248(x75951),f2(x75951)),x75952))
% 160.93/160.66 [7597]~P132(x75971)+~P1(f334(f334(f248(x75971),x75972),f2(x75971)))+P1(f334(f334(f248(x75971),f334(f334(f81(x75971),x75972),x75973)),f2(x75971)))+~P1(f334(f334(f248(x75971),f2(x75971)),x75973))
% 160.93/160.66 [7598]~P63(x75981)+~P1(f334(f334(f248(x75981),x75983),f2(x75981)))+P1(f334(f334(f248(x75981),f334(f334(f292(x75981),x75982),x75983)),f2(x75981)))+~P1(f334(f334(f248(x75981),f2(x75981)),x75982))
% 160.93/160.66 [7599]~P63(x75991)+~P1(f334(f334(f248(x75991),x75992),f2(x75991)))+P1(f334(f334(f248(x75991),f334(f334(f292(x75991),x75992),x75993)),f2(x75991)))+~P1(f334(f334(f248(x75991),f2(x75991)),x75993))
% 160.93/160.66 [7600]~P64(x76001)+~P1(f334(f334(f249(x76001),x76003),f2(x76001)))+P1(f334(f334(f248(x76001),f334(f334(f292(x76001),x76002),x76003)),f2(x76001)))+~P1(f334(f334(f248(x76001),f2(x76001)),x76002))
% 160.93/160.66 [7601]~P64(x76011)+~P1(f334(f334(f248(x76011),x76012),f2(x76011)))+P1(f334(f334(f248(x76011),f334(f334(f292(x76011),x76012),x76013)),f2(x76011)))+~P1(f334(f334(f249(x76011),f2(x76011)),x76013))
% 160.93/160.66 [7616]P145(x76161,x76162,x76163)+~P1(f334(x76161,x76162))+P1(f334(f334(f249(a1),x76163),f822(x76163,x76162,x76161)))+P1(f334(f334(f249(a1),f823(x76163,x76162,x76161)),x76163))
% 160.93/160.66 [7629]P146(x76291,x76292,x76293)+P1(f334(f334(f249(a1),x76293),f813(x76293,x76292,x76291)))+~P1(f334(x76291,f2(a1)))+P1(f334(f334(f249(a1),f814(x76293,x76292,x76291)),x76293))
% 160.93/160.66 [7679]P146(x76792,x76793,x76791)+E(x76791,f2(a1))+~P1(f334(x76792,f821(x76791,x76793,x76792)))+P1(f334(f334(f249(a1),f814(x76791,x76793,x76792)),x76791))
% 160.93/160.66 [7680]P145(x76802,x76803,x76801)+E(x76801,f2(a1))+~P1(f334(x76802,f822(x76801,x76803,x76802)))+P1(f334(f334(f249(a1),f823(x76801,x76803,x76802)),x76801))
% 160.93/160.66 [7690]P145(x76903,x76902,x76901)+~P1(f334(x76903,x76902))+E(f334(f334(f80(a1),f334(f334(f81(a1),x76901),f825(x76901,x76902,x76903))),f822(x76901,x76902,x76903)),x76902)+P1(f334(f334(f249(a1),f2(a1)),x76901))
% 160.93/160.66 [7707]P146(x77073,x77072,x77071)+E(f334(f334(f80(a1),f334(f334(f81(a1),x77071),f821(x77071,x77072,x77073))),f813(x77071,x77072,x77073)),x77072)+~P1(f334(x77073,f2(a1)))+P1(f334(f334(f249(a1),f2(a1)),x77071))
% 160.93/160.66 [7732]~P1(f334(x77321,x77323))+~P1(f334(f61(x77322),x77323))+P1(f334(f334(f336(x77322),f715(x77321,x77323,x77322)),f727(x77321,x77323,x77322)))+P1(f334(x77321,f196(f888(x77322,a876))))
% 160.93/160.66 [7743]P145(x77431,x77432,x77433)+~P1(f334(x77431,x77432))+~P1(f334(x77431,f822(x77433,x77432,x77431)))+P1(f334(f334(f249(a1),f823(x77433,x77432,x77431)),x77433))
% 160.93/160.66 [7748]P146(x77481,x77482,x77483)+~P1(f334(x77481,f821(x77483,x77482,x77481)))+~P1(f334(x77481,f2(a1)))+P1(f334(f334(f249(a1),f814(x77483,x77482,x77481)),x77483))
% 160.93/160.66 [7851]~P63(x78511)+~P1(f334(f334(f249(x78511),f334(f334(f292(x78511),x78513),x78512)),f2(x78511)))+P1(f334(f334(f249(x78511),x78512),f2(x78511)))+P1(f334(f334(f249(x78511),f2(x78511)),x78512))
% 160.93/160.66 [7852]~P63(x78521)+~P1(f334(f334(f249(x78521),f334(f334(f292(x78521),x78522),x78523)),f2(x78521)))+P1(f334(f334(f249(x78521),x78522),f2(x78521)))+P1(f334(f334(f249(x78521),f2(x78521)),x78522))
% 160.93/160.66 [7853]~P124(x78531)+~P1(f334(f334(f248(x78531),f334(f334(f81(x78531),x78533),x78532)),f2(x78531)))+P1(f334(f334(f248(x78531),x78532),f2(x78531)))+P1(f334(f334(f248(x78531),f2(x78531)),x78532))
% 160.93/160.66 [7854]~P124(x78541)+~P1(f334(f334(f248(x78541),f334(f334(f81(x78541),x78542),x78543)),f2(x78541)))+P1(f334(f334(f248(x78541),x78542),f2(x78541)))+P1(f334(f334(f248(x78541),f2(x78541)),x78542))
% 160.93/160.66 [7855]~P63(x78551)+~P1(f334(f334(f248(x78551),f334(f334(f292(x78551),x78553),x78552)),f2(x78551)))+P1(f334(f334(f248(x78551),x78552),f2(x78551)))+P1(f334(f334(f248(x78551),f2(x78551)),x78552))
% 160.93/160.66 [7856]~P63(x78561)+~P1(f334(f334(f248(x78561),f334(f334(f292(x78561),x78562),x78563)),f2(x78561)))+P1(f334(f334(f248(x78561),x78562),f2(x78561)))+P1(f334(f334(f248(x78561),f2(x78561)),x78562))
% 160.93/160.66 [7880]~P63(x78801)+~P1(f334(f334(f249(x78801),f334(f334(f292(x78801),x78802),x78803)),f2(x78801)))+P1(f334(f334(f249(x78801),f2(x78801)),x78802))+P1(f334(f334(f249(x78801),f2(x78801)),x78803))
% 160.93/160.66 [7881]~P124(x78811)+~P1(f334(f334(f248(x78811),f334(f334(f81(x78811),x78812),x78813)),f2(x78811)))+P1(f334(f334(f248(x78811),f2(x78811)),x78812))+P1(f334(f334(f248(x78811),f2(x78811)),x78813))
% 160.93/160.66 [7882]~P63(x78821)+~P1(f334(f334(f248(x78821),f334(f334(f292(x78821),x78822),x78823)),f2(x78821)))+P1(f334(f334(f248(x78821),f2(x78821)),x78822))+P1(f334(f334(f248(x78821),f2(x78821)),x78823))
% 160.93/160.66 [7903]P146(x79032,x79033,x79031)+E(x79031,f2(a1))+P1(f334(f334(f248(a1),f813(x79031,x79033,x79032)),f2(a1)))+P1(f334(f334(f249(a1),f814(x79031,x79033,x79032)),x79031))
% 160.93/160.66 [7904]P145(x79042,x79043,x79041)+E(x79041,f2(a1))+P1(f334(f334(f248(a1),f822(x79041,x79043,x79042)),f2(a1)))+P1(f334(f334(f249(a1),f823(x79041,x79043,x79042)),x79041))
% 160.93/160.66 [7911]~P106(x79111)+~P1(f334(f334(f249(x79111),x79112),f78(x79111)))+P1(f334(f334(f249(x79111),f334(f334(f259(x79111),x79112),f334(a116,x79113))),f78(x79111)))+~P1(f334(f334(f249(x79111),f2(x79111)),x79112))
% 160.93/160.66 [7966]~P108(x79661)+~E(x79663,f117(x79661))+~P16(x79661,f334(f171(x79661),x79663))+E(f334(f144(x79661,x79661,f334(f7(x79661,x79661,x79661),f247(x79661)),x79662),f334(f171(x79661),x79663)),x79662)
% 160.93/160.66 [7969]P145(x79691,x79692,x79693)+~P1(f334(x79691,x79692))+P1(f334(f334(f248(a1),f822(x79693,x79692,x79691)),f2(a1)))+P1(f334(f334(f249(a1),f823(x79693,x79692,x79691)),x79693))
% 160.93/160.66 [7976]P146(x79761,x79762,x79763)+~P1(f334(x79761,f2(a1)))+P1(f334(f334(f248(a1),f813(x79763,x79762,x79761)),f2(a1)))+P1(f334(f334(f249(a1),f814(x79763,x79762,x79761)),x79763))
% 160.93/160.66 [8201]P146(x82013,x82012,x82011)+E(x82011,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x82011),f821(x82011,x82012,x82013))),f813(x82011,x82012,x82013)),x82012)+P1(f334(f334(f249(a1),f814(x82011,x82012,x82013)),x82011))
% 160.93/160.66 [8202]P145(x82023,x82022,x82021)+E(x82021,f2(a1))+E(f334(f334(f80(a1),f334(f334(f81(a1),x82021),f825(x82021,x82022,x82023))),f822(x82021,x82022,x82023)),x82022)+P1(f334(f334(f249(a1),f823(x82021,x82022,x82023)),x82021))
% 160.93/160.66 [8244]P145(x82443,x82442,x82441)+~P1(f334(x82443,x82442))+E(f334(f334(f80(a1),f334(f334(f81(a1),x82441),f825(x82441,x82442,x82443))),f822(x82441,x82442,x82443)),x82442)+P1(f334(f334(f249(a1),f823(x82441,x82442,x82443)),x82441))
% 160.93/160.66 [8245]~P68(x82451)+~P74(x82451)+~P40(x82453)+E(f334(f334(f6(a881,x82451),f334(f334(f8(a1,x82451,a881),x82452),f104(a1))),f334(f313(a1,a881,a108),x82453)),f334(f334(f6(a1,x82451),x82452),x82453))
% 160.93/160.66 [8246]~P68(x82461)+~P74(x82461)+~P40(x82463)+E(f334(f334(f9(a881,x82461),f334(f334(f8(a1,x82461,a881),x82462),f104(a1))),f334(f313(a1,a881,a108),x82463)),f334(f334(f9(a1,x82461),x82462),x82463))
% 160.93/160.66 [8255]P146(x82553,x82552,x82551)+E(f334(f334(f80(a1),f334(f334(f81(a1),x82551),f821(x82551,x82552,x82553))),f813(x82551,x82552,x82553)),x82552)+~P1(f334(x82553,f2(a1)))+P1(f334(f334(f249(a1),f814(x82551,x82552,x82553)),x82551))
% 160.93/160.66 [8275]~E(x82752,f2(a881))+~E(f334(f268(a881,a881),x82753),f2(a881))+~E(x82751,f334(f334(f80(a881),f334(f334(f81(a881),f334(f268(a881,a881),x82753)),x82752)),f334(f272(a881,a881),x82753)))+P1(f334(f47(x82751,x82752),x82753))
% 160.93/160.66 [8328]P1(f334(x83281,x83282))+~P1(f334(f334(f336(x83283),f808(x83281,x83282,x83283)),f807(x83281,x83282,x83283)))+~P1(f334(f61(x83283),x83282))+~P1(f334(x83281,f196(f888(x83283,a876))))
% 160.93/160.66 [8946]P1(f334(x89461,x89462))+~P1(f334(f61(x89463),x89462))+~P1(f334(x89461,f334(f334(f312(x89463),f808(x89461,x89462,x89463)),f807(x89461,x89462,x89463))))+~P1(f334(x89461,f196(f888(x89463,a876))))
% 160.93/160.66 [9184]P1(f334(f334(f248(a1),x91841),f2(a1)))+~P1(f334(f334(f249(a1),f334(f334(f80(a1),f334(f334(f81(a1),x91842),x91841)),x91843)),f2(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x91842))+~P1(f334(f334(f248(a1),f2(a1)),x91843))
% 160.93/160.66 [5795]~P2(x57952)+E(x57951,f196(f888(x57952,a876)))+~P1(f334(f61(x57952),x57951))+E(f10(x57952,f334(f334(f312(x57952),x57953),x57951)),f334(f334(f114(x57952),x57953),f10(x57952,x57951)))
% 160.93/160.66 [5796]~P2(x57962)+E(x57961,f196(f888(x57962,a876)))+~P1(f334(f61(x57962),x57961))+E(f11(x57962,f334(f334(f312(x57962),x57963),x57961)),f334(f334(f105(x57962),x57963),f11(x57962,x57961)))
% 160.93/160.66 [5797]~P108(x57972)+E(x57971,f196(f888(x57972,a876)))+~P1(f334(f61(x57972),x57971))+E(f14(x57972,f334(f334(f312(x57972),x57973),x57971)),f334(f334(f246(x57972),x57973),f14(x57972,x57971)))
% 160.93/160.66 [5798]~P108(x57982)+E(x57981,f196(f888(x57982,a876)))+~P1(f334(f61(x57982),x57981))+E(f15(x57982,f334(f334(f312(x57982),x57983),x57981)),f334(f334(f247(x57982),x57983),f15(x57982,x57981)))
% 160.93/160.66 [6103]~P124(x61031)+~E(x61033,f2(x61031))+~E(x61032,f2(x61031))+E(f334(f334(f80(x61031),f334(f334(f81(x61031),x61032),x61032)),f334(f334(f81(x61031),x61033),x61033)),f2(x61031))
% 160.93/160.66 [6174]~P95(x61742)+E(x61741,f196(f888(x61742,a876)))+~P1(f334(f61(x61742),x61741))+E(f334(f63(x61742,f81(x61742)),f334(f334(f312(x61742),x61743),x61741)),f334(f334(f81(x61742),x61743),f334(f63(x61742,f81(x61742)),x61741)))
% 160.93/160.66 [6301]~P108(x63012)+E(x63011,f196(f888(x63012,a876)))+~P1(f334(f61(x63012),x63011))+E(f12(x63012,f247(x63012),f334(f334(f312(x63012),x63013),x63011)),f334(f334(f247(x63012),x63013),f12(x63012,f247(x63012),x63011)))
% 160.93/160.66 [6302]~P108(x63022)+E(x63021,f196(f888(x63022,a876)))+~P1(f334(f61(x63022),x63021))+E(f13(x63022,f246(x63022),f334(f334(f312(x63022),x63023),x63021)),f334(f334(f246(x63022),x63023),f13(x63022,f246(x63022),x63021)))
% 160.93/160.66 [6804]~P70(x68041)+~P1(f334(f61(x68041),x68043))+E(f334(f63(x68041,f81(x68041)),f334(f334(f312(x68041),x68042),x68043)),f334(f334(f64(x68041,x68041,f81(x68041)),x68042),x68043))+P1(f334(f334(f336(x68041),x68042),x68043))
% 160.93/160.66 [6885]~E(f334(f334(f80(a1),x68852),f334(f334(f81(a1),x68853),x68851)),x68853)+~P1(f334(f334(f249(a1),f2(a1)),x68853))+P1(f334(f334(f248(a1),f78(a1)),x68851))+~P1(f334(f334(f249(a1),x68852),x68853))
% 160.93/160.66 [6912]~E(f334(f334(f80(a1),x69122),f334(f334(f81(a1),x69123),x69121)),x69123)+P1(f334(f334(f248(a1),x69121),f78(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x69123))+~P1(f334(f334(f248(a1),f2(a1)),x69122))
% 160.93/160.66 [6928]E(x69281,f2(a881))+~P1(f334(f47(x69283,x69281),x69282))+~P1(f334(f334(f249(a881),f2(a881)),x69281))+P1(f334(f334(f249(a881),f334(f272(a881,a881),x69282)),x69281))
% 160.93/160.66 [6958]~P135(x69581)+~P1(f334(f334(f248(x69581),x69582),f2(x69581)))+~P1(f334(f334(f248(x69581),x69583),f2(x69581)))+E(f334(f334(f81(x69581),f334(f75(x69581),x69582)),f334(f75(x69581),x69583)),f334(f75(x69581),f334(f334(f81(x69581),x69582),x69583)))
% 160.93/160.66 [7008]~P135(x70081)+~P1(f334(f334(f248(x70081),x70082),f2(x70081)))+E(f334(f334(f81(x70081),f334(f75(x70081),x70082)),f334(f75(x70081),x70083)),f334(f75(x70081),f334(f334(f81(x70081),x70082),x70083)))+~P1(f334(f334(f248(x70081),f2(x70081)),x70083))
% 160.93/160.66 [7009]~P135(x70091)+~P1(f334(f334(f248(x70091),x70093),f2(x70091)))+E(f334(f334(f81(x70091),f334(f75(x70091),x70092)),f334(f75(x70091),x70093)),f334(f75(x70091),f334(f334(f81(x70091),x70092),x70093)))+~P1(f334(f334(f248(x70091),f2(x70091)),x70092))
% 160.93/160.66 [7063]~P135(x70631)+E(f334(f334(f81(x70631),f334(f75(x70631),x70632)),f334(f75(x70631),x70633)),f334(f75(x70631),f334(f334(f81(x70631),x70632),x70633)))+~P1(f334(f334(f248(x70631),f2(x70631)),x70632))+~P1(f334(f334(f248(x70631),f2(x70631)),x70633))
% 160.93/160.66 [7079]~P124(x70791)+~P1(f334(f334(f249(x70791),x70793),f2(x70791)))+~P1(f334(f334(f249(x70791),x70792),f2(x70791)))+P1(f334(f334(f249(x70791),f2(x70791)),f334(f334(f81(x70791),x70792),x70793)))
% 160.93/160.66 [7080]~P63(x70801)+~P1(f334(f334(f249(x70801),x70803),f2(x70801)))+~P1(f334(f334(f249(x70801),x70802),f2(x70801)))+P1(f334(f334(f249(x70801),f2(x70801)),f334(f334(f292(x70801),x70802),x70803)))
% 160.93/160.66 [7081]~P64(x70811)+~P1(f334(f334(f249(x70811),x70813),f2(x70811)))+~P1(f334(f334(f249(x70811),x70812),f2(x70811)))+P1(f334(f334(f249(x70811),f2(x70811)),f334(f334(f292(x70811),x70812),x70813)))
% 160.93/160.66 [7083]~P125(x70831)+~P1(f334(f334(f248(x70831),x70833),f2(x70831)))+~P1(f334(f334(f248(x70831),x70832),f2(x70831)))+P1(f334(f334(f248(x70831),f2(x70831)),f334(f334(f81(x70831),x70832),x70833)))
% 160.93/160.66 [7084]~P124(x70841)+~P1(f334(f334(f248(x70841),x70843),f2(x70841)))+~P1(f334(f334(f248(x70841),x70842),f2(x70841)))+P1(f334(f334(f248(x70841),f2(x70841)),f334(f334(f81(x70841),x70842),x70843)))
% 160.93/160.66 [7085]~P63(x70851)+~P1(f334(f334(f248(x70851),x70853),f2(x70851)))+~P1(f334(f334(f248(x70851),x70852),f2(x70851)))+P1(f334(f334(f248(x70851),f2(x70851)),f334(f334(f292(x70851),x70852),x70853)))
% 160.93/160.66 [7086]~P64(x70861)+~P1(f334(f334(f249(x70861),x70863),f2(x70861)))+~P1(f334(f334(f248(x70861),x70862),f2(x70861)))+P1(f334(f334(f248(x70861),f2(x70861)),f334(f334(f292(x70861),x70862),x70863)))
% 160.93/160.66 [7087]~P106(x70871)+~P1(f334(f334(f249(a881),f2(a881)),x70873))+~P1(f334(f334(f249(x70871),f78(x70871)),x70872))+P1(f334(f334(f249(x70871),f78(x70871)),f334(f334(f259(x70871),x70872),x70873)))
% 160.93/160.66 [7185]~P81(x71851)+~P1(f334(f334(f249(x71851),f2(x71851)),x71853))+~P1(f334(f334(f249(x71851),f2(x71851)),x71852))+P1(f334(f334(f249(x71851),f2(x71851)),f334(f334(f80(x71851),x71852),x71853)))
% 160.93/160.66 [7188]~P126(x71881)+~P1(f334(f334(f249(x71881),f2(x71881)),x71883))+~P1(f334(f334(f249(x71881),f2(x71881)),x71882))+P1(f334(f334(f249(x71881),f2(x71881)),f334(f334(f81(x71881),x71882),x71883)))
% 160.93/160.66 [7189]~P63(x71891)+~P1(f334(f334(f249(x71891),f2(x71891)),x71893))+~P1(f334(f334(f249(x71891),f2(x71891)),x71892))+P1(f334(f334(f249(x71891),f2(x71891)),f334(f334(f292(x71891),x71892),x71893)))
% 160.93/160.66 [7190]~P64(x71901)+~P1(f334(f334(f249(x71901),f2(x71901)),x71903))+~P1(f334(f334(f249(x71901),f2(x71901)),x71902))+P1(f334(f334(f249(x71901),f2(x71901)),f334(f334(f292(x71901),x71902),x71903)))
% 160.93/160.66 [7191]~P106(x71911)+~P1(f334(f334(f249(x71911),f78(x71911)),x71913))+~P1(f334(f334(f249(x71911),f78(x71911)),x71912))+P1(f334(f334(f249(x71911),f78(x71911)),f334(f334(f81(x71911),x71912),x71913)))
% 160.93/160.66 [7193]~P125(x71931)+~P1(f334(f334(f248(x71931),f2(x71931)),x71933))+~P1(f334(f334(f248(x71931),f2(x71931)),x71932))+P1(f334(f334(f248(x71931),f2(x71931)),f334(f334(f81(x71931),x71932),x71933)))
% 160.93/160.66 [7194]~P124(x71941)+~P1(f334(f334(f248(x71941),f2(x71941)),x71943))+~P1(f334(f334(f248(x71941),f2(x71941)),x71942))+P1(f334(f334(f248(x71941),f2(x71941)),f334(f334(f81(x71941),x71942),x71943)))
% 160.93/160.66 [7195]~P132(x71951)+~P1(f334(f334(f248(x71951),f2(x71951)),x71953))+~P1(f334(f334(f248(x71951),f2(x71951)),x71952))+P1(f334(f334(f248(x71951),f2(x71951)),f334(f334(f81(x71951),x71952),x71953)))
% 160.93/160.66 [7196]~P63(x71961)+~P1(f334(f334(f248(x71961),f2(x71961)),x71963))+~P1(f334(f334(f248(x71961),f2(x71961)),x71962))+P1(f334(f334(f248(x71961),f2(x71961)),f334(f334(f292(x71961),x71962),x71963)))
% 160.93/160.66 [7197]~P64(x71971)+~P1(f334(f334(f249(x71971),f2(x71971)),x71973))+~P1(f334(f334(f248(x71971),f2(x71971)),x71972))+P1(f334(f334(f248(x71971),f2(x71971)),f334(f334(f292(x71971),x71972),x71973)))
% 160.93/160.66 [7268]~P2(x72681)+~P1(f334(f61(x72681),x72683))+E(f10(x72681,f334(f334(f312(x72681),x72682),x72683)),x72682)+~E(f334(f334(f22(f888(x72681,a876)),x72683),f334(f334(f312(x72681),x72682),f196(f888(x72681,a876)))),f196(f888(x72681,a876)))
% 160.93/160.66 [7269]~P2(x72691)+~P1(f334(f61(x72691),x72693))+E(f11(x72691,f334(f334(f312(x72691),x72692),x72693)),x72692)+~E(f334(f334(f22(f888(x72691,a876)),x72693),f334(f334(f312(x72691),x72692),f196(f888(x72691,a876)))),f196(f888(x72691,a876)))
% 160.93/160.66 [7270]~P108(x72701)+~P1(f334(f61(x72701),x72703))+E(f14(x72701,f334(f334(f312(x72701),x72702),x72703)),x72702)+~E(f334(f334(f22(f888(x72701,a876)),x72703),f334(f334(f312(x72701),x72702),f196(f888(x72701,a876)))),f196(f888(x72701,a876)))
% 160.93/160.66 [7271]~P108(x72711)+~P1(f334(f61(x72711),x72713))+E(f15(x72711,f334(f334(f312(x72711),x72712),x72713)),x72712)+~E(f334(f334(f22(f888(x72711,a876)),x72713),f334(f334(f312(x72711),x72712),f196(f888(x72711,a876)))),f196(f888(x72711,a876)))
% 160.93/160.66 [7272]~P63(x72721)+P1(f334(f334(f249(x72721),x72722),f2(x72721)))+P1(f334(f334(f249(x72721),f2(x72721)),x72723))+~P1(f334(f334(f249(x72721),f2(x72721)),f334(f334(f292(x72721),x72723),x72722)))
% 160.93/160.66 [7273]~P63(x72731)+P1(f334(f334(f249(x72731),x72732),f2(x72731)))+P1(f334(f334(f249(x72731),f2(x72731)),x72733))+~P1(f334(f334(f249(x72731),f2(x72731)),f334(f334(f292(x72731),x72732),x72733)))
% 160.93/160.66 [7274]~P63(x72741)+P1(f334(f334(f249(x72741),x72742),f2(x72741)))+P1(f334(f334(f249(x72741),f2(x72741)),x72742))+~P1(f334(f334(f249(x72741),f2(x72741)),f334(f334(f292(x72741),x72743),x72742)))
% 160.93/160.66 [7275]~P63(x72751)+P1(f334(f334(f249(x72751),x72752),f2(x72751)))+P1(f334(f334(f249(x72751),f2(x72751)),x72752))+~P1(f334(f334(f249(x72751),f2(x72751)),f334(f334(f292(x72751),x72752),x72753)))
% 160.93/160.66 [7276]~P124(x72761)+P1(f334(f334(f248(x72761),x72762),f2(x72761)))+P1(f334(f334(f248(x72761),f2(x72761)),x72763))+~P1(f334(f334(f248(x72761),f2(x72761)),f334(f334(f81(x72761),x72763),x72762)))
% 160.93/160.66 [7277]~P124(x72771)+P1(f334(f334(f248(x72771),x72772),f2(x72771)))+P1(f334(f334(f248(x72771),f2(x72771)),x72773))+~P1(f334(f334(f248(x72771),f2(x72771)),f334(f334(f81(x72771),x72772),x72773)))
% 160.93/160.66 [7278]~P63(x72781)+P1(f334(f334(f248(x72781),x72782),f2(x72781)))+P1(f334(f334(f248(x72781),f2(x72781)),x72783))+~P1(f334(f334(f248(x72781),f2(x72781)),f334(f334(f292(x72781),x72783),x72782)))
% 160.93/160.66 [7279]~P63(x72791)+P1(f334(f334(f248(x72791),x72792),f2(x72791)))+P1(f334(f334(f248(x72791),f2(x72791)),x72793))+~P1(f334(f334(f248(x72791),f2(x72791)),f334(f334(f292(x72791),x72792),x72793)))
% 160.93/160.66 [7280]~P124(x72801)+P1(f334(f334(f248(x72801),x72802),f2(x72801)))+P1(f334(f334(f248(x72801),f2(x72801)),x72802))+~P1(f334(f334(f248(x72801),f2(x72801)),f334(f334(f81(x72801),x72803),x72802)))
% 160.93/160.66 [7281]~P124(x72811)+P1(f334(f334(f248(x72811),x72812),f2(x72811)))+P1(f334(f334(f248(x72811),f2(x72811)),x72812))+~P1(f334(f334(f248(x72811),f2(x72811)),f334(f334(f81(x72811),x72812),x72813)))
% 160.93/160.66 [7282]~P63(x72821)+P1(f334(f334(f248(x72821),x72822),f2(x72821)))+P1(f334(f334(f248(x72821),f2(x72821)),x72822))+~P1(f334(f334(f248(x72821),f2(x72821)),f334(f334(f292(x72821),x72823),x72822)))
% 160.93/160.66 [7283]~P63(x72831)+P1(f334(f334(f248(x72831),x72832),f2(x72831)))+P1(f334(f334(f248(x72831),f2(x72831)),x72832))+~P1(f334(f334(f248(x72831),f2(x72831)),f334(f334(f292(x72831),x72832),x72833)))
% 160.93/160.66 [7373]~E(f334(f334(f105(f888(x73731,a876)),f334(f174(x73731),x73732)),f334(f174(x73731),x73733)),f196(f888(x73731,a876)))+~P1(f334(f139(x73731),x73733))+~P1(f334(f139(x73731),x73732))+P1(f334(f139(x73731),f334(f334(f136(x73731),x73732),x73733)))
% 160.93/160.66 [7374]~P108(x73741)+~P1(f334(f61(x73741),x73743))+E(f12(x73741,f247(x73741),f334(f334(f312(x73741),x73742),x73743)),x73742)+~E(f334(f334(f22(f888(x73741,a876)),x73743),f334(f334(f312(x73741),x73742),f196(f888(x73741,a876)))),f196(f888(x73741,a876)))
% 160.93/160.66 [7375]~P108(x73751)+~P1(f334(f61(x73751),x73753))+E(f13(x73751,f246(x73751),f334(f334(f312(x73751),x73752),x73753)),x73752)+~E(f334(f334(f22(f888(x73751,a876)),x73753),f334(f334(f312(x73751),x73752),f196(f888(x73751,a876)))),f196(f888(x73751,a876)))
% 160.93/160.66 [7390]~P111(x73901)+~P1(f334(f334(f249(x73901),x73902),x73903))+~P1(f334(f334(f249(x73901),f334(f79(x73901),x73902)),x73903))+P1(f334(f334(f249(x73901),f334(f75(x73901),x73902)),x73903))
% 160.93/160.66 [7392]~P85(x73921)+~P1(f334(f334(f248(x73921),x73922),x73923))+~P1(f334(f334(f248(x73921),f334(f79(x73921),x73922)),x73923))+P1(f334(f334(f248(x73921),f334(f75(x73921),x73922)),x73923))
% 160.93/160.66 [7462]~P126(x74621)+P1(f334(f334(f249(x74621),f2(x74621)),x74622))+~P1(f334(f334(f249(x74621),f2(x74621)),x74623))+~P1(f334(f334(f249(x74621),f2(x74621)),f334(f334(f81(x74621),x74623),x74622)))
% 160.93/160.66 [7463]~P126(x74631)+P1(f334(f334(f249(x74631),f2(x74631)),x74632))+~P1(f334(f334(f249(x74631),f2(x74631)),x74633))+~P1(f334(f334(f249(x74631),f2(x74631)),f334(f334(f81(x74631),x74632),x74633)))
% 160.93/160.66 [7764]E(x77641,x77642)+~P1(f334(f61(x77643),x77641))+~P1(f334(f334(f248(a881),f334(f37(x77643),x77641)),f334(f37(x77643),x77642)))+~P1(f334(f334(f248(f888(x77643,a876)),x77642),x77641))
% 160.93/160.66 [7907]~P1(f334(f334(f249(a1),x79071),f2(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x79072))+~P1(f334(f334(f248(a1),x79072),x79073))+P1(f334(f334(f248(a1),f334(f334(f38(a1),x79071),x79072)),f334(f334(f38(a1),x79071),x79073)))
% 160.93/160.66 [7919]~P1(f334(f334(f249(a1),f2(a1)),x79193))+~P1(f334(f334(f248(a1),f2(a1)),x79191))+~P1(f334(f334(f248(a1),x79193),x79192))+P1(f334(f334(f248(a1),f334(f334(f38(a1),x79191),x79192)),f334(f334(f38(a1),x79191),x79193)))
% 160.93/160.66 [8052]E(f334(x80521,f455(x80522,x80521,x80523)),x80522)+~P1(f334(f334(f248(a1),x80522),f334(x80521,x80523)))+P1(f334(f334(f249(a881),f456(x80522,x80521,x80523)),x80523))+~P1(f334(f334(f248(a1),f334(x80521,f2(a881))),x80522))
% 160.93/160.66 [8053]E(f334(x80531,f461(x80532,x80531,x80533)),x80532)+~P1(f334(f334(f248(a1),x80532),f334(x80531,x80533)))+P1(f334(f334(f249(a881),f462(x80532,x80531,x80533)),x80533))+~P1(f334(f334(f248(a1),f334(x80531,f2(a881))),x80532))
% 160.93/160.66 [8158]~P1(f334(f61(x81581),x81583))+~P1(f334(f334(f249(a881),f334(f37(x81581),x81582)),f334(f37(x81581),x81583)))+~P1(f334(f334(f248(f888(x81581,a876)),x81582),x81583))+P1(f334(f334(f249(f888(x81581,a876)),x81582),x81583))
% 160.93/160.66 [8190]E(f334(f334(f80(a1),f373(x81903,x81901,x81902)),f374(x81903,x81901,x81902)),x81901)+E(f334(f334(f22(a1),x81901),x81902),x81901)+~P1(f334(f334(f249(a1),f2(a1)),x81902))+~P1(f334(f334(f336(a1),f334(f334(f22(a1),x81901),f78(a1))),x81903))
% 160.93/160.66 [8191]E(f334(f334(f22(a1),f388(x81913,x81911,x81912)),f389(x81913,x81911,x81912)),x81911)+E(f334(f334(f80(a1),x81911),x81912),x81911)+~P1(f334(f334(f249(a1),f2(a1)),x81912))+~P1(f334(f334(f336(a1),f334(f334(f80(a1),x81911),f78(a1))),x81913))
% 160.93/160.66 [8250]~P1(f334(f334(f248(a881),x82503),x82501))+P1(f334(f334(f249(a881),x82501),x82502))+~P1(f334(f334(f248(a881),x82503),x82502))+~P1(f334(f334(f249(a881),f334(f334(f22(a881),x82501),x82503)),f334(f334(f22(a881),x82502),x82503)))
% 160.93/160.66 [8251]~P1(f334(f334(f248(a881),x82513),x82511))+P1(f334(f334(f248(a881),x82511),x82512))+~P1(f334(f334(f248(a881),x82513),x82512))+~P1(f334(f334(f248(a881),f334(f334(f22(a881),x82511),x82513)),f334(f334(f22(a881),x82512),x82513)))
% 160.93/160.66 [8267]~P108(x82672)+E(x82671,f117(x82672))+~P16(x82672,f334(f171(x82672),x82671))+E(f334(f144(x82672,x82672,f334(f7(x82672,x82672,x82672),f247(x82672)),x82673),f334(f171(x82672),x82671)),f334(f334(f247(x82672),f334(f334(f167(x82672),x82671),f2(a881))),x82673))
% 160.93/160.66 [8333]E(f334(f334(f22(a1),x83331),x83332),x83331)+~P1(f334(f334(f249(a1),f2(a1)),x83332))+P1(f334(f334(f336(a1),f373(x83333,x83331,x83332)),x83333))+~P1(f334(f334(f336(a1),f334(f334(f22(a1),x83331),f78(a1))),x83333))
% 160.93/160.66 [8334]E(f334(f334(f80(a1),x83341),x83342),x83341)+~P1(f334(f334(f249(a1),f2(a1)),x83342))+P1(f334(f334(f336(a1),f388(x83343,x83341,x83342)),x83343))+~P1(f334(f334(f336(a1),f334(f334(f80(a1),x83341),f78(a1))),x83343))
% 160.93/160.66 [8408]~P1(f334(f334(f248(a1),x84081),f334(x84082,x84083)))+P1(f334(f334(f248(a881),f455(x84081,x84082,x84083)),x84083))+P1(f334(f334(f249(a881),f456(x84081,x84082,x84083)),x84083))+~P1(f334(f334(f248(a1),f334(x84082,f2(a881))),x84081))
% 160.93/160.66 [8409]~P1(f334(f334(f248(a1),x84091),f334(x84092,x84093)))+P1(f334(f334(f248(a881),f461(x84091,x84092,x84093)),x84093))+P1(f334(f334(f249(a881),f462(x84091,x84092,x84093)),x84093))+~P1(f334(f334(f248(a1),f334(x84092,f2(a881))),x84091))
% 160.93/160.66 [8481]E(f334(f334(f22(a1),x84811),x84812),x84811)+~P1(f334(f334(f249(a1),f2(a1)),x84812))+P1(f334(f334(f336(a1),f374(x84813,x84811,x84812)),f305(a1,f78(a1),x84812)))+~P1(f334(f334(f336(a1),f334(f334(f22(a1),x84811),f78(a1))),x84813))
% 160.93/160.66 [8482]E(f334(f334(f80(a1),x84821),x84822),x84821)+~P1(f334(f334(f249(a1),f2(a1)),x84822))+P1(f334(f334(f336(a1),f389(x84823,x84821,x84822)),f305(a1,f78(a1),x84822)))+~P1(f334(f334(f336(a1),f334(f334(f80(a1),x84821),f78(a1))),x84823))
% 160.93/160.66 [8618]~P106(x86181)+~P1(f334(f334(f249(x86181),x86182),f78(x86181)))+~P1(f334(f334(f249(x86181),f2(x86181)),x86182))+P1(f334(f334(f249(x86181),f334(f334(f81(x86181),x86182),f334(f334(f259(x86181),x86182),x86183))),f334(f334(f259(x86181),x86182),x86183)))
% 160.93/160.66 [8705]~P1(f334(x87051,x87052))+P1(f334(x87051,f2(a881)))+~P1(f334(f334(f249(a881),x87052),x87053))+~P1(f334(x87051,f44(a881,f334(a116,f502(x87052,x87051,x87053)),x87053)))
% 160.93/160.66 [8843]E(f528(x88431,x88432,x88433),f2(a881))+P1(f334(f334(x88431,x88433),x88432))+P1(f334(f334(x88431,f528(x88431,x88432,x88433)),f44(a881,f527(x88431,x88432,x88433),f528(x88431,x88432,x88433))))+~P1(f334(f322(f887(a881,a881),a232),f334(f334(f269(a881,a881),x88433),x88432)))
% 160.93/160.66 [8881]~P27(x88811,x88811,x88812,x88813)+E(f334(f313(x88811,x88811,x88812),x88813),x88813)+~P1(f334(f61(x88811),x88813))+~P1(f334(f334(f248(f888(x88811,a876)),f334(f313(x88811,x88811,x88812),x88813)),x88813))
% 160.93/160.66 [9108]P1(f334(f334(x91081,x91082),x91083))+P1(f334(f334(f249(a1),f819(x91081,x91083,x91082)),f820(x91081,x91083,x91082)))+P1(f334(f334(x91081,f819(x91081,x91083,x91082)),f334(f334(f80(a1),f820(x91081,x91083,x91082)),f78(a1))))+~P1(f334(f322(f887(a1,a1),a135),f334(f334(f269(a1,a1),x91082),x91083)))
% 160.93/160.66 [9125]P1(f334(f334(x91251,x91252),x91253))+~P1(f334(f334(f249(a1),f524(x91251,x91253,x91252)),f2(a1)))+P1(f334(f334(x91251,f334(f79(a1),f523(x91251,x91253,x91252))),f334(f79(a1),f524(x91251,x91253,x91252))))+~P1(f334(f322(f887(a1,a1),a237),f334(f334(f269(a1,a1),x91252),x91253)))
% 160.93/160.66 [9312]P1(f334(f334(x93121,x93122),x93123))+P1(f334(f334(x93121,f334(f334(f80(a1),f697(x93121,x93123,x93122)),f78(a1))),f699(x93121,x93123,x93122)))+~P1(f334(f334(f248(a1),f697(x93121,x93123,x93122)),f699(x93121,x93123,x93122)))+~P1(f334(f322(f887(a1,a1),a185),f334(f334(f269(a1,a1),x93122),x93123)))
% 160.93/160.66 [9743]~P60(x97432)+~P60(x97431)+~P1(f334(f58(f887(x97431,x97432)),x97433))+P1(f334(f58(x97431),f334(f334(f8(f888(x97432,a876),a876,x97431),f58(x97432)),f334(f334(f8(f888(x97432,f887(x97431,x97432)),f888(x97432,a876),x97431),f334(f8(f887(x97431,x97432),a876,x97432),x97433)),f269(x97431,x97432)))))
% 160.93/160.66 [9744]~P60(x97442)+~P60(x97441)+~P1(f334(f57(f887(x97441,x97442)),x97443))+P1(f334(f57(x97441),f334(f334(f8(f888(x97442,a876),a876,x97441),f57(x97442)),f334(f334(f8(f888(x97442,f887(x97441,x97442)),f888(x97442,a876),x97441),f334(f8(f887(x97441,x97442),a876,x97442),x97443)),f269(x97441,x97442)))))
% 160.93/160.66 [9846]~P60(x98462)+~P60(x98461)+P1(f334(f58(f887(x98461,x98462)),x98463))+~P1(f334(f58(x98461),f334(f334(f8(f888(x98462,a876),a876,x98461),f58(x98462)),f334(f334(f8(f888(x98462,f887(x98461,x98462)),f888(x98462,a876),x98461),f334(f8(f887(x98461,x98462),a876,x98462),x98463)),f269(x98461,x98462)))))
% 160.93/160.66 [9847]~P60(x98472)+~P60(x98471)+P1(f334(f57(f887(x98471,x98472)),x98473))+~P1(f334(f57(x98471),f334(f334(f8(f888(x98472,a876),a876,x98471),f57(x98472)),f334(f334(f8(f888(x98472,f887(x98471,x98472)),f888(x98472,a876),x98471),f334(f8(f887(x98471,x98472),a876,x98472),x98473)),f269(x98471,x98472)))))
% 160.93/160.66 [10017]E(f334(x100171,f455(x100172,x100171,x100173)),x100172)+~P1(f334(f334(f248(a1),x100172),f334(x100171,x100173)))+~P1(f334(f334(f248(a1),f334(f75(a1),f334(f334(f22(a1),f334(x100171,f334(f334(f80(a881),f456(x100172,x100171,x100173)),f78(a881)))),f334(x100171,f456(x100172,x100171,x100173))))),f78(a1)))+~P1(f334(f334(f248(a1),f334(x100171,f2(a881))),x100172))
% 160.93/160.66 [10018]E(f334(x100181,f461(x100182,x100181,x100183)),x100182)+~P1(f334(f334(f248(a1),x100182),f334(x100181,x100183)))+~P1(f334(f334(f248(a1),f334(f75(a1),f334(f334(f22(a1),f334(x100181,f334(f334(f80(a881),f462(x100182,x100181,x100183)),f78(a881)))),f334(x100181,f462(x100182,x100181,x100183))))),f78(a1)))+~P1(f334(f334(f248(a1),f334(x100181,f2(a881))),x100182))
% 160.93/160.66 [10022]~P1(f334(f334(f248(a1),x100221),f334(x100222,x100223)))+~P1(f334(f334(f248(a1),f334(f75(a1),f334(f334(f22(a1),f334(x100222,f334(f334(f80(a881),f456(x100221,x100222,x100223)),f78(a881)))),f334(x100222,f456(x100221,x100222,x100223))))),f78(a1)))+P1(f334(f334(f248(a881),f455(x100221,x100222,x100223)),x100223))+~P1(f334(f334(f248(a1),f334(x100222,f2(a881))),x100221))
% 160.93/160.66 [10023]~P1(f334(f334(f248(a1),x100231),f334(x100232,x100233)))+~P1(f334(f334(f248(a1),f334(f75(a1),f334(f334(f22(a1),f334(x100232,f334(f334(f80(a881),f462(x100231,x100232,x100233)),f78(a881)))),f334(x100232,f462(x100231,x100232,x100233))))),f78(a1)))+P1(f334(f334(f248(a881),f461(x100231,x100232,x100233)),x100233))+~P1(f334(f334(f248(a1),f334(x100232,f2(a881))),x100231))
% 160.93/160.66 [10079]E(x100791,x100792)+~E(f334(f144(f882(x100793),f882(x100793),f136(x100793),f117(x100793)),x100791),f334(f144(f882(x100793),f882(x100793),f136(x100793),f117(x100793)),x100792))+~E(f334(f197(f882(f882(x100793))),x100791),f334(f197(f882(f882(x100793))),x100792))+~P1(f334(f334(f273(f882(x100793),f882(x100793),a876),f334(f334(f7(f882(x100793),f888(f882(x100793),a881),f888(f882(x100793),a876)),f334(f334(f8(f888(a881,a876),f888(f888(f882(x100793),a881),f888(f882(x100793),a876)),f882(x100793)),f8(a881,a876,f882(x100793))),f334(f334(f8(a881,f888(a881,a876),f882(x100793)),a331),f197(f882(x100793))))),f197(f882(x100793)))),f745(x100791,x100792,x100793)))
% 160.93/160.66 [10080]E(x100801,x100802)+~E(f334(f144(f882(x100803),f882(x100803),f136(x100803),f117(x100803)),x100801),f334(f144(f882(x100803),f882(x100803),f136(x100803),f117(x100803)),x100802))+~E(f334(f197(f882(f882(x100803))),x100801),f334(f197(f882(f882(x100803))),x100802))+~P1(f334(f334(f273(f882(x100803),f882(x100803),a876),f334(f334(f7(f882(x100803),f888(f882(x100803),a881),f888(f882(x100803),a876)),f334(f334(f8(f888(a881,a876),f888(f888(f882(x100803),a881),f888(f882(x100803),a876)),f882(x100803)),f8(a881,a876,f882(x100803))),f334(f334(f8(a881,f888(a881,a876),f882(x100803)),a331),f197(f882(x100803))))),f197(f882(x100803)))),f746(x100802,x100801,x100803)))
% 160.93/160.66 [6791]~E(f78(a881),f2(a881))+~P1(f334(f61(x67911),x67913))+~P1(f334(f61(x67911),x67912))+E(f334(f334(f80(a881),f334(f37(x67911),x67912)),f334(f37(x67911),x67913)),f334(f37(x67911),f334(f334(f114(f888(x67911,a876)),x67912),x67913)))
% 160.93/160.66 [7204]~P100(x72041)+~P1(f334(f61(x72041),x72042))+~P1(f334(f334(f336(x72041),x72043),x72042))+P1(f334(f334(f248(x72041),f334(f63(x72041,f105(x72041)),x72042)),x72043))
% 160.93/160.66 [7205]~P108(x72051)+~P1(f334(f61(x72051),x72052))+~P1(f334(f334(f336(x72051),x72053),x72052))+P1(f334(f334(f248(x72051),f334(f63(x72051,f246(x72051)),x72052)),x72053))
% 160.93/160.66 [7456]~P1(f334(f61(x74561),x74563))+~P1(f334(f61(x74561),x74562))+~E(f334(f334(f105(f888(x74561,a876)),x74562),x74563),f196(f888(x74561,a876)))+E(f334(f334(f80(a881),f334(f37(x74561),x74562)),f334(f37(x74561),x74563)),f334(f37(x74561),f334(f334(f114(f888(x74561,a876)),x74562),x74563)))
% 160.93/160.66 [8256]~P39(x82561,x82563)+~P39(x82561,x82562)+~E(f334(f334(f105(f888(x82561,a876)),f334(f267(x82561,x82561),x82562)),f334(f265(x82561,x82561),x82563)),f196(f888(x82561,a876)))+P39(x82561,f334(f334(f114(f888(f887(x82561,x82561),a876)),x82562),x82563))
% 160.93/160.66 [8348]E(x83481,f334(f334(f38(a881),x83482),x83483))+~P1(f334(f334(f249(a881),f2(a881)),x83483))+~P1(f334(f334(f249(a881),x83482),f334(f334(f81(a881),x83483),f334(a116,x83481))))+~P1(f334(f334(f248(a881),f334(f334(f81(a881),x83483),x83481)),x83482))
% 160.93/160.66 [8479]~P1(f334(f61(x84791),x84792))+~P1(f334(f61(x84791),x84793))+E(f334(f334(f80(a881),f334(f37(x84791),x84792)),f334(f37(x84791),x84793)),f334(f37(x84791),f334(f334(f114(f888(x84791,a876)),x84792),x84793)))+P1(f334(f334(f336(x84791),f851(x84793,x84792,x84791)),f334(f334(f105(f888(x84791,a876)),x84792),x84793)))
% 160.93/160.66 [8855]~P124(x88552)+~E(x88551,f2(x88552))+~E(x88553,f2(x88552))+~P1(f334(f334(f249(x88552),f2(x88552)),f334(f334(f80(x88552),f334(f334(f81(x88552),x88553),x88553)),f334(f334(f81(x88552),x88551),x88551))))
% 160.93/160.66 [9391]~P39(x93911,x93913)+~P39(x93911,x93912)+P39(x93911,f334(f334(f114(f888(f887(x93911,x93911),a876)),x93912),x93913))+~P1(f334(f334(f248(f888(f887(x93911,x93911),a876)),f334(f334(f291(x93911,x93911,x93911),x93912),x93913)),x93912))
% 160.93/160.66 [9520]~P1(f334(x95201,x95203))+~P1(f334(f61(x95202),x95203))+P1(f334(x95201,f196(f888(x95202,a876))))+~P1(f334(x95201,f334(f334(f22(f888(x95202,a876)),f727(x95201,x95203,x95202)),f334(f334(f312(x95202),f715(x95201,x95203,x95202)),f196(f888(x95202,a876))))))
% 160.93/160.66 [9773]~P60(x97731)+~P60(x97732)+P12(x97731,f334(f334(f8(f888(x97732,x97731),a876,f882(x97731)),x97733),f334(f334(f8(f888(x97732,f885(x97731)),f888(x97732,x97731),f882(x97731)),f73(f885(x97731),x97731,x97732,f245(x97731))),f334(f334(f8(f882(f887(x97732,x97731)),f888(x97732,f885(x97731)),f882(x97731)),f180(x97732,x97731)),f334(f184(x97732,x97731),f55(x97732))))),f334(f197(f882(x97732)),f55(x97732)))+~P1(f334(f57(f888(x97732,x97731)),x97733))
% 160.93/160.66 [9774]~P60(x97741)+~P60(x97742)+P13(x97741,f334(f334(f8(f888(x97742,x97741),a876,f882(x97741)),x97743),f334(f334(f8(f888(x97742,f885(x97741)),f888(x97742,x97741),f882(x97741)),f73(f885(x97741),x97741,x97742,f245(x97741))),f334(f334(f8(f882(f887(x97742,x97741)),f888(x97742,f885(x97741)),f882(x97741)),f180(x97742,x97741)),f334(f184(x97742,x97741),f55(x97742))))),f334(f197(f882(x97742)),f55(x97742)))+~P1(f334(f58(f888(x97742,x97741)),x97743))
% 160.93/160.66 [9871]~P60(x98711)+~P60(x98712)+~P13(x98712,f334(f334(f8(f888(x98711,x98712),a876,f882(x98712)),x98713),f334(f334(f8(f888(x98711,f885(x98712)),f888(x98711,x98712),f882(x98712)),f73(f885(x98712),x98712,x98711,f245(x98712))),f334(f334(f8(f882(f887(x98711,x98712)),f888(x98711,f885(x98712)),f882(x98712)),f180(x98711,x98712)),f334(f184(x98711,x98712),f55(x98711))))),f334(f197(f882(x98711)),f55(x98711)))+P1(f334(f58(f888(x98711,x98712)),x98713))
% 160.93/160.66 [9872]~P60(x98721)+~P60(x98722)+~P12(x98722,f334(f334(f8(f888(x98721,x98722),a876,f882(x98722)),x98723),f334(f334(f8(f888(x98721,f885(x98722)),f888(x98721,x98722),f882(x98722)),f73(f885(x98722),x98722,x98721,f245(x98722))),f334(f334(f8(f882(f887(x98721,x98722)),f888(x98721,f885(x98722)),f882(x98722)),f180(x98721,x98722)),f334(f184(x98721,x98722),f55(x98721))))),f334(f197(f882(x98721)),f55(x98721)))+P1(f334(f57(f888(x98721,x98722)),x98723))
% 160.93/160.66 [8657]~P1(f334(f334(f249(a1),f2(a1)),x86573))+P1(f334(f334(f248(a1),f2(a1)),x86571))+~P1(f334(f334(f249(a1),x86572),x86573))+~P1(f334(f334(f248(a1),f2(a1)),f334(f334(f80(a1),f334(f334(f81(a1),x86573),x86571)),x86572)))
% 160.93/160.66 [8679]~P2(x86791)+~P1(f334(f61(x86791),x86792))+E(f334(f334(f22(f888(x86791,a876)),x86792),f334(f334(f312(x86791),x86793),f196(f888(x86791,a876)))),f196(f888(x86791,a876)))+E(f334(f334(f114(x86791),x86793),f10(x86791,f334(f334(f22(f888(x86791,a876)),x86792),f334(f334(f312(x86791),x86793),f196(f888(x86791,a876)))))),f10(x86791,f334(f334(f312(x86791),x86793),x86792)))
% 160.93/160.66 [8680]~P2(x86801)+~P1(f334(f61(x86801),x86802))+E(f334(f334(f22(f888(x86801,a876)),x86802),f334(f334(f312(x86801),x86803),f196(f888(x86801,a876)))),f196(f888(x86801,a876)))+E(f334(f334(f105(x86801),x86803),f11(x86801,f334(f334(f22(f888(x86801,a876)),x86802),f334(f334(f312(x86801),x86803),f196(f888(x86801,a876)))))),f11(x86801,f334(f334(f312(x86801),x86803),x86802)))
% 160.93/160.66 [8681]~P108(x86811)+~P1(f334(f61(x86811),x86812))+E(f334(f334(f22(f888(x86811,a876)),x86812),f334(f334(f312(x86811),x86813),f196(f888(x86811,a876)))),f196(f888(x86811,a876)))+E(f334(f334(f246(x86811),x86813),f14(x86811,f334(f334(f22(f888(x86811,a876)),x86812),f334(f334(f312(x86811),x86813),f196(f888(x86811,a876)))))),f14(x86811,f334(f334(f312(x86811),x86813),x86812)))
% 160.93/160.66 [8682]~P108(x86821)+~P1(f334(f61(x86821),x86822))+E(f334(f334(f22(f888(x86821,a876)),x86822),f334(f334(f312(x86821),x86823),f196(f888(x86821,a876)))),f196(f888(x86821,a876)))+E(f334(f334(f247(x86821),x86823),f15(x86821,f334(f334(f22(f888(x86821,a876)),x86822),f334(f334(f312(x86821),x86823),f196(f888(x86821,a876)))))),f15(x86821,f334(f334(f312(x86821),x86823),x86822)))
% 160.93/160.66 [8746]~P108(x87461)+~P1(f334(f61(x87461),x87462))+E(f334(f334(f22(f888(x87461,a876)),x87462),f334(f334(f312(x87461),x87463),f196(f888(x87461,a876)))),f196(f888(x87461,a876)))+E(f334(f334(f247(x87461),x87463),f12(x87461,f247(x87461),f334(f334(f22(f888(x87461,a876)),x87462),f334(f334(f312(x87461),x87463),f196(f888(x87461,a876)))))),f12(x87461,f247(x87461),f334(f334(f312(x87461),x87463),x87462)))
% 160.93/160.66 [8747]~P108(x87471)+~P1(f334(f61(x87471),x87472))+E(f334(f334(f22(f888(x87471,a876)),x87472),f334(f334(f312(x87471),x87473),f196(f888(x87471,a876)))),f196(f888(x87471,a876)))+E(f334(f334(f246(x87471),x87473),f13(x87471,f246(x87471),f334(f334(f22(f888(x87471,a876)),x87472),f334(f334(f312(x87471),x87473),f196(f888(x87471,a876)))))),f13(x87471,f246(x87471),f334(f334(f312(x87471),x87473),x87472)))
% 160.93/160.66 [9332]E(x93321,x93322)+~E(f334(f144(f882(x93323),f882(x93323),f136(x93323),f117(x93323)),x93321),f334(f144(f882(x93323),f882(x93323),f136(x93323),f117(x93323)),x93322))+~E(f334(f197(f882(f882(x93323))),x93321),f334(f197(f882(f882(x93323))),x93322))+P1(f334(f334(f336(f887(f882(x93323),f882(x93323))),f745(x93321,x93322,x93323)),f334(f174(f887(f882(x93323),f882(x93323))),f334(f334(f184(f882(x93323),f882(x93323)),x93322),x93321))))
% 160.93/160.66 [9333]E(x93331,x93332)+~E(f334(f144(f882(x93333),f882(x93333),f136(x93333),f117(x93333)),x93331),f334(f144(f882(x93333),f882(x93333),f136(x93333),f117(x93333)),x93332))+~E(f334(f197(f882(f882(x93333))),x93331),f334(f197(f882(f882(x93333))),x93332))+P1(f334(f334(f336(f887(f882(x93333),f882(x93333))),f746(x93332,x93331,x93333)),f334(f174(f887(f882(x93333),f882(x93333))),f334(f334(f184(f882(x93333),f882(x93333)),x93331),x93332))))
% 160.93/160.66 [10164]~P97(x101642)+E(x101641,f196(f888(x101642,a876)))+~P1(f334(f61(x101642),x101641))+E(f11(x101642,f334(f254(x101642),f334(f334(f8(f888(x101642,a876),a876,x101642),f87(x101642)),f334(f334(f7(x101642,f888(x101642,a876),f888(x101642,a876)),f334(f334(f8(f888(x101642,f888(a876,a876)),f888(f888(x101642,a876),f888(x101642,a876)),x101642),f18(x101642,a876,a876)),f334(f334(f8(f888(x101642,a876),f888(x101642,f888(a876,a876)),x101642),f334(f8(a876,f888(a876,a876),x101642),a332)),f334(f334(f7(x101642,f888(x101642,x101642),f888(x101642,a876)),f334(f334(f8(f888(x101642,a876),f888(f888(x101642,x101642),f888(x101642,a876)),x101642),f8(x101642,a876,x101642)),a331)),f334(f114(x101642),x101643))))),f334(f334(f7(x101642,f888(x101642,a876),a876),f336(x101642)),x101641))))),f334(f334(f114(x101642),x101643),f11(x101642,x101641)))
% 160.93/160.66 [10165]~P97(x101652)+E(x101651,f196(f888(x101652,a876)))+~P1(f334(f61(x101652),x101651))+E(f10(x101652,f334(f254(x101652),f334(f334(f8(f888(x101652,a876),a876,x101652),f87(x101652)),f334(f334(f7(x101652,f888(x101652,a876),f888(x101652,a876)),f334(f334(f8(f888(x101652,f888(a876,a876)),f888(f888(x101652,a876),f888(x101652,a876)),x101652),f18(x101652,a876,a876)),f334(f334(f8(f888(x101652,a876),f888(x101652,f888(a876,a876)),x101652),f334(f8(a876,f888(a876,a876),x101652),a332)),f334(f334(f7(x101652,f888(x101652,x101652),f888(x101652,a876)),f334(f334(f8(f888(x101652,a876),f888(f888(x101652,x101652),f888(x101652,a876)),x101652),f8(x101652,a876,x101652)),a331)),f334(f105(x101652),x101653))))),f334(f334(f7(x101652,f888(x101652,a876),a876),f336(x101652)),x101651))))),f334(f334(f105(x101652),x101653),f10(x101652,x101651)))
% 160.93/160.66 [10166]~P76(x101662)+E(x101661,f196(f888(x101662,a876)))+~P1(f334(f61(x101662),x101661))+E(f14(x101662,f334(f254(x101662),f334(f334(f8(f888(x101662,a876),a876,x101662),f87(x101662)),f334(f334(f7(x101662,f888(x101662,a876),f888(x101662,a876)),f334(f334(f8(f888(x101662,f888(a876,a876)),f888(f888(x101662,a876),f888(x101662,a876)),x101662),f18(x101662,a876,a876)),f334(f334(f8(f888(x101662,a876),f888(x101662,f888(a876,a876)),x101662),f334(f8(a876,f888(a876,a876),x101662),a332)),f334(f334(f7(x101662,f888(x101662,x101662),f888(x101662,a876)),f334(f334(f8(f888(x101662,a876),f888(f888(x101662,x101662),f888(x101662,a876)),x101662),f8(x101662,a876,x101662)),a331)),f334(f80(x101662),x101663))))),f334(f334(f7(x101662,f888(x101662,a876),a876),f336(x101662)),x101661))))),f334(f334(f80(x101662),x101663),f14(x101662,x101661)))
% 160.93/160.66 [10167]~P76(x101672)+E(x101671,f196(f888(x101672,a876)))+~P1(f334(f61(x101672),x101671))+E(f15(x101672,f334(f254(x101672),f334(f334(f8(f888(x101672,a876),a876,x101672),f87(x101672)),f334(f334(f7(x101672,f888(x101672,a876),f888(x101672,a876)),f334(f334(f8(f888(x101672,f888(a876,a876)),f888(f888(x101672,a876),f888(x101672,a876)),x101672),f18(x101672,a876,a876)),f334(f334(f8(f888(x101672,a876),f888(x101672,f888(a876,a876)),x101672),f334(f8(a876,f888(a876,a876),x101672),a332)),f334(f334(f7(x101672,f888(x101672,x101672),f888(x101672,a876)),f334(f334(f8(f888(x101672,a876),f888(f888(x101672,x101672),f888(x101672,a876)),x101672),f8(x101672,a876,x101672)),a331)),f334(f80(x101672),x101673))))),f334(f334(f7(x101672,f888(x101672,a876),a876),f336(x101672)),x101671))))),f334(f334(f80(x101672),x101673),f15(x101672,x101671)))
% 160.93/160.66 [10168]~P108(x101682)+E(x101681,f196(f888(x101682,a876)))+~P1(f334(f61(x101682),x101681))+E(f12(x101682,f247(x101682),f334(f254(x101682),f334(f334(f8(f888(x101682,a876),a876,x101682),f87(x101682)),f334(f334(f7(x101682,f888(x101682,a876),f888(x101682,a876)),f334(f334(f8(f888(x101682,f888(a876,a876)),f888(f888(x101682,a876),f888(x101682,a876)),x101682),f18(x101682,a876,a876)),f334(f334(f8(f888(x101682,a876),f888(x101682,f888(a876,a876)),x101682),f334(f8(a876,f888(a876,a876),x101682),a332)),f334(f334(f7(x101682,f888(x101682,x101682),f888(x101682,a876)),f334(f334(f8(f888(x101682,a876),f888(f888(x101682,x101682),f888(x101682,a876)),x101682),f8(x101682,a876,x101682)),a331)),f334(f246(x101682),x101683))))),f334(f334(f7(x101682,f888(x101682,a876),a876),f336(x101682)),x101681))))),f334(f334(f246(x101682),x101683),f12(x101682,f247(x101682),x101681)))
% 160.93/160.66 [10169]~P108(x101692)+E(x101691,f196(f888(x101692,a876)))+~P1(f334(f61(x101692),x101691))+E(f13(x101692,f246(x101692),f334(f254(x101692),f334(f334(f8(f888(x101692,a876),a876,x101692),f87(x101692)),f334(f334(f7(x101692,f888(x101692,a876),f888(x101692,a876)),f334(f334(f8(f888(x101692,f888(a876,a876)),f888(f888(x101692,a876),f888(x101692,a876)),x101692),f18(x101692,a876,a876)),f334(f334(f8(f888(x101692,a876),f888(x101692,f888(a876,a876)),x101692),f334(f8(a876,f888(a876,a876),x101692),a332)),f334(f334(f7(x101692,f888(x101692,x101692),f888(x101692,a876)),f334(f334(f8(f888(x101692,a876),f888(f888(x101692,x101692),f888(x101692,a876)),x101692),f8(x101692,a876,x101692)),a331)),f334(f247(x101692),x101693))))),f334(f334(f7(x101692,f888(x101692,a876),a876),f336(x101692)),x101691))))),f334(f334(f247(x101692),x101693),f13(x101692,f246(x101692),x101691)))
% 160.93/160.66 [9921]~P111(x99211)+~E(x99213,f2(x99211))+~E(x99212,f2(x99211))+E(f334(f334(f80(x99211),f334(f334(f259(x99211),x99212),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x99211),x99213),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f2(x99211))
% 160.93/160.66 [10064]~P106(x100641)+~P1(f334(f334(f248(x100641),f2(x100641)),x100643))+P1(f334(f334(f248(x100641),x100642),x100643))+~P1(f334(f334(f248(x100641),f334(f334(f259(x100641),x100642),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x100641),x100643),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))))
% 160.93/160.66 [10110]~P111(x101102)+~E(x101101,f2(x101102))+~E(x101103,f2(x101102))+~P1(f334(f334(f249(x101102),f2(x101102)),f334(f334(f80(x101102),f334(f334(f259(x101102),x101103),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101))))),f334(f334(f259(x101102),x101101),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))))
% 160.93/160.66 [9294]E(x92941,x92942)+~E(f670(x92941,x92942,x92944,x92943),f672(x92941,x92942,x92944,x92943))+P1(f334(f334(f336(f887(f882(x92943),f882(x92943))),f334(f334(f269(f882(x92943),f882(x92943)),x92942),x92941)),f149(x92943,x92944)))+P1(f334(f334(f336(f887(f882(x92943),f882(x92943))),f334(f334(f269(f882(x92943),f882(x92943)),x92941),x92942)),f149(x92943,x92944)))
% 160.93/160.66 [4855]~P61(x48552)+~E(x48554,f2(x48552))+~E(x48551,f2(x48552))+E(x48551,f334(f334(f292(x48552),x48553),x48554))
% 160.93/160.66 [4856]~P61(x48561)+~E(x48563,f2(x48561))+~E(x48564,f2(x48561))+E(f334(f334(f292(x48561),x48562),x48563),x48564)
% 160.93/160.66 [4965]~P61(x49652)+E(x49651,f2(x49652))+~E(x49653,f2(x49652))+~E(x49651,f334(f334(f292(x49652),x49654),x49653))
% 160.93/160.66 [4966]~P61(x49662)+E(x49661,f2(x49662))+~E(x49663,f2(x49662))+~E(f334(f334(f292(x49662),x49664),x49663),x49661)
% 160.93/160.66 [5141]~P120(x51412)+E(x51411,f2(x51412))+~E(f334(f334(f292(x51412),x51413),x51411),x51414)+E(x51413,f334(f334(f81(x51412),x51414),x51411))
% 160.93/160.66 [5143]~P120(x51432)+E(x51431,f2(x51432))+~E(f334(f334(f81(x51432),x51433),x51431),x51434)+E(x51433,f334(f334(f292(x51432),x51434),x51431))
% 160.93/160.66 [5144]~P61(x51442)+E(x51441,f2(x51442))+~E(f334(f334(f292(x51442),x51443),x51441),x51444)+E(x51443,f334(f334(f81(x51442),x51444),x51441))
% 160.93/160.66 [5145]~P61(x51452)+E(x51451,f2(x51452))+~E(f334(f334(f81(x51452),x51453),x51451),x51454)+E(x51453,f334(f334(f292(x51452),x51454),x51451))
% 160.93/160.66 [5146]~P120(x51462)+E(x51461,f2(x51462))+~E(x51463,f334(f334(f292(x51462),x51464),x51461))+E(f334(f334(f81(x51462),x51463),x51461),x51464)
% 160.93/160.66 [5148]~P120(x51482)+E(x51481,f2(x51482))+~E(x51483,f334(f334(f81(x51482),x51484),x51481))+E(f334(f334(f292(x51482),x51483),x51481),x51484)
% 160.93/160.66 [5149]~P61(x51492)+E(x51491,f2(x51492))+~E(x51493,f334(f334(f292(x51492),x51494),x51491))+E(f334(f334(f81(x51492),x51493),x51491),x51494)
% 160.93/160.66 [5150]~P61(x51502)+E(x51501,f2(x51502))+~E(x51503,f334(f334(f81(x51502),x51504),x51501))+E(f334(f334(f292(x51502),x51503),x51501),x51504)
% 160.93/160.66 [5182]~P61(x51822)+~E(x51821,f2(x51822))+~E(f334(f334(f81(x51822),x51821),x51824),x51823)+E(x51821,f334(f334(f292(x51822),x51823),x51824))
% 160.93/160.66 [5183]~P61(x51831)+~E(x51834,f2(x51831))+~E(x51832,f334(f334(f81(x51831),x51834),x51833))+E(f334(f334(f292(x51831),x51832),x51833),x51834)
% 160.93/160.66 [5257]~E(x52573,x52574)+~E(x52572,x52573)+~P109(x52571)+E(f305(x52571,x52572,x52573),f334(f334(f312(x52571),x52574),f196(f888(x52571,a876))))
% 160.93/160.66 [5460]~E(f118(x54602,x54601),x54603)+~E(f146(x54602,x54601),x54604)+E(x54601,f117(x54602))+E(f334(f334(f136(x54602),x54603),f334(f334(f153(x54602),x54604),f117(x54602))),x54601)
% 160.93/160.66 [6071]~P106(x60713)+E(x60711,x60712)+~E(f334(f334(f259(x60713),x60714),x60711),f334(f334(f259(x60713),x60714),x60712))+~P1(f334(f334(f249(x60713),f78(x60713)),x60714))
% 160.93/160.66 [6072]E(x60721,x60722)+~E(f334(f334(f312(x60723),x60724),x60721),f334(f334(f312(x60723),x60724),x60722))+P1(f334(f334(f336(x60723),x60724),x60722))+P1(f334(f334(f336(x60723),x60724),x60721))
% 160.93/160.66 [6110]E(f334(x61101,x61102),f2(a881))+~E(f334(f334(f6(x61103,a881),x61101),x61104),f2(a881))+~P1(f334(f61(x61103),x61104))+~P1(f334(f334(f336(x61103),x61102),x61104))
% 160.93/160.66 [6111]E(f334(x61111,x61112),f78(a881))+~E(f334(f334(f9(x61113,a881),x61111),x61114),f78(a881))+~P1(f334(f61(x61113),x61114))+~P1(f334(f334(f336(x61113),x61112),x61114))
% 160.93/160.66 [6334]~P109(x63341)+~P1(f334(f334(f249(x63341),x63344),x63343))+P1(f334(f334(f249(x63341),x63342),x63343))+~P1(f334(f334(f249(x63341),x63342),x63344))
% 160.93/160.66 [6335]~P109(x63351)+~P1(f334(f334(f248(x63351),x63354),x63353))+P1(f334(f334(f249(x63351),x63352),x63353))+~P1(f334(f334(f249(x63351),x63352),x63354))
% 160.93/160.66 [6336]~P109(x63361)+~P1(f334(f334(f248(x63361),x63362),x63364))+P1(f334(f334(f249(x63361),x63362),x63363))+~P1(f334(f334(f249(x63361),x63364),x63363))
% 160.93/160.66 [6337]~P107(x63371)+~P1(f334(f334(f249(x63371),x63372),x63374))+P1(f334(f334(f249(x63371),x63372),x63373))+~P1(f334(f334(f249(x63371),x63374),x63373))
% 160.93/160.66 [6338]~P107(x63381)+~P1(f334(f334(f248(x63381),x63382),x63384))+P1(f334(f334(f249(x63381),x63382),x63383))+~P1(f334(f334(f249(x63381),x63384),x63383))
% 160.93/160.66 [6339]~P107(x63391)+~P1(f334(f334(f248(x63391),x63394),x63393))+P1(f334(f334(f249(x63391),x63392),x63393))+~P1(f334(f334(f249(x63391),x63392),x63394))
% 160.93/160.66 [6340]~P109(x63401)+~P1(f334(f334(f248(x63401),x63404),x63403))+P1(f334(f334(f248(x63401),x63402),x63403))+~P1(f334(f334(f248(x63401),x63402),x63404))
% 160.93/160.66 [6341]~P107(x63411)+~P1(f334(f334(f248(x63411),x63412),x63414))+P1(f334(f334(f248(x63411),x63412),x63413))+~P1(f334(f334(f248(x63411),x63414),x63413))
% 160.93/160.66 [6421]~P37(x64214,x64213,x64212)+E(x64211,f811(x64212,x64213,x64214))+~P1(f334(x64213,x64211))+~P1(f334(f334(f336(x64214),x64211),f334(f174(x64214),x64212)))
% 160.93/160.66 [6565]~P5(x65651)+~P1(f334(f334(f248(x65651),x65652),f40(x65651,x65654)))+P1(f334(f334(f248(x65651),x65652),x65653))+~P1(f334(f334(f336(x65651),x65653),x65654))
% 160.93/160.66 [6712]~P108(x67121)+~P16(x67121,f334(f334(f153(x67121),x67122),x67124))+~P1(f334(f334(f336(x67121),x67123),f334(f174(x67121),x67124)))+P1(f334(f334(f248(x67121),x67122),x67123))
% 160.93/160.66 [6802]~P5(x68021)+~P1(f334(f334(f248(x68021),f39(x68021,x68024)),x68023))+P1(f334(f334(f248(x68021),x68022),x68023))+~P1(f334(f334(f336(x68021),x68022),x68024))
% 160.93/160.66 [7207]~P108(x72071)+E(f334(f334(f114(f888(x72071,a876)),f334(f304(x72071,x72072),x72073)),f334(f304(x72071,x72073),x72074)),f334(f304(x72071,x72072),x72074))+~P1(f334(f334(f248(x72071),x72073),x72074))+~P1(f334(f334(f248(x72071),x72072),x72073))
% 160.93/160.66 [7244]P37(x72441,x72442,x72443)+~E(f817(x72443,x72442,x72441,x72444),x72444)+~P1(f334(x72442,x72444))+~P1(f334(f334(f336(x72441),x72444),f334(f174(x72441),x72443)))
% 160.93/160.66 [7318]~P108(x73181)+E(f334(f334(f114(f888(x73181,a876)),f334(f304(x73181,x73182),x73183)),f305(x73181,x73183,x73184)),f305(x73181,x73182,x73184))+~P1(f334(f334(f248(x73181),x73183),x73184))+~P1(f334(f334(f248(x73181),x73182),x73183))
% 160.93/160.66 [7384]~P108(x73841)+E(f334(f334(f114(f888(x73841,a876)),f308(x73841,x73842,x73843)),f334(f304(x73841,x73843),x73844)),f308(x73841,x73842,x73844))+~P1(f334(f334(f249(x73841),x73842),x73843))+~P1(f334(f334(f248(x73841),x73843),x73844))
% 160.93/160.66 [7404]~P108(x74041)+E(f334(f334(f114(f888(x74041,a876)),f305(x74041,x74042,x74043)),f308(x74041,x74043,x74044)),f334(f304(x74041,x74042),x74044))+~P1(f334(f334(f249(x74041),x74043),x74044))+~P1(f334(f334(f248(x74041),x74042),x74043))
% 160.93/160.66 [7436]~P108(x74361)+E(f334(f334(f114(f888(x74361,a876)),f305(x74361,x74362,x74363)),f307(x74361,x74363,x74364)),f305(x74361,x74362,x74364))+~P1(f334(f334(f248(x74361),x74363),x74364))+~P1(f334(f334(f248(x74361),x74362),x74363))
% 160.93/160.66 [7437]~P108(x74371)+E(f334(f334(f114(f888(x74371,a876)),f308(x74371,x74372,x74373)),f305(x74371,x74373,x74374)),f307(x74371,x74372,x74374))+~P1(f334(f334(f249(x74371),x74372),x74373))+~P1(f334(f334(f248(x74371),x74373),x74374))
% 160.93/160.66 [7438]~P108(x74381)+E(f334(f334(f114(f888(x74381,a876)),f307(x74381,x74382,x74383)),f308(x74381,x74383,x74384)),f308(x74381,x74382,x74384))+~P1(f334(f334(f249(x74381),x74383),x74384))+~P1(f334(f334(f248(x74381),x74382),x74383))
% 160.93/160.66 [7439]~P108(x74391)+E(f334(f334(f114(f888(x74391,a876)),f307(x74391,x74392,x74393)),f307(x74391,x74393,x74394)),f307(x74391,x74392,x74394))+~P1(f334(f334(f248(x74391),x74393),x74394))+~P1(f334(f334(f248(x74391),x74392),x74393))
% 160.93/160.66 [8240]P27(x82401,x82402,f555(x82403,x82402,x82404,x82401),x82404)+~P1(f334(f61(x82402),x82403))+~P1(f334(f61(x82401),x82404))+~P1(f334(f334(f248(a881),f334(f37(x82401),x82404)),f334(f37(x82402),x82403)))
% 160.93/160.66 [8261]P37(x82611,x82612,x82613)+~P1(f334(x82612,x82614))+P1(f334(x82612,f817(x82613,x82612,x82611,x82614)))+~P1(f334(f334(f336(x82611),x82614),f334(f174(x82611),x82613)))
% 160.93/160.66 [8312]~P74(x83121)+~E(f334(x83123,f501(x83123,x83124,x83122,x83121)),f78(x83121))+E(f334(f334(f334(f65(x83121,x83122,f81(x83121)),x83123),f78(x83121)),x83124),f78(x83121))+~P1(f334(f61(x83122),x83124))
% 160.93/160.66 [8585]~P106(x85851)+~P1(f334(f334(f248(x85851),f2(x85851)),x85853))+P1(f334(f334(f248(x85851),x85852),x85853))+~P1(f334(f334(f248(x85851),f334(f334(f259(x85851),x85852),f334(a116,x85854))),f334(f334(f259(x85851),x85853),f334(a116,x85854))))
% 160.93/160.66 [8882]P37(x88821,x88822,x88823)+~P1(f334(x88822,x88824))+~P1(f334(f334(f336(x88821),x88824),f334(f174(x88821),x88823)))+P1(f334(f334(f336(x88821),f817(x88823,x88822,x88821,x88824)),f334(f174(x88821),x88823)))
% 160.93/160.66 [8967]~P74(x89671)+E(f334(f334(f334(f65(x89671,x89672,f81(x89671)),x89673),f78(x89671)),x89674),f78(x89671))+~P1(f334(f61(x89672),x89674))+P1(f334(f334(f336(x89672),f501(x89673,x89674,x89672,x89671)),x89674))
% 160.93/160.66 [9458]~P1(f334(f334(f248(a1),x94584),f2(a1)))+P1(f334(f334(f248(a1),f334(f334(f80(a1),f334(f334(f81(a1),x94581),f44(a1,x94582,x94583))),x94584)),f2(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x94583))+~P1(f334(f334(f249(a1),x94581),x94584))
% 160.93/160.66 [9914]~P1(f334(f61(x99141),x99142))+~P1(f334(f334(f336(x99141),x99144),x99142))+~P1(f334(f334(f336(x99141),x99143),x99142))+P1(f334(f334(f249(a881),f334(f37(x99141),f334(f334(f22(f888(x99141,a876)),f334(f334(f22(f888(x99141,a876)),x99142),f334(f334(f312(x99141),x99143),f196(f888(x99141,a876))))),f334(f334(f312(x99141),x99144),f196(f888(x99141,a876)))))),f334(f37(x99141),x99142)))
% 160.93/160.66 [6915]~P108(x69151)+~P1(f334(f334(f249(x69151),x69152),x69154))+~P1(f334(f334(f249(x69151),x69152),x69153))+P1(f334(f334(f249(x69151),x69152),f334(f334(f246(x69151),x69153),x69154)))
% 160.93/160.66 [6918]~P100(x69181)+~P1(f334(f334(f248(x69181),x69182),x69184))+~P1(f334(f334(f248(x69181),x69182),x69183))+P1(f334(f334(f248(x69181),x69182),f334(f334(f105(x69181),x69183),x69184)))
% 160.93/160.66 [6921]~P108(x69211)+~P1(f334(f334(f248(x69211),x69212),x69214))+~P1(f334(f334(f248(x69211),x69212),x69213))+P1(f334(f334(f248(x69211),x69212),f334(f334(f246(x69211),x69213),x69214)))
% 160.93/160.66 [6940]~P62(x69402)+E(x69401,f2(x69402))+E(f334(f334(f292(x69402),f334(f334(f259(x69402),x69401),x69403)),f334(f334(f259(x69402),x69401),x69404)),f334(f334(f259(x69402),x69401),f334(f334(f22(a881),x69403),x69404)))+~P1(f334(f334(f248(a881),x69404),x69403))
% 160.93/160.66 [6985]~P108(x69851)+~P16(x69851,f334(f334(f153(x69851),x69853),x69854))+P16(x69851,f334(f334(f153(x69851),x69852),f334(f334(f153(x69851),x69853),x69854)))+~P1(f334(f334(f248(x69851),x69852),x69853))
% 160.93/160.66 [7024]~P106(x70241)+~P1(f334(f334(f249(x70241),f2(x70241)),x70243))+~P1(f334(f334(f249(x70241),x70242),x70244))+P1(f334(f334(f249(x70241),x70242),f334(f334(f80(x70241),x70243),x70244)))
% 160.93/160.66 [7025]~P81(x70251)+~P1(f334(f334(f248(x70251),f2(x70251)),x70253))+~P1(f334(f334(f249(x70251),x70252),x70254))+P1(f334(f334(f249(x70251),x70252),f334(f334(f80(x70251),x70253),x70254)))
% 160.93/160.66 [7026]~P81(x70261)+~P1(f334(f334(f248(x70261),x70262),x70264))+~P1(f334(f334(f249(x70261),f2(x70261)),x70263))+P1(f334(f334(f249(x70261),x70262),f334(f334(f80(x70261),x70263),x70264)))
% 160.93/160.66 [7027]~P81(x70271)+~P1(f334(f334(f248(x70271),f2(x70271)),x70274))+~P1(f334(f334(f248(x70271),x70272),x70273))+P1(f334(f334(f248(x70271),x70272),f334(f334(f80(x70271),x70273),x70274)))
% 160.93/160.66 [7028]~P81(x70281)+~P1(f334(f334(f248(x70281),f2(x70281)),x70283))+~P1(f334(f334(f248(x70281),x70282),x70284))+P1(f334(f334(f248(x70281),x70282),f334(f334(f80(x70281),x70283),x70284)))
% 160.93/160.66 [7067]~P108(x70671)+P1(f334(f334(f249(x70671),x70672),x70673))+P1(f334(f334(f249(x70671),x70672),x70674))+~P1(f334(f334(f249(x70671),x70672),f334(f334(f247(x70671),x70674),x70673)))
% 160.93/160.66 [7068]~P108(x70681)+P1(f334(f334(f248(x70681),x70682),x70683))+P1(f334(f334(f248(x70681),x70682),x70684))+~P1(f334(f334(f248(x70681),x70682),f334(f334(f247(x70681),x70684),x70683)))
% 160.93/160.66 [7357]~P109(x73572)+~P60(x73571)+~P1(f334(f334(f249(f888(x73571,x73572)),x73573),x73574))+P1(f334(f334(f248(f888(x73571,x73572)),x73573),x73574))
% 160.93/160.66 [7726]~P64(x77261)+~P1(f334(f334(f249(x77261),x77264),f2(x77261)))+~P1(f334(f334(f249(x77261),x77263),f334(f334(f292(x77261),x77262),x77264)))+P1(f334(f334(f249(x77261),x77262),f334(f334(f81(x77261),x77263),x77264)))
% 160.93/160.66 [7727]~P64(x77271)+~P1(f334(f334(f249(x77271),x77274),f2(x77271)))+~P1(f334(f334(f249(x77271),x77273),f334(f334(f81(x77271),x77272),x77274)))+P1(f334(f334(f249(x77271),x77272),f334(f334(f292(x77271),x77273),x77274)))
% 160.93/160.66 [7728]~P64(x77281)+~P1(f334(f334(f249(x77281),x77284),f2(x77281)))+~P1(f334(f334(f248(x77281),x77283),f334(f334(f292(x77281),x77282),x77284)))+P1(f334(f334(f248(x77281),x77282),f334(f334(f81(x77281),x77283),x77284)))
% 160.93/160.66 [7729]~P64(x77291)+~P1(f334(f334(f249(x77291),x77294),f2(x77291)))+~P1(f334(f334(f248(x77291),x77293),f334(f334(f81(x77291),x77292),x77294)))+P1(f334(f334(f248(x77291),x77292),f334(f334(f292(x77291),x77293),x77294)))
% 160.93/160.66 [7837]~P124(x78371)+~P1(f334(f334(f249(x78371),x78373),f2(x78371)))+~P1(f334(f334(f249(x78371),x78374),x78372))+P1(f334(f334(f249(x78371),f334(f334(f81(x78371),x78372),x78373)),f334(f334(f81(x78371),x78374),x78373)))
% 160.93/160.66 [7838]~P124(x78381)+~P1(f334(f334(f249(x78381),x78382),f2(x78381)))+~P1(f334(f334(f249(x78381),x78384),x78383))+P1(f334(f334(f249(x78381),f334(f334(f81(x78381),x78382),x78383)),f334(f334(f81(x78381),x78382),x78384)))
% 160.93/160.66 [7839]~P64(x78391)+~P1(f334(f334(f249(x78391),x78393),f2(x78391)))+~P1(f334(f334(f249(x78391),x78394),x78392))+P1(f334(f334(f249(x78391),f334(f334(f292(x78391),x78392),x78393)),f334(f334(f292(x78391),x78394),x78393)))
% 160.93/160.66 [7840]~P125(x78401)+~P1(f334(f334(f248(x78401),x78402),f2(x78401)))+~P1(f334(f334(f248(x78401),x78404),x78403))+P1(f334(f334(f248(x78401),f334(f334(f81(x78401),x78402),x78403)),f334(f334(f81(x78401),x78402),x78404)))
% 160.93/160.66 [7841]~P124(x78411)+~P1(f334(f334(f249(x78411),x78412),f2(x78411)))+~P1(f334(f334(f248(x78411),x78414),x78413))+P1(f334(f334(f248(x78411),f334(f334(f81(x78411),x78412),x78413)),f334(f334(f81(x78411),x78412),x78414)))
% 160.93/160.66 [7842]~P125(x78421)+~P1(f334(f334(f248(x78421),x78423),f2(x78421)))+~P1(f334(f334(f248(x78421),x78424),x78422))+P1(f334(f334(f248(x78421),f334(f334(f81(x78421),x78422),x78423)),f334(f334(f81(x78421),x78424),x78423)))
% 160.93/160.66 [7843]~P63(x78431)+~P1(f334(f334(f248(x78431),x78433),f2(x78431)))+~P1(f334(f334(f248(x78431),x78434),x78432))+P1(f334(f334(f248(x78431),f334(f334(f292(x78431),x78432),x78433)),f334(f334(f292(x78431),x78434),x78433)))
% 160.93/160.66 [7845]~P106(x78451)+~P1(f334(f334(f249(x78451),f78(x78451)),x78452))+~P1(f334(f334(f249(a881),x78453),x78454))+P1(f334(f334(f249(x78451),f334(f334(f259(x78451),x78452),x78453)),f334(f334(f259(x78451),x78452),x78454)))
% 160.93/160.66 [7846]~P106(x78461)+~P1(f334(f334(f249(x78461),f78(x78461)),x78462))+~P1(f334(f334(f248(a881),x78463),x78464))+P1(f334(f334(f248(x78461),f334(f334(f259(x78461),x78462),x78463)),f334(f334(f259(x78461),x78462),x78464)))
% 160.93/160.66 [7847]~P106(x78471)+~P1(f334(f334(f248(x78471),f78(x78471)),x78472))+~P1(f334(f334(f248(a881),x78473),x78474))+P1(f334(f334(f248(x78471),f334(f334(f259(x78471),x78472),x78473)),f334(f334(f259(x78471),x78472),x78474)))
% 160.93/160.66 [7874]P1(f334(f334(f249(a881),f2(a881)),f334(x78741,x78742)))+~P1(f334(f61(x78743),x78744))+~P1(f334(f334(f336(x78743),x78742),x78744))+~P1(f334(f334(f249(a881),f2(a881)),f334(f334(f9(x78743,a881),x78741),x78744)))
% 160.93/160.66 [7884]~P117(x78841)+~P1(f334(f334(f249(x78841),x78843),x78844))+~P1(f334(f334(f249(x78841),f2(x78841)),x78842))+P1(f334(f334(f249(x78841),f334(f334(f81(x78841),x78842),x78843)),f334(f334(f81(x78841),x78842),x78844)))
% 160.93/160.66 [7885]~P126(x78851)+~P1(f334(f334(f249(x78851),x78853),x78854))+~P1(f334(f334(f249(x78851),f2(x78851)),x78852))+P1(f334(f334(f249(x78851),f334(f334(f81(x78851),x78852),x78853)),f334(f334(f81(x78851),x78852),x78854)))
% 160.93/160.66 [7886]~P124(x78861)+~P1(f334(f334(f249(x78861),x78862),x78864))+~P1(f334(f334(f249(x78861),f2(x78861)),x78863))+P1(f334(f334(f249(x78861),f334(f334(f81(x78861),x78862),x78863)),f334(f334(f81(x78861),x78864),x78863)))
% 160.93/160.66 [7887]~P126(x78871)+~P1(f334(f334(f249(x78871),x78872),x78874))+~P1(f334(f334(f249(x78871),f2(x78871)),x78873))+P1(f334(f334(f249(x78871),f334(f334(f81(x78871),x78872),x78873)),f334(f334(f81(x78871),x78874),x78873)))
% 160.93/160.66 [7888]~P124(x78881)+~P1(f334(f334(f249(x78881),x78883),x78884))+~P1(f334(f334(f249(x78881),f2(x78881)),x78882))+P1(f334(f334(f249(x78881),f334(f334(f81(x78881),x78882),x78883)),f334(f334(f81(x78881),x78882),x78884)))
% 160.93/160.66 [7889]~P64(x78891)+~P1(f334(f334(f249(x78891),x78892),x78894))+~P1(f334(f334(f249(x78891),f2(x78891)),x78893))+P1(f334(f334(f249(x78891),f334(f334(f292(x78891),x78892),x78893)),f334(f334(f292(x78891),x78894),x78893)))
% 160.93/160.66 [7890]~P124(x78901)+~P1(f334(f334(f249(x78901),f2(x78901)),x78902))+~P1(f334(f334(f248(x78901),x78903),x78904))+P1(f334(f334(f248(x78901),f334(f334(f81(x78901),x78902),x78903)),f334(f334(f81(x78901),x78902),x78904)))
% 160.93/160.66 [7891]~P134(x78911)+~P1(f334(f334(f248(x78911),x78913),x78914))+~P1(f334(f334(f248(x78911),f2(x78911)),x78912))+P1(f334(f334(f248(x78911),f334(f334(f81(x78911),x78912),x78913)),f334(f334(f81(x78911),x78912),x78914)))
% 160.93/160.66 [7892]~P133(x78921)+~P1(f334(f334(f248(x78921),x78923),x78924))+~P1(f334(f334(f248(x78921),f2(x78921)),x78922))+P1(f334(f334(f248(x78921),f334(f334(f81(x78921),x78922),x78923)),f334(f334(f81(x78921),x78922),x78924)))
% 160.93/160.66 [7893]~P134(x78931)+~P1(f334(f334(f248(x78931),x78932),x78934))+~P1(f334(f334(f248(x78931),f2(x78931)),x78933))+P1(f334(f334(f248(x78931),f334(f334(f81(x78931),x78932),x78933)),f334(f334(f81(x78931),x78934),x78933)))
% 160.93/160.66 [7894]~P106(x78941)+~P1(f334(f334(f248(x78941),x78942),x78944))+~P1(f334(f334(f248(x78941),f2(x78941)),x78942))+P1(f334(f334(f248(x78941),f334(f334(f259(x78941),x78942),x78943)),f334(f334(f259(x78941),x78944),x78943)))
% 160.93/160.66 [7895]~P63(x78951)+~P1(f334(f334(f248(x78951),x78952),x78954))+~P1(f334(f334(f248(x78951),f2(x78951)),x78953))+P1(f334(f334(f248(x78951),f334(f334(f292(x78951),x78952),x78953)),f334(f334(f292(x78951),x78954),x78953)))
% 160.93/160.66 [7938]~P110(x79382)+P1(f334(f334(f248(f888(x79381,x79382)),x79384),x79383))+~P1(f334(f334(f248(f888(x79381,x79382)),x79383),x79384))+P1(f334(f334(f249(f888(x79381,x79382)),x79383),x79384))
% 160.93/160.66 [7978]P1(f334(f334(f336(x79781),x79782),x79783))+P1(f334(f334(f336(x79781),x79782),x79784))+~P1(f334(f334(f248(f888(x79781,a876)),x79784),x79783))+P1(f334(f334(f249(f888(x79781,a876)),x79784),f334(f334(f312(x79781),x79782),x79783)))
% 160.93/160.66 [8135]P1(f334(f334(f336(x81351),x81352),x81353))+P1(f334(f334(f336(x81351),x81352),x81354))+~P1(f334(f334(f249(f888(x81351,a876)),x81354),f334(f334(f312(x81351),x81352),x81353)))+P1(f334(f334(f248(f888(x81351,a876)),x81354),x81353))
% 160.93/160.66 [8143]~P60(x81431)+P12(x81431,x81432,x81433)+~P1(f334(x81432,x81434))+~P1(f334(f334(f336(f882(x81431)),x81434),f334(f174(f882(x81431)),f54(x81431,x81433,f55(x81431)))))
% 160.93/160.66 [8155]~P13(x81553,x81551,x81554)+~P60(x81553)+P1(f334(x81551,x81552))+~P1(f334(f334(f336(f882(x81553)),x81552),f334(f174(f882(x81553)),f54(x81553,x81554,f55(x81553)))))
% 160.93/160.66 [8214]~P124(x82141)+P1(f334(f334(f249(x82141),x82143),x82142))+P1(f334(f334(f249(x82141),x82142),x82143))+~P1(f334(f334(f249(x82141),f334(f334(f81(x82141),x82144),x82142)),f334(f334(f81(x82141),x82144),x82143)))
% 160.93/160.66 [8215]~P124(x82151)+P1(f334(f334(f249(x82151),x82153),x82152))+P1(f334(f334(f249(x82151),x82152),x82153))+~P1(f334(f334(f249(x82151),f334(f334(f81(x82151),x82152),x82154)),f334(f334(f81(x82151),x82153),x82154)))
% 160.93/160.66 [8228]~P124(x82281)+P1(f334(f334(f249(x82281),x82284),f2(x82281)))+P1(f334(f334(f249(x82281),x82282),x82283))+~P1(f334(f334(f249(x82281),f334(f334(f81(x82281),x82282),x82284)),f334(f334(f81(x82281),x82283),x82284)))
% 160.93/160.66 [8229]~P124(x82291)+P1(f334(f334(f249(x82291),x82294),f2(x82291)))+P1(f334(f334(f249(x82291),x82292),x82293))+~P1(f334(f334(f249(x82291),f334(f334(f81(x82291),x82294),x82292)),f334(f334(f81(x82291),x82294),x82293)))
% 160.93/160.66 [8234]~P124(x82341)+P1(f334(f334(f249(x82341),x82342),x82343))+P1(f334(f334(f249(x82341),f2(x82341)),x82344))+~P1(f334(f334(f249(x82341),f334(f334(f81(x82341),x82344),x82343)),f334(f334(f81(x82341),x82344),x82342)))
% 160.93/160.66 [8235]~P124(x82351)+P1(f334(f334(f249(x82351),x82352),x82353))+P1(f334(f334(f249(x82351),f2(x82351)),x82354))+~P1(f334(f334(f249(x82351),f334(f334(f81(x82351),x82353),x82354)),f334(f334(f81(x82351),x82352),x82354)))
% 160.93/160.66 [8248]~P124(x82481)+P1(f334(f334(f249(x82481),x82482),f2(x82481)))+P1(f334(f334(f249(x82481),f2(x82481)),x82482))+~P1(f334(f334(f249(x82481),f334(f334(f81(x82481),x82483),x82482)),f334(f334(f81(x82481),x82484),x82482)))
% 160.93/160.66 [8249]~P124(x82491)+P1(f334(f334(f249(x82491),x82492),f2(x82491)))+P1(f334(f334(f249(x82491),f2(x82491)),x82492))+~P1(f334(f334(f249(x82491),f334(f334(f81(x82491),x82492),x82493)),f334(f334(f81(x82491),x82492),x82494)))
% 160.93/160.66 [8276]~P124(x82761)+~P1(f334(f334(f249(x82761),x82764),f2(x82761)))+P1(f334(f334(f249(x82761),x82762),x82763))+~P1(f334(f334(f249(x82761),f334(f334(f81(x82761),x82764),x82763)),f334(f334(f81(x82761),x82764),x82762)))
% 160.93/160.66 [8277]~P124(x82771)+~P1(f334(f334(f249(x82771),x82774),f2(x82771)))+P1(f334(f334(f248(x82771),x82772),x82773))+~P1(f334(f334(f248(x82771),f334(f334(f81(x82771),x82774),x82773)),f334(f334(f81(x82771),x82774),x82772)))
% 160.93/160.66 [8287]~P106(x82873)+~P1(f334(f334(f249(x82873),f78(x82873)),x82874))+P1(f334(f334(f249(a881),x82871),x82872))+~P1(f334(f334(f249(x82873),f334(f334(f259(x82873),x82874),x82871)),f334(f334(f259(x82873),x82874),x82872)))
% 160.93/160.66 [8289]~P106(x82893)+~P1(f334(f334(f249(x82893),f78(x82893)),x82894))+P1(f334(f334(f248(a881),x82891),x82892))+~P1(f334(f334(f248(x82893),f334(f334(f259(x82893),x82894),x82891)),f334(f334(f259(x82893),x82894),x82892)))
% 160.93/160.66 [8299]~P124(x82991)+P1(f334(f334(f249(x82991),x82992),x82993))+~P1(f334(f334(f249(x82991),f2(x82991)),x82994))+~P1(f334(f334(f249(x82991),f334(f334(f81(x82991),x82994),x82992)),f334(f334(f81(x82991),x82994),x82993)))
% 160.93/160.66 [8300]~P126(x83001)+P1(f334(f334(f249(x83001),x83002),x83003))+~P1(f334(f334(f248(x83001),f2(x83001)),x83004))+~P1(f334(f334(f249(x83001),f334(f334(f81(x83001),x83004),x83002)),f334(f334(f81(x83001),x83004),x83003)))
% 160.93/160.66 [8301]~P127(x83011)+P1(f334(f334(f249(x83011),x83012),x83013))+~P1(f334(f334(f248(x83011),f2(x83011)),x83014))+~P1(f334(f334(f249(x83011),f334(f334(f81(x83011),x83014),x83012)),f334(f334(f81(x83011),x83014),x83013)))
% 160.93/160.66 [8302]~P106(x83021)+~P1(f334(f334(f248(x83021),f2(x83021)),x83023))+P1(f334(f334(f249(x83021),x83022),x83023))+~P1(f334(f334(f249(x83021),f334(f334(f259(x83021),x83022),x83024)),f334(f334(f259(x83021),x83023),x83024)))
% 160.93/160.66 [8303]~P126(x83031)+P1(f334(f334(f249(x83031),x83032),x83033))+~P1(f334(f334(f248(x83031),f2(x83031)),x83034))+~P1(f334(f334(f249(x83031),f334(f334(f81(x83031),x83032),x83034)),f334(f334(f81(x83031),x83033),x83034)))
% 160.93/160.66 [8304]~P127(x83041)+P1(f334(f334(f249(x83041),x83042),x83043))+~P1(f334(f334(f248(x83041),f2(x83041)),x83044))+~P1(f334(f334(f249(x83041),f334(f334(f81(x83041),x83042),x83044)),f334(f334(f81(x83041),x83043),x83044)))
% 160.93/160.66 [8305]~P124(x83051)+P1(f334(f334(f248(x83051),x83052),x83053))+~P1(f334(f334(f249(x83051),f2(x83051)),x83054))+~P1(f334(f334(f248(x83051),f334(f334(f81(x83051),x83054),x83052)),f334(f334(f81(x83051),x83054),x83053)))
% 160.93/160.66 [8306]~P126(x83061)+P1(f334(f334(f248(x83061),x83062),x83063))+~P1(f334(f334(f249(x83061),f2(x83061)),x83064))+~P1(f334(f334(f248(x83061),f334(f334(f81(x83061),x83064),x83062)),f334(f334(f81(x83061),x83064),x83063)))
% 160.93/160.66 [8307]~P126(x83071)+P1(f334(f334(f248(x83071),x83072),x83073))+~P1(f334(f334(f249(x83071),f2(x83071)),x83074))+~P1(f334(f334(f248(x83071),f334(f334(f81(x83071),x83072),x83074)),f334(f334(f81(x83071),x83073),x83074)))
% 160.93/160.66 [8351]P1(f334(f334(f336(x83511),x83512),x83513))+~P1(f334(f334(f248(f888(x83511,a876)),x83513),x83514))+~P1(f334(f334(f249(f888(x83511,a876)),x83513),x83514))+P1(f334(f334(f249(f888(x83511,a876)),x83513),f334(f334(f312(x83511),x83512),x83514)))
% 160.93/160.66 [8608]~P60(x86081)+~P92(x86082)+~E(f334(x86083,f818(x86084,x86083,x86081,x86082)),f334(x86084,f818(x86084,x86083,x86081,x86082)))+P1(f334(f334(f91(f888(x86081,x86082)),x86083),x86084))
% 160.93/160.66 [8726]E(f334(f334(f22(a1),f392(x87261,x87262,x87263,x87264)),f393(x87261,x87262,x87263,x87264)),x87264)+~P1(f334(f334(f249(a1),f2(a1)),x87263))+~P1(f334(f334(f248(a1),x87261),x87264))+P1(f334(f334(f248(a1),x87261),f334(f334(f80(a1),x87264),x87263)))
% 160.93/160.66 [8727]E(f334(f334(f22(a1),f399(x87271,x87272,x87273,x87274)),f400(x87271,x87272,x87273,x87274)),x87274)+~P1(f334(f334(f249(a1),f2(a1)),x87273))+~P1(f334(f334(f249(a1),x87271),x87274))+P1(f334(f334(f249(a1),x87271),f334(f334(f80(a1),x87274),x87273)))
% 160.93/160.66 [8862]~E(f334(f334(f167(x88621),x88623),f698(x88624,x88623,x88621,x88622)),f334(f334(f167(x88621),x88624),f698(x88624,x88623,x88621,x88622)))+E(f334(f334(f177(x88621),x88622),x88623),f334(f334(f177(x88621),x88622),x88624))+~P1(f334(f334(f248(a881),x88622),f334(f197(f882(x88621)),x88623)))+~P1(f334(f334(f248(a881),x88622),f334(f197(f882(x88621)),x88624)))
% 160.93/160.66 [8933]~P1(f334(f334(f249(a1),f2(a1)),x89333))+~P1(f334(f334(f248(a1),x89331),x89334))+P1(f334(f334(f336(a1),f392(x89331,x89332,x89333,x89334)),x89332))+P1(f334(f334(f248(a1),x89331),f334(f334(f80(a1),x89334),x89333)))
% 160.93/160.66 [8934]~P1(f334(f334(f249(a1),f2(a1)),x89343))+~P1(f334(f334(f249(a1),x89341),x89344))+P1(f334(f334(f336(a1),f399(x89341,x89342,x89343,x89344)),x89342))+P1(f334(f334(f249(a1),x89341),f334(f334(f80(a1),x89344),x89343)))
% 160.93/160.66 [8978]~P100(x89781)+~P1(f334(f61(x89781),x89783))+~P1(f334(f334(f336(x89781),x89784),x89783))+P1(f334(f334(f248(x89781),f334(f334(f64(x89781,x89781,f105(x89781)),x89782),x89783)),f334(f334(f105(x89781),x89784),x89782)))
% 160.93/160.66 [8979]~P108(x89791)+~P1(f334(f61(x89791),x89793))+~P1(f334(f334(f336(x89791),x89794),x89793))+P1(f334(f334(f248(x89791),f334(f334(f64(x89791,x89791,f246(x89791)),x89792),x89793)),f334(f334(f246(x89791),x89794),x89792)))
% 160.93/160.66 [9024]E(f334(f334(f177(x90241),x90242),x90243),f334(f334(f177(x90241),x90242),x90244))+P1(f334(f334(f249(a881),f698(x90243,x90244,x90241,x90242)),x90242))+~P1(f334(f334(f248(a881),x90242),f334(f197(f882(x90241)),x90243)))+~P1(f334(f334(f248(a881),x90242),f334(f197(f882(x90241)),x90244)))
% 160.93/160.66 [9029]~P1(f334(f334(f249(a1),f2(a1)),x90293))+~P1(f334(f334(f249(a1),x90291),x90292))+P1(f334(f334(f336(a1),f400(x90291,x90294,x90293,x90292)),f305(a1,f78(a1),x90293)))+P1(f334(f334(f249(a1),x90291),f334(f334(f80(a1),x90292),x90293)))
% 160.93/160.66 [9030]~P1(f334(f334(f249(a1),f2(a1)),x90303))+~P1(f334(f334(f248(a1),x90301),x90302))+P1(f334(f334(f336(a1),f393(x90301,x90304,x90303,x90302)),f305(a1,f78(a1),x90303)))+P1(f334(f334(f248(a1),x90301),f334(f334(f80(a1),x90302),x90303)))
% 160.93/160.66 [9197]~E(f334(f180(x91971,x91972),x91973),f334(f180(x91971,x91972),x91974))+E(f334(f174(f887(x91971,x91972)),x91973),f334(f174(f887(x91971,x91972)),x91974))+~P1(f334(f139(x91971),f334(f334(f156(f887(x91971,x91972),x91971),f268(x91971,x91972)),x91974)))+~P1(f334(f139(x91971),f334(f334(f156(f887(x91971,x91972),x91971),f268(x91971,x91972)),x91973)))
% 160.93/160.66 [9209]E(f334(f180(x92091,x92092),x92093),f334(f180(x92091,x92092),x92094))+~E(f334(f174(f887(x92091,x92092)),x92093),f334(f174(f887(x92091,x92092)),x92094))+~P1(f334(f139(x92091),f334(f334(f156(f887(x92091,x92092),x92091),f268(x92091,x92092)),x92094)))+~P1(f334(f139(x92091),f334(f334(f156(f887(x92091,x92092),x92091),f268(x92091,x92092)),x92093)))
% 160.93/160.66 [9352]~P108(x93521)+~P1(f334(f61(x93521),x93524))+P1(f334(f334(f336(x93521),f504(x93522,x93523,x93524,x93521)),x93524))+P1(f334(f334(f248(x93521),f334(f334(f64(x93521,x93521,f247(x93521)),x93522),x93524)),f334(f334(f247(x93521),x93523),x93522)))
% 160.93/160.66 [9353]~P99(x93531)+~P1(f334(f61(x93531),x93534))+P1(f334(f334(f336(x93531),f513(x93532,x93533,x93534,x93531)),x93534))+P1(f334(f334(f248(x93531),f334(f334(f64(x93531,x93531,f114(x93531)),x93532),x93534)),f334(f334(f114(x93531),x93533),x93532)))
% 160.93/160.66 [9476]~P99(x94761)+~P1(f334(f61(x94761),x94763))+~P1(f334(f334(f248(x94761),f513(x94762,x94764,x94763,x94761)),x94764))+P1(f334(f334(f248(x94761),f334(f334(f64(x94761,x94761,f114(x94761)),x94762),x94763)),f334(f334(f114(x94761),x94764),x94762)))
% 160.93/160.66 [9477]~P108(x94771)+~P1(f334(f61(x94771),x94773))+~P1(f334(f334(f248(x94771),f504(x94772,x94774,x94773,x94771)),x94774))+P1(f334(f334(f248(x94771),f334(f334(f64(x94771,x94771,f247(x94771)),x94772),x94773)),f334(f334(f247(x94771),x94774),x94772)))
% 160.93/160.66 [9480]~P1(f334(f334(f249(a1),f2(a1)),x94803))+~P1(f334(f334(f248(a1),f2(a1)),x94804))+~P1(f334(f334(f249(a1),x94804),x94801))+P1(f334(f334(f249(a1),f334(f334(f80(a1),f334(f334(f81(a1),x94801),f44(a1,x94802,x94803))),x94804)),f334(f334(f81(a1),x94801),x94803)))
% 160.93/160.66 [9883]E(x98831,x98832)+P1(f334(f334(f336(f887(f882(x98833),f882(x98833))),f334(f334(f269(f882(x98833),f882(x98833)),x98832),x98831)),f149(x98833,x98834)))+P1(f334(f334(f336(f887(f882(x98833),f882(x98833))),f334(f334(f269(f882(x98833),f882(x98833)),x98831),x98832)),f149(x98833,x98834)))+~P1(f334(f334(f336(f887(x98833,x98833)),f334(f334(f269(x98833,x98833),f670(x98831,x98832,x98834,x98833)),f672(x98831,x98832,x98834,x98833))),x98834))
% 160.93/160.66 [9884]E(x98841,x98842)+P1(f334(f334(f336(f887(f882(x98843),f882(x98843))),f334(f334(f269(f882(x98843),f882(x98843)),x98842),x98841)),f149(x98843,x98844)))+P1(f334(f334(f336(f887(f882(x98843),f882(x98843))),f334(f334(f269(f882(x98843),f882(x98843)),x98841),x98842)),f149(x98843,x98844)))+~P1(f334(f334(f336(f887(x98843,x98843)),f334(f334(f269(x98843,x98843),f672(x98841,x98842,x98844,x98843)),f670(x98841,x98842,x98844,x98843))),x98844))
% 160.93/160.66 [7424]~P108(x74241)+~P1(f334(f334(f249(x74241),x74243),x74244))+~P1(f334(f334(f249(x74241),x74242),x74244))+P1(f334(f334(f249(x74241),f334(f334(f247(x74241),x74242),x74243)),x74244))
% 160.93/160.66 [7427]~P99(x74271)+~P1(f334(f334(f248(x74271),x74273),x74274))+~P1(f334(f334(f248(x74271),x74272),x74274))+P1(f334(f334(f248(x74271),f334(f334(f114(x74271),x74272),x74273)),x74274))
% 160.93/160.66 [7430]~P108(x74301)+~P1(f334(f334(f248(x74301),x74303),x74304))+~P1(f334(f334(f248(x74301),x74302),x74304))+P1(f334(f334(f248(x74301),f334(f334(f247(x74301),x74302),x74303)),x74304))
% 160.93/160.66 [7749]~E(x77491,x77493)+E(f141(a881,f334(f304(a881,x77491),x77492)),f334(f334(f153(a881),x77493),x77494))+~E(f141(a881,f334(f304(a881,f334(f334(f80(a881),x77491),f78(a881))),x77492)),x77494)+~P1(f334(f334(f249(a881),x77491),x77492))
% 160.93/160.66 [7758]~P108(x77581)+P1(f334(f334(f249(x77581),x77582),x77583))+P1(f334(f334(f249(x77581),x77584),x77583))+~P1(f334(f334(f249(x77581),f334(f334(f246(x77581),x77584),x77582)),x77583))
% 160.93/160.66 [7759]~P108(x77591)+P1(f334(f334(f248(x77591),x77592),x77593))+P1(f334(f334(f248(x77591),x77594),x77593))+~P1(f334(f334(f248(x77591),f334(f334(f246(x77591),x77594),x77592)),x77593))
% 160.93/160.66 [8034]~P63(x80341)+~P1(f334(f334(f249(x80341),f2(x80341)),x80343))+~P1(f334(f334(f249(x80341),x80342),f334(f334(f292(x80341),x80344),x80343)))+P1(f334(f334(f249(x80341),f334(f334(f81(x80341),x80342),x80343)),x80344))
% 160.93/160.66 [8035]~P64(x80351)+~P1(f334(f334(f249(x80351),f2(x80351)),x80353))+~P1(f334(f334(f249(x80351),x80352),f334(f334(f292(x80351),x80354),x80353)))+P1(f334(f334(f249(x80351),f334(f334(f81(x80351),x80352),x80353)),x80354))
% 160.93/160.66 [8036]~P63(x80361)+~P1(f334(f334(f249(x80361),f2(x80361)),x80363))+~P1(f334(f334(f249(x80361),x80362),f334(f334(f81(x80361),x80364),x80363)))+P1(f334(f334(f249(x80361),f334(f334(f292(x80361),x80362),x80363)),x80364))
% 160.93/160.66 [8038]~P64(x80381)+~P1(f334(f334(f249(x80381),f2(x80381)),x80383))+~P1(f334(f334(f249(x80381),x80382),f334(f334(f81(x80381),x80384),x80383)))+P1(f334(f334(f249(x80381),f334(f334(f292(x80381),x80382),x80383)),x80384))
% 160.93/160.66 [8039]~P63(x80391)+~P1(f334(f334(f249(x80391),f2(x80391)),x80393))+~P1(f334(f334(f248(x80391),x80392),f334(f334(f292(x80391),x80394),x80393)))+P1(f334(f334(f248(x80391),f334(f334(f81(x80391),x80392),x80393)),x80394))
% 160.93/160.66 [8040]~P64(x80401)+~P1(f334(f334(f249(x80401),f2(x80401)),x80403))+~P1(f334(f334(f248(x80401),x80402),f334(f334(f292(x80401),x80404),x80403)))+P1(f334(f334(f248(x80401),f334(f334(f81(x80401),x80402),x80403)),x80404))
% 160.93/160.66 [8041]~P63(x80411)+~P1(f334(f334(f249(x80411),f2(x80411)),x80413))+~P1(f334(f334(f248(x80411),x80412),f334(f334(f81(x80411),x80414),x80413)))+P1(f334(f334(f248(x80411),f334(f334(f292(x80411),x80412),x80413)),x80414))
% 160.93/160.66 [8043]~P64(x80431)+~P1(f334(f334(f249(x80431),f2(x80431)),x80433))+~P1(f334(f334(f248(x80431),x80432),f334(f334(f81(x80431),x80434),x80433)))+P1(f334(f334(f248(x80431),f334(f334(f292(x80431),x80432),x80433)),x80434))
% 160.93/160.66 [8180]~P63(x81801)+~P1(f334(f334(f249(x81801),f2(x81801)),x81804))+P1(f334(f334(f249(x81801),x81802),f334(f334(f81(x81801),x81803),x81804)))+~P1(f334(f334(f249(x81801),f334(f334(f292(x81801),x81802),x81804)),x81803))
% 160.93/160.66 [8181]~P63(x81811)+~P1(f334(f334(f249(x81811),f2(x81811)),x81814))+P1(f334(f334(f249(x81811),x81812),f334(f334(f292(x81811),x81813),x81814)))+~P1(f334(f334(f249(x81811),f334(f334(f81(x81811),x81812),x81814)),x81813))
% 160.93/160.66 [8183]~P64(x81831)+~P1(f334(f334(f249(x81831),f2(x81831)),x81834))+P1(f334(f334(f249(x81831),x81832),f334(f334(f81(x81831),x81833),x81834)))+~P1(f334(f334(f249(x81831),f334(f334(f292(x81831),x81832),x81834)),x81833))
% 160.93/160.66 [8184]~P64(x81841)+~P1(f334(f334(f249(x81841),f2(x81841)),x81844))+P1(f334(f334(f249(x81841),x81842),f334(f334(f292(x81841),x81843),x81844)))+~P1(f334(f334(f249(x81841),f334(f334(f81(x81841),x81842),x81844)),x81843))
% 160.93/160.66 [8185]~P63(x81851)+~P1(f334(f334(f249(x81851),f2(x81851)),x81854))+P1(f334(f334(f248(x81851),x81852),f334(f334(f81(x81851),x81853),x81854)))+~P1(f334(f334(f248(x81851),f334(f334(f292(x81851),x81852),x81854)),x81853))
% 160.93/160.66 [8186]~P63(x81861)+~P1(f334(f334(f249(x81861),f2(x81861)),x81864))+P1(f334(f334(f248(x81861),x81862),f334(f334(f292(x81861),x81863),x81864)))+~P1(f334(f334(f248(x81861),f334(f334(f81(x81861),x81862),x81864)),x81863))
% 160.93/160.66 [8188]~P64(x81881)+~P1(f334(f334(f249(x81881),f2(x81881)),x81884))+P1(f334(f334(f248(x81881),x81882),f334(f334(f81(x81881),x81883),x81884)))+~P1(f334(f334(f248(x81881),f334(f334(f292(x81881),x81882),x81884)),x81883))
% 160.93/160.66 [8189]~P64(x81891)+~P1(f334(f334(f249(x81891),f2(x81891)),x81894))+P1(f334(f334(f248(x81891),x81892),f334(f334(f292(x81891),x81893),x81894)))+~P1(f334(f334(f248(x81891),f334(f334(f81(x81891),x81892),x81894)),x81893))
% 160.93/160.66 [8355]~P64(x83551)+~P1(f334(f334(f249(x83551),x83553),f2(x83551)))+~P1(f334(f334(f249(x83551),f334(f334(f292(x83551),x83554),x83553)),x83552))+P1(f334(f334(f249(x83551),f334(f334(f81(x83551),x83552),x83553)),x83554))
% 160.93/160.66 [8356]~P64(x83561)+~P1(f334(f334(f249(x83561),x83563),f2(x83561)))+~P1(f334(f334(f249(x83561),f334(f334(f81(x83561),x83564),x83563)),x83562))+P1(f334(f334(f249(x83561),f334(f334(f292(x83561),x83562),x83563)),x83564))
% 160.93/160.66 [8357]~P64(x83571)+~P1(f334(f334(f249(x83571),x83573),f2(x83571)))+~P1(f334(f334(f248(x83571),f334(f334(f292(x83571),x83574),x83573)),x83572))+P1(f334(f334(f248(x83571),f334(f334(f81(x83571),x83572),x83573)),x83574))
% 160.93/160.66 [8358]~P64(x83581)+~P1(f334(f334(f249(x83581),x83583),f2(x83581)))+~P1(f334(f334(f248(x83581),f334(f334(f81(x83581),x83584),x83583)),x83582))+P1(f334(f334(f248(x83581),f334(f334(f292(x83581),x83582),x83583)),x83584))
% 160.93/160.66 [8368]~P1(f334(x83681,x83684))+~P1(f334(f334(f249(a881),x83682),f334(f334(f81(a881),x83683),f334(a116,x83684))))+P1(f334(x83681,f334(f334(f38(a881),x83682),x83683)))+~P1(f334(f334(f248(a881),f334(f334(f81(a881),x83683),x83684)),x83682))
% 160.93/160.66 [8582]~P99(x85821)+~P1(f334(f61(x85821),x85824))+~P1(f334(f334(f336(x85821),x85822),x85824))+P1(f334(f334(f248(x85821),f334(f334(f114(x85821),x85822),x85823)),f334(f334(f64(x85821,x85821,f114(x85821)),x85823),x85824)))
% 160.93/160.66 [8583]~P108(x85831)+~P1(f334(f61(x85831),x85834))+~P1(f334(f334(f336(x85831),x85832),x85834))+P1(f334(f334(f248(x85831),f334(f334(f247(x85831),x85832),x85833)),f334(f334(f64(x85831,x85831,f247(x85831)),x85833),x85834)))
% 160.93/160.66 [8728]~P1(f334(f61(x87281),x87282))+E(f334(f37(x87281),f334(f334(f22(f888(x87281,a876)),x87282),f334(f334(f312(x87281),x87283),x87284))),f334(f334(f22(a881),f334(f37(x87281),f334(f334(f22(f888(x87281,a876)),x87282),x87284))),f78(a881)))+P1(f334(f334(f336(x87281),x87283),x87284))+~P1(f334(f334(f336(x87281),x87283),x87282))
% 160.93/160.66 [8798]E(f334(f334(f80(a1),f394(x87981,x87982,x87983,x87984)),f395(x87981,x87982,x87983,x87984)),x87984)+~P1(f334(f334(f249(a1),f2(a1)),x87983))+~P1(f334(f334(f248(a1),x87984),x87981))+P1(f334(f334(f248(a1),f334(f334(f22(a1),x87984),x87983)),x87981))
% 160.93/160.66 [8799]E(f334(f334(f80(a1),f401(x87991,x87992,x87993,x87994)),f402(x87991,x87992,x87993,x87994)),x87994)+~P1(f334(f334(f249(a1),f2(a1)),x87993))+~P1(f334(f334(f249(a1),x87994),x87991))+P1(f334(f334(f249(a1),f334(f334(f22(a1),x87994),x87993)),x87991))
% 160.93/160.66 [9009]~P1(f334(f334(f249(a1),f2(a1)),x90093))+~P1(f334(f334(f248(a1),x90094),x90091))+P1(f334(f334(f336(a1),f394(x90091,x90092,x90093,x90094)),x90092))+P1(f334(f334(f248(a1),f334(f334(f22(a1),x90094),x90093)),x90091))
% 160.93/160.66 [9010]~P1(f334(f334(f249(a1),f2(a1)),x90103))+~P1(f334(f334(f249(a1),x90104),x90101))+P1(f334(f334(f336(a1),f401(x90101,x90102,x90103,x90104)),x90102))+P1(f334(f334(f249(a1),f334(f334(f22(a1),x90104),x90103)),x90101))
% 160.93/160.66 [9098]~P1(f334(f334(f249(a1),f2(a1)),x90982))+~P1(f334(f334(f249(a1),x90981),x90983))+P1(f334(f334(f336(a1),f402(x90983,x90984,x90982,x90981)),f305(a1,f78(a1),x90982)))+P1(f334(f334(f249(a1),f334(f334(f22(a1),x90981),x90982)),x90983))
% 160.93/160.66 [9099]~P1(f334(f334(f249(a1),f2(a1)),x90992))+~P1(f334(f334(f248(a1),x90991),x90993))+P1(f334(f334(f336(a1),f395(x90993,x90994,x90992,x90991)),f305(a1,f78(a1),x90992)))+P1(f334(f334(f248(a1),f334(f334(f22(a1),x90991),x90992)),x90993))
% 160.93/160.66 [9116]~P1(f334(f334(f249(a1),f2(a1)),x91163))+~P1(f334(f334(f248(a1),f2(a1)),x91164))+~P1(f334(f334(f249(a1),x91164),x91161))+P1(f334(f334(f248(a1),f2(a1)),f334(f334(f80(a1),f334(f334(f81(a1),x91161),f44(a1,x91162,x91163))),x91164)))
% 160.93/160.66 [9180]~P100(x91801)+~P1(f334(f61(x91801),x91804))+~P1(f334(f334(f248(x91801),x91802),f512(x91803,x91802,x91804,x91801)))+P1(f334(f334(f248(x91801),f334(f334(f105(x91801),x91802),x91803)),f334(f334(f64(x91801,x91801,f105(x91801)),x91803),x91804)))
% 160.93/160.66 [9181]~P108(x91811)+~P1(f334(f61(x91811),x91814))+~P1(f334(f334(f248(x91811),x91812),f503(x91813,x91812,x91814,x91811)))+P1(f334(f334(f248(x91811),f334(f334(f246(x91811),x91812),x91813)),f334(f334(f64(x91811,x91811,f246(x91811)),x91813),x91814)))
% 160.93/160.66 [9196]~P1(f334(f334(f248(a1),x91964),f2(a1)))+~P1(f334(f334(f249(a1),f2(a1)),x91962))+~P1(f334(f334(f249(a1),x91961),x91964))+P1(f334(f334(f249(a1),f334(f334(f81(a1),x91961),x91962)),f334(f334(f80(a1),f334(f334(f81(a1),x91961),f44(a1,x91963,x91962))),x91964)))
% 160.93/160.66 [9218]P1(f334(f61(x92181),x92182))+~P1(f334(f61(x92181),x92183))+~P1(f334(f334(f336(f888(x92181,a876)),x92182),f334(f334(f60(x92181),x92183),x92184)))+~P1(f334(f334(f248(f888(f887(x92181,x92181),a876)),x92184),f334(f334(f271(x92181,x92181),x92183),f334(f16(f888(x92181,a876),x92181),x92183))))
% 160.93/160.66 [9246]~P108(x92461)+~P1(f334(f61(x92461),x92464))+P1(f334(f334(f336(x92461),f503(x92462,x92463,x92464,x92461)),x92464))+P1(f334(f334(f248(x92461),f334(f334(f246(x92461),x92463),x92462)),f334(f334(f64(x92461,x92461,f246(x92461)),x92462),x92464)))
% 160.93/160.66 [9247]~P100(x92471)+~P1(f334(f61(x92471),x92474))+P1(f334(f334(f336(x92471),f512(x92472,x92473,x92474,x92471)),x92474))+P1(f334(f334(f248(x92471),f334(f334(f105(x92471),x92473),x92472)),f334(f334(f64(x92471,x92471,f105(x92471)),x92472),x92474)))
% 160.93/160.66 [9648]~P1(f334(f61(x96482),x96484))+~P1(f334(f61(x96481),x96483))+~P1(f334(f334(f248(a881),f334(f37(x96482),x96484)),f334(f37(x96481),x96483)))+P1(f334(f334(f248(f888(x96481,a876)),f334(f313(x96482,x96481,f555(x96483,x96481,x96484,x96482)),x96484)),x96483))
% 160.93/160.66 [9293]~P1(f334(f334(f336(x92931),x92932),x92934))+P1(f334(f334(f336(x92931),x92932),x92933))+~P1(f334(f334(f249(f888(x92931,a876)),x92934),f334(f334(f312(x92931),x92932),x92933)))+P1(f334(f334(f249(f888(x92931,a876)),f334(f334(f22(f888(x92931,a876)),x92934),f334(f334(f312(x92931),x92932),f196(f888(x92931,a876))))),x92933))
% 160.93/160.66 [9454]~P1(f334(f334(f336(x94541),x94542),x94544))+P1(f334(f334(f336(x94541),x94542),x94543))+P1(f334(f334(f249(f888(x94541,a876)),x94544),f334(f334(f312(x94541),x94542),x94543)))+~P1(f334(f334(f249(f888(x94541,a876)),f334(f334(f22(f888(x94541,a876)),x94544),f334(f334(f312(x94541),x94542),f196(f888(x94541,a876))))),x94543))
% 160.93/160.66 [9483]P1(f334(f334(f336(x94831),x94832),x94833))+~P1(f334(f334(f248(f888(x94831,a876)),x94834),x94833))+P1(f334(f334(f249(f888(x94831,a876)),x94834),f334(f334(f312(x94831),x94832),x94833)))+~P1(f334(f334(f249(f888(x94831,a876)),f334(f334(f22(f888(x94831,a876)),x94834),f334(f334(f312(x94831),x94832),f196(f888(x94831,a876))))),x94833))
% 160.93/160.66 [9488]~P1(f334(f334(f336(x94881),x94883),x94882))+~P1(f334(f334(f249(f888(x94881,a876)),x94882),x94884))+P1(f334(f334(f249(f888(x94881,a876)),x94882),f334(f334(f312(x94881),x94883),x94884)))+~P1(f334(f334(f249(f888(x94881,a876)),f334(f334(f22(f888(x94881,a876)),x94882),f334(f334(f312(x94881),x94883),f196(f888(x94881,a876))))),x94884))
% 160.93/160.66 [9501]~P1(f334(f334(f248(f888(x95011,a876)),x95012),x95014))+~P1(f334(f334(f249(f888(x95011,a876)),x95012),x95014))+P1(f334(f334(f249(f888(x95011,a876)),x95012),f334(f334(f312(x95011),x95013),x95014)))+~P1(f334(f334(f249(f888(x95011,a876)),f334(f334(f22(f888(x95011,a876)),x95012),f334(f334(f312(x95011),x95013),f196(f888(x95011,a876))))),x95014))
% 160.93/160.66 [9549]~P109(x95492)+~P60(x95491)+~P1(f334(f334(f248(f888(x95491,x95492)),x95493),x95494))+P1(f334(f58(x95491),f334(f334(f18(x95491,x95492,a876),f334(f334(f8(x95492,f888(x95492,a876),x95491),f248(x95492)),x95493)),x95494)))
% 160.93/160.66 [9696]~P109(x96962)+~P60(x96961)+P1(f334(f334(f248(f888(x96961,x96962)),x96963),x96964))+~P1(f334(f58(x96961),f334(f334(f18(x96961,x96962,a876),f334(f334(f8(x96962,f888(x96962,a876),x96961),f248(x96962)),x96963)),x96964)))
% 160.93/160.66 [9867]E(f334(f334(f167(x98671),f334(f334(f167(f882(x98671)),f182(x98671,x98672)),x98673)),x98674),f334(f334(f167(x98671),f334(f334(f167(f882(x98671)),x98672),x98674)),x98673))+~P1(f334(f334(f249(a881),x98673),f334(f197(f882(f882(x98671))),f182(x98671,x98672))))+~P16(a881,f334(f171(a881),f334(f334(f156(f882(x98671),a881),f197(f882(x98671))),x98672)))+~P1(f334(f334(f249(a881),x98674),f334(f197(f882(f882(x98671))),f334(f138(f882(x98671),f334(f334(f8(a881,a876,f882(x98671)),f334(f249(a881),x98673)),f197(f882(x98671)))),x98672))))
% 160.93/160.66 [9896]~P1(f334(f334(f336(f887(a881,a881)),x98964),x98961))+~P1(f334(f334(f336(f887(f887(a881,a881),f887(a881,a881))),f334(f334(f269(f887(a881,a881),f887(a881,a881)),x98964),x98962)),a70))+~P1(f334(f334(f336(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f334(f334(f269(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),x98961),x98963)),a71))+P1(f334(f334(f336(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f334(f334(f269(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),x98961),f334(f334(f312(f887(a881,a881)),x98962),x98963))),a71))
% 160.93/160.66 [9897]~P1(f334(f334(f336(f887(a881,a881)),x98974),x98971))+~P1(f334(f334(f336(f887(f887(a881,a881),f887(a881,a881))),f334(f334(f269(f887(a881,a881),f887(a881,a881)),x98974),x98972)),a35))+~P1(f334(f334(f336(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f334(f334(f269(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),x98971),x98973)),a68))+P1(f334(f334(f336(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f334(f334(f269(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),x98971),f334(f334(f312(f887(a881,a881)),x98972),x98973))),a68))
% 160.93/160.66 [9780]~P109(x97802)+~P60(x97801)+~P1(f334(f334(f249(f888(x97801,x97802)),x97803),x97804))+P1(f334(f57(x97801),f334(f334(f8(a876,a876,x97801),a329),f334(f334(f18(x97801,x97802,a876),f334(f334(f8(x97802,f888(x97802,a876),x97801),a331),x97803)),x97804))))
% 160.93/160.66 [9910]~P1(f334(f334(f336(f887(a881,a881)),x99104),x99103))+~P1(f334(f334(f336(f887(f887(a881,a881),f887(a881,a881))),f334(f334(f269(f887(a881,a881),f887(a881,a881)),x99101),x99104)),a35))+~P1(f334(f334(f336(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f334(f334(f269(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),x99102),x99103)),a36))+P1(f334(f334(f336(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f334(f334(f269(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),f334(f334(f312(f887(a881,a881)),x99101),x99102)),x99103)),a36))
% 160.93/160.66 [9911]~P1(f334(f334(f336(f887(a881,a881)),x99114),x99113))+~P1(f334(f334(f336(f887(f887(a881,a881),f887(a881,a881))),f334(f334(f269(f887(a881,a881),f887(a881,a881)),x99111),x99114)),a70))+~P1(f334(f334(f336(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f334(f334(f269(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),x99112),x99113)),a69))+P1(f334(f334(f336(f887(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876))),f334(f334(f269(f888(f887(a881,a881),a876),f888(f887(a881,a881),a876)),f334(f334(f312(f887(a881,a881)),x99111),x99112)),x99113)),a69))
% 160.93/160.66 [6020]~P7(x60204,x60201)+~P1(f334(f334(x60201,x60202),x60205))+P1(f334(f334(x60201,x60202),x60203))+~P1(f334(f334(x60201,x60205),x60203))
% 160.93/160.66 [5288]~P67(x52885)+E(x52881,x52882)+~E(x52883,x52884)+~E(f334(f334(f22(x52885),x52883),x52884),f334(f334(f22(x52885),x52881),x52882))
% 160.93/160.66 [6128]~P19(x61285,x61281,x61283)+E(f334(f334(x61281,x61282),f334(x61283,x61284)),f334(x61283,x61284))+~P1(f334(f61(x61285),x61284))+~P1(f334(f334(f336(x61285),x61282),x61284))
% 160.93/160.66 [6325]~P83(x63251)+~E(f334(f334(f22(x63251),x63254),x63255),f334(f334(f22(x63251),x63252),x63253))+~P1(f334(f334(f249(x63251),x63254),x63255))+P1(f334(f334(f249(x63251),x63252),x63253))
% 160.93/160.66 [6327]~P83(x63271)+~E(f334(f334(f22(x63271),x63274),x63275),f334(f334(f22(x63271),x63272),x63273))+~P1(f334(f334(f248(x63271),x63274),x63275))+P1(f334(f334(f248(x63271),x63272),x63273))
% 160.93/160.66 [7285]~E(x72852,f334(f334(f153(x72851),x72854),x72855))+P1(f334(f334(f336(f882(x72851)),x72852),f163(x72851,x72853)))+~P1(f334(f334(f336(f882(x72851)),x72855),f163(x72851,x72853)))+~P1(f334(f334(f336(x72851),x72854),x72853))
% 160.93/160.66 [7702]~E(f334(f197(f882(x77021)),x77023),f334(f197(f882(x77022)),x77024))+~E(f334(f334(f156(f887(x77021,x77022),x77022),f272(x77021,x77022)),x77025),x77024)+~E(f334(f334(f156(f887(x77021,x77022),x77021),f268(x77021,x77022)),x77025),x77023)+E(f334(f334(f184(x77021,x77022),x77023),x77024),x77025)
% 160.93/160.66 [8031]~P109(x80311)+P1(f334(f334(f249(f888(x80311,a876)),f305(x80311,x80312,x80313)),f305(x80311,x80314,x80315)))+~P1(f334(f334(f248(x80311),x80314),x80315))+P1(f334(f334(f248(x80311),x80312),x80313))
% 160.93/160.66 [8128]~P109(x81281)+P1(f334(f334(f248(f888(x81281,a876)),f305(x81281,x81282,x81283)),f305(x81281,x81284,x81285)))+~P1(f334(f334(f248(x81281),x81283),x81285))+~P1(f334(f334(f248(x81281),x81284),x81282))
% 160.93/160.66 [8263]~P108(x82631)+P1(f334(f334(f248(x82631),x82632),x82633))+P1(f334(f334(f248(x82631),x82634),x82633))+~P1(f334(f334(f248(f888(x82631,a876)),f334(f304(x82631,x82633),x82632)),f334(f304(x82631,x82634),x82635)))
% 160.93/160.66 [8264]~P108(x82641)+P1(f334(f334(f248(x82641),x82642),x82643))+P1(f334(f334(f248(x82641),x82642),x82644))+~P1(f334(f334(f248(f888(x82641,a876)),f334(f304(x82641,x82643),x82642)),f334(f304(x82641,x82645),x82644)))
% 160.93/160.66 [8493]~P109(x84931)+~P1(f334(f334(f249(f888(x84931,a876)),f305(x84931,x84934,x84932)),f305(x84931,x84935,x84933)))+P1(f334(f334(f248(x84931),x84932),x84933))+~P1(f334(f334(f248(x84931),x84934),x84932))
% 160.93/160.66 [8494]~P109(x84941)+~P1(f334(f334(f248(f888(x84941,a876)),f305(x84941,x84944,x84942)),f305(x84941,x84945,x84943)))+P1(f334(f334(f248(x84941),x84942),x84943))+~P1(f334(f334(f248(x84941),x84944),x84942))
% 160.93/160.66 [8495]~P109(x84951)+~P1(f334(f334(f249(f888(x84951,a876)),f305(x84951,x84953,x84954)),f305(x84951,x84952,x84955)))+P1(f334(f334(f248(x84951),x84952),x84953))+~P1(f334(f334(f248(x84951),x84953),x84954))
% 160.93/160.66 [8496]~P109(x84961)+~P1(f334(f334(f248(f888(x84961,a876)),f305(x84961,x84963,x84964)),f305(x84961,x84962,x84965)))+P1(f334(f334(f248(x84961),x84962),x84963))+~P1(f334(f334(f248(x84961),x84963),x84964))
% 160.93/160.66 [6019]~P19(x60192,x60195,x60193)+E(x60191,f196(f888(x60192,a876)))+~P1(f334(f61(x60192),x60191))+E(f334(x60193,f334(f334(f312(x60192),x60194),x60191)),f334(f334(x60195,x60194),f334(x60193,x60191)))
% 160.93/160.66 [6789]~E(x67891,x67892)+~E(f334(f334(f105(f888(x67893,a876)),x67894),x67895),f196(f888(x67893,a876)))+~P1(f334(f334(f336(x67893),x67892),x67895))+~P1(f334(f334(f336(x67893),x67891),x67894))
% 160.93/160.66 [6870]~P20(x68702,x68705,x68701)+~P1(f334(f61(x68702),x68704))+E(f334(x68701,f334(f334(f312(x68702),x68703),x68704)),f334(f334(f64(x68702,x68702,x68705),x68703),x68704))+P1(f334(f334(f336(x68702),x68703),x68704))
% 160.93/160.66 [6936]~P68(x69362)+~P1(f334(f61(x69361),x69365))+E(f334(f334(f6(x69361,x69362),x69363),f334(f334(f312(x69361),x69364),x69365)),f334(f334(f80(x69362),f334(x69363,x69364)),f334(f334(f6(x69361,x69362),x69363),x69365)))+P1(f334(f334(f336(x69361),x69364),x69365))
% 160.93/160.66 [6938]~P74(x69382)+~P1(f334(f61(x69381),x69385))+E(f334(f334(f9(x69381,x69382),x69383),f334(f334(f312(x69381),x69384),x69385)),f334(f334(f81(x69382),f334(x69383,x69384)),f334(f334(f9(x69381,x69382),x69383),x69385)))+P1(f334(f334(f336(x69381),x69384),x69385))
% 160.93/160.66 [7441]~P20(x74412,x74415,x74411)+~P1(f334(f61(x74412),x74414))+E(f334(x74411,f334(f334(f312(x74412),x74413),x74414)),x74413)+~E(f334(f334(f22(f888(x74412,a876)),x74414),f334(f334(f312(x74412),x74413),f196(f888(x74412,a876)))),f196(f888(x74412,a876)))
% 160.93/160.66 [7804]~P86(x78041)+~P1(f334(f334(f249(x78041),x78043),x78045))+~P1(f334(f334(f249(x78041),x78042),x78044))+P1(f334(f334(f249(x78041),f334(f334(f80(x78041),x78042),x78043)),f334(f334(f80(x78041),x78044),x78045)))
% 160.93/160.66 [7805]~P86(x78051)+~P1(f334(f334(f248(x78051),x78052),x78054))+~P1(f334(f334(f249(x78051),x78053),x78055))+P1(f334(f334(f249(x78051),f334(f334(f80(x78051),x78052),x78053)),f334(f334(f80(x78051),x78054),x78055)))
% 160.93/160.66 [7806]~P86(x78061)+~P1(f334(f334(f248(x78061),x78063),x78065))+~P1(f334(f334(f249(x78061),x78062),x78064))+P1(f334(f334(f249(x78061),f334(f334(f80(x78061),x78062),x78063)),f334(f334(f80(x78061),x78064),x78065)))
% 160.93/160.66 [7807]~P99(x78071)+~P1(f334(f334(f248(x78071),x78073),x78075))+~P1(f334(f334(f248(x78071),x78072),x78074))+P1(f334(f334(f248(x78071),f334(f334(f114(x78071),x78072),x78073)),f334(f334(f114(x78071),x78074),x78075)))
% 160.93/160.66 [7808]~P100(x78081)+~P1(f334(f334(f248(x78081),x78083),x78085))+~P1(f334(f334(f248(x78081),x78082),x78084))+P1(f334(f334(f248(x78081),f334(f334(f105(x78081),x78082),x78083)),f334(f334(f105(x78081),x78084),x78085)))
% 160.93/160.66 [7809]~P84(x78091)+~P1(f334(f334(f248(x78091),x78093),x78095))+~P1(f334(f334(f248(x78091),x78092),x78094))+P1(f334(f334(f248(x78091),f334(f334(f80(x78091),x78092),x78093)),f334(f334(f80(x78091),x78094),x78095)))
% 160.93/160.66 [7810]~P108(x78101)+~P1(f334(f334(f248(x78101),x78103),x78105))+~P1(f334(f334(f248(x78101),x78102),x78104))+P1(f334(f334(f248(x78101),f334(f334(f246(x78101),x78102),x78103)),f334(f334(f246(x78101),x78104),x78105)))
% 160.93/160.66 [7811]~P108(x78111)+~P1(f334(f334(f248(x78111),x78113),x78115))+~P1(f334(f334(f248(x78111),x78112),x78114))+P1(f334(f334(f248(x78111),f334(f334(f247(x78111),x78112),x78113)),f334(f334(f247(x78111),x78114),x78115)))
% 160.93/160.66 [7948]~P143(x79485)+E(x79481,x79482)+E(x79483,x79484)+~E(f334(f334(f80(x79485),f334(f334(f81(x79485),x79483),x79481)),f334(f334(f81(x79485),x79484),x79482)),f334(f334(f80(x79485),f334(f334(f81(x79485),x79483),x79482)),f334(f334(f81(x79485),x79484),x79481)))
% 160.93/160.66 [8082]P29(x80821,x80822,x80823)+~P30(x80821,x80824,x80825)+~P29(x80821,x80822,f603(x80825,x80824,x80821,x80822))+~P1(f334(f334(f336(f880(x80821)),x80823),x80825))
% 160.93/160.66 [8145]~P1(f334(x81451,x81453))+~P1(f334(f334(f334(a202,x81452),x81453),x81455))+~P1(f334(f334(f334(a202,f32(x81451,x81452)),x81455),x81454))+P1(f334(f334(f334(a202,f32(x81451,x81452)),x81453),x81454))
% 160.93/160.66 [8152]~P108(x81524)+~P1(f334(f139(x81521),x81523))+P1(f334(f334(f336(x81521),x81522),f334(f174(x81521),x81523)))+P1(f334(f139(x81521),f334(f334(f150(x81521,x81524,x81525),x81522),x81523)))
% 160.93/160.66 [8308]~P67(x83081)+E(f334(f334(f22(x83081),f334(f334(f6(a881,x83081),x83082),f334(f304(a881,x83083),x83084))),f334(f334(f6(a881,x83081),x83082),f334(f304(a881,x83083),x83085))),f334(f334(f6(a881,x83081),x83082),f334(f304(a881,x83085),x83084)))+~P1(f334(f334(f248(a881),x83085),x83084))+~P1(f334(f334(f248(a881),x83083),x83085))
% 160.93/160.66 [8309]~P68(x83091)+E(f334(f334(f80(x83091),f334(f334(f6(a881,x83091),x83092),f334(f304(a881,x83093),x83094))),f334(f334(f6(a881,x83091),x83092),f334(f304(a881,x83094),x83095))),f334(f334(f6(a881,x83091),x83092),f334(f304(a881,x83093),x83095)))+~P1(f334(f334(f248(a881),x83094),x83095))+~P1(f334(f334(f248(a881),x83093),x83094))
% 160.93/160.66 [8640]~P62(x86402)+E(x86401,f2(x86402))+E(x86403,f2(x86402))+E(f334(f334(f292(x86402),f334(f334(f22(x86402),f334(f334(f81(x86402),x86404),x86401)),f334(f334(f81(x86402),x86405),x86403))),f334(f334(f81(x86402),x86403),x86401)),f334(f334(f22(x86402),f334(f334(f292(x86402),x86404),x86403)),f334(f334(f292(x86402),x86405),x86401)))
% 160.93/160.66 [8641]~P62(x86412)+E(x86411,f2(x86412))+E(x86413,f2(x86412))+E(f334(f334(f292(x86412),f334(f334(f80(x86412),f334(f334(f81(x86412),x86414),x86411)),f334(f334(f81(x86412),x86415),x86413))),f334(f334(f81(x86412),x86413),x86411)),f334(f334(f80(x86412),f334(f334(f292(x86412),x86414),x86413)),f334(f334(f292(x86412),x86415),x86411)))
% 160.93/160.66 [8653]~E(x86532,f334(x86533,x86531))+E(x86531,f551(x86532,x86533,x86534,x86535))+~P27(x86535,x86534,x86533,f257(f888(x86535,a876)))+~P1(f334(f334(f336(x86534),x86532),f334(f313(x86535,x86534,x86533),f257(f888(x86535,a876)))))
% 160.93/160.66 [8847]~P111(x88471)+~P1(f334(f334(f249(x88471),f334(f75(x88471),x88472)),x88474))+P1(f334(f334(f249(x88471),f334(f334(f81(x88471),f334(f75(x88471),x88472)),f334(f75(x88471),x88473))),f334(f334(f81(x88471),x88474),x88475)))+~P1(f334(f334(f249(x88471),f334(f75(x88471),x88473)),x88475))
% 160.93/160.66 [8864]~P30(x88641,x88645,x88644)+P29(x88641,x88642,x88643)+P1(f334(f334(f336(f880(x88641)),f603(x88644,x88645,x88641,x88642)),x88645))+~P1(f334(f334(f336(f880(x88641)),x88643),x88644))
% 160.93/160.66 [8968]~P27(x89681,x89683,x89685,x89682)+~P1(f334(f61(x89683),x89684))+P1(f334(f334(f248(a881),f334(f37(x89681),x89682)),f334(f37(x89683),x89684)))+~P1(f334(f334(f248(f888(x89683,a876)),f334(f313(x89681,x89683,x89685),x89682)),x89684))
% 160.93/160.66 [9038]~P68(x90382)+~P27(x90381,x90381,x90384,x90385)+~P1(f334(f61(x90381),x90385))+E(f334(f334(f6(x90381,x90382),f334(f73(x90381,x90382,x90381,x90383),x90384)),x90385),f334(f334(f6(x90381,x90382),x90383),f334(f313(x90381,x90381,x90384),x90385)))
% 160.93/160.66 [9039]~P74(x90392)+~P27(x90391,x90391,x90394,x90395)+~P1(f334(f61(x90391),x90395))+E(f334(f334(f9(x90391,x90392),f334(f73(x90391,x90392,x90391,x90393),x90394)),x90395),f334(f334(f9(x90391,x90392),x90393),f334(f313(x90391,x90391,x90394),x90395)))
% 160.93/160.66 [9157]~P39(x91571,x91572)+~P1(f334(f334(f336(x91571),x91573),x91574))+~P1(f334(f334(f336(x91571),x91575),x91574))+~P1(f334(f334(f336(f887(x91571,x91571)),f334(f334(f269(x91571,x91571),x91575),f633(x91572,x91571,x91574))),x91572))
% 160.93/160.66 [9195]~P27(x91952,x91953,x91955,x91951)+E(x91951,f196(f888(x91952,a876)))+E(f334(f313(x91953,x91952,f553(x91954,x91953,x91952,x91951)),x91954),x91951)+~P1(f334(f334(f248(f888(x91953,a876)),f334(f313(x91952,x91953,x91955),x91951)),x91954))
% 160.93/160.66 [9677]~P5(x96775)+~P108(x96775)+P1(f334(f334(f336(x96771),f845(x96772,x96773,x96771,x96774,x96775)),x96773))+~P1(f334(f334(f249(x96775),x96774),f334(f334(f41(x96771,x96775),x96773),x96772)))
% 160.93/160.66 [9682]~P5(x96821)+~P108(x96821)+P1(f334(f334(f249(x96821),x96822),f334(x96823,f845(x96823,x96824,x96825,x96822,x96821))))+~P1(f334(f334(f249(x96821),x96822),f334(f334(f41(x96825,x96821),x96824),x96823)))
% 160.93/160.66 [9760]~P70(x97601)+~P1(f334(f66(x97601,x97601,f81(x97601),x97602,x97603),x97605))+P1(f334(f334(f336(x97601),x97602),x97603))+P1(f334(f66(x97601,x97601,f81(x97601),x97604,f334(f334(f312(x97601),x97602),x97603)),f334(f334(f81(x97601),x97604),x97605)))
% 160.93/160.66 [9978]~P68(x99782)+~P1(f334(f61(x99781),x99785))+E(f334(f334(f6(x99781,x99782),f334(f334(f7(x99781,x99782,x99782),f334(f334(f18(x99781,x99782,f888(x99782,x99782)),f334(f334(f8(a876,f888(x99782,f888(x99782,x99782)),x99781),f100(x99782)),f334(a331,x99783))),x99784)),f2(x99782))),x99785),f2(x99782))+P1(f334(f334(f336(x99781),x99783),x99785))
% 160.93/160.66 [9979]~P74(x99792)+~P1(f334(f61(x99791),x99795))+E(f334(f334(f9(x99791,x99792),f334(f334(f7(x99791,x99792,x99792),f334(f334(f18(x99791,x99792,f888(x99792,x99792)),f334(f334(f8(a876,f888(x99792,f888(x99792,x99792)),x99791),f100(x99792)),f334(a331,x99793))),x99794)),f78(x99792))),x99795),f78(x99792))+P1(f334(f334(f336(x99791),x99793),x99795))
% 160.93/160.66 [9980]~P68(x99802)+~P1(f334(f61(x99801),x99805))+E(f334(f334(f6(x99801,x99802),f334(f334(f7(x99801,x99802,x99802),f334(f334(f18(x99801,x99802,f888(x99802,x99802)),f334(f334(f8(a876,f888(x99802,f888(x99802,x99802)),x99801),f100(x99802)),f334(a331,x99803))),x99804)),f2(x99802))),x99805),f334(x99804,x99803))+~P1(f334(f334(f336(x99801),x99803),x99805))
% 160.93/160.66 [9981]~P74(x99812)+~P1(f334(f61(x99811),x99815))+E(f334(f334(f9(x99811,x99812),f334(f334(f7(x99811,x99812,x99812),f334(f334(f18(x99811,x99812,f888(x99812,x99812)),f334(f334(f8(a876,f888(x99812,f888(x99812,x99812)),x99811),f100(x99812)),f334(a331,x99813))),x99814)),f78(x99812))),x99815),f334(x99814,x99813))+~P1(f334(f334(f336(x99811),x99813),x99815))
% 160.93/160.66 [10036]~P68(x100362)+~P1(f334(f61(x100361),x100365))+E(f334(f334(f6(x100361,x100362),f334(f334(f7(x100361,x100362,x100362),f334(f334(f18(x100361,x100362,f888(x100362,x100362)),f334(f334(f8(a876,f888(x100362,f888(x100362,x100362)),x100361),f100(x100362)),f334(f334(f7(x100361,x100361,a876),a331),x100363))),x100364)),f2(x100362))),x100365),f2(x100362))+P1(f334(f334(f336(x100361),x100363),x100365))
% 160.93/160.66 [10037]~P74(x100372)+~P1(f334(f61(x100371),x100375))+E(f334(f334(f9(x100371,x100372),f334(f334(f7(x100371,x100372,x100372),f334(f334(f18(x100371,x100372,f888(x100372,x100372)),f334(f334(f8(a876,f888(x100372,f888(x100372,x100372)),x100371),f100(x100372)),f334(f334(f7(x100371,x100371,a876),a331),x100373))),x100374)),f78(x100372))),x100375),f78(x100372))+P1(f334(f334(f336(x100371),x100373),x100375))
% 160.93/160.66 [10039]~P68(x100392)+~P1(f334(f61(x100391),x100395))+E(f334(f334(f6(x100391,x100392),f334(f334(f7(x100391,x100392,x100392),f334(f334(f18(x100391,x100392,f888(x100392,x100392)),f334(f334(f8(a876,f888(x100392,f888(x100392,x100392)),x100391),f100(x100392)),f334(f334(f7(x100391,x100391,a876),a331),x100393))),x100394)),f2(x100392))),x100395),f334(x100394,x100393))+~P1(f334(f334(f336(x100391),x100393),x100395))
% 160.93/160.66 [10040]~P74(x100402)+~P1(f334(f61(x100401),x100405))+E(f334(f334(f9(x100401,x100402),f334(f334(f7(x100401,x100402,x100402),f334(f334(f18(x100401,x100402,f888(x100402,x100402)),f334(f334(f8(a876,f888(x100402,f888(x100402,x100402)),x100401),f100(x100402)),f334(f334(f7(x100401,x100401,a876),a331),x100403))),x100404)),f78(x100402))),x100405),f334(x100404,x100403))+~P1(f334(f334(f336(x100401),x100403),x100405))
% 160.93/160.66 [7803]~P67(x78032)+~P1(f334(f61(x78031),x78034))+E(f334(f334(f6(x78031,x78032),x78033),f334(f334(f22(f888(x78031,a876)),x78034),f334(f334(f312(x78031),x78035),f196(f888(x78031,a876))))),f334(f334(f6(x78031,x78032),x78033),x78034))+P1(f334(f334(f336(x78031),x78035),x78034))
% 160.93/160.66 [8315]~P105(x83152)+~P1(f334(f61(x83151),x83154))+E(f334(f334(f6(x83151,x83152),x83153),f334(f334(f22(f888(x83151,a876)),x83154),f334(f334(f312(x83151),x83155),f196(f888(x83151,a876))))),f334(f334(f22(x83152),f334(f334(f6(x83151,x83152),x83153),x83154)),f334(x83153,x83155)))+~P1(f334(f334(f336(x83151),x83155),x83154))
% 160.93/160.66 [8316]~P67(x83162)+~P1(f334(f61(x83161),x83164))+E(f334(f334(f6(x83161,x83162),x83163),f334(f334(f22(f888(x83161,a876)),x83164),f334(f334(f312(x83161),x83165),f196(f888(x83161,a876))))),f334(f334(f22(x83162),f334(f334(f6(x83161,x83162),x83163),x83164)),f334(x83163,x83165)))+~P1(f334(f334(f336(x83161),x83165),x83164))
% 160.93/160.66 [8347]~P67(x83471)+~P1(f334(f61(x83472),x83474))+E(f334(f334(f22(x83471),f334(f334(f6(x83472,x83471),x83473),x83474)),f334(f334(f6(x83472,x83471),x83473),x83475)),f334(f334(f6(x83472,x83471),x83473),f334(f334(f22(f888(x83472,a876)),x83474),x83475)))+~P1(f334(f334(f248(f888(x83472,a876)),x83475),x83474))
% 160.93/160.66 [8367]P1(f334(f61(x83671),f334(x83672,x83673)))+~P1(f334(f61(x83674),x83675))+~P1(f334(f334(f336(x83674),x83673),x83675))+~P1(f334(f61(x83671),f334(f334(f41(x83674,f888(x83671,a876)),x83675),x83672)))
% 160.93/160.66 [8810]~P8(x88101,x88105,x88104)+~E(f334(f288(x88101,x88101,x88104),f334(f334(f312(x88101),x88102),f196(f888(x88101,a876)))),f334(f288(x88101,x88101,x88104),f334(f334(f312(x88101),x88103),f196(f888(x88101,a876)))))+~P1(f334(f334(f336(x88101),x88103),x88105))+P1(f334(f334(f336(f887(x88101,x88101)),f334(f334(f269(x88101,x88101),x88102),x88103)),x88104))
% 160.93/160.66 [9114]~P1(f334(x91141,x91145))+P1(f334(x91141,f844(x91141,x91142,x91143,x91144)))+P1(f334(x91141,f834(x91141,x91142,x91143,x91144)))+~P1(f334(f334(f336(x91144),x91145),f334(f334(f114(f888(x91144,a876)),x91143),x91142)))
% 160.93/160.66 [9298]~P1(f334(x92981,x92985))+P1(f334(x92981,f834(x92981,x92982,x92983,x92984)))+P1(f334(f334(f336(x92984),f844(x92981,x92982,x92983,x92984)),x92982))+~P1(f334(f334(f336(x92984),x92985),f334(f334(f114(f888(x92984,a876)),x92983),x92982)))
% 160.93/160.66 [9299]~P1(f334(x92991,x92995))+P1(f334(x92991,f844(x92991,x92992,x92993,x92994)))+P1(f334(f334(f336(x92994),f834(x92991,x92992,x92993,x92994)),x92993))+~P1(f334(f334(f336(x92994),x92995),f334(f334(f114(f888(x92994,a876)),x92993),x92992)))
% 160.93/160.66 [9305]P1(f334(x93051,x93052))+~P1(f334(x93051,f780(x93051,x93053,x93054,x93055)))+~P1(f334(x93051,f673(x93051,x93053,x93054,x93055)))+~P1(f334(f334(f336(x93055),x93052),f334(f334(f114(f888(x93055,a876)),x93054),x93053)))
% 160.93/160.66 [9347]E(x93471,x93472)+~P1(f334(f334(f336(f887(x93473,x93473)),f334(f334(f269(x93473,x93473),x93471),x93472)),f310(x93473,x93475)))+P1(f334(f334(f336(x93473),x93471),x93474))+~P1(f334(f334(f248(f888(f887(x93473,x93473),a876)),x93475),f334(f334(f271(x93473,x93473),x93474),f334(f16(f888(x93473,a876),x93473),x93474))))
% 160.93/160.66 [9366]P1(f334(x93661,x93662))+~P1(f334(x93661,f673(x93661,x93664,x93665,x93663)))+P1(f334(f334(f336(x93663),f780(x93661,x93664,x93665,x93663)),x93664))+~P1(f334(f334(f336(x93663),x93662),f334(f334(f114(f888(x93663,a876)),x93665),x93664)))
% 160.93/160.66 [9367]P1(f334(x93671,x93672))+~P1(f334(x93671,f780(x93671,x93674,x93675,x93673)))+P1(f334(f334(f336(x93673),f673(x93671,x93674,x93675,x93673)),x93675))+~P1(f334(f334(f336(x93673),x93672),f334(f334(f114(f888(x93673,a876)),x93675),x93674)))
% 160.93/160.66 [9428]P1(f334(x94281,x94282))+P1(f334(f334(f336(x94283),f780(x94281,x94284,x94285,x94283)),x94284))+P1(f334(f334(f336(x94283),f673(x94281,x94284,x94285,x94283)),x94285))+~P1(f334(f334(f336(x94283),x94282),f334(f334(f114(f888(x94283,a876)),x94285),x94284)))
% 160.93/160.66 [9430]~P1(f334(x94302,x94305))+P1(f334(f334(f336(x94301),f844(x94302,x94303,x94304,x94301)),x94303))+P1(f334(f334(f336(x94301),f834(x94302,x94303,x94304,x94301)),x94304))+~P1(f334(f334(f336(x94301),x94305),f334(f334(f114(f888(x94301,a876)),x94304),x94303)))
% 160.93/160.66 [9582]~P8(x95821,x95825,x95824)+~P1(f334(f334(f336(x95821),x95823),x95825))+P1(f334(f334(f336(f887(x95821,x95821)),f334(f334(f269(x95821,x95821),x95822),x95823)),x95824))+~P1(f334(f334(f248(f888(x95821,a876)),f334(f288(x95821,x95821,x95824),f334(f334(f312(x95821),x95823),f196(f888(x95821,a876))))),f334(f288(x95821,x95821,x95824),f334(f334(f312(x95821),x95822),f196(f888(x95821,a876))))))
% 160.93/160.66 [9708]~P5(x97085)+~P108(x97085)+P1(f334(f334(f336(x97081),f493(x97082,x97083,x97084,x97081,x97085)),x97084))+~P1(f334(f334(f249(x97085),f334(f334(f42(x97081,x97085),x97084),x97083)),x97082))
% 160.93/160.66 [9740]~P79(x97405)+~P84(x97405)+P1(f334(f334(f336(x97401),f719(x97402,x97403,x97404,x97401,x97405)),f334(f174(x97401),x97404)))+P1(f334(f334(f248(x97405),f334(f168(x97405),f334(f334(f156(x97401,x97405),x97403),x97404))),f334(f168(x97405),f334(f334(f156(x97401,x97405),x97402),x97404))))
% 160.93/160.66 [9855]~P5(x98551)+~P108(x98551)+P1(f334(f334(f249(x98551),f334(x98552,f493(x98553,x98552,x98554,x98555,x98551))),x98553))+~P1(f334(f334(f249(x98551),f334(f334(f42(x98555,x98551),x98554),x98552)),x98553))
% 160.93/160.66 [9996]~P79(x99961)+~P84(x99961)+~P1(f334(f334(f248(x99961),f334(x99963,f719(x99965,x99963,x99964,x99962,x99961))),f334(x99965,f719(x99965,x99963,x99964,x99962,x99961))))+P1(f334(f334(f248(x99961),f334(f168(x99961),f334(f334(f156(x99962,x99961),x99963),x99964))),f334(f168(x99961),f334(f334(f156(x99962,x99961),x99965),x99964))))
% 160.93/160.66 [8661]~P68(x86611)+~P1(f334(f61(x86614),x86615))+~P1(f334(f334(f336(x86614),x86613),x86615))+E(f334(f334(f80(x86611),f334(x86612,x86613)),f334(f334(f6(x86614,x86611),x86612),f334(f334(f22(f888(x86614,a876)),x86615),f334(f334(f312(x86614),x86613),f196(f888(x86614,a876)))))),f334(f334(f6(x86614,x86611),x86612),x86615))
% 160.93/160.66 [8662]~P74(x86621)+~P1(f334(f61(x86624),x86625))+~P1(f334(f334(f336(x86624),x86623),x86625))+E(f334(f334(f81(x86621),f334(x86622,x86623)),f334(f334(f9(x86624,x86621),x86622),f334(f334(f22(f888(x86624,a876)),x86625),f334(f334(f312(x86624),x86623),f196(f888(x86624,a876)))))),f334(f334(f9(x86624,x86621),x86622),x86625))
% 160.93/160.66 [8717]~P20(x87171,x87174,x87175)+~P1(f334(f61(x87171),x87172))+E(f334(f334(f22(f888(x87171,a876)),x87172),f334(f334(f312(x87171),x87173),f196(f888(x87171,a876)))),f196(f888(x87171,a876)))+E(f334(f334(x87174,x87173),f334(x87175,f334(f334(f22(f888(x87171,a876)),x87172),f334(f334(f312(x87171),x87173),f196(f888(x87171,a876)))))),f334(x87175,f334(f334(f312(x87171),x87173),x87172)))
% 160.93/160.66 [9093]~P68(x90931)+~P1(f334(f61(x90932),x90935))+~P1(f334(f61(x90932),x90934))+E(f334(f334(f80(x90931),f334(f334(f6(x90932,x90931),x90933),f334(f334(f114(f888(x90932,a876)),x90934),x90935))),f334(f334(f6(x90932,x90931),x90933),f334(f334(f105(f888(x90932,a876)),x90934),x90935))),f334(f334(f80(x90931),f334(f334(f6(x90932,x90931),x90933),x90934)),f334(f334(f6(x90932,x90931),x90933),x90935)))
% 160.93/160.66 [9095]~P74(x90951)+~P1(f334(f61(x90952),x90955))+~P1(f334(f61(x90952),x90954))+E(f334(f334(f81(x90951),f334(f334(f9(x90952,x90951),x90953),f334(f334(f114(f888(x90952,a876)),x90954),x90955))),f334(f334(f9(x90952,x90951),x90953),f334(f334(f105(f888(x90952,a876)),x90954),x90955))),f334(f334(f81(x90951),f334(f334(f9(x90952,x90951),x90953),x90954)),f334(f334(f9(x90952,x90951),x90953),x90955)))
% 160.93/160.66 [9237]~P67(x92371)+~P1(f334(f61(x92372),x92375))+~P1(f334(f61(x92372),x92374))+E(f334(f334(f22(x92371),f334(f334(f80(x92371),f334(f334(f6(x92372,x92371),x92373),x92374)),f334(f334(f6(x92372,x92371),x92373),x92375))),f334(f334(f6(x92372,x92371),x92373),f334(f334(f105(f888(x92372,a876)),x92374),x92375))),f334(f334(f6(x92372,x92371),x92373),f334(f334(f114(f888(x92372,a876)),x92374),x92375)))
% 160.93/160.66 [9439]~P27(x94391,x94392,x94393,x94395)+~P27(x94391,x94392,x94393,x94394)+P27(x94391,x94392,x94393,f334(f334(f114(f888(x94391,a876)),x94394),x94395))+~E(f334(f334(f105(f888(x94392,a876)),f334(f313(x94391,x94392,x94393),f334(f334(f22(f888(x94391,a876)),x94394),x94395))),f334(f313(x94391,x94392,x94393),f334(f334(f22(f888(x94391,a876)),x94395),x94394))),f196(f888(x94392,a876)))
% 160.93/160.66 [9557]E(x95571,f2(a1))+~P1(f334(f334(f249(a1),f2(a1)),x95573))+~P1(f334(f48(x95572,x95571),f334(f334(f269(a1,a1),x95574),x95575)))+P1(f334(f48(x95572,f334(f334(f81(a1),x95571),x95573)),f334(f334(f269(a1,a1),f334(f334(f38(a1),x95574),x95573)),f334(f334(f80(a1),f334(f334(f81(a1),x95571),f44(a1,x95574,x95573))),x95575))))
% 160.93/160.66 [9565]~P1(f334(f334(f249(a881),f2(a881)),x95653))+~P1(f334(f334(f249(a881),f2(a881)),x95652))+~P1(f334(f47(x95651,x95652),f334(f334(f269(a881,a881),x95654),x95655)))+P1(f334(f47(x95651,f334(f334(f81(a881),x95652),x95653)),f334(f334(f269(a881,a881),f334(f334(f38(a881),x95654),x95653)),f334(f334(f80(a881),f334(f334(f81(a881),x95652),f44(a881,x95654,x95653))),x95655))))
% 160.93/160.66 [9614]~P74(x96141)+~P1(f334(f61(x96142),x96145))+~P1(f334(f61(x96142),x96144))+E(f334(f334(f81(x96141),f334(f334(f334(f65(x96141,x96142,f81(x96141)),x96143),f78(x96141)),f334(f334(f114(f888(x96142,a876)),x96144),x96145))),f334(f334(f334(f65(x96141,x96142,f81(x96141)),x96143),f78(x96141)),f334(f334(f105(f888(x96142,a876)),x96144),x96145))),f334(f334(f81(x96141),f334(f334(f334(f65(x96141,x96142,f81(x96141)),x96143),f78(x96141)),x96144)),f334(f334(f334(f65(x96141,x96142,f81(x96141)),x96143),f78(x96141)),x96145)))
% 160.93/160.66 [9616]~E(f334(f334(f177(x96161),x96165),x96162),f334(f334(f177(x96161),x96165),x96163))+P1(f334(f334(f336(f887(f882(x96161),f882(x96161))),f334(f334(f269(f882(x96161),f882(x96161)),x96162),x96163)),f149(x96161,x96164)))+~P1(f334(f334(f249(a881),x96165),f334(f334(f246(a881),f334(f197(f882(x96161)),x96162)),f334(f197(f882(x96161)),x96163))))+~P1(f334(f334(f336(f887(x96161,x96161)),f334(f334(f269(x96161,x96161),f334(f334(f167(x96161),x96162),x96165)),f334(f334(f167(x96161),x96163),x96165))),x96164))
% 160.93/160.66 [9728]~P142(x97285)+~P84(x97285)+P1(f334(f334(f336(x97281),f407(x97282,x97283,x97284,x97281,x97285)),x97284))+P1(f334(f334(f248(x97285),f334(f334(f6(x97281,x97285),x97283),x97284)),f334(f334(f81(x97285),f334(f104(x97285),f334(f37(x97281),x97284))),x97282)))
% 160.93/160.66 [9924]~P142(x99241)+~P84(x99241)+~P1(f334(f334(f248(x99241),f334(x99243,f407(x99245,x99243,x99244,x99242,x99241))),x99245))+P1(f334(f334(f248(x99241),f334(f334(f6(x99242,x99241),x99243),x99244)),f334(f334(f81(x99241),f334(f104(x99241),f334(f37(x99242),x99244))),x99245)))
% 160.93/160.66 [8689]E(f334(f334(f136(x86891),x86892),x86893),f334(f334(f136(x86891),x86894),x86895))+~E(f334(f334(f177(x86891),f334(f197(f882(x86891)),x86892)),x86894),x86892)+~E(f334(f334(f136(x86891),f334(f334(f140(x86891),f334(f197(f882(x86891)),x86892)),x86894)),x86895),x86893)+P1(f334(f334(f248(a881),f334(f197(f882(x86891)),x86894)),f334(f197(f882(x86891)),x86892)))
% 160.93/160.66 [8809]E(f334(f334(f136(x88091),x88092),x88093),f334(f334(f136(x88091),x88094),x88095))+~E(f334(f334(f177(x88091),f334(f197(f882(x88091)),x88092)),x88094),x88092)+~E(x88093,f334(f334(f136(x88091),f334(f334(f140(x88091),f334(f197(f882(x88091)),x88092)),x88094)),x88095))+~P1(f334(f334(f248(a881),f334(f197(f882(x88091)),x88092)),f334(f197(f882(x88091)),x88094)))
% 160.93/160.66 [10059]~P1(f334(x100595,x100594))+~P1(f334(f61(x100592),f334(f254(x100592),x100595)))+P1(f334(f61(x100591),f334(f254(x100591),f334(f334(f7(x100591,x100592,a876),x100593),x100594))))+~P1(f334(f61(x100591),f334(f254(x100591),f334(f334(f8(f888(x100592,a876),a876,x100591),f87(x100592)),f334(f334(f8(f888(x100592,a876),f888(x100592,a876),x100591),f334(f18(x100592,a876,a876),f334(f334(f8(a876,f888(a876,a876),x100592),a332),x100595))),x100593)))))
% 160.93/160.66 [8473]~P21(x84735,x84731,x84736,x84732)+E(f334(f73(x84731,x84731,x84731,f334(x84732,x84733)),f334(x84732,x84734)),f334(f73(x84731,x84731,x84731,f334(x84732,x84734)),f334(x84732,x84733)))+~P1(f334(f61(x84735),x84734))+~P1(f334(f61(x84735),x84733))
% 160.93/160.66 [7859]~P27(x78591,x78592,x78594,x78593)+~E(f334(x78594,x78596),x78595)+E(f334(f77(x78591,x78592,x78593,x78594),x78595),x78596)+~P1(f334(f334(f336(x78591),x78596),x78593))
% 160.93/160.66 [8051]~P22(x80516,x80511,x80514,x80512)+E(f334(f73(x80511,x80511,x80511,f334(x80512,x80513)),f334(x80514,x80515)),f334(x80512,x80513))+~P1(f334(f61(x80516),x80513))+~P1(f334(f334(f336(x80516),x80515),x80513))
% 160.93/160.66 [9284]~P21(x92843,x92841,x92846,x92842)+E(f334(f73(x92841,x92841,x92841,f334(x92842,f334(f334(f22(f888(x92843,a876)),x92844),f334(f334(f312(x92843),x92845),f196(f888(x92843,a876)))))),f334(x92846,x92845)),f334(x92842,x92844))+~P1(f334(f61(x92843),x92844))+~P1(f334(f334(f336(x92843),x92845),x92844))
% 160.93/160.66 [6941]~P59(x69411)+~E(f44(x69411,x69413,x69414),f44(x69411,x69416,x69414))+~E(f44(x69411,x69412,x69414),f44(x69411,x69415,x69414))+E(f44(x69411,f334(f334(f22(x69411),x69412),x69413),x69414),f44(x69411,f334(f334(f22(x69411),x69415),x69416),x69414))
% 160.93/160.66 [6942]~P58(x69421)+~E(f44(x69421,x69423,x69424),f44(x69421,x69426,x69424))+~E(f44(x69421,x69422,x69424),f44(x69421,x69425,x69424))+E(f44(x69421,f334(f334(f80(x69421),x69422),x69423),x69424),f44(x69421,f334(f334(f80(x69421),x69425),x69426),x69424))
% 160.93/160.66 [6943]~P58(x69431)+~E(f44(x69431,x69433,x69434),f44(x69431,x69436,x69434))+~E(f44(x69431,x69432,x69434),f44(x69431,x69435,x69434))+E(f44(x69431,f334(f334(f81(x69431),x69432),x69433),x69434),f44(x69431,f334(f334(f81(x69431),x69435),x69436),x69434))
% 160.93/160.66 [7753]~P18(x77531,x77532,x77533)+~P1(f334(f61(x77531),x77536))+E(f334(f334(f64(x77531,x77532,x77533),x77534),f334(f334(f312(x77531),x77535),x77536)),f334(f334(f64(x77531,x77532,x77533),f334(f334(x77533,x77535),x77534)),x77536))+P1(f334(f334(f336(x77531),x77535),x77536))
% 160.93/160.66 [7817]~P5(x78171)+P1(f334(f334(f248(x78171),x78172),f334(x78173,x78174)))+~P1(f334(f334(f336(x78175),x78174),x78176))+~P1(f334(f334(f248(x78171),x78172),f334(f334(f42(x78175,x78171),x78176),x78173)))
% 160.93/160.66 [7975]~P18(x79751,x79752,x79753)+~P1(f334(f61(x79751),x79756))+E(f334(f334(f64(x79751,x79752,x79753),x79754),f334(f334(f312(x79751),x79755),x79756)),f334(f334(x79753,x79755),f334(f334(f64(x79751,x79752,x79753),x79754),x79756)))+P1(f334(f334(f336(x79751),x79755),x79756))
% 160.93/160.66 [8067]~P108(x80673)+~P1(f334(x80672,x80675))+~P16(x80673,f334(f334(f156(x80671,x80673),x80674),x80676))+E(f334(f138(x80671,x80672),f334(f334(f150(x80671,x80673,x80674),x80675),x80676)),f334(f334(f150(x80671,x80673,x80674),x80675),f334(f138(x80671,x80672),x80676)))
% 160.93/160.66 [8090]E(x80901,x80902)+E(x80903,f2(a1))+~P1(f334(f48(x80904,x80903),f334(f334(f269(a1,a1),x80905),x80902)))+~P1(f334(f48(x80904,x80903),f334(f334(f269(a1,a1),x80906),x80901)))
% 160.93/160.66 [8091]E(x80911,x80912)+E(x80913,f2(a1))+~P1(f334(f48(x80914,x80913),f334(f334(f269(a1,a1),x80912),x80915)))+~P1(f334(f48(x80914,x80913),f334(f334(f269(a1,a1),x80911),x80916)))
% 160.93/160.66 [8112]~P21(x81122,x81125,x81126,x81121)+~P1(f334(f61(x81122),x81124))+E(f334(x81121,f334(f334(f312(x81122),x81123),x81124)),f334(f73(x81125,x81125,x81125,f334(x81121,x81124)),f334(x81126,x81123)))+P1(f334(f334(f336(x81122),x81123),x81124))
% 160.93/160.66 [8350]~P22(x83505,x83501,x83506,x83502)+E(f334(f73(x83501,x83501,x83501,f334(x83502,x83503)),f334(x83502,x83504)),f334(x83502,x83503))+~P1(f334(f61(x83505),x83503))+~P1(f334(f334(f248(f888(x83505,a876)),x83504),x83503))
% 160.93/160.66 [9485]~P27(x94851,x94852,x94854,x94853)+~P1(f334(f334(f336(x94852),x94855),f334(f313(x94851,x94852,x94854),x94853)))+P1(f334(f334(f336(x94851),f334(f77(x94851,x94852,x94853,x94854),x94855)),x94856))+~P1(f334(f334(f248(f888(x94851,a876)),x94853),x94856))
% 160.93/160.66 [9869]~P68(x98692)+~E(f830(x98691,x98693,x98695,x98696,x98694,x98692),f831(x98691,x98693,x98695,x98696,x98694,x98692))+~P1(f334(f61(x98694),x98696))+E(f334(f334(f6(x98691,x98692),x98693),f334(f313(x98694,x98691,x98695),x98696)),f334(f334(f6(x98694,x98692),f334(f73(x98691,x98692,x98694,x98693),x98695)),x98696))
% 160.93/160.66 [9906]~P68(x99066)+E(f334(x99061,f830(x99062,x99063,x99061,x99064,x99065,x99066)),f334(x99061,f831(x99062,x99063,x99061,x99064,x99065,x99066)))+E(f334(f334(f6(x99062,x99066),x99063),f334(f313(x99065,x99062,x99061),x99064)),f334(f334(f6(x99065,x99066),f334(f73(x99062,x99066,x99065,x99063),x99061)),x99064))+~P1(f334(f61(x99065),x99064))
% 160.93/160.66 [9946]~P68(x99462)+~E(f334(x99463,f334(x99465,f831(x99461,x99463,x99465,x99466,x99464,x99462))),f2(x99462))+~P1(f334(f61(x99464),x99466))+E(f334(f334(f6(x99461,x99462),x99463),f334(f313(x99464,x99461,x99465),x99466)),f334(f334(f6(x99464,x99462),f334(f73(x99461,x99462,x99464,x99463),x99465)),x99466))
% 160.93/160.66 [10004]~P68(x100042)+~P1(f334(f61(x100044),x100046))+E(f334(f334(f6(x100041,x100042),x100043),f334(f313(x100044,x100041,x100045),x100046)),f334(f334(f6(x100044,x100042),f334(f73(x100041,x100042,x100044,x100043),x100045)),x100046))+P1(f334(f334(f336(x100044),f831(x100041,x100043,x100045,x100046,x100044,x100042)),x100046))
% 160.93/160.66 [10005]~P68(x100052)+~P1(f334(f61(x100054),x100056))+E(f334(f334(f6(x100051,x100052),x100053),f334(f313(x100054,x100051,x100055),x100056)),f334(f334(f6(x100054,x100052),f334(f73(x100051,x100052,x100054,x100053),x100055)),x100056))+P1(f334(f334(f336(x100054),f830(x100051,x100053,x100055,x100056,x100054,x100052)),x100056))
% 160.93/160.66 [10118]~P74(x101181)+~P1(f334(f61(x101182),x101186))+E(f334(f334(f334(f65(x101181,x101182,f81(x101181)),f334(f334(f18(x101182,f888(x101183,a876),x101181),f334(f334(f7(x101182,x101181,f888(f888(x101183,a876),x101181)),f334(f334(f8(f888(x101183,x101181),f888(x101181,f888(f888(x101183,a876),x101181)),x101182),f65(x101181,x101183,f81(x101181))),x101184)),f78(x101181))),x101185)),f78(x101181)),x101186),f334(f334(f334(f65(x101181,f887(x101182,x101183),f81(x101181)),f334(f273(x101182,x101183,x101181),x101184)),f78(x101181)),f334(f334(f271(x101182,x101183),x101186),x101185)))+P1(f334(f334(f336(x101182),f578(x101184,x101185,x101183,x101186,x101182,x101181)),x101186))
% 160.93/160.66 [10136]~P74(x101361)+~P1(f334(f61(x101362),x101366))+E(f334(f334(f334(f65(x101361,x101362,f81(x101361)),f334(f334(f18(x101362,f888(x101363,a876),x101361),f334(f334(f7(x101362,x101361,f888(f888(x101363,a876),x101361)),f334(f334(f8(f888(x101363,x101361),f888(x101361,f888(f888(x101363,a876),x101361)),x101362),f65(x101361,x101363,f81(x101361))),x101364)),f78(x101361))),x101365)),f78(x101361)),x101366),f334(f334(f334(f65(x101361,f887(x101362,x101363),f81(x101361)),f334(f273(x101362,x101363,x101361),x101364)),f78(x101361)),f334(f334(f271(x101362,x101363),x101366),x101365)))+~P1(f334(f61(x101363),f334(x101365,f578(x101364,x101365,x101363,x101366,x101362,x101361))))
% 160.93/160.66 [8262]~P22(x82622,x82625,x82626,x82621)+~P1(f334(f61(x82622),x82624))+~P1(f334(f61(x82622),x82623))+E(f334(x82621,f334(f334(f114(f888(x82622,a876)),x82623),x82624)),f334(f73(x82625,x82625,x82625,f334(x82621,x82623)),f334(x82621,x82624)))
% 160.93/160.66 [8474]~P5(x84741)+P1(f334(f334(f248(x84741),f334(x84742,x84743)),x84744))+~P1(f334(f334(f336(x84745),x84743),x84746))+~P1(f334(f334(f248(x84741),f334(f334(f41(x84745,x84741),x84746),x84742)),x84744))
% 160.93/160.66 [8888]~P27(x88882,x88881,x88883,x88886)+E(f334(f334(f22(f888(x88881,a876)),f334(f313(x88882,x88881,x88883),x88884)),f334(f313(x88882,x88881,x88883),x88885)),f334(f313(x88882,x88881,x88883),f334(f334(f22(f888(x88882,a876)),x88884),x88885)))+~P1(f334(f334(f248(f888(x88882,a876)),x88885),x88886))+~P1(f334(f334(f248(f888(x88882,a876)),x88884),x88886))
% 160.93/160.66 [8889]~P27(x88892,x88891,x88893,x88896)+E(f334(f334(f105(f888(x88891,a876)),f334(f313(x88892,x88891,x88893),x88894)),f334(f313(x88892,x88891,x88893),x88895)),f334(f313(x88892,x88891,x88893),f334(f334(f105(f888(x88892,a876)),x88894),x88895)))+~P1(f334(f334(f248(f888(x88892,a876)),x88895),x88896))+~P1(f334(f334(f248(f888(x88892,a876)),x88894),x88896))
% 160.93/160.66 [8926]~P1(f334(x89261,x89263))+~P1(f334(f334(f334(f334(a204,x89262),x89263),x89264),x89266))+~P1(f334(f334(f334(f334(a204,f32(x89261,x89262)),x89266),x89264),x89265))+P1(f334(f334(f334(f334(a204,f32(x89261,x89262)),x89263),x89264),x89265))
% 160.93/160.66 [9159]E(x91591,x91592)+~P52(x91593,x91594,x91595)+~P1(f334(f334(f336(f887(x91593,x91594)),f334(f334(f269(x91593,x91594),x91596),x91592)),x91595))+~P1(f334(f334(f336(f887(x91593,x91594)),f334(f334(f269(x91593,x91594),x91596),x91591)),x91595))
% 160.93/160.66 [9941]~P70(x99411)+~E(f334(x99413,f509(x99414,x99416,x99413,x99415,x99412,x99411)),f334(x99416,f509(x99414,x99416,x99413,x99415,x99412,x99411)))+~P1(f334(f61(x99412),x99415))+E(f334(f334(f334(f65(x99411,x99412,f81(x99411)),x99413),x99414),x99415),f334(f334(f334(f65(x99411,x99412,f81(x99411)),x99416),x99414),x99415))
% 160.93/160.66 [10002]~P70(x100021)+~P1(f334(f61(x100022),x100025))+E(f334(f334(f334(f65(x100021,x100022,f81(x100021)),x100023),x100024),x100025),f334(f334(f334(f65(x100021,x100022,f81(x100021)),x100026),x100024),x100025))+P1(f334(f334(f336(x100022),f509(x100024,x100023,x100026,x100025,x100022,x100021)),x100025))
% 160.93/160.66 [8702]~P70(x87021)+~P1(f334(f61(x87022),x87026))+P1(f334(f334(f336(x87022),x87025),x87026))+E(f334(f334(f334(f65(x87021,x87022,f81(x87021)),x87023),x87024),f334(f334(f312(x87022),x87025),x87026)),f334(f334(f81(x87021),f334(x87023,x87025)),f334(f334(f334(f65(x87021,x87022,f81(x87021)),x87023),x87024),x87026)))
% 160.93/160.66 [8748]~P8(x87481,x87486,x87483)+~P14(x87481,f888(x87482,a876),x87483,x87485)+~P1(f334(f334(f336(x87481),x87484),x87486))+E(f334(f334(f41(x87481,f888(x87482,a876)),f334(f288(x87481,x87481,x87483),f334(f334(f312(x87481),x87484),f196(f888(x87481,a876))))),x87485),f334(x87485,x87484))
% 160.93/160.66 [8865]~P18(x88653,x88654,x88651)+~P1(f334(f61(x88653),x88656))+~P1(f334(f334(f336(x88653),x88652),x88656))+E(f334(f334(x88651,x88652),f334(f334(f64(x88653,x88654,x88651),x88655),f334(f334(f22(f888(x88653,a876)),x88656),f334(f334(f312(x88653),x88652),f196(f888(x88653,a876)))))),f334(f334(f64(x88653,x88654,x88651),x88655),x88656))
% 160.93/160.66 [9172]~P21(x91723,x91721,x91726,x91722)+~P1(f334(f61(x91723),x91725))+~P1(f334(f61(x91723),x91724))+E(f334(f73(x91721,x91721,x91721,f334(x91722,f334(f334(f114(f888(x91723,a876)),x91724),x91725))),f334(x91722,f334(f334(f105(f888(x91723,a876)),x91724),x91725))),f334(f73(x91721,x91721,x91721,f334(x91722,x91724)),f334(x91722,x91725)))
% 160.93/160.66 [9507]~E(x95073,f334(f334(f161(x95071,x95072),x95075),x95076))+P1(f334(f334(f336(f887(f882(x95071),f882(x95071))),f334(f334(f269(f882(x95071),f882(x95071)),x95072),x95073)),f159(x95071,x95074)))+~P1(f334(f334(f249(a881),x95075),f334(f197(f882(x95071)),x95072)))+~P1(f334(f334(f336(f887(x95071,x95071)),f334(f334(f269(x95071,x95071),f334(f334(f167(x95071),x95072),x95075)),x95076)),x95074))
% 160.93/160.66 [10015]~P68(x100152)+~P1(f334(f61(x100151),x100156))+P1(f334(f334(f336(x100151),f576(x100154,x100155,x100153,x100156,x100151,x100152)),x100156))+E(f334(f334(f6(x100151,x100152),f334(f334(f18(x100151,f888(x100153,a876),x100152),f334(f334(f8(f888(x100153,x100152),f888(f888(x100153,a876),x100152),x100151),f6(x100153,x100152)),x100154)),x100155)),x100156),f334(f334(f6(f887(x100151,x100153),x100152),f334(f273(x100151,x100153,x100152),x100154)),f334(f334(f271(x100151,x100153),x100156),x100155)))
% 160.93/160.66 [10016]~P74(x100162)+~P1(f334(f61(x100161),x100166))+P1(f334(f334(f336(x100161),f577(x100164,x100165,x100163,x100166,x100161,x100162)),x100166))+E(f334(f334(f9(x100161,x100162),f334(f334(f18(x100161,f888(x100163,a876),x100162),f334(f334(f8(f888(x100163,x100162),f888(f888(x100163,a876),x100162),x100161),f9(x100163,x100162)),x100164)),x100165)),x100166),f334(f334(f9(f887(x100161,x100163),x100162),f334(f273(x100161,x100163,x100162),x100164)),f334(f334(f271(x100161,x100163),x100166),x100165)))
% 160.93/160.66 [10056]~P68(x100562)+~P1(f334(f61(x100561),x100566))+~P1(f334(f61(x100563),f334(x100565,f576(x100564,x100565,x100563,x100566,x100561,x100562))))+E(f334(f334(f6(x100561,x100562),f334(f334(f18(x100561,f888(x100563,a876),x100562),f334(f334(f8(f888(x100563,x100562),f888(f888(x100563,a876),x100562),x100561),f6(x100563,x100562)),x100564)),x100565)),x100566),f334(f334(f6(f887(x100561,x100563),x100562),f334(f273(x100561,x100563,x100562),x100564)),f334(f334(f271(x100561,x100563),x100566),x100565)))
% 160.93/160.66 [10057]~P74(x100572)+~P1(f334(f61(x100571),x100576))+~P1(f334(f61(x100573),f334(x100575,f577(x100574,x100575,x100573,x100576,x100571,x100572))))+E(f334(f334(f9(x100571,x100572),f334(f334(f18(x100571,f888(x100573,a876),x100572),f334(f334(f8(f888(x100573,x100572),f888(f888(x100573,a876),x100572),x100571),f9(x100573,x100572)),x100574)),x100575)),x100576),f334(f334(f9(f887(x100571,x100573),x100572),f334(f273(x100571,x100573,x100572),x100574)),f334(f334(f271(x100571,x100573),x100576),x100575)))
% 160.93/160.66 [10038]~P74(x100382)+~P1(f334(f61(x100381),x100386))+P1(f334(f334(f336(x100381),x100383),x100386))+E(f334(f334(f9(x100381,x100382),f334(f334(f7(x100381,x100382,x100382),f334(f334(f18(x100381,x100382,f888(x100382,x100382)),f334(f334(f8(a876,f888(x100382,f888(x100382,x100382)),x100381),f100(x100382)),f334(f334(f7(x100381,x100381,a876),a331),x100383))),x100384)),x100385)),x100386),f334(f334(f259(x100382),x100385),f334(f37(x100381),x100386)))
% 160.93/160.66 [10043]~P74(x100432)+~P1(f334(f61(x100431),x100436))+~P1(f334(f334(f336(x100431),x100433),x100436))+E(f334(f334(f9(x100431,x100432),f334(f334(f7(x100431,x100432,x100432),f334(f334(f18(x100431,x100432,f888(x100432,x100432)),f334(f334(f8(a876,f888(x100432,f888(x100432,x100432)),x100431),f100(x100432)),f334(f334(f7(x100431,x100431,a876),a331),x100433))),x100434)),x100435)),x100436),f334(f334(f81(x100432),f334(x100434,x100433)),f334(f334(f259(x100432),x100435),f334(f334(f22(a881),f334(f37(x100431),x100436)),f78(a881)))))
% 160.93/160.66 [10111]~P1(f334(f61(x101111),x101115))+~P1(f334(f61(x101112),x101113))+P1(f334(f334(f336(x101112),f450(x101116,x101114,x101113,x101112,x101115,x101111)),x101113))+E(f334(f334(f6(x101111,a881),f334(f334(f8(f888(x101112,a876),a881,x101111),f37(x101112)),f334(f334(f8(f888(x101112,a876),f888(x101112,a876),x101111),f254(x101112)),f334(f334(f8(f888(x101112,a876),f888(x101112,a876),x101111),f334(f18(x101112,a876,a876),f334(f334(f8(a876,f888(a876,a876),x101112),a332),f334(f334(f7(x101112,f888(x101112,a876),a876),f336(x101112)),x101113)))),x101114)))),x101115),f334(f334(f81(a881),x101116),f334(f37(x101112),x101113)))
% 160.93/160.66 [10112]~P1(f334(f61(x101121),x101125))+~P1(f334(f61(x101122),x101123))+P1(f334(f334(f336(x101122),f460(x101126,x101124,x101123,x101122,x101125,x101121)),x101123))+E(f334(f334(f6(x101121,a881),f334(f334(f8(f888(x101122,a876),a881,x101121),f37(x101122)),f334(f334(f8(f888(x101122,a876),f888(x101122,a876),x101121),f254(x101122)),f334(f334(f8(f888(x101122,a876),f888(x101122,a876),x101121),f334(f18(x101122,a876,a876),f334(f334(f8(a876,f888(a876,a876),x101122),a332),f334(f334(f7(x101122,f888(x101122,a876),a876),f336(x101122)),x101123)))),x101124)))),x101125),f334(f334(f6(x101122,a881),x101126),x101123))
% 160.93/160.66 [10142]~P1(f334(f61(x101422),x101423))+~P1(f334(f61(x101421),x101425))+~E(f334(f37(x101421),f334(f254(x101421),f334(f334(f18(x101421,a876,a876),f334(f334(f8(a876,f888(a876,a876),x101421),a332),f334(f334(f7(x101421,f888(x101421,a876),a876),f336(x101421)),x101425))),f334(f334(f7(x101421,x101422,a876),x101424),f450(x101426,x101424,x101423,x101422,x101425,x101421))))),x101426)+E(f334(f334(f6(x101421,a881),f334(f334(f8(f888(x101422,a876),a881,x101421),f37(x101422)),f334(f334(f8(f888(x101422,a876),f888(x101422,a876),x101421),f254(x101422)),f334(f334(f8(f888(x101422,a876),f888(x101422,a876),x101421),f334(f18(x101422,a876,a876),f334(f334(f8(a876,f888(a876,a876),x101422),a332),f334(f334(f7(x101422,f888(x101422,a876),a876),f336(x101422)),x101423)))),x101424)))),x101425),f334(f334(f81(a881),x101426),f334(f37(x101422),x101423)))
% 160.93/160.66 [10144]~P1(f334(f61(x101442),x101443))+~P1(f334(f61(x101441),x101445))+~E(f334(f37(x101441),f334(f254(x101441),f334(f334(f18(x101441,a876,a876),f334(f334(f8(a876,f888(a876,a876),x101441),a332),f334(f334(f7(x101441,f888(x101441,a876),a876),f336(x101441)),x101445))),f334(f334(f7(x101441,x101442,a876),x101444),f460(x101446,x101444,x101443,x101442,x101445,x101441))))),f334(x101446,f460(x101446,x101444,x101443,x101442,x101445,x101441)))+E(f334(f334(f6(x101441,a881),f334(f334(f8(f888(x101442,a876),a881,x101441),f37(x101442)),f334(f334(f8(f888(x101442,a876),f888(x101442,a876),x101441),f254(x101442)),f334(f334(f8(f888(x101442,a876),f888(x101442,a876),x101441),f334(f18(x101442,a876,a876),f334(f334(f8(a876,f888(a876,a876),x101442),a332),f334(f334(f7(x101442,f888(x101442,a876),a876),f336(x101442)),x101443)))),x101444)))),x101445),f334(f334(f6(x101442,a881),x101446),x101443))
% 160.93/160.66 [9795]E(x97951,x97952)+~P18(x97953,x97954,x97955)+~P1(f334(f66(x97953,x97954,x97955,x97956,x97957),x97952))+~P1(f334(f66(x97953,x97954,x97955,x97956,x97957),x97951))
% 160.93/160.66 [9585]P1(f334(x95851,x95852))+~P1(f334(f334(f336(x95857),x95852),f334(x95856,x95854)))+~P1(f334(x95851,f835(x95851,x95856,x95855,x95853,x95857)))+~P1(f334(f334(f336(x95853),x95854),x95855))
% 160.93/160.66 [10030]~P18(x100307,x100306,x100301)+E(f334(f334(x100301,x100302),f859(x100302,x100303,x100304,x100305,x100301,x100306,x100307)),x100303)+~P1(f334(f66(x100307,x100306,x100301,x100305,x100304),x100303))+~P1(f334(f334(f336(x100307),x100302),x100304))
% 160.93/160.66 [10096]~P18(x100961,x100962,x100963)+~P1(f334(f66(x100961,x100962,x100963,x100964,x100965),x100967))+P1(f334(f66(x100961,x100962,x100963,x100964,f334(f334(f22(f888(x100961,a876)),x100965),f334(f334(f312(x100961),x100966),f196(f888(x100961,a876))))),f859(x100966,x100967,x100965,x100964,x100963,x100962,x100961)))+~P1(f334(f334(f336(x100961),x100966),x100965))
% 160.93/160.66 [9481]~P70(x94811)+~P27(x94815,x94812,x94816,x94817)+~P1(f334(f61(x94815),x94817))+E(f334(f334(f334(f65(x94811,x94812,f81(x94811)),x94813),x94814),f334(f313(x94815,x94812,x94816),x94817)),f334(f334(f334(f65(x94811,x94815,f81(x94811)),f334(f73(x94812,x94811,x94815,x94813),x94816)),x94814),x94817))
% 160.93/160.66 [9609]~E(f334(f334(f312(x96091),x96095),x96096),f334(f334(f312(x96091),x96092),x96093))+~P1(f334(f66(x96091,x96091,x96094,x96092,x96093),x96097))+P1(f334(f334(f336(x96091),x96092),x96093))+P1(f334(f62(x96091,x96094,f334(f334(f312(x96091),x96095),x96096)),x96097))
% 160.93/160.66 [9695]P1(f334(x96951,x96952))+~P1(f334(f334(f336(x96953),x96952),f334(x96954,x96957)))+~P1(f334(f334(f336(x96956),x96957),x96955))+P1(f334(f334(f336(x96953),f835(x96951,x96954,x96955,x96956,x96953)),f334(f334(f41(x96956,f888(x96953,a876)),x96955),x96954)))
% 160.93/160.66 [9709]~P27(x97092,x97091,x97095,x97094)+~P27(x97091,x97093,x97096,f334(f313(x97092,x97091,x97095),x97094))+E(f334(f334(f73(x97091,x97092,x97093,f77(x97092,x97091,x97094,x97095)),f77(x97091,x97093,f334(f313(x97092,x97091,x97095),x97094),x97096)),x97097),f334(f77(x97092,x97093,x97094,f334(f73(x97091,x97093,x97092,x97096),x97095)),x97097))+~P1(f334(f334(f336(x97093),x97097),f334(f313(x97091,x97093,x97096),f334(f313(x97092,x97091,x97095),x97094))))
% 160.93/160.66 [10031]~P18(x100317,x100316,x100311)+E(f334(f334(x100311,x100312),f860(x100313,x100314,x100312,x100315,x100311,x100316,x100317)),x100313)+P1(f334(f334(f336(x100317),x100312),x100314))+~P1(f334(f66(x100317,x100316,x100311,x100315,f334(f334(f312(x100317),x100312),x100314)),x100313))
% 160.93/160.66 [10095]~P18(x100951,x100954,x100955)+P1(f334(f66(x100951,x100954,x100955,x100956,x100953),f860(x100957,x100953,x100952,x100956,x100955,x100954,x100951)))+P1(f334(f334(f336(x100951),x100952),x100953))+~P1(f334(f66(x100951,x100954,x100955,x100956,f334(f334(f312(x100951),x100952),x100953)),x100957))
% 160.93/160.66 [9777]E(x97771,f2(a1))+~P1(f334(f48(x97773,x97771),f334(f334(f269(a1,a1),x97775),x97777)))+~P1(f334(f48(x97772,x97771),f334(f334(f269(a1,a1),x97774),x97776)))+P1(f334(f48(f334(f334(f80(a1),x97772),x97773),x97771),f334(f334(f269(a1,a1),f334(f334(f80(a1),f334(f334(f80(a1),x97774),x97775)),f334(f334(f38(a1),f334(f334(f80(a1),x97776),x97777)),x97771))),f44(a1,f334(f334(f80(a1),x97776),x97777),x97771))))
% 160.93/160.66 [9779]~P1(f334(f334(f249(a881),f2(a881)),x97793))+~P1(f334(f47(x97792,x97793),f334(f334(f269(a881,a881),x97795),x97797)))+~P1(f334(f47(x97791,x97793),f334(f334(f269(a881,a881),x97794),x97796)))+P1(f334(f47(f334(f334(f80(a881),x97791),x97792),x97793),f334(f334(f269(a881,a881),f334(f334(f80(a881),f334(f334(f80(a881),x97794),x97795)),f334(f334(f38(a881),f334(f334(f80(a881),x97796),x97797)),x97793))),f44(a881,f334(f334(f80(a881),x97796),x97797),x97793))))
% 160.93/160.66 [10141]~P68(x101412)+~P1(f334(f61(x101413),x101415))+~P1(f334(f61(x101411),x101417))+E(f334(f334(f6(x101411,x101412),f334(f334(f18(x101411,f888(x101413,a876),x101412),f334(f334(f8(f888(x101413,x101412),f888(f888(x101413,a876),x101412),x101411),f6(x101413,x101412)),x101414)),f334(f334(f8(f888(x101413,a876),f888(x101413,a876),x101411),f254(x101413)),f334(f334(f8(f888(x101413,a876),f888(x101413,a876),x101411),f334(f18(x101413,a876,a876),f334(f334(f8(a876,f888(a876,a876),x101413),a332),f334(f334(f7(x101413,f888(x101413,a876),a876),f336(x101413)),x101415)))),x101416)))),x101417),f334(f334(f6(x101413,x101412),f334(f334(f18(x101413,f888(x101411,a876),x101412),f334(f334(f8(f888(x101411,x101412),f888(f888(x101411,a876),x101412),x101413),f6(x101411,x101412)),f334(f7(x101411,x101413,x101412),x101414))),f334(f334(f8(f888(x101411,a876),f888(x101411,a876),x101413),f254(x101411)),f334(f334(f8(f888(x101411,a876),f888(x101411,a876),x101413),f334(f18(x101411,a876,a876),f334(f334(f8(a876,f888(a876,a876),x101411),a332),f334(f334(f7(x101411,f888(x101411,a876),a876),f336(x101411)),x101417)))),f334(f7(x101411,x101413,a876),x101416))))),x101415))
% 160.93/160.66 [9647]~P24(x96477,x96476,x96471,x96478,x96472,x96474)+E(f334(f334(x96471,f334(x96472,x96473)),f334(x96474,x96475)),f334(x96474,x96475))+~P1(f334(f61(x96476),x96475))+~P1(f334(f334(f336(x96476),x96473),x96475))
% 160.93/160.66 [9651]~P15(x96516,x96511,x96512,x96518,x96513,x96514)+~P8(x96516,x96517,x96518)+P14(x96511,x96512,x96513,f334(x96514,x96515))+~P1(f334(f334(f336(x96516),x96515),x96517))
% 160.93/160.66 [8068]~P29(x80688,x80687,f334(f334(f334(f92(x80688),x80684),x80686),x80681))+P1(f334(f334(x80681,x80682),x80683))+~P1(f334(f334(x80684,x80682),x80685))+~P1(f334(f334(f334(f334(a204,x80686),x80685),x80687),x80683))
% 160.93/160.66 [9266]~P21(x92667,x92661,x92668,x92663)+~P1(f334(f61(x92667),x92665))+~P1(f334(f61(x92667),x92664))+E(f334(f73(x92661,x92661,x92662,f334(x92663,x92664)),f334(f73(x92661,x92661,x92662,f334(x92663,x92665)),x92666)),f334(f73(x92661,x92661,x92662,f334(x92663,x92665)),f334(f73(x92661,x92661,x92662,f334(x92663,x92664)),x92666)))
% 160.93/160.66 [9274]~P36(x92741,x92742,x92743,x92744,x92747)+P36(x92741,x92742,x92743,f334(f334(f161(x92741,x92744),x92745),x92746),f334(f334(f161(x92742,x92747),x92745),x92748))+~P1(f334(f334(x92743,x92746),x92748))+~P1(f334(f334(f249(a881),x92745),f334(f197(f882(x92741)),x92744)))
% 160.93/160.66 [9275]~P36(x92751,x92752,x92753,x92754,x92757)+P36(x92751,x92752,x92753,f334(f334(f161(x92751,x92754),x92755),x92756),f334(f334(f161(x92752,x92757),x92755),x92758))+~P1(f334(f334(x92753,x92756),x92758))+~P1(f334(f334(f249(a881),x92755),f334(f197(f882(x92752)),x92757)))
% 160.93/160.66 [9354]~P27(x93542,x93542,x93545,x93546)+~P23(x93543,x93542,x93547,x93548,x93541)+~P1(f334(f61(x93542),x93546))+E(f334(f334(x93541,f334(f73(x93542,x93543,x93542,x93544),x93545)),x93546),f334(f334(x93541,x93544),f334(f313(x93542,x93542,x93545),x93546)))
% 160.93/160.66 [9649]~P25(x96497,x96492,x96495,x96498,x96496,x96491)+~P1(f334(f61(x96492),x96494))+E(f334(x96491,f334(f334(f312(x96492),x96493),x96494)),f334(f334(x96495,f334(x96496,x96493)),f334(x96491,x96494)))+P1(f334(f334(f336(x96492),x96493),x96494))
% 160.93/160.66 [9660]~P24(x96606,x96605,x96601,x96607,x96608,x96602)+E(f334(f334(x96601,f334(x96602,x96603)),f334(x96602,x96604)),f334(x96602,x96604))+~P1(f334(f61(x96605),x96604))+~P1(f334(f334(f248(f888(x96605,a876)),x96603),x96604))
% 160.93/160.66 [9252]P1(f334(f334(f336(f887(f882(x92521),f882(x92521))),f334(f334(f269(f882(x92521),f882(x92521)),x92522),x92523)),f159(x92521,x92524)))+~E(x92523,f334(f334(f136(x92521),x92525),f334(f334(f153(x92521),x92526),x92527)))+~E(x92522,f334(f334(f136(x92521),x92525),f334(f334(f153(x92521),x92528),x92527)))+~P1(f334(f334(f336(f887(x92521,x92521)),f334(f334(f269(x92521,x92521),x92528),x92526)),x92524))
% 160.93/160.66 [9654]~P24(x96546,x96542,x96545,x96547,x96548,x96541)+~P1(f334(f61(x96542),x96544))+~P1(f334(f61(x96542),x96543))+E(f334(x96541,f334(f334(f114(f888(x96542,a876)),x96543),x96544)),f334(f334(x96545,f334(x96541,x96543)),f334(x96541,x96544)))
% 160.93/160.66 [10179]~P27(x101794,x101792,x101795,x101798)+E(f334(f334(f42(x101791,f888(x101792,a876)),x101793),f334(f334(f8(f888(x101794,a876),f888(x101792,a876),x101791),f313(x101794,x101792,x101795)),x101796)),f334(f313(x101794,x101792,x101795),f334(f334(f42(x101791,f888(x101794,a876)),x101793),x101796)))+~P1(f334(f334(f336(x101791),x101797),x101793))+P1(f334(f334(f336(x101791),f557(x101797,x101796,x101793,x101791,x101798,x101795,x101792,x101794)),x101793))
% 160.93/160.66 [10203]~P27(x102034,x102032,x102035,x102037)+E(f334(f334(f42(x102031,f888(x102032,a876)),x102033),f334(f334(f8(f888(x102034,a876),f888(x102032,a876),x102031),f313(x102034,x102032,x102035)),x102036)),f334(f313(x102034,x102032,x102035),f334(f334(f42(x102031,f888(x102034,a876)),x102033),x102036)))+~P1(f334(f334(f336(x102031),x102038),x102033))+~P1(f334(f334(f248(f888(x102034,a876)),f334(x102036,f557(x102038,x102036,x102033,x102031,x102037,x102035,x102032,x102034))),x102037))
% 160.93/160.66 [9718]~P25(x97187,x97185,x97181,x97188,x97182,x97184)+~P1(f334(f61(x97185),x97186))+~P1(f334(f334(f336(x97185),x97183),x97186))+E(f334(f334(x97181,f334(x97182,x97183)),f334(x97184,f334(f334(f22(f888(x97185,a876)),x97186),f334(f334(f312(x97185),x97183),f196(f888(x97185,a876)))))),f334(x97184,x97186))
% 160.93/160.66 [9726]~P25(x97266,x97263,x97261,x97267,x97268,x97262)+~P1(f334(f61(x97263),x97265))+~P1(f334(f61(x97263),x97264))+E(f334(f334(x97261,f334(x97262,f334(f334(f114(f888(x97263,a876)),x97264),x97265))),f334(x97262,f334(f334(f105(f888(x97263,a876)),x97264),x97265))),f334(f334(x97261,f334(x97262,x97264)),f334(x97262,x97265)))
% 160.93/160.66 [9818]P44(x98181,x98182,x98183,x98184,x98185,f334(f334(x98183,x98186),x98187))+~P44(x98181,x98182,x98183,x98184,f334(f334(f22(f888(x98181,a876)),x98185),f334(f334(f312(x98181),x98188),f196(f888(x98181,a876)))),x98189)+~E(f334(f334(x98183,x98186),x98187),f334(f334(x98183,x98188),x98189))+~P1(f334(f334(f336(x98181),x98188),x98185))
% 160.93/160.66 [10218]P26(x102181,x102182,f334(f334(f312(f880(x102181)),f334(f334(f334(f92(x102181),f334(x102183,f584(x102184,x102185,x102186,x102187,x102183,x102182,x102181,x102188,x102189))),f334(x102187,f584(x102184,x102185,x102186,x102187,x102183,x102182,x102181,x102188,x102189))),f334(x102186,f584(x102184,x102185,x102186,x102187,x102183,x102182,x102181,x102188,x102189)))),f196(f888(f880(x102181),a876))))+~P1(f334(f61(x102189),x102188))+~P26(x102181,x102182,f334(f313(x102189,f880(x102181),f334(f334(f18(x102189,f888(x102181,f888(a877,a876)),f880(x102181)),f334(f334(f18(x102189,a878,f888(f888(x102181,f888(a877,a876)),f880(x102181))),f334(f334(f8(f888(x102181,f888(a877,a876)),f888(a878,f888(f888(x102181,f888(a877,a876)),f880(x102181))),x102189),f92(x102181)),x102183)),x102187)),x102186)),x102188))+P26(x102181,x102182,f334(f313(x102189,f880(x102181),f334(f334(f18(x102189,f888(x102181,f888(a877,a876)),f880(x102181)),f334(f334(f18(x102189,a878,f888(f888(x102181,f888(a877,a876)),f880(x102181))),f334(f334(f8(f888(x102181,f888(a877,a876)),f888(a878,f888(f888(x102181,f888(a877,a876)),f880(x102181))),x102189),f92(x102181)),x102185)),x102187)),x102184)),x102188))
% 160.93/160.66 [10219]~P26(x102191,x102192,f334(f334(f312(f880(x102191)),f334(f334(f334(f92(x102191),f334(x102194,f584(x102196,x102194,x102198,x102195,x102199,x102192,x102191,x102197,x102193))),f334(x102195,f584(x102196,x102194,x102198,x102195,x102199,x102192,x102191,x102197,x102193))),f334(x102196,f584(x102196,x102194,x102198,x102195,x102199,x102192,x102191,x102197,x102193)))),f196(f888(f880(x102191),a876))))+~P1(f334(f61(x102193),x102197))+~P26(x102191,x102192,f334(f313(x102193,f880(x102191),f334(f334(f18(x102193,f888(x102191,f888(a877,a876)),f880(x102191)),f334(f334(f18(x102193,a878,f888(f888(x102191,f888(a877,a876)),f880(x102191))),f334(f334(f8(f888(x102191,f888(a877,a876)),f888(a878,f888(f888(x102191,f888(a877,a876)),f880(x102191))),x102193),f92(x102191)),x102199)),x102195)),x102198)),x102197))+P26(x102191,x102192,f334(f313(x102193,f880(x102191),f334(f334(f18(x102193,f888(x102191,f888(a877,a876)),f880(x102191)),f334(f334(f18(x102193,a878,f888(f888(x102191,f888(a877,a876)),f880(x102191))),f334(f334(f8(f888(x102191,f888(a877,a876)),f888(a878,f888(f888(x102191,f888(a877,a876)),f880(x102191))),x102193),f92(x102191)),x102194)),x102195)),x102196)),x102197))
% 160.93/160.66 [9752]~P15(x97526,x97527,x97528,x97529,x975210,x97521)+E(f334(f334(x97521,x97522),x97523),f334(f334(x97521,x97524),x97525))+~P1(f334(f334(f336(f887(x97527,x97527)),f334(f334(f269(x97527,x97527),x97523),x97525)),x975210))+~P1(f334(f334(f336(f887(x97526,x97526)),f334(f334(f269(x97526,x97526),x97522),x97524)),x97529))
% 160.93/160.66 [9356]~P2(x93562)+E(x93561,f196(f888(x93562,a876)))+~P1(f334(f61(x93562),x93561))+P1(f334(f334(f336(x93562),f10(x93562,x93561)),x93561))+~P1(f334(f334(f336(x93562),f334(f334(f114(x93562),f605(x93561,x93562)),f615(x93561,x93562))),f334(f334(f312(x93562),f605(x93561,x93562)),f334(f334(f312(x93562),f615(x93561,x93562)),f196(f888(x93562,a876))))))
% 160.93/160.66 [9357]~P2(x93572)+E(x93571,f196(f888(x93572,a876)))+~P1(f334(f61(x93572),x93571))+P1(f334(f334(f336(x93572),f11(x93572,x93571)),x93571))+~P1(f334(f334(f336(x93572),f334(f334(f105(x93572),f741(x93571,x93572)),f747(x93571,x93572))),f334(f334(f312(x93572),f741(x93571,x93572)),f334(f334(f312(x93572),f747(x93571,x93572)),f196(f888(x93572,a876))))))
% 160.93/160.66 [9388]~P70(x93882)+E(x93881,f196(f888(x93882,a876)))+~P1(f334(f61(x93882),x93881))+P1(f334(f334(f336(x93882),f334(f63(x93882,f81(x93882)),x93881)),x93881))+~P1(f334(f334(f336(x93882),f334(f334(f81(x93882),f861(x93881,x93882)),f862(x93881,x93882))),f334(f334(f312(x93882),f861(x93881,x93882)),f334(f334(f312(x93882),f862(x93881,x93882)),f196(f888(x93882,a876))))))
% 160.93/160.66 [9394]~P108(x93942)+E(x93941,f196(f888(x93942,a876)))+~P1(f334(f61(x93942),x93941))+P1(f334(f334(f336(x93942),f12(x93942,f247(x93942),x93941)),x93941))+~P1(f334(f334(f336(x93942),f334(f334(f247(x93942),f470(x93941,x93942)),f472(x93941,x93942))),f334(f334(f312(x93942),f470(x93941,x93942)),f334(f334(f312(x93942),f472(x93941,x93942)),f196(f888(x93942,a876))))))
% 160.93/160.66 [9395]~P108(x93952)+E(x93951,f196(f888(x93952,a876)))+~P1(f334(f61(x93952),x93951))+P1(f334(f334(f336(x93952),f13(x93952,f246(x93952),x93951)),x93951))+~P1(f334(f334(f336(x93952),f334(f334(f246(x93952),f473(x93951,x93952)),f474(x93951,x93952))),f334(f334(f312(x93952),f473(x93951,x93952)),f334(f334(f312(x93952),f474(x93951,x93952)),f196(f888(x93952,a876))))))
% 160.93/160.66 [6511]~P81(x65112)+E(x65111,f2(x65112))+~E(f334(f334(f80(x65112),x65113),x65111),f2(x65112))+~P1(f334(f334(f248(x65112),f2(x65112)),x65113))+~P1(f334(f334(f248(x65112),f2(x65112)),x65111))
% 160.93/160.66 [6512]~P81(x65122)+E(x65121,f2(x65122))+~E(f334(f334(f80(x65122),x65121),x65123),f2(x65122))+~P1(f334(f334(f248(x65122),f2(x65122)),x65123))+~P1(f334(f334(f248(x65122),f2(x65122)),x65121))
% 160.93/160.66 [7041]~P108(x70412)+~P16(x70412,x70411)+E(x70411,f117(x70412))+~P1(f334(f334(f336(x70412),x70413),f334(f174(x70412),f748(x70411,x70412))))+P1(f334(f334(f248(x70412),f766(x70411,x70412)),x70413))
% 160.93/160.66 [7209]~P108(x72091)+E(f14(x72091,x72092),x72093)+~P1(f334(f61(x72091),x72092))+~P1(f334(f334(f248(x72091),x72093),f508(x72093,x72092,x72091)))+~P1(f334(f334(f336(x72091),x72093),x72092))
% 160.93/160.66 [7240]~P108(x72401)+~P16(x72401,x72402)+~P16(x72401,x72403)+P16(x72401,f334(f334(f136(x72401),x72402),x72403))+P1(f334(f334(f336(x72401),f754(x72403,x72402,x72401)),f334(f174(x72401),x72402)))
% 160.93/160.66 [7241]~P108(x72411)+~P16(x72411,x72412)+~P16(x72411,x72413)+P16(x72411,f334(f334(f136(x72411),x72412),x72413))+P1(f334(f334(f336(x72411),f755(x72413,x72412,x72411)),f334(f174(x72411),x72413)))
% 160.93/160.66 [7297]~P108(x72971)+E(f14(x72971,x72972),x72973)+~P1(f334(f61(x72971),x72972))+P1(f334(f334(f336(x72971),f508(x72973,x72972,x72971)),x72972))+~P1(f334(f334(f336(x72971),x72973),x72972))
% 160.93/160.66 [7298]~P108(x72981)+E(f15(x72981,x72982),x72983)+~P1(f334(f61(x72981),x72982))+P1(f334(f334(f336(x72981),f511(x72983,x72982,x72981)),x72982))+~P1(f334(f334(f336(x72981),x72983),x72982))
% 160.93/160.66 [7877]~P108(x78771)+E(f15(x78771,x78772),x78773)+~P1(f334(f61(x78771),x78772))+~P1(f334(f334(f336(x78771),x78773),x78772))+~P1(f334(f334(f248(x78771),f511(x78773,x78772,x78771)),x78773))
% 160.93/160.66 [8204]~P108(x82041)+~P16(x82041,x82042)+~P16(x82041,x82043)+P16(x82041,f334(f334(f136(x82041),x82042),x82043))+~P1(f334(f334(f248(x82041),f754(x82043,x82042,x82041)),f755(x82043,x82042,x82041)))
% 160.93/160.66 [8994]~P2(x89942)+E(x89941,f196(f888(x89942,a876)))+~E(f334(f334(f114(x89942),f334(x89943,f638(x89941,x89943,x89942))),f334(x89943,f659(x89941,x89943,x89942))),f334(x89943,f334(f334(f114(x89942),f638(x89941,x89943,x89942)),f659(x89941,x89943,x89942))))+E(f10(x89942,f334(f313(x89942,x89942,x89943),x89941)),f334(x89943,f10(x89942,x89941)))+~P1(f334(f61(x89942),x89941))
% 160.93/160.66 [8995]~P2(x89952)+E(x89951,f196(f888(x89952,a876)))+~E(f334(f334(f105(x89952),f334(x89953,f759(x89951,x89953,x89952))),f334(x89953,f772(x89951,x89953,x89952))),f334(x89953,f334(f334(f105(x89952),f759(x89951,x89953,x89952)),f772(x89951,x89953,x89952))))+E(f11(x89952,f334(f313(x89952,x89952,x89953),x89951)),f334(x89953,f11(x89952,x89951)))+~P1(f334(f61(x89952),x89951))
% 160.93/160.66 [8996]~P108(x89962)+E(x89961,f196(f888(x89962,a876)))+~E(f334(f334(f246(x89962),f334(x89963,f487(x89961,x89963,x89962))),f334(x89963,f488(x89961,x89963,x89962))),f334(x89963,f334(f334(f246(x89962),f487(x89961,x89963,x89962)),f488(x89961,x89963,x89962))))+E(f14(x89962,f334(f313(x89962,x89962,x89963),x89961)),f334(x89963,f14(x89962,x89961)))+~P1(f334(f61(x89962),x89961))
% 160.93/160.66 [8997]~P108(x89972)+E(x89971,f196(f888(x89972,a876)))+~E(f334(f334(f247(x89972),f334(x89973,f476(x89971,x89973,x89972))),f334(x89973,f485(x89971,x89973,x89972))),f334(x89973,f334(f334(f247(x89972),f476(x89971,x89973,x89972)),f485(x89971,x89973,x89972))))+E(f15(x89972,f334(f313(x89972,x89972,x89973),x89971)),f334(x89973,f15(x89972,x89971)))+~P1(f334(f61(x89972),x89971))
% 160.93/160.66 [9066]~P108(x90662)+E(x90661,f196(f888(x90662,a876)))+~E(f334(f334(f247(x90662),f334(x90663,f477(x90661,x90663,x90662))),f334(x90663,f482(x90661,x90663,x90662))),f334(x90663,f334(f334(f247(x90662),f477(x90661,x90663,x90662)),f482(x90661,x90663,x90662))))+E(f12(x90662,f247(x90662),f334(f313(x90662,x90662,x90663),x90661)),f334(x90663,f12(x90662,f247(x90662),x90661)))+~P1(f334(f61(x90662),x90661))
% 160.93/160.66 [9067]~P108(x90672)+E(x90671,f196(f888(x90672,a876)))+~E(f334(f334(f246(x90672),f334(x90673,f483(x90671,x90673,x90672))),f334(x90673,f484(x90671,x90673,x90672))),f334(x90673,f334(f334(f246(x90672),f483(x90671,x90673,x90672)),f484(x90671,x90673,x90672))))+E(f13(x90672,f246(x90672),f334(f313(x90672,x90672,x90673),x90671)),f334(x90673,f13(x90672,f246(x90672),x90671)))+~P1(f334(f61(x90672),x90671))
% 160.93/160.66 [6527]~P70(x65272)+E(x65271,f196(f888(x65272,a876)))+~P1(f334(f61(x65272),x65271))+E(f334(f63(x65272,f81(x65272)),f334(f334(f312(x65272),x65273),x65271)),f334(f334(f81(x65272),x65273),f334(f63(x65272,f81(x65272)),x65271)))+P1(f334(f334(f336(x65272),x65273),x65271))
% 160.93/160.66 [7047]~P2(x70472)+E(f334(f334(f114(x70472),f10(x70472,x70471)),f10(x70472,x70473)),f10(x70472,x70473))+E(x70471,f196(f888(x70472,a876)))+~P1(f334(f61(x70472),x70473))+~P1(f334(f334(f248(f888(x70472,a876)),x70471),x70473))
% 160.93/160.66 [7048]~P2(x70482)+E(f334(f334(f105(x70482),f11(x70482,x70481)),f11(x70482,x70483)),f11(x70482,x70483))+E(x70481,f196(f888(x70482,a876)))+~P1(f334(f61(x70482),x70483))+~P1(f334(f334(f248(f888(x70482,a876)),x70481),x70483))
% 160.93/160.66 [7049]~P108(x70492)+E(f334(f334(f246(x70492),f14(x70492,x70491)),f14(x70492,x70493)),f14(x70492,x70493))+E(x70491,f196(f888(x70492,a876)))+~P1(f334(f61(x70492),x70493))+~P1(f334(f334(f248(f888(x70492,a876)),x70491),x70493))
% 160.93/160.66 [7050]~P108(x70502)+E(f334(f334(f247(x70502),f15(x70502,x70501)),f15(x70502,x70503)),f15(x70502,x70503))+E(x70501,f196(f888(x70502,a876)))+~P1(f334(f61(x70502),x70503))+~P1(f334(f334(f248(f888(x70502,a876)),x70501),x70503))
% 160.93/160.66 [7349]~P108(x73492)+E(x73491,f196(f888(x73492,a876)))+~P1(f334(f61(x73492),x73493))+P1(f334(f334(f248(x73492),f14(x73492,x73493)),f14(x73492,x73491)))+~P1(f334(f334(f248(f888(x73492,a876)),x73491),x73493))
% 160.93/160.66 [7350]~P108(x73502)+E(x73501,f196(f888(x73502,a876)))+~P1(f334(f61(x73502),x73503))+P1(f334(f334(f248(x73502),f15(x73502,x73501)),f15(x73502,x73503)))+~P1(f334(f334(f248(f888(x73502,a876)),x73501),x73503))
% 160.93/160.66 [7408]~P2(x74081)+E(f10(x74081,x74082),x74083)+~P1(f334(f61(x74081),x74082))+~E(f334(f334(f22(f888(x74081,a876)),x74082),f334(f334(f312(x74081),x74083),f196(f888(x74081,a876)))),f196(f888(x74081,a876)))+~P1(f334(f334(f336(x74081),x74083),x74082))
% 160.93/160.66 [7409]~P2(x74091)+E(f11(x74091,x74092),x74093)+~P1(f334(f61(x74091),x74092))+~E(f334(f334(f22(f888(x74091,a876)),x74092),f334(f334(f312(x74091),x74093),f196(f888(x74091,a876)))),f196(f888(x74091,a876)))+~P1(f334(f334(f336(x74091),x74093),x74092))
% 160.93/160.66 [7410]~P108(x74101)+E(f14(x74101,x74102),x74103)+~P1(f334(f61(x74101),x74102))+~E(f334(f334(f22(f888(x74101,a876)),x74102),f334(f334(f312(x74101),x74103),f196(f888(x74101,a876)))),f196(f888(x74101,a876)))+~P1(f334(f334(f336(x74101),x74103),x74102))
% 160.93/160.66 [7411]~P108(x74111)+E(f15(x74111,x74112),x74113)+~P1(f334(f61(x74111),x74112))+~E(f334(f334(f22(f888(x74111,a876)),x74112),f334(f334(f312(x74111),x74113),f196(f888(x74111,a876)))),f196(f888(x74111,a876)))+~P1(f334(f334(f336(x74111),x74113),x74112))
% 160.93/160.66 [7509]~P108(x75091)+E(f12(x75091,f247(x75091),x75092),x75093)+~P1(f334(f61(x75091),x75092))+~E(f334(f334(f22(f888(x75091,a876)),x75092),f334(f334(f312(x75091),x75093),f196(f888(x75091,a876)))),f196(f888(x75091,a876)))+~P1(f334(f334(f336(x75091),x75093),x75092))
% 160.93/160.66 [7510]~P108(x75101)+E(f13(x75101,f246(x75101),x75102),x75103)+~P1(f334(f61(x75101),x75102))+~E(f334(f334(f22(f888(x75101,a876)),x75102),f334(f334(f312(x75101),x75103),f196(f888(x75101,a876)))),f196(f888(x75101,a876)))+~P1(f334(f334(f336(x75101),x75103),x75102))
% 160.93/160.66 [7547]~P108(x75472)+E(x75471,f196(f888(x75472,a876)))+~P1(f334(f61(x75472),x75471))+~P1(f334(f334(f249(x75472),x75473),f453(x75473,x75471,x75472)))+P1(f334(f334(f249(x75472),x75473),f334(f63(x75472,f246(x75472)),x75471)))
% 160.93/160.66 [7548]~P100(x75482)+E(x75481,f196(f888(x75482,a876)))+~P1(f334(f61(x75482),x75481))+~P1(f334(f334(f248(x75482),x75483),f355(x75483,x75481,x75482)))+P1(f334(f334(f248(x75482),x75483),f334(f63(x75482,f105(x75482)),x75481)))
% 160.93/160.66 [7549]~P108(x75492)+E(x75491,f196(f888(x75492,a876)))+~P1(f334(f61(x75492),x75491))+~P1(f334(f334(f248(x75492),x75493),f454(x75493,x75491,x75492)))+P1(f334(f334(f248(x75492),x75493),f334(f63(x75492,f246(x75492)),x75491)))
% 160.93/160.66 [7636]~P100(x76362)+E(x76361,f196(f888(x76362,a876)))+~P1(f334(f61(x76362),x76361))+P1(f334(f334(f336(x76362),f355(x76363,x76361,x76362)),x76361))+P1(f334(f334(f248(x76362),x76363),f334(f63(x76362,f105(x76362)),x76361)))
% 160.93/160.66 [7637]~P108(x76372)+E(x76371,f196(f888(x76372,a876)))+~P1(f334(f61(x76372),x76371))+P1(f334(f334(f336(x76372),f454(x76373,x76371,x76372)),x76371))+P1(f334(f334(f248(x76372),x76373),f334(f63(x76372,f246(x76372)),x76371)))
% 160.93/160.66 [7638]~P108(x76382)+E(x76381,f196(f888(x76382,a876)))+~P1(f334(f61(x76382),x76381))+P1(f334(f334(f336(x76382),f453(x76383,x76381,x76382)),x76381))+P1(f334(f334(f249(x76382),x76383),f334(f63(x76382,f246(x76382)),x76381)))
% 160.93/160.66 [7755]~P108(x77552)+E(x77551,f196(f888(x77552,a876)))+E(f334(f334(f246(x77552),f13(x77552,f246(x77552),x77551)),f13(x77552,f246(x77552),x77553)),f13(x77552,f246(x77552),x77553))+~P1(f334(f61(x77552),x77553))+~P1(f334(f334(f248(f888(x77552,a876)),x77551),x77553))
% 160.93/160.66 [7756]~P108(x77562)+E(x77561,f196(f888(x77562,a876)))+E(f334(f334(f247(x77562),f12(x77562,f247(x77562),x77561)),f12(x77562,f247(x77562),x77563)),f12(x77562,f247(x77562),x77563))+~P1(f334(f61(x77562),x77563))+~P1(f334(f334(f248(f888(x77562,a876)),x77561),x77563))
% 160.93/160.66 [7956]~E(f429(x79561,x79563,x79562),f430(x79561,x79563,x79562))+~E(f334(f37(x79562),f431(x79561,x79563,x79562)),x79561)+E(f334(f334(f81(a881),x79561),f334(f37(f888(x79562,a876)),x79563)),f334(f37(x79562),f39(f888(x79562,a876),x79563)))+~P1(f334(f61(x79562),f39(f888(x79562,a876),x79563)))+~P1(f334(f61(f888(x79562,a876)),x79563))
% 160.93/160.66 [8133]~P108(x81332)+E(x81331,f196(f888(x81332,a876)))+~P1(f334(f61(x81332),x81333))+P1(f334(f334(f248(x81332),f334(f63(x81332,f246(x81332)),x81333)),f334(f63(x81332,f246(x81332)),x81331)))+~P1(f334(f334(f248(f888(x81332,a876)),x81331),x81333))
% 160.93/160.66 [8446]~E(f429(x84461,x84463,x84462),f430(x84461,x84463,x84462))+E(f334(f334(f81(a881),x84461),f334(f37(f888(x84462,a876)),x84463)),f334(f37(x84462),f39(f888(x84462,a876),x84463)))+P1(f334(f334(f336(f888(x84462,a876)),f431(x84461,x84463,x84462)),x84463))+~P1(f334(f61(x84462),f39(f888(x84462,a876),x84463)))+~P1(f334(f61(f888(x84462,a876)),x84463))
% 160.93/160.66 [8470]~E(f334(f37(x84702),f431(x84701,x84703,x84702)),x84701)+E(f334(f334(f81(a881),x84701),f334(f37(f888(x84702,a876)),x84703)),f334(f37(x84702),f39(f888(x84702,a876),x84703)))+P1(f334(f334(f336(f888(x84702,a876)),f430(x84701,x84703,x84702)),x84703))+~P1(f334(f61(x84702),f39(f888(x84702,a876),x84703)))+~P1(f334(f61(f888(x84702,a876)),x84703))
% 160.93/160.66 [8471]~E(f334(f37(x84712),f431(x84711,x84713,x84712)),x84711)+E(f334(f334(f81(a881),x84711),f334(f37(f888(x84712,a876)),x84713)),f334(f37(x84712),f39(f888(x84712,a876),x84713)))+P1(f334(f334(f336(f888(x84712,a876)),f429(x84711,x84713,x84712)),x84713))+~P1(f334(f61(x84712),f39(f888(x84712,a876),x84713)))+~P1(f334(f61(f888(x84712,a876)),x84713))
% 160.93/160.66 [8497]~E(f334(f37(x84972),f431(x84971,x84973,x84972)),x84971)+~E(f334(f334(f105(f888(x84972,a876)),f430(x84971,x84973,x84972)),f429(x84971,x84973,x84972)),f196(f888(x84972,a876)))+E(f334(f334(f81(a881),x84971),f334(f37(f888(x84972,a876)),x84973)),f334(f37(x84972),f39(f888(x84972,a876),x84973)))+~P1(f334(f61(f888(x84972,a876)),x84973))+~P1(f334(f61(x84972),f39(f888(x84972,a876),x84973)))
% 160.93/160.66 [8753]E(f334(f334(f81(a881),x87531),f334(f37(f888(x87532,a876)),x87533)),f334(f37(x87532),f39(f888(x87532,a876),x87533)))+P1(f334(f334(f336(f888(x87532,a876)),f431(x87531,x87533,x87532)),x87533))+P1(f334(f334(f336(f888(x87532,a876)),f430(x87531,x87533,x87532)),x87533))+~P1(f334(f61(f888(x87532,a876)),x87533))+~P1(f334(f61(x87532),f39(f888(x87532,a876),x87533)))
% 160.93/160.66 [8754]E(f334(f334(f81(a881),x87541),f334(f37(f888(x87542,a876)),x87543)),f334(f37(x87542),f39(f888(x87542,a876),x87543)))+P1(f334(f334(f336(f888(x87542,a876)),f431(x87541,x87543,x87542)),x87543))+P1(f334(f334(f336(f888(x87542,a876)),f429(x87541,x87543,x87542)),x87543))+~P1(f334(f61(f888(x87542,a876)),x87543))+~P1(f334(f61(x87542),f39(f888(x87542,a876),x87543)))
% 160.93/160.66 [8779]~E(f334(f334(f105(f888(x87792,a876)),f430(x87791,x87793,x87792)),f429(x87791,x87793,x87792)),f196(f888(x87792,a876)))+E(f334(f334(f81(a881),x87791),f334(f37(f888(x87792,a876)),x87793)),f334(f37(x87792),f39(f888(x87792,a876),x87793)))+~P1(f334(f61(f888(x87792,a876)),x87793))+P1(f334(f334(f336(f888(x87792,a876)),f431(x87791,x87793,x87792)),x87793))+~P1(f334(f61(x87792),f39(f888(x87792,a876),x87793)))
% 160.93/160.66 [9040]~P95(x90402)+E(x90401,f196(f888(x90402,a876)))+~E(f334(f334(f81(x90402),f334(x90403,f865(x90401,x90403,x90402))),f334(x90403,f867(x90401,x90403,x90402))),f334(x90403,f334(f334(f81(x90402),f865(x90401,x90403,x90402)),f867(x90401,x90403,x90402))))+~P1(f334(f61(x90402),x90401))+E(f334(f63(x90402,f81(x90402)),f334(f313(x90402,x90402,x90403),x90401)),f334(x90403,f334(f63(x90402,f81(x90402)),x90401)))
% 160.93/160.66 [9976]P1(f334(f334(x99761,x99762),x99763))+P1(f334(f334(f249(a1),f521(x99761,x99763,x99762)),f522(x99761,x99763,x99762)))+P1(f334(f334(f248(a1),f522(x99761,x99763,x99762)),f2(a1)))+P1(f334(f334(x99761,f521(x99761,x99763,x99762)),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f522(x99761,x99763,x99762))))+~P1(f334(f322(f887(a1,a1),a56),f334(f334(f269(a1,a1),x99762),x99763)))
% 160.93/160.66 [9982]P1(f334(f334(x99821,x99822),x99823))+P1(f334(f334(f248(a1),f520(x99821,x99823,x99822)),f2(a1)))+P1(f334(f334(x99821,f515(x99821,x99823,x99822)),f334(f334(f81(a1),f334(f107(a1),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f520(x99821,x99823,x99822))))+P1(f334(f334(f248(a1),f2(a1)),f334(f334(f80(a1),f515(x99821,x99823,x99822)),f520(x99821,x99823,x99822))))+~P1(f334(f322(f887(a1,a1),a51),f334(f334(f269(a1,a1),x99822),x99823)))
% 160.93/160.66 [7927]~P111(x79271)+~P1(f334(f334(f248(x79271),x79272),f78(x79271)))+~P1(f334(f334(f248(x79271),f2(x79271)),x79272))+~P1(f334(f334(f248(x79271),f2(x79271)),x79273))+P1(f334(f334(f248(x79271),f334(f334(f81(x79271),x79272),x79273)),x79273))
% 160.93/160.66 [7928]~P111(x79281)+~P1(f334(f334(f248(x79281),x79283),f78(x79281)))+~P1(f334(f334(f248(x79281),f2(x79281)),x79283))+~P1(f334(f334(f248(x79281),f2(x79281)),x79282))+P1(f334(f334(f248(x79281),f334(f334(f81(x79281),x79282),x79283)),x79282))
% 160.93/160.66 [8293]~P108(x82932)+E(x82931,f196(f888(x82932,a876)))+~P1(f334(f61(x82932),x82931))+P1(f334(f334(f336(x82932),f465(x82933,x82931,x82932)),x82931))+~P1(f334(f334(f248(x82932),f334(f63(x82932,f246(x82932)),x82931)),x82933))
% 160.93/160.66 [8294]~P108(x82942)+E(x82941,f196(f888(x82942,a876)))+~P1(f334(f61(x82942),x82941))+P1(f334(f334(f336(x82942),f466(x82943,x82941,x82942)),x82941))+~P1(f334(f334(f249(x82942),f334(f63(x82942,f246(x82942)),x82941)),x82943))
% 160.93/160.66 [8295]~P108(x82952)+E(x82951,f196(f888(x82952,a876)))+~P1(f334(f61(x82952),x82951))+P1(f334(f334(f249(x82952),f466(x82953,x82951,x82952)),x82953))+~P1(f334(f334(f249(x82952),f334(f63(x82952,f246(x82952)),x82951)),x82953))
% 160.93/160.66 [8296]~P108(x82962)+E(x82961,f196(f888(x82962,a876)))+~P1(f334(f61(x82962),x82961))+P1(f334(f334(f248(x82962),f465(x82963,x82961,x82962)),x82963))+~P1(f334(f334(f248(x82962),f334(f63(x82962,f246(x82962)),x82961)),x82963))
% 160.93/160.66 [8381]~P1(f334(x83811,x83813))+P1(f334(x83811,f396(x83811,x83812)))+P1(f334(x83811,f391(x83811,x83812)))+~P1(f334(f334(f249(a1),f2(a1)),x83812))+P1(f334(x83811,f334(f334(f22(a1),f391(x83811,x83812)),f334(f334(f81(a1),f397(x83811,x83812)),x83812))))
% 160.93/160.66 [8602]~P1(f334(x86021,x86023))+P1(f334(x86021,f391(x86021,x86022)))+~P1(f334(f334(f249(a1),f2(a1)),x86022))+P1(f334(f334(f336(a1),f396(x86021,x86022)),f305(a1,f78(a1),x86022)))+P1(f334(x86021,f334(f334(f22(a1),f391(x86021,x86022)),f334(f334(f81(a1),f397(x86021,x86022)),x86022))))
% 160.93/160.66 [8801]~P1(f334(x88011,x88013))+~P1(f334(x88011,f391(x88011,x88012)))+P1(f334(x88011,f396(x88011,x88012)))+~P1(f334(f334(f249(a1),f2(a1)),x88012))+~P1(f334(x88011,f334(f334(f22(a1),f391(x88011,x88012)),f334(f334(f81(a1),f397(x88011,x88012)),x88012))))
% 160.93/160.66 [8924]~P1(f334(x89241,x89243))+~P1(f334(x89241,f391(x89241,x89242)))+~P1(f334(f334(f249(a1),f2(a1)),x89242))+P1(f334(f334(f336(a1),f396(x89241,x89242)),f305(a1,f78(a1),x89242)))+~P1(f334(x89241,f334(f334(f22(a1),f391(x89241,x89242)),f334(f334(f81(a1),f397(x89241,x89242)),x89242))))
% 160.93/160.66 [8713]~P2(x87131)+~P1(f334(f61(x87131),x87132))+E(f334(f334(f22(f888(x87131,a876)),x87132),f334(f334(f312(x87131),x87133),f196(f888(x87131,a876)))),f196(f888(x87131,a876)))+~P1(f334(f334(f336(x87131),x87133),x87132))+E(f334(f334(f114(x87131),x87133),f10(x87131,f334(f334(f22(f888(x87131,a876)),x87132),f334(f334(f312(x87131),x87133),f196(f888(x87131,a876)))))),f10(x87131,x87132))
% 160.93/160.66 [8714]~P2(x87141)+~P1(f334(f61(x87141),x87142))+E(f334(f334(f22(f888(x87141,a876)),x87142),f334(f334(f312(x87141),x87143),f196(f888(x87141,a876)))),f196(f888(x87141,a876)))+~P1(f334(f334(f336(x87141),x87143),x87142))+E(f334(f334(f105(x87141),x87143),f11(x87141,f334(f334(f22(f888(x87141,a876)),x87142),f334(f334(f312(x87141),x87143),f196(f888(x87141,a876)))))),f11(x87141,x87142))
% 160.93/160.66 [8715]~P108(x87151)+~P1(f334(f61(x87151),x87152))+E(f334(f334(f22(f888(x87151,a876)),x87152),f334(f334(f312(x87151),x87153),f196(f888(x87151,a876)))),f196(f888(x87151,a876)))+~P1(f334(f334(f336(x87151),x87153),x87152))+E(f334(f334(f246(x87151),x87153),f14(x87151,f334(f334(f22(f888(x87151,a876)),x87152),f334(f334(f312(x87151),x87153),f196(f888(x87151,a876)))))),f14(x87151,x87152))
% 160.93/160.66 [8716]~P108(x87161)+~P1(f334(f61(x87161),x87162))+E(f334(f334(f22(f888(x87161,a876)),x87162),f334(f334(f312(x87161),x87163),f196(f888(x87161,a876)))),f196(f888(x87161,a876)))+~P1(f334(f334(f336(x87161),x87163),x87162))+E(f334(f334(f247(x87161),x87163),f15(x87161,f334(f334(f22(f888(x87161,a876)),x87162),f334(f334(f312(x87161),x87163),f196(f888(x87161,a876)))))),f15(x87161,x87162))
% 160.93/160.66 [8773]~P108(x87731)+~P1(f334(f61(x87731),x87732))+E(f334(f334(f22(f888(x87731,a876)),x87732),f334(f334(f312(x87731),x87733),f196(f888(x87731,a876)))),f196(f888(x87731,a876)))+~P1(f334(f334(f336(x87731),x87733),x87732))+E(f334(f334(f247(x87731),x87733),f12(x87731,f247(x87731),f334(f334(f22(f888(x87731,a876)),x87732),f334(f334(f312(x87731),x87733),f196(f888(x87731,a876)))))),f12(x87731,f247(x87731),x87732))
% 160.93/160.66 [8774]~P108(x87741)+~P1(f334(f61(x87741),x87742))+E(f334(f334(f22(f888(x87741,a876)),x87742),f334(f334(f312(x87741),x87743),f196(f888(x87741,a876)))),f196(f888(x87741,a876)))+~P1(f334(f334(f336(x87741),x87743),x87742))+E(f334(f334(f246(x87741),x87743),f13(x87741,f246(x87741),f334(f334(f22(f888(x87741,a876)),x87742),f334(f334(f312(x87741),x87743),f196(f888(x87741,a876)))))),f13(x87741,f246(x87741),x87742))
% 160.93/160.66 [8788]~P2(x87881)+~P1(f334(f61(x87881),x87883))+~P1(f334(f61(x87881),x87882))+E(f334(f334(f105(f888(x87881,a876)),x87882),x87883),f196(f888(x87881,a876)))+E(f334(f334(f114(x87881),f10(x87881,f334(f334(f114(f888(x87881,a876)),x87882),x87883))),f10(x87881,f334(f334(f105(f888(x87881,a876)),x87882),x87883))),f334(f334(f114(x87881),f10(x87881,x87882)),f10(x87881,x87883)))
% 160.93/160.66 [8789]~P2(x87891)+~P1(f334(f61(x87891),x87893))+~P1(f334(f61(x87891),x87892))+E(f334(f334(f105(f888(x87891,a876)),x87892),x87893),f196(f888(x87891,a876)))+E(f334(f334(f105(x87891),f11(x87891,f334(f334(f114(f888(x87891,a876)),x87892),x87893))),f11(x87891,f334(f334(f105(f888(x87891,a876)),x87892),x87893))),f334(f334(f105(x87891),f11(x87891,x87892)),f11(x87891,x87893)))
% 160.93/160.66 [8790]~P108(x87901)+~P1(f334(f61(x87901),x87903))+~P1(f334(f61(x87901),x87902))+E(f334(f334(f105(f888(x87901,a876)),x87902),x87903),f196(f888(x87901,a876)))+E(f334(f334(f246(x87901),f14(x87901,f334(f334(f114(f888(x87901,a876)),x87902),x87903))),f14(x87901,f334(f334(f105(f888(x87901,a876)),x87902),x87903))),f334(f334(f246(x87901),f14(x87901,x87902)),f14(x87901,x87903)))
% 160.93/160.66 [8791]~P108(x87911)+~P1(f334(f61(x87911),x87913))+~P1(f334(f61(x87911),x87912))+E(f334(f334(f105(f888(x87911,a876)),x87912),x87913),f196(f888(x87911,a876)))+E(f334(f334(f247(x87911),f15(x87911,f334(f334(f114(f888(x87911,a876)),x87912),x87913))),f15(x87911,f334(f334(f105(f888(x87911,a876)),x87912),x87913))),f334(f334(f247(x87911),f15(x87911,x87912)),f15(x87911,x87913)))
% 160.93/160.66 [9012]~P108(x90121)+~P1(f334(f61(x90121),x90123))+~P1(f334(f61(x90121),x90122))+E(f334(f334(f105(f888(x90121,a876)),x90122),x90123),f196(f888(x90121,a876)))+E(f334(f334(f246(x90121),f13(x90121,f246(x90121),f334(f334(f114(f888(x90121,a876)),x90122),x90123))),f13(x90121,f246(x90121),f334(f334(f105(f888(x90121,a876)),x90122),x90123))),f334(f334(f246(x90121),f13(x90121,f246(x90121),x90122)),f13(x90121,f246(x90121),x90123)))
% 160.93/160.66 [9013]~P108(x90131)+~P1(f334(f61(x90131),x90133))+~P1(f334(f61(x90131),x90132))+E(f334(f334(f105(f888(x90131,a876)),x90132),x90133),f196(f888(x90131,a876)))+E(f334(f334(f247(x90131),f12(x90131,f247(x90131),f334(f334(f114(f888(x90131,a876)),x90132),x90133))),f12(x90131,f247(x90131),f334(f334(f105(f888(x90131,a876)),x90132),x90133))),f334(f334(f247(x90131),f12(x90131,f247(x90131),x90132)),f12(x90131,f247(x90131),x90133)))
% 160.93/160.66 [9815]~P106(x98153)+E(x98151,x98152)+~P1(f334(f334(f248(x98153),f2(x98153)),x98152))+~P1(f334(f334(f248(x98153),f2(x98153)),x98151))+~E(f334(f334(f259(x98153),x98151),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))),f334(f334(f259(x98153),x98152),f334(f107(a881),f334(f334(f80(a1),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)),f334(f334(f22(a1),f334(f334(f80(a1),a83),a83)),a101)))))
% 160.93/160.66 [6329]E(f828(x63291,x63292,x63293),x63294)+E(f334(x63291,x63294),f2(a881))+~E(f334(f334(f6(x63293,a881),x63291),x63292),f78(a881))+~P1(f334(f61(x63293),x63292))+~P1(f334(f334(f336(x63293),x63294),x63292))
% 160.93/160.66 [6390]E(f800(x63901,x63902,x63903),x63904)+E(f334(x63901,x63904),f2(a881))+~E(f334(f334(f6(x63903,a881),x63901),x63902),f334(a116,f2(a881)))+~P1(f334(f61(x63903),x63902))+~P1(f334(f334(f336(x63903),x63904),x63902))
% 160.93/160.66 [6496]~P5(x64961)+~P108(x64961)+P1(f334(f334(f249(x64961),x64962),f39(x64961,x64963)))+~P1(f334(f334(f249(x64961),x64962),x64964))+~P1(f334(f334(f336(x64961),x64964),x64963))
% 160.93/160.66 [6669]~P5(x66691)+~P108(x66691)+~P1(f334(f334(f249(x66691),x66694),x66693))+P1(f334(f334(f249(x66691),f40(x66691,x66692)),x66693))+~P1(f334(f334(f336(x66691),x66694),x66692))
% 160.93/160.66 [6927]~P106(x69273)+E(x69271,x69272)+~E(f334(f334(f259(x69273),x69271),f334(a116,x69274)),f334(f334(f259(x69273),x69272),f334(a116,x69274)))+~P1(f334(f334(f248(x69273),f2(x69273)),x69272))+~P1(f334(f334(f248(x69273),f2(x69273)),x69271))
% 160.93/160.66 [7136]~E(f832(x71362,x71363,x71361,x71364),x71364)+~E(f334(x71362,x71364),f78(a881))+E(f334(f334(f6(x71361,a881),x71362),x71363),f78(a881))+~P1(f334(f61(x71361),x71363))+~P1(f334(f334(f336(x71361),x71364),x71363))
% 160.93/160.66 [7143]~P130(x71434)+~P118(x71434)+E(f334(x71431,f350(x71431,x71432,x71433,x71434)),f2(x71434))+~E(f334(f334(f9(x71433,x71434),x71431),x71432),f2(x71434))+~P1(f334(f61(x71433),x71432))
% 160.93/160.66 [7231]~E(f816(x72312,x72313,x72311,x72314),x72314)+~E(f334(x72312,x72314),f334(a116,f2(a881)))+E(f334(f334(f6(x72311,a881),x72312),x72313),f334(a116,f2(a881)))+~P1(f334(f61(x72311),x72313))+~P1(f334(f334(f336(x72311),x72314),x72313))
% 160.93/160.66 [7968]~E(f334(x79682,x79684),f78(a881))+~E(f334(x79682,f832(x79682,x79683,x79681,x79684)),f2(a881))+E(f334(f334(f6(x79681,a881),x79682),x79683),f78(a881))+~P1(f334(f61(x79681),x79683))+~P1(f334(f334(f336(x79681),x79684),x79683))
% 160.93/160.66 [8006]~E(f334(x80062,x80064),f334(a116,f2(a881)))+~E(f334(x80062,f816(x80062,x80063,x80061,x80064)),f2(a881))+E(f334(f334(f6(x80061,a881),x80062),x80063),f334(a116,f2(a881)))+~P1(f334(f61(x80061),x80063))+~P1(f334(f334(f336(x80061),x80064),x80063))
% 160.93/160.66 [8572]~P108(x85721)+~P16(x85721,x85724)+P16(x85721,x85722)+~E(x85722,f334(f334(f153(x85721),x85723),x85724))+~P1(f334(f334(f248(x85721),x85723),f768(x85722,x85721,x85724,x85723)))
% 160.93/160.66 [8606]E(x86061,x86062)+E(f334(f334(f22(a1),f375(x86063,x86062,x86064,x86061)),f376(x86063,x86062,x86064,x86061)),x86061)+~E(f334(f334(f80(a1),x86061),x86064),x86062)+~P1(f334(f334(f249(a1),f2(a1)),x86064))+~P1(f334(f334(f336(a1),x86062),x86063))
% 160.93/160.66 [8607]E(x86071,x86072)+E(f334(f334(f80(a1),f382(x86073,x86072,x86074,x86071)),f383(x86073,x86072,x86074,x86071)),x86071)+~E(f334(f334(f22(a1),x86071),x86074),x86072)+~P1(f334(f334(f249(a1),f2(a1)),x86074))+~P1(f334(f334(f336(a1),x86072),x86073))
% 160.93/160.66 [8786]E(f334(x87861,f653(x87862,x87861,x87863,x87864)),x87862)+P1(f334(f334(f248(a881),x87864),f654(x87862,x87861,x87863,x87864)))+~P1(f334(f334(f248(a1),x87862),f334(x87861,x87863)))+~P1(f334(f334(f249(a881),x87864),x87863))+~P1(f334(f334(f248(a1),f334(x87861,x87864)),x87862))
% 160.93/160.66 [8787]~P108(x87871)+~P16(x87871,x87873)+P16(x87871,x87872)+~E(x87872,f334(f334(f153(x87871),x87874),x87873))+P1(f334(f334(f336(x87871),f768(x87872,x87871,x87873,x87874)),f334(f174(x87871),x87873)))
% 160.93/160.66 [8805]~P130(x88054)+~P118(x88054)+~E(f334(f334(f9(x88051,x88054),x88052),x88053),f2(x88054))+~P1(f334(f61(x88051),x88053))+P1(f334(f334(f336(x88051),f350(x88052,x88053,x88051,x88054)),x88053))
% 160.93/160.66 [8839]~E(f334(x88392,x88394),f78(a881))+E(f334(f334(f6(x88391,a881),x88392),x88393),f78(a881))+~P1(f334(f61(x88391),x88393))+~P1(f334(f334(f336(x88391),x88394),x88393))+P1(f334(f334(f336(x88391),f832(x88392,x88393,x88391,x88394)),x88393))
% 160.93/160.66 [8848]E(x88481,x88482)+~E(f334(f334(f80(a1),x88482),x88484),x88481)+~P1(f334(f334(f249(a1),f2(a1)),x88484))+~P1(f334(f334(f336(a1),x88481),x88483))+P1(f334(f334(f336(a1),f375(x88483,x88481,x88484,x88482)),x88483))
% 160.93/160.66 [8849]E(x88491,x88492)+~E(f334(f334(f22(a1),x88492),x88494),x88491)+~P1(f334(f334(f249(a1),f2(a1)),x88494))+~P1(f334(f334(f336(a1),x88491),x88493))+P1(f334(f334(f336(a1),f382(x88493,x88491,x88494,x88492)),x88493))
% 160.93/160.66 [8851]~E(f334(x88512,x88514),f334(a116,f2(a881)))+E(f334(f334(f6(x88511,a881),x88512),x88513),f334(a116,f2(a881)))+~P1(f334(f61(x88511),x88513))+~P1(f334(f334(f336(x88511),x88514),x88513))+P1(f334(f334(f336(x88511),f816(x88512,x88513,x88511,x88514)),x88513))
% 160.93/160.66 [8856]P56(x88562,x88563,x88564,x88561)+E(x88561,f196(f888(x88562,a876)))+~P1(f334(f61(x88562),x88564))+~P1(f334(f61(x88562),x88561))+P1(f334(f334(f336(x88562),f559(x88561,x88564,x88563,x88562)),x88564))
% 160.93/160.66 [8938]E(x89381,x89382)+~E(f334(f334(f80(a1),x89382),x89384),x89381)+~P1(f334(f334(f249(a1),f2(a1)),x89384))+~P1(f334(f334(f336(a1),x89381),x89383))+P1(f334(f334(f336(a1),f376(x89383,x89381,x89384,x89382)),f305(a1,f78(a1),x89384)))
% 160.93/160.66 [8939]E(x89391,x89392)+~E(f334(f334(f22(a1),x89392),x89394),x89391)+~P1(f334(f334(f249(a1),f2(a1)),x89394))+~P1(f334(f334(f336(a1),x89391),x89393))+P1(f334(f334(f336(a1),f383(x89393,x89391,x89394,x89392)),f305(a1,f78(a1),x89394)))
% 160.93/160.66 [9018]P1(f334(f334(f248(a881),x90181),f653(x90182,x90183,x90184,x90181)))+~P1(f334(f334(f248(a1),x90182),f334(x90183,x90184)))+P1(f334(f334(f248(a881),x90181),f654(x90182,x90183,x90184,x90181)))+~P1(f334(f334(f249(a881),x90181),x90184))+~P1(f334(f334(f248(a1),f334(x90183,x90181)),x90182))
% 160.93/160.66 [9132]E(f334(x91321,f653(x91322,x91321,x91323,x91324)),x91322)+~P1(f334(f334(f248(a1),x91322),f334(x91321,x91323)))+P1(f334(f334(f249(a881),f654(x91322,x91321,x91323,x91324)),x91323))+~P1(f334(f334(f249(a881),x91324),x91323))+~P1(f334(f334(f248(a1),f334(x91321,x91324)),x91322))
% 160.93/160.66 [9263]~P1(f334(f334(f248(a1),x92632),f334(x92633,x92634)))+P1(f334(f334(f248(a881),x92631),f654(x92632,x92633,x92634,x92631)))+P1(f334(f334(f248(a881),f653(x92632,x92633,x92634,x92631)),x92634))+~P1(f334(f334(f249(a881),x92631),x92634))+~P1(f334(f334(f248(a1),f334(x92633,x92631)),x92632))
% 160.93/160.66 [9264]~P1(f334(f334(f248(a1),x92642),f334(x92643,x92644)))+P1(f334(f334(f248(a881),x92641),f653(x92642,x92643,x92644,x92641)))+P1(f334(f334(f249(a881),f654(x92642,x92643,x92644,x92641)),x92644))+~P1(f334(f334(f249(a881),x92641),x92644))+~P1(f334(f334(f248(a1),f334(x92643,x92641)),x92642))
% 160.93/160.66 [9371]~P1(f334(f334(f248(a1),x93711),f334(x93712,x93713)))+P1(f334(f334(f248(a881),f653(x93711,x93712,x93713,x93714)),x93713))+~P1(f334(f334(f249(a881),x93714),x93713))+~P1(f334(f334(f248(a1),f334(x93712,x93714)),x93711))+P1(f334(f334(f249(a881),f654(x93711,x93712,x93713,x93714)),x93713))
% 160.93/160.66 [9449]E(x94491,f196(f888(x94492,a876)))+~P1(f334(f61(x94492),x94494))+~P1(f334(f61(x94492),x94491))+P1(f334(f334(f336(f887(f888(x94492,a876),f888(x94492,a876))),f334(f334(f269(f888(x94492,a876),f888(x94492,a876)),x94494),x94491)),f325(x94492,x94493)))+P1(f334(f334(f336(x94492),f566(x94493,x94491,x94494,x94492)),x94494))
% 160.93/160.66 [9450]E(x94501,f196(f888(x94502,a876)))+~P1(f334(f61(x94502),x94504))+~P1(f334(f61(x94502),x94501))+P1(f334(f334(f336(f887(f888(x94502,a876),f888(x94502,a876))),f334(f334(f269(f888(x94502,a876),f888(x94502,a876)),x94504),x94501)),f325(x94502,x94503)))+P1(f334(f334(f336(x94502),f622(x94503,x94501,x94504,x94502)),x94504))
% 160.93/160.66 [10119]E(f334(x101191,f653(x101192,x101191,x101193,x101194)),x101192)+~P1(f334(f334(f248(a1),x101192),f334(x101191,x101193)))+~P1(f334(f334(f248(a1),f334(f75(a1),f334(f334(f22(a1),f334(x101191,f334(f334(f80(a881),f654(x101192,x101191,x101193,x101194)),f78(a881)))),f334(x101191,f654(x101192,x101191,x101193,x101194))))),f78(a1)))+~P1(f334(f334(f249(a881),x101194),x101193))+~P1(f334(f334(f248(a1),f334(x101191,x101194)),x101192))
% 160.93/160.66 [10120]~P1(f334(f334(f248(a1),x101202),f334(x101203,x101204)))+P1(f334(f334(f248(a881),x101201),f653(x101202,x101203,x101204,x101201)))+~P1(f334(f334(f248(a1),f334(f75(a1),f334(f334(f22(a1),f334(x101203,f334(f334(f80(a881),f654(x101202,x101203,x101204,x101201)),f78(a881)))),f334(x101203,f654(x101202,x101203,x101204,x101201))))),f78(a1)))+~P1(f334(f334(f249(a881),x101201),x101204))+~P1(f334(f334(f248(a1),f334(x101203,x101201)),x101202))
% 160.93/160.66 [10121]~P1(f334(f334(f248(a1),x101211),f334(x101212,x101213)))+~P1(f334(f334(f248(a1),f334(f75(a1),f334(f334(f22(a1),f334(x101212,f334(f334(f80(a881),f654(x101211,x101212,x101213,x101214)),f78(a881)))),f334(x101212,f654(x101211,x101212,x101213,x101214))))),f78(a1)))+~P1(f334(f334(f249(a881),x101214),x101213))+~P1(f334(f334(f248(a1),f334(x101212,x101214)),x101211))+P1(f334(f334(f248(a881),f653(x101211,x101212,x101213,x101214)),x101213))
% 160.93/160.66 [7198]~P63(x71981)+P1(f334(f334(f249(x71981),x71982),f2(x71981)))+~P1(f334(f334(f249(x71981),x71983),f2(x71981)))+P1(f334(f334(f249(x71981),f2(x71981)),x71982))+P1(f334(f334(f249(x71981),x71983),f334(f334(f292(x71981),x71984),x71982)))
% 160.93/160.66 [7199]~P63(x71991)+P1(f334(f334(f249(x71991),x71992),f2(x71991)))+~P1(f334(f334(f248(x71991),x71993),f2(x71991)))+P1(f334(f334(f249(x71991),f2(x71991)),x71992))+P1(f334(f334(f248(x71991),x71993),f334(f334(f292(x71991),x71994),x71992)))
% 160.93/160.66 [7447]~P63(x74471)+P1(f334(f334(f249(x74471),x74472),f2(x74471)))+P1(f334(f334(f249(x74471),x74473),f2(x74471)))+P1(f334(f334(f249(x74471),f2(x74471)),x74473))+~P1(f334(f334(f249(x74471),x74472),f334(f334(f292(x74471),x74474),x74473)))
% 160.93/160.66 [7448]~P63(x74481)+P1(f334(f334(f249(x74481),x74482),f2(x74481)))+P1(f334(f334(f248(x74481),x74483),f2(x74481)))+P1(f334(f334(f249(x74481),f2(x74481)),x74482))+~P1(f334(f334(f248(x74481),x74483),f334(f334(f292(x74481),x74484),x74482)))
% 160.93/160.66 [7567]E(x75671,x75672)+~E(f334(f334(f167(x75673),x75674),x75671),f334(f334(f167(x75673),x75674),x75672))+~P1(f334(f139(x75673),x75674))+~P1(f334(f334(f249(a881),x75672),f334(f197(f882(x75673)),x75674)))+~P1(f334(f334(f249(a881),x75671),f334(f197(f882(x75673)),x75674)))
% 160.93/160.66 [7929]~P63(x79291)+~P1(f334(f334(f249(x79291),x79293),f2(x79291)))+P1(f334(f334(f249(x79291),f2(x79291)),x79292))+~P1(f334(f334(f249(x79291),x79294),f334(f334(f81(x79291),x79293),x79292)))+P1(f334(f334(f249(x79291),x79293),f334(f334(f292(x79291),x79294),x79292)))
% 160.93/160.66 [7930]~P63(x79301)+~P1(f334(f334(f248(x79301),x79303),f2(x79301)))+P1(f334(f334(f249(x79301),f2(x79301)),x79302))+~P1(f334(f334(f248(x79301),x79304),f334(f334(f81(x79301),x79303),x79302)))+P1(f334(f334(f248(x79301),x79303),f334(f334(f292(x79301),x79304),x79302)))
% 160.93/160.66 [7931]~P63(x79311)+~P1(f334(f334(f249(x79311),x79312),f2(x79311)))+P1(f334(f334(f249(x79311),f2(x79311)),x79312))+~P1(f334(f334(f249(x79311),x79314),f334(f334(f81(x79311),x79313),x79312)))+P1(f334(f334(f249(x79311),x79313),f334(f334(f292(x79311),x79314),x79312)))
% 160.93/160.66 [7932]~P63(x79321)+~P1(f334(f334(f249(x79321),x79322),f2(x79321)))+P1(f334(f334(f249(x79321),f2(x79321)),x79322))+~P1(f334(f334(f249(x79321),x79324),f334(f334(f292(x79321),x79323),x79322)))+P1(f334(f334(f249(x79321),x79323),f334(f334(f81(x79321),x79324),x79322)))
% 160.93/160.66 [7933]~P63(x79331)+~P1(f334(f334(f249(x79331),x79332),f2(x79331)))+P1(f334(f334(f249(x79331),f2(x79331)),x79332))+~P1(f334(f334(f248(x79331),x79334),f334(f334(f81(x79331),x79333),x79332)))+P1(f334(f334(f248(x79331),x79333),f334(f334(f292(x79331),x79334),x79332)))
% 160.93/160.66 [7934]~P63(x79341)+~P1(f334(f334(f249(x79341),x79342),f2(x79341)))+P1(f334(f334(f249(x79341),f2(x79341)),x79342))+~P1(f334(f334(f248(x79341),x79344),f334(f334(f292(x79341),x79343),x79342)))+P1(f334(f334(f248(x79341),x79343),f334(f334(f81(x79341),x79344),x79342)))
% 160.93/160.66 [8072]~P108(x80721)+~P16(x80721,x80722)+~P1(f334(f334(f248(a881),x80723),x80724))+P1(f334(f334(f248(x80721),f334(f334(f167(x80721),x80722),x80723)),f334(f334(f167(x80721),x80722),x80724)))+~P1(f334(f334(f249(a881),x80724),f334(f197(f882(x80721)),x80722)))
% 160.93/160.66 [8124]~P106(x81241)+~P1(f334(f334(f249(x81241),x81242),f78(x81241)))+~P1(f334(f334(f249(x81241),f2(x81241)),x81242))+~P1(f334(f334(f249(a881),x81244),x81243))+P1(f334(f334(f249(x81241),f334(f334(f259(x81241),x81242),x81243)),f334(f334(f259(x81241),x81242),x81244)))
% 160.93/160.66 [8125]~P106(x81251)+~P1(f334(f334(f248(x81251),x81252),f78(x81251)))+~P1(f334(f334(f248(x81251),f2(x81251)),x81252))+~P1(f334(f334(f248(a881),x81254),x81253))+P1(f334(f334(f248(x81251),f334(f334(f259(x81251),x81252),x81253)),f334(f334(f259(x81251),x81252),x81254)))
% 160.93/160.66 [8126]~P106(x81261)+~P1(f334(f334(f248(x81261),f2(x81261)),x81262))+~P1(f334(f334(f249(a881),f2(a881)),x81263))+~P1(f334(f334(f249(x81261),x81262),x81264))+P1(f334(f334(f249(x81261),f334(f334(f259(x81261),x81262),x81263)),f334(f334(f259(x81261),x81264),x81263)))
% 160.93/160.66 [8147]~P108(x81471)+~P16(x81471,f334(f171(x81471),x81472))+~P1(f334(f334(f248(a881),x81474),x81473))+P1(f334(f334(f248(x81471),f334(f334(f167(x81471),x81472),x81473)),f334(f334(f167(x81471),x81472),x81474)))+~P1(f334(f334(f249(a881),x81473),f334(f197(f882(x81471)),x81472)))
% 160.93/160.66 [8403]~P64(x84031)+~P1(f334(f334(f249(x84031),x84032),f2(x84031)))+~P1(f334(f334(f249(x84031),x84033),x84034))+~P1(f334(f334(f249(x84031),f2(x84031)),f334(f334(f81(x84031),x84033),x84034)))+P1(f334(f334(f249(x84031),f334(f334(f292(x84031),x84032),x84033)),f334(f334(f292(x84031),x84032),x84034)))
% 160.93/160.66 [8404]~P63(x84041)+~P1(f334(f334(f248(x84041),x84042),f2(x84041)))+~P1(f334(f334(f248(x84041),x84043),x84044))+~P1(f334(f334(f249(x84041),f2(x84041)),f334(f334(f81(x84041),x84043),x84044)))+P1(f334(f334(f248(x84041),f334(f334(f292(x84041),x84042),x84043)),f334(f334(f292(x84041),x84042),x84044)))
% 160.93/160.66 [8413]~P64(x84131)+~P1(f334(f334(f249(x84131),x84134),x84133))+~P1(f334(f334(f249(x84131),f2(x84131)),x84132))+~P1(f334(f334(f249(x84131),f2(x84131)),f334(f334(f81(x84131),x84133),x84134)))+P1(f334(f334(f249(x84131),f334(f334(f292(x84131),x84132),x84133)),f334(f334(f292(x84131),x84132),x84134)))
% 160.93/160.66 [8414]~P64(x84141)+~P1(f334(f334(f248(x84141),x84144),x84143))+~P1(f334(f334(f248(x84141),f2(x84141)),x84142))+~P1(f334(f334(f249(x84141),f2(x84141)),f334(f334(f81(x84141),x84143),x84144)))+P1(f334(f334(f248(x84141),f334(f334(f292(x84141),x84142),x84143)),f334(f334(f292(x84141),x84142),x84144)))
% 160.93/160.66 [8515]P1(f334(x85151,x85152))+~P1(f334(f61(x85154),x85152))+P1(f334(x85151,f435(x85151,x85153,x85152,x85154)))+~P1(f334(x85151,f196(f888(x85154,a876))))+~P1(f334(f334(f248(f888(x85154,a876)),x85152),x85153))
% 160.93/160.66 [8523]P1(f334(x85231,x85232))+P1(f334(f61(x85233),f435(x85231,x85234,x85232,x85233)))+~P1(f334(f61(x85233),x85232))+~P1(f334(x85231,f196(f888(x85233,a876))))+~P1(f334(f334(f248(f888(x85233,a876)),x85232),x85234))
% 160.93/160.66 [8781]E(f334(f334(f80(a1),f384(x87811,x87812,x87813,x87814)),f385(x87811,x87812,x87813,x87814)),x87814)+~P1(f334(f334(f249(a1),f2(a1)),x87813))+~P1(f334(f334(f249(a1),x87812),x87814))+~P1(f334(f334(f336(a1),x87812),x87811))+P1(f334(f334(f249(a1),x87812),f334(f334(f22(a1),x87814),x87813)))
% 160.93/160.66 [9000]~P1(f334(f334(f249(a1),f2(a1)),x90003))+~P1(f334(f334(f249(a1),x90002),x90004))+~P1(f334(f334(f336(a1),x90002),x90001))+P1(f334(f334(f336(a1),f384(x90001,x90002,x90003,x90004)),x90001))+P1(f334(f334(f249(a1),x90002),f334(f334(f22(a1),x90004),x90003)))
% 160.93/160.66 [9011]P1(f334(x90111,x90112))+~P1(f334(f61(x90113),x90112))+P1(f334(f334(f336(x90113),f436(x90111,x90114,x90112,x90113)),x90114))+~P1(f334(x90111,f196(f888(x90113,a876))))+~P1(f334(f334(f248(f888(x90113,a876)),x90112),x90114))
% 160.93/160.66 [9028]E(f334(f334(f80(a1),f377(x90281,x90282,x90283,x90284)),f378(x90281,x90282,x90283,x90284)),x90284)+~P1(f334(f334(f249(a1),f2(a1)),x90283))+~P1(f334(f334(f248(a1),x90282),x90284))+P1(f334(f334(f248(a1),x90282),f334(f334(f22(a1),x90284),x90283)))+~P1(f334(f334(f336(a1),f334(f334(f22(a1),x90282),f78(a1))),x90281))
% 160.93/160.66 [9083]~P1(f334(f334(f249(a1),f2(a1)),x90833))+~P1(f334(f334(f249(a1),x90831),x90832))+~P1(f334(f334(f336(a1),x90831),x90834))+P1(f334(f334(f336(a1),f385(x90834,x90831,x90833,x90832)),f305(a1,f78(a1),x90833)))+P1(f334(f334(f249(a1),x90831),f334(f334(f22(a1),x90832),x90833)))
% 160.93/160.66 [9179]~P1(f334(f334(f249(a1),f2(a1)),x91793))+~P1(f334(f334(f248(a1),x91792),x91794))+P1(f334(f334(f336(a1),f377(x91791,x91792,x91793,x91794)),x91791))+P1(f334(f334(f248(a1),x91792),f334(f334(f22(a1),x91794),x91793)))+~P1(f334(f334(f336(a1),f334(f334(f22(a1),x91792),f78(a1))),x91791))
% 160.93/160.66 [9219]~P1(f334(f334(f249(a1),f2(a1)),x92193))+~P1(f334(f334(f248(a1),x92191),x92192))+P1(f334(f334(f336(a1),f378(x92194,x92191,x92193,x92192)),f305(a1,f78(a1),x92193)))+P1(f334(f334(f248(a1),x92191),f334(f334(f22(a1),x92192),x92193)))+~P1(f334(f334(f336(a1),f334(f334(f22(a1),x92191),f78(a1))),x92194))
% 160.93/160.66 [9452]P1(f334(x94521,x94522))+~P1(f334(f334(f336(x94523),f436(x94521,x94524,x94522,x94523)),f435(x94521,x94524,x94522,x94523)))+~P1(f334(f61(x94523),x94522))+~P1(f334(x94521,f196(f888(x94523,a876))))+~P1(f334(f334(f248(f888(x94523,a876)),x94522),x94524))
% 160.93/160.66 [9674]P1(f334(x96741,x96742))+~P1(f334(f61(x96743),x96742))+~P1(f334(x96741,f334(f334(f312(x96743),f436(x96741,x96744,x96742,x96743)),f435(x96741,x96744,x96742,x96743))))+~P1(f334(x96741,f196(f888(x96743,a876))))+~P1(f334(f334(f248(f888(x96743,a876)),x96742),x96744))
% 160.93/160.66 [7703]~P63(x77031)+P1(f334(f334(f249(x77031),x77032),f2(x77031)))+P1(f334(f334(f249(x77031),f2(x77031)),x77032))+~P1(f334(f334(f249(x77031),f2(x77031)),x77034))+P1(f334(f334(f249(x77031),f334(f334(f292(x77031),x77033),x77032)),x77034))
% 160.93/160.66 [7704]~P63(x77041)+P1(f334(f334(f249(x77041),x77042),f2(x77041)))+~P1(f334(f334(f248(x77041),f2(x77041)),x77044))+P1(f334(f334(f249(x77041),f2(x77041)),x77042))+P1(f334(f334(f248(x77041),f334(f334(f292(x77041),x77043),x77042)),x77044))
% 160.93/160.66 [7981]~P1(f334(f334(f248(a1),x79814),f2(a1)))+~E(x79812,f334(f334(f80(a1),f334(f334(f81(a1),x79811),x79813)),x79814))+P1(f334(f334(f249(a1),f2(a1)),x79811))+~P1(f334(f334(f249(a1),x79811),x79814))+P1(f334(f48(x79812,x79811),f334(f334(f269(a1,a1),x79813),x79814)))
% 160.93/160.66 [8015]~P1(f334(x80151,x80154))+P1(f334(x80151,f419(x80152,x80151,x80153)))+~P1(f334(f334(f249(a1),f2(a1)),x80153))+~P1(f334(f334(f248(a1),f2(a1)),x80152))+P1(f334(x80151,f334(f334(f22(a1),x80154),f334(f334(f81(a1),x80152),x80153))))
% 160.93/160.66 [8016]~P1(f334(x80161,x80164))+P1(f334(x80161,f423(x80162,x80161,x80163)))+~P1(f334(f334(f249(a1),f2(a1)),x80163))+~P1(f334(f334(f248(a1),f2(a1)),x80162))+P1(f334(x80161,f334(f334(f80(a1),x80164),f334(f334(f81(a1),x80162),x80163))))
% 160.93/160.66 [8017]~P63(x80171)+P1(f334(f334(f249(x80171),x80172),f2(x80171)))+P1(f334(f334(f249(x80171),f2(x80171)),x80172))+P1(f334(f334(f249(x80171),f2(x80171)),x80173))+~P1(f334(f334(f249(x80171),f334(f334(f292(x80171),x80174),x80172)),x80173))
% 160.93/160.66 [8018]~P63(x80181)+P1(f334(f334(f249(x80181),x80182),f2(x80181)))+P1(f334(f334(f249(x80181),f2(x80181)),x80182))+P1(f334(f334(f248(x80181),f2(x80181)),x80183))+~P1(f334(f334(f248(x80181),f334(f334(f292(x80181),x80184),x80182)),x80183))
% 160.93/160.66 [8066]~E(x80661,f334(f334(f80(a1),f334(f334(f81(a1),x80662),x80663)),x80664))+~P1(f334(f334(f249(a1),f2(a1)),x80662))+~P1(f334(f334(f248(a1),f2(a1)),x80664))+~P1(f334(f334(f249(a1),x80664),x80662))+P1(f334(f48(x80661,x80662),f334(f334(f269(a1,a1),x80663),x80664)))
% 160.93/160.66 [8194]~P63(x81941)+P1(f334(f334(f249(x81941),x81942),f2(x81941)))+~P1(f334(f334(f249(x81941),f2(x81941)),x81944))+~P1(f334(f334(f249(x81941),x81943),f334(f334(f81(x81941),x81944),x81942)))+P1(f334(f334(f249(x81941),f334(f334(f292(x81941),x81943),x81942)),x81944))
% 160.93/160.66 [8195]~P63(x81951)+P1(f334(f334(f249(x81951),x81952),f2(x81951)))+~P1(f334(f334(f248(x81951),f2(x81951)),x81954))+~P1(f334(f334(f248(x81951),x81953),f334(f334(f81(x81951),x81954),x81952)))+P1(f334(f334(f248(x81951),f334(f334(f292(x81951),x81953),x81952)),x81954))
% 160.93/160.66 [8283]~P63(x82831)+P1(f334(f334(f249(x82831),x82832),f2(x82831)))+~P1(f334(f334(f249(x82831),x82833),f2(x82831)))+P1(f334(f334(f249(x82831),x82833),f334(f334(f292(x82831),x82834),x82832)))+~P1(f334(f334(f249(x82831),f334(f334(f81(x82831),x82833),x82832)),x82834))
% 160.93/160.66 [8284]~P63(x82841)+P1(f334(f334(f249(x82841),x82842),f2(x82841)))+~P1(f334(f334(f248(x82841),x82843),f2(x82841)))+P1(f334(f334(f248(x82841),x82843),f334(f334(f292(x82841),x82844),x82842)))+~P1(f334(f334(f248(x82841),f334(f334(f81(x82841),x82843),x82842)),x82844))
% 160.93/160.66 [8435]~P63(x84351)+~P1(f334(f334(f249(x84351),x84352),f2(x84351)))+P1(f334(f334(f249(x84351),f2(x84351)),x84352))+~P1(f334(f334(f249(x84351),f334(f334(f292(x84351),x84354),x84352)),x84353))+P1(f334(f334(f249(x84351),f334(f334(f81(x84351),x84353),x84352)),x84354))
% 160.93/160.66 [8436]~P63(x84361)+~P1(f334(f334(f249(x84361),x84362),f2(x84361)))+P1(f334(f334(f249(x84361),f2(x84361)),x84362))+~P1(f334(f334(f249(x84361),f334(f334(f81(x84361),x84364),x84362)),x84363))+P1(f334(f334(f249(x84361),f334(f334(f292(x84361),x84363),x84362)),x84364))
% 160.93/160.66 [8437]~P63(x84371)+~P1(f334(f334(f249(x84371),x84372),f2(x84371)))+P1(f334(f334(f249(x84371),f2(x84371)),x84372))+~P1(f334(f334(f248(x84371),f334(f334(f292(x84371),x84374),x84372)),x84373))+P1(f334(f334(f248(x84371),f334(f334(f81(x84371),x84373),x84372)),x84374))
% 160.93/160.66 [8438]~P63(x84381)+~P1(f334(f334(f249(x84381),x84382),f2(x84381)))+P1(f334(f334(f249(x84381),f2(x84381)),x84382))+~P1(f334(f334(f248(x84381),f334(f334(f81(x84381),x84384),x84382)),x84383))+P1(f334(f334(f248(x84381),f334(f334(f292(x84381),x84383),x84382)),x84384))
% 160.93/160.66 [8457]~P63(x84571)+~P1(f334(f334(f249(x84571),f2(x84571)),x84574))+P1(f334(f334(f249(x84571),f2(x84571)),x84572))+~P1(f334(f334(f249(x84571),f334(f334(f81(x84571),x84574),x84572)),x84573))+P1(f334(f334(f249(x84571),f334(f334(f292(x84571),x84573),x84572)),x84574))
% 160.93/160.66 [8458]~P63(x84581)+~P1(f334(f334(f248(x84581),f2(x84581)),x84584))+P1(f334(f334(f249(x84581),f2(x84581)),x84582))+~P1(f334(f334(f248(x84581),f334(f334(f81(x84581),x84584),x84582)),x84583))+P1(f334(f334(f248(x84581),f334(f334(f292(x84581),x84583),x84582)),x84584))
% 160.93/160.66 [8531]~P63(x85311)+~P1(f334(f334(f249(x85311),x85314),f2(x85311)))+~P1(f334(f334(f249(x85311),x85313),f334(f334(f81(x85311),x85312),x85314)))+P1(f334(f334(f249(x85311),x85312),f334(f334(f292(x85311),x85313),x85314)))+~P1(f334(f334(f249(x85311),f334(f334(f81(x85311),x85312),x85314)),x85313))
% 160.93/160.66 [8532]~P63(x85321)+~P1(f334(f334(f249(x85321),x85322),f2(x85321)))+~P1(f334(f334(f249(x85321),x85323),f334(f334(f81(x85321),x85322),x85324)))+P1(f334(f334(f249(x85321),x85322),f334(f334(f292(x85321),x85323),x85324)))+~P1(f334(f334(f249(x85321),f334(f334(f81(x85321),x85322),x85324)),x85323))
% 160.93/160.66 [8533]~P63(x85331)+~P1(f334(f334(f249(x85331),x85334),f2(x85331)))+~P1(f334(f334(f248(x85331),x85333),f334(f334(f81(x85331),x85332),x85334)))+P1(f334(f334(f248(x85331),x85332),f334(f334(f292(x85331),x85333),x85334)))+~P1(f334(f334(f248(x85331),f334(f334(f81(x85331),x85332),x85334)),x85333))
% 160.93/160.66 [8534]~P63(x85341)+~P1(f334(f334(f248(x85341),x85342),f2(x85341)))+~P1(f334(f334(f248(x85341),x85343),f334(f334(f81(x85341),x85342),x85344)))+P1(f334(f334(f248(x85341),x85342),f334(f334(f292(x85341),x85343),x85344)))+~P1(f334(f334(f248(x85341),f334(f334(f81(x85341),x85342),x85344)),x85343))
% 160.93/160.66 [8658]~P63(x86581)+~P1(f334(f334(f249(x86581),x86583),f2(x86581)))+~P1(f334(f334(f249(x86581),x86582),f334(f334(f81(x86581),x86584),x86583)))+~P1(f334(f334(f249(x86581),f334(f334(f81(x86581),x86584),x86583)),x86582))+P1(f334(f334(f249(x86581),f334(f334(f292(x86581),x86582),x86583)),x86584))
% 160.93/160.66 [8659]~P63(x86591)+~P1(f334(f334(f249(x86591),x86593),f2(x86591)))+~P1(f334(f334(f248(x86591),x86592),f334(f334(f81(x86591),x86594),x86593)))+~P1(f334(f334(f248(x86591),f334(f334(f81(x86591),x86594),x86593)),x86592))+P1(f334(f334(f248(x86591),f334(f334(f292(x86591),x86592),x86593)),x86594))
% 160.93/160.66 [8674]~P63(x86741)+~P1(f334(f334(f249(x86741),f2(x86741)),x86744))+~P1(f334(f334(f249(x86741),x86742),f334(f334(f81(x86741),x86744),x86743)))+~P1(f334(f334(f249(x86741),f334(f334(f81(x86741),x86744),x86743)),x86742))+P1(f334(f334(f249(x86741),f334(f334(f292(x86741),x86742),x86743)),x86744))
% 160.93/160.66 [8675]~P63(x86751)+~P1(f334(f334(f248(x86751),f2(x86751)),x86754))+~P1(f334(f334(f248(x86751),x86752),f334(f334(f81(x86751),x86754),x86753)))+~P1(f334(f334(f248(x86751),f334(f334(f81(x86751),x86754),x86753)),x86752))+P1(f334(f334(f248(x86751),f334(f334(f292(x86751),x86752),x86753)),x86754))
% 160.93/160.66 [8841]E(f334(f334(f22(a1),f386(x88411,x88412,x88413,x88414)),f387(x88411,x88412,x88413,x88414)),x88414)+~P1(f334(f334(f249(a1),f2(a1)),x88413))+~P1(f334(f334(f336(a1),x88412),x88411))+~P1(f334(f334(f249(a1),x88414),x88412))+P1(f334(f334(f249(a1),f334(f334(f80(a1),x88414),x88413)),x88412))
% 160.93/160.66 [8920]~P1(f334(x89201,x89202))+~P1(f334(f334(f249(a1),f2(a1)),x89204))+~P1(f334(f334(f248(a1),f2(a1)),x89203))+~P1(f334(x89201,f334(f334(f22(a1),f419(x89203,x89201,x89204)),x89204)))+P1(f334(x89201,f334(f334(f22(a1),x89202),f334(f334(f81(a1),x89203),x89204))))
% 160.93/160.66 [8921]~P1(f334(x89211,x89212))+~P1(f334(f334(f249(a1),f2(a1)),x89214))+~P1(f334(f334(f248(a1),f2(a1)),x89213))+~P1(f334(x89211,f334(f334(f80(a1),f423(x89213,x89211,x89214)),x89214)))+P1(f334(x89211,f334(f334(f80(a1),x89212),f334(f334(f81(a1),x89213),x89214))))
% 160.93/160.66 [9075]~P1(f334(f334(f249(a1),f2(a1)),x90753))+~P1(f334(f334(f336(a1),x90752),x90751))+~P1(f334(f334(f249(a1),x90754),x90752))+P1(f334(f334(f336(a1),f386(x90751,x90752,x90753,x90754)),x90751))+P1(f334(f334(f249(a1),f334(f334(f80(a1),x90754),x90753)),x90752))
% 160.93/160.66 [9097]E(f334(f334(f22(a1),f379(x90971,x90972,x90973,x90974)),f380(x90971,x90972,x90973,x90974)),x90974)+~P1(f334(f334(f249(a1),f2(a1)),x90973))+~P1(f334(f334(f248(a1),x90974),x90972))+~P1(f334(f334(f336(a1),f334(f334(f80(a1),x90972),f78(a1))),x90971))+P1(f334(f334(f248(a1),f334(f334(f80(a1),x90974),x90973)),x90972))
% 160.93/160.66 [9124]~P1(f334(f334(f249(a1),f2(a1)),x91242))+~P1(f334(f334(f336(a1),x91243),x91244))+~P1(f334(f334(f249(a1),x91241),x91243))+P1(f334(f334(f336(a1),f387(x91244,x91243,x91242,x91241)),f305(a1,f78(a1),x91242)))+P1(f334(f334(f249(a1),f334(f334(f80(a1),x91241),x91242)),x91243))
% 160.93/160.66 [9214]~P1(f334(f334(f249(a1),f2(a1)),x92143))+~P1(f334(f334(f248(a1),x92144),x92142))+P1(f334(f334(f336(a1),f379(x92141,x92142,x92143,x92144)),x92141))+~P1(f334(f334(f336(a1),f334(f334(f80(a1),x92142),f78(a1))),x92141))+P1(f334(f334(f248(a1),f334(f334(f80(a1),x92144),x92143)),x92142))
% 160.93/160.66 [9259]~P1(f334(f334(f249(a1),f2(a1)),x92592))+~P1(f334(f334(f248(a1),x92591),x92593))+P1(f334(f334(f336(a1),f380(x92594,x92593,x92592,x92591)),f305(a1,f78(a1),x92592)))+~P1(f334(f334(f336(a1),f334(f334(f80(a1),x92593),f78(a1))),x92594))+P1(f334(f334(f248(a1),f334(f334(f80(a1),x92591),x92592)),x92593))
% 160.93/160.66 [9548]~P39(x95481,x95483)+~P28(x95481,x95484)+P39(x95481,f334(f334(f114(f888(f887(x95481,x95481),a876)),x95482),x95483))+~P1(f334(f334(f248(f888(f887(x95481,x95481),a876)),x95482),f334(f268(f888(f887(x95481,x95481),a876),f888(f887(x95481,x95481),a876)),x95484)))+~P1(f334(f334(f248(f888(f887(x95481,x95481),a876)),x95483),f334(f272(f888(f887(x95481,x95481),a876),f888(f887(x95481,x95481),a876)),x95484)))
% 160.93/160.66 [9843]~E(f334(f728(x98431,x98434,x98433,x98432),f730(x98431,x98434,x98433,x98432)),f210(f882(a330)))+P1(f334(f334(f249(a1),f729(x98431,x98434,x98433,x98432)),f730(x98431,x98434,x98433,x98432)))+P1(f334(f334(f334(x98431,x98432),x98433),x98434))+P1(f334(f334(f334(x98431,f728(x98431,x98434,x98433,x98432)),f729(x98431,x98434,x98433,x98432)),f334(f334(f80(a1),f730(x98431,x98434,x98433,x98432)),f78(a1))))+~P1(f334(f322(f887(f888(a1,f885(f882(a330))),f887(a1,a1)),a320),f334(f334(f269(f888(a1,f885(f882(a330))),f887(a1,a1)),x98432),f334(f334(f269(a1,a1),x98433),x98434))))
% 160.93/160.66 [9945]~P20(x99452,x99454,x99453)+E(x99451,f196(f888(x99452,a876)))+~P1(f334(f61(x99452),x99451))+P1(f334(f334(f336(x99452),f334(x99453,x99451)),x99451))+~P1(f334(f334(f336(x99452),f334(f334(x99454,f627(x99451,x99453,x99454,x99452)),f642(x99451,x99453,x99454,x99452))),f334(f334(f312(x99452),f627(x99451,x99453,x99454,x99452)),f334(f334(f312(x99452),f642(x99451,x99453,x99454,x99452)),f196(f888(x99452,a876))))))
% 160.93/160.66 [9876]~P109(x98762)+~P60(x98761)+~P1(f334(f334(f248(f888(x98761,x98762)),x98763),x98764))+P1(f334(f334(f249(f888(x98761,x98762)),x98763),x98764))+~P1(f334(f57(x98761),f334(f334(f8(a876,a876,x98761),a329),f334(f334(f18(x98761,x98762,a876),f334(f334(f8(x98762,f888(x98762,a876),x98761),a331),x98763)),x98764))))
% 160.93/160.66 [9460]~P52(x94601,x94601,x94604)+P1(f334(f334(f336(f887(x94601,x94601)),f334(f334(f269(x94601,x94601),x94602),x94603)),f310(x94601,x94604)))+P1(f334(f334(f336(f887(x94601,x94601)),f334(f334(f269(x94601,x94601),x94603),x94602)),f310(x94601,x94604)))+~P1(f334(f334(f336(f887(x94601,x94601)),f334(f334(f269(x94601,x94601),x94605),x94602)),f310(x94601,x94604)))+~P1(f334(f334(f336(f887(x94601,x94601)),f334(f334(f269(x94601,x94601),x94605),x94603)),f310(x94601,x94604)))
% 160.93/160.66 [5613]E(x56131,f2(a881))+~E(f334(f37(x56132),x56135),x56131)+E(f334(f37(x56132),x56133),f334(a116,x56131))+~E(x56133,f334(f334(f312(x56132),x56134),x56135))+P1(f334(f334(f336(x56132),x56134),x56135))
% 160.93/160.66 [5738]~P62(x57382)+E(x57381,f2(x57382))+E(x57383,f2(x57382))+~E(f334(f334(f292(x57382),x57384),x57383),f334(f334(f292(x57382),x57385),x57381))+E(f334(f334(f81(x57382),x57384),x57381),f334(f334(f81(x57382),x57385),x57383))
% 160.93/160.66 [5739]~P62(x57392)+E(x57391,f2(x57392))+E(x57393,f2(x57392))+~E(f334(f334(f81(x57392),x57394),x57393),f334(f334(f81(x57392),x57395),x57391))+E(f334(f334(f292(x57392),x57394),x57391),f334(f334(f292(x57392),x57395),x57393))
% 160.93/160.66 [5805]~E(f334(f37(x58051),x58055),x58053)+~E(x58055,f196(f888(x58051,a876)))+E(f334(f37(x58051),x58052),f334(a116,x58053))+~E(x58052,f334(f334(f312(x58051),x58054),x58055))+P1(f334(f334(f336(x58051),x58054),x58055))
% 160.93/160.66 [6029]~P118(x60292)+~E(f334(x60293,x60295),f2(x60292))+E(f334(f334(f9(x60291,x60292),x60293),x60294),f2(x60292))+~P1(f334(f61(x60291),x60294))+~P1(f334(f334(f336(x60291),x60295),x60294))
% 160.93/160.66 [6403]~P108(x64033)+E(x64031,x64032)+~E(f334(f304(x64033,x64034),x64031),f334(f304(x64033,x64035),x64032))+~P1(f334(f334(f249(x64033),x64035),x64032))+~P1(f334(f334(f249(x64033),x64034),x64031))
% 160.93/160.66 [6404]~P108(x64043)+E(x64041,x64042)+~E(f334(f304(x64043,x64041),x64044),f334(f304(x64043,x64042),x64045))+~P1(f334(f334(f249(x64043),x64042),x64045))+~P1(f334(f334(f249(x64043),x64041),x64044))
% 160.93/160.66 [7464]~P108(x74641)+~P16(x74641,f334(f334(f136(x74641),x74644),x74645))+~P1(f334(f334(f336(x74641),x74643),f334(f174(x74641),x74645)))+~P1(f334(f334(f336(x74641),x74642),f334(f174(x74641),x74644)))+P1(f334(f334(f248(x74641),x74642),x74643))
% 160.93/160.66 [8574]~P109(x85741)+~P1(f334(f334(f249(f888(x85741,a876)),f305(x85741,x85745,x85742)),f305(x85741,x85744,x85743)))+~P1(f334(f334(f248(x85741),x85745),x85742))+P1(f334(f334(f249(x85741),x85742),x85743))+P1(f334(f334(f249(x85741),x85744),x85745))
% 160.93/160.66 [9988]~P19(x99882,x99885,x99883)+E(x99881,f196(f888(x99882,a876)))+~E(f334(f334(x99885,f334(x99884,f674(x99881,x99884,x99883,x99885,x99882))),f334(x99884,f684(x99881,x99884,x99883,x99885,x99882))),f334(x99884,f334(f334(x99885,f674(x99881,x99884,x99883,x99885,x99882)),f684(x99881,x99884,x99883,x99885,x99882))))+E(f334(x99883,f334(f313(x99882,x99882,x99884),x99881)),f334(x99884,f334(x99883,x99881)))+~P1(f334(f61(x99882),x99881))
% 160.93/160.66 [6400]~P20(x64002,x64005,x64003)+E(x64001,f196(f888(x64002,a876)))+~P1(f334(f61(x64002),x64001))+E(f334(x64003,f334(f334(f312(x64002),x64004),x64001)),f334(f334(x64005,x64004),f334(x64003,x64001)))+P1(f334(f334(f336(x64002),x64004),x64001))
% 160.93/160.66 [7222]~P19(x72222,x72223,x72224)+E(f334(f334(x72223,f334(x72224,x72221)),f334(x72224,x72225)),f334(x72224,x72225))+E(x72221,f196(f888(x72222,a876)))+~P1(f334(f61(x72222),x72225))+~P1(f334(f334(f248(f888(x72222,a876)),x72221),x72225))
% 160.93/160.66 [7440]~P60(x74404)+~P92(x74405)+E(f334(x74401,x74402),f334(x74403,x74402))+~P1(f334(f334(f336(x74404),x74402),f334(f174(x74404),f55(x74404))))+~P1(f334(f334(f91(f888(x74404,x74405)),x74401),x74403))
% 160.93/160.66 [7602]~P20(x76024,x76025,x76021)+E(f334(x76021,x76022),x76023)+~P1(f334(f61(x76024),x76022))+~E(f334(f334(f22(f888(x76024,a876)),x76022),f334(f334(f312(x76024),x76023),f196(f888(x76024,a876)))),f196(f888(x76024,a876)))+~P1(f334(f334(f336(x76024),x76023),x76022))
% 160.93/160.66 [7686]E(x76861,x76862)+~E(f334(f197(f882(x76863)),x76862),f334(f197(f882(x76864)),x76865))+~E(f334(f197(f882(x76863)),x76861),f334(f197(f882(x76864)),x76865))+~E(f334(f180(x76864,x76863),f334(f334(f184(x76864,x76863),x76865),x76861)),f334(f180(x76864,x76863),f334(f334(f184(x76864,x76863),x76865),x76862)))+~P1(f334(f139(x76864),x76865))
% 160.93/160.66 [8539]E(x85391,x85392)+~P8(x85393,x85394,x85395)+E(f334(f334(f105(f888(x85393,a876)),x85391),x85392),f196(f888(x85393,a876)))+~P1(f334(f334(f336(f888(x85393,a876)),x85392),f334(f334(f60(x85393),x85394),x85395)))+~P1(f334(f334(f336(f888(x85393,a876)),x85391),f334(f334(f60(x85393),x85394),x85395)))
% 160.93/160.66 [9341]~P68(x93412)+~E(f334(x93413,f432(x93413,x93414,x93415,x93411,x93412)),f2(x93412))+E(f334(f334(f6(x93411,x93412),x93413),x93414),f334(f334(f6(x93411,x93412),x93413),x93415))+~P1(f334(f61(x93411),x93415))+~P1(f334(f334(f248(f888(x93411,a876)),x93414),x93415))
% 160.93/160.66 [9342]~P68(x93422)+~E(f334(x93423,f433(x93423,x93424,x93425,x93421,x93422)),f2(x93422))+E(f334(f334(f6(x93421,x93422),x93423),x93424),f334(f334(f6(x93421,x93422),x93423),x93425))+~P1(f334(f61(x93421),x93425))+~P1(f334(f334(f248(f888(x93421,a876)),x93424),x93425))
% 160.93/160.66 [9343]~P74(x93432)+~E(f334(x93433,f426(x93433,x93434,x93435,x93431,x93432)),f78(x93432))+E(f334(f334(f9(x93431,x93432),x93433),x93434),f334(f334(f9(x93431,x93432),x93433),x93435))+~P1(f334(f61(x93431),x93435))+~P1(f334(f334(f248(f888(x93431,a876)),x93434),x93435))
% 160.93/160.66 [9344]~P74(x93442)+~E(f334(x93443,f427(x93443,x93444,x93445,x93441,x93442)),f78(x93442))+E(f334(f334(f9(x93441,x93442),x93443),x93444),f334(f334(f9(x93441,x93442),x93443),x93445))+~P1(f334(f61(x93441),x93445))+~P1(f334(f334(f248(f888(x93441,a876)),x93444),x93445))
% 160.93/160.66 [9823]~P81(x98231)+~P1(f334(f61(x98232),x98235))+~P1(f334(f334(f248(x98231),f2(x98231)),f334(x98233,f361(x98233,x98234,x98235,x98232,x98231))))+P1(f334(f334(f248(x98231),f334(f334(f6(x98232,x98231),x98233),x98234)),f334(f334(f6(x98232,x98231),x98233),x98235)))+~P1(f334(f334(f248(f888(x98232,a876)),x98234),x98235))
% 160.93/160.66 [7461]E(x74611,f2(a881))+P1(f334(x74612,x74613))+~E(x74614,f334(f334(f80(a881),f334(f334(f81(a881),x74611),x74613)),x74615))+~P1(f334(f334(f249(a881),x74615),x74611))+~P1(f334(x74612,f334(f334(f38(a881),x74614),x74611)))
% 160.93/160.66 [7541]E(x75411,f2(a881))+P1(f334(x75412,x75413))+~P1(f334(x75412,f44(a881,x75414,x75411)))+~E(x75414,f334(f334(f80(a881),f334(f334(f81(a881),x75411),x75415)),x75413))+~P1(f334(f334(f249(a881),x75413),x75411))
% 160.93/160.66 [7830]~P62(x78303)+E(f334(x78301,x78302),f2(x78303))+~P1(f334(f61(x78304),x78305))+E(f334(f334(f9(x78304,x78303),x78301),f334(f334(f22(f888(x78304,a876)),x78305),f334(f334(f312(x78304),x78302),f196(f888(x78304,a876))))),f334(f334(f9(x78304,x78303),x78301),x78305))+P1(f334(f334(f336(x78304),x78302),x78305))
% 160.93/160.66 [8241]~P68(x82411)+~P1(f334(f61(x82412),x82415))+~P1(f334(f61(x82412),x82414))+~E(f334(f334(f105(f888(x82412,a876)),x82414),x82415),f196(f888(x82412,a876)))+E(f334(f334(f80(x82411),f334(f334(f6(x82412,x82411),x82413),x82414)),f334(f334(f6(x82412,x82411),x82413),x82415)),f334(f334(f6(x82412,x82411),x82413),f334(f334(f114(f888(x82412,a876)),x82414),x82415)))
% 160.93/160.66 [8243]~P74(x82431)+~P1(f334(f61(x82432),x82435))+~P1(f334(f61(x82432),x82434))+~E(f334(f334(f105(f888(x82432,a876)),x82434),x82435),f196(f888(x82432,a876)))+E(f334(f334(f81(x82431),f334(f334(f9(x82432,x82431),x82433),x82434)),f334(f334(f9(x82432,x82431),x82433),x82435)),f334(f334(f9(x82432,x82431),x82433),f334(f334(f114(f888(x82432,a876)),x82434),x82435)))
% 160.93/160.66 [8336]~P62(x83363)+E(f334(x83361,x83362),f2(x83363))+~P1(f334(f61(x83364),x83365))+E(f334(f334(f9(x83364,x83363),x83361),f334(f334(f22(f888(x83364,a876)),x83365),f334(f334(f312(x83364),x83362),f196(f888(x83364,a876))))),f334(f334(f292(x83363),f334(f334(f9(x83364,x83363),x83361),x83365)),f334(x83361,x83362)))+~P1(f334(f334(f336(x83364),x83362),x83365))
% 160.93/160.66 [9053]~P8(x90531,x90535,x90534)+~E(f334(f334(f60(x90531),f334(f334(f312(x90531),x90532),f196(f888(x90531,a876)))),x90534),f334(f334(f60(x90531),f334(f334(f312(x90531),x90533),f196(f888(x90531,a876)))),x90534))+~P1(f334(f334(f336(x90531),x90533),x90535))+~P1(f334(f334(f336(x90531),x90532),x90535))+P1(f334(f334(f336(f887(x90531,x90531)),f334(f334(f269(x90531,x90531),x90532),x90533)),x90534))
% 160.93/160.66 [9074]~P8(x90741,x90745,x90743)+E(f334(f334(f60(x90741),f334(f334(f312(x90741),x90742),f196(f888(x90741,a876)))),x90743),f334(f334(f60(x90741),f334(f334(f312(x90741),x90744),f196(f888(x90741,a876)))),x90743))+~P1(f334(f334(f336(x90741),x90744),x90745))+~P1(f334(f334(f336(x90741),x90742),x90745))+~P1(f334(f334(f336(f887(x90741,x90741)),f334(f334(f269(x90741,x90741),x90742),x90744)),x90743))
% 160.93/160.66 [9370]~P74(x93701)+~P1(f334(f61(x93702),x93705))+~P1(f334(f61(x93702),x93704))+~E(f334(f334(f105(f888(x93702,a876)),x93704),x93705),f196(f888(x93702,a876)))+E(f334(f334(f81(x93701),f334(f334(f334(f65(x93701,x93702,f81(x93701)),x93703),f78(x93701)),x93704)),f334(f334(f334(f65(x93701,x93702,f81(x93701)),x93703),f78(x93701)),x93705)),f334(f334(f334(f65(x93701,x93702,f81(x93701)),x93703),f78(x93701)),f334(f334(f114(f888(x93702,a876)),x93704),x93705)))
% 160.93/160.66 [9379]~P68(x93791)+~E(f334(x93793,f852(x93793,x93795,x93794,x93792,x93791)),f2(x93791))+~P1(f334(f61(x93792),x93794))+~P1(f334(f61(x93792),x93795))+E(f334(f334(f80(x93791),f334(f334(f6(x93792,x93791),x93793),x93794)),f334(f334(f6(x93792,x93791),x93793),x93795)),f334(f334(f6(x93792,x93791),x93793),f334(f334(f114(f888(x93792,a876)),x93794),x93795)))
% 160.93/160.66 [9380]~P68(x93801)+~E(f334(x93803,f854(x93803,x93805,x93804,x93802,x93801)),f2(x93801))+~P1(f334(f61(x93802),x93804))+~P1(f334(f61(x93802),x93805))+E(f334(f334(f80(x93801),f334(f334(f6(x93802,x93801),x93803),x93804)),f334(f334(f6(x93802,x93801),x93803),x93805)),f334(f334(f6(x93802,x93801),x93803),f334(f334(f114(f888(x93802,a876)),x93804),x93805)))
% 160.93/160.66 [9381]~P74(x93811)+~E(f334(x93813,f404(x93813,x93815,x93814,x93812,x93811)),f78(x93811))+~P1(f334(f61(x93812),x93814))+~P1(f334(f61(x93812),x93815))+E(f334(f334(f81(x93811),f334(f334(f9(x93812,x93811),x93813),x93814)),f334(f334(f9(x93812,x93811),x93813),x93815)),f334(f334(f9(x93812,x93811),x93813),f334(f334(f114(f888(x93812,a876)),x93814),x93815)))
% 160.93/160.66 [9382]~P74(x93821)+~E(f334(x93823,f405(x93823,x93825,x93824,x93822,x93821)),f78(x93821))+~P1(f334(f61(x93822),x93824))+~P1(f334(f61(x93822),x93825))+E(f334(f334(f81(x93821),f334(f334(f9(x93822,x93821),x93823),x93824)),f334(f334(f9(x93822,x93821),x93823),x93825)),f334(f334(f9(x93822,x93821),x93823),f334(f334(f114(f888(x93822,a876)),x93824),x93825)))
% 160.93/160.66 [9592]~P74(x95921)+~E(f334(x95923,f853(x95923,x95925,x95924,x95922,x95921)),f78(x95921))+~P1(f334(f61(x95922),x95924))+~P1(f334(f61(x95922),x95925))+E(f334(f334(f81(x95921),f334(f334(f334(f65(x95921,x95922,f81(x95921)),x95923),f78(x95921)),x95924)),f334(f334(f334(f65(x95921,x95922,f81(x95921)),x95923),f78(x95921)),x95925)),f334(f334(f334(f65(x95921,x95922,f81(x95921)),x95923),f78(x95921)),f334(f334(f114(f888(x95922,a876)),x95924),x95925)))
% 160.93/160.66 [9702]~P68(x97022)+E(f334(f334(f6(x97021,x97022),x97023),x97024),f334(f334(f6(x97021,x97022),x97023),x97025))+~P1(f334(f61(x97021),x97025))+~P1(f334(f334(f248(f888(x97021,a876)),x97024),x97025))+P1(f334(f334(f336(x97021),f432(x97023,x97024,x97025,x97021,x97022)),f334(f334(f22(f888(x97021,a876)),x97025),x97024)))
% 160.93/160.66 [9703]~P68(x97032)+E(f334(f334(f6(x97031,x97032),x97033),x97034),f334(f334(f6(x97031,x97032),x97033),x97035))+~P1(f334(f61(x97031),x97035))+~P1(f334(f334(f248(f888(x97031,a876)),x97034),x97035))+P1(f334(f334(f336(x97031),f433(x97033,x97034,x97035,x97031,x97032)),f334(f334(f22(f888(x97031,a876)),x97035),x97034)))
% 160.93/160.66 [9704]~P74(x97042)+E(f334(f334(f9(x97041,x97042),x97043),x97044),f334(f334(f9(x97041,x97042),x97043),x97045))+~P1(f334(f61(x97041),x97045))+~P1(f334(f334(f248(f888(x97041,a876)),x97044),x97045))+P1(f334(f334(f336(x97041),f426(x97043,x97044,x97045,x97041,x97042)),f334(f334(f22(f888(x97041,a876)),x97045),x97044)))
% 160.93/160.66 [9705]~P74(x97052)+E(f334(f334(f9(x97051,x97052),x97053),x97054),f334(f334(f9(x97051,x97052),x97053),x97055))+~P1(f334(f61(x97051),x97055))+~P1(f334(f334(f248(f888(x97051,a876)),x97054),x97055))+P1(f334(f334(f336(x97051),f427(x97053,x97054,x97055,x97051,x97052)),f334(f334(f22(f888(x97051,a876)),x97055),x97054)))
% 160.93/160.66 [9722]~P68(x97221)+~P1(f334(f61(x97222),x97224))+~P1(f334(f61(x97222),x97225))+E(f334(f334(f80(x97221),f334(f334(f6(x97222,x97221),x97223),x97224)),f334(f334(f6(x97222,x97221),x97223),x97225)),f334(f334(f6(x97222,x97221),x97223),f334(f334(f114(f888(x97222,a876)),x97224),x97225)))+P1(f334(f334(f336(x97222),f852(x97223,x97225,x97224,x97222,x97221)),f334(f334(f105(f888(x97222,a876)),x97224),x97225)))
% 160.93/160.66 [9723]~P68(x97231)+~P1(f334(f61(x97232),x97234))+~P1(f334(f61(x97232),x97235))+E(f334(f334(f80(x97231),f334(f334(f6(x97232,x97231),x97233),x97234)),f334(f334(f6(x97232,x97231),x97233),x97235)),f334(f334(f6(x97232,x97231),x97233),f334(f334(f114(f888(x97232,a876)),x97234),x97235)))+P1(f334(f334(f336(x97232),f854(x97233,x97235,x97234,x97232,x97231)),f334(f334(f105(f888(x97232,a876)),x97234),x97235)))
% 160.93/160.66 [9724]~P74(x97241)+~P1(f334(f61(x97242),x97244))+~P1(f334(f61(x97242),x97245))+E(f334(f334(f81(x97241),f334(f334(f9(x97242,x97241),x97243),x97244)),f334(f334(f9(x97242,x97241),x97243),x97245)),f334(f334(f9(x97242,x97241),x97243),f334(f334(f114(f888(x97242,a876)),x97244),x97245)))+P1(f334(f334(f336(x97242),f404(x97243,x97245,x97244,x97242,x97241)),f334(f334(f105(f888(x97242,a876)),x97244),x97245)))
% 160.93/160.66 [9725]~P74(x97251)+~P1(f334(f61(x97252),x97254))+~P1(f334(f61(x97252),x97255))+E(f334(f334(f81(x97251),f334(f334(f9(x97252,x97251),x97253),x97254)),f334(f334(f9(x97252,x97251),x97253),x97255)),f334(f334(f9(x97252,x97251),x97253),f334(f334(f114(f888(x97252,a876)),x97254),x97255)))+P1(f334(f334(f336(x97252),f405(x97253,x97255,x97254,x97252,x97251)),f334(f334(f105(f888(x97252,a876)),x97254),x97255)))
% 160.93/160.66 [9732]~P81(x97325)+~P1(f334(f61(x97321),x97324))+P1(f334(f334(f248(x97325),f334(f334(f6(x97321,x97325),x97322),x97323)),f334(f334(f6(x97321,x97325),x97322),x97324)))+~P1(f334(f334(f248(f888(x97321,a876)),x97323),x97324))+P1(f334(f334(f336(x97321),f361(x97322,x97323,x97324,x97321,x97325)),f334(f334(f22(f888(x97321,a876)),x97324),x97323)))
% 160.93/160.66 [9786]~P74(x97861)+~P1(f334(f61(x97862),x97864))+~P1(f334(f61(x97862),x97865))+E(f334(f334(f81(x97861),f334(f334(f334(f65(x97861,x97862,f81(x97861)),x97863),f78(x97861)),x97864)),f334(f334(f334(f65(x97861,x97862,f81(x97861)),x97863),f78(x97861)),x97865)),f334(f334(f334(f65(x97861,x97862,f81(x97861)),x97863),f78(x97861)),f334(f334(f114(f888(x97862,a876)),x97864),x97865)))+P1(f334(f334(f336(x97862),f853(x97863,x97865,x97864,x97862,x97861)),f334(f334(f105(f888(x97862,a876)),x97864),x97865)))
% 160.93/160.66 [8742]~P20(x87421,x87424,x87425)+~P1(f334(f61(x87421),x87422))+E(f334(f334(f22(f888(x87421,a876)),x87422),f334(f334(f312(x87421),x87423),f196(f888(x87421,a876)))),f196(f888(x87421,a876)))+~P1(f334(f334(f336(x87421),x87423),x87422))+E(f334(f334(x87424,x87423),f334(x87425,f334(f334(f22(f888(x87421,a876)),x87422),f334(f334(f312(x87421),x87423),f196(f888(x87421,a876)))))),f334(x87425,x87422))
% 160.93/160.66 [8815]~P20(x88151,x88154,x88155)+~P1(f334(f61(x88151),x88153))+~P1(f334(f61(x88151),x88152))+E(f334(f334(f105(f888(x88151,a876)),x88152),x88153),f196(f888(x88151,a876)))+E(f334(f334(x88154,f334(x88155,f334(f334(f114(f888(x88151,a876)),x88152),x88153))),f334(x88155,f334(f334(f105(f888(x88151,a876)),x88152),x88153))),f334(f334(x88154,f334(x88155,x88152)),f334(x88155,x88153)))
% 160.93/160.66 [9384]~P1(f334(f334(f248(a1),x93844),f2(a1)))+~P1(f334(f334(f249(a1),x93843),x93845))+P1(f334(f334(f248(a1),x93841),x93842))+~P1(f334(f334(f249(a1),x93843),x93844))+~P1(f334(f334(f248(a1),f334(f334(f80(a1),f334(f334(f81(a1),x93843),x93842)),x93845)),f334(f334(f80(a1),f334(f334(f81(a1),x93843),x93841)),x93844)))
% 160.93/160.66 [9386]~P1(f334(f334(f248(a1),f2(a1)),x93865))+P1(f334(f334(f248(a1),x93861),x93862))+~P1(f334(f334(f249(a1),x93863),x93864))+~P1(f334(f334(f249(a1),x93865),x93864))+~P1(f334(f334(f248(a1),f334(f334(f80(a1),f334(f334(f81(a1),x93864),x93861)),x93865)),f334(f334(f80(a1),f334(f334(f81(a1),x93864),x93862)),x93863)))
% 160.93/160.66 [9497]~P62(x94975)+E(f334(x94971,f420(x94971,x94972,x94973,x94974,x94975)),f2(x94975))+~P1(f334(f61(x94974),x94973))+~P1(f334(f61(x94974),x94972))+E(f334(f334(f292(x94975),f334(f334(f81(x94975),f334(f334(f9(x94974,x94975),x94971),x94973)),f334(f334(f9(x94974,x94975),x94971),x94972))),f334(f334(f9(x94974,x94975),x94971),f334(f334(f105(f888(x94974,a876)),x94973),x94972))),f334(f334(f9(x94974,x94975),x94971),f334(f334(f114(f888(x94974,a876)),x94973),x94972)))
% 160.93/160.66 [9778]~P62(x97781)+~P1(f334(f61(x97782),x97784))+~P1(f334(f61(x97782),x97785))+E(f334(f334(f292(x97781),f334(f334(f81(x97781),f334(f334(f9(x97782,x97781),x97783),x97784)),f334(f334(f9(x97782,x97781),x97783),x97785))),f334(f334(f9(x97782,x97781),x97783),f334(f334(f105(f888(x97782,a876)),x97784),x97785))),f334(f334(f9(x97782,x97781),x97783),f334(f334(f114(f888(x97782,a876)),x97784),x97785)))+P1(f334(f334(f336(x97782),f420(x97783,x97785,x97784,x97782,x97781)),f334(f334(f105(f888(x97782,a876)),x97784),x97785)))
% 160.93/160.66 [9096]E(f334(f334(f136(x90961),x90962),x90963),f334(f334(f136(x90961),x90964),x90965))+~E(f334(f334(f177(x90961),f334(f197(f882(x90961)),x90964)),x90962),x90964)+~E(f334(f334(f177(x90961),f334(f197(f882(x90961)),x90962)),x90964),x90962)+~E(x90965,f334(f334(f136(x90961),f334(f334(f140(x90961),f334(f197(f882(x90961)),x90964)),x90962)),x90963))+~E(f334(f334(f136(x90961),f334(f334(f140(x90961),f334(f197(f882(x90961)),x90962)),x90964)),x90965),x90963)
% 160.93/160.66 [9495]~P108(x94952)+E(f334(f334(f150(x94951,x94952,x94953),x94954),f172(x94951,x94954,x94955)),x94955)+~P16(x94952,f334(f334(f156(x94951,x94952),x94953),x94955))+~P1(f334(f334(f336(x94951),x94954),f334(f174(x94951),x94955)))+~E(f334(f143(x94951),f334(f138(x94951,f334(f334(f8(x94952,a876,x94951),f334(a331,f334(x94953,x94954))),x94953)),x94955)),x94954)
% 160.93/160.66 [9840]~P70(x98401)+~P1(f334(f66(x98401,x98401,f81(x98401),x98402,x98403),x98405))+~P1(f334(f334(f336(x98401),x98404),x98403))+P1(f334(f334(f336(x98401),x98402),x98403))+P1(f334(f66(x98401,x98401,f81(x98401),x98404,f334(f334(f312(x98401),x98402),f334(f334(f22(f888(x98401,a876)),x98403),f334(f334(f312(x98401),x98404),f196(f888(x98401,a876)))))),x98405))
% 160.93/160.66 [7230]E(x72301,x72302)+~P27(x72304,x72305,x72303,x72306)+~E(f334(x72303,x72301),f334(x72303,x72302))+~P1(f334(f334(f336(x72304),x72302),x72306))+~P1(f334(f334(f336(x72304),x72301),x72306))
% 160.93/160.66 [6491]~P143(x64914)+E(x64911,x64912)+~E(x64915,x64916)+E(x64913,f2(x64914))+~E(f334(f334(f80(x64914),x64915),f334(f334(f81(x64914),x64913),x64911)),f334(f334(f80(x64914),x64916),f334(f334(f81(x64914),x64913),x64912)))
% 160.93/160.66 [7521]~P5(x75211)+~P108(x75211)+~P1(f334(f334(f249(x75211),x75212),f334(x75215,x75216)))+~P1(f334(f334(f336(x75213),x75216),x75214))+P1(f334(f334(f249(x75211),x75212),f334(f334(f41(x75213,x75211),x75214),x75215)))
% 160.93/160.66 [8205]~P5(x82051)+~P108(x82051)+~P1(f334(f334(f249(x82051),f334(x82054,x82056)),x82055))+~P1(f334(f334(f336(x82052),x82056),x82053))+P1(f334(f334(f249(x82051),f334(f334(f42(x82052,x82051),x82053),x82054)),x82055))
% 160.93/160.66 [8464]~P21(x84642,x84645,x84646,x84641)+~P1(f334(f61(x84642),x84644))+~P1(f334(f61(x84642),x84643))+~E(f334(f334(f105(f888(x84642,a876)),x84643),x84644),f196(f888(x84642,a876)))+E(f334(x84641,f334(f334(f114(f888(x84642,a876)),x84643),x84644)),f334(f73(x84645,x84645,x84645,f334(x84641,x84643)),f334(x84641,x84644)))
% 160.93/160.66 [8785]E(x87851,x87852)+~P54(x87854,x87855,x87856,x87853,x87857)+~E(f334(x87853,x87851),f334(x87853,x87852))+~P1(f334(f334(f336(x87855),x87852),x87857))+~P1(f334(f334(f336(x87855),x87851),x87857))
% 160.93/160.66 [10087]~P1(f334(x100872,x100874))+~E(x100875,f334(f138(x100871,x100872),x100877))+E(f334(f138(x100871,x100872),x100873),f334(f334(f153(x100871),x100874),x100875))+~E(x100873,f334(f334(f136(x100871),x100876),f334(f334(f153(x100871),x100874),x100877)))+P1(f334(x100872,f795(x100875,x100874,x100873,x100872,x100871,x100876,x100877)))
% 160.93/160.66 [10088]~P1(f334(x100884,x100882))+~E(x100883,f334(f138(x100881,x100884),x100887))+E(f334(f334(f153(x100881),x100882),x100883),f334(f138(x100881,x100884),x100885))+~E(x100885,f334(f334(f136(x100881),x100886),f334(f334(f153(x100881),x100882),x100887)))+P1(f334(x100884,f794(x100885,x100884,x100883,x100882,x100881,x100886,x100887)))
% 160.93/160.66 [10122]~P1(f334(x101222,x101224))+~E(x101225,f334(f138(x101221,x101222),x101227))+E(f334(f138(x101221,x101222),x101223),f334(f334(f153(x101221),x101224),x101225))+~E(x101223,f334(f334(f136(x101221),x101226),f334(f334(f153(x101221),x101224),x101227)))+P1(f334(f334(f336(x101221),f795(x101225,x101224,x101223,x101222,x101221,x101226,x101227)),f334(f174(x101221),x101226)))
% 160.93/160.66 [10123]~P1(f334(x101234,x101232))+~E(x101233,f334(f138(x101231,x101234),x101237))+E(f334(f334(f153(x101231),x101232),x101233),f334(f138(x101231,x101234),x101235))+~E(x101235,f334(f334(f136(x101231),x101236),f334(f334(f153(x101231),x101232),x101237)))+P1(f334(f334(f336(x101231),f794(x101235,x101234,x101233,x101232,x101231,x101236,x101237)),f334(f174(x101231),x101236)))
% 160.93/160.66 [10126]~P8(x101261,x101267,x101266)+~P14(x101261,f888(x101265,a876),x101266,x101264)+P1(f334(f334(f336(x101261),f545(x101262,x101263,x101264,x101265,x101266,x101267,x101261)),x101267))+~P1(f334(f334(f336(f888(x101261,a876)),x101263),f334(f334(f60(x101261),x101267),x101266)))+P1(f334(f334(f336(f888(x101265,a876)),f334(f334(f41(x101261,f888(x101265,a876)),x101263),x101264)),x101262))
% 160.93/160.66 [10171]~P8(x101712,x101716,x101717)+~P14(x101712,f888(x101711,a876),x101717,x101714)+~P1(f334(f334(f336(f888(x101712,a876)),x101713),f334(f334(f60(x101712),x101716),x101717)))+~P1(f334(f334(f336(f888(x101711,a876)),f334(x101714,f545(x101715,x101713,x101714,x101711,x101717,x101716,x101712))),x101715))+P1(f334(f334(f336(f888(x101711,a876)),f334(f334(f41(x101712,f888(x101711,a876)),x101713),x101714)),x101715))
% 160.93/160.66 [8380]~P74(x83802)+~P27(x83801,x83805,x83808,x83804)+~E(x83803,f334(f73(x83805,x83802,x83801,x83806),x83808))+~E(x83807,f334(f313(x83801,x83805,x83808),x83804))+E(f334(f334(f9(x83801,x83802),x83803),x83804),f334(f334(f9(x83805,x83802),x83806),x83807))
% 160.93/160.66 [10175]~P74(x101752)+~P27(x101755,x101751,x101758,x101757)+~E(f334(x101756,f556(x101753,x101756,x101754,x101757,x101758,x101751,x101755,x101752)),f334(f334(f73(x101751,x101752,x101755,x101753),x101758),f556(x101753,x101756,x101754,x101757,x101758,x101751,x101755,x101752)))+~E(x101754,f334(f313(x101755,x101751,x101758),x101757))+E(f334(f334(f9(x101751,x101752),x101753),x101754),f334(f334(f9(x101755,x101752),x101756),x101757))
% 160.93/160.66 [10177]~P68(x101772)+~P27(x101771,x101775,x101778,x101774)+~E(x101777,f334(f313(x101771,x101775,x101778),x101774))+E(f334(f334(f6(x101771,x101772),x101773),x101774),f334(f334(f6(x101775,x101772),x101776),x101777))+P1(f334(f334(f336(x101771),f625(x101776,x101773,x101777,x101774,x101778,x101775,x101771,x101772)),x101774))
% 160.93/160.66 [10178]~P74(x101782)+~P27(x101781,x101785,x101788,x101784)+~E(x101787,f334(f313(x101781,x101785,x101788),x101784))+E(f334(f334(f9(x101781,x101782),x101783),x101784),f334(f334(f9(x101785,x101782),x101786),x101787))+P1(f334(f334(f336(x101781),f556(x101786,x101783,x101787,x101784,x101788,x101785,x101781,x101782)),x101784))
% 160.93/160.66 [10184]~P68(x101842)+~P27(x101845,x101841,x101848,x101847)+~E(x101844,f334(f313(x101845,x101841,x101848),x101847))+~E(f334(x101846,f625(x101843,x101846,x101844,x101847,x101848,x101841,x101845,x101842)),f334(x101843,f334(x101848,f625(x101843,x101846,x101844,x101847,x101848,x101841,x101845,x101842))))+E(f334(f334(f6(x101841,x101842),x101843),x101844),f334(f334(f6(x101845,x101842),x101846),x101847))
% 160.93/160.66 [9554]~E(f334(f197(f882(x95542)),x95545),f334(f197(f882(x95541)),x95543))+~E(f334(f197(f882(x95542)),x95544),f334(f197(f882(x95541)),x95543))+~E(f334(f334(f334(f72(x95541,f885(x95542)),f334(f180(x95541,x95542),f334(f334(f184(x95541,x95542),x95543),x95544))),x95546),f334(f241(x95542),x95547)),f334(f334(f334(f72(x95541,f885(x95542)),f334(f180(x95541,x95542),f334(f334(f184(x95541,x95542),x95543),x95545))),x95546),f334(f241(x95542),x95548)))+E(f334(f180(x95541,x95542),f334(f334(f184(x95541,x95542),x95543),x95544)),f334(f180(x95541,x95542),f334(f334(f184(x95541,x95542),x95543),x95545)))+P1(f334(f334(f336(x95541),x95546),f334(f174(x95541),x95543)))
% 160.93/160.66 [9669]~P25(x96696,x96692,x96695,x96697,x96698,x96691)+~P1(f334(f61(x96692),x96694))+~P1(f334(f61(x96692),x96693))+~E(f334(f334(f105(f888(x96692,a876)),x96693),x96694),f196(f888(x96692,a876)))+E(f334(x96691,f334(f334(f114(f888(x96692,a876)),x96693),x96694)),f334(f334(x96695,f334(x96691,x96693)),f334(x96691,x96694)))
% 160.93/160.66 [10074]~P25(x100748,x100742,x100745,x100747,x100746,x100741)+~E(f334(x100746,f781(x100744,x100743,x100741,x100746,x100747,x100745,x100742)),x100747)+~P1(f334(f61(x100742),x100743))+~P1(f334(f61(x100742),x100744))+E(f334(x100741,f334(f334(f114(f888(x100742,a876)),x100743),x100744)),f334(f334(x100745,f334(x100741,x100743)),f334(x100741,x100744)))
% 160.93/160.66 [10131]~P25(x101318,x101312,x101315,x101317,x101316,x101311)+~P1(f334(f61(x101312),x101313))+~P1(f334(f61(x101312),x101314))+E(f334(x101311,f334(f334(f114(f888(x101312,a876)),x101313),x101314)),f334(f334(x101315,f334(x101311,x101313)),f334(x101311,x101314)))+P1(f334(f334(f336(x101312),f781(x101314,x101313,x101311,x101316,x101317,x101315,x101312)),f334(f334(f105(f888(x101312,a876)),x101313),x101314)))
% 160.93/160.66 [9828]~P8(x98284,x98288,x98285)+~P8(x98281,x98289,x98283)+~P15(x98281,x98284,f888(x98282,a876),x98283,x98285,x98287)+P14(x98281,f888(x98282,a876),x98283,f334(f334(f8(f888(x98284,f888(x98282,a876)),f888(x98282,a876),x98281),f334(f41(x98284,f888(x98282,a876)),f334(f288(x98284,x98284,x98285),f334(f334(f312(x98284),x98286),f196(f888(x98284,a876)))))),x98287))+~P1(f334(f334(f336(x98284),x98286),x98288))
% 160.93/160.66 [5420]~P108(x54203)+~P16(x54203,x54201)+E(x54201,f765(x54202,x54203))+~E(f334(f174(x54203),x54201),x54202)+~P1(f334(f61(x54203),x54202))+~P1(f334(f139(x54203),x54201))
% 160.93/160.66 [5045]~P136(x50452)+~P130(x50452)+~P131(x50452)+~P113(x50452)+E(x50451,f2(x50452))+~E(f334(f334(f259(x50452),x50451),x50453),f2(x50452))
% 160.93/160.66 [5046]~P136(x50462)+~P130(x50462)+~P131(x50462)+~P113(x50462)+~E(x50461,f2(a881))+~E(f334(f334(f259(x50462),x50463),x50461),f2(x50462))
% 160.93/160.66 [6473]~P81(x64731)+~E(x64733,f2(x64731))+~E(x64732,f2(x64731))+E(f334(f334(f80(x64731),x64732),x64733),f2(x64731))+~P1(f334(f334(f248(x64731),f2(x64731)),x64733))+~P1(f334(f334(f248(x64731),f2(x64731)),x64732))
% 160.93/160.66 [8846]~E(f334(f268(a881,a881),x88463),f2(a881))+~E(x88461,f334(f334(f80(a881),f334(f334(f81(a881),f334(f268(a881,a881),x88463)),x88462)),f334(f272(a881,a881),x88463)))+P1(f334(f47(x88461,x88462),x88463))+~P1(f334(f334(f248(a881),f334(f272(a881,a881),x88463)),f2(a881)))+P1(f334(f334(f249(a881),f2(a881)),x88462))+~P1(f334(f334(f249(a881),x88462),f334(f272(a881,a881),x88463)))
% 160.93/160.66 [8854]E(x88541,f2(a881))+~E(x88542,f334(f334(f80(a881),f334(f334(f81(a881),f334(f268(a881,a881),x88543)),x88541)),f334(f272(a881,a881),x88543)))+P1(f334(f47(x88542,x88541),x88543))+~P1(f334(f334(f249(a881),f2(a881)),x88541))+~P1(f334(f334(f248(a881),f2(a881)),f334(f272(a881,a881),x88543)))+~P1(f334(f334(f249(a881),f334(f272(a881,a881),x88543)),x88541))
% 160.93/160.66 [8872]~E(f334(f268(a881,a881),x88723),f2(a881))+~E(x88721,f334(f334(f80(a881),f334(f334(f81(a881),f334(f268(a881,a881),x88723)),x88722)),f334(f272(a881,a881),x88723)))+P1(f334(f47(x88721,x88722),x88723))+~P1(f334(f334(f249(a881),f2(a881)),x88722))+~P1(f334(f334(f248(a881),f2(a881)),f334(f272(a881,a881),x88723)))+~P1(f334(f334(f249(a881),f334(f272(a881,a881),x88723)),x88722))
% 160.93/160.66 [6854]~P2(x68542)+E(x68541,f196(f888(x68542,a876)))+E(x68543,f196(f888(x68542,a876)))+~P1(f334(f61(x68542),x68541))+~P1(f334(f61(x68542),x68543))+E(f10(x68542,f334(f334(f114(f888(x68542,a876)),x68543),x68541)),f334(f334(f114(x68542),f10(x68542,x68543)),f10(x68542,x68541)))
% 160.93/160.66 [6855]~P2(x68552)+E(x68551,f196(f888(x68552,a876)))+E(x68553,f196(f888(x68552,a876)))+~P1(f334(f61(x68552),x68551))+~P1(f334(f61(x68552),x68553))+E(f11(x68552,f334(f334(f114(f888(x68552,a876)),x68553),x68551)),f334(f334(f105(x68552),f11(x68552,x68553)),f11(x68552,x68551)))
% 160.93/160.66 [6856]~P108(x68562)+E(x68561,f196(f888(x68562,a876)))+E(x68563,f196(f888(x68562,a876)))+~P1(f334(f61(x68562),x68561))+~P1(f334(f61(x68562),x68563))+E(f14(x68562,f334(f334(f114(f888(x68562,a876)),x68563),x68561)),f334(f334(f246(x68562),f14(x68562,x68563)),f14(x68562,x68561)))
% 160.93/160.66 [6857]~P108(x68572)+E(x68571,f196(f888(x68572,a876)))+E(x68573,f196(f888(x68572,a876)))+~P1(f334(f61(x68572),x68571))+~P1(f334(f61(x68572),x68573))+E(f15(x68572,f334(f334(f114(f888(x68572,a876)),x68573),x68571)),f334(f334(f247(x68572),f15(x68572,x68573)),f15(x68572,x68571)))
% 160.93/160.66 [7496]~P95(x74962)+E(x74961,f196(f888(x74962,a876)))+E(x74963,f196(f888(x74962,a876)))+~P1(f334(f61(x74962),x74961))+~P1(f334(f61(x74962),x74963))+E(f334(f334(f81(x74962),f334(f63(x74962,f81(x74962)),x74963)),f334(f63(x74962,f81(x74962)),x74961)),f334(f63(x74962,f81(x74962)),f334(f334(f114(f888(x74962,a876)),x74963),x74961)))
% 160.93/160.66 [7656]~P108(x76562)+E(x76561,f196(f888(x76562,a876)))+E(x76563,f196(f888(x76562,a876)))+~P1(f334(f61(x76562),x76561))+~P1(f334(f61(x76562),x76563))+E(f334(f334(f247(x76562),f12(x76562,f247(x76562),x76563)),f12(x76562,f247(x76562),x76561)),f12(x76562,f247(x76562),f334(f334(f114(f888(x76562,a876)),x76563),x76561)))
% 160.93/160.66 [7657]~P108(x76572)+E(x76571,f196(f888(x76572,a876)))+E(x76573,f196(f888(x76572,a876)))+~P1(f334(f61(x76572),x76571))+~P1(f334(f61(x76572),x76573))+E(f334(f334(f246(x76572),f13(x76572,f246(x76572),x76573)),f13(x76572,f246(x76572),x76571)),f13(x76572,f246(x76572),f334(f334(f114(f888(x76572,a876)),x76573),x76571)))
% 160.93/160.66 [8695]~P1(f334(x86951,x86953))+P1(f334(x86951,f398(x86951,x86952)))+P1(f334(x86951,f391(x86951,x86952)))+~P1(f334(f334(f249(a1),f2(a1)),x86952))+~P1(f334(f334(f336(a1),x86953),f305(a1,f78(a1),x86952)))+P1(f334(x86951,f334(f334(f22(a1),f391(x86951,x86952)),f334(f334(f81(a1),f397(x86951,x86952)),x86952))))
% 160.93/160.66 [8993]~P1(f334(x89931,x89933))+~P1(f334(x89931,f391(x89931,x89932)))+P1(f334(x89931,f398(x89931,x89932)))+~P1(f334(f334(f249(a1),f2(a1)),x89932))+~P1(f334(f334(f336(a1),x89933),f305(a1,f78(a1),x89932)))+~P1(f334(x89931,f334(f334(f22(a1),f391(x89931,x89932)),f334(f334(f81(a1),f397(x89931,x89932)),x89932))))
% 160.93/160.66 [10209]~P97(x102092)+E(x102091,f196(f888(x102092,a876)))+E(x102093,f196(f888(x102092,a876)))+~P1(f334(f61(x102092),x102091))+~P1(f334(f61(x102092),x102093))+E(f11(x102092,f334(f254(x102092),f334(f334(f8(f888(x102092,a876),a876,x102092),f87(x102092)),f334(f334(f8(f888(x102092,f888(x102092,a876)),f888(x102092,a876),x102092),f334(f8(f888(x102092,a876),a876,x102092),f87(x102092))),f334(f334(f7(x102092,f888(x102092,f888(x102092,a876)),f888(x102092,f888(x102092,a876))),f334(f334(f8(f888(x102092,f888(f888(x102092,a876),f888(x102092,a876))),f888(f888(x102092,f888(x102092,a876)),f888(x102092,f888(x102092,a876))),x102092),f18(x102092,f888(x102092,a876),f888(x102092,a876))),f334(f334(f8(f888(x102092,f888(x102092,f888(a876,a876))),f888(x102092,f888(f888(x102092,a876),f888(x102092,a876))),x102092),f334(f8(f888(x102092,f888(a876,a876)),f888(f888(x102092,a876),f888(x102092,a876)),x102092),f18(x102092,a876,a876))),f334(f334(f8(f888(x102092,f888(x102092,a876)),f888(x102092,f888(x102092,f888(a876,a876))),x102092),f334(f8(f888(x102092,a876),f888(x102092,f888(a876,a876)),x102092),f334(f8(a876,f888(a876,a876),x102092),a332))),f334(f334(f7(x102092,f888(x102092,f888(x102092,x102092)),f888(x102092,f888(x102092,a876))),f334(f334(f8(f888(f888(x102092,x102092),f888(x102092,a876)),f888(f888(x102092,f888(x102092,x102092)),f888(x102092,f888(x102092,a876))),x102092),f8(f888(x102092,x102092),f888(x102092,a876),x102092)),f334(f334(f8(f888(x102092,a876),f888(f888(x102092,x102092),f888(x102092,a876)),x102092),f8(x102092,a876,x102092)),a331))),f114(x102092)))))),f334(f334(f7(x102092,f888(x102092,a876),f888(x102092,a876)),f334(f334(f8(f888(a876,a876),f888(f888(x102092,a876),f888(x102092,a876)),x102092),f8(a876,a876,x102092)),f334(f334(f8(a876,f888(a876,a876),x102092),a332),f334(f334(f7(x102092,f888(x102092,a876),a876),f336(x102092)),x102093)))),f334(f334(f7(x102092,f888(x102092,a876),a876),f336(x102092)),x102091))))))),f334(f334(f114(x102092),f11(x102092,x102093)),f11(x102092,x102091)))
% 160.93/160.66 [10210]~P97(x102102)+E(x102101,f196(f888(x102102,a876)))+E(x102103,f196(f888(x102102,a876)))+~P1(f334(f61(x102102),x102101))+~P1(f334(f61(x102102),x102103))+E(f10(x102102,f334(f254(x102102),f334(f334(f8(f888(x102102,a876),a876,x102102),f87(x102102)),f334(f334(f8(f888(x102102,f888(x102102,a876)),f888(x102102,a876),x102102),f334(f8(f888(x102102,a876),a876,x102102),f87(x102102))),f334(f334(f7(x102102,f888(x102102,f888(x102102,a876)),f888(x102102,f888(x102102,a876))),f334(f334(f8(f888(x102102,f888(f888(x102102,a876),f888(x102102,a876))),f888(f888(x102102,f888(x102102,a876)),f888(x102102,f888(x102102,a876))),x102102),f18(x102102,f888(x102102,a876),f888(x102102,a876))),f334(f334(f8(f888(x102102,f888(x102102,f888(a876,a876))),f888(x102102,f888(f888(x102102,a876),f888(x102102,a876))),x102102),f334(f8(f888(x102102,f888(a876,a876)),f888(f888(x102102,a876),f888(x102102,a876)),x102102),f18(x102102,a876,a876))),f334(f334(f8(f888(x102102,f888(x102102,a876)),f888(x102102,f888(x102102,f888(a876,a876))),x102102),f334(f8(f888(x102102,a876),f888(x102102,f888(a876,a876)),x102102),f334(f8(a876,f888(a876,a876),x102102),a332))),f334(f334(f7(x102102,f888(x102102,f888(x102102,x102102)),f888(x102102,f888(x102102,a876))),f334(f334(f8(f888(f888(x102102,x102102),f888(x102102,a876)),f888(f888(x102102,f888(x102102,x102102)),f888(x102102,f888(x102102,a876))),x102102),f8(f888(x102102,x102102),f888(x102102,a876),x102102)),f334(f334(f8(f888(x102102,a876),f888(f888(x102102,x102102),f888(x102102,a876)),x102102),f8(x102102,a876,x102102)),a331))),f105(x102102)))))),f334(f334(f7(x102102,f888(x102102,a876),f888(x102102,a876)),f334(f334(f8(f888(a876,a876),f888(f888(x102102,a876),f888(x102102,a876)),x102102),f8(a876,a876,x102102)),f334(f334(f8(a876,f888(a876,a876),x102102),a332),f334(f334(f7(x102102,f888(x102102,a876),a876),f336(x102102)),x102103)))),f334(f334(f7(x102102,f888(x102102,a876),a876),f336(x102102)),x102101))))))),f334(f334(f105(x102102),f10(x102102,x102103)),f10(x102102,x102101)))
% 160.93/160.66 [10211]~P108(x102112)+E(x102111,f196(f888(x102112,a876)))+E(x102113,f196(f888(x102112,a876)))+~P1(f334(f61(x102112),x102111))+~P1(f334(f61(x102112),x102113))+E(f12(x102112,f247(x102112),f334(f254(x102112),f334(f334(f8(f888(x102112,a876),a876,x102112),f87(x102112)),f334(f334(f8(f888(x102112,f888(x102112,a876)),f888(x102112,a876),x102112),f334(f8(f888(x102112,a876),a876,x102112),f87(x102112))),f334(f334(f7(x102112,f888(x102112,f888(x102112,a876)),f888(x102112,f888(x102112,a876))),f334(f334(f8(f888(x102112,f888(f888(x102112,a876),f888(x102112,a876))),f888(f888(x102112,f888(x102112,a876)),f888(x102112,f888(x102112,a876))),x102112),f18(x102112,f888(x102112,a876),f888(x102112,a876))),f334(f334(f8(f888(x102112,f888(x102112,f888(a876,a876))),f888(x102112,f888(f888(x102112,a876),f888(x102112,a876))),x102112),f334(f8(f888(x102112,f888(a876,a876)),f888(f888(x102112,a876),f888(x102112,a876)),x102112),f18(x102112,a876,a876))),f334(f334(f8(f888(x102112,f888(x102112,a876)),f888(x102112,f888(x102112,f888(a876,a876))),x102112),f334(f8(f888(x102112,a876),f888(x102112,f888(a876,a876)),x102112),f334(f8(a876,f888(a876,a876),x102112),a332))),f334(f334(f7(x102112,f888(x102112,f888(x102112,x102112)),f888(x102112,f888(x102112,a876))),f334(f334(f8(f888(f888(x102112,x102112),f888(x102112,a876)),f888(f888(x102112,f888(x102112,x102112)),f888(x102112,f888(x102112,a876))),x102112),f8(f888(x102112,x102112),f888(x102112,a876),x102112)),f334(f334(f8(f888(x102112,a876),f888(f888(x102112,x102112),f888(x102112,a876)),x102112),f8(x102112,a876,x102112)),a331))),f246(x102112)))))),f334(f334(f7(x102112,f888(x102112,a876),f888(x102112,a876)),f334(f334(f8(f888(a876,a876),f888(f888(x102112,a876),f888(x102112,a876)),x102112),f8(a876,a876,x102112)),f334(f334(f8(a876,f888(a876,a876),x102112),a332),f334(f334(f7(x102112,f888(x102112,a876),a876),f336(x102112)),x102113)))),f334(f334(f7(x102112,f888(x102112,a876),a876),f336(x102112)),x102111))))))),f334(f334(f246(x102112),f12(x102112,f247(x102112),x102113)),f12(x102112,f247(x102112),x102111)))
% 160.93/160.66 [10212]~P108(x102122)+E(x102121,f196(f888(x102122,a876)))+E(x102123,f196(f888(x102122,a876)))+~P1(f334(f61(x102122),x102121))+~P1(f334(f61(x102122),x102123))+E(f13(x102122,f246(x102122),f334(f254(x102122),f334(f334(f8(f888(x102122,a876),a876,x102122),f87(x102122)),f334(f334(f8(f888(x102122,f888(x102122,a876)),f888(x102122,a876),x102122),f334(f8(f888(x102122,a876),a876,x102122),f87(x102122))),f334(f334(f7(x102122,f888(x102122,f888(x102122,a876)),f888(x102122,f888(x102122,a876))),f334(f334(f8(f888(x102122,f888(f888(x102122,a876),f888(x102122,a876))),f888(f888(x102122,f888(x102122,a876)),f888(x102122,f888(x102122,a876))),x102122),f18(x102122,f888(x102122,a876),f888(x102122,a876))),f334(f334(f8(f888(x102122,f888(x102122,f888(a876,a876))),f888(x102122,f888(f888(x102122,a876),f888(x102122,a876))),x102122),f334(f8(f888(x102122,f888(a876,a876)),f888(f888(x102122,a876),f888(x102122,a876)),x102122),f18(x102122,a876,a876))),f334(f334(f8(f888(x102122,f888(x102122,a876)),f888(x102122,f888(x102122,f888(a876,a876))),x102122),f334(f8(f888(x102122,a876),f888(x102122,f888(a876,a876)),x102122),f334(f8(a876,f888(a876,a876),x102122),a332))),f334(f334(f7(x102122,f888(x102122,f888(x102122,x102122)),f888(x102122,f888(x102122,a876))),f334(f334(f8(f888(f888(x102122,x102122),f888(x102122,a876)),f888(f888(x102122,f888(x102122,x102122)),f888(x102122,f888(x102122,a876))),x102122),f8(f888(x102122,x102122),f888(x102122,a876),x102122)),f334(f334(f8(f888(x102122,a876),f888(f888(x102122,x102122),f888(x102122,a876)),x102122),f8(x102122,a876,x102122)),a331))),f247(x102122)))))),f334(f334(f7(x102122,f888(x102122,a876),f888(x102122,a876)),f334(f334(f8(f888(a876,a876),f888(f888(x102122,a876),f888(x102122,a876)),x102122),f8(a876,a876,x102122)),f334(f334(f8(a876,f888(a876,a876),x102122),a332),f334(f334(f7(x102122,f888(x102122,a876),a876),f336(x102122)),x102123)))),f334(f334(f7(x102122,f888(x102122,a876),a876),f336(x102122)),x102121))))))),f334(f334(f247(x102122),f13(x102122,f246(x102122),x102123)),f13(x102122,f246(x102122),x102121)))
% 160.93/160.66 [7179]~P106(x71793)+E(x71791,x71792)+~E(f334(f334(f259(x71793),x71791),x71794),f334(f334(f259(x71793),x71792),x71794))+~P1(f334(f334(f248(x71793),f2(x71793)),x71792))+~P1(f334(f334(f248(x71793),f2(x71793)),x71791))+~P1(f334(f334(f249(a881),f2(a881)),x71794))
% 160.93/160.66 [7453]~P108(x74532)+E(x74531,f196(f888(x74532,a876)))+~P1(f334(f61(x74532),x74531))+~P1(f334(f334(f336(x74532),x74534),x74531))+P1(f334(f334(f249(x74532),x74533),x74534))+~P1(f334(f334(f249(x74532),x74533),f334(f63(x74532,f246(x74532)),x74531)))
% 160.93/160.66 [7454]~P100(x74542)+E(x74541,f196(f888(x74542,a876)))+~P1(f334(f61(x74542),x74541))+~P1(f334(f334(f336(x74542),x74544),x74541))+P1(f334(f334(f248(x74542),x74543),x74544))+~P1(f334(f334(f248(x74542),x74543),f334(f63(x74542,f105(x74542)),x74541)))
% 160.93/160.66 [7455]~P108(x74552)+E(x74551,f196(f888(x74552,a876)))+~P1(f334(f61(x74552),x74551))+~P1(f334(f334(f336(x74552),x74554),x74551))+P1(f334(f334(f248(x74552),x74553),x74554))+~P1(f334(f334(f248(x74552),x74553),f334(f63(x74552,f246(x74552)),x74551)))
% 160.93/160.66 [7355]E(x73551,f2(a1))+E(f334(f334(f38(a1),x73552),x73551),x73553)+~P1(f334(f334(f248(a1),x73554),f2(a1)))+~E(x73552,f334(f334(f80(a1),f334(f334(f81(a1),x73551),x73553)),x73554))+P1(f334(f334(f249(a1),f2(a1)),x73551))+~P1(f334(f334(f249(a1),x73551),x73554))
% 160.93/160.66 [7370]E(f44(a1,x73702,x73701),x73703)+E(x73701,f2(a1))+~P1(f334(f334(f248(a1),x73703),f2(a1)))+~E(x73702,f334(f334(f80(a1),f334(f334(f81(a1),x73701),x73704)),x73703))+P1(f334(f334(f249(a1),f2(a1)),x73701))+~P1(f334(f334(f249(a1),x73701),x73703))
% 160.93/160.66 [7495]E(x74951,f2(a1))+E(f334(f334(f38(a1),x74952),x74951),x74953)+~E(x74952,f334(f334(f80(a1),f334(f334(f81(a1),x74951),x74953)),x74954))+~P1(f334(f334(f249(a1),f2(a1)),x74951))+~P1(f334(f334(f248(a1),f2(a1)),x74954))+~P1(f334(f334(f249(a1),x74954),x74951))
% 160.93/160.66 [7517]E(f44(a1,x75172,x75171),x75173)+E(x75171,f2(a1))+~E(x75172,f334(f334(f80(a1),f334(f334(f81(a1),x75171),x75174)),x75173))+~P1(f334(f334(f249(a1),f2(a1)),x75171))+~P1(f334(f334(f248(a1),f2(a1)),x75173))+~P1(f334(f334(f249(a1),x75173),x75171))
% 160.93/160.66 [7660]~P108(x76602)+E(x76601,f196(f888(x76602,a876)))+~P1(f334(f61(x76602),x76601))+~P1(f334(f334(f249(x76602),x76604),x76603))+~P1(f334(f334(f336(x76602),x76604),x76601))+P1(f334(f334(f249(x76602),f334(f63(x76602,f246(x76602)),x76601)),x76603))
% 160.93/160.66 [7661]~P108(x76612)+E(x76611,f196(f888(x76612,a876)))+~P1(f334(f61(x76612),x76611))+~P1(f334(f334(f248(x76612),x76614),x76613))+~P1(f334(f334(f336(x76612),x76614),x76611))+P1(f334(f334(f248(x76612),f334(f63(x76612,f246(x76612)),x76611)),x76613))
% 160.93/160.66 [8236]~P1(f334(f334(f248(a1),x82364),f2(a1)))+~E(x82361,f334(f334(f80(a1),f334(f334(f81(a1),x82362),x82363)),x82364))+~P1(f334(f334(f248(a1),f2(a1)),x82364))+~P1(f334(f334(f249(a1),x82364),x82362))+~P1(f334(f334(f249(a1),x82362),x82364))+P1(f334(f48(x82361,x82362),f334(f334(f269(a1,a1),x82363),x82364)))
% 160.93/160.66 [9189]~P60(x91893)+~P60(x91894)+E(x91891,x91892)+~E(f334(f197(f882(x91893)),x91892),f334(f197(f882(x91894)),f55(x91894)))+~E(f334(f197(f882(x91893)),x91891),f334(f197(f882(x91894)),f55(x91894)))+~E(f334(f73(f885(x91893),x91893,x91894,f245(x91893)),f334(f180(x91894,x91893),f334(f334(f184(x91894,x91893),f55(x91894)),x91891))),f334(f73(f885(x91893),x91893,x91894,f245(x91893)),f334(f180(x91894,x91893),f334(f334(f184(x91894,x91893),f55(x91894)),x91892))))
% 160.93/160.66 [8400]~P109(x84001)+P1(f334(f334(f249(f888(x84001,a876)),f305(x84001,x84002,x84003)),f305(x84001,x84004,x84005)))+~P1(f334(f334(f249(x84001),x84003),x84005))+~P1(f334(f334(f248(x84001),x84004),x84002))+~P1(f334(f334(f248(x84001),x84004),x84005))+~P1(f334(f334(f248(x84001),x84003),x84005))
% 160.93/160.66 [8401]~P109(x84011)+P1(f334(f334(f249(f888(x84011,a876)),f305(x84011,x84012,x84013)),f305(x84011,x84014,x84015)))+~P1(f334(f334(f249(x84011),x84014),x84012))+~P1(f334(f334(f248(x84011),x84013),x84015))+~P1(f334(f334(f248(x84011),x84014),x84015))+~P1(f334(f334(f248(x84011),x84014),x84012))
% 160.93/160.66 [9254]P56(x92542,x92543,x92544,x92541)+E(x92541,f196(f888(x92542,a876)))+~P1(f334(f61(x92542),x92544))+~P1(f334(f61(x92542),x92541))+~P1(f334(f334(x92543,f559(x92541,x92544,x92543,x92542)),x92545))+~P1(f334(f334(f336(x92542),x92545),x92541))
% 160.93/160.66 [9402]~E(x94023,x94025)+~P68(x94021)+~P74(x94021)+~P40(x94023)+E(f334(f334(f6(a1,x94021),x94022),x94023),f334(f334(f6(a1,x94021),x94024),x94025))+P1(f334(f334(f248(a1),f2(a1)),f444(x94022,x94024,x94023,x94025,x94021)))
% 160.93/160.66 [9403]~E(x94033,x94035)+~P68(x94031)+~P74(x94031)+~P40(x94033)+E(f334(f334(f9(a1,x94031),x94032),x94033),f334(f334(f9(a1,x94031),x94034),x94035))+P1(f334(f334(f248(a1),f2(a1)),f439(x94032,x94034,x94033,x94035,x94031)))
% 160.93/160.66 [9575]~E(x95755,x95753)+~P68(x95751)+~P74(x95751)+~P40(x95755)+~E(f334(x95752,f444(x95754,x95752,x95755,x95753,x95751)),f334(x95754,f444(x95754,x95752,x95755,x95753,x95751)))+E(f334(f334(f6(a1,x95751),x95752),x95753),f334(f334(f6(a1,x95751),x95754),x95755))
% 160.93/160.66 [9576]~E(x95765,x95763)+~P68(x95761)+~P74(x95761)+~P40(x95765)+~E(f334(x95762,f439(x95764,x95762,x95765,x95763,x95761)),f334(x95764,f439(x95764,x95762,x95765,x95763,x95761)))+E(f334(f334(f9(a1,x95761),x95762),x95763),f334(f334(f9(a1,x95761),x95764),x95765))
% 160.93/160.66 [9666]~P83(x96663)+E(f334(x96661,x96662),f2(x96663))+~E(f334(f334(f6(x96664,x96663),x96661),x96665),f2(x96663))+~P1(f334(f61(x96664),x96665))+P1(f334(f334(f336(x96664),f406(x96662,x96661,x96665,x96664,x96663)),x96665))+~P1(f334(f334(f336(x96664),x96662),x96665))
% 160.93/160.66 [9802]~P83(x98023)+E(f334(x98021,x98022),f2(x98023))+~E(f334(f334(f6(x98024,x98023),x98021),x98025),f2(x98023))+~P1(f334(f61(x98024),x98025))+~P1(f334(f334(f336(x98024),x98022),x98025))+~P1(f334(f334(f248(x98023),f2(x98023)),f334(x98021,f406(x98022,x98021,x98025,x98024,x98023))))
% 160.93/160.66 [8317]~P126(x83171)+~P1(f334(f334(f248(x83171),f2(x83171)),x83173))+~P1(f334(f334(f249(x83171),x83173),x83175))+~P1(f334(f334(f249(x83171),x83172),x83174))+~P1(f334(f334(f249(x83171),f2(x83171)),x83174))+P1(f334(f334(f249(x83171),f334(f334(f81(x83171),x83172),x83173)),f334(f334(f81(x83171),x83174),x83175)))
% 160.93/160.66 [8318]~P126(x83181)+~P1(f334(f334(f248(x83181),f2(x83181)),x83183))+~P1(f334(f334(f248(x83181),f2(x83181)),x83182))+~P1(f334(f334(f249(x83181),x83183),x83185))+~P1(f334(f334(f249(x83181),x83182),x83184))+P1(f334(f334(f249(x83181),f334(f334(f81(x83181),x83182),x83183)),f334(f334(f81(x83181),x83184),x83185)))
% 160.93/160.66 [8319]~P126(x83191)+~P1(f334(f334(f248(x83191),x83192),x83194))+~P1(f334(f334(f248(x83191),f2(x83191)),x83193))+~P1(f334(f334(f249(x83191),x83193),x83195))+~P1(f334(f334(f249(x83191),f2(x83191)),x83192))+P1(f334(f334(f249(x83191),f334(f334(f81(x83191),x83192),x83193)),f334(f334(f81(x83191),x83194),x83195)))
% 160.93/160.66 [8320]~P126(x83201)+~P1(f334(f334(f248(x83201),x83203),x83205))+~P1(f334(f334(f248(x83201),f2(x83201)),x83202))+~P1(f334(f334(f249(x83201),x83202),x83204))+~P1(f334(f334(f249(x83201),f2(x83201)),x83203))+P1(f334(f334(f249(x83201),f334(f334(f81(x83201),x83202),x83203)),f334(f334(f81(x83201),x83204),x83205)))
% 160.93/160.66 [8321]~P64(x83211)+~P1(f334(f334(f248(x83211),x83212),x83214))+~P1(f334(f334(f249(x83211),x83215),x83213))+~P1(f334(f334(f249(x83211),f2(x83211)),x83215))+~P1(f334(f334(f249(x83211),f2(x83211)),x83212))+P1(f334(f334(f249(x83211),f334(f334(f292(x83211),x83212),x83213)),f334(f334(f292(x83211),x83214),x83215)))
% 160.93/160.66 [8322]~P64(x83221)+~P1(f334(f334(f248(x83221),x83225),x83223))+~P1(f334(f334(f248(x83221),f2(x83221)),x83222))+~P1(f334(f334(f249(x83221),x83222),x83224))+~P1(f334(f334(f249(x83221),f2(x83221)),x83225))+P1(f334(f334(f249(x83221),f334(f334(f292(x83221),x83222),x83223)),f334(f334(f292(x83221),x83224),x83225)))
% 160.93/160.66 [8323]~P134(x83231)+~P1(f334(f334(f248(x83231),x83233),x83235))+~P1(f334(f334(f248(x83231),x83232),x83234))+~P1(f334(f334(f248(x83231),f2(x83231)),x83233))+~P1(f334(f334(f248(x83231),f2(x83231)),x83234))+P1(f334(f334(f248(x83231),f334(f334(f81(x83231),x83232),x83233)),f334(f334(f81(x83231),x83234),x83235)))
% 160.93/160.66 [8324]~P134(x83241)+~P1(f334(f334(f248(x83241),x83243),x83245))+~P1(f334(f334(f248(x83241),x83242),x83244))+~P1(f334(f334(f248(x83241),f2(x83241)),x83243))+~P1(f334(f334(f248(x83241),f2(x83241)),x83242))+P1(f334(f334(f248(x83241),f334(f334(f81(x83241),x83242),x83243)),f334(f334(f81(x83241),x83244),x83245)))
% 160.93/160.66 [8325]~P64(x83251)+~P1(f334(f334(f249(x83251),f2(x83251)),x83255))+~P1(f334(f334(f248(x83251),x83255),x83253))+~P1(f334(f334(f248(x83251),x83252),x83254))+~P1(f334(f334(f248(x83251),f2(x83251)),x83252))+P1(f334(f334(f248(x83251),f334(f334(f292(x83251),x83252),x83253)),f334(f334(f292(x83251),x83254),x83255)))
% 160.93/160.66 [9706]~P68(x97065)+~P86(x97065)+E(x97061,f196(f888(x97062,a876)))+~P1(f334(f61(x97062),x97061))+P1(f334(f334(f336(x97062),f855(x97063,x97064,x97061,x97062,x97065)),x97061))+P1(f334(f334(f249(x97065),f334(f334(f6(x97062,x97065),x97064),x97061)),f334(f334(f6(x97062,x97065),x97063),x97061)))
% 160.93/160.66 [9824]~P68(x98241)+~P84(x98241)+~P1(f334(f61(x98242),x98245))+~P1(f334(f334(f248(x98241),f2(x98241)),f334(x98243,f408(x98243,x98244,x98245,x98242,x98241))))+P1(f334(f334(f248(x98241),f334(f334(f6(x98242,x98241),x98243),x98244)),f334(f334(f6(x98242,x98241),x98243),x98245)))+~P1(f334(f334(f248(f888(x98242,a876)),x98244),x98245))
% 160.93/160.66 [9993]~P68(x99933)+~P86(x99933)+E(x99931,f196(f888(x99932,a876)))+~P1(f334(f61(x99932),x99931))+~P1(f334(f334(f249(x99933),f334(x99934,f855(x99935,x99934,x99931,x99932,x99933))),f334(x99935,f855(x99935,x99934,x99931,x99932,x99933))))+P1(f334(f334(f249(x99933),f334(f334(f6(x99932,x99933),x99934),x99931)),f334(f334(f6(x99932,x99933),x99935),x99931)))
% 160.93/160.66 [7038]~P19(x70382,x70385,x70384)+E(x70381,f196(f888(x70382,a876)))+E(x70383,f196(f888(x70382,a876)))+~P1(f334(f61(x70382),x70381))+~P1(f334(f61(x70382),x70383))+E(f334(x70384,f334(f334(f114(f888(x70382,a876)),x70383),x70381)),f334(f334(x70385,f334(x70384,x70383)),f334(x70384,x70381)))
% 160.93/160.66 [7626]~P146(x76261,x76263,x76264)+P1(f334(x76261,x76262))+~P1(f334(f334(f249(a1),x76264),f2(a1)))+~P1(f334(f334(f248(a1),x76265),f2(a1)))+~E(x76263,f334(f334(f80(a1),f334(f334(f81(a1),x76264),x76262)),x76265))+~P1(f334(f334(f249(a1),x76264),x76265))
% 160.93/160.66 [7627]~P145(x76271,x76273,x76274)+P1(f334(x76271,x76272))+~P1(f334(f334(f249(a1),x76274),f2(a1)))+~P1(f334(f334(f248(a1),x76272),f2(a1)))+~E(x76273,f334(f334(f80(a1),f334(f334(f81(a1),x76274),x76275)),x76272))+~P1(f334(f334(f249(a1),x76274),x76272))
% 160.93/160.66 [7669]~P146(x76691,x76693,x76694)+P1(f334(x76691,x76692))+~E(x76693,f334(f334(f80(a1),f334(f334(f81(a1),x76694),x76692)),x76695))+~P1(f334(f334(f249(a1),f2(a1)),x76694))+~P1(f334(f334(f248(a1),f2(a1)),x76695))+~P1(f334(f334(f249(a1),x76695),x76694))
% 160.93/160.66 [7670]~P145(x76701,x76703,x76704)+P1(f334(x76701,x76702))+~E(x76703,f334(f334(f80(a1),f334(f334(f81(a1),x76704),x76705)),x76702))+~P1(f334(f334(f249(a1),f2(a1)),x76704))+~P1(f334(f334(f248(a1),f2(a1)),x76702))+~P1(f334(f334(f249(a1),x76702),x76704))
% 160.93/160.66 [8613]P1(f334(f334(x86131,x86132),x86133))+~P1(f334(f334(x86131,f334(f334(f38(a1),x86134),x86135)),f44(a1,x86134,x86135)))+~P1(f334(f334(f249(a1),x86135),f2(a1)))+~P1(f334(f334(f248(a1),x86133),f2(a1)))+~E(x86134,f334(f334(f80(a1),f334(f334(f81(a1),x86135),x86132)),x86133))+~P1(f334(f334(f249(a1),x86135),x86133))
% 160.93/160.66 [8622]P1(f334(f334(x86221,x86222),x86223))+~P1(f334(f334(x86221,f334(f334(f38(a1),x86224),x86225)),f44(a1,x86224,x86225)))+~E(x86224,f334(f334(f80(a1),f334(f334(f81(a1),x86225),x86222)),x86223))+~P1(f334(f334(f249(a1),f2(a1)),x86225))+~P1(f334(f334(f248(a1),f2(a1)),x86223))+~P1(f334(f334(f249(a1),x86223),x86225))
% 160.93/160.66 [8860]E(x88601,x88602)+~P53(x88603,x88605,x88604)+~P1(f334(f334(f336(x88603),x88602),x88605))+~P1(f334(f334(f336(x88603),x88601),x88605))+P1(f334(f334(f336(f887(x88603,x88603)),f334(f334(f269(x88603,x88603),x88601),x88602)),x88604))+P1(f334(f334(f336(f887(x88603,x88603)),f334(f334(f269(x88603,x88603),x88602),x88601)),x88604))
% 160.93/160.66 [9733]~P68(x97335)+~P84(x97335)+~P1(f334(f61(x97331),x97334))+P1(f334(f334(f248(x97335),f334(f334(f6(x97331,x97335),x97332),x97333)),f334(f334(f6(x97331,x97335),x97332),x97334)))+~P1(f334(f334(f248(f888(x97331,a876)),x97333),x97334))+P1(f334(f334(f336(x97331),f408(x97332,x97333,x97334,x97331,x97335)),f334(f334(f22(f888(x97331,a876)),x97334),x97333)))
% 160.93/160.66 [9832]E(x98321,f196(f888(x98322,a876)))+~P1(f334(f61(x98322),x98323))+~P1(f334(f61(x98322),x98321))+P1(f334(f334(f336(f887(f888(x98322,a876),f888(x98322,a876))),f334(f334(f269(f888(x98322,a876),f888(x98322,a876)),x98323),x98321)),f325(x98322,x98324)))+~P1(f334(f334(f336(x98322),x98325),x98321))+~P1(f334(f334(f336(f887(x98322,x98322)),f334(f334(f269(x98322,x98322),f566(x98324,x98321,x98323,x98322)),x98325)),x98324))
% 160.93/160.66 [9833]E(x98331,f196(f888(x98332,a876)))+~P1(f334(f61(x98332),x98333))+~P1(f334(f61(x98332),x98331))+P1(f334(f334(f336(f887(f888(x98332,a876),f888(x98332,a876))),f334(f334(f269(f888(x98332,a876),f888(x98332,a876)),x98333),x98331)),f325(x98332,x98334)))+~P1(f334(f334(f336(x98332),x98335),x98331))+~P1(f334(f334(f336(f887(x98332,x98332)),f334(f334(f269(x98332,x98332),f622(x98334,x98331,x98333,x98332)),x98335)),x98334))
% 160.93/160.66 [9997]~P83(x99971)+~E(f334(f334(f6(x99975,x99971),x99972),x99976),x99974)+~P1(f334(f61(x99975),x99976))+P1(f334(f334(f336(x99975),f409(x99973,x99974,x99972,x99976,x99975,x99971)),x99976))+P1(f334(f334(f248(x99971),f334(x99972,x99973)),x99974))+~P1(f334(f334(f336(x99975),x99973),x99976))
% 160.93/160.66 [10044]~P83(x100441)+~E(f334(f334(f6(x100445,x100441),x100442),x100446),x100444)+~P1(f334(f61(x100445),x100446))+~P1(f334(f334(f336(x100445),x100443),x100446))+~P1(f334(f334(f248(x100441),f2(x100441)),f334(x100442,f409(x100443,x100444,x100442,x100446,x100445,x100441))))+P1(f334(f334(f248(x100441),f334(x100442,x100443)),x100444))
% 160.93/160.66 [10157]~E(x101575,x101578)+~E(x101574,x101577)+~P68(x101572)+~P110(x101571)+E(f334(f334(f6(x101571,x101572),x101573),f334(f304(x101571,x101574),x101575)),f334(f334(f6(x101571,x101572),x101576),f334(f304(x101571,x101577),x101578)))+P1(f334(f334(f248(x101571),x101574),f514(x101573,x101576,x101575,x101578,x101574,x101577,x101571,x101572)))
% 160.93/160.66 [10174]~E(x101747,x101744)+~E(x101748,x101745)+~P68(x101742)+~P110(x101741)+~E(f334(x101743,f514(x101746,x101743,x101748,x101745,x101747,x101744,x101741,x101742)),f334(x101746,f514(x101746,x101743,x101748,x101745,x101747,x101744,x101741,x101742)))+E(f334(f334(f6(x101741,x101742),x101743),f334(f304(x101741,x101744),x101745)),f334(f334(f6(x101741,x101742),x101746),f334(f304(x101741,x101747),x101748)))
% 160.93/160.66 [10176]~E(x101764,x101767)+~E(x101765,x101768)+~P68(x101762)+~P110(x101761)+E(f334(f334(f6(x101761,x101762),x101763),f334(f304(x101761,x101764),x101765)),f334(f334(f6(x101761,x101762),x101766),f334(f304(x101761,x101767),x101768)))+P1(f334(f334(f249(x101761),f514(x101763,x101766,x101765,x101768,x101764,x101767,x101761,x101762)),x101765))
% 160.93/160.66 [9838]~P8(x98385,x98389,x98386)+~P8(x98381,x983810,x98383)+~P15(x98381,x98385,f888(x98382,a876),x98383,x98386,x98388)+~P1(f334(f334(f336(x98385),x98387),x98389))+~P1(f334(f334(f336(x98381),x98384),x983810))+E(f334(f334(f41(x98381,f888(x98382,a876)),f334(f288(x98381,x98381,x98383),f334(f334(f312(x98381),x98384),f196(f888(x98381,a876))))),f334(f334(f8(f888(x98385,f888(x98382,a876)),f888(x98382,a876),x98381),f334(f41(x98385,f888(x98382,a876)),f334(f288(x98385,x98385,x98386),f334(f334(f312(x98385),x98387),f196(f888(x98385,a876)))))),x98388)),f334(f334(x98388,x98384),x98387))
% 160.93/160.66 [5585]~P108(x55853)+~P16(x55853,x55852)+~P16(x55853,x55851)+E(x55851,x55852)+~E(f334(f174(x55853),x55851),f334(f174(x55853),x55852))+~P1(f334(f139(x55853),x55852))+~P1(f334(f139(x55853),x55851))
% 160.93/160.66 [4928]~P136(x49282)+~P130(x49282)+~P131(x49282)+~P113(x49282)+~E(x49283,f2(x49282))+E(x49281,f2(a881))+E(f334(f334(f259(x49282),x49283),x49281),f2(x49282))
% 160.93/160.66 [9130]E(x91301,f2(a881))+~E(x91302,f334(f334(f80(a881),f334(f334(f81(a881),f334(f268(a881,a881),x91303)),x91301)),f334(f272(a881,a881),x91303)))+P1(f334(f47(x91302,x91301),x91303))+~P1(f334(f334(f248(a881),f334(f272(a881,a881),x91303)),f2(a881)))+~P1(f334(f334(f248(a881),f2(a881)),f334(f272(a881,a881),x91303)))+~P1(f334(f334(f249(a881),x91301),f334(f272(a881,a881),x91303)))+~P1(f334(f334(f249(a881),f334(f272(a881,a881),x91303)),x91301))
% 160.93/160.66 [9139]~E(f334(f268(a881,a881),x91393),f2(a881))+~E(x91391,f334(f334(f80(a881),f334(f334(f81(a881),f334(f268(a881,a881),x91393)),x91392)),f334(f272(a881,a881),x91393)))+P1(f334(f47(x91391,x91392),x91393))+~P1(f334(f334(f248(a881),f334(f272(a881,a881),x91393)),f2(a881)))+~P1(f334(f334(f248(a881),f2(a881)),f334(f272(a881,a881),x91393)))+~P1(f334(f334(f249(a881),x91392),f334(f272(a881,a881),x91393)))+~P1(f334(f334(f249(a881),f334(f272(a881,a881),x91393)),x91392))
% 160.93/160.66 [7977]~P70(x79772)+E(x79771,f196(f888(x79772,a876)))+E(x79773,f196(f888(x79772,a876)))+~P1(f334(f61(x79772),x79771))+~P1(f334(f61(x79772),x79773))+~E(f334(f334(f105(f888(x79772,a876)),x79773),x79771),f196(f888(x79772,a876)))+E(f334(f334(f81(x79772),f334(f63(x79772,f81(x79772)),x79773)),f334(f63(x79772,f81(x79772)),x79771)),f334(f63(x79772,f81(x79772)),f334(f334(f114(f888(x79772,a876)),x79773),x79771)))
% 160.93/160.66 [7761]E(x77611,f2(a1))+E(f334(f334(f38(a1),x77612),x77611),x77613)+~P1(f334(f334(f248(a1),x77614),f2(a1)))+~E(x77612,f334(f334(f80(a1),f334(f334(f81(a1),x77611),x77613)),x77614))+~P1(f334(f334(f248(a1),f2(a1)),x77614))+~P1(f334(f334(f249(a1),x77614),x77611))+~P1(f334(f334(f249(a1),x77611),x77614))
% 160.93/160.66 [7769]E(f44(a1,x77692,x77691),x77693)+E(x77691,f2(a1))+~P1(f334(f334(f248(a1),x77693),f2(a1)))+~E(x77692,f334(f334(f80(a1),f334(f334(f81(a1),x77691),x77694)),x77693))+~P1(f334(f334(f248(a1),f2(a1)),x77693))+~P1(f334(f334(f249(a1),x77693),x77691))+~P1(f334(f334(f249(a1),x77691),x77693))
% 160.93/160.66 [7677]~P20(x76772,x76775,x76774)+E(x76771,f196(f888(x76772,a876)))+E(x76773,f196(f888(x76772,a876)))+~P1(f334(f61(x76772),x76771))+~P1(f334(f61(x76772),x76773))+~E(f334(f334(f105(f888(x76772,a876)),x76773),x76771),f196(f888(x76772,a876)))+E(f334(x76774,f334(f334(f114(f888(x76772,a876)),x76773),x76771)),f334(f334(x76775,f334(x76774,x76773)),f334(x76774,x76771)))
% 160.93/160.66 [9375]~P27(x93753,x93751,x93755,x93754)+~P27(x93751,x93753,x93756,x93752)+E(f334(f37(x93751),x93752),f334(f37(x93753),x93754))+~P1(f334(f61(x93753),x93754))+~P1(f334(f61(x93751),x93752))+~P1(f334(f334(f248(f888(x93753,a876)),f334(f313(x93751,x93753,x93756),x93752)),x93754))+~P1(f334(f334(f248(f888(x93751,a876)),f334(f313(x93753,x93751,x93755),x93754)),x93752))
% 160.93/160.66 [9319]~P1(f334(f334(f249(a1),f334(f334(f80(a1),f334(f334(f81(a1),x93195),x93191)),x93196)),f2(a1)))+~E(f334(f334(f80(a1),f334(f334(f81(a1),x93193),x93192)),x93194),f334(f334(f80(a1),f334(f334(f81(a1),x93195),x93191)),x93196))+~P1(f334(f334(f249(a1),f2(a1)),x93195))+~P1(f334(f334(f248(a1),f2(a1)),x93196))+~P1(f334(f334(f249(a1),x93194),x93193))+~P1(f334(f334(f248(a1),x93195),x93193))+P1(f334(f334(f248(a1),x93191),x93192))
% 160.93/160.66 [9082]~E(f334(f334(f80(a1),f334(f334(f81(a1),x90823),x90821)),x90824),f334(f334(f80(a1),f334(f334(f81(a1),x90825),x90822)),x90826))+~P1(f334(f334(f249(a1),f2(a1)),x90825))+~P1(f334(f334(f248(a1),f2(a1)),x90824))+~P1(f334(f334(f249(a1),x90826),x90825))+~P1(f334(f334(f248(a1),x90825),x90823))+P1(f334(f334(f248(a1),x90821),x90822))+~P1(f334(f334(f248(a1),f2(a1)),f334(f334(f80(a1),f334(f334(f81(a1),x90825),x90822)),x90826)))
% 160.93/160.66 [9260]~P129(x92601)+~E(f334(f334(f80(x92601),x92602),x92604),f78(x92601))+~P1(f334(f334(f248(x92601),f2(x92601)),x92604))+~P1(f334(f334(f248(x92601),f2(x92601)),x92602))+~P1(f334(f334(f249(x92601),x92605),x92606))+~P1(f334(f334(f249(x92601),x92603),x92606))+P1(f334(f334(f249(x92601),f334(f334(f80(x92601),f334(f334(f81(x92601),x92602),x92603)),f334(f334(f81(x92601),x92604),x92605))),x92606))
% 160.93/160.66 [9261]~P128(x92611)+~E(f334(f334(f80(x92611),x92612),x92614),f78(x92611))+~P1(f334(f334(f248(x92611),x92615),x92616))+~P1(f334(f334(f248(x92611),x92613),x92616))+~P1(f334(f334(f248(x92611),f2(x92611)),x92614))+~P1(f334(f334(f248(x92611),f2(x92611)),x92612))+P1(f334(f334(f248(x92611),f334(f334(f80(x92611),f334(f334(f81(x92611),x92612),x92613)),f334(f334(f81(x92611),x92614),x92615))),x92616))
% 160.93/160.66 [10090]~P8(x100907,x100906,x100905)+E(x100901,x100902)+~P14(x100907,f888(x100904,a876),x100905,x100903)+E(f334(x100903,f543(x100901,x100902,x100903,x100904,x100905,x100906,x100907)),f334(x100903,f544(x100901,x100902,x100903,x100904,x100905,x100906,x100907)))+~E(f334(f334(f41(x100907,f888(x100904,a876)),x100901),x100903),f334(f334(f41(x100907,f888(x100904,a876)),x100902),x100903))+~P1(f334(f334(f336(f888(x100907,a876)),x100902),f334(f334(f60(x100907),x100906),x100905)))+~P1(f334(f334(f336(f888(x100907,a876)),x100901),f334(f334(f60(x100907),x100906),x100905)))
% 160.93/160.66 [10124]~P8(x101243,x101247,x101246)+E(x101241,x101242)+~P14(x101243,f888(x101245,a876),x101246,x101244)+~E(f334(f334(f41(x101243,f888(x101245,a876)),x101241),x101244),f334(f334(f41(x101243,f888(x101245,a876)),x101242),x101244))+P1(f334(f334(f336(x101243),f544(x101241,x101242,x101244,x101245,x101246,x101247,x101243)),x101247))+~P1(f334(f334(f336(f888(x101243,a876)),x101242),f334(f334(f60(x101243),x101247),x101246)))+~P1(f334(f334(f336(f888(x101243,a876)),x101241),f334(f334(f60(x101243),x101247),x101246)))
% 160.93/160.66 [10125]~P8(x101253,x101257,x101256)+E(x101251,x101252)+~P14(x101253,f888(x101255,a876),x101256,x101254)+~E(f334(f334(f41(x101253,f888(x101255,a876)),x101251),x101254),f334(f334(f41(x101253,f888(x101255,a876)),x101252),x101254))+P1(f334(f334(f336(x101253),f543(x101251,x101252,x101254,x101255,x101256,x101257,x101253)),x101257))+~P1(f334(f334(f336(f888(x101253,a876)),x101252),f334(f334(f60(x101253),x101257),x101256)))+~P1(f334(f334(f336(f888(x101253,a876)),x101251),f334(f334(f60(x101253),x101257),x101256)))
% 160.93/160.66 [10193]E(x101931,x101932)+~P8(x101933,x101936,x101937)+~P14(x101933,f888(x101934,a876),x101937,x101935)+~E(f334(f334(f41(x101933,f888(x101934,a876)),x101931),x101935),f334(f334(f41(x101933,f888(x101934,a876)),x101932),x101935))+~P1(f334(f334(f336(f887(x101933,x101933)),f334(f334(f269(x101933,x101933),f544(x101931,x101932,x101935,x101934,x101937,x101936,x101933)),f543(x101931,x101932,x101935,x101934,x101937,x101936,x101933))),x101937))+~P1(f334(f334(f336(f888(x101933,a876)),x101932),f334(f334(f60(x101933),x101936),x101937)))+~P1(f334(f334(f336(f888(x101933,a876)),x101931),f334(f334(f60(x101933),x101936),x101937)))
% 160.93/160.66 [9081]~P8(x90811,x90817,x90814)+~E(x90815,x90816)+~P1(f334(f334(f336(x90811),x90813),x90816))+~P1(f334(f334(f336(x90811),x90812),x90815))+~P1(f334(f334(f336(f888(x90811,a876)),x90816),f334(f334(f60(x90811),x90817),x90814)))+~P1(f334(f334(f336(f888(x90811,a876)),x90815),f334(f334(f60(x90811),x90817),x90814)))+P1(f334(f334(f336(f887(x90811,x90811)),f334(f334(f269(x90811,x90811),x90812),x90813)),x90814))
% 160.93/160.66 [9217]E(x92171,x92172)+~P8(x92173,x92174,x92175)+~P1(f334(f334(f336(x92173),x92176),x92172))+~P1(f334(f334(f336(x92173),x92177),x92171))+~P1(f334(f334(f336(f888(x92173,a876)),x92172),f334(f334(f60(x92173),x92174),x92175)))+~P1(f334(f334(f336(f888(x92173,a876)),x92171),f334(f334(f60(x92173),x92174),x92175)))+~P1(f334(f334(f336(f887(x92173,x92173)),f334(f334(f269(x92173,x92173),x92177),x92176)),x92175))
% 160.93/160.66 [10216]~P8(x102169,x102168,x102167)+~P8(x102161,x1021611,x1021610)+~P15(x102161,x102169,f888(x102166,a876),x1021610,x102167,x102165)+P1(f334(f334(f336(x102161),f546(x102162,x102163,x102164,x102165,x102166,x102167,x102168,x102169,x1021610,x1021611,x102161)),x1021611))+~P1(f334(f334(f336(f888(x102169,a876)),x102163),f334(f334(f60(x102169),x102168),x102167)))+~P1(f334(f334(f336(f888(x102161,a876)),x102164),f334(f334(f60(x102161),x1021611),x1021610)))+P1(f334(f334(f336(f888(x102166,a876)),f334(f334(f41(x102161,f888(x102166,a876)),x102164),f334(f334(f8(f888(x102169,f888(x102166,a876)),f888(x102166,a876),x102161),f334(f41(x102169,f888(x102166,a876)),x102163)),x102165))),x102162))
% 160.93/160.66 [10217]~P8(x1021711,x1021710,x102179)+~P8(x102171,x102178,x102177)+~P15(x1021711,x102171,f888(x102176,a876),x102179,x102177,x102175)+P1(f334(f334(f336(x102171),f547(x102172,x102173,x102174,x102175,x102176,x102177,x102178,x102171,x102179,x1021710,x1021711)),x102178))+~P1(f334(f334(f336(f888(x1021711,a876)),x102174),f334(f334(f60(x1021711),x1021710),x102179)))+~P1(f334(f334(f336(f888(x102171,a876)),x102173),f334(f334(f60(x102171),x102178),x102177)))+P1(f334(f334(f336(f888(x102176,a876)),f334(f334(f41(x1021711,f888(x102176,a876)),x102174),f334(f334(f8(f888(x102171,f888(x102176,a876)),f888(x102176,a876),x1021711),f334(f41(x102171,f888(x102176,a876)),x102173)),x102175))),x102172))
% 160.93/160.66 [10220]~P8(x102202,x102208,x102209)+~P8(x102204,x1022010,x1022011)+~P15(x102202,x102204,f888(x102201,a876),x102209,x1022011,x102206)+~P1(f334(f334(f336(f888(x102202,a876)),x102203),f334(f334(f60(x102202),x102208),x102209)))+~P1(f334(f334(f336(f888(x102204,a876)),x102205),f334(f334(f60(x102204),x1022010),x1022011)))+~P1(f334(f334(f336(f888(x102201,a876)),f334(f334(x102206,f546(x102207,x102205,x102203,x102206,x102201,x1022011,x1022010,x102204,x102209,x102208,x102202)),f547(x102207,x102205,x102203,x102206,x102201,x1022011,x1022010,x102204,x102209,x102208,x102202))),x102207))+P1(f334(f334(f336(f888(x102201,a876)),f334(f334(f41(x102202,f888(x102201,a876)),x102203),f334(f334(f8(f888(x102204,f888(x102201,a876)),f888(x102201,a876),x102202),f334(f41(x102204,f888(x102201,a876)),x102205)),x102206))),x102207))
% 160.93/160.66 [9117]E(x91171,x91172)+~P108(x91174)+~P27(x91173,x91174,x91175,f334(f334(f114(f888(x91173,a876)),f334(f174(x91173),x91171)),f334(f174(x91173),x91172)))+~E(f334(f174(x91173),x91171),f334(f174(x91173),x91172))+~P16(x91174,f334(f334(f156(x91173,x91174),x91175),x91172))+~P16(x91174,f334(f334(f156(x91173,x91174),x91175),x91171))+~P1(f334(f139(x91174),f334(f334(f156(x91173,x91174),x91175),x91172)))+~P1(f334(f139(x91174),f334(f334(f156(x91173,x91174),x91175),x91171)))
% 160.93/160.66 %EqnAxiom
% 160.93/160.66 [1]E(x11,x11)
% 160.93/160.66 [2]E(x22,x21)+~E(x21,x22)
% 160.93/160.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 160.93/160.66 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 160.93/160.66 [5]~E(x51,x52)+E(f104(x51),f104(x52))
% 160.93/160.66 [6]~E(x61,x62)+E(f22(x61),f22(x62))
% 160.93/160.66 [7]~E(x71,x72)+E(f196(x71),f196(x72))
% 160.93/160.66 [8]~E(x81,x82)+E(f334(x81,x83),f334(x82,x83))
% 160.93/160.66 [9]~E(x91,x92)+E(f334(x93,x91),f334(x93,x92))
% 160.93/160.66 [10]~E(x101,x102)+E(f31(x101),f31(x102))
% 160.93/160.66 [11]~E(x111,x112)+E(f882(x111),f882(x112))
% 160.93/160.66 [12]~E(x121,x122)+E(f105(x121),f105(x122))
% 160.93/160.66 [13]~E(x131,x132)+E(f246(x131),f246(x132))
% 160.93/160.66 [14]~E(x141,x142)+E(f114(x141),f114(x142))
% 160.93/160.66 [15]~E(x151,x152)+E(f247(x151),f247(x152))
% 160.93/160.66 [16]~E(x161,x162)+E(f106(x161),f106(x162))
% 160.93/160.66 [17]~E(x171,x172)+E(f34(x171),f34(x172))
% 160.93/160.66 [18]~E(x181,x182)+E(f84(x181),f84(x182))
% 160.93/160.66 [19]~E(x191,x192)+E(f248(x191),f248(x192))
% 160.93/160.66 [20]~E(x201,x202)+E(f80(x201),f80(x202))
% 160.93/160.66 [21]~E(x211,x212)+E(f547(x211,x213,x214,x215,x216,x217,x218,x219,x2110,x2111,x2112),f547(x212,x213,x214,x215,x216,x217,x218,x219,x2110,x2111,x2112))
% 160.93/160.66 [22]~E(x221,x222)+E(f547(x223,x221,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212),f547(x223,x222,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212))
% 160.93/160.66 [23]~E(x231,x232)+E(f547(x233,x234,x231,x235,x236,x237,x238,x239,x2310,x2311,x2312),f547(x233,x234,x232,x235,x236,x237,x238,x239,x2310,x2311,x2312))
% 160.93/160.66 [24]~E(x241,x242)+E(f547(x243,x244,x245,x241,x246,x247,x248,x249,x2410,x2411,x2412),f547(x243,x244,x245,x242,x246,x247,x248,x249,x2410,x2411,x2412))
% 160.93/160.66 [25]~E(x251,x252)+E(f547(x253,x254,x255,x256,x251,x257,x258,x259,x2510,x2511,x2512),f547(x253,x254,x255,x256,x252,x257,x258,x259,x2510,x2511,x2512))
% 160.93/160.66 [26]~E(x261,x262)+E(f547(x263,x264,x265,x266,x267,x261,x268,x269,x2610,x2611,x2612),f547(x263,x264,x265,x266,x267,x262,x268,x269,x2610,x2611,x2612))
% 160.93/160.66 [27]~E(x271,x272)+E(f547(x273,x274,x275,x276,x277,x278,x271,x279,x2710,x2711,x2712),f547(x273,x274,x275,x276,x277,x278,x272,x279,x2710,x2711,x2712))
% 160.93/160.66 [28]~E(x281,x282)+E(f547(x283,x284,x285,x286,x287,x288,x289,x281,x2810,x2811,x2812),f547(x283,x284,x285,x286,x287,x288,x289,x282,x2810,x2811,x2812))
% 160.93/160.66 [29]~E(x291,x292)+E(f547(x293,x294,x295,x296,x297,x298,x299,x2910,x291,x2911,x2912),f547(x293,x294,x295,x296,x297,x298,x299,x2910,x292,x2911,x2912))
% 160.93/160.66 [30]~E(x301,x302)+E(f547(x303,x304,x305,x306,x307,x308,x309,x3010,x3011,x301,x3012),f547(x303,x304,x305,x306,x307,x308,x309,x3010,x3011,x302,x3012))
% 160.93/160.66 [31]~E(x311,x312)+E(f547(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x3112,x311),f547(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x3112,x312))
% 160.93/160.66 [32]~E(x321,x322)+E(f182(x321,x323),f182(x322,x323))
% 160.93/160.66 [33]~E(x331,x332)+E(f182(x333,x331),f182(x333,x332))
% 160.93/160.66 [34]~E(x341,x342)+E(f78(x341),f78(x342))
% 160.93/160.66 [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))
% 160.93/160.66 [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))
% 160.93/160.66 [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))
% 160.93/160.66 [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))
% 160.93/160.66 [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))
% 160.93/160.66 [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))
% 160.93/160.66 [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))
% 160.93/160.66 [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))
% 160.93/160.66 [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))
% 160.93/160.66 [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))
% 160.93/160.66 [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))
% 160.93/160.66 [46]~E(x461,x462)+E(f4(x461),f4(x462))
% 160.93/160.66 [47]~E(x471,x472)+E(f336(x471),f336(x472))
% 160.93/160.66 [48]~E(x481,x482)+E(f888(x481,x483),f888(x482,x483))
% 160.93/160.66 [49]~E(x491,x492)+E(f888(x493,x491),f888(x493,x492))
% 160.93/160.66 [50]~E(x501,x502)+E(f115(x501),f115(x502))
% 160.93/160.66 [51]~E(x511,x512)+E(f153(x511),f153(x512))
% 160.93/160.66 [52]~E(x521,x522)+E(f880(x521),f880(x522))
% 160.93/160.66 [53]~E(x531,x532)+E(f885(x531),f885(x532))
% 160.93/160.66 [54]~E(x541,x542)+E(f822(x541,x543,x544),f822(x542,x543,x544))
% 160.93/160.66 [55]~E(x551,x552)+E(f822(x553,x551,x554),f822(x553,x552,x554))
% 160.93/160.66 [56]~E(x561,x562)+E(f822(x563,x564,x561),f822(x563,x564,x562))
% 160.93/160.66 [57]~E(x571,x572)+E(f883(x571),f883(x572))
% 160.93/160.66 [58]~E(x581,x582)+E(f171(x581),f171(x582))
% 160.93/160.66 [59]~E(x591,x592)+E(f75(x591),f75(x592))
% 160.93/160.66 [60]~E(x601,x602)+E(f313(x601,x603,x604),f313(x602,x603,x604))
% 160.93/160.66 [61]~E(x611,x612)+E(f313(x613,x611,x614),f313(x613,x612,x614))
% 160.93/160.66 [62]~E(x621,x622)+E(f313(x623,x624,x621),f313(x623,x624,x622))
% 160.93/160.66 [63]~E(x631,x632)+E(f310(x631,x633),f310(x632,x633))
% 160.93/160.66 [64]~E(x641,x642)+E(f310(x643,x641),f310(x643,x642))
% 160.93/160.66 [65]~E(x651,x652)+E(f79(x651),f79(x652))
% 160.93/160.66 [66]~E(x661,x662)+E(f61(x661),f61(x662))
% 160.93/160.66 [67]~E(x671,x672)+E(f197(x671),f197(x672))
% 160.93/160.66 [68]~E(x681,x682)+E(f15(x681,x683),f15(x682,x683))
% 160.93/160.66 [69]~E(x691,x692)+E(f15(x693,x691),f15(x693,x692))
% 160.93/160.66 [70]~E(x701,x702)+E(f107(x701),f107(x702))
% 160.93/160.66 [71]~E(x711,x712)+E(f8(x711,x713,x714),f8(x712,x713,x714))
% 160.93/160.66 [72]~E(x721,x722)+E(f8(x723,x721,x724),f8(x723,x722,x724))
% 160.93/160.66 [73]~E(x731,x732)+E(f8(x733,x734,x731),f8(x733,x734,x732))
% 160.93/160.66 [74]~E(x741,x742)+E(f158(x741,x743,x744,x745),f158(x742,x743,x744,x745))
% 160.93/160.66 [75]~E(x751,x752)+E(f158(x753,x751,x754,x755),f158(x753,x752,x754,x755))
% 160.93/160.66 [76]~E(x761,x762)+E(f158(x763,x764,x761,x765),f158(x763,x764,x762,x765))
% 160.93/160.66 [77]~E(x771,x772)+E(f158(x773,x774,x775,x771),f158(x773,x774,x775,x772))
% 160.93/160.66 [78]~E(x781,x782)+E(f117(x781),f117(x782))
% 160.93/160.66 [79]~E(x791,x792)+E(f14(x791,x793),f14(x792,x793))
% 160.93/160.66 [80]~E(x801,x802)+E(f14(x803,x801),f14(x803,x802))
% 160.93/160.66 [81]~E(x811,x812)+E(f60(x811),f60(x812))
% 160.93/160.66 [82]~E(x821,x822)+E(f249(x821),f249(x822))
% 160.93/160.66 [83]~E(x831,x832)+E(f887(x831,x833),f887(x832,x833))
% 160.93/160.66 [84]~E(x841,x842)+E(f887(x843,x841),f887(x843,x842))
% 160.93/160.66 [85]~E(x851,x852)+E(f241(x851),f241(x852))
% 160.93/160.66 [86]~E(x861,x862)+E(f7(x861,x863,x864),f7(x862,x863,x864))
% 160.93/160.66 [87]~E(x871,x872)+E(f7(x873,x871,x874),f7(x873,x872,x874))
% 160.93/160.66 [88]~E(x881,x882)+E(f7(x883,x884,x881),f7(x883,x884,x882))
% 160.93/160.66 [89]~E(x891,x892)+E(f81(x891),f81(x892))
% 160.93/160.66 [90]~E(x901,x902)+E(f292(x901),f292(x902))
% 160.93/160.66 [91]~E(x911,x912)+E(f91(x911),f91(x912))
% 160.93/160.66 [92]~E(x921,x922)+E(f268(x921,x923),f268(x922,x923))
% 160.93/160.66 [93]~E(x931,x932)+E(f268(x933,x931),f268(x933,x932))
% 160.93/160.66 [94]~E(x941,x942)+E(f272(x941,x943),f272(x942,x943))
% 160.93/160.66 [95]~E(x951,x952)+E(f272(x953,x951),f272(x953,x952))
% 160.93/160.66 [96]~E(x961,x962)+E(f245(x961),f245(x962))
% 160.93/160.66 [97]~E(x971,x972)+E(f174(x971),f174(x972))
% 160.93/160.66 [98]~E(x981,x982)+E(f144(x981,x983,x984,x985),f144(x982,x983,x984,x985))
% 160.93/160.66 [99]~E(x991,x992)+E(f144(x993,x991,x994,x995),f144(x993,x992,x994,x995))
% 160.93/160.66 [100]~E(x1001,x1002)+E(f144(x1003,x1004,x1001,x1005),f144(x1003,x1004,x1002,x1005))
% 160.93/160.66 [101]~E(x1011,x1012)+E(f144(x1013,x1014,x1015,x1011),f144(x1013,x1014,x1015,x1012))
% 160.93/160.66 [102]~E(x1021,x1022)+E(f269(x1021,x1023),f269(x1022,x1023))
% 160.93/160.66 [103]~E(x1031,x1032)+E(f269(x1033,x1031),f269(x1033,x1032))
% 160.93/160.66 [104]~E(x1041,x1042)+E(f42(x1041,x1043),f42(x1042,x1043))
% 160.93/160.66 [105]~E(x1051,x1052)+E(f42(x1053,x1051),f42(x1053,x1052))
% 160.93/160.66 [106]~E(x1061,x1062)+E(f323(x1061,x1063),f323(x1062,x1063))
% 160.93/160.66 [107]~E(x1071,x1072)+E(f323(x1073,x1071),f323(x1073,x1072))
% 160.93/160.66 [108]~E(x1081,x1082)+E(f294(x1081,x1083),f294(x1082,x1083))
% 160.93/160.66 [109]~E(x1091,x1092)+E(f294(x1093,x1091),f294(x1093,x1092))
% 160.93/160.66 [110]~E(x1101,x1102)+E(f764(x1101,x1103,x1104,x1105),f764(x1102,x1103,x1104,x1105))
% 160.93/160.66 [111]~E(x1111,x1112)+E(f764(x1113,x1111,x1114,x1115),f764(x1113,x1112,x1114,x1115))
% 160.93/160.66 [112]~E(x1121,x1122)+E(f764(x1123,x1124,x1121,x1125),f764(x1123,x1124,x1122,x1125))
% 160.93/160.66 [113]~E(x1131,x1132)+E(f764(x1133,x1134,x1135,x1131),f764(x1133,x1134,x1135,x1132))
% 160.93/160.66 [114]~E(x1141,x1142)+E(f836(x1141,x1143,x1144,x1145,x1146),f836(x1142,x1143,x1144,x1145,x1146))
% 160.93/160.66 [115]~E(x1151,x1152)+E(f836(x1153,x1151,x1154,x1155,x1156),f836(x1153,x1152,x1154,x1155,x1156))
% 160.93/160.66 [116]~E(x1161,x1162)+E(f836(x1163,x1164,x1161,x1165,x1166),f836(x1163,x1164,x1162,x1165,x1166))
% 160.93/160.66 [117]~E(x1171,x1172)+E(f836(x1173,x1174,x1175,x1171,x1176),f836(x1173,x1174,x1175,x1172,x1176))
% 160.93/160.66 [118]~E(x1181,x1182)+E(f836(x1183,x1184,x1185,x1186,x1181),f836(x1183,x1184,x1185,x1186,x1182))
% 160.93/160.66 [119]~E(x1191,x1192)+E(f16(x1191,x1193),f16(x1192,x1193))
% 160.93/160.66 [120]~E(x1201,x1202)+E(f16(x1203,x1201),f16(x1203,x1202))
% 160.93/160.66 [121]~E(x1211,x1212)+E(f312(x1211),f312(x1212))
% 160.93/160.66 [122]~E(x1221,x1222)+E(f44(x1221,x1223,x1224),f44(x1222,x1223,x1224))
% 160.93/160.66 [123]~E(x1231,x1232)+E(f44(x1233,x1231,x1234),f44(x1233,x1232,x1234))
% 160.93/160.66 [124]~E(x1241,x1242)+E(f44(x1243,x1244,x1241),f44(x1243,x1244,x1242))
% 160.93/160.66 [125]~E(x1251,x1252)+E(f136(x1251),f136(x1252))
% 160.93/160.66 [126]~E(x1261,x1262)+E(f518(x1261,x1263,x1264),f518(x1262,x1263,x1264))
% 160.93/160.66 [127]~E(x1271,x1272)+E(f518(x1273,x1271,x1274),f518(x1273,x1272,x1274))
% 160.93/160.66 [128]~E(x1281,x1282)+E(f518(x1283,x1284,x1281),f518(x1283,x1284,x1282))
% 160.93/160.66 [129]~E(x1291,x1292)+E(f289(x1291,x1293),f289(x1292,x1293))
% 160.93/160.66 [130]~E(x1301,x1302)+E(f289(x1303,x1301),f289(x1303,x1302))
% 160.93/160.66 [131]~E(x1311,x1312)+E(f271(x1311,x1313),f271(x1312,x1313))
% 160.93/160.66 [132]~E(x1321,x1322)+E(f271(x1323,x1321),f271(x1323,x1322))
% 160.93/160.66 [133]~E(x1331,x1332)+E(f224(x1331,x1333,x1334,x1335,x1336,x1337,x1338),f224(x1332,x1333,x1334,x1335,x1336,x1337,x1338))
% 160.93/160.66 [134]~E(x1341,x1342)+E(f224(x1343,x1341,x1344,x1345,x1346,x1347,x1348),f224(x1343,x1342,x1344,x1345,x1346,x1347,x1348))
% 160.93/160.66 [135]~E(x1351,x1352)+E(f224(x1353,x1354,x1351,x1355,x1356,x1357,x1358),f224(x1353,x1354,x1352,x1355,x1356,x1357,x1358))
% 160.93/160.66 [136]~E(x1361,x1362)+E(f224(x1363,x1364,x1365,x1361,x1366,x1367,x1368),f224(x1363,x1364,x1365,x1362,x1366,x1367,x1368))
% 160.93/160.66 [137]~E(x1371,x1372)+E(f224(x1373,x1374,x1375,x1376,x1371,x1377,x1378),f224(x1373,x1374,x1375,x1376,x1372,x1377,x1378))
% 160.93/160.66 [138]~E(x1381,x1382)+E(f224(x1383,x1384,x1385,x1386,x1387,x1381,x1388),f224(x1383,x1384,x1385,x1386,x1387,x1382,x1388))
% 160.93/160.66 [139]~E(x1391,x1392)+E(f224(x1393,x1394,x1395,x1396,x1397,x1398,x1391),f224(x1393,x1394,x1395,x1396,x1397,x1398,x1392))
% 160.93/160.66 [140]~E(x1401,x1402)+E(f40(x1401,x1403),f40(x1402,x1403))
% 160.93/160.66 [141]~E(x1411,x1412)+E(f40(x1413,x1411),f40(x1413,x1412))
% 160.93/160.66 [142]~E(x1421,x1422)+E(f77(x1421,x1423,x1424,x1425),f77(x1422,x1423,x1424,x1425))
% 160.93/160.66 [143]~E(x1431,x1432)+E(f77(x1433,x1431,x1434,x1435),f77(x1433,x1432,x1434,x1435))
% 160.93/160.66 [144]~E(x1441,x1442)+E(f77(x1443,x1444,x1441,x1445),f77(x1443,x1444,x1442,x1445))
% 160.93/160.66 [145]~E(x1451,x1452)+E(f77(x1453,x1454,x1455,x1451),f77(x1453,x1454,x1455,x1452))
% 160.93/160.66 [146]~E(x1461,x1462)+E(f92(x1461),f92(x1462))
% 160.93/160.66 [147]~E(x1471,x1472)+E(f429(x1471,x1473,x1474),f429(x1472,x1473,x1474))
% 160.93/160.66 [148]~E(x1481,x1482)+E(f429(x1483,x1481,x1484),f429(x1483,x1482,x1484))
% 160.93/160.66 [149]~E(x1491,x1492)+E(f429(x1493,x1494,x1491),f429(x1493,x1494,x1492))
% 160.93/160.66 [150]~E(x1501,x1502)+E(f41(x1501,x1503),f41(x1502,x1503))
% 160.93/160.66 [151]~E(x1511,x1512)+E(f41(x1513,x1511),f41(x1513,x1512))
% 160.93/160.66 [152]~E(x1521,x1522)+E(f305(x1521,x1523,x1524),f305(x1522,x1523,x1524))
% 160.93/160.66 [153]~E(x1531,x1532)+E(f305(x1533,x1531,x1534),f305(x1533,x1532,x1534))
% 160.93/160.66 [154]~E(x1541,x1542)+E(f305(x1543,x1544,x1541),f305(x1543,x1544,x1542))
% 160.93/160.66 [155]~E(x1551,x1552)+E(f587(x1551,x1553,x1554),f587(x1552,x1553,x1554))
% 160.93/160.66 [156]~E(x1561,x1562)+E(f587(x1563,x1561,x1564),f587(x1563,x1562,x1564))
% 160.93/160.66 [157]~E(x1571,x1572)+E(f587(x1573,x1574,x1571),f587(x1573,x1574,x1572))
% 160.93/160.66 [158]~E(x1581,x1582)+E(f6(x1581,x1583),f6(x1582,x1583))
% 160.93/160.66 [159]~E(x1591,x1592)+E(f6(x1593,x1591),f6(x1593,x1592))
% 160.93/160.66 [160]~E(x1601,x1602)+E(f257(x1601),f257(x1602))
% 160.93/160.66 [161]~E(x1611,x1612)+E(f109(x1611),f109(x1612))
% 160.93/160.66 [162]~E(x1621,x1622)+E(f111(x1621),f111(x1622))
% 160.93/160.66 [163]~E(x1631,x1632)+E(f335(x1631),f335(x1632))
% 160.93/160.66 [164]~E(x1641,x1642)+E(f156(x1641,x1643),f156(x1642,x1643))
% 160.93/160.66 [165]~E(x1651,x1652)+E(f156(x1653,x1651),f156(x1653,x1652))
% 160.93/160.66 [166]~E(x1661,x1662)+E(f378(x1661,x1663,x1664,x1665),f378(x1662,x1663,x1664,x1665))
% 160.93/160.66 [167]~E(x1671,x1672)+E(f378(x1673,x1671,x1674,x1675),f378(x1673,x1672,x1674,x1675))
% 160.93/160.66 [168]~E(x1681,x1682)+E(f378(x1683,x1684,x1681,x1685),f378(x1683,x1684,x1682,x1685))
% 160.93/160.66 [169]~E(x1691,x1692)+E(f378(x1693,x1694,x1695,x1691),f378(x1693,x1694,x1695,x1692))
% 160.93/160.66 [170]~E(x1701,x1702)+E(f82(x1701,x1703),f82(x1702,x1703))
% 160.93/160.66 [171]~E(x1711,x1712)+E(f82(x1713,x1711),f82(x1713,x1712))
% 160.93/160.66 [172]~E(x1721,x1722)+E(f161(x1721,x1723),f161(x1722,x1723))
% 160.93/160.66 [173]~E(x1731,x1732)+E(f161(x1733,x1731),f161(x1733,x1732))
% 160.93/160.66 [174]~E(x1741,x1742)+E(f5(x1741),f5(x1742))
% 160.93/160.66 [175]~E(x1751,x1752)+E(f258(x1751,x1753,x1754),f258(x1752,x1753,x1754))
% 160.93/160.66 [176]~E(x1761,x1762)+E(f258(x1763,x1761,x1764),f258(x1763,x1762,x1764))
% 160.93/160.66 [177]~E(x1771,x1772)+E(f258(x1773,x1774,x1771),f258(x1773,x1774,x1772))
% 160.93/160.66 [178]~E(x1781,x1782)+E(f254(x1781),f254(x1782))
% 160.93/160.66 [179]~E(x1791,x1792)+E(f517(x1791,x1793,x1794),f517(x1792,x1793,x1794))
% 160.93/160.66 [180]~E(x1801,x1802)+E(f517(x1803,x1801,x1804),f517(x1803,x1802,x1804))
% 160.93/160.66 [181]~E(x1811,x1812)+E(f517(x1813,x1814,x1811),f517(x1813,x1814,x1812))
% 160.93/160.66 [182]~E(x1821,x1822)+E(f211(x1821,x1823),f211(x1822,x1823))
% 160.93/160.66 [183]~E(x1831,x1832)+E(f211(x1833,x1831),f211(x1833,x1832))
% 160.93/160.66 [184]~E(x1841,x1842)+E(f150(x1841,x1843,x1844),f150(x1842,x1843,x1844))
% 160.93/160.66 [185]~E(x1851,x1852)+E(f150(x1853,x1851,x1854),f150(x1853,x1852,x1854))
% 160.93/160.66 [186]~E(x1861,x1862)+E(f150(x1863,x1864,x1861),f150(x1863,x1864,x1862))
% 160.93/160.66 [187]~E(x1871,x1872)+E(f139(x1871),f139(x1872))
% 160.93/160.66 [188]~E(x1881,x1882)+E(f72(x1881,x1883),f72(x1882,x1883))
% 160.93/160.66 [189]~E(x1891,x1892)+E(f72(x1893,x1891),f72(x1893,x1892))
% 160.93/160.66 [190]~E(x1901,x1902)+E(f85(x1901,x1903),f85(x1902,x1903))
% 160.93/160.66 [191]~E(x1911,x1912)+E(f85(x1913,x1911),f85(x1913,x1912))
% 160.93/160.66 [192]~E(x1921,x1922)+E(f30(x1921,x1923,x1924),f30(x1922,x1923,x1924))
% 160.93/160.66 [193]~E(x1931,x1932)+E(f30(x1933,x1931,x1934),f30(x1933,x1932,x1934))
% 160.93/160.66 [194]~E(x1941,x1942)+E(f30(x1943,x1944,x1941),f30(x1943,x1944,x1942))
% 160.93/160.66 [195]~E(x1951,x1952)+E(f823(x1951,x1953,x1954),f823(x1952,x1953,x1954))
% 160.93/160.66 [196]~E(x1961,x1962)+E(f823(x1963,x1961,x1964),f823(x1963,x1962,x1964))
% 160.93/160.66 [197]~E(x1971,x1972)+E(f823(x1973,x1974,x1971),f823(x1973,x1974,x1972))
% 160.93/160.66 [198]~E(x1981,x1982)+E(f243(x1981,x1983,x1984,x1985),f243(x1982,x1983,x1984,x1985))
% 160.93/160.66 [199]~E(x1991,x1992)+E(f243(x1993,x1991,x1994,x1995),f243(x1993,x1992,x1994,x1995))
% 160.93/160.66 [200]~E(x2001,x2002)+E(f243(x2003,x2004,x2001,x2005),f243(x2003,x2004,x2002,x2005))
% 160.93/160.66 [201]~E(x2011,x2012)+E(f243(x2013,x2014,x2015,x2011),f243(x2013,x2014,x2015,x2012))
% 160.93/160.66 [202]~E(x2021,x2022)+E(f149(x2021,x2023),f149(x2022,x2023))
% 160.93/160.66 [203]~E(x2031,x2032)+E(f149(x2033,x2031),f149(x2033,x2032))
% 160.93/160.66 [204]~E(x2041,x2042)+E(f184(x2041,x2043),f184(x2042,x2043))
% 160.93/160.66 [205]~E(x2051,x2052)+E(f184(x2053,x2051),f184(x2053,x2052))
% 160.93/160.66 [206]~E(x2061,x2062)+E(f37(x2061),f37(x2062))
% 160.93/160.66 [207]~E(x2071,x2072)+E(f702(x2071,x2073,x2074,x2075,x2076),f702(x2072,x2073,x2074,x2075,x2076))
% 160.93/160.66 [208]~E(x2081,x2082)+E(f702(x2083,x2081,x2084,x2085,x2086),f702(x2083,x2082,x2084,x2085,x2086))
% 160.93/160.66 [209]~E(x2091,x2092)+E(f702(x2093,x2094,x2091,x2095,x2096),f702(x2093,x2094,x2092,x2095,x2096))
% 160.93/160.66 [210]~E(x2101,x2102)+E(f702(x2103,x2104,x2105,x2101,x2106),f702(x2103,x2104,x2105,x2102,x2106))
% 160.93/160.66 [211]~E(x2111,x2112)+E(f702(x2113,x2114,x2115,x2116,x2111),f702(x2113,x2114,x2115,x2116,x2112))
% 160.93/160.66 [212]~E(x2121,x2122)+E(f465(x2121,x2123,x2124),f465(x2122,x2123,x2124))
% 160.93/160.66 [213]~E(x2131,x2132)+E(f465(x2133,x2131,x2134),f465(x2133,x2132,x2134))
% 160.93/160.66 [214]~E(x2141,x2142)+E(f465(x2143,x2144,x2141),f465(x2143,x2144,x2142))
% 160.93/160.66 [215]~E(x2151,x2152)+E(f18(x2151,x2153,x2154),f18(x2152,x2153,x2154))
% 160.93/160.66 [216]~E(x2161,x2162)+E(f18(x2163,x2161,x2164),f18(x2163,x2162,x2164))
% 160.93/160.66 [217]~E(x2171,x2172)+E(f18(x2173,x2174,x2171),f18(x2173,x2174,x2172))
% 160.93/160.66 [218]~E(x2181,x2182)+E(f167(x2181),f167(x2182))
% 160.93/160.66 [219]~E(x2191,x2192)+E(f63(x2191,x2193),f63(x2192,x2193))
% 160.93/160.66 [220]~E(x2201,x2202)+E(f63(x2203,x2201),f63(x2203,x2202))
% 160.93/160.66 [221]~E(x2211,x2212)+E(f13(x2211,x2213,x2214),f13(x2212,x2213,x2214))
% 160.93/160.66 [222]~E(x2221,x2222)+E(f13(x2223,x2221,x2224),f13(x2223,x2222,x2224))
% 160.93/160.66 [223]~E(x2231,x2232)+E(f13(x2233,x2234,x2231),f13(x2233,x2234,x2232))
% 160.93/160.66 [224]~E(x2241,x2242)+E(f118(x2241,x2243),f118(x2242,x2243))
% 160.93/160.66 [225]~E(x2251,x2252)+E(f118(x2253,x2251),f118(x2253,x2252))
% 160.93/160.66 [226]~E(x2261,x2262)+E(f187(x2261,x2263,x2264,x2265),f187(x2262,x2263,x2264,x2265))
% 160.93/160.66 [227]~E(x2271,x2272)+E(f187(x2273,x2271,x2274,x2275),f187(x2273,x2272,x2274,x2275))
% 160.93/160.66 [228]~E(x2281,x2282)+E(f187(x2283,x2284,x2281,x2285),f187(x2283,x2284,x2282,x2285))
% 160.93/160.66 [229]~E(x2291,x2292)+E(f187(x2293,x2294,x2295,x2291),f187(x2293,x2294,x2295,x2292))
% 160.93/160.66 [230]~E(x2301,x2302)+E(f193(x2301,x2303,x2304,x2305),f193(x2302,x2303,x2304,x2305))
% 160.93/160.66 [231]~E(x2311,x2312)+E(f193(x2313,x2311,x2314,x2315),f193(x2313,x2312,x2314,x2315))
% 160.93/160.66 [232]~E(x2321,x2322)+E(f193(x2323,x2324,x2321,x2325),f193(x2323,x2324,x2322,x2325))
% 160.93/160.66 [233]~E(x2331,x2332)+E(f193(x2333,x2334,x2335,x2331),f193(x2333,x2334,x2335,x2332))
% 160.93/160.66 [234]~E(x2341,x2342)+E(f265(x2341,x2343),f265(x2342,x2343))
% 160.93/160.66 [235]~E(x2351,x2352)+E(f265(x2353,x2351),f265(x2353,x2352))
% 160.93/160.66 [236]~E(x2361,x2362)+E(f90(x2361,x2363),f90(x2362,x2363))
% 160.93/160.66 [237]~E(x2371,x2372)+E(f90(x2373,x2371),f90(x2373,x2372))
% 160.93/160.66 [238]~E(x2381,x2382)+E(f259(x2381),f259(x2382))
% 160.93/160.66 [239]~E(x2391,x2392)+E(f321(x2391,x2393,x2394,x2395),f321(x2392,x2393,x2394,x2395))
% 160.93/160.66 [240]~E(x2401,x2402)+E(f321(x2403,x2401,x2404,x2405),f321(x2403,x2402,x2404,x2405))
% 160.93/160.66 [241]~E(x2411,x2412)+E(f321(x2413,x2414,x2411,x2415),f321(x2413,x2414,x2412,x2415))
% 160.93/160.66 [242]~E(x2421,x2422)+E(f321(x2423,x2424,x2425,x2421),f321(x2423,x2424,x2425,x2422))
% 160.93/160.66 [243]~E(x2431,x2432)+E(f322(x2431,x2433),f322(x2432,x2433))
% 160.93/160.66 [244]~E(x2441,x2442)+E(f322(x2443,x2441),f322(x2443,x2442))
% 160.93/160.66 [245]~E(x2451,x2452)+E(f449(x2451,x2453,x2454,x2455,x2456),f449(x2452,x2453,x2454,x2455,x2456))
% 160.93/160.66 [246]~E(x2461,x2462)+E(f449(x2463,x2461,x2464,x2465,x2466),f449(x2463,x2462,x2464,x2465,x2466))
% 160.93/160.66 [247]~E(x2471,x2472)+E(f449(x2473,x2474,x2471,x2475,x2476),f449(x2473,x2474,x2472,x2475,x2476))
% 160.93/160.66 [248]~E(x2481,x2482)+E(f449(x2483,x2484,x2485,x2481,x2486),f449(x2483,x2484,x2485,x2482,x2486))
% 160.93/160.66 [249]~E(x2491,x2492)+E(f449(x2493,x2494,x2495,x2496,x2491),f449(x2493,x2494,x2495,x2496,x2492))
% 160.93/160.66 [250]~E(x2501,x2502)+E(f147(x2501,x2503),f147(x2502,x2503))
% 160.93/160.66 [251]~E(x2511,x2512)+E(f147(x2513,x2511),f147(x2513,x2512))
% 160.93/160.66 [252]~E(x2521,x2522)+E(f165(x2521,x2523,x2524,x2525),f165(x2522,x2523,x2524,x2525))
% 160.93/160.66 [253]~E(x2531,x2532)+E(f165(x2533,x2531,x2534,x2535),f165(x2533,x2532,x2534,x2535))
% 160.93/160.66 [254]~E(x2541,x2542)+E(f165(x2543,x2544,x2541,x2545),f165(x2543,x2544,x2542,x2545))
% 160.93/160.66 [255]~E(x2551,x2552)+E(f165(x2553,x2554,x2555,x2551),f165(x2553,x2554,x2555,x2552))
% 160.93/160.66 [256]~E(x2561,x2562)+E(f763(x2561,x2563,x2564,x2565),f763(x2562,x2563,x2564,x2565))
% 160.93/160.66 [257]~E(x2571,x2572)+E(f763(x2573,x2571,x2574,x2575),f763(x2573,x2572,x2574,x2575))
% 160.93/160.66 [258]~E(x2581,x2582)+E(f763(x2583,x2584,x2581,x2585),f763(x2583,x2584,x2582,x2585))
% 160.93/160.66 [259]~E(x2591,x2592)+E(f763(x2593,x2594,x2595,x2591),f763(x2593,x2594,x2595,x2592))
% 160.93/160.66 [260]~E(x2601,x2602)+E(f38(x2601),f38(x2602))
% 160.93/160.66 [261]~E(x2611,x2612)+E(f143(x2611),f143(x2612))
% 160.93/160.66 [262]~E(x2621,x2622)+E(f761(x2621,x2623),f761(x2622,x2623))
% 160.93/160.66 [263]~E(x2631,x2632)+E(f761(x2633,x2631),f761(x2633,x2632))
% 160.93/160.66 [264]~E(x2641,x2642)+E(f756(x2641,x2643),f756(x2642,x2643))
% 160.93/160.66 [265]~E(x2651,x2652)+E(f756(x2653,x2651),f756(x2653,x2652))
% 160.93/160.66 [266]~E(x2661,x2662)+E(f160(x2661,x2663),f160(x2662,x2663))
% 160.93/160.66 [267]~E(x2671,x2672)+E(f160(x2673,x2671),f160(x2673,x2672))
% 160.93/160.66 [268]~E(x2681,x2682)+E(f303(x2681),f303(x2682))
% 160.93/160.66 [269]~E(x2691,x2692)+E(f57(x2691),f57(x2692))
% 160.93/160.66 [270]~E(x2701,x2702)+E(f154(x2701,x2703),f154(x2702,x2703))
% 160.93/160.66 [271]~E(x2711,x2712)+E(f154(x2713,x2711),f154(x2713,x2712))
% 160.93/160.66 [272]~E(x2721,x2722)+E(f824(x2721,x2723,x2724),f824(x2722,x2723,x2724))
% 160.93/160.66 [273]~E(x2731,x2732)+E(f824(x2733,x2731,x2734),f824(x2733,x2732,x2734))
% 160.93/160.66 [274]~E(x2741,x2742)+E(f824(x2743,x2744,x2741),f824(x2743,x2744,x2742))
% 160.93/160.66 [275]~E(x2751,x2752)+E(f199(x2751),f199(x2752))
% 160.93/160.66 [276]~E(x2761,x2762)+E(f11(x2761,x2763),f11(x2762,x2763))
% 160.93/160.66 [277]~E(x2771,x2772)+E(f11(x2773,x2771),f11(x2773,x2772))
% 160.93/160.66 [278]~E(x2781,x2782)+E(f119(x2781),f119(x2782))
% 160.93/160.66 [279]~E(x2791,x2792)+E(f431(x2791,x2793,x2794),f431(x2792,x2793,x2794))
% 160.93/160.66 [280]~E(x2801,x2802)+E(f431(x2803,x2801,x2804),f431(x2803,x2802,x2804))
% 160.93/160.66 [281]~E(x2811,x2812)+E(f431(x2813,x2814,x2811),f431(x2813,x2814,x2812))
% 160.93/160.66 [282]~E(x2821,x2822)+E(f12(x2821,x2823,x2824),f12(x2822,x2823,x2824))
% 160.93/160.66 [283]~E(x2831,x2832)+E(f12(x2833,x2831,x2834),f12(x2833,x2832,x2834))
% 160.93/160.66 [284]~E(x2841,x2842)+E(f12(x2843,x2844,x2841),f12(x2843,x2844,x2842))
% 160.93/160.66 [285]~E(x2851,x2852)+E(f191(x2851,x2853),f191(x2852,x2853))
% 160.93/160.66 [286]~E(x2861,x2862)+E(f191(x2863,x2861),f191(x2863,x2862))
% 160.93/160.66 [287]~E(x2871,x2872)+E(f86(x2871,x2873),f86(x2872,x2873))
% 160.93/160.66 [288]~E(x2881,x2882)+E(f86(x2883,x2881),f86(x2883,x2882))
% 160.93/160.66 [289]~E(x2891,x2892)+E(f32(x2891,x2893),f32(x2892,x2893))
% 160.93/160.66 [290]~E(x2901,x2902)+E(f32(x2903,x2901),f32(x2903,x2902))
% 160.93/160.66 [291]~E(x2911,x2912)+E(f886(x2911,x2913),f886(x2912,x2913))
% 160.93/160.66 [292]~E(x2921,x2922)+E(f886(x2923,x2921),f886(x2923,x2922))
% 160.93/160.66 [293]~E(x2931,x2932)+E(f256(x2931),f256(x2932))
% 160.93/160.66 [294]~E(x2941,x2942)+E(f270(x2941,x2943,x2944,x2945,x2946),f270(x2942,x2943,x2944,x2945,x2946))
% 160.93/160.66 [295]~E(x2951,x2952)+E(f270(x2953,x2951,x2954,x2955,x2956),f270(x2953,x2952,x2954,x2955,x2956))
% 160.93/160.66 [296]~E(x2961,x2962)+E(f270(x2963,x2964,x2961,x2965,x2966),f270(x2963,x2964,x2962,x2965,x2966))
% 160.93/160.66 [297]~E(x2971,x2972)+E(f270(x2973,x2974,x2975,x2971,x2976),f270(x2973,x2974,x2975,x2972,x2976))
% 160.93/160.66 [298]~E(x2981,x2982)+E(f270(x2983,x2984,x2985,x2986,x2981),f270(x2983,x2984,x2985,x2986,x2982))
% 160.93/160.66 [299]~E(x2991,x2992)+E(f87(x2991),f87(x2992))
% 160.93/160.66 [300]~E(x3001,x3002)+E(f170(x3001),f170(x3002))
% 160.93/160.66 [301]~E(x3011,x3012)+E(f168(x3011),f168(x3012))
% 160.93/160.66 [302]~E(x3021,x3022)+E(f146(x3021,x3023),f146(x3022,x3023))
% 160.93/160.66 [303]~E(x3031,x3032)+E(f146(x3033,x3031),f146(x3033,x3032))
% 160.93/160.66 [304]~E(x3041,x3042)+E(f66(x3041,x3043,x3044,x3045,x3046),f66(x3042,x3043,x3044,x3045,x3046))
% 160.93/160.66 [305]~E(x3051,x3052)+E(f66(x3053,x3051,x3054,x3055,x3056),f66(x3053,x3052,x3054,x3055,x3056))
% 160.93/160.66 [306]~E(x3061,x3062)+E(f66(x3063,x3064,x3061,x3065,x3066),f66(x3063,x3064,x3062,x3065,x3066))
% 160.93/160.66 [307]~E(x3071,x3072)+E(f66(x3073,x3074,x3075,x3071,x3076),f66(x3073,x3074,x3075,x3072,x3076))
% 160.93/160.66 [308]~E(x3081,x3082)+E(f66(x3083,x3084,x3085,x3086,x3081),f66(x3083,x3084,x3085,x3086,x3082))
% 160.93/160.66 [309]~E(x3091,x3092)+E(f173(x3091),f173(x3092))
% 160.93/160.66 [310]~E(x3101,x3102)+E(f813(x3101,x3103,x3104),f813(x3102,x3103,x3104))
% 160.93/160.66 [311]~E(x3111,x3112)+E(f813(x3113,x3111,x3114),f813(x3113,x3112,x3114))
% 160.93/160.66 [312]~E(x3121,x3122)+E(f813(x3123,x3124,x3121),f813(x3123,x3124,x3122))
% 160.93/160.66 [313]~E(x3131,x3132)+E(f348(x3131,x3133),f348(x3132,x3133))
% 160.93/160.66 [314]~E(x3141,x3142)+E(f348(x3143,x3141),f348(x3143,x3142))
% 160.93/160.66 [315]~E(x3151,x3152)+E(f399(x3151,x3153,x3154,x3155),f399(x3152,x3153,x3154,x3155))
% 160.93/160.66 [316]~E(x3161,x3162)+E(f399(x3163,x3161,x3164,x3165),f399(x3163,x3162,x3164,x3165))
% 160.93/160.66 [317]~E(x3171,x3172)+E(f399(x3173,x3174,x3171,x3175),f399(x3173,x3174,x3172,x3175))
% 160.93/160.66 [318]~E(x3181,x3182)+E(f399(x3183,x3184,x3185,x3181),f399(x3183,x3184,x3185,x3182))
% 160.93/160.66 [319]~E(x3191,x3192)+E(f867(x3191,x3193,x3194),f867(x3192,x3193,x3194))
% 160.93/160.66 [320]~E(x3201,x3202)+E(f867(x3203,x3201,x3204),f867(x3203,x3202,x3204))
% 160.93/160.66 [321]~E(x3211,x3212)+E(f867(x3213,x3214,x3211),f867(x3213,x3214,x3212))
% 160.93/160.66 [322]~E(x3221,x3222)+E(f177(x3221),f177(x3222))
% 160.93/160.66 [323]~E(x3231,x3232)+E(f502(x3231,x3233,x3234),f502(x3232,x3233,x3234))
% 160.93/160.66 [324]~E(x3241,x3242)+E(f502(x3243,x3241,x3244),f502(x3243,x3242,x3244))
% 160.93/160.66 [325]~E(x3251,x3252)+E(f502(x3253,x3254,x3251),f502(x3253,x3254,x3252))
% 160.93/160.66 [326]~E(x3261,x3262)+E(f485(x3261,x3263,x3264),f485(x3262,x3263,x3264))
% 160.93/160.66 [327]~E(x3271,x3272)+E(f485(x3273,x3271,x3274),f485(x3273,x3272,x3274))
% 160.93/160.66 [328]~E(x3281,x3282)+E(f485(x3283,x3284,x3281),f485(x3283,x3284,x3282))
% 160.93/160.66 [329]~E(x3291,x3292)+E(f361(x3291,x3293,x3294,x3295,x3296),f361(x3292,x3293,x3294,x3295,x3296))
% 160.93/160.66 [330]~E(x3301,x3302)+E(f361(x3303,x3301,x3304,x3305,x3306),f361(x3303,x3302,x3304,x3305,x3306))
% 160.93/160.66 [331]~E(x3311,x3312)+E(f361(x3313,x3314,x3311,x3315,x3316),f361(x3313,x3314,x3312,x3315,x3316))
% 160.93/160.66 [332]~E(x3321,x3322)+E(f361(x3323,x3324,x3325,x3321,x3326),f361(x3323,x3324,x3325,x3322,x3326))
% 160.93/160.66 [333]~E(x3331,x3332)+E(f361(x3333,x3334,x3335,x3336,x3331),f361(x3333,x3334,x3335,x3336,x3332))
% 160.93/160.66 [334]~E(x3341,x3342)+E(f58(x3341),f58(x3342))
% 160.93/160.66 [335]~E(x3351,x3352)+E(f770(x3351,x3353),f770(x3352,x3353))
% 160.93/160.66 [336]~E(x3361,x3362)+E(f770(x3363,x3361),f770(x3363,x3362))
% 160.93/160.66 [337]~E(x3371,x3372)+E(f316(x3371,x3373,x3374),f316(x3372,x3373,x3374))
% 160.93/160.66 [338]~E(x3381,x3382)+E(f316(x3383,x3381,x3384),f316(x3383,x3382,x3384))
% 160.93/160.66 [339]~E(x3391,x3392)+E(f316(x3393,x3394,x3391),f316(x3393,x3394,x3392))
% 160.93/160.66 [340]~E(x3401,x3402)+E(f180(x3401,x3403),f180(x3402,x3403))
% 160.93/160.66 [341]~E(x3411,x3412)+E(f180(x3413,x3411),f180(x3413,x3412))
% 160.93/160.66 [342]~E(x3421,x3422)+E(f304(x3421,x3423),f304(x3422,x3423))
% 160.93/160.66 [343]~E(x3431,x3432)+E(f304(x3433,x3431),f304(x3433,x3432))
% 160.93/160.66 [344]~E(x3441,x3442)+E(f233(x3441,x3443),f233(x3442,x3443))
% 160.93/160.66 [345]~E(x3451,x3452)+E(f233(x3453,x3451),f233(x3453,x3452))
% 160.93/160.66 [346]~E(x3461,x3462)+E(f325(x3461,x3463),f325(x3462,x3463))
% 160.93/160.66 [347]~E(x3471,x3472)+E(f325(x3473,x3471),f325(x3473,x3472))
% 160.93/160.66 [348]~E(x3481,x3482)+E(f210(x3481),f210(x3482))
% 160.93/160.66 [349]~E(x3491,x3492)+E(f327(x3491,x3493),f327(x3492,x3493))
% 160.93/160.66 [350]~E(x3501,x3502)+E(f327(x3503,x3501),f327(x3503,x3502))
% 160.93/160.66 [351]~E(x3511,x3512)+E(f700(x3511,x3513,x3514,x3515,x3516),f700(x3512,x3513,x3514,x3515,x3516))
% 160.93/160.66 [352]~E(x3521,x3522)+E(f700(x3523,x3521,x3524,x3525,x3526),f700(x3523,x3522,x3524,x3525,x3526))
% 160.93/160.66 [353]~E(x3531,x3532)+E(f700(x3533,x3534,x3531,x3535,x3536),f700(x3533,x3534,x3532,x3535,x3536))
% 160.93/160.66 [354]~E(x3541,x3542)+E(f700(x3543,x3544,x3545,x3541,x3546),f700(x3543,x3544,x3545,x3542,x3546))
% 160.93/160.66 [355]~E(x3551,x3552)+E(f700(x3553,x3554,x3555,x3556,x3551),f700(x3553,x3554,x3555,x3556,x3552))
% 160.93/160.66 [356]~E(x3561,x3562)+E(f39(x3561,x3563),f39(x3562,x3563))
% 160.93/160.66 [357]~E(x3571,x3572)+E(f39(x3573,x3571),f39(x3573,x3572))
% 160.93/160.66 [358]~E(x3581,x3582)+E(f782(x3581,x3583,x3584),f782(x3582,x3583,x3584))
% 160.93/160.66 [359]~E(x3591,x3592)+E(f782(x3593,x3591,x3594),f782(x3593,x3592,x3594))
% 160.93/160.66 [360]~E(x3601,x3602)+E(f782(x3603,x3604,x3601),f782(x3603,x3604,x3602))
% 160.93/160.66 [361]~E(x3611,x3612)+E(f306(x3611),f306(x3612))
% 160.93/160.66 [362]~E(x3621,x3622)+E(f291(x3621,x3623,x3624),f291(x3622,x3623,x3624))
% 160.93/160.66 [363]~E(x3631,x3632)+E(f291(x3633,x3631,x3634),f291(x3633,x3632,x3634))
% 160.93/160.66 [364]~E(x3641,x3642)+E(f291(x3643,x3644,x3641),f291(x3643,x3644,x3642))
% 160.93/160.66 [365]~E(x3651,x3652)+E(f474(x3651,x3653),f474(x3652,x3653))
% 160.93/160.66 [366]~E(x3661,x3662)+E(f474(x3663,x3661),f474(x3663,x3662))
% 160.93/160.66 [367]~E(x3671,x3672)+E(f541(x3671,x3673,x3674,x3675),f541(x3672,x3673,x3674,x3675))
% 160.93/160.66 [368]~E(x3681,x3682)+E(f541(x3683,x3681,x3684,x3685),f541(x3683,x3682,x3684,x3685))
% 160.93/160.66 [369]~E(x3691,x3692)+E(f541(x3693,x3694,x3691,x3695),f541(x3693,x3694,x3692,x3695))
% 160.93/160.66 [370]~E(x3701,x3702)+E(f541(x3703,x3704,x3705,x3701),f541(x3703,x3704,x3705,x3702))
% 160.93/160.66 [371]~E(x3711,x3712)+E(f9(x3711,x3713),f9(x3712,x3713))
% 160.93/160.66 [372]~E(x3721,x3722)+E(f9(x3723,x3721),f9(x3723,x3722))
% 160.93/160.66 [373]~E(x3731,x3732)+E(f172(x3731,x3733,x3734),f172(x3732,x3733,x3734))
% 160.93/160.66 [374]~E(x3741,x3742)+E(f172(x3743,x3741,x3744),f172(x3743,x3742,x3744))
% 160.93/160.66 [375]~E(x3751,x3752)+E(f172(x3753,x3754,x3751),f172(x3753,x3754,x3752))
% 160.93/160.66 [376]~E(x3761,x3762)+E(f287(x3761),f287(x3762))
% 160.93/160.66 [377]~E(x3771,x3772)+E(f821(x3771,x3773,x3774),f821(x3772,x3773,x3774))
% 160.93/160.66 [378]~E(x3781,x3782)+E(f821(x3783,x3781,x3784),f821(x3783,x3782,x3784))
% 160.93/160.66 [379]~E(x3791,x3792)+E(f821(x3793,x3794,x3791),f821(x3793,x3794,x3792))
% 160.93/160.66 [380]~E(x3801,x3802)+E(f47(x3801,x3803),f47(x3802,x3803))
% 160.93/160.66 [381]~E(x3811,x3812)+E(f47(x3813,x3811),f47(x3813,x3812))
% 160.93/160.66 [382]~E(x3821,x3822)+E(f793(x3821,x3823,x3824,x3825,x3826),f793(x3822,x3823,x3824,x3825,x3826))
% 160.93/160.66 [383]~E(x3831,x3832)+E(f793(x3833,x3831,x3834,x3835,x3836),f793(x3833,x3832,x3834,x3835,x3836))
% 160.93/160.66 [384]~E(x3841,x3842)+E(f793(x3843,x3844,x3841,x3845,x3846),f793(x3843,x3844,x3842,x3845,x3846))
% 160.93/160.66 [385]~E(x3851,x3852)+E(f793(x3853,x3854,x3855,x3851,x3856),f793(x3853,x3854,x3855,x3852,x3856))
% 160.93/160.66 [386]~E(x3861,x3862)+E(f793(x3863,x3864,x3865,x3866,x3861),f793(x3863,x3864,x3865,x3866,x3862))
% 160.93/160.66 [387]~E(x3871,x3872)+E(f189(x3871,x3873,x3874,x3875,x3876),f189(x3872,x3873,x3874,x3875,x3876))
% 160.93/160.66 [388]~E(x3881,x3882)+E(f189(x3883,x3881,x3884,x3885,x3886),f189(x3883,x3882,x3884,x3885,x3886))
% 160.93/160.66 [389]~E(x3891,x3892)+E(f189(x3893,x3894,x3891,x3895,x3896),f189(x3893,x3894,x3892,x3895,x3896))
% 160.93/160.66 [390]~E(x3901,x3902)+E(f189(x3903,x3904,x3905,x3901,x3906),f189(x3903,x3904,x3905,x3902,x3906))
% 160.93/160.66 [391]~E(x3911,x3912)+E(f189(x3913,x3914,x3915,x3916,x3911),f189(x3913,x3914,x3915,x3916,x3912))
% 160.93/160.66 [392]~E(x3921,x3922)+E(f815(x3921,x3923,x3924),f815(x3922,x3923,x3924))
% 160.93/160.66 [393]~E(x3931,x3932)+E(f815(x3933,x3931,x3934),f815(x3933,x3932,x3934))
% 160.93/160.66 [394]~E(x3941,x3942)+E(f815(x3943,x3944,x3941),f815(x3943,x3944,x3942))
% 160.93/160.66 [395]~E(x3951,x3952)+E(f64(x3951,x3953,x3954),f64(x3952,x3953,x3954))
% 160.93/160.66 [396]~E(x3961,x3962)+E(f64(x3963,x3961,x3964),f64(x3963,x3962,x3964))
% 160.93/160.66 [397]~E(x3971,x3972)+E(f64(x3973,x3974,x3971),f64(x3973,x3974,x3972))
% 160.93/160.66 [398]~E(x3981,x3982)+E(f466(x3981,x3983,x3984),f466(x3982,x3983,x3984))
% 160.93/160.66 [399]~E(x3991,x3992)+E(f466(x3993,x3991,x3994),f466(x3993,x3992,x3994))
% 160.93/160.66 [400]~E(x4001,x4002)+E(f466(x4003,x4004,x4001),f466(x4003,x4004,x4002))
% 160.93/160.66 [401]~E(x4011,x4012)+E(f141(x4011,x4013),f141(x4012,x4013))
% 160.93/160.66 [402]~E(x4021,x4022)+E(f141(x4023,x4021),f141(x4023,x4022))
% 160.93/160.66 [403]~E(x4031,x4032)+E(f228(x4031,x4033),f228(x4032,x4033))
% 160.93/160.66 [404]~E(x4041,x4042)+E(f228(x4043,x4041),f228(x4043,x4042))
% 160.93/160.66 [405]~E(x4051,x4052)+E(f181(x4051,x4053),f181(x4052,x4053))
% 160.93/160.66 [406]~E(x4061,x4062)+E(f181(x4063,x4061),f181(x4063,x4062))
% 160.93/160.66 [407]~E(x4071,x4072)+E(f155(x4071,x4073),f155(x4072,x4073))
% 160.93/160.66 [408]~E(x4081,x4082)+E(f155(x4083,x4081),f155(x4083,x4082))
% 160.93/160.66 [409]~E(x4091,x4092)+E(f798(x4091,x4093,x4094),f798(x4092,x4093,x4094))
% 160.93/160.66 [410]~E(x4101,x4102)+E(f798(x4103,x4101,x4104),f798(x4103,x4102,x4104))
% 160.93/160.66 [411]~E(x4111,x4112)+E(f798(x4113,x4114,x4111),f798(x4113,x4114,x4112))
% 160.93/160.66 [412]~E(x4121,x4122)+E(f283(x4121,x4123,x4124,x4125),f283(x4122,x4123,x4124,x4125))
% 160.93/160.66 [413]~E(x4131,x4132)+E(f283(x4133,x4131,x4134,x4135),f283(x4133,x4132,x4134,x4135))
% 160.93/160.66 [414]~E(x4141,x4142)+E(f283(x4143,x4144,x4141,x4145),f283(x4143,x4144,x4142,x4145))
% 160.93/160.66 [415]~E(x4151,x4152)+E(f283(x4153,x4154,x4155,x4151),f283(x4153,x4154,x4155,x4152))
% 160.93/160.66 [416]~E(x4161,x4162)+E(f43(x4161),f43(x4162))
% 160.93/160.66 [417]~E(x4171,x4172)+E(f209(x4171,x4173,x4174,x4175),f209(x4172,x4173,x4174,x4175))
% 160.93/160.66 [418]~E(x4181,x4182)+E(f209(x4183,x4181,x4184,x4185),f209(x4183,x4182,x4184,x4185))
% 160.93/160.66 [419]~E(x4191,x4192)+E(f209(x4193,x4194,x4191,x4195),f209(x4193,x4194,x4192,x4195))
% 160.93/160.66 [420]~E(x4201,x4202)+E(f209(x4203,x4204,x4205,x4201),f209(x4203,x4204,x4205,x4202))
% 160.93/160.66 [421]~E(x4211,x4212)+E(f460(x4211,x4213,x4214,x4215,x4216,x4217),f460(x4212,x4213,x4214,x4215,x4216,x4217))
% 160.93/160.66 [422]~E(x4221,x4222)+E(f460(x4223,x4221,x4224,x4225,x4226,x4227),f460(x4223,x4222,x4224,x4225,x4226,x4227))
% 160.93/160.66 [423]~E(x4231,x4232)+E(f460(x4233,x4234,x4231,x4235,x4236,x4237),f460(x4233,x4234,x4232,x4235,x4236,x4237))
% 160.93/160.66 [424]~E(x4241,x4242)+E(f460(x4243,x4244,x4245,x4241,x4246,x4247),f460(x4243,x4244,x4245,x4242,x4246,x4247))
% 160.93/160.66 [425]~E(x4251,x4252)+E(f460(x4253,x4254,x4255,x4256,x4251,x4257),f460(x4253,x4254,x4255,x4256,x4252,x4257))
% 160.93/160.66 [426]~E(x4261,x4262)+E(f460(x4263,x4264,x4265,x4266,x4267,x4261),f460(x4263,x4264,x4265,x4266,x4267,x4262))
% 160.93/160.66 [427]~E(x4271,x4272)+E(f789(x4271,x4273,x4274,x4275,x4276),f789(x4272,x4273,x4274,x4275,x4276))
% 160.93/160.66 [428]~E(x4281,x4282)+E(f789(x4283,x4281,x4284,x4285,x4286),f789(x4283,x4282,x4284,x4285,x4286))
% 160.93/160.66 [429]~E(x4291,x4292)+E(f789(x4293,x4294,x4291,x4295,x4296),f789(x4293,x4294,x4292,x4295,x4296))
% 160.93/160.66 [430]~E(x4301,x4302)+E(f789(x4303,x4304,x4305,x4301,x4306),f789(x4303,x4304,x4305,x4302,x4306))
% 160.93/160.66 [431]~E(x4311,x4312)+E(f789(x4313,x4314,x4315,x4316,x4311),f789(x4313,x4314,x4315,x4316,x4312))
% 160.93/160.66 [432]~E(x4321,x4322)+E(f811(x4321,x4323,x4324),f811(x4322,x4323,x4324))
% 160.93/160.66 [433]~E(x4331,x4332)+E(f811(x4333,x4331,x4334),f811(x4333,x4332,x4334))
% 160.93/160.66 [434]~E(x4341,x4342)+E(f811(x4343,x4344,x4341),f811(x4343,x4344,x4342))
% 160.93/160.66 [435]~E(x4351,x4352)+E(f10(x4351,x4353),f10(x4352,x4353))
% 160.93/160.66 [436]~E(x4361,x4362)+E(f10(x4363,x4361),f10(x4363,x4362))
% 160.93/160.66 [437]~E(x4371,x4372)+E(f314(x4371,x4373,x4374),f314(x4372,x4373,x4374))
% 160.93/160.66 [438]~E(x4381,x4382)+E(f314(x4383,x4381,x4384),f314(x4383,x4382,x4384))
% 160.93/160.66 [439]~E(x4391,x4392)+E(f314(x4393,x4394,x4391),f314(x4393,x4394,x4392))
% 160.93/160.66 [440]~E(x4401,x4402)+E(f186(x4401,x4403,x4404),f186(x4402,x4403,x4404))
% 160.93/160.66 [441]~E(x4411,x4412)+E(f186(x4413,x4411,x4414),f186(x4413,x4412,x4414))
% 160.93/160.66 [442]~E(x4421,x4422)+E(f186(x4423,x4424,x4421),f186(x4423,x4424,x4422))
% 160.93/160.66 [443]~E(x4431,x4432)+E(f133(x4431,x4433,x4434,x4435),f133(x4432,x4433,x4434,x4435))
% 160.93/160.66 [444]~E(x4441,x4442)+E(f133(x4443,x4441,x4444,x4445),f133(x4443,x4442,x4444,x4445))
% 160.93/160.66 [445]~E(x4451,x4452)+E(f133(x4453,x4454,x4451,x4455),f133(x4453,x4454,x4452,x4455))
% 160.93/160.66 [446]~E(x4461,x4462)+E(f133(x4463,x4464,x4465,x4461),f133(x4463,x4464,x4465,x4462))
% 160.93/160.66 [447]~E(x4471,x4472)+E(f127(x4471,x4473),f127(x4472,x4473))
% 160.93/160.66 [448]~E(x4481,x4482)+E(f127(x4483,x4481),f127(x4483,x4482))
% 160.93/160.66 [449]~E(x4491,x4492)+E(f302(x4491,x4493,x4494,x4495,x4496),f302(x4492,x4493,x4494,x4495,x4496))
% 160.93/160.66 [450]~E(x4501,x4502)+E(f302(x4503,x4501,x4504,x4505,x4506),f302(x4503,x4502,x4504,x4505,x4506))
% 160.93/160.66 [451]~E(x4511,x4512)+E(f302(x4513,x4514,x4511,x4515,x4516),f302(x4513,x4514,x4512,x4515,x4516))
% 160.93/160.66 [452]~E(x4521,x4522)+E(f302(x4523,x4524,x4525,x4521,x4526),f302(x4523,x4524,x4525,x4522,x4526))
% 160.93/160.66 [453]~E(x4531,x4532)+E(f302(x4533,x4534,x4535,x4536,x4531),f302(x4533,x4534,x4535,x4536,x4532))
% 160.93/160.66 [454]~E(x4541,x4542)+E(f163(x4541,x4543),f163(x4542,x4543))
% 160.93/160.66 [455]~E(x4551,x4552)+E(f163(x4553,x4551),f163(x4553,x4552))
% 160.93/160.66 [456]~E(x4561,x4562)+E(f511(x4561,x4563,x4564),f511(x4562,x4563,x4564))
% 160.93/160.66 [457]~E(x4571,x4572)+E(f511(x4573,x4571,x4574),f511(x4573,x4572,x4574))
% 160.93/160.66 [458]~E(x4581,x4582)+E(f511(x4583,x4584,x4581),f511(x4583,x4584,x4582))
% 160.93/160.66 [459]~E(x4591,x4592)+E(f138(x4591,x4593),f138(x4592,x4593))
% 160.93/160.66 [460]~E(x4601,x4602)+E(f138(x4603,x4601),f138(x4603,x4602))
% 160.93/160.66 [461]~E(x4611,x4612)+E(f412(x4611),f412(x4612))
% 160.93/160.66 [462]~E(x4621,x4622)+E(f274(x4621,x4623,x4624,x4625,x4626,x4627),f274(x4622,x4623,x4624,x4625,x4626,x4627))
% 160.93/160.66 [463]~E(x4631,x4632)+E(f274(x4633,x4631,x4634,x4635,x4636,x4637),f274(x4633,x4632,x4634,x4635,x4636,x4637))
% 160.93/160.66 [464]~E(x4641,x4642)+E(f274(x4643,x4644,x4641,x4645,x4646,x4647),f274(x4643,x4644,x4642,x4645,x4646,x4647))
% 160.93/160.66 [465]~E(x4651,x4652)+E(f274(x4653,x4654,x4655,x4651,x4656,x4657),f274(x4653,x4654,x4655,x4652,x4656,x4657))
% 160.93/160.66 [466]~E(x4661,x4662)+E(f274(x4663,x4664,x4665,x4666,x4661,x4667),f274(x4663,x4664,x4665,x4666,x4662,x4667))
% 160.93/160.66 [467]~E(x4671,x4672)+E(f274(x4673,x4674,x4675,x4676,x4677,x4671),f274(x4673,x4674,x4675,x4676,x4677,x4672))
% 160.93/160.66 [468]~E(x4681,x4682)+E(f273(x4681,x4683,x4684),f273(x4682,x4683,x4684))
% 160.93/160.66 [469]~E(x4691,x4692)+E(f273(x4693,x4691,x4694),f273(x4693,x4692,x4694))
% 160.93/160.66 [470]~E(x4701,x4702)+E(f273(x4703,x4704,x4701),f273(x4703,x4704,x4702))
% 160.93/160.66 [471]~E(x4711,x4712)+E(f121(x4711,x4713,x4714),f121(x4712,x4713,x4714))
% 160.93/160.66 [472]~E(x4721,x4722)+E(f121(x4723,x4721,x4724),f121(x4723,x4722,x4724))
% 160.93/160.66 [473]~E(x4731,x4732)+E(f121(x4733,x4734,x4731),f121(x4733,x4734,x4732))
% 160.93/160.66 [474]~E(x4741,x4742)+E(f48(x4741,x4743),f48(x4742,x4743))
% 160.93/160.66 [475]~E(x4751,x4752)+E(f48(x4753,x4751),f48(x4753,x4752))
% 160.93/160.66 [476]~E(x4761,x4762)+E(f550(x4761,x4763,x4764,x4765),f550(x4762,x4763,x4764,x4765))
% 160.93/160.66 [477]~E(x4771,x4772)+E(f550(x4773,x4771,x4774,x4775),f550(x4773,x4772,x4774,x4775))
% 160.93/160.66 [478]~E(x4781,x4782)+E(f550(x4783,x4784,x4781,x4785),f550(x4783,x4784,x4782,x4785))
% 160.93/160.66 [479]~E(x4791,x4792)+E(f550(x4793,x4794,x4795,x4791),f550(x4793,x4794,x4795,x4792))
% 160.93/160.66 [480]~E(x4801,x4802)+E(f190(x4801,x4803,x4804,x4805),f190(x4802,x4803,x4804,x4805))
% 160.93/160.66 [481]~E(x4811,x4812)+E(f190(x4813,x4811,x4814,x4815),f190(x4813,x4812,x4814,x4815))
% 160.93/160.66 [482]~E(x4821,x4822)+E(f190(x4823,x4824,x4821,x4825),f190(x4823,x4824,x4822,x4825))
% 160.93/160.66 [483]~E(x4831,x4832)+E(f190(x4833,x4834,x4835,x4831),f190(x4833,x4834,x4835,x4832))
% 160.93/160.66 [484]~E(x4841,x4842)+E(f206(x4841,x4843,x4844,x4845),f206(x4842,x4843,x4844,x4845))
% 160.93/160.66 [485]~E(x4851,x4852)+E(f206(x4853,x4851,x4854,x4855),f206(x4853,x4852,x4854,x4855))
% 160.93/160.66 [486]~E(x4861,x4862)+E(f206(x4863,x4864,x4861,x4865),f206(x4863,x4864,x4862,x4865))
% 160.93/160.66 [487]~E(x4871,x4872)+E(f206(x4873,x4874,x4875,x4871),f206(x4873,x4874,x4875,x4872))
% 160.93/160.66 [488]~E(x4881,x4882)+E(f267(x4881,x4883),f267(x4882,x4883))
% 160.93/160.66 [489]~E(x4891,x4892)+E(f267(x4893,x4891),f267(x4893,x4892))
% 160.93/160.66 [490]~E(x4901,x4902)+E(f280(x4901,x4903),f280(x4902,x4903))
% 160.93/160.66 [491]~E(x4911,x4912)+E(f280(x4913,x4911),f280(x4913,x4912))
% 160.93/160.66 [492]~E(x4921,x4922)+E(f363(x4921,x4923),f363(x4922,x4923))
% 160.93/160.66 [493]~E(x4931,x4932)+E(f363(x4933,x4931),f363(x4933,x4932))
% 160.93/160.66 [494]~E(x4941,x4942)+E(f686(x4941,x4943,x4944),f686(x4942,x4943,x4944))
% 160.93/160.66 [495]~E(x4951,x4952)+E(f686(x4953,x4951,x4954),f686(x4953,x4952,x4954))
% 160.93/160.66 [496]~E(x4961,x4962)+E(f686(x4963,x4964,x4961),f686(x4963,x4964,x4962))
% 160.93/160.66 [497]~E(x4971,x4972)+E(f225(x4971),f225(x4972))
% 160.93/160.66 [498]~E(x4981,x4982)+E(f309(x4981),f309(x4982))
% 160.93/160.66 [499]~E(x4991,x4992)+E(f140(x4991),f140(x4992))
% 160.93/160.66 [500]~E(x5001,x5002)+E(f812(x5001,x5003,x5004),f812(x5002,x5003,x5004))
% 160.93/160.66 [501]~E(x5011,x5012)+E(f812(x5013,x5011,x5014),f812(x5013,x5012,x5014))
% 160.93/160.66 [502]~E(x5021,x5022)+E(f812(x5023,x5024,x5021),f812(x5023,x5024,x5022))
% 160.93/160.66 [503]~E(x5031,x5032)+E(f311(x5031),f311(x5032))
% 160.93/160.66 [504]~E(x5041,x5042)+E(f715(x5041,x5043,x5044),f715(x5042,x5043,x5044))
% 160.93/160.66 [505]~E(x5051,x5052)+E(f715(x5053,x5051,x5054),f715(x5053,x5052,x5054))
% 160.93/160.66 [506]~E(x5061,x5062)+E(f715(x5063,x5064,x5061),f715(x5063,x5064,x5062))
% 160.93/160.66 [507]~E(x5071,x5072)+E(f616(x5071,x5073,x5074),f616(x5072,x5073,x5074))
% 160.93/160.66 [508]~E(x5081,x5082)+E(f616(x5083,x5081,x5084),f616(x5083,x5082,x5084))
% 160.93/160.66 [509]~E(x5091,x5092)+E(f616(x5093,x5094,x5091),f616(x5093,x5094,x5092))
% 160.93/160.66 [510]~E(x5101,x5102)+E(f179(x5101,x5103,x5104),f179(x5102,x5103,x5104))
% 160.93/160.66 [511]~E(x5111,x5112)+E(f179(x5113,x5111,x5114),f179(x5113,x5112,x5114))
% 160.93/160.66 [512]~E(x5121,x5122)+E(f179(x5123,x5124,x5121),f179(x5123,x5124,x5122))
% 160.93/160.66 [513]~E(x5131,x5132)+E(f255(x5131),f255(x5132))
% 160.93/160.66 [514]~E(x5141,x5142)+E(f73(x5141,x5143,x5144,x5145),f73(x5142,x5143,x5144,x5145))
% 160.93/160.66 [515]~E(x5151,x5152)+E(f73(x5153,x5151,x5154,x5155),f73(x5153,x5152,x5154,x5155))
% 160.93/160.66 [516]~E(x5161,x5162)+E(f73(x5163,x5164,x5161,x5165),f73(x5163,x5164,x5162,x5165))
% 160.93/160.66 [517]~E(x5171,x5172)+E(f73(x5173,x5174,x5175,x5171),f73(x5173,x5174,x5175,x5172))
% 160.93/160.66 [518]~E(x5181,x5182)+E(f307(x5181,x5183,x5184),f307(x5182,x5183,x5184))
% 160.93/160.66 [519]~E(x5191,x5192)+E(f307(x5193,x5191,x5194),f307(x5193,x5192,x5194))
% 160.93/160.66 [520]~E(x5201,x5202)+E(f307(x5203,x5204,x5201),f307(x5203,x5204,x5202))
% 160.93/160.66 [521]~E(x5211,x5212)+E(f654(x5211,x5213,x5214,x5215),f654(x5212,x5213,x5214,x5215))
% 160.93/160.66 [522]~E(x5221,x5222)+E(f654(x5223,x5221,x5224,x5225),f654(x5223,x5222,x5224,x5225))
% 160.93/160.66 [523]~E(x5231,x5232)+E(f654(x5233,x5234,x5231,x5235),f654(x5233,x5234,x5232,x5235))
% 160.93/160.66 [524]~E(x5241,x5242)+E(f654(x5243,x5244,x5245,x5241),f654(x5243,x5244,x5245,x5242))
% 160.93/160.66 [525]~E(x5251,x5252)+E(f816(x5251,x5253,x5254,x5255),f816(x5252,x5253,x5254,x5255))
% 160.93/160.66 [526]~E(x5261,x5262)+E(f816(x5263,x5261,x5264,x5265),f816(x5263,x5262,x5264,x5265))
% 160.93/160.66 [527]~E(x5271,x5272)+E(f816(x5273,x5274,x5271,x5275),f816(x5273,x5274,x5272,x5275))
% 160.93/160.66 [528]~E(x5281,x5282)+E(f816(x5283,x5284,x5285,x5281),f816(x5283,x5284,x5285,x5282))
% 160.93/160.66 [529]~E(x5291,x5292)+E(f395(x5291,x5293,x5294,x5295),f395(x5292,x5293,x5294,x5295))
% 160.93/160.66 [530]~E(x5301,x5302)+E(f395(x5303,x5301,x5304,x5305),f395(x5303,x5302,x5304,x5305))
% 160.93/160.66 [531]~E(x5311,x5312)+E(f395(x5313,x5314,x5311,x5315),f395(x5313,x5314,x5312,x5315))
% 160.93/160.66 [532]~E(x5321,x5322)+E(f395(x5323,x5324,x5325,x5321),f395(x5323,x5324,x5325,x5322))
% 160.93/160.66 [533]~E(x5331,x5332)+E(f748(x5331,x5333),f748(x5332,x5333))
% 160.93/160.66 [534]~E(x5341,x5342)+E(f748(x5343,x5341),f748(x5343,x5342))
% 160.93/160.66 [535]~E(x5351,x5352)+E(f236(x5351,x5353,x5354),f236(x5352,x5353,x5354))
% 160.93/160.66 [536]~E(x5361,x5362)+E(f236(x5363,x5361,x5364),f236(x5363,x5362,x5364))
% 160.93/160.66 [537]~E(x5371,x5372)+E(f236(x5373,x5374,x5371),f236(x5373,x5374,x5372))
% 160.93/160.66 [538]~E(x5381,x5382)+E(f308(x5381,x5383,x5384),f308(x5382,x5383,x5384))
% 160.93/160.66 [539]~E(x5391,x5392)+E(f308(x5393,x5391,x5394),f308(x5393,x5392,x5394))
% 160.93/160.66 [540]~E(x5401,x5402)+E(f308(x5403,x5404,x5401),f308(x5403,x5404,x5402))
% 160.93/160.66 [541]~E(x5411,x5412)+E(f427(x5411,x5413,x5414,x5415,x5416),f427(x5412,x5413,x5414,x5415,x5416))
% 160.93/160.66 [542]~E(x5421,x5422)+E(f427(x5423,x5421,x5424,x5425,x5426),f427(x5423,x5422,x5424,x5425,x5426))
% 160.93/160.66 [543]~E(x5431,x5432)+E(f427(x5433,x5434,x5431,x5435,x5436),f427(x5433,x5434,x5432,x5435,x5436))
% 160.93/160.66 [544]~E(x5441,x5442)+E(f427(x5443,x5444,x5445,x5441,x5446),f427(x5443,x5444,x5445,x5442,x5446))
% 160.93/160.66 [545]~E(x5451,x5452)+E(f427(x5453,x5454,x5455,x5456,x5451),f427(x5453,x5454,x5455,x5456,x5452))
% 160.93/160.66 [546]~E(x5461,x5462)+E(f400(x5461,x5463,x5464,x5465),f400(x5462,x5463,x5464,x5465))
% 160.93/160.66 [547]~E(x5471,x5472)+E(f400(x5473,x5471,x5474,x5475),f400(x5473,x5472,x5474,x5475))
% 160.93/160.66 [548]~E(x5481,x5482)+E(f400(x5483,x5484,x5481,x5485),f400(x5483,x5484,x5482,x5485))
% 160.93/160.66 [549]~E(x5491,x5492)+E(f400(x5493,x5494,x5495,x5491),f400(x5493,x5494,x5495,x5492))
% 160.93/160.66 [550]~E(x5501,x5502)+E(f814(x5501,x5503,x5504),f814(x5502,x5503,x5504))
% 160.93/160.66 [551]~E(x5511,x5512)+E(f814(x5513,x5511,x5514),f814(x5513,x5512,x5514))
% 160.93/160.66 [552]~E(x5521,x5522)+E(f814(x5523,x5524,x5521),f814(x5523,x5524,x5522))
% 160.93/160.66 [553]~E(x5531,x5532)+E(f473(x5531,x5533),f473(x5532,x5533))
% 160.93/160.66 [554]~E(x5541,x5542)+E(f473(x5543,x5541),f473(x5543,x5542))
% 160.93/160.66 [555]~E(x5551,x5552)+E(f169(x5551,x5553,x5554),f169(x5552,x5553,x5554))
% 160.93/160.66 [556]~E(x5561,x5562)+E(f169(x5563,x5561,x5564),f169(x5563,x5562,x5564))
% 160.93/160.66 [557]~E(x5571,x5572)+E(f169(x5573,x5574,x5571),f169(x5573,x5574,x5572))
% 160.93/160.66 [558]~E(x5581,x5582)+E(f522(x5581,x5583,x5584),f522(x5582,x5583,x5584))
% 160.93/160.66 [559]~E(x5591,x5592)+E(f522(x5593,x5591,x5594),f522(x5593,x5592,x5594))
% 160.93/160.66 [560]~E(x5601,x5602)+E(f522(x5603,x5604,x5601),f522(x5603,x5604,x5602))
% 160.93/160.66 [561]~E(x5611,x5612)+E(f100(x5611),f100(x5612))
% 160.93/160.66 [562]~E(x5621,x5622)+E(f842(x5621,x5623,x5624),f842(x5622,x5623,x5624))
% 160.93/160.66 [563]~E(x5631,x5632)+E(f842(x5633,x5631,x5634),f842(x5633,x5632,x5634))
% 160.93/160.66 [564]~E(x5641,x5642)+E(f842(x5643,x5644,x5641),f842(x5643,x5644,x5642))
% 160.93/160.66 [565]~E(x5651,x5652)+E(f367(x5651,x5653),f367(x5652,x5653))
% 160.93/160.66 [566]~E(x5661,x5662)+E(f367(x5663,x5661),f367(x5663,x5662))
% 160.93/160.66 [567]~E(x5671,x5672)+E(f783(x5671,x5673),f783(x5672,x5673))
% 160.93/160.66 [568]~E(x5681,x5682)+E(f783(x5683,x5681),f783(x5683,x5682))
% 160.93/160.66 [569]~E(x5691,x5692)+E(f152(x5691,x5693,x5694,x5695),f152(x5692,x5693,x5694,x5695))
% 160.93/160.66 [570]~E(x5701,x5702)+E(f152(x5703,x5701,x5704,x5705),f152(x5703,x5702,x5704,x5705))
% 160.93/160.66 [571]~E(x5711,x5712)+E(f152(x5713,x5714,x5711,x5715),f152(x5713,x5714,x5712,x5715))
% 160.93/160.66 [572]~E(x5721,x5722)+E(f152(x5723,x5724,x5725,x5721),f152(x5723,x5724,x5725,x5722))
% 160.93/160.66 [573]~E(x5731,x5732)+E(f240(x5731,x5733),f240(x5732,x5733))
% 160.93/160.66 [574]~E(x5741,x5742)+E(f240(x5743,x5741),f240(x5743,x5742))
% 160.93/160.66 [575]~E(x5751,x5752)+E(f362(x5751),f362(x5752))
% 160.93/160.66 [576]~E(x5761,x5762)+E(f769(x5761,x5763),f769(x5762,x5763))
% 160.93/160.66 [577]~E(x5771,x5772)+E(f769(x5773,x5771),f769(x5773,x5772))
% 160.93/160.66 [578]~E(x5781,x5782)+E(f65(x5781,x5783,x5784),f65(x5782,x5783,x5784))
% 160.93/160.66 [579]~E(x5791,x5792)+E(f65(x5793,x5791,x5794),f65(x5793,x5792,x5794))
% 160.93/160.66 [580]~E(x5801,x5802)+E(f65(x5803,x5804,x5801),f65(x5803,x5804,x5802))
% 160.93/160.66 [581]~E(x5811,x5812)+E(f668(x5811,x5813,x5814,x5815),f668(x5812,x5813,x5814,x5815))
% 160.93/160.66 [582]~E(x5821,x5822)+E(f668(x5823,x5821,x5824,x5825),f668(x5823,x5822,x5824,x5825))
% 160.93/160.66 [583]~E(x5831,x5832)+E(f668(x5833,x5834,x5831,x5835),f668(x5833,x5834,x5832,x5835))
% 160.93/160.66 [584]~E(x5841,x5842)+E(f668(x5843,x5844,x5845,x5841),f668(x5843,x5844,x5845,x5842))
% 160.93/160.66 [585]~E(x5851,x5852)+E(f439(x5851,x5853,x5854,x5855,x5856),f439(x5852,x5853,x5854,x5855,x5856))
% 160.93/160.66 [586]~E(x5861,x5862)+E(f439(x5863,x5861,x5864,x5865,x5866),f439(x5863,x5862,x5864,x5865,x5866))
% 160.93/160.66 [587]~E(x5871,x5872)+E(f439(x5873,x5874,x5871,x5875,x5876),f439(x5873,x5874,x5872,x5875,x5876))
% 160.93/160.66 [588]~E(x5881,x5882)+E(f439(x5883,x5884,x5885,x5881,x5886),f439(x5883,x5884,x5885,x5882,x5886))
% 160.93/160.66 [589]~E(x5891,x5892)+E(f439(x5893,x5894,x5895,x5896,x5891),f439(x5893,x5894,x5895,x5896,x5892))
% 160.93/160.66 [590]~E(x5901,x5902)+E(f341(x5901),f341(x5902))
% 160.93/160.66 [591]~E(x5911,x5912)+E(f514(x5911,x5913,x5914,x5915,x5916,x5917,x5918,x5919),f514(x5912,x5913,x5914,x5915,x5916,x5917,x5918,x5919))
% 160.93/160.66 [592]~E(x5921,x5922)+E(f514(x5923,x5921,x5924,x5925,x5926,x5927,x5928,x5929),f514(x5923,x5922,x5924,x5925,x5926,x5927,x5928,x5929))
% 160.93/160.66 [593]~E(x5931,x5932)+E(f514(x5933,x5934,x5931,x5935,x5936,x5937,x5938,x5939),f514(x5933,x5934,x5932,x5935,x5936,x5937,x5938,x5939))
% 160.93/160.66 [594]~E(x5941,x5942)+E(f514(x5943,x5944,x5945,x5941,x5946,x5947,x5948,x5949),f514(x5943,x5944,x5945,x5942,x5946,x5947,x5948,x5949))
% 160.93/160.66 [595]~E(x5951,x5952)+E(f514(x5953,x5954,x5955,x5956,x5951,x5957,x5958,x5959),f514(x5953,x5954,x5955,x5956,x5952,x5957,x5958,x5959))
% 160.93/160.66 [596]~E(x5961,x5962)+E(f514(x5963,x5964,x5965,x5966,x5967,x5961,x5968,x5969),f514(x5963,x5964,x5965,x5966,x5967,x5962,x5968,x5969))
% 160.93/160.66 [597]~E(x5971,x5972)+E(f514(x5973,x5974,x5975,x5976,x5977,x5978,x5971,x5979),f514(x5973,x5974,x5975,x5976,x5977,x5978,x5972,x5979))
% 160.93/160.66 [598]~E(x5981,x5982)+E(f514(x5983,x5984,x5985,x5986,x5987,x5988,x5989,x5981),f514(x5983,x5984,x5985,x5986,x5987,x5988,x5989,x5982))
% 160.93/160.66 [599]~E(x5991,x5992)+E(f360(x5991,x5993,x5994,x5995),f360(x5992,x5993,x5994,x5995))
% 160.93/160.66 [600]~E(x6001,x6002)+E(f360(x6003,x6001,x6004,x6005),f360(x6003,x6002,x6004,x6005))
% 160.93/160.66 [601]~E(x6011,x6012)+E(f360(x6013,x6014,x6011,x6015),f360(x6013,x6014,x6012,x6015))
% 160.93/160.66 [602]~E(x6021,x6022)+E(f360(x6023,x6024,x6025,x6021),f360(x6023,x6024,x6025,x6022))
% 160.93/160.66 [603]~E(x6031,x6032)+E(f176(x6031,x6033,x6034),f176(x6032,x6033,x6034))
% 160.93/160.66 [604]~E(x6041,x6042)+E(f176(x6043,x6041,x6044),f176(x6043,x6042,x6044))
% 160.93/160.66 [605]~E(x6051,x6052)+E(f176(x6053,x6054,x6051),f176(x6053,x6054,x6052))
% 160.93/160.66 [606]~E(x6061,x6062)+E(f498(x6061,x6063,x6064),f498(x6062,x6063,x6064))
% 160.93/160.66 [607]~E(x6071,x6072)+E(f498(x6073,x6071,x6074),f498(x6073,x6072,x6074))
% 160.93/160.66 [608]~E(x6081,x6082)+E(f498(x6083,x6084,x6081),f498(x6083,x6084,x6082))
% 160.93/160.66 [609]~E(x6091,x6092)+E(f742(x6091,x6093,x6094,x6095,x6096),f742(x6092,x6093,x6094,x6095,x6096))
% 160.93/160.66 [610]~E(x6101,x6102)+E(f742(x6103,x6101,x6104,x6105,x6106),f742(x6103,x6102,x6104,x6105,x6106))
% 160.93/160.66 [611]~E(x6111,x6112)+E(f742(x6113,x6114,x6111,x6115,x6116),f742(x6113,x6114,x6112,x6115,x6116))
% 160.93/160.66 [612]~E(x6121,x6122)+E(f742(x6123,x6124,x6125,x6121,x6126),f742(x6123,x6124,x6125,x6122,x6126))
% 160.93/160.66 [613]~E(x6131,x6132)+E(f742(x6133,x6134,x6135,x6136,x6131),f742(x6133,x6134,x6135,x6136,x6132))
% 160.93/160.66 [614]~E(x6141,x6142)+E(f760(x6141,x6143,x6144,x6145,x6146),f760(x6142,x6143,x6144,x6145,x6146))
% 160.93/160.66 [615]~E(x6151,x6152)+E(f760(x6153,x6151,x6154,x6155,x6156),f760(x6153,x6152,x6154,x6155,x6156))
% 160.93/160.66 [616]~E(x6161,x6162)+E(f760(x6163,x6164,x6161,x6165,x6166),f760(x6163,x6164,x6162,x6165,x6166))
% 160.93/160.66 [617]~E(x6171,x6172)+E(f760(x6173,x6174,x6175,x6171,x6176),f760(x6173,x6174,x6175,x6172,x6176))
% 160.93/160.66 [618]~E(x6181,x6182)+E(f760(x6183,x6184,x6185,x6186,x6181),f760(x6183,x6184,x6185,x6186,x6182))
% 160.93/160.66 [619]~E(x6191,x6192)+E(f326(x6191,x6193,x6194,x6195),f326(x6192,x6193,x6194,x6195))
% 160.93/160.66 [620]~E(x6201,x6202)+E(f326(x6203,x6201,x6204,x6205),f326(x6203,x6202,x6204,x6205))
% 160.93/160.66 [621]~E(x6211,x6212)+E(f326(x6213,x6214,x6211,x6215),f326(x6213,x6214,x6212,x6215))
% 160.93/160.66 [622]~E(x6221,x6222)+E(f326(x6223,x6224,x6225,x6221),f326(x6223,x6224,x6225,x6222))
% 160.93/160.66 [623]~E(x6231,x6232)+E(f590(x6231,x6233,x6234),f590(x6232,x6233,x6234))
% 160.93/160.66 [624]~E(x6241,x6242)+E(f590(x6243,x6241,x6244),f590(x6243,x6242,x6244))
% 160.93/160.66 [625]~E(x6251,x6252)+E(f590(x6253,x6254,x6251),f590(x6253,x6254,x6252))
% 160.93/160.66 [626]~E(x6261,x6262)+E(f286(x6261,x6263,x6264,x6265),f286(x6262,x6263,x6264,x6265))
% 160.93/160.66 [627]~E(x6271,x6272)+E(f286(x6273,x6271,x6274,x6275),f286(x6273,x6272,x6274,x6275))
% 160.93/160.66 [628]~E(x6281,x6282)+E(f286(x6283,x6284,x6281,x6285),f286(x6283,x6284,x6282,x6285))
% 160.93/160.66 [629]~E(x6291,x6292)+E(f286(x6293,x6294,x6295,x6291),f286(x6293,x6294,x6295,x6292))
% 160.93/160.66 [630]~E(x6301,x6302)+E(f563(x6301,x6303,x6304,x6305),f563(x6302,x6303,x6304,x6305))
% 160.93/160.66 [631]~E(x6311,x6312)+E(f563(x6313,x6311,x6314,x6315),f563(x6313,x6312,x6314,x6315))
% 160.93/160.66 [632]~E(x6321,x6322)+E(f563(x6323,x6324,x6321,x6325),f563(x6323,x6324,x6322,x6325))
% 160.93/160.66 [633]~E(x6331,x6332)+E(f563(x6333,x6334,x6335,x6331),f563(x6333,x6334,x6335,x6332))
% 160.93/160.66 [634]~E(x6341,x6342)+E(f288(x6341,x6343,x6344),f288(x6342,x6343,x6344))
% 160.93/160.66 [635]~E(x6351,x6352)+E(f288(x6353,x6351,x6354),f288(x6353,x6352,x6354))
% 160.93/160.66 [636]~E(x6361,x6362)+E(f288(x6363,x6364,x6361),f288(x6363,x6364,x6362))
% 160.93/160.66 [637]~E(x6371,x6372)+E(f162(x6371,x6373),f162(x6372,x6373))
% 160.93/160.66 [638]~E(x6381,x6382)+E(f162(x6383,x6381),f162(x6383,x6382))
% 160.93/160.66 [639]~E(x6391,x6392)+E(f159(x6391,x6393),f159(x6392,x6393))
% 160.93/160.66 [640]~E(x6401,x6402)+E(f159(x6403,x6401),f159(x6403,x6402))
% 160.93/160.66 [641]~E(x6411,x6412)+E(f656(x6411,x6413,x6414),f656(x6412,x6413,x6414))
% 160.93/160.66 [642]~E(x6421,x6422)+E(f656(x6423,x6421,x6424),f656(x6423,x6422,x6424))
% 160.93/160.66 [643]~E(x6431,x6432)+E(f656(x6433,x6434,x6431),f656(x6433,x6434,x6432))
% 160.93/160.66 [644]~E(x6441,x6442)+E(f52(x6441,x6443),f52(x6442,x6443))
% 160.93/160.66 [645]~E(x6451,x6452)+E(f52(x6453,x6451),f52(x6453,x6452))
% 160.93/160.66 [646]~E(x6461,x6462)+E(f801(x6461,x6463,x6464),f801(x6462,x6463,x6464))
% 160.93/160.66 [647]~E(x6471,x6472)+E(f801(x6473,x6471,x6474),f801(x6473,x6472,x6474))
% 160.93/160.66 [648]~E(x6481,x6482)+E(f801(x6483,x6484,x6481),f801(x6483,x6484,x6482))
% 160.93/160.66 [649]~E(x6491,x6492)+E(f670(x6491,x6493,x6494,x6495),f670(x6492,x6493,x6494,x6495))
% 160.93/160.66 [650]~E(x6501,x6502)+E(f670(x6503,x6501,x6504,x6505),f670(x6503,x6502,x6504,x6505))
% 160.93/160.66 [651]~E(x6511,x6512)+E(f670(x6513,x6514,x6511,x6515),f670(x6513,x6514,x6512,x6515))
% 160.93/160.66 [652]~E(x6521,x6522)+E(f670(x6523,x6524,x6525,x6521),f670(x6523,x6524,x6525,x6522))
% 160.93/160.66 [653]~E(x6531,x6532)+E(f672(x6531,x6533,x6534,x6535),f672(x6532,x6533,x6534,x6535))
% 160.93/160.66 [654]~E(x6541,x6542)+E(f672(x6543,x6541,x6544,x6545),f672(x6543,x6542,x6544,x6545))
% 160.93/160.66 [655]~E(x6551,x6552)+E(f672(x6553,x6554,x6551,x6555),f672(x6553,x6554,x6552,x6555))
% 160.93/160.66 [656]~E(x6561,x6562)+E(f672(x6563,x6564,x6565,x6561),f672(x6563,x6564,x6565,x6562))
% 160.93/160.66 [657]~E(x6571,x6572)+E(f55(x6571),f55(x6572))
% 160.93/160.66 [658]~E(x6581,x6582)+E(f33(x6581,x6583),f33(x6582,x6583))
% 160.93/160.66 [659]~E(x6591,x6592)+E(f33(x6593,x6591),f33(x6593,x6592))
% 160.93/160.66 [660]~E(x6601,x6602)+E(f423(x6601,x6603,x6604),f423(x6602,x6603,x6604))
% 160.93/160.66 [661]~E(x6611,x6612)+E(f423(x6613,x6611,x6614),f423(x6613,x6612,x6614))
% 160.93/160.66 [662]~E(x6621,x6622)+E(f423(x6623,x6624,x6621),f423(x6623,x6624,x6622))
% 160.93/160.66 [663]~E(x6631,x6632)+E(f696(x6631,x6633,x6634),f696(x6632,x6633,x6634))
% 160.93/160.66 [664]~E(x6641,x6642)+E(f696(x6643,x6641,x6644),f696(x6643,x6642,x6644))
% 160.93/160.66 [665]~E(x6651,x6652)+E(f696(x6653,x6654,x6651),f696(x6653,x6654,x6652))
% 160.93/160.66 [666]~E(x6661,x6662)+E(f432(x6661,x6663,x6664,x6665,x6666),f432(x6662,x6663,x6664,x6665,x6666))
% 160.93/160.66 [667]~E(x6671,x6672)+E(f432(x6673,x6671,x6674,x6675,x6676),f432(x6673,x6672,x6674,x6675,x6676))
% 160.93/160.66 [668]~E(x6681,x6682)+E(f432(x6683,x6684,x6681,x6685,x6686),f432(x6683,x6684,x6682,x6685,x6686))
% 160.93/160.66 [669]~E(x6691,x6692)+E(f432(x6693,x6694,x6695,x6691,x6696),f432(x6693,x6694,x6695,x6692,x6696))
% 160.93/160.66 [670]~E(x6701,x6702)+E(f432(x6703,x6704,x6705,x6706,x6701),f432(x6703,x6704,x6705,x6706,x6702))
% 160.93/160.66 [671]~E(x6711,x6712)+E(f49(x6711,x6713),f49(x6712,x6713))
% 160.93/160.66 [672]~E(x6721,x6722)+E(f49(x6723,x6721),f49(x6723,x6722))
% 160.93/160.66 [673]~E(x6731,x6732)+E(f852(x6731,x6733,x6734,x6735,x6736),f852(x6732,x6733,x6734,x6735,x6736))
% 160.93/160.66 [674]~E(x6741,x6742)+E(f852(x6743,x6741,x6744,x6745,x6746),f852(x6743,x6742,x6744,x6745,x6746))
% 160.93/160.66 [675]~E(x6751,x6752)+E(f852(x6753,x6754,x6751,x6755,x6756),f852(x6753,x6754,x6752,x6755,x6756))
% 160.93/160.66 [676]~E(x6761,x6762)+E(f852(x6763,x6764,x6765,x6761,x6766),f852(x6763,x6764,x6765,x6762,x6766))
% 160.93/160.66 [677]~E(x6771,x6772)+E(f852(x6773,x6774,x6775,x6776,x6771),f852(x6773,x6774,x6775,x6776,x6772))
% 160.93/160.66 [678]~E(x6781,x6782)+E(f661(x6781,x6783,x6784,x6785,x6786),f661(x6782,x6783,x6784,x6785,x6786))
% 160.93/160.66 [679]~E(x6791,x6792)+E(f661(x6793,x6791,x6794,x6795,x6796),f661(x6793,x6792,x6794,x6795,x6796))
% 160.93/160.66 [680]~E(x6801,x6802)+E(f661(x6803,x6804,x6801,x6805,x6806),f661(x6803,x6804,x6802,x6805,x6806))
% 160.93/160.66 [681]~E(x6811,x6812)+E(f661(x6813,x6814,x6815,x6811,x6816),f661(x6813,x6814,x6815,x6812,x6816))
% 160.93/160.66 [682]~E(x6821,x6822)+E(f661(x6823,x6824,x6825,x6826,x6821),f661(x6823,x6824,x6825,x6826,x6822))
% 160.93/160.66 [683]~E(x6831,x6832)+E(f148(x6831,x6833),f148(x6832,x6833))
% 160.93/160.66 [684]~E(x6841,x6842)+E(f148(x6843,x6841),f148(x6843,x6842))
% 160.93/160.66 [685]~E(x6851,x6852)+E(f359(x6851,x6853),f359(x6852,x6853))
% 160.93/160.66 [686]~E(x6861,x6862)+E(f359(x6863,x6861),f359(x6863,x6862))
% 160.93/160.66 [687]~E(x6871,x6872)+E(f450(x6871,x6873,x6874,x6875,x6876,x6877),f450(x6872,x6873,x6874,x6875,x6876,x6877))
% 160.93/160.66 [688]~E(x6881,x6882)+E(f450(x6883,x6881,x6884,x6885,x6886,x6887),f450(x6883,x6882,x6884,x6885,x6886,x6887))
% 160.93/160.66 [689]~E(x6891,x6892)+E(f450(x6893,x6894,x6891,x6895,x6896,x6897),f450(x6893,x6894,x6892,x6895,x6896,x6897))
% 160.93/160.66 [690]~E(x6901,x6902)+E(f450(x6903,x6904,x6905,x6901,x6906,x6907),f450(x6903,x6904,x6905,x6902,x6906,x6907))
% 160.93/160.66 [691]~E(x6911,x6912)+E(f450(x6913,x6914,x6915,x6916,x6911,x6917),f450(x6913,x6914,x6915,x6916,x6912,x6917))
% 160.93/160.66 [692]~E(x6921,x6922)+E(f450(x6923,x6924,x6925,x6926,x6927,x6921),f450(x6923,x6924,x6925,x6926,x6927,x6922))
% 160.93/160.66 [693]~E(x6931,x6932)+E(f680(x6931,x6933,x6934),f680(x6932,x6933,x6934))
% 160.93/160.66 [694]~E(x6941,x6942)+E(f680(x6943,x6941,x6944),f680(x6943,x6942,x6944))
% 160.93/160.66 [695]~E(x6951,x6952)+E(f680(x6953,x6954,x6951),f680(x6953,x6954,x6952))
% 160.93/160.66 [696]~E(x6961,x6962)+E(f500(x6961,x6963,x6964),f500(x6962,x6963,x6964))
% 160.93/160.66 [697]~E(x6971,x6972)+E(f500(x6973,x6971,x6974),f500(x6973,x6972,x6974))
% 160.93/160.66 [698]~E(x6981,x6982)+E(f500(x6983,x6984,x6981),f500(x6983,x6984,x6982))
% 160.93/160.66 [699]~E(x6991,x6992)+E(f831(x6991,x6993,x6994,x6995,x6996,x6997),f831(x6992,x6993,x6994,x6995,x6996,x6997))
% 160.93/160.66 [700]~E(x7001,x7002)+E(f831(x7003,x7001,x7004,x7005,x7006,x7007),f831(x7003,x7002,x7004,x7005,x7006,x7007))
% 160.93/160.66 [701]~E(x7011,x7012)+E(f831(x7013,x7014,x7011,x7015,x7016,x7017),f831(x7013,x7014,x7012,x7015,x7016,x7017))
% 160.93/160.66 [702]~E(x7021,x7022)+E(f831(x7023,x7024,x7025,x7021,x7026,x7027),f831(x7023,x7024,x7025,x7022,x7026,x7027))
% 160.93/160.66 [703]~E(x7031,x7032)+E(f831(x7033,x7034,x7035,x7036,x7031,x7037),f831(x7033,x7034,x7035,x7036,x7032,x7037))
% 160.93/160.66 [704]~E(x7041,x7042)+E(f831(x7043,x7044,x7045,x7046,x7047,x7041),f831(x7043,x7044,x7045,x7046,x7047,x7042))
% 160.93/160.66 [705]~E(x7051,x7052)+E(f603(x7051,x7053,x7054,x7055),f603(x7052,x7053,x7054,x7055))
% 160.93/160.66 [706]~E(x7061,x7062)+E(f603(x7063,x7061,x7064,x7065),f603(x7063,x7062,x7064,x7065))
% 160.93/160.66 [707]~E(x7071,x7072)+E(f603(x7073,x7074,x7071,x7075),f603(x7073,x7074,x7072,x7075))
% 160.93/160.66 [708]~E(x7081,x7082)+E(f603(x7083,x7084,x7085,x7081),f603(x7083,x7084,x7085,x7082))
% 160.93/160.66 [709]~E(x7091,x7092)+E(f619(x7091,x7093,x7094,x7095,x7096,x7097),f619(x7092,x7093,x7094,x7095,x7096,x7097))
% 160.93/160.66 [710]~E(x7101,x7102)+E(f619(x7103,x7101,x7104,x7105,x7106,x7107),f619(x7103,x7102,x7104,x7105,x7106,x7107))
% 160.93/160.66 [711]~E(x7111,x7112)+E(f619(x7113,x7114,x7111,x7115,x7116,x7117),f619(x7113,x7114,x7112,x7115,x7116,x7117))
% 160.93/160.66 [712]~E(x7121,x7122)+E(f619(x7123,x7124,x7125,x7121,x7126,x7127),f619(x7123,x7124,x7125,x7122,x7126,x7127))
% 160.93/160.66 [713]~E(x7131,x7132)+E(f619(x7133,x7134,x7135,x7136,x7131,x7137),f619(x7133,x7134,x7135,x7136,x7132,x7137))
% 160.93/160.66 [714]~E(x7141,x7142)+E(f619(x7143,x7144,x7145,x7146,x7147,x7141),f619(x7143,x7144,x7145,x7146,x7147,x7142))
% 160.93/160.66 [715]~E(x7151,x7152)+E(f843(x7151,x7153,x7154),f843(x7152,x7153,x7154))
% 160.93/160.66 [716]~E(x7161,x7162)+E(f843(x7163,x7161,x7164),f843(x7163,x7162,x7164))
% 160.93/160.66 [717]~E(x7171,x7172)+E(f843(x7173,x7174,x7171),f843(x7173,x7174,x7172))
% 160.93/160.66 [718]~E(x7181,x7182)+E(f458(x7181,x7183),f458(x7182,x7183))
% 160.93/160.66 [719]~E(x7191,x7192)+E(f458(x7193,x7191),f458(x7193,x7192))
% 160.93/160.66 [720]~E(x7201,x7202)+E(f825(x7201,x7203,x7204),f825(x7202,x7203,x7204))
% 160.93/160.66 [721]~E(x7211,x7212)+E(f825(x7213,x7211,x7214),f825(x7213,x7212,x7214))
% 160.93/160.66 [722]~E(x7221,x7222)+E(f825(x7223,x7224,x7221),f825(x7223,x7224,x7222))
% 160.93/160.66 [723]~E(x7231,x7232)+E(f279(x7231),f279(x7232))
% 160.93/160.66 [724]~E(x7241,x7242)+E(f703(x7241,x7243,x7244,x7245,x7246),f703(x7242,x7243,x7244,x7245,x7246))
% 160.93/160.66 [725]~E(x7251,x7252)+E(f703(x7253,x7251,x7254,x7255,x7256),f703(x7253,x7252,x7254,x7255,x7256))
% 160.93/160.66 [726]~E(x7261,x7262)+E(f703(x7263,x7264,x7261,x7265,x7266),f703(x7263,x7264,x7262,x7265,x7266))
% 160.93/160.66 [727]~E(x7271,x7272)+E(f703(x7273,x7274,x7275,x7271,x7276),f703(x7273,x7274,x7275,x7272,x7276))
% 160.93/160.66 [728]~E(x7281,x7282)+E(f703(x7283,x7284,x7285,x7286,x7281),f703(x7283,x7284,x7285,x7286,x7282))
% 160.93/160.66 [729]~E(x7291,x7292)+E(f129(x7291,x7293,x7294),f129(x7292,x7293,x7294))
% 160.93/160.66 [730]~E(x7301,x7302)+E(f129(x7303,x7301,x7304),f129(x7303,x7302,x7304))
% 160.93/160.66 [731]~E(x7311,x7312)+E(f129(x7313,x7314,x7311),f129(x7313,x7314,x7312))
% 160.93/160.66 [732]~E(x7321,x7322)+E(f430(x7321,x7323,x7324),f430(x7322,x7323,x7324))
% 160.93/160.66 [733]~E(x7331,x7332)+E(f430(x7333,x7331,x7334),f430(x7333,x7332,x7334))
% 160.93/160.66 [734]~E(x7341,x7342)+E(f430(x7343,x7344,x7341),f430(x7343,x7344,x7342))
% 160.93/160.66 [735]~E(x7351,x7352)+E(f497(x7351,x7353,x7354,x7355,x7356),f497(x7352,x7353,x7354,x7355,x7356))
% 160.93/160.66 [736]~E(x7361,x7362)+E(f497(x7363,x7361,x7364,x7365,x7366),f497(x7363,x7362,x7364,x7365,x7366))
% 160.93/160.66 [737]~E(x7371,x7372)+E(f497(x7373,x7374,x7371,x7375,x7376),f497(x7373,x7374,x7372,x7375,x7376))
% 160.93/160.66 [738]~E(x7381,x7382)+E(f497(x7383,x7384,x7385,x7381,x7386),f497(x7383,x7384,x7385,x7382,x7386))
% 160.93/160.66 [739]~E(x7391,x7392)+E(f497(x7393,x7394,x7395,x7396,x7391),f497(x7393,x7394,x7395,x7396,x7392))
% 160.93/160.66 [740]~E(x7401,x7402)+E(f192(x7401,x7403,x7404),f192(x7402,x7403,x7404))
% 160.93/160.66 [741]~E(x7411,x7412)+E(f192(x7413,x7411,x7414),f192(x7413,x7412,x7414))
% 160.93/160.66 [742]~E(x7421,x7422)+E(f192(x7423,x7424,x7421),f192(x7423,x7424,x7422))
% 160.93/160.66 [743]~E(x7431,x7432)+E(f577(x7431,x7433,x7434,x7435,x7436,x7437),f577(x7432,x7433,x7434,x7435,x7436,x7437))
% 160.93/160.66 [744]~E(x7441,x7442)+E(f577(x7443,x7441,x7444,x7445,x7446,x7447),f577(x7443,x7442,x7444,x7445,x7446,x7447))
% 160.93/160.66 [745]~E(x7451,x7452)+E(f577(x7453,x7454,x7451,x7455,x7456,x7457),f577(x7453,x7454,x7452,x7455,x7456,x7457))
% 160.93/160.66 [746]~E(x7461,x7462)+E(f577(x7463,x7464,x7465,x7461,x7466,x7467),f577(x7463,x7464,x7465,x7462,x7466,x7467))
% 160.93/160.66 [747]~E(x7471,x7472)+E(f577(x7473,x7474,x7475,x7476,x7471,x7477),f577(x7473,x7474,x7475,x7476,x7472,x7477))
% 160.93/160.66 [748]~E(x7481,x7482)+E(f577(x7483,x7484,x7485,x7486,x7487,x7481),f577(x7483,x7484,x7485,x7486,x7487,x7482))
% 160.93/160.66 [749]~E(x7491,x7492)+E(f496(x7491,x7493,x7494,x7495,x7496,x7497,x7498),f496(x7492,x7493,x7494,x7495,x7496,x7497,x7498))
% 160.93/160.66 [750]~E(x7501,x7502)+E(f496(x7503,x7501,x7504,x7505,x7506,x7507,x7508),f496(x7503,x7502,x7504,x7505,x7506,x7507,x7508))
% 160.93/160.66 [751]~E(x7511,x7512)+E(f496(x7513,x7514,x7511,x7515,x7516,x7517,x7518),f496(x7513,x7514,x7512,x7515,x7516,x7517,x7518))
% 160.93/160.66 [752]~E(x7521,x7522)+E(f496(x7523,x7524,x7525,x7521,x7526,x7527,x7528),f496(x7523,x7524,x7525,x7522,x7526,x7527,x7528))
% 160.93/160.66 [753]~E(x7531,x7532)+E(f496(x7533,x7534,x7535,x7536,x7531,x7537,x7538),f496(x7533,x7534,x7535,x7536,x7532,x7537,x7538))
% 160.93/160.66 [754]~E(x7541,x7542)+E(f496(x7543,x7544,x7545,x7546,x7547,x7541,x7548),f496(x7543,x7544,x7545,x7546,x7547,x7542,x7548))
% 160.93/160.66 [755]~E(x7551,x7552)+E(f496(x7553,x7554,x7555,x7556,x7557,x7558,x7551),f496(x7553,x7554,x7555,x7556,x7557,x7558,x7552))
% 160.93/160.66 [756]~E(x7561,x7562)+E(f377(x7561,x7563,x7564,x7565),f377(x7562,x7563,x7564,x7565))
% 160.93/160.66 [757]~E(x7571,x7572)+E(f377(x7573,x7571,x7574,x7575),f377(x7573,x7572,x7574,x7575))
% 160.93/160.66 [758]~E(x7581,x7582)+E(f377(x7583,x7584,x7581,x7585),f377(x7583,x7584,x7582,x7585))
% 160.93/160.66 [759]~E(x7591,x7592)+E(f377(x7593,x7594,x7595,x7591),f377(x7593,x7594,x7595,x7592))
% 160.93/160.66 [760]~E(x7601,x7602)+E(f29(x7601,x7603,x7604),f29(x7602,x7603,x7604))
% 160.93/160.66 [761]~E(x7611,x7612)+E(f29(x7613,x7611,x7614),f29(x7613,x7612,x7614))
% 160.93/160.66 [762]~E(x7621,x7622)+E(f29(x7623,x7624,x7621),f29(x7623,x7624,x7622))
% 160.93/160.66 [763]~E(x7631,x7632)+E(f482(x7631,x7633,x7634),f482(x7632,x7633,x7634))
% 160.93/160.66 [764]~E(x7641,x7642)+E(f482(x7643,x7641,x7644),f482(x7643,x7642,x7644))
% 160.93/160.66 [765]~E(x7651,x7652)+E(f482(x7653,x7654,x7651),f482(x7653,x7654,x7652))
% 160.93/160.66 [766]~E(x7661,x7662)+E(f526(x7661,x7663),f526(x7662,x7663))
% 160.93/160.66 [767]~E(x7671,x7672)+E(f526(x7673,x7671),f526(x7673,x7672))
% 160.93/160.66 [768]~E(x7681,x7682)+E(f489(x7681,x7683,x7684,x7685),f489(x7682,x7683,x7684,x7685))
% 160.93/160.66 [769]~E(x7691,x7692)+E(f489(x7693,x7691,x7694,x7695),f489(x7693,x7692,x7694,x7695))
% 160.93/160.66 [770]~E(x7701,x7702)+E(f489(x7703,x7704,x7701,x7705),f489(x7703,x7704,x7702,x7705))
% 160.93/160.66 [771]~E(x7711,x7712)+E(f489(x7713,x7714,x7715,x7711),f489(x7713,x7714,x7715,x7712))
% 160.93/160.66 [772]~E(x7721,x7722)+E(f46(x7721,x7723),f46(x7722,x7723))
% 160.93/160.66 [773]~E(x7731,x7732)+E(f46(x7733,x7731),f46(x7733,x7732))
% 160.93/160.66 [774]~E(x7741,x7742)+E(f444(x7741,x7743,x7744,x7745,x7746),f444(x7742,x7743,x7744,x7745,x7746))
% 160.93/160.66 [775]~E(x7751,x7752)+E(f444(x7753,x7751,x7754,x7755,x7756),f444(x7753,x7752,x7754,x7755,x7756))
% 160.93/160.66 [776]~E(x7761,x7762)+E(f444(x7763,x7764,x7761,x7765,x7766),f444(x7763,x7764,x7762,x7765,x7766))
% 160.93/160.66 [777]~E(x7771,x7772)+E(f444(x7773,x7774,x7775,x7771,x7776),f444(x7773,x7774,x7775,x7772,x7776))
% 160.93/160.66 [778]~E(x7781,x7782)+E(f444(x7783,x7784,x7785,x7786,x7781),f444(x7783,x7784,x7785,x7786,x7782))
% 160.93/160.66 [779]~E(x7791,x7792)+E(f219(x7791,x7793,x7794,x7795),f219(x7792,x7793,x7794,x7795))
% 160.93/160.66 [780]~E(x7801,x7802)+E(f219(x7803,x7801,x7804,x7805),f219(x7803,x7802,x7804,x7805))
% 160.93/160.66 [781]~E(x7811,x7812)+E(f219(x7813,x7814,x7811,x7815),f219(x7813,x7814,x7812,x7815))
% 160.93/160.66 [782]~E(x7821,x7822)+E(f219(x7823,x7824,x7825,x7821),f219(x7823,x7824,x7825,x7822))
% 160.93/160.66 [783]~E(x7831,x7832)+E(f235(x7831,x7833,x7834,x7835),f235(x7832,x7833,x7834,x7835))
% 160.93/160.66 [784]~E(x7841,x7842)+E(f235(x7843,x7841,x7844,x7845),f235(x7843,x7842,x7844,x7845))
% 160.93/160.66 [785]~E(x7851,x7852)+E(f235(x7853,x7854,x7851,x7855),f235(x7853,x7854,x7852,x7855))
% 160.93/160.66 [786]~E(x7861,x7862)+E(f235(x7863,x7864,x7865,x7861),f235(x7863,x7864,x7865,x7862))
% 160.93/160.66 [787]~E(x7871,x7872)+E(f730(x7871,x7873,x7874,x7875),f730(x7872,x7873,x7874,x7875))
% 160.93/160.66 [788]~E(x7881,x7882)+E(f730(x7883,x7881,x7884,x7885),f730(x7883,x7882,x7884,x7885))
% 160.93/160.66 [789]~E(x7891,x7892)+E(f730(x7893,x7894,x7891,x7895),f730(x7893,x7894,x7892,x7895))
% 160.93/160.66 [790]~E(x7901,x7902)+E(f730(x7903,x7904,x7905,x7901),f730(x7903,x7904,x7905,x7902))
% 160.93/160.66 [791]~E(x7911,x7912)+E(f791(x7911,x7913,x7914,x7915,x7916),f791(x7912,x7913,x7914,x7915,x7916))
% 160.93/160.66 [792]~E(x7921,x7922)+E(f791(x7923,x7921,x7924,x7925,x7926),f791(x7923,x7922,x7924,x7925,x7926))
% 160.93/160.66 [793]~E(x7931,x7932)+E(f791(x7933,x7934,x7931,x7935,x7936),f791(x7933,x7934,x7932,x7935,x7936))
% 160.93/160.66 [794]~E(x7941,x7942)+E(f791(x7943,x7944,x7945,x7941,x7946),f791(x7943,x7944,x7945,x7942,x7946))
% 160.93/160.66 [795]~E(x7951,x7952)+E(f791(x7953,x7954,x7955,x7956,x7951),f791(x7953,x7954,x7955,x7956,x7952))
% 160.93/160.66 [796]~E(x7961,x7962)+E(f421(x7961,x7963,x7964),f421(x7962,x7963,x7964))
% 160.93/160.66 [797]~E(x7971,x7972)+E(f421(x7973,x7971,x7974),f421(x7973,x7972,x7974))
% 160.93/160.66 [798]~E(x7981,x7982)+E(f421(x7983,x7984,x7981),f421(x7983,x7984,x7982))
% 160.93/160.66 [799]~E(x7991,x7992)+E(f682(x7991,x7993,x7994,x7995),f682(x7992,x7993,x7994,x7995))
% 160.93/160.66 [800]~E(x8001,x8002)+E(f682(x8003,x8001,x8004,x8005),f682(x8003,x8002,x8004,x8005))
% 160.93/160.66 [801]~E(x8011,x8012)+E(f682(x8013,x8014,x8011,x8015),f682(x8013,x8014,x8012,x8015))
% 160.93/160.66 [802]~E(x8021,x8022)+E(f682(x8023,x8024,x8025,x8021),f682(x8023,x8024,x8025,x8022))
% 160.93/160.66 [803]~E(x8031,x8032)+E(f113(x8031),f113(x8032))
% 160.93/160.66 [804]~E(x8041,x8042)+E(f857(x8041,x8043,x8044,x8045),f857(x8042,x8043,x8044,x8045))
% 160.93/160.66 [805]~E(x8051,x8052)+E(f857(x8053,x8051,x8054,x8055),f857(x8053,x8052,x8054,x8055))
% 160.93/160.66 [806]~E(x8061,x8062)+E(f857(x8063,x8064,x8061,x8065),f857(x8063,x8064,x8062,x8065))
% 160.93/160.66 [807]~E(x8071,x8072)+E(f857(x8073,x8074,x8075,x8071),f857(x8073,x8074,x8075,x8072))
% 160.93/160.66 [808]~E(x8081,x8082)+E(f62(x8081,x8083,x8084),f62(x8082,x8083,x8084))
% 160.93/160.66 [809]~E(x8091,x8092)+E(f62(x8093,x8091,x8094),f62(x8093,x8092,x8094))
% 160.93/160.66 [810]~E(x8101,x8102)+E(f62(x8103,x8104,x8101),f62(x8103,x8104,x8102))
% 160.93/160.66 [811]~E(x8111,x8112)+E(f263(x8111,x8113,x8114),f263(x8112,x8113,x8114))
% 160.93/160.66 [812]~E(x8121,x8122)+E(f263(x8123,x8121,x8124),f263(x8123,x8122,x8124))
% 160.93/160.66 [813]~E(x8131,x8132)+E(f263(x8133,x8134,x8131),f263(x8133,x8134,x8132))
% 160.93/160.66 [814]~E(x8141,x8142)+E(f203(x8141,x8143),f203(x8142,x8143))
% 160.93/160.66 [815]~E(x8151,x8152)+E(f203(x8153,x8151),f203(x8153,x8152))
% 160.93/160.66 [816]~E(x8161,x8162)+E(f542(x8161,x8163,x8164),f542(x8162,x8163,x8164))
% 160.93/160.66 [817]~E(x8171,x8172)+E(f542(x8173,x8171,x8174),f542(x8173,x8172,x8174))
% 160.93/160.66 [818]~E(x8181,x8182)+E(f542(x8183,x8184,x8181),f542(x8183,x8184,x8182))
% 160.93/160.66 [819]~E(x8191,x8192)+E(f868(x8191,x8193,x8194,x8195,x8196),f868(x8192,x8193,x8194,x8195,x8196))
% 160.93/160.66 [820]~E(x8201,x8202)+E(f868(x8203,x8201,x8204,x8205,x8206),f868(x8203,x8202,x8204,x8205,x8206))
% 160.93/160.66 [821]~E(x8211,x8212)+E(f868(x8213,x8214,x8211,x8215,x8216),f868(x8213,x8214,x8212,x8215,x8216))
% 160.93/160.66 [822]~E(x8221,x8222)+E(f868(x8223,x8224,x8225,x8221,x8226),f868(x8223,x8224,x8225,x8222,x8226))
% 160.93/160.66 [823]~E(x8231,x8232)+E(f868(x8233,x8234,x8235,x8236,x8231),f868(x8233,x8234,x8235,x8236,x8232))
% 160.93/160.66 [824]~E(x8241,x8242)+E(f608(x8241,x8243,x8244),f608(x8242,x8243,x8244))
% 160.93/160.66 [825]~E(x8251,x8252)+E(f608(x8253,x8251,x8254),f608(x8253,x8252,x8254))
% 160.93/160.66 [826]~E(x8261,x8262)+E(f608(x8263,x8264,x8261),f608(x8263,x8264,x8262))
% 160.93/160.66 [827]~E(x8271,x8272)+E(f470(x8271,x8273),f470(x8272,x8273))
% 160.93/160.66 [828]~E(x8281,x8282)+E(f470(x8283,x8281),f470(x8283,x8282))
% 160.93/160.66 [829]~E(x8291,x8292)+E(f622(x8291,x8293,x8294,x8295),f622(x8292,x8293,x8294,x8295))
% 160.93/160.66 [830]~E(x8301,x8302)+E(f622(x8303,x8301,x8304,x8305),f622(x8303,x8302,x8304,x8305))
% 160.93/160.66 [831]~E(x8311,x8312)+E(f622(x8313,x8314,x8311,x8315),f622(x8313,x8314,x8312,x8315))
% 160.93/160.66 [832]~E(x8321,x8322)+E(f622(x8323,x8324,x8325,x8321),f622(x8323,x8324,x8325,x8322))
% 160.93/160.66 [833]~E(x8331,x8332)+E(f436(x8331,x8333,x8334,x8335),f436(x8332,x8333,x8334,x8335))
% 160.93/160.66 [834]~E(x8341,x8342)+E(f436(x8343,x8341,x8344,x8345),f436(x8343,x8342,x8344,x8345))
% 160.93/160.66 [835]~E(x8351,x8352)+E(f436(x8353,x8354,x8351,x8355),f436(x8353,x8354,x8352,x8355))
% 160.93/160.66 [836]~E(x8361,x8362)+E(f436(x8363,x8364,x8365,x8361),f436(x8363,x8364,x8365,x8362))
% 160.93/160.66 [837]~E(x8371,x8372)+E(f213(x8371),f213(x8372))
% 160.93/160.66 [838]~E(x8381,x8382)+E(f524(x8381,x8383,x8384),f524(x8382,x8383,x8384))
% 160.93/160.66 [839]~E(x8391,x8392)+E(f524(x8393,x8391,x8394),f524(x8393,x8392,x8394))
% 160.93/160.66 [840]~E(x8401,x8402)+E(f524(x8403,x8404,x8401),f524(x8403,x8404,x8402))
% 160.93/160.66 [841]~E(x8411,x8412)+E(f790(x8411,x8413,x8414,x8415,x8416),f790(x8412,x8413,x8414,x8415,x8416))
% 160.93/160.66 [842]~E(x8421,x8422)+E(f790(x8423,x8421,x8424,x8425,x8426),f790(x8423,x8422,x8424,x8425,x8426))
% 160.93/160.66 [843]~E(x8431,x8432)+E(f790(x8433,x8434,x8431,x8435,x8436),f790(x8433,x8434,x8432,x8435,x8436))
% 160.93/160.66 [844]~E(x8441,x8442)+E(f790(x8443,x8444,x8445,x8441,x8446),f790(x8443,x8444,x8445,x8442,x8446))
% 160.93/160.66 [845]~E(x8451,x8452)+E(f790(x8453,x8454,x8455,x8456,x8451),f790(x8453,x8454,x8455,x8456,x8452))
% 160.93/160.66 [846]~E(x8461,x8462)+E(f845(x8461,x8463,x8464,x8465,x8466),f845(x8462,x8463,x8464,x8465,x8466))
% 160.93/160.66 [847]~E(x8471,x8472)+E(f845(x8473,x8471,x8474,x8475,x8476),f845(x8473,x8472,x8474,x8475,x8476))
% 160.93/160.66 [848]~E(x8481,x8482)+E(f845(x8483,x8484,x8481,x8485,x8486),f845(x8483,x8484,x8482,x8485,x8486))
% 160.93/160.66 [849]~E(x8491,x8492)+E(f845(x8493,x8494,x8495,x8491,x8496),f845(x8493,x8494,x8495,x8492,x8496))
% 160.93/160.66 [850]~E(x8501,x8502)+E(f845(x8503,x8504,x8505,x8506,x8501),f845(x8503,x8504,x8505,x8506,x8502))
% 160.93/160.66 [851]~E(x8511,x8512)+E(f346(x8511),f346(x8512))
% 160.93/160.66 [852]~E(x8521,x8522)+E(f765(x8521,x8523),f765(x8522,x8523))
% 160.93/160.66 [853]~E(x8531,x8532)+E(f765(x8533,x8531),f765(x8533,x8532))
% 160.93/160.66 [854]~E(x8541,x8542)+E(f835(x8541,x8543,x8544,x8545,x8546),f835(x8542,x8543,x8544,x8545,x8546))
% 160.93/160.66 [855]~E(x8551,x8552)+E(f835(x8553,x8551,x8554,x8555,x8556),f835(x8553,x8552,x8554,x8555,x8556))
% 160.93/160.66 [856]~E(x8561,x8562)+E(f835(x8563,x8564,x8561,x8565,x8566),f835(x8563,x8564,x8562,x8565,x8566))
% 160.93/160.66 [857]~E(x8571,x8572)+E(f835(x8573,x8574,x8575,x8571,x8576),f835(x8573,x8574,x8575,x8572,x8576))
% 160.93/160.66 [858]~E(x8581,x8582)+E(f835(x8583,x8584,x8585,x8586,x8581),f835(x8583,x8584,x8585,x8586,x8582))
% 160.93/160.66 [859]~E(x8591,x8592)+E(f617(x8591,x8593,x8594),f617(x8592,x8593,x8594))
% 160.93/160.66 [860]~E(x8601,x8602)+E(f617(x8603,x8601,x8604),f617(x8603,x8602,x8604))
% 160.93/160.66 [861]~E(x8611,x8612)+E(f617(x8613,x8614,x8611),f617(x8613,x8614,x8612))
% 160.93/160.66 [862]~E(x8621,x8622)+E(f640(x8621,x8623,x8624,x8625,x8626),f640(x8622,x8623,x8624,x8625,x8626))
% 160.93/160.66 [863]~E(x8631,x8632)+E(f640(x8633,x8631,x8634,x8635,x8636),f640(x8633,x8632,x8634,x8635,x8636))
% 160.93/160.66 [864]~E(x8641,x8642)+E(f640(x8643,x8644,x8641,x8645,x8646),f640(x8643,x8644,x8642,x8645,x8646))
% 160.93/160.66 [865]~E(x8651,x8652)+E(f640(x8653,x8654,x8655,x8651,x8656),f640(x8653,x8654,x8655,x8652,x8656))
% 160.93/160.66 [866]~E(x8661,x8662)+E(f640(x8663,x8664,x8665,x8666,x8661),f640(x8663,x8664,x8665,x8666,x8662))
% 160.93/160.66 [867]~E(x8671,x8672)+E(f850(x8671,x8673,x8674),f850(x8672,x8673,x8674))
% 160.93/160.66 [868]~E(x8681,x8682)+E(f850(x8683,x8681,x8684),f850(x8683,x8682,x8684))
% 160.93/160.66 [869]~E(x8691,x8692)+E(f850(x8693,x8694,x8691),f850(x8693,x8694,x8692))
% 160.93/160.66 [870]~E(x8701,x8702)+E(f54(x8701,x8703,x8704),f54(x8702,x8703,x8704))
% 160.93/160.66 [871]~E(x8711,x8712)+E(f54(x8713,x8711,x8714),f54(x8713,x8712,x8714))
% 160.93/160.66 [872]~E(x8721,x8722)+E(f54(x8723,x8724,x8721),f54(x8723,x8724,x8722))
% 160.93/160.66 [873]~E(x8731,x8732)+E(f568(x8731,x8733,x8734,x8735),f568(x8732,x8733,x8734,x8735))
% 160.93/160.66 [874]~E(x8741,x8742)+E(f568(x8743,x8741,x8744,x8745),f568(x8743,x8742,x8744,x8745))
% 160.93/160.66 [875]~E(x8751,x8752)+E(f568(x8753,x8754,x8751,x8755),f568(x8753,x8754,x8752,x8755))
% 160.93/160.66 [876]~E(x8761,x8762)+E(f568(x8763,x8764,x8765,x8761),f568(x8763,x8764,x8765,x8762))
% 160.93/160.66 [877]~E(x8771,x8772)+E(f383(x8771,x8773,x8774,x8775),f383(x8772,x8773,x8774,x8775))
% 160.93/160.66 [878]~E(x8781,x8782)+E(f383(x8783,x8781,x8784,x8785),f383(x8783,x8782,x8784,x8785))
% 160.93/160.66 [879]~E(x8791,x8792)+E(f383(x8793,x8794,x8791,x8795),f383(x8793,x8794,x8792,x8795))
% 160.93/160.66 [880]~E(x8801,x8802)+E(f383(x8803,x8804,x8805,x8801),f383(x8803,x8804,x8805,x8802))
% 160.93/160.66 [881]~E(x8811,x8812)+E(f637(x8811,x8813,x8814),f637(x8812,x8813,x8814))
% 160.93/160.66 [882]~E(x8821,x8822)+E(f637(x8823,x8821,x8824),f637(x8823,x8822,x8824))
% 160.93/160.66 [883]~E(x8831,x8832)+E(f637(x8833,x8834,x8831),f637(x8833,x8834,x8832))
% 160.93/160.66 [884]~E(x8841,x8842)+E(f744(x8841,x8843,x8844,x8845,x8846),f744(x8842,x8843,x8844,x8845,x8846))
% 160.93/160.66 [885]~E(x8851,x8852)+E(f744(x8853,x8851,x8854,x8855,x8856),f744(x8853,x8852,x8854,x8855,x8856))
% 160.93/160.66 [886]~E(x8861,x8862)+E(f744(x8863,x8864,x8861,x8865,x8866),f744(x8863,x8864,x8862,x8865,x8866))
% 160.93/160.66 [887]~E(x8871,x8872)+E(f744(x8873,x8874,x8875,x8871,x8876),f744(x8873,x8874,x8875,x8872,x8876))
% 160.93/160.66 [888]~E(x8881,x8882)+E(f744(x8883,x8884,x8885,x8886,x8881),f744(x8883,x8884,x8885,x8886,x8882))
% 160.93/160.66 [889]~E(x8891,x8892)+E(f589(x8891,x8893,x8894,x8895,x8896,x8897,x8898,x8899),f589(x8892,x8893,x8894,x8895,x8896,x8897,x8898,x8899))
% 160.93/160.66 [890]~E(x8901,x8902)+E(f589(x8903,x8901,x8904,x8905,x8906,x8907,x8908,x8909),f589(x8903,x8902,x8904,x8905,x8906,x8907,x8908,x8909))
% 160.93/160.66 [891]~E(x8911,x8912)+E(f589(x8913,x8914,x8911,x8915,x8916,x8917,x8918,x8919),f589(x8913,x8914,x8912,x8915,x8916,x8917,x8918,x8919))
% 160.93/160.66 [892]~E(x8921,x8922)+E(f589(x8923,x8924,x8925,x8921,x8926,x8927,x8928,x8929),f589(x8923,x8924,x8925,x8922,x8926,x8927,x8928,x8929))
% 160.93/160.66 [893]~E(x8931,x8932)+E(f589(x8933,x8934,x8935,x8936,x8931,x8937,x8938,x8939),f589(x8933,x8934,x8935,x8936,x8932,x8937,x8938,x8939))
% 160.93/160.66 [894]~E(x8941,x8942)+E(f589(x8943,x8944,x8945,x8946,x8947,x8941,x8948,x8949),f589(x8943,x8944,x8945,x8946,x8947,x8942,x8948,x8949))
% 160.93/160.66 [895]~E(x8951,x8952)+E(f589(x8953,x8954,x8955,x8956,x8957,x8958,x8951,x8959),f589(x8953,x8954,x8955,x8956,x8957,x8958,x8952,x8959))
% 160.93/160.66 [896]~E(x8961,x8962)+E(f589(x8963,x8964,x8965,x8966,x8967,x8968,x8969,x8961),f589(x8963,x8964,x8965,x8966,x8967,x8968,x8969,x8962))
% 160.93/160.66 [897]~E(x8971,x8972)+E(f775(x8971,x8973,x8974,x8975),f775(x8972,x8973,x8974,x8975))
% 160.93/160.66 [898]~E(x8981,x8982)+E(f775(x8983,x8981,x8984,x8985),f775(x8983,x8982,x8984,x8985))
% 160.93/160.66 [899]~E(x8991,x8992)+E(f775(x8993,x8994,x8991,x8995),f775(x8993,x8994,x8992,x8995))
% 160.93/160.66 [900]~E(x9001,x9002)+E(f775(x9003,x9004,x9005,x9001),f775(x9003,x9004,x9005,x9002))
% 160.93/160.66 [901]~E(x9011,x9012)+E(f124(x9011,x9013,x9014,x9015),f124(x9012,x9013,x9014,x9015))
% 160.93/160.66 [902]~E(x9021,x9022)+E(f124(x9023,x9021,x9024,x9025),f124(x9023,x9022,x9024,x9025))
% 160.93/160.66 [903]~E(x9031,x9032)+E(f124(x9033,x9034,x9031,x9035),f124(x9033,x9034,x9032,x9035))
% 160.93/160.66 [904]~E(x9041,x9042)+E(f124(x9043,x9044,x9045,x9041),f124(x9043,x9044,x9045,x9042))
% 160.93/160.66 [905]~E(x9051,x9052)+E(f142(x9051,x9053,x9054),f142(x9052,x9053,x9054))
% 160.93/160.66 [906]~E(x9061,x9062)+E(f142(x9063,x9061,x9064),f142(x9063,x9062,x9064))
% 160.93/160.66 [907]~E(x9071,x9072)+E(f142(x9073,x9074,x9071),f142(x9073,x9074,x9072))
% 160.93/160.66 [908]~E(x9081,x9082)+E(f683(x9081,x9083,x9084),f683(x9082,x9083,x9084))
% 160.93/160.66 [909]~E(x9091,x9092)+E(f683(x9093,x9091,x9094),f683(x9093,x9092,x9094))
% 160.93/160.66 [910]~E(x9101,x9102)+E(f683(x9103,x9104,x9101),f683(x9103,x9104,x9102))
% 160.93/160.66 [911]~E(x9111,x9112)+E(f820(x9111,x9113,x9114),f820(x9112,x9113,x9114))
% 160.93/160.66 [912]~E(x9121,x9122)+E(f820(x9123,x9121,x9124),f820(x9123,x9122,x9124))
% 160.93/160.66 [913]~E(x9131,x9132)+E(f820(x9133,x9134,x9131),f820(x9133,x9134,x9132))
% 160.93/160.66 [914]~E(x9141,x9142)+E(f200(x9141,x9143),f200(x9142,x9143))
% 160.93/160.66 [915]~E(x9151,x9152)+E(f200(x9153,x9151),f200(x9153,x9152))
% 160.93/160.66 [916]~E(x9161,x9162)+E(f403(x9161,x9163,x9164,x9165,x9166,x9167),f403(x9162,x9163,x9164,x9165,x9166,x9167))
% 160.93/160.66 [917]~E(x9171,x9172)+E(f403(x9173,x9171,x9174,x9175,x9176,x9177),f403(x9173,x9172,x9174,x9175,x9176,x9177))
% 160.93/160.66 [918]~E(x9181,x9182)+E(f403(x9183,x9184,x9181,x9185,x9186,x9187),f403(x9183,x9184,x9182,x9185,x9186,x9187))
% 160.93/160.66 [919]~E(x9191,x9192)+E(f403(x9193,x9194,x9195,x9191,x9196,x9197),f403(x9193,x9194,x9195,x9192,x9196,x9197))
% 160.93/160.66 [920]~E(x9201,x9202)+E(f403(x9203,x9204,x9205,x9206,x9201,x9207),f403(x9203,x9204,x9205,x9206,x9202,x9207))
% 160.93/160.66 [921]~E(x9211,x9212)+E(f403(x9213,x9214,x9215,x9216,x9217,x9211),f403(x9213,x9214,x9215,x9216,x9217,x9212))
% 160.93/160.66 [922]~E(x9221,x9222)+E(f123(x9221,x9223),f123(x9222,x9223))
% 160.93/160.66 [923]~E(x9231,x9232)+E(f123(x9233,x9231),f123(x9233,x9232))
% 160.93/160.66 [924]~E(x9241,x9242)+E(f630(x9241,x9243,x9244),f630(x9242,x9243,x9244))
% 160.93/160.66 [925]~E(x9251,x9252)+E(f630(x9253,x9251,x9254),f630(x9253,x9252,x9254))
% 160.93/160.66 [926]~E(x9261,x9262)+E(f630(x9263,x9264,x9261),f630(x9263,x9264,x9262))
% 160.93/160.66 [927]~E(x9271,x9272)+E(f442(x9271,x9273,x9274,x9275),f442(x9272,x9273,x9274,x9275))
% 160.93/160.66 [928]~E(x9281,x9282)+E(f442(x9283,x9281,x9284,x9285),f442(x9283,x9282,x9284,x9285))
% 160.93/160.66 [929]~E(x9291,x9292)+E(f442(x9293,x9294,x9291,x9295),f442(x9293,x9294,x9292,x9295))
% 160.93/160.66 [930]~E(x9301,x9302)+E(f442(x9303,x9304,x9305,x9301),f442(x9303,x9304,x9305,x9302))
% 160.93/160.66 [931]~E(x9311,x9312)+E(f428(x9311,x9313,x9314),f428(x9312,x9313,x9314))
% 160.93/160.66 [932]~E(x9321,x9322)+E(f428(x9323,x9321,x9324),f428(x9323,x9322,x9324))
% 160.93/160.66 [933]~E(x9331,x9332)+E(f428(x9333,x9334,x9331),f428(x9333,x9334,x9332))
% 160.93/160.66 [934]~E(x9341,x9342)+E(f301(x9341,x9343,x9344,x9345),f301(x9342,x9343,x9344,x9345))
% 160.93/160.66 [935]~E(x9351,x9352)+E(f301(x9353,x9351,x9354,x9355),f301(x9353,x9352,x9354,x9355))
% 160.93/160.66 [936]~E(x9361,x9362)+E(f301(x9363,x9364,x9361,x9365),f301(x9363,x9364,x9362,x9365))
% 160.93/160.66 [937]~E(x9371,x9372)+E(f301(x9373,x9374,x9375,x9371),f301(x9373,x9374,x9375,x9372))
% 160.93/160.66 [938]~E(x9381,x9382)+E(f583(x9381,x9383,x9384,x9385),f583(x9382,x9383,x9384,x9385))
% 160.93/160.66 [939]~E(x9391,x9392)+E(f583(x9393,x9391,x9394,x9395),f583(x9393,x9392,x9394,x9395))
% 160.93/160.66 [940]~E(x9401,x9402)+E(f583(x9403,x9404,x9401,x9405),f583(x9403,x9404,x9402,x9405))
% 160.93/160.66 [941]~E(x9411,x9412)+E(f583(x9413,x9414,x9415,x9411),f583(x9413,x9414,x9415,x9412))
% 160.93/160.66 [942]~E(x9421,x9422)+E(f472(x9421,x9423),f472(x9422,x9423))
% 160.93/160.66 [943]~E(x9431,x9432)+E(f472(x9433,x9431),f472(x9433,x9432))
% 160.93/160.66 [944]~E(x9441,x9442)+E(f231(x9441,x9443),f231(x9442,x9443))
% 160.93/160.66 [945]~E(x9451,x9452)+E(f231(x9453,x9451),f231(x9453,x9452))
% 160.93/160.66 [946]~E(x9461,x9462)+E(f574(x9461,x9463,x9464,x9465),f574(x9462,x9463,x9464,x9465))
% 160.93/160.66 [947]~E(x9471,x9472)+E(f574(x9473,x9471,x9474,x9475),f574(x9473,x9472,x9474,x9475))
% 160.93/160.66 [948]~E(x9481,x9482)+E(f574(x9483,x9484,x9481,x9485),f574(x9483,x9484,x9482,x9485))
% 160.93/160.66 [949]~E(x9491,x9492)+E(f574(x9493,x9494,x9495,x9491),f574(x9493,x9494,x9495,x9492))
% 160.93/160.66 [950]~E(x9501,x9502)+E(f455(x9501,x9503,x9504),f455(x9502,x9503,x9504))
% 160.93/160.66 [951]~E(x9511,x9512)+E(f455(x9513,x9511,x9514),f455(x9513,x9512,x9514))
% 160.93/160.66 [952]~E(x9521,x9522)+E(f455(x9523,x9524,x9521),f455(x9523,x9524,x9522))
% 160.93/160.66 [953]~E(x9531,x9532)+E(f671(x9531,x9533),f671(x9532,x9533))
% 160.93/160.66 [954]~E(x9541,x9542)+E(f671(x9543,x9541),f671(x9543,x9542))
% 160.93/160.66 [955]~E(x9551,x9552)+E(f53(x9551,x9553),f53(x9552,x9553))
% 160.93/160.66 [956]~E(x9561,x9562)+E(f53(x9563,x9561),f53(x9563,x9562))
% 160.93/160.66 [957]~E(x9571,x9572)+E(f601(x9571,x9573,x9574),f601(x9572,x9573,x9574))
% 160.93/160.66 [958]~E(x9581,x9582)+E(f601(x9583,x9581,x9584),f601(x9583,x9582,x9584))
% 160.93/160.66 [959]~E(x9591,x9592)+E(f601(x9593,x9594,x9591),f601(x9593,x9594,x9592))
% 160.93/160.66 [960]~E(x9601,x9602)+E(f787(x9601,x9603,x9604,x9605),f787(x9602,x9603,x9604,x9605))
% 160.93/160.66 [961]~E(x9611,x9612)+E(f787(x9613,x9611,x9614,x9615),f787(x9613,x9612,x9614,x9615))
% 160.93/160.66 [962]~E(x9621,x9622)+E(f787(x9623,x9624,x9621,x9625),f787(x9623,x9624,x9622,x9625))
% 160.93/160.66 [963]~E(x9631,x9632)+E(f787(x9633,x9634,x9635,x9631),f787(x9633,x9634,x9635,x9632))
% 160.93/160.66 [964]~E(x9641,x9642)+E(f839(x9641,x9643,x9644,x9645,x9646),f839(x9642,x9643,x9644,x9645,x9646))
% 160.93/160.66 [965]~E(x9651,x9652)+E(f839(x9653,x9651,x9654,x9655,x9656),f839(x9653,x9652,x9654,x9655,x9656))
% 160.93/160.66 [966]~E(x9661,x9662)+E(f839(x9663,x9664,x9661,x9665,x9666),f839(x9663,x9664,x9662,x9665,x9666))
% 160.93/160.66 [967]~E(x9671,x9672)+E(f839(x9673,x9674,x9675,x9671,x9676),f839(x9673,x9674,x9675,x9672,x9676))
% 160.93/160.66 [968]~E(x9681,x9682)+E(f839(x9683,x9684,x9685,x9686,x9681),f839(x9683,x9684,x9685,x9686,x9682))
% 160.93/160.66 [969]~E(x9691,x9692)+E(f866(x9691),f866(x9692))
% 160.93/160.66 [970]~E(x9701,x9702)+E(f773(x9701,x9703,x9704,x9705,x9706,x9707,x9708),f773(x9702,x9703,x9704,x9705,x9706,x9707,x9708))
% 160.93/160.66 [971]~E(x9711,x9712)+E(f773(x9713,x9711,x9714,x9715,x9716,x9717,x9718),f773(x9713,x9712,x9714,x9715,x9716,x9717,x9718))
% 160.93/160.66 [972]~E(x9721,x9722)+E(f773(x9723,x9724,x9721,x9725,x9726,x9727,x9728),f773(x9723,x9724,x9722,x9725,x9726,x9727,x9728))
% 160.93/160.66 [973]~E(x9731,x9732)+E(f773(x9733,x9734,x9735,x9731,x9736,x9737,x9738),f773(x9733,x9734,x9735,x9732,x9736,x9737,x9738))
% 160.93/160.66 [974]~E(x9741,x9742)+E(f773(x9743,x9744,x9745,x9746,x9741,x9747,x9748),f773(x9743,x9744,x9745,x9746,x9742,x9747,x9748))
% 160.93/160.66 [975]~E(x9751,x9752)+E(f773(x9753,x9754,x9755,x9756,x9757,x9751,x9758),f773(x9753,x9754,x9755,x9756,x9757,x9752,x9758))
% 160.93/160.66 [976]~E(x9761,x9762)+E(f773(x9763,x9764,x9765,x9766,x9767,x9768,x9761),f773(x9763,x9764,x9765,x9766,x9767,x9768,x9762))
% 160.93/160.66 [977]~E(x9771,x9772)+E(f728(x9771,x9773,x9774,x9775),f728(x9772,x9773,x9774,x9775))
% 160.93/160.66 [978]~E(x9781,x9782)+E(f728(x9783,x9781,x9784,x9785),f728(x9783,x9782,x9784,x9785))
% 160.93/160.66 [979]~E(x9791,x9792)+E(f728(x9793,x9794,x9791,x9795),f728(x9793,x9794,x9792,x9795))
% 160.93/160.66 [980]~E(x9801,x9802)+E(f728(x9803,x9804,x9805,x9801),f728(x9803,x9804,x9805,x9802))
% 160.93/160.66 [981]~E(x9811,x9812)+E(f648(x9811,x9813,x9814,x9815,x9816),f648(x9812,x9813,x9814,x9815,x9816))
% 160.93/160.66 [982]~E(x9821,x9822)+E(f648(x9823,x9821,x9824,x9825,x9826),f648(x9823,x9822,x9824,x9825,x9826))
% 160.93/160.66 [983]~E(x9831,x9832)+E(f648(x9833,x9834,x9831,x9835,x9836),f648(x9833,x9834,x9832,x9835,x9836))
% 160.93/160.66 [984]~E(x9841,x9842)+E(f648(x9843,x9844,x9845,x9841,x9846),f648(x9843,x9844,x9845,x9842,x9846))
% 160.93/160.66 [985]~E(x9851,x9852)+E(f648(x9853,x9854,x9855,x9856,x9851),f648(x9853,x9854,x9855,x9856,x9852))
% 160.93/160.66 [986]~E(x9861,x9862)+E(f660(x9861,x9863),f660(x9862,x9863))
% 160.93/160.66 [987]~E(x9871,x9872)+E(f660(x9873,x9871),f660(x9873,x9872))
% 160.93/160.66 [988]~E(x9881,x9882)+E(f515(x9881,x9883,x9884),f515(x9882,x9883,x9884))
% 160.93/160.66 [989]~E(x9891,x9892)+E(f515(x9893,x9891,x9894),f515(x9893,x9892,x9894))
% 160.93/160.66 [990]~E(x9901,x9902)+E(f515(x9903,x9904,x9901),f515(x9903,x9904,x9902))
% 160.93/160.66 [991]~E(x9911,x9912)+E(f390(x9911,x9913,x9914,x9915,x9916,x9917),f390(x9912,x9913,x9914,x9915,x9916,x9917))
% 160.93/160.66 [992]~E(x9921,x9922)+E(f390(x9923,x9921,x9924,x9925,x9926,x9927),f390(x9923,x9922,x9924,x9925,x9926,x9927))
% 160.93/160.66 [993]~E(x9931,x9932)+E(f390(x9933,x9934,x9931,x9935,x9936,x9937),f390(x9933,x9934,x9932,x9935,x9936,x9937))
% 160.93/160.66 [994]~E(x9941,x9942)+E(f390(x9943,x9944,x9945,x9941,x9946,x9947),f390(x9943,x9944,x9945,x9942,x9946,x9947))
% 160.93/160.66 [995]~E(x9951,x9952)+E(f390(x9953,x9954,x9955,x9956,x9951,x9957),f390(x9953,x9954,x9955,x9956,x9952,x9957))
% 160.93/160.66 [996]~E(x9961,x9962)+E(f390(x9963,x9964,x9965,x9966,x9967,x9961),f390(x9963,x9964,x9965,x9966,x9967,x9962))
% 160.93/160.66 [997]~E(x9971,x9972)+E(f266(x9971,x9973),f266(x9972,x9973))
% 160.93/160.66 [998]~E(x9981,x9982)+E(f266(x9983,x9981),f266(x9983,x9982))
% 160.93/160.66 [999]~E(x9991,x9992)+E(f410(x9991,x9993,x9994,x9995,x9996,x9997),f410(x9992,x9993,x9994,x9995,x9996,x9997))
% 160.93/160.66 [1000]~E(x10001,x10002)+E(f410(x10003,x10001,x10004,x10005,x10006,x10007),f410(x10003,x10002,x10004,x10005,x10006,x10007))
% 160.93/160.66 [1001]~E(x10011,x10012)+E(f410(x10013,x10014,x10011,x10015,x10016,x10017),f410(x10013,x10014,x10012,x10015,x10016,x10017))
% 160.93/160.66 [1002]~E(x10021,x10022)+E(f410(x10023,x10024,x10025,x10021,x10026,x10027),f410(x10023,x10024,x10025,x10022,x10026,x10027))
% 160.93/160.66 [1003]~E(x10031,x10032)+E(f410(x10033,x10034,x10035,x10036,x10031,x10037),f410(x10033,x10034,x10035,x10036,x10032,x10037))
% 160.93/160.66 [1004]~E(x10041,x10042)+E(f410(x10043,x10044,x10045,x10046,x10047,x10041),f410(x10043,x10044,x10045,x10046,x10047,x10042))
% 160.93/160.66 [1005]~E(x10051,x10052)+E(f300(x10051,x10053,x10054),f300(x10052,x10053,x10054))
% 160.93/160.66 [1006]~E(x10061,x10062)+E(f300(x10063,x10061,x10064),f300(x10063,x10062,x10064))
% 160.93/160.66 [1007]~E(x10071,x10072)+E(f300(x10073,x10074,x10071),f300(x10073,x10074,x10072))
% 160.93/160.66 [1008]~E(x10081,x10082)+E(f388(x10081,x10083,x10084),f388(x10082,x10083,x10084))
% 160.93/160.66 [1009]~E(x10091,x10092)+E(f388(x10093,x10091,x10094),f388(x10093,x10092,x10094))
% 160.93/160.66 [1010]~E(x10101,x10102)+E(f388(x10103,x10104,x10101),f388(x10103,x10104,x10102))
% 160.93/160.66 [1011]~E(x10111,x10112)+E(f819(x10111,x10113,x10114),f819(x10112,x10113,x10114))
% 160.93/160.66 [1012]~E(x10121,x10122)+E(f819(x10123,x10121,x10124),f819(x10123,x10122,x10124))
% 160.93/160.66 [1013]~E(x10131,x10132)+E(f819(x10133,x10134,x10131),f819(x10133,x10134,x10132))
% 160.93/160.66 [1014]~E(x10141,x10142)+E(f621(x10141,x10143),f621(x10142,x10143))
% 160.93/160.66 [1015]~E(x10151,x10152)+E(f621(x10153,x10151),f621(x10153,x10152))
% 160.93/160.66 [1016]~E(x10161,x10162)+E(f275(x10161,x10163,x10164,x10165),f275(x10162,x10163,x10164,x10165))
% 160.93/160.66 [1017]~E(x10171,x10172)+E(f275(x10173,x10171,x10174,x10175),f275(x10173,x10172,x10174,x10175))
% 160.93/160.66 [1018]~E(x10181,x10182)+E(f275(x10183,x10184,x10181,x10185),f275(x10183,x10184,x10182,x10185))
% 160.93/160.66 [1019]~E(x10191,x10192)+E(f275(x10193,x10194,x10195,x10191),f275(x10193,x10194,x10195,x10192))
% 160.93/160.66 [1020]~E(x10201,x10202)+E(f88(x10201),f88(x10202))
% 160.93/160.66 [1021]~E(x10211,x10212)+E(f414(x10211,x10213,x10214),f414(x10212,x10213,x10214))
% 160.93/160.66 [1022]~E(x10221,x10222)+E(f414(x10223,x10221,x10224),f414(x10223,x10222,x10224))
% 160.93/160.66 [1023]~E(x10231,x10232)+E(f414(x10233,x10234,x10231),f414(x10233,x10234,x10232))
% 160.93/160.66 [1024]~E(x10241,x10242)+E(f447(x10241,x10243,x10244),f447(x10242,x10243,x10244))
% 160.93/160.66 [1025]~E(x10251,x10252)+E(f447(x10253,x10251,x10254),f447(x10253,x10252,x10254))
% 160.93/160.66 [1026]~E(x10261,x10262)+E(f447(x10263,x10264,x10261),f447(x10263,x10264,x10262))
% 160.93/160.66 [1027]~E(x10271,x10272)+E(f865(x10271,x10273,x10274),f865(x10272,x10273,x10274))
% 160.93/160.66 [1028]~E(x10281,x10282)+E(f865(x10283,x10281,x10284),f865(x10283,x10282,x10284))
% 160.93/160.66 [1029]~E(x10291,x10292)+E(f865(x10293,x10294,x10291),f865(x10293,x10294,x10292))
% 160.93/160.66 [1030]~E(x10301,x10302)+E(f512(x10301,x10303,x10304,x10305),f512(x10302,x10303,x10304,x10305))
% 160.93/160.66 [1031]~E(x10311,x10312)+E(f512(x10313,x10311,x10314,x10315),f512(x10313,x10312,x10314,x10315))
% 160.93/160.66 [1032]~E(x10321,x10322)+E(f512(x10323,x10324,x10321,x10325),f512(x10323,x10324,x10322,x10325))
% 160.93/160.66 [1033]~E(x10331,x10332)+E(f512(x10333,x10334,x10335,x10331),f512(x10333,x10334,x10335,x10332))
% 160.93/160.66 [1034]~E(x10341,x10342)+E(f556(x10341,x10343,x10344,x10345,x10346,x10347,x10348,x10349),f556(x10342,x10343,x10344,x10345,x10346,x10347,x10348,x10349))
% 160.93/160.66 [1035]~E(x10351,x10352)+E(f556(x10353,x10351,x10354,x10355,x10356,x10357,x10358,x10359),f556(x10353,x10352,x10354,x10355,x10356,x10357,x10358,x10359))
% 160.93/160.66 [1036]~E(x10361,x10362)+E(f556(x10363,x10364,x10361,x10365,x10366,x10367,x10368,x10369),f556(x10363,x10364,x10362,x10365,x10366,x10367,x10368,x10369))
% 160.93/160.66 [1037]~E(x10371,x10372)+E(f556(x10373,x10374,x10375,x10371,x10376,x10377,x10378,x10379),f556(x10373,x10374,x10375,x10372,x10376,x10377,x10378,x10379))
% 160.93/160.66 [1038]~E(x10381,x10382)+E(f556(x10383,x10384,x10385,x10386,x10381,x10387,x10388,x10389),f556(x10383,x10384,x10385,x10386,x10382,x10387,x10388,x10389))
% 160.93/160.66 [1039]~E(x10391,x10392)+E(f556(x10393,x10394,x10395,x10396,x10397,x10391,x10398,x10399),f556(x10393,x10394,x10395,x10396,x10397,x10392,x10398,x10399))
% 160.93/160.66 [1040]~E(x10401,x10402)+E(f556(x10403,x10404,x10405,x10406,x10407,x10408,x10401,x10409),f556(x10403,x10404,x10405,x10406,x10407,x10408,x10402,x10409))
% 160.93/160.66 [1041]~E(x10411,x10412)+E(f556(x10413,x10414,x10415,x10416,x10417,x10418,x10419,x10411),f556(x10413,x10414,x10415,x10416,x10417,x10418,x10419,x10412))
% 160.93/160.66 [1042]~E(x10421,x10422)+E(f796(x10421,x10423,x10424),f796(x10422,x10423,x10424))
% 160.93/160.66 [1043]~E(x10431,x10432)+E(f796(x10433,x10431,x10434),f796(x10433,x10432,x10434))
% 160.93/160.66 [1044]~E(x10441,x10442)+E(f796(x10443,x10444,x10441),f796(x10443,x10444,x10442))
% 160.93/160.66 [1045]~E(x10451,x10452)+E(f699(x10451,x10453,x10454),f699(x10452,x10453,x10454))
% 160.93/160.66 [1046]~E(x10461,x10462)+E(f699(x10463,x10461,x10464),f699(x10463,x10462,x10464))
% 160.93/160.66 [1047]~E(x10471,x10472)+E(f699(x10473,x10474,x10471),f699(x10473,x10474,x10472))
% 160.93/160.66 [1048]~E(x10481,x10482)+E(f652(x10481,x10483,x10484,x10485),f652(x10482,x10483,x10484,x10485))
% 160.93/160.66 [1049]~E(x10491,x10492)+E(f652(x10493,x10491,x10494,x10495),f652(x10493,x10492,x10494,x10495))
% 160.93/160.66 [1050]~E(x10501,x10502)+E(f652(x10503,x10504,x10501,x10505),f652(x10503,x10504,x10502,x10505))
% 160.93/160.66 [1051]~E(x10511,x10512)+E(f652(x10513,x10514,x10515,x10511),f652(x10513,x10514,x10515,x10512))
% 160.93/160.66 [1052]~E(x10521,x10522)+E(f710(x10521,x10523),f710(x10522,x10523))
% 160.93/160.66 [1053]~E(x10531,x10532)+E(f710(x10533,x10531),f710(x10533,x10532))
% 160.93/160.66 [1054]~E(x10541,x10542)+E(f727(x10541,x10543,x10544),f727(x10542,x10543,x10544))
% 160.93/160.66 [1055]~E(x10551,x10552)+E(f727(x10553,x10551,x10554),f727(x10553,x10552,x10554))
% 160.93/160.66 [1056]~E(x10561,x10562)+E(f727(x10563,x10564,x10561),f727(x10563,x10564,x10562))
% 160.93/160.66 [1057]~E(x10571,x10572)+E(f571(x10571,x10573),f571(x10572,x10573))
% 160.93/160.66 [1058]~E(x10581,x10582)+E(f571(x10583,x10581),f571(x10583,x10582))
% 160.93/160.66 [1059]~E(x10591,x10592)+E(f99(x10591,x10593,x10594,x10595),f99(x10592,x10593,x10594,x10595))
% 160.93/160.66 [1060]~E(x10601,x10602)+E(f99(x10603,x10601,x10604,x10605),f99(x10603,x10602,x10604,x10605))
% 160.93/160.66 [1061]~E(x10611,x10612)+E(f99(x10613,x10614,x10611,x10615),f99(x10613,x10614,x10612,x10615))
% 160.93/160.66 [1062]~E(x10621,x10622)+E(f99(x10623,x10624,x10625,x10621),f99(x10623,x10624,x10625,x10622))
% 160.93/160.66 [1063]~E(x10631,x10632)+E(f352(x10631,x10633,x10634,x10635,x10636),f352(x10632,x10633,x10634,x10635,x10636))
% 160.93/160.66 [1064]~E(x10641,x10642)+E(f352(x10643,x10641,x10644,x10645,x10646),f352(x10643,x10642,x10644,x10645,x10646))
% 160.93/160.66 [1065]~E(x10651,x10652)+E(f352(x10653,x10654,x10651,x10655,x10656),f352(x10653,x10654,x10652,x10655,x10656))
% 160.93/160.66 [1066]~E(x10661,x10662)+E(f352(x10663,x10664,x10665,x10661,x10666),f352(x10663,x10664,x10665,x10662,x10666))
% 160.93/160.66 [1067]~E(x10671,x10672)+E(f352(x10673,x10674,x10675,x10676,x10671),f352(x10673,x10674,x10675,x10676,x10672))
% 160.93/160.66 [1068]~E(x10681,x10682)+E(f562(x10681,x10683,x10684,x10685),f562(x10682,x10683,x10684,x10685))
% 160.93/160.66 [1069]~E(x10691,x10692)+E(f562(x10693,x10691,x10694,x10695),f562(x10693,x10692,x10694,x10695))
% 160.93/160.66 [1070]~E(x10701,x10702)+E(f562(x10703,x10704,x10701,x10705),f562(x10703,x10704,x10702,x10705))
% 160.93/160.66 [1071]~E(x10711,x10712)+E(f562(x10713,x10714,x10715,x10711),f562(x10713,x10714,x10715,x10712))
% 160.93/160.66 [1072]~E(x10721,x10722)+E(f633(x10721,x10723,x10724),f633(x10722,x10723,x10724))
% 160.93/160.66 [1073]~E(x10731,x10732)+E(f633(x10733,x10731,x10734),f633(x10733,x10732,x10734))
% 160.93/160.66 [1074]~E(x10741,x10742)+E(f633(x10743,x10744,x10741),f633(x10743,x10744,x10742))
% 160.93/160.66 [1075]~E(x10751,x10752)+E(f96(x10751,x10753,x10754,x10755),f96(x10752,x10753,x10754,x10755))
% 160.93/160.66 [1076]~E(x10761,x10762)+E(f96(x10763,x10761,x10764,x10765),f96(x10763,x10762,x10764,x10765))
% 160.93/160.66 [1077]~E(x10771,x10772)+E(f96(x10773,x10774,x10771,x10775),f96(x10773,x10774,x10772,x10775))
% 160.93/160.66 [1078]~E(x10781,x10782)+E(f96(x10783,x10784,x10785,x10781),f96(x10783,x10784,x10785,x10782))
% 160.93/160.66 [1079]~E(x10791,x10792)+E(f415(x10791,x10793,x10794),f415(x10792,x10793,x10794))
% 160.93/160.66 [1080]~E(x10801,x10802)+E(f415(x10803,x10801,x10804),f415(x10803,x10802,x10804))
% 160.93/160.66 [1081]~E(x10811,x10812)+E(f415(x10813,x10814,x10811),f415(x10813,x10814,x10812))
% 160.93/160.66 [1082]~E(x10821,x10822)+E(f503(x10821,x10823,x10824,x10825),f503(x10822,x10823,x10824,x10825))
% 160.93/160.66 [1083]~E(x10831,x10832)+E(f503(x10833,x10831,x10834,x10835),f503(x10833,x10832,x10834,x10835))
% 160.93/160.66 [1084]~E(x10841,x10842)+E(f503(x10843,x10844,x10841,x10845),f503(x10843,x10844,x10842,x10845))
% 160.93/160.66 [1085]~E(x10851,x10852)+E(f503(x10853,x10854,x10855,x10851),f503(x10853,x10854,x10855,x10852))
% 160.93/160.66 [1086]~E(x10861,x10862)+E(f694(x10861,x10863),f694(x10862,x10863))
% 160.93/160.66 [1087]~E(x10871,x10872)+E(f694(x10873,x10871),f694(x10873,x10872))
% 160.93/160.66 [1088]~E(x10881,x10882)+E(f506(x10881,x10883,x10884),f506(x10882,x10883,x10884))
% 160.93/160.66 [1089]~E(x10891,x10892)+E(f506(x10893,x10891,x10894),f506(x10893,x10892,x10894))
% 160.93/160.66 [1090]~E(x10901,x10902)+E(f506(x10903,x10904,x10901),f506(x10903,x10904,x10902))
% 160.93/160.66 [1091]~E(x10911,x10912)+E(f419(x10911,x10913,x10914),f419(x10912,x10913,x10914))
% 160.93/160.66 [1092]~E(x10921,x10922)+E(f419(x10923,x10921,x10924),f419(x10923,x10922,x10924))
% 160.93/160.66 [1093]~E(x10931,x10932)+E(f419(x10933,x10934,x10931),f419(x10933,x10934,x10932))
% 160.93/160.66 [1094]~E(x10941,x10942)+E(f122(x10941,x10943,x10944),f122(x10942,x10943,x10944))
% 160.93/160.66 [1095]~E(x10951,x10952)+E(f122(x10953,x10951,x10954),f122(x10953,x10952,x10954))
% 160.93/160.66 [1096]~E(x10961,x10962)+E(f122(x10963,x10964,x10961),f122(x10963,x10964,x10962))
% 160.93/160.66 [1097]~E(x10971,x10972)+E(f708(x10971,x10973,x10974,x10975,x10976),f708(x10972,x10973,x10974,x10975,x10976))
% 160.93/160.66 [1098]~E(x10981,x10982)+E(f708(x10983,x10981,x10984,x10985,x10986),f708(x10983,x10982,x10984,x10985,x10986))
% 160.93/160.66 [1099]~E(x10991,x10992)+E(f708(x10993,x10994,x10991,x10995,x10996),f708(x10993,x10994,x10992,x10995,x10996))
% 160.93/160.66 [1100]~E(x11001,x11002)+E(f708(x11003,x11004,x11005,x11001,x11006),f708(x11003,x11004,x11005,x11002,x11006))
% 160.93/160.66 [1101]~E(x11011,x11012)+E(f708(x11013,x11014,x11015,x11016,x11011),f708(x11013,x11014,x11015,x11016,x11012))
% 160.93/160.66 [1102]~E(x11021,x11022)+E(f422(x11021,x11023,x11024,x11025,x11026,x11027),f422(x11022,x11023,x11024,x11025,x11026,x11027))
% 160.93/160.66 [1103]~E(x11031,x11032)+E(f422(x11033,x11031,x11034,x11035,x11036,x11037),f422(x11033,x11032,x11034,x11035,x11036,x11037))
% 160.93/160.66 [1104]~E(x11041,x11042)+E(f422(x11043,x11044,x11041,x11045,x11046,x11047),f422(x11043,x11044,x11042,x11045,x11046,x11047))
% 160.93/160.66 [1105]~E(x11051,x11052)+E(f422(x11053,x11054,x11055,x11051,x11056,x11057),f422(x11053,x11054,x11055,x11052,x11056,x11057))
% 160.93/160.66 [1106]~E(x11061,x11062)+E(f422(x11063,x11064,x11065,x11066,x11061,x11067),f422(x11063,x11064,x11065,x11066,x11062,x11067))
% 160.93/160.66 [1107]~E(x11071,x11072)+E(f422(x11073,x11074,x11075,x11076,x11077,x11071),f422(x11073,x11074,x11075,x11076,x11077,x11072))
% 160.93/160.66 [1108]~E(x11081,x11082)+E(f594(x11081,x11083),f594(x11082,x11083))
% 160.93/160.66 [1109]~E(x11091,x11092)+E(f594(x11093,x11091),f594(x11093,x11092))
% 160.93/160.66 [1110]~E(x11101,x11102)+E(f251(x11101,x11103),f251(x11102,x11103))
% 160.93/160.66 [1111]~E(x11111,x11112)+E(f251(x11113,x11111),f251(x11113,x11112))
% 160.93/160.66 [1112]~E(x11121,x11122)+E(f653(x11121,x11123,x11124,x11125),f653(x11122,x11123,x11124,x11125))
% 160.93/160.66 [1113]~E(x11131,x11132)+E(f653(x11133,x11131,x11134,x11135),f653(x11133,x11132,x11134,x11135))
% 160.93/160.66 [1114]~E(x11141,x11142)+E(f653(x11143,x11144,x11141,x11145),f653(x11143,x11144,x11142,x11145))
% 160.93/160.66 [1115]~E(x11151,x11152)+E(f653(x11153,x11154,x11155,x11151),f653(x11153,x11154,x11155,x11152))
% 160.93/160.66 [1116]~E(x11161,x11162)+E(f290(x11161,x11163),f290(x11162,x11163))
% 160.93/160.66 [1117]~E(x11171,x11172)+E(f290(x11173,x11171),f290(x11173,x11172))
% 160.93/160.66 [1118]~E(x11181,x11182)+E(f157(x11181,x11183,x11184),f157(x11182,x11183,x11184))
% 160.93/160.66 [1119]~E(x11191,x11192)+E(f157(x11193,x11191,x11194),f157(x11193,x11192,x11194))
% 160.93/160.66 [1120]~E(x11201,x11202)+E(f157(x11203,x11204,x11201),f157(x11203,x11204,x11202))
% 160.93/160.66 [1121]~E(x11211,x11212)+E(f805(x11211,x11213,x11214),f805(x11212,x11213,x11214))
% 160.93/160.66 [1122]~E(x11221,x11222)+E(f805(x11223,x11221,x11224),f805(x11223,x11222,x11224))
% 160.93/160.66 [1123]~E(x11231,x11232)+E(f805(x11233,x11234,x11231),f805(x11233,x11234,x11232))
% 160.93/160.66 [1124]~E(x11241,x11242)+E(f242(x11241,x11243,x11244),f242(x11242,x11243,x11244))
% 160.93/160.66 [1125]~E(x11251,x11252)+E(f242(x11253,x11251,x11254),f242(x11253,x11252,x11254))
% 160.93/160.66 [1126]~E(x11261,x11262)+E(f242(x11263,x11264,x11261),f242(x11263,x11264,x11262))
% 160.93/160.66 [1127]~E(x11271,x11272)+E(f391(x11271,x11273),f391(x11272,x11273))
% 160.93/160.66 [1128]~E(x11281,x11282)+E(f391(x11283,x11281),f391(x11283,x11282))
% 160.93/160.66 [1129]~E(x11291,x11292)+E(f437(x11291,x11293,x11294),f437(x11292,x11293,x11294))
% 160.93/160.66 [1130]~E(x11301,x11302)+E(f437(x11303,x11301,x11304),f437(x11303,x11302,x11304))
% 160.93/160.66 [1131]~E(x11311,x11312)+E(f437(x11313,x11314,x11311),f437(x11313,x11314,x11312))
% 160.93/160.66 [1132]~E(x11321,x11322)+E(f731(x11321,x11323,x11324),f731(x11322,x11323,x11324))
% 160.93/160.66 [1133]~E(x11331,x11332)+E(f731(x11333,x11331,x11334),f731(x11333,x11332,x11334))
% 160.93/160.66 [1134]~E(x11341,x11342)+E(f731(x11343,x11344,x11341),f731(x11343,x11344,x11342))
% 160.93/160.66 [1135]~E(x11351,x11352)+E(f757(x11351,x11353,x11354),f757(x11352,x11353,x11354))
% 160.93/160.66 [1136]~E(x11361,x11362)+E(f757(x11363,x11361,x11364),f757(x11363,x11362,x11364))
% 160.93/160.66 [1137]~E(x11371,x11372)+E(f757(x11373,x11374,x11371),f757(x11373,x11374,x11372))
% 160.93/160.66 [1138]~E(x11381,x11382)+E(f250(x11381,x11383),f250(x11382,x11383))
% 160.93/160.66 [1139]~E(x11391,x11392)+E(f250(x11393,x11391),f250(x11393,x11392))
% 160.93/160.66 [1140]~E(x11401,x11402)+E(f701(x11401,x11403,x11404,x11405,x11406),f701(x11402,x11403,x11404,x11405,x11406))
% 160.93/160.66 [1141]~E(x11411,x11412)+E(f701(x11413,x11411,x11414,x11415,x11416),f701(x11413,x11412,x11414,x11415,x11416))
% 160.93/160.66 [1142]~E(x11421,x11422)+E(f701(x11423,x11424,x11421,x11425,x11426),f701(x11423,x11424,x11422,x11425,x11426))
% 160.93/160.66 [1143]~E(x11431,x11432)+E(f701(x11433,x11434,x11435,x11431,x11436),f701(x11433,x11434,x11435,x11432,x11436))
% 160.93/160.66 [1144]~E(x11441,x11442)+E(f701(x11443,x11444,x11445,x11446,x11441),f701(x11443,x11444,x11445,x11446,x11442))
% 160.93/160.66 [1145]~E(x11451,x11452)+E(f684(x11451,x11453,x11454,x11455,x11456),f684(x11452,x11453,x11454,x11455,x11456))
% 160.93/160.66 [1146]~E(x11461,x11462)+E(f684(x11463,x11461,x11464,x11465,x11466),f684(x11463,x11462,x11464,x11465,x11466))
% 160.93/160.66 [1147]~E(x11471,x11472)+E(f684(x11473,x11474,x11471,x11475,x11476),f684(x11473,x11474,x11472,x11475,x11476))
% 160.93/160.66 [1148]~E(x11481,x11482)+E(f684(x11483,x11484,x11485,x11481,x11486),f684(x11483,x11484,x11485,x11482,x11486))
% 160.93/160.66 [1149]~E(x11491,x11492)+E(f684(x11493,x11494,x11495,x11496,x11491),f684(x11493,x11494,x11495,x11496,x11492))
% 160.93/160.66 [1150]~E(x11501,x11502)+E(f178(x11501,x11503,x11504),f178(x11502,x11503,x11504))
% 160.93/160.66 [1151]~E(x11511,x11512)+E(f178(x11513,x11511,x11514),f178(x11513,x11512,x11514))
% 160.93/160.66 [1152]~E(x11521,x11522)+E(f178(x11523,x11524,x11521),f178(x11523,x11524,x11522))
% 160.93/160.66 [1153]~E(x11531,x11532)+E(f606(x11531,x11533),f606(x11532,x11533))
% 160.93/160.66 [1154]~E(x11541,x11542)+E(f606(x11543,x11541),f606(x11543,x11542))
% 160.93/160.66 [1155]~E(x11551,x11552)+E(f674(x11551,x11553,x11554,x11555,x11556),f674(x11552,x11553,x11554,x11555,x11556))
% 160.93/160.66 [1156]~E(x11561,x11562)+E(f674(x11563,x11561,x11564,x11565,x11566),f674(x11563,x11562,x11564,x11565,x11566))
% 160.93/160.66 [1157]~E(x11571,x11572)+E(f674(x11573,x11574,x11571,x11575,x11576),f674(x11573,x11574,x11572,x11575,x11576))
% 160.93/160.66 [1158]~E(x11581,x11582)+E(f674(x11583,x11584,x11585,x11581,x11586),f674(x11583,x11584,x11585,x11582,x11586))
% 160.93/160.66 [1159]~E(x11591,x11592)+E(f674(x11593,x11594,x11595,x11596,x11591),f674(x11593,x11594,x11595,x11596,x11592))
% 160.93/160.66 [1160]~E(x11601,x11602)+E(f425(x11601,x11603,x11604),f425(x11602,x11603,x11604))
% 160.93/160.66 [1161]~E(x11611,x11612)+E(f425(x11613,x11611,x11614),f425(x11613,x11612,x11614))
% 160.93/160.66 [1162]~E(x11621,x11622)+E(f425(x11623,x11624,x11621),f425(x11623,x11624,x11622))
% 160.93/160.66 [1163]~E(x11631,x11632)+E(f426(x11631,x11633,x11634,x11635,x11636),f426(x11632,x11633,x11634,x11635,x11636))
% 160.93/160.66 [1164]~E(x11641,x11642)+E(f426(x11643,x11641,x11644,x11645,x11646),f426(x11643,x11642,x11644,x11645,x11646))
% 160.93/160.66 [1165]~E(x11651,x11652)+E(f426(x11653,x11654,x11651,x11655,x11656),f426(x11653,x11654,x11652,x11655,x11656))
% 160.93/160.66 [1166]~E(x11661,x11662)+E(f426(x11663,x11664,x11665,x11661,x11666),f426(x11663,x11664,x11665,x11662,x11666))
% 160.93/160.66 [1167]~E(x11671,x11672)+E(f426(x11673,x11674,x11675,x11676,x11671),f426(x11673,x11674,x11675,x11676,x11672))
% 160.93/160.66 [1168]~E(x11681,x11682)+E(f736(x11681,x11683,x11684),f736(x11682,x11683,x11684))
% 160.93/160.66 [1169]~E(x11691,x11692)+E(f736(x11693,x11691,x11694),f736(x11693,x11692,x11694))
% 160.93/160.66 [1170]~E(x11701,x11702)+E(f736(x11703,x11704,x11701),f736(x11703,x11704,x11702))
% 160.93/160.66 [1171]~E(x11711,x11712)+E(f456(x11711,x11713,x11714),f456(x11712,x11713,x11714))
% 160.93/160.66 [1172]~E(x11721,x11722)+E(f456(x11723,x11721,x11724),f456(x11723,x11722,x11724))
% 160.93/160.66 [1173]~E(x11731,x11732)+E(f456(x11733,x11734,x11731),f456(x11733,x11734,x11732))
% 160.93/160.66 [1174]~E(x11741,x11742)+E(f134(x11741,x11743),f134(x11742,x11743))
% 160.93/160.66 [1175]~E(x11751,x11752)+E(f134(x11753,x11751),f134(x11753,x11752))
% 160.93/160.66 [1176]~E(x11761,x11762)+E(f554(x11761,x11763,x11764),f554(x11762,x11763,x11764))
% 160.93/160.66 [1177]~E(x11771,x11772)+E(f554(x11773,x11771,x11774),f554(x11773,x11772,x11774))
% 160.93/160.66 [1178]~E(x11781,x11782)+E(f554(x11783,x11784,x11781),f554(x11783,x11784,x11782))
% 160.93/160.66 [1179]~E(x11791,x11792)+E(f227(x11791,x11793),f227(x11792,x11793))
% 160.93/160.66 [1180]~E(x11801,x11802)+E(f227(x11803,x11801),f227(x11803,x11802))
% 160.93/160.66 [1181]~E(x11811,x11812)+E(f198(x11811,x11813,x11814,x11815),f198(x11812,x11813,x11814,x11815))
% 160.93/160.66 [1182]~E(x11821,x11822)+E(f198(x11823,x11821,x11824,x11825),f198(x11823,x11822,x11824,x11825))
% 160.93/160.66 [1183]~E(x11831,x11832)+E(f198(x11833,x11834,x11831,x11835),f198(x11833,x11834,x11832,x11835))
% 160.93/160.66 [1184]~E(x11841,x11842)+E(f198(x11843,x11844,x11845,x11841),f198(x11843,x11844,x11845,x11842))
% 160.93/160.66 [1185]~E(x11851,x11852)+E(f214(x11851),f214(x11852))
% 160.93/160.66 [1186]~E(x11861,x11862)+E(f479(x11861,x11863),f479(x11862,x11863))
% 160.93/160.66 [1187]~E(x11871,x11872)+E(f479(x11873,x11871),f479(x11873,x11872))
% 160.93/160.66 [1188]~E(x11881,x11882)+E(f537(x11881),f537(x11882))
% 160.93/160.66 [1189]~E(x11891,x11892)+E(f659(x11891,x11893,x11894),f659(x11892,x11893,x11894))
% 160.93/160.66 [1190]~E(x11901,x11902)+E(f659(x11903,x11901,x11904),f659(x11903,x11902,x11904))
% 160.93/160.66 [1191]~E(x11911,x11912)+E(f659(x11913,x11914,x11911),f659(x11913,x11914,x11912))
% 160.93/160.66 [1192]~E(x11921,x11922)+E(f725(x11921,x11923,x11924),f725(x11922,x11923,x11924))
% 160.93/160.66 [1193]~E(x11931,x11932)+E(f725(x11933,x11931,x11934),f725(x11933,x11932,x11934))
% 160.93/160.66 [1194]~E(x11941,x11942)+E(f725(x11943,x11944,x11941),f725(x11943,x11944,x11942))
% 160.93/160.66 [1195]~E(x11951,x11952)+E(f385(x11951,x11953,x11954,x11955),f385(x11952,x11953,x11954,x11955))
% 160.93/160.66 [1196]~E(x11961,x11962)+E(f385(x11963,x11961,x11964,x11965),f385(x11963,x11962,x11964,x11965))
% 160.93/160.66 [1197]~E(x11971,x11972)+E(f385(x11973,x11974,x11971,x11975),f385(x11973,x11974,x11972,x11975))
% 160.93/160.66 [1198]~E(x11981,x11982)+E(f385(x11983,x11984,x11985,x11981),f385(x11983,x11984,x11985,x11982))
% 160.93/160.66 [1199]~E(x11991,x11992)+E(f396(x11991,x11993),f396(x11992,x11993))
% 160.93/160.66 [1200]~E(x12001,x12002)+E(f396(x12003,x12001),f396(x12003,x12002))
% 160.93/160.66 [1201]~E(x12011,x12012)+E(f641(x12011,x12013,x12014,x12015,x12016),f641(x12012,x12013,x12014,x12015,x12016))
% 160.93/160.66 [1202]~E(x12021,x12022)+E(f641(x12023,x12021,x12024,x12025,x12026),f641(x12023,x12022,x12024,x12025,x12026))
% 160.93/160.66 [1203]~E(x12031,x12032)+E(f641(x12033,x12034,x12031,x12035,x12036),f641(x12033,x12034,x12032,x12035,x12036))
% 160.93/160.66 [1204]~E(x12041,x12042)+E(f641(x12043,x12044,x12045,x12041,x12046),f641(x12043,x12044,x12045,x12042,x12046))
% 160.93/160.66 [1205]~E(x12051,x12052)+E(f641(x12053,x12054,x12055,x12056,x12051),f641(x12053,x12054,x12055,x12056,x12052))
% 160.93/160.66 [1206]~E(x12061,x12062)+E(f509(x12061,x12063,x12064,x12065,x12066,x12067),f509(x12062,x12063,x12064,x12065,x12066,x12067))
% 160.93/160.66 [1207]~E(x12071,x12072)+E(f509(x12073,x12071,x12074,x12075,x12076,x12077),f509(x12073,x12072,x12074,x12075,x12076,x12077))
% 160.93/160.66 [1208]~E(x12081,x12082)+E(f509(x12083,x12084,x12081,x12085,x12086,x12087),f509(x12083,x12084,x12082,x12085,x12086,x12087))
% 160.93/160.66 [1209]~E(x12091,x12092)+E(f509(x12093,x12094,x12095,x12091,x12096,x12097),f509(x12093,x12094,x12095,x12092,x12096,x12097))
% 160.93/160.66 [1210]~E(x12101,x12102)+E(f509(x12103,x12104,x12105,x12106,x12101,x12107),f509(x12103,x12104,x12105,x12106,x12102,x12107))
% 160.93/160.66 [1211]~E(x12111,x12112)+E(f509(x12113,x12114,x12115,x12116,x12117,x12111),f509(x12113,x12114,x12115,x12116,x12117,x12112))
% 160.93/160.66 [1212]~E(x12121,x12122)+E(f635(x12121,x12123,x12124),f635(x12122,x12123,x12124))
% 160.93/160.66 [1213]~E(x12131,x12132)+E(f635(x12133,x12131,x12134),f635(x12133,x12132,x12134))
% 160.93/160.66 [1214]~E(x12141,x12142)+E(f635(x12143,x12144,x12141),f635(x12143,x12144,x12142))
% 160.93/160.66 [1215]~E(x12151,x12152)+E(f745(x12151,x12153,x12154),f745(x12152,x12153,x12154))
% 160.93/160.66 [1216]~E(x12161,x12162)+E(f745(x12163,x12161,x12164),f745(x12163,x12162,x12164))
% 160.93/160.66 [1217]~E(x12171,x12172)+E(f745(x12173,x12174,x12171),f745(x12173,x12174,x12172))
% 160.93/160.66 [1218]~E(x12181,x12182)+E(f17(x12181,x12183,x12184,x12185),f17(x12182,x12183,x12184,x12185))
% 160.93/160.66 [1219]~E(x12191,x12192)+E(f17(x12193,x12191,x12194,x12195),f17(x12193,x12192,x12194,x12195))
% 160.93/160.66 [1220]~E(x12201,x12202)+E(f17(x12203,x12204,x12201,x12205),f17(x12203,x12204,x12202,x12205))
% 160.93/160.66 [1221]~E(x12211,x12212)+E(f17(x12213,x12214,x12215,x12211),f17(x12213,x12214,x12215,x12212))
% 160.93/160.66 [1222]~E(x12221,x12222)+E(f592(x12221,x12223,x12224),f592(x12222,x12223,x12224))
% 160.93/160.66 [1223]~E(x12231,x12232)+E(f592(x12233,x12231,x12234),f592(x12233,x12232,x12234))
% 160.93/160.66 [1224]~E(x12241,x12242)+E(f592(x12243,x12244,x12241),f592(x12243,x12244,x12242))
% 160.93/160.66 [1225]~E(x12251,x12252)+E(f212(x12251,x12253),f212(x12252,x12253))
% 160.93/160.66 [1226]~E(x12261,x12262)+E(f212(x12263,x12261),f212(x12263,x12262))
% 160.93/160.66 [1227]~E(x12271,x12272)+E(f342(x12271),f342(x12272))
% 160.93/160.66 [1228]~E(x12281,x12282)+E(f128(x12281),f128(x12282))
% 160.93/160.66 [1229]~E(x12291,x12292)+E(f598(x12291),f598(x12292))
% 160.93/160.66 [1230]~E(x12301,x12302)+E(f657(x12301,x12303,x12304),f657(x12302,x12303,x12304))
% 160.93/160.66 [1231]~E(x12311,x12312)+E(f657(x12313,x12311,x12314),f657(x12313,x12312,x12314))
% 160.93/160.66 [1232]~E(x12321,x12322)+E(f657(x12323,x12324,x12321),f657(x12323,x12324,x12322))
% 160.93/160.66 [1233]~E(x12331,x12332)+E(f869(x12331,x12333,x12334,x12335,x12336),f869(x12332,x12333,x12334,x12335,x12336))
% 160.93/160.66 [1234]~E(x12341,x12342)+E(f869(x12343,x12341,x12344,x12345,x12346),f869(x12343,x12342,x12344,x12345,x12346))
% 160.93/160.66 [1235]~E(x12351,x12352)+E(f869(x12353,x12354,x12351,x12355,x12356),f869(x12353,x12354,x12352,x12355,x12356))
% 160.93/160.66 [1236]~E(x12361,x12362)+E(f869(x12363,x12364,x12365,x12361,x12366),f869(x12363,x12364,x12365,x12362,x12366))
% 160.93/160.66 [1237]~E(x12371,x12372)+E(f869(x12373,x12374,x12375,x12376,x12371),f869(x12373,x12374,x12375,x12376,x12372))
% 160.93/160.66 [1238]~E(x12381,x12382)+E(f349(x12381,x12383,x12384),f349(x12382,x12383,x12384))
% 160.93/160.66 [1239]~E(x12391,x12392)+E(f349(x12393,x12391,x12394),f349(x12393,x12392,x12394))
% 160.93/160.66 [1240]~E(x12401,x12402)+E(f349(x12403,x12404,x12401),f349(x12403,x12404,x12402))
% 160.93/160.66 [1241]~E(x12411,x12412)+E(f448(x12411,x12413,x12414),f448(x12412,x12413,x12414))
% 160.93/160.66 [1242]~E(x12421,x12422)+E(f448(x12423,x12421,x12424),f448(x12423,x12422,x12424))
% 160.93/160.66 [1243]~E(x12431,x12432)+E(f448(x12433,x12434,x12431),f448(x12433,x12434,x12432))
% 160.93/160.66 [1244]~E(x12441,x12442)+E(f354(x12441,x12443,x12444,x12445,x12446),f354(x12442,x12443,x12444,x12445,x12446))
% 160.93/160.66 [1245]~E(x12451,x12452)+E(f354(x12453,x12451,x12454,x12455,x12456),f354(x12453,x12452,x12454,x12455,x12456))
% 160.93/160.66 [1246]~E(x12461,x12462)+E(f354(x12463,x12464,x12461,x12465,x12466),f354(x12463,x12464,x12462,x12465,x12466))
% 160.93/160.66 [1247]~E(x12471,x12472)+E(f354(x12473,x12474,x12475,x12471,x12476),f354(x12473,x12474,x12475,x12472,x12476))
% 160.93/160.66 [1248]~E(x12481,x12482)+E(f354(x12483,x12484,x12485,x12486,x12481),f354(x12483,x12484,x12485,x12486,x12482))
% 160.93/160.66 [1249]~E(x12491,x12492)+E(f353(x12491,x12493,x12494,x12495,x12496),f353(x12492,x12493,x12494,x12495,x12496))
% 160.93/160.66 [1250]~E(x12501,x12502)+E(f353(x12503,x12501,x12504,x12505,x12506),f353(x12503,x12502,x12504,x12505,x12506))
% 160.93/160.66 [1251]~E(x12511,x12512)+E(f353(x12513,x12514,x12511,x12515,x12516),f353(x12513,x12514,x12512,x12515,x12516))
% 160.93/160.66 [1252]~E(x12521,x12522)+E(f353(x12523,x12524,x12525,x12521,x12526),f353(x12523,x12524,x12525,x12522,x12526))
% 160.93/160.66 [1253]~E(x12531,x12532)+E(f353(x12533,x12534,x12535,x12536,x12531),f353(x12533,x12534,x12535,x12536,x12532))
% 160.93/160.66 [1254]~E(x12541,x12542)+E(f188(x12541,x12543,x12544),f188(x12542,x12543,x12544))
% 160.93/160.66 [1255]~E(x12551,x12552)+E(f188(x12553,x12551,x12554),f188(x12553,x12552,x12554))
% 160.93/160.66 [1256]~E(x12561,x12562)+E(f188(x12563,x12564,x12561),f188(x12563,x12564,x12562))
% 160.93/160.66 [1257]~E(x12571,x12572)+E(f646(x12571,x12573,x12574,x12575,x12576),f646(x12572,x12573,x12574,x12575,x12576))
% 160.93/160.66 [1258]~E(x12581,x12582)+E(f646(x12583,x12581,x12584,x12585,x12586),f646(x12583,x12582,x12584,x12585,x12586))
% 160.93/160.66 [1259]~E(x12591,x12592)+E(f646(x12593,x12594,x12591,x12595,x12596),f646(x12593,x12594,x12592,x12595,x12596))
% 160.93/160.66 [1260]~E(x12601,x12602)+E(f646(x12603,x12604,x12605,x12601,x12606),f646(x12603,x12604,x12605,x12602,x12606))
% 160.93/160.66 [1261]~E(x12611,x12612)+E(f646(x12613,x12614,x12615,x12616,x12611),f646(x12613,x12614,x12615,x12616,x12612))
% 160.93/160.66 [1262]~E(x12621,x12622)+E(f771(x12621,x12623),f771(x12622,x12623))
% 160.93/160.66 [1263]~E(x12631,x12632)+E(f771(x12633,x12631),f771(x12633,x12632))
% 160.93/160.66 [1264]~E(x12641,x12642)+E(f691(x12641,x12643,x12644,x12645),f691(x12642,x12643,x12644,x12645))
% 160.93/160.66 [1265]~E(x12651,x12652)+E(f691(x12653,x12651,x12654,x12655),f691(x12653,x12652,x12654,x12655))
% 160.93/160.66 [1266]~E(x12661,x12662)+E(f691(x12663,x12664,x12661,x12665),f691(x12663,x12664,x12662,x12665))
% 160.93/160.66 [1267]~E(x12671,x12672)+E(f691(x12673,x12674,x12675,x12671),f691(x12673,x12674,x12675,x12672))
% 160.93/160.66 [1268]~E(x12681,x12682)+E(f374(x12681,x12683,x12684),f374(x12682,x12683,x12684))
% 160.93/160.66 [1269]~E(x12691,x12692)+E(f374(x12693,x12691,x12694),f374(x12693,x12692,x12694))
% 160.93/160.66 [1270]~E(x12701,x12702)+E(f374(x12703,x12704,x12701),f374(x12703,x12704,x12702))
% 160.93/160.66 [1271]~E(x12711,x12712)+E(f406(x12711,x12713,x12714,x12715,x12716),f406(x12712,x12713,x12714,x12715,x12716))
% 160.93/160.66 [1272]~E(x12721,x12722)+E(f406(x12723,x12721,x12724,x12725,x12726),f406(x12723,x12722,x12724,x12725,x12726))
% 160.93/160.66 [1273]~E(x12731,x12732)+E(f406(x12733,x12734,x12731,x12735,x12736),f406(x12733,x12734,x12732,x12735,x12736))
% 160.93/160.66 [1274]~E(x12741,x12742)+E(f406(x12743,x12744,x12745,x12741,x12746),f406(x12743,x12744,x12745,x12742,x12746))
% 160.93/160.66 [1275]~E(x12751,x12752)+E(f406(x12753,x12754,x12755,x12756,x12751),f406(x12753,x12754,x12755,x12756,x12752))
% 160.93/160.66 [1276]~E(x12761,x12762)+E(f175(x12761,x12763,x12764),f175(x12762,x12763,x12764))
% 160.93/160.66 [1277]~E(x12771,x12772)+E(f175(x12773,x12771,x12774),f175(x12773,x12772,x12774))
% 160.93/160.66 [1278]~E(x12781,x12782)+E(f175(x12783,x12784,x12781),f175(x12783,x12784,x12782))
% 160.93/160.66 [1279]~E(x12791,x12792)+E(f476(x12791,x12793,x12794),f476(x12792,x12793,x12794))
% 160.93/160.66 [1280]~E(x12801,x12802)+E(f476(x12803,x12801,x12804),f476(x12803,x12802,x12804))
% 160.93/160.66 [1281]~E(x12811,x12812)+E(f476(x12813,x12814,x12811),f476(x12813,x12814,x12812))
% 160.93/160.66 [1282]~E(x12821,x12822)+E(f800(x12821,x12823,x12824),f800(x12822,x12823,x12824))
% 160.93/160.66 [1283]~E(x12831,x12832)+E(f800(x12833,x12831,x12834),f800(x12833,x12832,x12834))
% 160.93/160.66 [1284]~E(x12841,x12842)+E(f800(x12843,x12844,x12841),f800(x12843,x12844,x12842))
% 160.93/160.66 [1285]~E(x12851,x12852)+E(f262(x12851,x12853),f262(x12852,x12853))
% 160.93/160.66 [1286]~E(x12861,x12862)+E(f262(x12863,x12861),f262(x12863,x12862))
% 160.93/160.66 [1287]~E(x12871,x12872)+E(f507(x12871,x12873,x12874,x12875),f507(x12872,x12873,x12874,x12875))
% 160.93/160.66 [1288]~E(x12881,x12882)+E(f507(x12883,x12881,x12884,x12885),f507(x12883,x12882,x12884,x12885))
% 160.93/160.66 [1289]~E(x12891,x12892)+E(f507(x12893,x12894,x12891,x12895),f507(x12893,x12894,x12892,x12895))
% 160.93/160.66 [1290]~E(x12901,x12902)+E(f507(x12903,x12904,x12905,x12901),f507(x12903,x12904,x12905,x12902))
% 160.93/160.66 [1291]~E(x12911,x12912)+E(f707(x12911,x12913,x12914,x12915),f707(x12912,x12913,x12914,x12915))
% 160.93/160.66 [1292]~E(x12921,x12922)+E(f707(x12923,x12921,x12924,x12925),f707(x12923,x12922,x12924,x12925))
% 160.93/160.66 [1293]~E(x12931,x12932)+E(f707(x12933,x12934,x12931,x12935),f707(x12933,x12934,x12932,x12935))
% 160.93/160.66 [1294]~E(x12941,x12942)+E(f707(x12943,x12944,x12945,x12941),f707(x12943,x12944,x12945,x12942))
% 160.93/160.66 [1295]~E(x12951,x12952)+E(f673(x12951,x12953,x12954,x12955),f673(x12952,x12953,x12954,x12955))
% 160.93/160.66 [1296]~E(x12961,x12962)+E(f673(x12963,x12961,x12964,x12965),f673(x12963,x12962,x12964,x12965))
% 160.93/160.66 [1297]~E(x12971,x12972)+E(f673(x12973,x12974,x12971,x12975),f673(x12973,x12974,x12972,x12975))
% 160.93/160.66 [1298]~E(x12981,x12982)+E(f673(x12983,x12984,x12985,x12981),f673(x12983,x12984,x12985,x12982))
% 160.93/160.66 [1299]~E(x12991,x12992)+E(f389(x12991,x12993,x12994),f389(x12992,x12993,x12994))
% 160.93/160.66 [1300]~E(x13001,x13002)+E(f389(x13003,x13001,x13004),f389(x13003,x13002,x13004))
% 160.93/160.66 [1301]~E(x13011,x13012)+E(f389(x13013,x13014,x13011),f389(x13013,x13014,x13012))
% 160.93/160.66 [1302]~E(x13021,x13022)+E(f151(x13021,x13023,x13024,x13025,x13026),f151(x13022,x13023,x13024,x13025,x13026))
% 160.93/160.66 [1303]~E(x13031,x13032)+E(f151(x13033,x13031,x13034,x13035,x13036),f151(x13033,x13032,x13034,x13035,x13036))
% 160.93/160.66 [1304]~E(x13041,x13042)+E(f151(x13043,x13044,x13041,x13045,x13046),f151(x13043,x13044,x13042,x13045,x13046))
% 160.93/160.66 [1305]~E(x13051,x13052)+E(f151(x13053,x13054,x13055,x13051,x13056),f151(x13053,x13054,x13055,x13052,x13056))
% 160.93/160.66 [1306]~E(x13061,x13062)+E(f151(x13063,x13064,x13065,x13066,x13061),f151(x13063,x13064,x13065,x13066,x13062))
% 160.93/160.66 [1307]~E(x13071,x13072)+E(f531(x13071,x13073,x13074,x13075,x13076,x13077,x13078),f531(x13072,x13073,x13074,x13075,x13076,x13077,x13078))
% 160.93/160.66 [1308]~E(x13081,x13082)+E(f531(x13083,x13081,x13084,x13085,x13086,x13087,x13088),f531(x13083,x13082,x13084,x13085,x13086,x13087,x13088))
% 160.93/160.66 [1309]~E(x13091,x13092)+E(f531(x13093,x13094,x13091,x13095,x13096,x13097,x13098),f531(x13093,x13094,x13092,x13095,x13096,x13097,x13098))
% 160.93/160.66 [1310]~E(x13101,x13102)+E(f531(x13103,x13104,x13105,x13101,x13106,x13107,x13108),f531(x13103,x13104,x13105,x13102,x13106,x13107,x13108))
% 160.93/160.66 [1311]~E(x13111,x13112)+E(f531(x13113,x13114,x13115,x13116,x13111,x13117,x13118),f531(x13113,x13114,x13115,x13116,x13112,x13117,x13118))
% 160.93/160.66 [1312]~E(x13121,x13122)+E(f531(x13123,x13124,x13125,x13126,x13127,x13121,x13128),f531(x13123,x13124,x13125,x13126,x13127,x13122,x13128))
% 160.93/160.66 [1313]~E(x13131,x13132)+E(f531(x13133,x13134,x13135,x13136,x13137,x13138,x13131),f531(x13133,x13134,x13135,x13136,x13137,x13138,x13132))
% 160.93/160.66 [1314]~E(x13141,x13142)+E(f844(x13141,x13143,x13144,x13145),f844(x13142,x13143,x13144,x13145))
% 160.93/160.66 [1315]~E(x13151,x13152)+E(f844(x13153,x13151,x13154,x13155),f844(x13153,x13152,x13154,x13155))
% 160.93/160.66 [1316]~E(x13161,x13162)+E(f844(x13163,x13164,x13161,x13165),f844(x13163,x13164,x13162,x13165))
% 160.93/160.66 [1317]~E(x13171,x13172)+E(f844(x13173,x13174,x13175,x13171),f844(x13173,x13174,x13175,x13172))
% 160.93/160.66 [1318]~E(x13181,x13182)+E(f718(x13181,x13183,x13184,x13185,x13186),f718(x13182,x13183,x13184,x13185,x13186))
% 160.93/160.66 [1319]~E(x13191,x13192)+E(f718(x13193,x13191,x13194,x13195,x13196),f718(x13193,x13192,x13194,x13195,x13196))
% 160.93/160.66 [1320]~E(x13201,x13202)+E(f718(x13203,x13204,x13201,x13205,x13206),f718(x13203,x13204,x13202,x13205,x13206))
% 160.93/160.66 [1321]~E(x13211,x13212)+E(f718(x13213,x13214,x13215,x13211,x13216),f718(x13213,x13214,x13215,x13212,x13216))
% 160.93/160.66 [1322]~E(x13221,x13222)+E(f718(x13223,x13224,x13225,x13226,x13221),f718(x13223,x13224,x13225,x13226,x13222))
% 160.93/160.66 [1323]~E(x13231,x13232)+E(f628(x13231,x13233,x13234,x13235,x13236),f628(x13232,x13233,x13234,x13235,x13236))
% 160.93/160.66 [1324]~E(x13241,x13242)+E(f628(x13243,x13241,x13244,x13245,x13246),f628(x13243,x13242,x13244,x13245,x13246))
% 160.93/160.66 [1325]~E(x13251,x13252)+E(f628(x13253,x13254,x13251,x13255,x13256),f628(x13253,x13254,x13252,x13255,x13256))
% 160.93/160.66 [1326]~E(x13261,x13262)+E(f628(x13263,x13264,x13265,x13261,x13266),f628(x13263,x13264,x13265,x13262,x13266))
% 160.93/160.66 [1327]~E(x13271,x13272)+E(f628(x13273,x13274,x13275,x13276,x13271),f628(x13273,x13274,x13275,x13276,x13272))
% 160.93/160.66 [1328]~E(x13281,x13282)+E(f461(x13281,x13283,x13284),f461(x13282,x13283,x13284))
% 160.93/160.66 [1329]~E(x13291,x13292)+E(f461(x13293,x13291,x13294),f461(x13293,x13292,x13294))
% 160.93/160.66 [1330]~E(x13301,x13302)+E(f461(x13303,x13304,x13301),f461(x13303,x13304,x13302))
% 160.93/160.66 [1331]~E(x13311,x13312)+E(f795(x13311,x13313,x13314,x13315,x13316,x13317,x13318),f795(x13312,x13313,x13314,x13315,x13316,x13317,x13318))
% 160.93/160.66 [1332]~E(x13321,x13322)+E(f795(x13323,x13321,x13324,x13325,x13326,x13327,x13328),f795(x13323,x13322,x13324,x13325,x13326,x13327,x13328))
% 160.93/160.66 [1333]~E(x13331,x13332)+E(f795(x13333,x13334,x13331,x13335,x13336,x13337,x13338),f795(x13333,x13334,x13332,x13335,x13336,x13337,x13338))
% 160.93/160.66 [1334]~E(x13341,x13342)+E(f795(x13343,x13344,x13345,x13341,x13346,x13347,x13348),f795(x13343,x13344,x13345,x13342,x13346,x13347,x13348))
% 160.93/160.66 [1335]~E(x13351,x13352)+E(f795(x13353,x13354,x13355,x13356,x13351,x13357,x13358),f795(x13353,x13354,x13355,x13356,x13352,x13357,x13358))
% 160.93/160.66 [1336]~E(x13361,x13362)+E(f795(x13363,x13364,x13365,x13366,x13367,x13361,x13368),f795(x13363,x13364,x13365,x13366,x13367,x13362,x13368))
% 160.93/160.66 [1337]~E(x13371,x13372)+E(f795(x13373,x13374,x13375,x13376,x13377,x13378,x13371),f795(x13373,x13374,x13375,x13376,x13377,x13378,x13372))
% 160.93/160.66 [1338]~E(x13381,x13382)+E(f613(x13381,x13383,x13384,x13385,x13386,x13387),f613(x13382,x13383,x13384,x13385,x13386,x13387))
% 160.93/160.66 [1339]~E(x13391,x13392)+E(f613(x13393,x13391,x13394,x13395,x13396,x13397),f613(x13393,x13392,x13394,x13395,x13396,x13397))
% 160.93/160.66 [1340]~E(x13401,x13402)+E(f613(x13403,x13404,x13401,x13405,x13406,x13407),f613(x13403,x13404,x13402,x13405,x13406,x13407))
% 160.93/160.66 [1341]~E(x13411,x13412)+E(f613(x13413,x13414,x13415,x13411,x13416,x13417),f613(x13413,x13414,x13415,x13412,x13416,x13417))
% 160.93/160.66 [1342]~E(x13421,x13422)+E(f613(x13423,x13424,x13425,x13426,x13421,x13427),f613(x13423,x13424,x13425,x13426,x13422,x13427))
% 160.93/160.66 [1343]~E(x13431,x13432)+E(f613(x13433,x13434,x13435,x13436,x13437,x13431),f613(x13433,x13434,x13435,x13436,x13437,x13432))
% 160.93/160.66 [1344]~E(x13441,x13442)+E(f565(x13441,x13443,x13444),f565(x13442,x13443,x13444))
% 160.93/160.66 [1345]~E(x13451,x13452)+E(f565(x13453,x13451,x13454),f565(x13453,x13452,x13454))
% 160.93/160.66 [1346]~E(x13461,x13462)+E(f565(x13463,x13464,x13461),f565(x13463,x13464,x13462))
% 160.93/160.66 [1347]~E(x13471,x13472)+E(f755(x13471,x13473,x13474),f755(x13472,x13473,x13474))
% 160.93/160.66 [1348]~E(x13481,x13482)+E(f755(x13483,x13481,x13484),f755(x13483,x13482,x13484))
% 160.93/160.66 [1349]~E(x13491,x13492)+E(f755(x13493,x13494,x13491),f755(x13493,x13494,x13492))
% 160.93/160.66 [1350]~E(x13501,x13502)+E(f768(x13501,x13503,x13504,x13505),f768(x13502,x13503,x13504,x13505))
% 160.93/160.66 [1351]~E(x13511,x13512)+E(f768(x13513,x13511,x13514,x13515),f768(x13513,x13512,x13514,x13515))
% 160.93/160.66 [1352]~E(x13521,x13522)+E(f768(x13523,x13524,x13521,x13525),f768(x13523,x13524,x13522,x13525))
% 160.93/160.66 [1353]~E(x13531,x13532)+E(f768(x13533,x13534,x13535,x13531),f768(x13533,x13534,x13535,x13532))
% 160.93/160.66 [1354]~E(x13541,x13542)+E(f392(x13541,x13543,x13544,x13545),f392(x13542,x13543,x13544,x13545))
% 160.93/160.66 [1355]~E(x13551,x13552)+E(f392(x13553,x13551,x13554,x13555),f392(x13553,x13552,x13554,x13555))
% 160.93/160.66 [1356]~E(x13561,x13562)+E(f392(x13563,x13564,x13561,x13565),f392(x13563,x13564,x13562,x13565))
% 160.93/160.66 [1357]~E(x13571,x13572)+E(f392(x13573,x13574,x13575,x13571),f392(x13573,x13574,x13575,x13572))
% 160.93/160.66 [1358]~E(x13581,x13582)+E(f120(x13581,x13583,x13584),f120(x13582,x13583,x13584))
% 160.93/160.66 [1359]~E(x13591,x13592)+E(f120(x13593,x13591,x13594),f120(x13593,x13592,x13594))
% 160.93/160.66 [1360]~E(x13601,x13602)+E(f120(x13603,x13604,x13601),f120(x13603,x13604,x13602))
% 160.93/160.66 [1361]~E(x13611,x13612)+E(f776(x13611,x13613,x13614,x13615,x13616),f776(x13612,x13613,x13614,x13615,x13616))
% 160.93/160.66 [1362]~E(x13621,x13622)+E(f776(x13623,x13621,x13624,x13625,x13626),f776(x13623,x13622,x13624,x13625,x13626))
% 160.93/160.66 [1363]~E(x13631,x13632)+E(f776(x13633,x13634,x13631,x13635,x13636),f776(x13633,x13634,x13632,x13635,x13636))
% 160.93/160.66 [1364]~E(x13641,x13642)+E(f776(x13643,x13644,x13645,x13641,x13646),f776(x13643,x13644,x13645,x13642,x13646))
% 160.93/160.66 [1365]~E(x13651,x13652)+E(f776(x13653,x13654,x13655,x13656,x13651),f776(x13653,x13654,x13655,x13656,x13652))
% 160.93/160.66 [1366]~E(x13661,x13662)+E(f368(x13661,x13663),f368(x13662,x13663))
% 160.93/160.66 [1367]~E(x13671,x13672)+E(f368(x13673,x13671),f368(x13673,x13672))
% 160.93/160.66 [1368]~E(x13681,x13682)+E(f328(x13681,x13683,x13684),f328(x13682,x13683,x13684))
% 160.93/160.66 [1369]~E(x13691,x13692)+E(f328(x13693,x13691,x13694),f328(x13693,x13692,x13694))
% 160.93/160.66 [1370]~E(x13701,x13702)+E(f328(x13703,x13704,x13701),f328(x13703,x13704,x13702))
% 160.93/160.66 [1371]~E(x13711,x13712)+E(f229(x13711,x13713),f229(x13712,x13713))
% 160.93/160.66 [1372]~E(x13721,x13722)+E(f229(x13723,x13721),f229(x13723,x13722))
% 160.93/160.66 [1373]~E(x13731,x13732)+E(f855(x13731,x13733,x13734,x13735,x13736),f855(x13732,x13733,x13734,x13735,x13736))
% 160.93/160.66 [1374]~E(x13741,x13742)+E(f855(x13743,x13741,x13744,x13745,x13746),f855(x13743,x13742,x13744,x13745,x13746))
% 160.93/160.66 [1375]~E(x13751,x13752)+E(f855(x13753,x13754,x13751,x13755,x13756),f855(x13753,x13754,x13752,x13755,x13756))
% 160.93/160.66 [1376]~E(x13761,x13762)+E(f855(x13763,x13764,x13765,x13761,x13766),f855(x13763,x13764,x13765,x13762,x13766))
% 160.93/160.66 [1377]~E(x13771,x13772)+E(f855(x13773,x13774,x13775,x13776,x13771),f855(x13773,x13774,x13775,x13776,x13772))
% 160.93/160.66 [1378]~E(x13781,x13782)+E(f397(x13781,x13783),f397(x13782,x13783))
% 160.93/160.66 [1379]~E(x13791,x13792)+E(f397(x13793,x13791),f397(x13793,x13792))
% 160.93/160.66 [1380]~E(x13801,x13802)+E(f384(x13801,x13803,x13804,x13805),f384(x13802,x13803,x13804,x13805))
% 160.93/160.66 [1381]~E(x13811,x13812)+E(f384(x13813,x13811,x13814,x13815),f384(x13813,x13812,x13814,x13815))
% 160.93/160.66 [1382]~E(x13821,x13822)+E(f384(x13823,x13824,x13821,x13825),f384(x13823,x13824,x13822,x13825))
% 160.93/160.66 [1383]~E(x13831,x13832)+E(f384(x13833,x13834,x13835,x13831),f384(x13833,x13834,x13835,x13832))
% 160.93/160.66 [1384]~E(x13841,x13842)+E(f834(x13841,x13843,x13844,x13845),f834(x13842,x13843,x13844,x13845))
% 160.93/160.66 [1385]~E(x13851,x13852)+E(f834(x13853,x13851,x13854,x13855),f834(x13853,x13852,x13854,x13855))
% 160.93/160.66 [1386]~E(x13861,x13862)+E(f834(x13863,x13864,x13861,x13865),f834(x13863,x13864,x13862,x13865))
% 160.93/160.66 [1387]~E(x13871,x13872)+E(f834(x13873,x13874,x13875,x13871),f834(x13873,x13874,x13875,x13872))
% 160.93/160.66 [1388]~E(x13881,x13882)+E(f634(x13881,x13883),f634(x13882,x13883))
% 160.93/160.66 [1389]~E(x13891,x13892)+E(f634(x13893,x13891),f634(x13893,x13892))
% 160.93/160.66 [1390]~E(x13901,x13902)+E(f612(x13901,x13903,x13904,x13905,x13906,x13907),f612(x13902,x13903,x13904,x13905,x13906,x13907))
% 160.93/160.66 [1391]~E(x13911,x13912)+E(f612(x13913,x13911,x13914,x13915,x13916,x13917),f612(x13913,x13912,x13914,x13915,x13916,x13917))
% 160.93/160.66 [1392]~E(x13921,x13922)+E(f612(x13923,x13924,x13921,x13925,x13926,x13927),f612(x13923,x13924,x13922,x13925,x13926,x13927))
% 160.93/160.66 [1393]~E(x13931,x13932)+E(f612(x13933,x13934,x13935,x13931,x13936,x13937),f612(x13933,x13934,x13935,x13932,x13936,x13937))
% 160.93/160.66 [1394]~E(x13941,x13942)+E(f612(x13943,x13944,x13945,x13946,x13941,x13947),f612(x13943,x13944,x13945,x13946,x13942,x13947))
% 160.93/160.66 [1395]~E(x13951,x13952)+E(f612(x13953,x13954,x13955,x13956,x13957,x13951),f612(x13953,x13954,x13955,x13956,x13957,x13952))
% 160.93/160.66 [1396]~E(x13961,x13962)+E(f792(x13961,x13963,x13964,x13965,x13966),f792(x13962,x13963,x13964,x13965,x13966))
% 160.93/160.66 [1397]~E(x13971,x13972)+E(f792(x13973,x13971,x13974,x13975,x13976),f792(x13973,x13972,x13974,x13975,x13976))
% 160.93/160.66 [1398]~E(x13981,x13982)+E(f792(x13983,x13984,x13981,x13985,x13986),f792(x13983,x13984,x13982,x13985,x13986))
% 160.93/160.66 [1399]~E(x13991,x13992)+E(f792(x13993,x13994,x13995,x13991,x13996),f792(x13993,x13994,x13995,x13992,x13996))
% 160.93/160.66 [1400]~E(x14001,x14002)+E(f792(x14003,x14004,x14005,x14006,x14001),f792(x14003,x14004,x14005,x14006,x14002))
% 160.93/160.66 [1401]~E(x14011,x14012)+E(f695(x14011),f695(x14012))
% 160.93/160.66 [1402]~E(x14021,x14022)+E(f318(x14021,x14023,x14024),f318(x14022,x14023,x14024))
% 160.93/160.66 [1403]~E(x14031,x14032)+E(f318(x14033,x14031,x14034),f318(x14033,x14032,x14034))
% 160.93/160.66 [1404]~E(x14041,x14042)+E(f318(x14043,x14044,x14041),f318(x14043,x14044,x14042))
% 160.93/160.66 [1405]~E(x14051,x14052)+E(f282(x14051,x14053),f282(x14052,x14053))
% 160.93/160.66 [1406]~E(x14061,x14062)+E(f282(x14063,x14061),f282(x14063,x14062))
% 160.93/160.66 [1407]~E(x14071,x14072)+E(f643(x14071,x14073,x14074,x14075,x14076),f643(x14072,x14073,x14074,x14075,x14076))
% 160.93/160.66 [1408]~E(x14081,x14082)+E(f643(x14083,x14081,x14084,x14085,x14086),f643(x14083,x14082,x14084,x14085,x14086))
% 160.93/160.66 [1409]~E(x14091,x14092)+E(f643(x14093,x14094,x14091,x14095,x14096),f643(x14093,x14094,x14092,x14095,x14096))
% 160.93/160.66 [1410]~E(x14101,x14102)+E(f643(x14103,x14104,x14105,x14101,x14106),f643(x14103,x14104,x14105,x14102,x14106))
% 160.93/160.66 [1411]~E(x14111,x14112)+E(f643(x14113,x14114,x14115,x14116,x14111),f643(x14113,x14114,x14115,x14116,x14112))
% 160.93/160.66 [1412]~E(x14121,x14122)+E(f666(x14121,x14123,x14124,x14125,x14126,x14127),f666(x14122,x14123,x14124,x14125,x14126,x14127))
% 160.93/160.66 [1413]~E(x14131,x14132)+E(f666(x14133,x14131,x14134,x14135,x14136,x14137),f666(x14133,x14132,x14134,x14135,x14136,x14137))
% 160.93/160.66 [1414]~E(x14141,x14142)+E(f666(x14143,x14144,x14141,x14145,x14146,x14147),f666(x14143,x14144,x14142,x14145,x14146,x14147))
% 160.93/160.66 [1415]~E(x14151,x14152)+E(f666(x14153,x14154,x14155,x14151,x14156,x14157),f666(x14153,x14154,x14155,x14152,x14156,x14157))
% 160.93/160.66 [1416]~E(x14161,x14162)+E(f666(x14163,x14164,x14165,x14166,x14161,x14167),f666(x14163,x14164,x14165,x14166,x14162,x14167))
% 160.93/160.66 [1417]~E(x14171,x14172)+E(f666(x14173,x14174,x14175,x14176,x14177,x14171),f666(x14173,x14174,x14175,x14176,x14177,x14172))
% 160.93/160.66 [1418]~E(x14181,x14182)+E(f355(x14181,x14183,x14184),f355(x14182,x14183,x14184))
% 160.93/160.66 [1419]~E(x14191,x14192)+E(f355(x14193,x14191,x14194),f355(x14193,x14192,x14194))
% 160.93/160.66 [1420]~E(x14201,x14202)+E(f355(x14203,x14204,x14201),f355(x14203,x14204,x14202))
% 160.93/160.66 [1421]~E(x14211,x14212)+E(f747(x14211,x14213),f747(x14212,x14213))
% 160.93/160.66 [1422]~E(x14221,x14222)+E(f747(x14223,x14221),f747(x14223,x14222))
% 160.93/160.66 [1423]~E(x14231,x14232)+E(f667(x14231,x14233,x14234,x14235,x14236,x14237),f667(x14232,x14233,x14234,x14235,x14236,x14237))
% 160.93/160.66 [1424]~E(x14241,x14242)+E(f667(x14243,x14241,x14244,x14245,x14246,x14247),f667(x14243,x14242,x14244,x14245,x14246,x14247))
% 160.93/160.66 [1425]~E(x14251,x14252)+E(f667(x14253,x14254,x14251,x14255,x14256,x14257),f667(x14253,x14254,x14252,x14255,x14256,x14257))
% 160.93/160.66 [1426]~E(x14261,x14262)+E(f667(x14263,x14264,x14265,x14261,x14266,x14267),f667(x14263,x14264,x14265,x14262,x14266,x14267))
% 160.93/160.66 [1427]~E(x14271,x14272)+E(f667(x14273,x14274,x14275,x14276,x14271,x14277),f667(x14273,x14274,x14275,x14276,x14272,x14277))
% 160.93/160.66 [1428]~E(x14281,x14282)+E(f667(x14283,x14284,x14285,x14286,x14287,x14281),f667(x14283,x14284,x14285,x14286,x14287,x14282))
% 160.93/160.66 [1429]~E(x14291,x14292)+E(f544(x14291,x14293,x14294,x14295,x14296,x14297,x14298),f544(x14292,x14293,x14294,x14295,x14296,x14297,x14298))
% 160.93/160.66 [1430]~E(x14301,x14302)+E(f544(x14303,x14301,x14304,x14305,x14306,x14307,x14308),f544(x14303,x14302,x14304,x14305,x14306,x14307,x14308))
% 160.93/160.66 [1431]~E(x14311,x14312)+E(f544(x14313,x14314,x14311,x14315,x14316,x14317,x14318),f544(x14313,x14314,x14312,x14315,x14316,x14317,x14318))
% 160.93/160.66 [1432]~E(x14321,x14322)+E(f544(x14323,x14324,x14325,x14321,x14326,x14327,x14328),f544(x14323,x14324,x14325,x14322,x14326,x14327,x14328))
% 160.93/160.66 [1433]~E(x14331,x14332)+E(f544(x14333,x14334,x14335,x14336,x14331,x14337,x14338),f544(x14333,x14334,x14335,x14336,x14332,x14337,x14338))
% 160.93/160.66 [1434]~E(x14341,x14342)+E(f544(x14343,x14344,x14345,x14346,x14347,x14341,x14348),f544(x14343,x14344,x14345,x14346,x14347,x14342,x14348))
% 160.93/160.66 [1435]~E(x14351,x14352)+E(f544(x14353,x14354,x14355,x14356,x14357,x14358,x14351),f544(x14353,x14354,x14355,x14356,x14357,x14358,x14352))
% 160.93/160.66 [1436]~E(x14361,x14362)+E(f471(x14361,x14363,x14364,x14365),f471(x14362,x14363,x14364,x14365))
% 160.93/160.66 [1437]~E(x14371,x14372)+E(f471(x14373,x14371,x14374,x14375),f471(x14373,x14372,x14374,x14375))
% 160.93/160.66 [1438]~E(x14381,x14382)+E(f471(x14383,x14384,x14381,x14385),f471(x14383,x14384,x14382,x14385))
% 160.93/160.66 [1439]~E(x14391,x14392)+E(f471(x14393,x14394,x14395,x14391),f471(x14393,x14394,x14395,x14392))
% 160.93/160.66 [1440]~E(x14401,x14402)+E(f669(x14401,x14403,x14404,x14405),f669(x14402,x14403,x14404,x14405))
% 160.93/160.66 [1441]~E(x14411,x14412)+E(f669(x14413,x14411,x14414,x14415),f669(x14413,x14412,x14414,x14415))
% 160.93/160.66 [1442]~E(x14421,x14422)+E(f669(x14423,x14424,x14421,x14425),f669(x14423,x14424,x14422,x14425))
% 160.93/160.66 [1443]~E(x14431,x14432)+E(f669(x14433,x14434,x14435,x14431),f669(x14433,x14434,x14435,x14432))
% 160.93/160.66 [1444]~E(x14441,x14442)+E(f411(x14441,x14443),f411(x14442,x14443))
% 160.93/160.66 [1445]~E(x14451,x14452)+E(f411(x14453,x14451),f411(x14453,x14452))
% 160.93/160.66 [1446]~E(x14461,x14462)+E(f451(x14461),f451(x14462))
% 160.93/160.66 [1447]~E(x14471,x14472)+E(f591(x14471,x14473,x14474),f591(x14472,x14473,x14474))
% 160.93/160.66 [1448]~E(x14481,x14482)+E(f591(x14483,x14481,x14484),f591(x14483,x14482,x14484))
% 160.93/160.66 [1449]~E(x14491,x14492)+E(f591(x14493,x14494,x14491),f591(x14493,x14494,x14492))
% 160.93/160.66 [1450]~E(x14501,x14502)+E(f810(x14501,x14503,x14504),f810(x14502,x14503,x14504))
% 160.93/160.66 [1451]~E(x14511,x14512)+E(f810(x14513,x14511,x14514),f810(x14513,x14512,x14514))
% 160.93/160.66 [1452]~E(x14521,x14522)+E(f810(x14523,x14524,x14521),f810(x14523,x14524,x14522))
% 160.93/160.66 [1453]~E(x14531,x14532)+E(f434(x14531,x14533,x14534,x14535,x14536),f434(x14532,x14533,x14534,x14535,x14536))
% 160.93/160.66 [1454]~E(x14541,x14542)+E(f434(x14543,x14541,x14544,x14545,x14546),f434(x14543,x14542,x14544,x14545,x14546))
% 160.93/160.66 [1455]~E(x14551,x14552)+E(f434(x14553,x14554,x14551,x14555,x14556),f434(x14553,x14554,x14552,x14555,x14556))
% 160.93/160.66 [1456]~E(x14561,x14562)+E(f434(x14563,x14564,x14565,x14561,x14566),f434(x14563,x14564,x14565,x14562,x14566))
% 160.93/160.66 [1457]~E(x14571,x14572)+E(f434(x14573,x14574,x14575,x14576,x14571),f434(x14573,x14574,x14575,x14576,x14572))
% 160.93/160.66 [1458]~E(x14581,x14582)+E(f737(x14581,x14583),f737(x14582,x14583))
% 160.93/160.66 [1459]~E(x14591,x14592)+E(f737(x14593,x14591),f737(x14593,x14592))
% 160.93/160.66 [1460]~E(x14601,x14602)+E(f478(x14601,x14603),f478(x14602,x14603))
% 160.93/160.66 [1461]~E(x14611,x14612)+E(f478(x14613,x14611),f478(x14613,x14612))
% 160.93/160.66 [1462]~E(x14621,x14622)+E(f584(x14621,x14623,x14624,x14625,x14626,x14627,x14628,x14629,x146210),f584(x14622,x14623,x14624,x14625,x14626,x14627,x14628,x14629,x146210))
% 160.93/160.66 [1463]~E(x14631,x14632)+E(f584(x14633,x14631,x14634,x14635,x14636,x14637,x14638,x14639,x146310),f584(x14633,x14632,x14634,x14635,x14636,x14637,x14638,x14639,x146310))
% 160.93/160.66 [1464]~E(x14641,x14642)+E(f584(x14643,x14644,x14641,x14645,x14646,x14647,x14648,x14649,x146410),f584(x14643,x14644,x14642,x14645,x14646,x14647,x14648,x14649,x146410))
% 160.93/160.66 [1465]~E(x14651,x14652)+E(f584(x14653,x14654,x14655,x14651,x14656,x14657,x14658,x14659,x146510),f584(x14653,x14654,x14655,x14652,x14656,x14657,x14658,x14659,x146510))
% 160.93/160.66 [1466]~E(x14661,x14662)+E(f584(x14663,x14664,x14665,x14666,x14661,x14667,x14668,x14669,x146610),f584(x14663,x14664,x14665,x14666,x14662,x14667,x14668,x14669,x146610))
% 160.93/160.66 [1467]~E(x14671,x14672)+E(f584(x14673,x14674,x14675,x14676,x14677,x14671,x14678,x14679,x146710),f584(x14673,x14674,x14675,x14676,x14677,x14672,x14678,x14679,x146710))
% 160.93/160.66 [1468]~E(x14681,x14682)+E(f584(x14683,x14684,x14685,x14686,x14687,x14688,x14681,x14689,x146810),f584(x14683,x14684,x14685,x14686,x14687,x14688,x14682,x14689,x146810))
% 160.93/160.66 [1469]~E(x14691,x14692)+E(f584(x14693,x14694,x14695,x14696,x14697,x14698,x14699,x14691,x146910),f584(x14693,x14694,x14695,x14696,x14697,x14698,x14699,x14692,x146910))
% 160.93/160.66 [1470]~E(x14701,x14702)+E(f584(x14703,x14704,x14705,x14706,x14707,x14708,x14709,x147010,x14701),f584(x14703,x14704,x14705,x14706,x14707,x14708,x14709,x147010,x14702))
% 160.93/160.66 [1471]~E(x14711,x14712)+E(f567(x14711,x14713,x14714,x14715),f567(x14712,x14713,x14714,x14715))
% 160.93/160.66 [1472]~E(x14721,x14722)+E(f567(x14723,x14721,x14724,x14725),f567(x14723,x14722,x14724,x14725))
% 160.93/160.66 [1473]~E(x14731,x14732)+E(f567(x14733,x14734,x14731,x14735),f567(x14733,x14734,x14732,x14735))
% 160.93/160.66 [1474]~E(x14741,x14742)+E(f567(x14743,x14744,x14745,x14741),f567(x14743,x14744,x14745,x14742))
% 160.93/160.66 [1475]~E(x14751,x14752)+E(f750(x14751,x14753),f750(x14752,x14753))
% 160.93/160.66 [1476]~E(x14761,x14762)+E(f750(x14763,x14761),f750(x14763,x14762))
% 160.93/160.66 [1477]~E(x14771,x14772)+E(f239(x14771,x14773,x14774,x14775),f239(x14772,x14773,x14774,x14775))
% 160.93/160.66 [1478]~E(x14781,x14782)+E(f239(x14783,x14781,x14784,x14785),f239(x14783,x14782,x14784,x14785))
% 160.93/160.66 [1479]~E(x14791,x14792)+E(f239(x14793,x14794,x14791,x14795),f239(x14793,x14794,x14792,x14795))
% 160.93/160.66 [1480]~E(x14801,x14802)+E(f239(x14803,x14804,x14805,x14801),f239(x14803,x14804,x14805,x14802))
% 160.93/160.66 [1481]~E(x14811,x14812)+E(f675(x14811,x14813,x14814,x14815,x14816),f675(x14812,x14813,x14814,x14815,x14816))
% 160.93/160.66 [1482]~E(x14821,x14822)+E(f675(x14823,x14821,x14824,x14825,x14826),f675(x14823,x14822,x14824,x14825,x14826))
% 160.93/160.66 [1483]~E(x14831,x14832)+E(f675(x14833,x14834,x14831,x14835,x14836),f675(x14833,x14834,x14832,x14835,x14836))
% 160.93/160.66 [1484]~E(x14841,x14842)+E(f675(x14843,x14844,x14845,x14841,x14846),f675(x14843,x14844,x14845,x14842,x14846))
% 160.93/160.66 [1485]~E(x14851,x14852)+E(f675(x14853,x14854,x14855,x14856,x14851),f675(x14853,x14854,x14855,x14856,x14852))
% 160.93/160.66 [1486]~E(x14861,x14862)+E(f401(x14861,x14863,x14864,x14865),f401(x14862,x14863,x14864,x14865))
% 160.93/160.66 [1487]~E(x14871,x14872)+E(f401(x14873,x14871,x14874,x14875),f401(x14873,x14872,x14874,x14875))
% 160.93/160.66 [1488]~E(x14881,x14882)+E(f401(x14883,x14884,x14881,x14885),f401(x14883,x14884,x14882,x14885))
% 160.93/160.66 [1489]~E(x14891,x14892)+E(f401(x14893,x14894,x14895,x14891),f401(x14893,x14894,x14895,x14892))
% 160.93/160.66 [1490]~E(x14901,x14902)+E(f393(x14901,x14903,x14904,x14905),f393(x14902,x14903,x14904,x14905))
% 160.93/160.66 [1491]~E(x14911,x14912)+E(f393(x14913,x14911,x14914,x14915),f393(x14913,x14912,x14914,x14915))
% 160.93/160.66 [1492]~E(x14921,x14922)+E(f393(x14923,x14924,x14921,x14925),f393(x14923,x14924,x14922,x14925))
% 160.93/160.66 [1493]~E(x14931,x14932)+E(f393(x14933,x14934,x14935,x14931),f393(x14933,x14934,x14935,x14932))
% 160.93/160.66 [1494]~E(x14941,x14942)+E(f859(x14941,x14943,x14944,x14945,x14946,x14947,x14948),f859(x14942,x14943,x14944,x14945,x14946,x14947,x14948))
% 160.93/160.66 [1495]~E(x14951,x14952)+E(f859(x14953,x14951,x14954,x14955,x14956,x14957,x14958),f859(x14953,x14952,x14954,x14955,x14956,x14957,x14958))
% 160.93/160.66 [1496]~E(x14961,x14962)+E(f859(x14963,x14964,x14961,x14965,x14966,x14967,x14968),f859(x14963,x14964,x14962,x14965,x14966,x14967,x14968))
% 160.93/160.66 [1497]~E(x14971,x14972)+E(f859(x14973,x14974,x14975,x14971,x14976,x14977,x14978),f859(x14973,x14974,x14975,x14972,x14976,x14977,x14978))
% 160.93/160.66 [1498]~E(x14981,x14982)+E(f859(x14983,x14984,x14985,x14986,x14981,x14987,x14988),f859(x14983,x14984,x14985,x14986,x14982,x14987,x14988))
% 160.93/160.66 [1499]~E(x14991,x14992)+E(f859(x14993,x14994,x14995,x14996,x14997,x14991,x14998),f859(x14993,x14994,x14995,x14996,x14997,x14992,x14998))
% 160.93/160.66 [1500]~E(x15001,x15002)+E(f859(x15003,x15004,x15005,x15006,x15007,x15008,x15001),f859(x15003,x15004,x15005,x15006,x15007,x15008,x15002))
% 160.93/160.66 [1501]~E(x15011,x15012)+E(f632(x15011,x15013),f632(x15012,x15013))
% 160.93/160.66 [1502]~E(x15021,x15022)+E(f632(x15023,x15021),f632(x15023,x15022))
% 160.93/160.66 [1503]~E(x15031,x15032)+E(f651(x15031,x15033,x15034,x15035,x15036),f651(x15032,x15033,x15034,x15035,x15036))
% 160.93/160.66 [1504]~E(x15041,x15042)+E(f651(x15043,x15041,x15044,x15045,x15046),f651(x15043,x15042,x15044,x15045,x15046))
% 160.93/160.66 [1505]~E(x15051,x15052)+E(f651(x15053,x15054,x15051,x15055,x15056),f651(x15053,x15054,x15052,x15055,x15056))
% 160.93/160.66 [1506]~E(x15061,x15062)+E(f651(x15063,x15064,x15065,x15061,x15066),f651(x15063,x15064,x15065,x15062,x15066))
% 160.93/160.66 [1507]~E(x15071,x15072)+E(f651(x15073,x15074,x15075,x15076,x15071),f651(x15073,x15074,x15075,x15076,x15072))
% 160.93/160.66 [1508]~E(x15081,x15082)+E(f380(x15081,x15083,x15084,x15085),f380(x15082,x15083,x15084,x15085))
% 160.93/160.66 [1509]~E(x15091,x15092)+E(f380(x15093,x15091,x15094,x15095),f380(x15093,x15092,x15094,x15095))
% 160.93/160.66 [1510]~E(x15101,x15102)+E(f380(x15103,x15104,x15101,x15105),f380(x15103,x15104,x15102,x15105))
% 160.93/160.66 [1511]~E(x15111,x15112)+E(f380(x15113,x15114,x15115,x15111),f380(x15113,x15114,x15115,x15112))
% 160.93/160.66 [1512]~E(x15121,x15122)+E(f467(x15121,x15123,x15124),f467(x15122,x15123,x15124))
% 160.93/160.66 [1513]~E(x15131,x15132)+E(f467(x15133,x15131,x15134),f467(x15133,x15132,x15134))
% 160.93/160.66 [1514]~E(x15141,x15142)+E(f467(x15143,x15144,x15141),f467(x15143,x15144,x15142))
% 160.93/160.66 [1515]~E(x15151,x15152)+E(f45(x15151,x15153),f45(x15152,x15153))
% 160.93/160.66 [1516]~E(x15161,x15162)+E(f45(x15163,x15161),f45(x15163,x15162))
% 160.93/160.66 [1517]~E(x15171,x15172)+E(f873(x15171,x15173),f873(x15172,x15173))
% 160.93/160.66 [1518]~E(x15181,x15182)+E(f873(x15183,x15181),f873(x15183,x15182))
% 160.93/160.66 [1519]~E(x15191,x15192)+E(f655(x15191,x15193,x15194),f655(x15192,x15193,x15194))
% 160.93/160.66 [1520]~E(x15201,x15202)+E(f655(x15203,x15201,x15204),f655(x15203,x15202,x15204))
% 160.93/160.66 [1521]~E(x15211,x15212)+E(f655(x15213,x15214,x15211),f655(x15213,x15214,x15212))
% 160.93/160.66 [1522]~E(x15221,x15222)+E(f832(x15221,x15223,x15224,x15225),f832(x15222,x15223,x15224,x15225))
% 160.93/160.66 [1523]~E(x15231,x15232)+E(f832(x15233,x15231,x15234,x15235),f832(x15233,x15232,x15234,x15235))
% 160.93/160.66 [1524]~E(x15241,x15242)+E(f832(x15243,x15244,x15241,x15245),f832(x15243,x15244,x15242,x15245))
% 160.93/160.66 [1525]~E(x15251,x15252)+E(f832(x15253,x15254,x15255,x15251),f832(x15253,x15254,x15255,x15252))
% 160.93/160.66 [1526]~E(x15261,x15262)+E(f863(x15261,x15263,x15264),f863(x15262,x15263,x15264))
% 160.93/160.66 [1527]~E(x15271,x15272)+E(f863(x15273,x15271,x15274),f863(x15273,x15272,x15274))
% 160.93/160.66 [1528]~E(x15281,x15282)+E(f863(x15283,x15284,x15281),f863(x15283,x15284,x15282))
% 160.93/160.66 [1529]~E(x15291,x15292)+E(f665(x15291,x15293,x15294,x15295,x15296,x15297),f665(x15292,x15293,x15294,x15295,x15296,x15297))
% 160.93/160.66 [1530]~E(x15301,x15302)+E(f665(x15303,x15301,x15304,x15305,x15306,x15307),f665(x15303,x15302,x15304,x15305,x15306,x15307))
% 160.93/160.66 [1531]~E(x15311,x15312)+E(f665(x15313,x15314,x15311,x15315,x15316,x15317),f665(x15313,x15314,x15312,x15315,x15316,x15317))
% 160.93/160.66 [1532]~E(x15321,x15322)+E(f665(x15323,x15324,x15325,x15321,x15326,x15327),f665(x15323,x15324,x15325,x15322,x15326,x15327))
% 160.93/160.66 [1533]~E(x15331,x15332)+E(f665(x15333,x15334,x15335,x15336,x15331,x15337),f665(x15333,x15334,x15335,x15336,x15332,x15337))
% 160.93/160.66 [1534]~E(x15341,x15342)+E(f665(x15343,x15344,x15345,x15346,x15347,x15341),f665(x15343,x15344,x15345,x15346,x15347,x15342))
% 160.93/160.66 [1535]~E(x15351,x15352)+E(f527(x15351,x15353,x15354),f527(x15352,x15353,x15354))
% 160.93/160.66 [1536]~E(x15361,x15362)+E(f527(x15363,x15361,x15364),f527(x15363,x15362,x15364))
% 160.93/160.66 [1537]~E(x15371,x15372)+E(f527(x15373,x15374,x15371),f527(x15373,x15374,x15372))
% 160.93/160.66 [1538]~E(x15381,x15382)+E(f751(x15381,x15383,x15384),f751(x15382,x15383,x15384))
% 160.93/160.66 [1539]~E(x15391,x15392)+E(f751(x15393,x15391,x15394),f751(x15393,x15392,x15394))
% 160.93/160.66 [1540]~E(x15401,x15402)+E(f751(x15403,x15404,x15401),f751(x15403,x15404,x15402))
% 160.93/160.66 [1541]~E(x15411,x15412)+E(f501(x15411,x15413,x15414,x15415),f501(x15412,x15413,x15414,x15415))
% 160.93/160.66 [1542]~E(x15421,x15422)+E(f501(x15423,x15421,x15424,x15425),f501(x15423,x15422,x15424,x15425))
% 160.93/160.66 [1543]~E(x15431,x15432)+E(f501(x15433,x15434,x15431,x15435),f501(x15433,x15434,x15432,x15435))
% 160.93/160.66 [1544]~E(x15441,x15442)+E(f501(x15443,x15444,x15445,x15441),f501(x15443,x15444,x15445,x15442))
% 160.93/160.66 [1545]~E(x15451,x15452)+E(f462(x15451,x15453,x15454),f462(x15452,x15453,x15454))
% 160.93/160.66 [1546]~E(x15461,x15462)+E(f462(x15463,x15461,x15464),f462(x15463,x15462,x15464))
% 160.93/160.66 [1547]~E(x15471,x15472)+E(f462(x15473,x15474,x15471),f462(x15473,x15474,x15472))
% 160.93/160.66 [1548]~E(x15481,x15482)+E(f705(x15481,x15483,x15484,x15485),f705(x15482,x15483,x15484,x15485))
% 160.93/160.66 [1549]~E(x15491,x15492)+E(f705(x15493,x15491,x15494,x15495),f705(x15493,x15492,x15494,x15495))
% 160.93/160.66 [1550]~E(x15501,x15502)+E(f705(x15503,x15504,x15501,x15505),f705(x15503,x15504,x15502,x15505))
% 160.93/160.66 [1551]~E(x15511,x15512)+E(f705(x15513,x15514,x15515,x15511),f705(x15513,x15514,x15515,x15512))
% 160.93/160.66 [1552]~E(x15521,x15522)+E(f74(x15521,x15523),f74(x15522,x15523))
% 160.93/160.66 [1553]~E(x15531,x15532)+E(f74(x15533,x15531),f74(x15533,x15532))
% 160.93/160.66 [1554]~E(x15541,x15542)+E(f749(x15541,x15543),f749(x15542,x15543))
% 160.93/160.66 [1555]~E(x15551,x15552)+E(f749(x15553,x15551),f749(x15553,x15552))
% 160.93/160.66 [1556]~E(x15561,x15562)+E(f864(x15561,x15563,x15564),f864(x15562,x15563,x15564))
% 160.93/160.66 [1557]~E(x15571,x15572)+E(f864(x15573,x15571,x15574),f864(x15573,x15572,x15574))
% 160.93/160.66 [1558]~E(x15581,x15582)+E(f864(x15583,x15584,x15581),f864(x15583,x15584,x15582))
% 160.93/160.66 [1559]~E(x15591,x15592)+E(f650(x15591,x15593,x15594,x15595,x15596),f650(x15592,x15593,x15594,x15595,x15596))
% 160.93/160.66 [1560]~E(x15601,x15602)+E(f650(x15603,x15601,x15604,x15605,x15606),f650(x15603,x15602,x15604,x15605,x15606))
% 160.93/160.66 [1561]~E(x15611,x15612)+E(f650(x15613,x15614,x15611,x15615,x15616),f650(x15613,x15614,x15612,x15615,x15616))
% 160.93/160.66 [1562]~E(x15621,x15622)+E(f650(x15623,x15624,x15625,x15621,x15626),f650(x15623,x15624,x15625,x15622,x15626))
% 160.93/160.66 [1563]~E(x15631,x15632)+E(f650(x15633,x15634,x15635,x15636,x15631),f650(x15633,x15634,x15635,x15636,x15632))
% 160.93/160.66 [1564]~E(x15641,x15642)+E(f639(x15641,x15643,x15644,x15645,x15646),f639(x15642,x15643,x15644,x15645,x15646))
% 160.93/160.66 [1565]~E(x15651,x15652)+E(f639(x15653,x15651,x15654,x15655,x15656),f639(x15653,x15652,x15654,x15655,x15656))
% 160.93/160.66 [1566]~E(x15661,x15662)+E(f639(x15663,x15664,x15661,x15665,x15666),f639(x15663,x15664,x15662,x15665,x15666))
% 160.93/160.66 [1567]~E(x15671,x15672)+E(f639(x15673,x15674,x15675,x15671,x15676),f639(x15673,x15674,x15675,x15672,x15676))
% 160.93/160.66 [1568]~E(x15681,x15682)+E(f639(x15683,x15684,x15685,x15686,x15681),f639(x15683,x15684,x15685,x15686,x15682))
% 160.93/160.66 [1569]~E(x15691,x15692)+E(f697(x15691,x15693,x15694),f697(x15692,x15693,x15694))
% 160.93/160.66 [1570]~E(x15701,x15702)+E(f697(x15703,x15701,x15704),f697(x15703,x15702,x15704))
% 160.93/160.66 [1571]~E(x15711,x15712)+E(f697(x15713,x15714,x15711),f697(x15713,x15714,x15712))
% 160.93/160.66 [1572]~E(x15721,x15722)+E(f827(x15721,x15723),f827(x15722,x15723))
% 160.93/160.66 [1573]~E(x15731,x15732)+E(f827(x15733,x15731),f827(x15733,x15732))
% 160.93/160.66 [1574]~E(x15741,x15742)+E(f386(x15741,x15743,x15744,x15745),f386(x15742,x15743,x15744,x15745))
% 160.93/160.66 [1575]~E(x15751,x15752)+E(f386(x15753,x15751,x15754,x15755),f386(x15753,x15752,x15754,x15755))
% 160.93/160.66 [1576]~E(x15761,x15762)+E(f386(x15763,x15764,x15761,x15765),f386(x15763,x15764,x15762,x15765))
% 160.93/160.66 [1577]~E(x15771,x15772)+E(f386(x15773,x15774,x15775,x15771),f386(x15773,x15774,x15775,x15772))
% 160.93/160.66 [1578]~E(x15781,x15782)+E(f357(x15781,x15783),f357(x15782,x15783))
% 160.93/160.66 [1579]~E(x15791,x15792)+E(f357(x15793,x15791),f357(x15793,x15792))
% 160.93/160.66 [1580]~E(x15801,x15802)+E(f826(x15801),f826(x15802))
% 160.93/160.66 [1581]~E(x15811,x15812)+E(f216(x15811,x15813,x15814),f216(x15812,x15813,x15814))
% 160.93/160.66 [1582]~E(x15821,x15822)+E(f216(x15823,x15821,x15824),f216(x15823,x15822,x15824))
% 160.93/160.66 [1583]~E(x15831,x15832)+E(f216(x15833,x15834,x15831),f216(x15833,x15834,x15832))
% 160.93/160.66 [1584]~E(x15841,x15842)+E(f689(x15841,x15843),f689(x15842,x15843))
% 160.93/160.66 [1585]~E(x15851,x15852)+E(f689(x15853,x15851),f689(x15853,x15852))
% 160.93/160.66 [1586]~E(x15861,x15862)+E(f698(x15861,x15863,x15864,x15865),f698(x15862,x15863,x15864,x15865))
% 160.93/160.66 [1587]~E(x15871,x15872)+E(f698(x15873,x15871,x15874,x15875),f698(x15873,x15872,x15874,x15875))
% 160.93/160.66 [1588]~E(x15881,x15882)+E(f698(x15883,x15884,x15881,x15885),f698(x15883,x15884,x15882,x15885))
% 160.93/160.66 [1589]~E(x15891,x15892)+E(f698(x15893,x15894,x15895,x15891),f698(x15893,x15894,x15895,x15892))
% 160.93/160.66 [1590]~E(x15901,x15902)+E(f494(x15901,x15903,x15904),f494(x15902,x15903,x15904))
% 160.93/160.66 [1591]~E(x15911,x15912)+E(f494(x15913,x15911,x15914),f494(x15913,x15912,x15914))
% 160.93/160.66 [1592]~E(x15921,x15922)+E(f494(x15923,x15924,x15921),f494(x15923,x15924,x15922))
% 160.93/160.66 [1593]~E(x15931,x15932)+E(f862(x15931,x15933),f862(x15932,x15933))
% 160.93/160.66 [1594]~E(x15941,x15942)+E(f862(x15943,x15941),f862(x15943,x15942))
% 160.93/160.66 [1595]~E(x15951,x15952)+E(f625(x15951,x15953,x15954,x15955,x15956,x15957,x15958,x15959),f625(x15952,x15953,x15954,x15955,x15956,x15957,x15958,x15959))
% 160.93/160.66 [1596]~E(x15961,x15962)+E(f625(x15963,x15961,x15964,x15965,x15966,x15967,x15968,x15969),f625(x15963,x15962,x15964,x15965,x15966,x15967,x15968,x15969))
% 160.93/160.66 [1597]~E(x15971,x15972)+E(f625(x15973,x15974,x15971,x15975,x15976,x15977,x15978,x15979),f625(x15973,x15974,x15972,x15975,x15976,x15977,x15978,x15979))
% 160.93/160.66 [1598]~E(x15981,x15982)+E(f625(x15983,x15984,x15985,x15981,x15986,x15987,x15988,x15989),f625(x15983,x15984,x15985,x15982,x15986,x15987,x15988,x15989))
% 160.93/160.66 [1599]~E(x15991,x15992)+E(f625(x15993,x15994,x15995,x15996,x15991,x15997,x15998,x15999),f625(x15993,x15994,x15995,x15996,x15992,x15997,x15998,x15999))
% 160.93/160.66 [1600]~E(x16001,x16002)+E(f625(x16003,x16004,x16005,x16006,x16007,x16001,x16008,x16009),f625(x16003,x16004,x16005,x16006,x16007,x16002,x16008,x16009))
% 160.93/160.66 [1601]~E(x16011,x16012)+E(f625(x16013,x16014,x16015,x16016,x16017,x16018,x16011,x16019),f625(x16013,x16014,x16015,x16016,x16017,x16018,x16012,x16019))
% 160.93/160.66 [1602]~E(x16021,x16022)+E(f625(x16023,x16024,x16025,x16026,x16027,x16028,x16029,x16021),f625(x16023,x16024,x16025,x16026,x16027,x16028,x16029,x16022))
% 160.93/160.66 [1603]~E(x16031,x16032)+E(f445(x16031,x16033),f445(x16032,x16033))
% 160.93/160.66 [1604]~E(x16041,x16042)+E(f445(x16043,x16041),f445(x16043,x16042))
% 160.93/160.66 [1605]~E(x16051,x16052)+E(f797(x16051,x16053,x16054),f797(x16052,x16053,x16054))
% 160.93/160.66 [1606]~E(x16061,x16062)+E(f797(x16063,x16061,x16064),f797(x16063,x16062,x16064))
% 160.93/160.66 [1607]~E(x16071,x16072)+E(f797(x16073,x16074,x16071),f797(x16073,x16074,x16072))
% 160.93/160.66 [1608]~E(x16081,x16082)+E(f828(x16081,x16083,x16084),f828(x16082,x16083,x16084))
% 160.93/160.66 [1609]~E(x16091,x16092)+E(f828(x16093,x16091,x16094),f828(x16093,x16092,x16094))
% 160.93/160.66 [1610]~E(x16101,x16102)+E(f828(x16103,x16104,x16101),f828(x16103,x16104,x16102))
% 160.93/160.66 [1611]~E(x16111,x16112)+E(f394(x16111,x16113,x16114,x16115),f394(x16112,x16113,x16114,x16115))
% 160.93/160.66 [1612]~E(x16121,x16122)+E(f394(x16123,x16121,x16124,x16125),f394(x16123,x16122,x16124,x16125))
% 160.93/160.66 [1613]~E(x16131,x16132)+E(f394(x16133,x16134,x16131,x16135),f394(x16133,x16134,x16132,x16135))
% 160.93/160.66 [1614]~E(x16141,x16142)+E(f394(x16143,x16144,x16145,x16141),f394(x16143,x16144,x16145,x16142))
% 160.93/160.66 [1615]~E(x16151,x16152)+E(f543(x16151,x16153,x16154,x16155,x16156,x16157,x16158),f543(x16152,x16153,x16154,x16155,x16156,x16157,x16158))
% 160.93/160.66 [1616]~E(x16161,x16162)+E(f543(x16163,x16161,x16164,x16165,x16166,x16167,x16168),f543(x16163,x16162,x16164,x16165,x16166,x16167,x16168))
% 160.93/160.66 [1617]~E(x16171,x16172)+E(f543(x16173,x16174,x16171,x16175,x16176,x16177,x16178),f543(x16173,x16174,x16172,x16175,x16176,x16177,x16178))
% 160.93/160.66 [1618]~E(x16181,x16182)+E(f543(x16183,x16184,x16185,x16181,x16186,x16187,x16188),f543(x16183,x16184,x16185,x16182,x16186,x16187,x16188))
% 160.93/160.66 [1619]~E(x16191,x16192)+E(f543(x16193,x16194,x16195,x16196,x16191,x16197,x16198),f543(x16193,x16194,x16195,x16196,x16192,x16197,x16198))
% 160.93/160.66 [1620]~E(x16201,x16202)+E(f543(x16203,x16204,x16205,x16206,x16207,x16201,x16208),f543(x16203,x16204,x16205,x16206,x16207,x16202,x16208))
% 160.93/160.66 [1621]~E(x16211,x16212)+E(f543(x16213,x16214,x16215,x16216,x16217,x16218,x16211),f543(x16213,x16214,x16215,x16216,x16217,x16218,x16212))
% 160.93/160.66 [1622]~E(x16221,x16222)+E(f772(x16221,x16223,x16224),f772(x16222,x16223,x16224))
% 160.93/160.66 [1623]~E(x16231,x16232)+E(f772(x16233,x16231,x16234),f772(x16233,x16232,x16234))
% 160.93/160.66 [1624]~E(x16241,x16242)+E(f772(x16243,x16244,x16241),f772(x16243,x16244,x16242))
% 160.93/160.66 [1625]~E(x16251,x16252)+E(f758(x16251,x16253,x16254),f758(x16252,x16253,x16254))
% 160.93/160.66 [1626]~E(x16261,x16262)+E(f758(x16263,x16261,x16264),f758(x16263,x16262,x16264))
% 160.93/160.66 [1627]~E(x16271,x16272)+E(f758(x16273,x16274,x16271),f758(x16273,x16274,x16272))
% 160.93/160.66 [1628]~E(x16281,x16282)+E(f714(x16281,x16283,x16284),f714(x16282,x16283,x16284))
% 160.93/160.66 [1629]~E(x16291,x16292)+E(f714(x16293,x16291,x16294),f714(x16293,x16292,x16294))
% 160.93/160.66 [1630]~E(x16301,x16302)+E(f714(x16303,x16304,x16301),f714(x16303,x16304,x16302))
% 160.93/160.66 [1631]~E(x16311,x16312)+E(f560(x16311,x16313,x16314,x16315,x16316),f560(x16312,x16313,x16314,x16315,x16316))
% 160.93/160.66 [1632]~E(x16321,x16322)+E(f560(x16323,x16321,x16324,x16325,x16326),f560(x16323,x16322,x16324,x16325,x16326))
% 160.93/160.66 [1633]~E(x16331,x16332)+E(f560(x16333,x16334,x16331,x16335,x16336),f560(x16333,x16334,x16332,x16335,x16336))
% 160.93/160.66 [1634]~E(x16341,x16342)+E(f560(x16343,x16344,x16345,x16341,x16346),f560(x16343,x16344,x16345,x16342,x16346))
% 160.93/160.66 [1635]~E(x16351,x16352)+E(f560(x16353,x16354,x16355,x16356,x16351),f560(x16353,x16354,x16355,x16356,x16352))
% 160.93/160.66 [1636]~E(x16361,x16362)+E(f468(x16361,x16363,x16364,x16365),f468(x16362,x16363,x16364,x16365))
% 160.93/160.66 [1637]~E(x16371,x16372)+E(f468(x16373,x16371,x16374,x16375),f468(x16373,x16372,x16374,x16375))
% 160.93/160.66 [1638]~E(x16381,x16382)+E(f468(x16383,x16384,x16381,x16385),f468(x16383,x16384,x16382,x16385))
% 160.93/160.66 [1639]~E(x16391,x16392)+E(f468(x16393,x16394,x16395,x16391),f468(x16393,x16394,x16395,x16392))
% 160.93/160.66 [1640]~E(x16401,x16402)+E(f372(x16401),f372(x16402))
% 160.93/160.66 [1641]~E(x16411,x16412)+E(f778(x16411,x16413,x16414,x16415),f778(x16412,x16413,x16414,x16415))
% 160.93/160.66 [1642]~E(x16421,x16422)+E(f778(x16423,x16421,x16424,x16425),f778(x16423,x16422,x16424,x16425))
% 160.93/160.66 [1643]~E(x16431,x16432)+E(f778(x16433,x16434,x16431,x16435),f778(x16433,x16434,x16432,x16435))
% 160.93/160.66 [1644]~E(x16441,x16442)+E(f778(x16443,x16444,x16445,x16441),f778(x16443,x16444,x16445,x16442))
% 160.93/160.66 [1645]~E(x16451,x16452)+E(f95(x16451,x16453,x16454),f95(x16452,x16453,x16454))
% 160.93/160.66 [1646]~E(x16461,x16462)+E(f95(x16463,x16461,x16464),f95(x16463,x16462,x16464))
% 160.93/160.66 [1647]~E(x16471,x16472)+E(f95(x16473,x16474,x16471),f95(x16473,x16474,x16472))
% 160.93/160.66 [1648]~E(x16481,x16482)+E(f260(x16481,x16483,x16484),f260(x16482,x16483,x16484))
% 160.93/160.66 [1649]~E(x16491,x16492)+E(f260(x16493,x16491,x16494),f260(x16493,x16492,x16494))
% 160.93/160.66 [1650]~E(x16501,x16502)+E(f260(x16503,x16504,x16501),f260(x16503,x16504,x16502))
% 160.93/160.66 [1651]~E(x16511,x16512)+E(f533(x16511),f533(x16512))
% 160.93/160.66 [1652]~E(x16521,x16522)+E(f779(x16521,x16523,x16524,x16525,x16526),f779(x16522,x16523,x16524,x16525,x16526))
% 160.93/160.66 [1653]~E(x16531,x16532)+E(f779(x16533,x16531,x16534,x16535,x16536),f779(x16533,x16532,x16534,x16535,x16536))
% 160.93/160.66 [1654]~E(x16541,x16542)+E(f779(x16543,x16544,x16541,x16545,x16546),f779(x16543,x16544,x16542,x16545,x16546))
% 160.93/160.66 [1655]~E(x16551,x16552)+E(f779(x16553,x16554,x16555,x16551,x16556),f779(x16553,x16554,x16555,x16552,x16556))
% 160.93/160.66 [1656]~E(x16561,x16562)+E(f779(x16563,x16564,x16565,x16566,x16561),f779(x16563,x16564,x16565,x16566,x16562))
% 160.93/160.66 [1657]~E(x16571,x16572)+E(f581(x16571,x16573,x16574,x16575),f581(x16572,x16573,x16574,x16575))
% 160.93/160.66 [1658]~E(x16581,x16582)+E(f581(x16583,x16581,x16584,x16585),f581(x16583,x16582,x16584,x16585))
% 160.93/160.66 [1659]~E(x16591,x16592)+E(f581(x16593,x16594,x16591,x16595),f581(x16593,x16594,x16592,x16595))
% 160.93/160.66 [1660]~E(x16601,x16602)+E(f581(x16603,x16604,x16605,x16601),f581(x16603,x16604,x16605,x16602))
% 160.93/160.66 [1661]~E(x16611,x16612)+E(f452(x16611,x16613,x16614),f452(x16612,x16613,x16614))
% 160.93/160.66 [1662]~E(x16621,x16622)+E(f452(x16623,x16621,x16624),f452(x16623,x16622,x16624))
% 160.93/160.66 [1663]~E(x16631,x16632)+E(f452(x16633,x16634,x16631),f452(x16633,x16634,x16632))
% 160.93/160.66 [1664]~E(x16641,x16642)+E(f76(x16641,x16643,x16644,x16645,x16646),f76(x16642,x16643,x16644,x16645,x16646))
% 160.93/160.66 [1665]~E(x16651,x16652)+E(f76(x16653,x16651,x16654,x16655,x16656),f76(x16653,x16652,x16654,x16655,x16656))
% 160.93/160.66 [1666]~E(x16661,x16662)+E(f76(x16663,x16664,x16661,x16665,x16666),f76(x16663,x16664,x16662,x16665,x16666))
% 160.93/160.66 [1667]~E(x16671,x16672)+E(f76(x16673,x16674,x16675,x16671,x16676),f76(x16673,x16674,x16675,x16672,x16676))
% 160.93/160.66 [1668]~E(x16681,x16682)+E(f76(x16683,x16684,x16685,x16686,x16681),f76(x16683,x16684,x16685,x16686,x16682))
% 160.93/160.66 [1669]~E(x16691,x16692)+E(f687(x16691,x16693,x16694,x16695),f687(x16692,x16693,x16694,x16695))
% 160.93/160.66 [1670]~E(x16701,x16702)+E(f687(x16703,x16701,x16704,x16705),f687(x16703,x16702,x16704,x16705))
% 160.93/160.66 [1671]~E(x16711,x16712)+E(f687(x16713,x16714,x16711,x16715),f687(x16713,x16714,x16712,x16715))
% 160.93/160.66 [1672]~E(x16721,x16722)+E(f687(x16723,x16724,x16725,x16721),f687(x16723,x16724,x16725,x16722))
% 160.93/160.66 [1673]~E(x16731,x16732)+E(f350(x16731,x16733,x16734,x16735),f350(x16732,x16733,x16734,x16735))
% 160.93/160.66 [1674]~E(x16741,x16742)+E(f350(x16743,x16741,x16744,x16745),f350(x16743,x16742,x16744,x16745))
% 160.93/160.66 [1675]~E(x16751,x16752)+E(f350(x16753,x16754,x16751,x16755),f350(x16753,x16754,x16752,x16755))
% 160.93/160.66 [1676]~E(x16761,x16762)+E(f350(x16763,x16764,x16765,x16761),f350(x16763,x16764,x16765,x16762))
% 160.93/160.66 [1677]~E(x16771,x16772)+E(f838(x16771,x16773,x16774,x16775,x16776),f838(x16772,x16773,x16774,x16775,x16776))
% 160.93/160.66 [1678]~E(x16781,x16782)+E(f838(x16783,x16781,x16784,x16785,x16786),f838(x16783,x16782,x16784,x16785,x16786))
% 160.93/160.66 [1679]~E(x16791,x16792)+E(f838(x16793,x16794,x16791,x16795,x16796),f838(x16793,x16794,x16792,x16795,x16796))
% 160.93/160.66 [1680]~E(x16801,x16802)+E(f838(x16803,x16804,x16805,x16801,x16806),f838(x16803,x16804,x16805,x16802,x16806))
% 160.93/160.66 [1681]~E(x16811,x16812)+E(f838(x16813,x16814,x16815,x16816,x16811),f838(x16813,x16814,x16815,x16816,x16812))
% 160.93/160.66 [1682]~E(x16821,x16822)+E(f636(x16821,x16823),f636(x16822,x16823))
% 160.93/160.66 [1683]~E(x16831,x16832)+E(f636(x16833,x16831),f636(x16833,x16832))
% 160.93/160.66 [1684]~E(x16841,x16842)+E(f851(x16841,x16843,x16844),f851(x16842,x16843,x16844))
% 160.93/160.66 [1685]~E(x16851,x16852)+E(f851(x16853,x16851,x16854),f851(x16853,x16852,x16854))
% 160.93/160.66 [1686]~E(x16861,x16862)+E(f851(x16863,x16864,x16861),f851(x16863,x16864,x16862))
% 160.93/160.66 [1687]~E(x16871,x16872)+E(f407(x16871,x16873,x16874,x16875,x16876),f407(x16872,x16873,x16874,x16875,x16876))
% 160.93/160.66 [1688]~E(x16881,x16882)+E(f407(x16883,x16881,x16884,x16885,x16886),f407(x16883,x16882,x16884,x16885,x16886))
% 160.93/160.66 [1689]~E(x16891,x16892)+E(f407(x16893,x16894,x16891,x16895,x16896),f407(x16893,x16894,x16892,x16895,x16896))
% 160.93/160.66 [1690]~E(x16901,x16902)+E(f407(x16903,x16904,x16905,x16901,x16906),f407(x16903,x16904,x16905,x16902,x16906))
% 160.93/160.66 [1691]~E(x16911,x16912)+E(f407(x16913,x16914,x16915,x16916,x16911),f407(x16913,x16914,x16915,x16916,x16912))
% 160.93/160.66 [1692]~E(x16921,x16922)+E(f484(x16921,x16923,x16924),f484(x16922,x16923,x16924))
% 160.93/160.66 [1693]~E(x16931,x16932)+E(f484(x16933,x16931,x16934),f484(x16933,x16932,x16934))
% 160.93/160.66 [1694]~E(x16941,x16942)+E(f484(x16943,x16944,x16941),f484(x16943,x16944,x16942))
% 160.93/160.66 [1695]~E(x16951,x16952)+E(f753(x16951,x16953,x16954),f753(x16952,x16953,x16954))
% 160.93/160.66 [1696]~E(x16961,x16962)+E(f753(x16963,x16961,x16964),f753(x16963,x16962,x16964))
% 160.93/160.66 [1697]~E(x16971,x16972)+E(f753(x16973,x16974,x16971),f753(x16973,x16974,x16972))
% 160.93/160.66 [1698]~E(x16981,x16982)+E(f647(x16981,x16983,x16984,x16985,x16986),f647(x16982,x16983,x16984,x16985,x16986))
% 160.93/160.66 [1699]~E(x16991,x16992)+E(f647(x16993,x16991,x16994,x16995,x16996),f647(x16993,x16992,x16994,x16995,x16996))
% 160.93/160.66 [1700]~E(x17001,x17002)+E(f647(x17003,x17004,x17001,x17005,x17006),f647(x17003,x17004,x17002,x17005,x17006))
% 160.93/160.66 [1701]~E(x17011,x17012)+E(f647(x17013,x17014,x17015,x17011,x17016),f647(x17013,x17014,x17015,x17012,x17016))
% 160.93/160.66 [1702]~E(x17021,x17022)+E(f647(x17023,x17024,x17025,x17026,x17021),f647(x17023,x17024,x17025,x17026,x17022))
% 160.93/160.66 [1703]~E(x17031,x17032)+E(f803(x17031,x17033,x17034),f803(x17032,x17033,x17034))
% 160.93/160.66 [1704]~E(x17041,x17042)+E(f803(x17043,x17041,x17044),f803(x17043,x17042,x17044))
% 160.93/160.66 [1705]~E(x17051,x17052)+E(f803(x17053,x17054,x17051),f803(x17053,x17054,x17052))
% 160.93/160.66 [1706]~E(x17061,x17062)+E(f477(x17061,x17063,x17064),f477(x17062,x17063,x17064))
% 160.93/160.66 [1707]~E(x17071,x17072)+E(f477(x17073,x17071,x17074),f477(x17073,x17072,x17074))
% 160.93/160.66 [1708]~E(x17081,x17082)+E(f477(x17083,x17084,x17081),f477(x17083,x17084,x17082))
% 160.93/160.66 [1709]~E(x17091,x17092)+E(f785(x17091,x17093,x17094),f785(x17092,x17093,x17094))
% 160.93/160.66 [1710]~E(x17101,x17102)+E(f785(x17103,x17101,x17104),f785(x17103,x17102,x17104))
% 160.93/160.66 [1711]~E(x17111,x17112)+E(f785(x17113,x17114,x17111),f785(x17113,x17114,x17112))
% 160.93/160.66 [1712]~E(x17121,x17122)+E(f413(x17121,x17123,x17124),f413(x17122,x17123,x17124))
% 160.93/160.66 [1713]~E(x17131,x17132)+E(f413(x17133,x17131,x17134),f413(x17133,x17132,x17134))
% 160.93/160.66 [1714]~E(x17141,x17142)+E(f413(x17143,x17144,x17141),f413(x17143,x17144,x17142))
% 160.93/160.66 [1715]~E(x17151,x17152)+E(f580(x17151,x17153,x17154,x17155,x17156),f580(x17152,x17153,x17154,x17155,x17156))
% 160.93/160.66 [1716]~E(x17161,x17162)+E(f580(x17163,x17161,x17164,x17165,x17166),f580(x17163,x17162,x17164,x17165,x17166))
% 160.93/160.66 [1717]~E(x17171,x17172)+E(f580(x17173,x17174,x17171,x17175,x17176),f580(x17173,x17174,x17172,x17175,x17176))
% 160.93/160.66 [1718]~E(x17181,x17182)+E(f580(x17183,x17184,x17185,x17181,x17186),f580(x17183,x17184,x17185,x17182,x17186))
% 160.93/160.66 [1719]~E(x17191,x17192)+E(f580(x17193,x17194,x17195,x17196,x17191),f580(x17193,x17194,x17195,x17196,x17192))
% 160.93/160.66 [1720]~E(x17201,x17202)+E(f716(x17201,x17203,x17204,x17205,x17206),f716(x17202,x17203,x17204,x17205,x17206))
% 160.93/160.66 [1721]~E(x17211,x17212)+E(f716(x17213,x17211,x17214,x17215,x17216),f716(x17213,x17212,x17214,x17215,x17216))
% 160.93/160.66 [1722]~E(x17221,x17222)+E(f716(x17223,x17224,x17221,x17225,x17226),f716(x17223,x17224,x17222,x17225,x17226))
% 160.93/160.66 [1723]~E(x17231,x17232)+E(f716(x17233,x17234,x17235,x17231,x17236),f716(x17233,x17234,x17235,x17232,x17236))
% 160.93/160.66 [1724]~E(x17241,x17242)+E(f716(x17243,x17244,x17245,x17246,x17241),f716(x17243,x17244,x17245,x17246,x17242))
% 160.93/160.66 [1725]~E(x17251,x17252)+E(f578(x17251,x17253,x17254,x17255,x17256,x17257),f578(x17252,x17253,x17254,x17255,x17256,x17257))
% 160.93/160.66 [1726]~E(x17261,x17262)+E(f578(x17263,x17261,x17264,x17265,x17266,x17267),f578(x17263,x17262,x17264,x17265,x17266,x17267))
% 160.93/160.66 [1727]~E(x17271,x17272)+E(f578(x17273,x17274,x17271,x17275,x17276,x17277),f578(x17273,x17274,x17272,x17275,x17276,x17277))
% 160.93/160.66 [1728]~E(x17281,x17282)+E(f578(x17283,x17284,x17285,x17281,x17286,x17287),f578(x17283,x17284,x17285,x17282,x17286,x17287))
% 160.93/160.66 [1729]~E(x17291,x17292)+E(f578(x17293,x17294,x17295,x17296,x17291,x17297),f578(x17293,x17294,x17295,x17296,x17292,x17297))
% 160.93/160.66 [1730]~E(x17301,x17302)+E(f578(x17303,x17304,x17305,x17306,x17307,x17301),f578(x17303,x17304,x17305,x17306,x17307,x17302))
% 160.93/160.66 [1731]~E(x17311,x17312)+E(f315(x17311,x17313),f315(x17312,x17313))
% 160.93/160.66 [1732]~E(x17321,x17322)+E(f315(x17323,x17321),f315(x17323,x17322))
% 160.93/160.66 [1733]~E(x17331,x17332)+E(f433(x17331,x17333,x17334,x17335,x17336),f433(x17332,x17333,x17334,x17335,x17336))
% 160.93/160.66 [1734]~E(x17341,x17342)+E(f433(x17343,x17341,x17344,x17345,x17346),f433(x17343,x17342,x17344,x17345,x17346))
% 160.93/160.66 [1735]~E(x17351,x17352)+E(f433(x17353,x17354,x17351,x17355,x17356),f433(x17353,x17354,x17352,x17355,x17356))
% 160.93/160.66 [1736]~E(x17361,x17362)+E(f433(x17363,x17364,x17365,x17361,x17366),f433(x17363,x17364,x17365,x17362,x17366))
% 160.93/160.66 [1737]~E(x17371,x17372)+E(f433(x17373,x17374,x17375,x17376,x17371),f433(x17373,x17374,x17375,x17376,x17372))
% 160.93/160.66 [1738]~E(x17381,x17382)+E(f278(x17381,x17383),f278(x17382,x17383))
% 160.93/160.66 [1739]~E(x17391,x17392)+E(f278(x17393,x17391),f278(x17393,x17392))
% 160.93/160.66 [1740]~E(x17401,x17402)+E(f534(x17401),f534(x17402))
% 160.93/160.66 [1741]~E(x17411,x17412)+E(f720(x17411,x17413,x17414,x17415,x17416),f720(x17412,x17413,x17414,x17415,x17416))
% 160.93/160.66 [1742]~E(x17421,x17422)+E(f720(x17423,x17421,x17424,x17425,x17426),f720(x17423,x17422,x17424,x17425,x17426))
% 160.93/160.66 [1743]~E(x17431,x17432)+E(f720(x17433,x17434,x17431,x17435,x17436),f720(x17433,x17434,x17432,x17435,x17436))
% 160.93/160.66 [1744]~E(x17441,x17442)+E(f720(x17443,x17444,x17445,x17441,x17446),f720(x17443,x17444,x17445,x17442,x17446))
% 160.93/160.66 [1745]~E(x17451,x17452)+E(f720(x17453,x17454,x17455,x17456,x17451),f720(x17453,x17454,x17455,x17456,x17452))
% 160.93/160.66 [1746]~E(x17461,x17462)+E(f739(x17461,x17463,x17464,x17465),f739(x17462,x17463,x17464,x17465))
% 160.93/160.66 [1747]~E(x17471,x17472)+E(f739(x17473,x17471,x17474,x17475),f739(x17473,x17472,x17474,x17475))
% 160.93/160.66 [1748]~E(x17481,x17482)+E(f739(x17483,x17484,x17481,x17485),f739(x17483,x17484,x17482,x17485))
% 160.93/160.66 [1749]~E(x17491,x17492)+E(f739(x17493,x17494,x17495,x17491),f739(x17493,x17494,x17495,x17492))
% 160.93/160.66 [1750]~E(x17501,x17502)+E(f620(x17501,x17503,x17504),f620(x17502,x17503,x17504))
% 160.93/160.66 [1751]~E(x17511,x17512)+E(f620(x17513,x17511,x17514),f620(x17513,x17512,x17514))
% 160.93/160.66 [1752]~E(x17521,x17522)+E(f620(x17523,x17524,x17521),f620(x17523,x17524,x17522))
% 160.93/160.66 [1753]~E(x17531,x17532)+E(f366(x17531,x17533),f366(x17532,x17533))
% 160.93/160.66 [1754]~E(x17541,x17542)+E(f366(x17543,x17541),f366(x17543,x17542))
% 160.93/160.66 [1755]~E(x17551,x17552)+E(f487(x17551,x17553,x17554),f487(x17552,x17553,x17554))
% 160.93/160.66 [1756]~E(x17561,x17562)+E(f487(x17563,x17561,x17564),f487(x17563,x17562,x17564))
% 160.93/160.66 [1757]~E(x17571,x17572)+E(f487(x17573,x17574,x17571),f487(x17573,x17574,x17572))
% 160.93/160.66 [1758]~E(x17581,x17582)+E(f59(x17581,x17583,x17584,x17585),f59(x17582,x17583,x17584,x17585))
% 160.93/160.66 [1759]~E(x17591,x17592)+E(f59(x17593,x17591,x17594,x17595),f59(x17593,x17592,x17594,x17595))
% 160.93/160.66 [1760]~E(x17601,x17602)+E(f59(x17603,x17604,x17601,x17605),f59(x17603,x17604,x17602,x17605))
% 160.93/160.66 [1761]~E(x17611,x17612)+E(f59(x17613,x17614,x17615,x17611),f59(x17613,x17614,x17615,x17612))
% 160.93/160.66 [1762]~E(x17621,x17622)+E(f627(x17621,x17623,x17624,x17625),f627(x17622,x17623,x17624,x17625))
% 160.93/160.66 [1763]~E(x17631,x17632)+E(f627(x17633,x17631,x17634,x17635),f627(x17633,x17632,x17634,x17635))
% 160.93/160.66 [1764]~E(x17641,x17642)+E(f627(x17643,x17644,x17641,x17645),f627(x17643,x17644,x17642,x17645))
% 160.93/160.66 [1765]~E(x17651,x17652)+E(f627(x17653,x17654,x17655,x17651),f627(x17653,x17654,x17655,x17652))
% 160.93/160.66 [1766]~E(x17661,x17662)+E(f215(x17661,x17663),f215(x17662,x17663))
% 160.93/160.66 [1767]~E(x17671,x17672)+E(f215(x17673,x17671),f215(x17673,x17672))
% 160.93/160.66 [1768]~E(x17681,x17682)+E(f759(x17681,x17683,x17684),f759(x17682,x17683,x17684))
% 160.93/160.66 [1769]~E(x17691,x17692)+E(f759(x17693,x17691,x17694),f759(x17693,x17692,x17694))
% 160.93/160.66 [1770]~E(x17701,x17702)+E(f759(x17703,x17704,x17701),f759(x17703,x17704,x17702))
% 160.93/160.66 [1771]~E(x17711,x17712)+E(f475(x17711,x17713),f475(x17712,x17713))
% 160.93/160.66 [1772]~E(x17721,x17722)+E(f475(x17723,x17721),f475(x17723,x17722))
% 160.93/160.66 [1773]~E(x17731,x17732)+E(f582(x17731,x17733,x17734,x17735,x17736),f582(x17732,x17733,x17734,x17735,x17736))
% 160.93/160.66 [1774]~E(x17741,x17742)+E(f582(x17743,x17741,x17744,x17745,x17746),f582(x17743,x17742,x17744,x17745,x17746))
% 160.93/160.66 [1775]~E(x17751,x17752)+E(f582(x17753,x17754,x17751,x17755,x17756),f582(x17753,x17754,x17752,x17755,x17756))
% 160.93/160.66 [1776]~E(x17761,x17762)+E(f582(x17763,x17764,x17765,x17761,x17766),f582(x17763,x17764,x17765,x17762,x17766))
% 160.93/160.66 [1777]~E(x17771,x17772)+E(f582(x17773,x17774,x17775,x17776,x17771),f582(x17773,x17774,x17775,x17776,x17772))
% 160.93/160.66 [1778]~E(x17781,x17782)+E(f752(x17781,x17783,x17784),f752(x17782,x17783,x17784))
% 160.93/160.66 [1779]~E(x17791,x17792)+E(f752(x17793,x17791,x17794),f752(x17793,x17792,x17794))
% 160.93/160.66 [1780]~E(x17801,x17802)+E(f752(x17803,x17804,x17801),f752(x17803,x17804,x17802))
% 160.93/160.66 [1781]~E(x17811,x17812)+E(f417(x17811),f417(x17812))
% 160.93/160.66 [1782]~E(x17821,x17822)+E(f218(x17821),f218(x17822))
% 160.93/160.66 [1783]~E(x17831,x17832)+E(f404(x17831,x17833,x17834,x17835,x17836),f404(x17832,x17833,x17834,x17835,x17836))
% 160.93/160.66 [1784]~E(x17841,x17842)+E(f404(x17843,x17841,x17844,x17845,x17846),f404(x17843,x17842,x17844,x17845,x17846))
% 160.93/160.66 [1785]~E(x17851,x17852)+E(f404(x17853,x17854,x17851,x17855,x17856),f404(x17853,x17854,x17852,x17855,x17856))
% 160.93/160.66 [1786]~E(x17861,x17862)+E(f404(x17863,x17864,x17865,x17861,x17866),f404(x17863,x17864,x17865,x17862,x17866))
% 160.93/160.66 [1787]~E(x17871,x17872)+E(f404(x17873,x17874,x17875,x17876,x17871),f404(x17873,x17874,x17875,x17876,x17872))
% 160.93/160.66 [1788]~E(x17881,x17882)+E(f261(x17881,x17883,x17884),f261(x17882,x17883,x17884))
% 160.93/160.66 [1789]~E(x17891,x17892)+E(f261(x17893,x17891,x17894),f261(x17893,x17892,x17894))
% 160.93/160.66 [1790]~E(x17901,x17902)+E(f261(x17903,x17904,x17901),f261(x17903,x17904,x17902))
% 160.93/160.66 [1791]~E(x17911,x17912)+E(f600(x17911,x17913),f600(x17912,x17913))
% 160.93/160.66 [1792]~E(x17921,x17922)+E(f600(x17923,x17921),f600(x17923,x17922))
% 160.93/160.66 [1793]~E(x17931,x17932)+E(f597(x17931,x17933,x17934,x17935),f597(x17932,x17933,x17934,x17935))
% 160.93/160.66 [1794]~E(x17941,x17942)+E(f597(x17943,x17941,x17944,x17945),f597(x17943,x17942,x17944,x17945))
% 160.93/160.66 [1795]~E(x17951,x17952)+E(f597(x17953,x17954,x17951,x17955),f597(x17953,x17954,x17952,x17955))
% 160.93/160.66 [1796]~E(x17961,x17962)+E(f597(x17963,x17964,x17965,x17961),f597(x17963,x17964,x17965,x17962))
% 160.93/160.66 [1797]~E(x17971,x17972)+E(f387(x17971,x17973,x17974,x17975),f387(x17972,x17973,x17974,x17975))
% 160.93/160.66 [1798]~E(x17981,x17982)+E(f387(x17983,x17981,x17984,x17985),f387(x17983,x17982,x17984,x17985))
% 160.93/160.66 [1799]~E(x17991,x17992)+E(f387(x17993,x17994,x17991,x17995),f387(x17993,x17994,x17992,x17995))
% 160.93/160.66 [1800]~E(x18001,x18002)+E(f387(x18003,x18004,x18005,x18001),f387(x18003,x18004,x18005,x18002))
% 160.93/160.66 [1801]~E(x18011,x18012)+E(f481(x18011,x18013,x18014,x18015),f481(x18012,x18013,x18014,x18015))
% 160.93/160.66 [1802]~E(x18021,x18022)+E(f481(x18023,x18021,x18024,x18025),f481(x18023,x18022,x18024,x18025))
% 160.93/160.66 [1803]~E(x18031,x18032)+E(f481(x18033,x18034,x18031,x18035),f481(x18033,x18034,x18032,x18035))
% 160.93/160.66 [1804]~E(x18041,x18042)+E(f481(x18043,x18044,x18045,x18041),f481(x18043,x18044,x18045,x18042))
% 160.93/160.66 [1805]~E(x18051,x18052)+E(f722(x18051,x18053),f722(x18052,x18053))
% 160.93/160.66 [1806]~E(x18061,x18062)+E(f722(x18063,x18061),f722(x18063,x18062))
% 160.93/160.66 [1807]~E(x18071,x18072)+E(f808(x18071,x18073,x18074),f808(x18072,x18073,x18074))
% 160.93/160.66 [1808]~E(x18081,x18082)+E(f808(x18083,x18081,x18084),f808(x18083,x18082,x18084))
% 160.93/160.66 [1809]~E(x18091,x18092)+E(f808(x18093,x18094,x18091),f808(x18093,x18094,x18092))
% 160.93/160.66 [1810]~E(x18101,x18102)+E(f457(x18101,x18103),f457(x18102,x18103))
% 160.93/160.66 [1811]~E(x18111,x18112)+E(f457(x18113,x18111),f457(x18113,x18112))
% 160.93/160.66 [1812]~E(x18121,x18122)+E(f510(x18121,x18123,x18124),f510(x18122,x18123,x18124))
% 160.93/160.66 [1813]~E(x18131,x18132)+E(f510(x18133,x18131,x18134),f510(x18133,x18132,x18134))
% 160.93/160.66 [1814]~E(x18141,x18142)+E(f510(x18143,x18144,x18141),f510(x18143,x18144,x18142))
% 160.93/160.66 [1815]~E(x18151,x18152)+E(f464(x18151,x18153,x18154),f464(x18152,x18153,x18154))
% 160.93/160.66 [1816]~E(x18161,x18162)+E(f464(x18163,x18161,x18164),f464(x18163,x18162,x18164))
% 160.93/160.66 [1817]~E(x18171,x18172)+E(f464(x18173,x18174,x18171),f464(x18173,x18174,x18172))
% 160.93/160.66 [1818]~E(x18181,x18182)+E(f858(x18181,x18183,x18184,x18185),f858(x18182,x18183,x18184,x18185))
% 160.93/160.66 [1819]~E(x18191,x18192)+E(f858(x18193,x18191,x18194,x18195),f858(x18193,x18192,x18194,x18195))
% 160.93/160.66 [1820]~E(x18201,x18202)+E(f858(x18203,x18204,x18201,x18205),f858(x18203,x18204,x18202,x18205))
% 160.93/160.66 [1821]~E(x18211,x18212)+E(f858(x18213,x18214,x18215,x18211),f858(x18213,x18214,x18215,x18212))
% 160.93/160.66 [1822]~E(x18221,x18222)+E(f658(x18221,x18223,x18224),f658(x18222,x18223,x18224))
% 160.93/160.66 [1823]~E(x18231,x18232)+E(f658(x18233,x18231,x18234),f658(x18233,x18232,x18234))
% 160.93/160.66 [1824]~E(x18241,x18242)+E(f658(x18243,x18244,x18241),f658(x18243,x18244,x18242))
% 160.93/160.66 [1825]~E(x18251,x18252)+E(f297(x18251,x18253,x18254),f297(x18252,x18253,x18254))
% 160.93/160.66 [1826]~E(x18261,x18262)+E(f297(x18263,x18261,x18264),f297(x18263,x18262,x18264))
% 160.93/160.66 [1827]~E(x18271,x18272)+E(f297(x18273,x18274,x18271),f297(x18273,x18274,x18272))
% 160.93/160.66 [1828]~E(x18281,x18282)+E(f418(x18281,x18283),f418(x18282,x18283))
% 160.93/160.66 [1829]~E(x18291,x18292)+E(f418(x18293,x18291),f418(x18293,x18292))
% 160.93/160.66 [1830]~E(x18301,x18302)+E(f807(x18301,x18303,x18304),f807(x18302,x18303,x18304))
% 160.93/160.66 [1831]~E(x18311,x18312)+E(f807(x18313,x18311,x18314),f807(x18313,x18312,x18314))
% 160.93/160.66 [1832]~E(x18321,x18322)+E(f807(x18323,x18324,x18321),f807(x18323,x18324,x18322))
% 160.93/160.66 [1833]~E(x18331,x18332)+E(f319(x18331),f319(x18332))
% 160.93/160.66 [1834]~E(x18341,x18342)+E(f520(x18341,x18343,x18344),f520(x18342,x18343,x18344))
% 160.93/160.66 [1835]~E(x18351,x18352)+E(f520(x18353,x18351,x18354),f520(x18353,x18352,x18354))
% 160.93/160.66 [1836]~E(x18361,x18362)+E(f520(x18363,x18364,x18361),f520(x18363,x18364,x18362))
% 160.93/160.66 [1837]~E(x18371,x18372)+E(f837(x18371,x18373,x18374,x18375,x18376),f837(x18372,x18373,x18374,x18375,x18376))
% 160.93/160.66 [1838]~E(x18381,x18382)+E(f837(x18383,x18381,x18384,x18385,x18386),f837(x18383,x18382,x18384,x18385,x18386))
% 160.93/160.66 [1839]~E(x18391,x18392)+E(f837(x18393,x18394,x18391,x18395,x18396),f837(x18393,x18394,x18392,x18395,x18396))
% 160.93/160.66 [1840]~E(x18401,x18402)+E(f837(x18403,x18404,x18405,x18401,x18406),f837(x18403,x18404,x18405,x18402,x18406))
% 160.93/160.66 [1841]~E(x18411,x18412)+E(f837(x18413,x18414,x18415,x18416,x18411),f837(x18413,x18414,x18415,x18416,x18412))
% 160.93/160.66 [1842]~E(x18421,x18422)+E(f588(x18421,x18423,x18424,x18425,x18426,x18427,x18428,x18429),f588(x18422,x18423,x18424,x18425,x18426,x18427,x18428,x18429))
% 160.93/160.66 [1843]~E(x18431,x18432)+E(f588(x18433,x18431,x18434,x18435,x18436,x18437,x18438,x18439),f588(x18433,x18432,x18434,x18435,x18436,x18437,x18438,x18439))
% 160.93/160.66 [1844]~E(x18441,x18442)+E(f588(x18443,x18444,x18441,x18445,x18446,x18447,x18448,x18449),f588(x18443,x18444,x18442,x18445,x18446,x18447,x18448,x18449))
% 160.93/160.66 [1845]~E(x18451,x18452)+E(f588(x18453,x18454,x18455,x18451,x18456,x18457,x18458,x18459),f588(x18453,x18454,x18455,x18452,x18456,x18457,x18458,x18459))
% 160.93/160.66 [1846]~E(x18461,x18462)+E(f588(x18463,x18464,x18465,x18466,x18461,x18467,x18468,x18469),f588(x18463,x18464,x18465,x18466,x18462,x18467,x18468,x18469))
% 160.93/160.66 [1847]~E(x18471,x18472)+E(f588(x18473,x18474,x18475,x18476,x18477,x18471,x18478,x18479),f588(x18473,x18474,x18475,x18476,x18477,x18472,x18478,x18479))
% 160.93/160.66 [1848]~E(x18481,x18482)+E(f588(x18483,x18484,x18485,x18486,x18487,x18488,x18481,x18489),f588(x18483,x18484,x18485,x18486,x18487,x18488,x18482,x18489))
% 160.93/160.66 [1849]~E(x18491,x18492)+E(f588(x18493,x18494,x18495,x18496,x18497,x18498,x18499,x18491),f588(x18493,x18494,x18495,x18496,x18497,x18498,x18499,x18492))
% 160.93/160.66 [1850]~E(x18501,x18502)+E(f402(x18501,x18503,x18504,x18505),f402(x18502,x18503,x18504,x18505))
% 160.93/160.66 [1851]~E(x18511,x18512)+E(f402(x18513,x18511,x18514,x18515),f402(x18513,x18512,x18514,x18515))
% 160.93/160.66 [1852]~E(x18521,x18522)+E(f402(x18523,x18524,x18521,x18525),f402(x18523,x18524,x18522,x18525))
% 160.93/160.66 [1853]~E(x18531,x18532)+E(f402(x18533,x18534,x18535,x18531),f402(x18533,x18534,x18535,x18532))
% 160.93/160.66 [1854]~E(x18541,x18542)+E(f381(x18541,x18543,x18544,x18545,x18546),f381(x18542,x18543,x18544,x18545,x18546))
% 160.93/160.66 [1855]~E(x18551,x18552)+E(f381(x18553,x18551,x18554,x18555,x18556),f381(x18553,x18552,x18554,x18555,x18556))
% 160.93/160.66 [1856]~E(x18561,x18562)+E(f381(x18563,x18564,x18561,x18565,x18566),f381(x18563,x18564,x18562,x18565,x18566))
% 160.93/160.66 [1857]~E(x18571,x18572)+E(f381(x18573,x18574,x18575,x18571,x18576),f381(x18573,x18574,x18575,x18572,x18576))
% 160.93/160.66 [1858]~E(x18581,x18582)+E(f381(x18583,x18584,x18585,x18586,x18581),f381(x18583,x18584,x18585,x18586,x18582))
% 160.93/160.66 [1859]~E(x18591,x18592)+E(f493(x18591,x18593,x18594,x18595,x18596),f493(x18592,x18593,x18594,x18595,x18596))
% 160.93/160.66 [1860]~E(x18601,x18602)+E(f493(x18603,x18601,x18604,x18605,x18606),f493(x18603,x18602,x18604,x18605,x18606))
% 160.93/160.66 [1861]~E(x18611,x18612)+E(f493(x18613,x18614,x18611,x18615,x18616),f493(x18613,x18614,x18612,x18615,x18616))
% 160.93/160.66 [1862]~E(x18621,x18622)+E(f493(x18623,x18624,x18625,x18621,x18626),f493(x18623,x18624,x18625,x18622,x18626))
% 160.93/160.66 [1863]~E(x18631,x18632)+E(f493(x18633,x18634,x18635,x18636,x18631),f493(x18633,x18634,x18635,x18636,x18632))
% 160.93/160.66 [1864]~E(x18641,x18642)+E(f780(x18641,x18643,x18644,x18645),f780(x18642,x18643,x18644,x18645))
% 160.93/160.66 [1865]~E(x18651,x18652)+E(f780(x18653,x18651,x18654,x18655),f780(x18653,x18652,x18654,x18655))
% 160.93/160.66 [1866]~E(x18661,x18662)+E(f780(x18663,x18664,x18661,x18665),f780(x18663,x18664,x18662,x18665))
% 160.93/160.66 [1867]~E(x18671,x18672)+E(f780(x18673,x18674,x18675,x18671),f780(x18673,x18674,x18675,x18672))
% 160.93/160.66 [1868]~E(x18681,x18682)+E(f343(x18681),f343(x18682))
% 160.93/160.66 [1869]~E(x18691,x18692)+E(f513(x18691,x18693,x18694,x18695),f513(x18692,x18693,x18694,x18695))
% 160.93/160.66 [1870]~E(x18701,x18702)+E(f513(x18703,x18701,x18704,x18705),f513(x18703,x18702,x18704,x18705))
% 160.93/160.66 [1871]~E(x18711,x18712)+E(f513(x18713,x18714,x18711,x18715),f513(x18713,x18714,x18712,x18715))
% 160.93/160.66 [1872]~E(x18721,x18722)+E(f513(x18723,x18724,x18725,x18721),f513(x18723,x18724,x18725,x18722))
% 160.93/160.66 [1873]~E(x18731,x18732)+E(f551(x18731,x18733,x18734,x18735),f551(x18732,x18733,x18734,x18735))
% 160.93/160.66 [1874]~E(x18741,x18742)+E(f551(x18743,x18741,x18744,x18745),f551(x18743,x18742,x18744,x18745))
% 160.93/160.66 [1875]~E(x18751,x18752)+E(f551(x18753,x18754,x18751,x18755),f551(x18753,x18754,x18752,x18755))
% 160.93/160.66 [1876]~E(x18761,x18762)+E(f551(x18763,x18764,x18765,x18761),f551(x18763,x18764,x18765,x18762))
% 160.93/160.66 [1877]~E(x18771,x18772)+E(f530(x18771,x18773,x18774,x18775,x18776),f530(x18772,x18773,x18774,x18775,x18776))
% 160.93/160.66 [1878]~E(x18781,x18782)+E(f530(x18783,x18781,x18784,x18785,x18786),f530(x18783,x18782,x18784,x18785,x18786))
% 160.93/160.66 [1879]~E(x18791,x18792)+E(f530(x18793,x18794,x18791,x18795,x18796),f530(x18793,x18794,x18792,x18795,x18796))
% 160.93/160.66 [1880]~E(x18801,x18802)+E(f530(x18803,x18804,x18805,x18801,x18806),f530(x18803,x18804,x18805,x18802,x18806))
% 160.93/160.66 [1881]~E(x18811,x18812)+E(f530(x18813,x18814,x18815,x18816,x18811),f530(x18813,x18814,x18815,x18816,x18812))
% 160.93/160.66 [1882]~E(x18821,x18822)+E(f693(x18821,x18823,x18824,x18825),f693(x18822,x18823,x18824,x18825))
% 160.93/160.66 [1883]~E(x18831,x18832)+E(f693(x18833,x18831,x18834,x18835),f693(x18833,x18832,x18834,x18835))
% 160.93/160.66 [1884]~E(x18841,x18842)+E(f693(x18843,x18844,x18841,x18845),f693(x18843,x18844,x18842,x18845))
% 160.93/160.66 [1885]~E(x18851,x18852)+E(f693(x18853,x18854,x18855,x18851),f693(x18853,x18854,x18855,x18852))
% 160.93/160.66 [1886]~E(x18861,x18862)+E(f166(x18861,x18863,x18864,x18865),f166(x18862,x18863,x18864,x18865))
% 160.93/160.66 [1887]~E(x18871,x18872)+E(f166(x18873,x18871,x18874,x18875),f166(x18873,x18872,x18874,x18875))
% 160.93/160.66 [1888]~E(x18881,x18882)+E(f166(x18883,x18884,x18881,x18885),f166(x18883,x18884,x18882,x18885))
% 160.93/160.66 [1889]~E(x18891,x18892)+E(f166(x18893,x18894,x18895,x18891),f166(x18893,x18894,x18895,x18892))
% 160.93/160.66 [1890]~E(x18901,x18902)+E(f607(x18901,x18903,x18904),f607(x18902,x18903,x18904))
% 160.93/160.66 [1891]~E(x18911,x18912)+E(f607(x18913,x18911,x18914),f607(x18913,x18912,x18914))
% 160.93/160.66 [1892]~E(x18921,x18922)+E(f607(x18923,x18924,x18921),f607(x18923,x18924,x18922))
% 160.93/160.66 [1893]~E(x18931,x18932)+E(f222(x18931,x18933,x18934,x18935),f222(x18932,x18933,x18934,x18935))
% 160.93/160.66 [1894]~E(x18941,x18942)+E(f222(x18943,x18941,x18944,x18945),f222(x18943,x18942,x18944,x18945))
% 160.93/160.66 [1895]~E(x18951,x18952)+E(f222(x18953,x18954,x18951,x18955),f222(x18953,x18954,x18952,x18955))
% 160.93/160.66 [1896]~E(x18961,x18962)+E(f222(x18963,x18964,x18965,x18961),f222(x18963,x18964,x18965,x18962))
% 160.93/160.66 [1897]~E(x18971,x18972)+E(f125(x18971,x18973),f125(x18972,x18973))
% 160.93/160.66 [1898]~E(x18981,x18982)+E(f125(x18983,x18981),f125(x18983,x18982))
% 160.93/160.66 [1899]~E(x18991,x18992)+E(f443(x18991,x18993,x18994),f443(x18992,x18993,x18994))
% 160.93/160.66 [1900]~E(x19001,x19002)+E(f443(x19003,x19001,x19004),f443(x19003,x19002,x19004))
% 160.93/160.66 [1901]~E(x19011,x19012)+E(f443(x19013,x19014,x19011),f443(x19013,x19014,x19012))
% 160.93/160.66 [1902]~E(x19021,x19022)+E(f871(x19021,x19023,x19024,x19025,x19026),f871(x19022,x19023,x19024,x19025,x19026))
% 160.93/160.66 [1903]~E(x19031,x19032)+E(f871(x19033,x19031,x19034,x19035,x19036),f871(x19033,x19032,x19034,x19035,x19036))
% 160.93/160.66 [1904]~E(x19041,x19042)+E(f871(x19043,x19044,x19041,x19045,x19046),f871(x19043,x19044,x19042,x19045,x19046))
% 160.93/160.66 [1905]~E(x19051,x19052)+E(f871(x19053,x19054,x19055,x19051,x19056),f871(x19053,x19054,x19055,x19052,x19056))
% 160.93/160.66 [1906]~E(x19061,x19062)+E(f871(x19063,x19064,x19065,x19066,x19061),f871(x19063,x19064,x19065,x19066,x19062))
% 160.93/160.66 [1907]~E(x19071,x19072)+E(f264(x19071,x19073,x19074),f264(x19072,x19073,x19074))
% 160.93/160.66 [1908]~E(x19081,x19082)+E(f264(x19083,x19081,x19084),f264(x19083,x19082,x19084))
% 160.93/160.66 [1909]~E(x19091,x19092)+E(f264(x19093,x19094,x19091),f264(x19093,x19094,x19092))
% 160.93/160.66 [1910]~E(x19101,x19102)+E(f440(x19101,x19103,x19104),f440(x19102,x19103,x19104))
% 160.93/160.66 [1911]~E(x19111,x19112)+E(f440(x19113,x19111,x19114),f440(x19113,x19112,x19114))
% 160.93/160.66 [1912]~E(x19121,x19122)+E(f440(x19123,x19124,x19121),f440(x19123,x19124,x19122))
% 160.93/160.66 [1913]~E(x19131,x19132)+E(f217(x19131),f217(x19132))
% 160.93/160.66 [1914]~E(x19141,x19142)+E(f480(x19141,x19143,x19144),f480(x19142,x19143,x19144))
% 160.93/160.66 [1915]~E(x19151,x19152)+E(f480(x19153,x19151,x19154),f480(x19153,x19152,x19154))
% 160.93/160.66 [1916]~E(x19161,x19162)+E(f480(x19163,x19164,x19161),f480(x19163,x19164,x19162))
% 160.93/160.66 [1917]~E(x19171,x19172)+E(f164(x19171,x19173),f164(x19172,x19173))
% 160.93/160.66 [1918]~E(x19181,x19182)+E(f164(x19183,x19181),f164(x19183,x19182))
% 160.93/160.66 [1919]~E(x19191,x19192)+E(f194(x19191),f194(x19192))
% 160.93/160.66 [1920]~E(x19201,x19202)+E(f504(x19201,x19203,x19204,x19205),f504(x19202,x19203,x19204,x19205))
% 160.93/160.66 [1921]~E(x19211,x19212)+E(f504(x19213,x19211,x19214,x19215),f504(x19213,x19212,x19214,x19215))
% 160.93/160.66 [1922]~E(x19221,x19222)+E(f504(x19223,x19224,x19221,x19225),f504(x19223,x19224,x19222,x19225))
% 160.93/160.66 [1923]~E(x19231,x19232)+E(f504(x19233,x19234,x19235,x19231),f504(x19233,x19234,x19235,x19232))
% 160.93/160.66 [1924]~E(x19241,x19242)+E(f317(x19241,x19243,x19244),f317(x19242,x19243,x19244))
% 160.93/160.66 [1925]~E(x19251,x19252)+E(f317(x19253,x19251,x19254),f317(x19253,x19252,x19254))
% 160.93/160.66 [1926]~E(x19261,x19262)+E(f317(x19263,x19264,x19261),f317(x19263,x19264,x19262))
% 160.93/160.66 [1927]~E(x19271,x19272)+E(f817(x19271,x19273,x19274,x19275),f817(x19272,x19273,x19274,x19275))
% 160.93/160.66 [1928]~E(x19281,x19282)+E(f817(x19283,x19281,x19284,x19285),f817(x19283,x19282,x19284,x19285))
% 160.93/160.66 [1929]~E(x19291,x19292)+E(f817(x19293,x19294,x19291,x19295),f817(x19293,x19294,x19292,x19295))
% 160.93/160.66 [1930]~E(x19301,x19302)+E(f817(x19303,x19304,x19305,x19301),f817(x19303,x19304,x19305,x19302))
% 160.93/160.66 [1931]~E(x19311,x19312)+E(f516(x19311,x19313),f516(x19312,x19313))
% 160.93/160.66 [1932]~E(x19321,x19322)+E(f516(x19323,x19321),f516(x19323,x19322))
% 160.93/160.66 [1933]~E(x19331,x19332)+E(f285(x19331,x19333),f285(x19332,x19333))
% 160.93/160.66 [1934]~E(x19341,x19342)+E(f285(x19343,x19341),f285(x19343,x19342))
% 160.93/160.66 [1935]~E(x19351,x19352)+E(f649(x19351,x19353,x19354,x19355,x19356),f649(x19352,x19353,x19354,x19355,x19356))
% 160.93/160.66 [1936]~E(x19361,x19362)+E(f649(x19363,x19361,x19364,x19365,x19366),f649(x19363,x19362,x19364,x19365,x19366))
% 160.93/160.66 [1937]~E(x19371,x19372)+E(f649(x19373,x19374,x19371,x19375,x19376),f649(x19373,x19374,x19372,x19375,x19376))
% 160.93/160.66 [1938]~E(x19381,x19382)+E(f649(x19383,x19384,x19385,x19381,x19386),f649(x19383,x19384,x19385,x19382,x19386))
% 160.93/160.66 [1939]~E(x19391,x19392)+E(f649(x19393,x19394,x19395,x19396,x19391),f649(x19393,x19394,x19395,x19396,x19392))
% 160.93/160.66 [1940]~E(x19401,x19402)+E(f626(x19401,x19403,x19404),f626(x19402,x19403,x19404))
% 160.93/160.66 [1941]~E(x19411,x19412)+E(f626(x19413,x19411,x19414),f626(x19413,x19412,x19414))
% 160.93/160.66 [1942]~E(x19421,x19422)+E(f626(x19423,x19424,x19421),f626(x19423,x19424,x19422))
% 160.93/160.66 [1943]~E(x19431,x19432)+E(f829(x19431,x19433,x19434,x19435),f829(x19432,x19433,x19434,x19435))
% 160.93/160.66 [1944]~E(x19441,x19442)+E(f829(x19443,x19441,x19444,x19445),f829(x19443,x19442,x19444,x19445))
% 160.93/160.66 [1945]~E(x19451,x19452)+E(f829(x19453,x19454,x19451,x19455),f829(x19453,x19454,x19452,x19455))
% 160.93/160.66 [1946]~E(x19461,x19462)+E(f829(x19463,x19464,x19465,x19461),f829(x19463,x19464,x19465,x19462))
% 160.93/160.66 [1947]~E(x19471,x19472)+E(f611(x19471,x19473,x19474,x19475,x19476,x19477),f611(x19472,x19473,x19474,x19475,x19476,x19477))
% 160.93/160.66 [1948]~E(x19481,x19482)+E(f611(x19483,x19481,x19484,x19485,x19486,x19487),f611(x19483,x19482,x19484,x19485,x19486,x19487))
% 160.93/160.66 [1949]~E(x19491,x19492)+E(f611(x19493,x19494,x19491,x19495,x19496,x19497),f611(x19493,x19494,x19492,x19495,x19496,x19497))
% 160.93/160.66 [1950]~E(x19501,x19502)+E(f611(x19503,x19504,x19505,x19501,x19506,x19507),f611(x19503,x19504,x19505,x19502,x19506,x19507))
% 160.93/160.66 [1951]~E(x19511,x19512)+E(f611(x19513,x19514,x19515,x19516,x19511,x19517),f611(x19513,x19514,x19515,x19516,x19512,x19517))
% 160.93/160.66 [1952]~E(x19521,x19522)+E(f611(x19523,x19524,x19525,x19526,x19527,x19521),f611(x19523,x19524,x19525,x19526,x19527,x19522))
% 160.93/160.66 [1953]~E(x19531,x19532)+E(f735(x19531,x19533,x19534),f735(x19532,x19533,x19534))
% 160.93/160.66 [1954]~E(x19541,x19542)+E(f735(x19543,x19541,x19544),f735(x19543,x19542,x19544))
% 160.93/160.66 [1955]~E(x19551,x19552)+E(f735(x19553,x19554,x19551),f735(x19553,x19554,x19552))
% 160.93/160.66 [1956]~E(x19561,x19562)+E(f841(x19561,x19563,x19564,x19565),f841(x19562,x19563,x19564,x19565))
% 160.93/160.66 [1957]~E(x19571,x19572)+E(f841(x19573,x19571,x19574,x19575),f841(x19573,x19572,x19574,x19575))
% 160.93/160.66 [1958]~E(x19581,x19582)+E(f841(x19583,x19584,x19581,x19585),f841(x19583,x19584,x19582,x19585))
% 160.93/160.66 [1959]~E(x19591,x19592)+E(f841(x19593,x19594,x19595,x19591),f841(x19593,x19594,x19595,x19592))
% 160.93/160.66 [1960]~E(x19601,x19602)+E(f93(x19601,x19603,x19604),f93(x19602,x19603,x19604))
% 160.93/160.66 [1961]~E(x19611,x19612)+E(f93(x19613,x19611,x19614),f93(x19613,x19612,x19614))
% 160.93/160.66 [1962]~E(x19621,x19622)+E(f93(x19623,x19624,x19621),f93(x19623,x19624,x19622))
% 160.93/160.66 [1963]~E(x19631,x19632)+E(f298(x19631,x19633,x19634,x19635),f298(x19632,x19633,x19634,x19635))
% 160.93/160.66 [1964]~E(x19641,x19642)+E(f298(x19643,x19641,x19644,x19645),f298(x19643,x19642,x19644,x19645))
% 160.93/160.66 [1965]~E(x19651,x19652)+E(f298(x19653,x19654,x19651,x19655),f298(x19653,x19654,x19652,x19655))
% 160.93/160.66 [1966]~E(x19661,x19662)+E(f298(x19663,x19664,x19665,x19661),f298(x19663,x19664,x19665,x19662))
% 160.93/160.66 [1967]~E(x19671,x19672)+E(f609(x19671,x19673,x19674),f609(x19672,x19673,x19674))
% 160.93/160.66 [1968]~E(x19681,x19682)+E(f609(x19683,x19681,x19684),f609(x19683,x19682,x19684))
% 160.93/160.66 [1969]~E(x19691,x19692)+E(f609(x19693,x19694,x19691),f609(x19693,x19694,x19692))
% 160.93/160.66 [1970]~E(x19701,x19702)+E(f505(x19701,x19703,x19704),f505(x19702,x19703,x19704))
% 160.93/160.66 [1971]~E(x19711,x19712)+E(f505(x19713,x19711,x19714),f505(x19713,x19712,x19714))
% 160.93/160.66 [1972]~E(x19721,x19722)+E(f505(x19723,x19724,x19721),f505(x19723,x19724,x19722))
% 160.93/160.66 [1973]~E(x19731,x19732)+E(f713(x19731,x19733,x19734),f713(x19732,x19733,x19734))
% 160.93/160.66 [1974]~E(x19741,x19742)+E(f713(x19743,x19741,x19744),f713(x19743,x19742,x19744))
% 160.93/160.66 [1975]~E(x19751,x19752)+E(f713(x19753,x19754,x19751),f713(x19753,x19754,x19752))
% 160.93/160.66 [1976]~E(x19761,x19762)+E(f435(x19761,x19763,x19764,x19765),f435(x19762,x19763,x19764,x19765))
% 160.93/160.66 [1977]~E(x19771,x19772)+E(f435(x19773,x19771,x19774,x19775),f435(x19773,x19772,x19774,x19775))
% 160.93/160.66 [1978]~E(x19781,x19782)+E(f435(x19783,x19784,x19781,x19785),f435(x19783,x19784,x19782,x19785))
% 160.93/160.66 [1979]~E(x19791,x19792)+E(f435(x19793,x19794,x19795,x19791),f435(x19793,x19794,x19795,x19792))
% 160.93/160.66 [1980]~E(x19801,x19802)+E(f806(x19801,x19803,x19804),f806(x19802,x19803,x19804))
% 160.93/160.66 [1981]~E(x19811,x19812)+E(f806(x19813,x19811,x19814),f806(x19813,x19812,x19814))
% 160.93/160.66 [1982]~E(x19821,x19822)+E(f806(x19823,x19824,x19821),f806(x19823,x19824,x19822))
% 160.93/160.66 [1983]~E(x19831,x19832)+E(f67(x19831,x19833,x19834),f67(x19832,x19833,x19834))
% 160.93/160.66 [1984]~E(x19841,x19842)+E(f67(x19843,x19841,x19844),f67(x19843,x19842,x19844))
% 160.93/160.66 [1985]~E(x19851,x19852)+E(f67(x19853,x19854,x19851),f67(x19853,x19854,x19852))
% 160.93/160.66 [1986]~E(x19861,x19862)+E(f561(x19861,x19863,x19864,x19865),f561(x19862,x19863,x19864,x19865))
% 160.93/160.66 [1987]~E(x19871,x19872)+E(f561(x19873,x19871,x19874,x19875),f561(x19873,x19872,x19874,x19875))
% 160.93/160.66 [1988]~E(x19881,x19882)+E(f561(x19883,x19884,x19881,x19885),f561(x19883,x19884,x19882,x19885))
% 160.93/160.66 [1989]~E(x19891,x19892)+E(f561(x19893,x19894,x19895,x19891),f561(x19893,x19894,x19895,x19892))
% 160.93/160.66 [1990]~E(x19901,x19902)+E(f183(x19901),f183(x19902))
% 160.93/160.66 [1991]~E(x19911,x19912)+E(f538(x19911,x19913,x19914,x19915),f538(x19912,x19913,x19914,x19915))
% 160.93/160.66 [1992]~E(x19921,x19922)+E(f538(x19923,x19921,x19924,x19925),f538(x19923,x19922,x19924,x19925))
% 160.93/160.66 [1993]~E(x19931,x19932)+E(f538(x19933,x19934,x19931,x19935),f538(x19933,x19934,x19932,x19935))
% 160.93/160.66 [1994]~E(x19941,x19942)+E(f538(x19943,x19944,x19945,x19941),f538(x19943,x19944,x19945,x19942))
% 160.93/160.66 [1995]~E(x19951,x19952)+E(f529(x19951,x19953,x19954,x19955),f529(x19952,x19953,x19954,x19955))
% 160.93/160.66 [1996]~E(x19961,x19962)+E(f529(x19963,x19961,x19964,x19965),f529(x19963,x19962,x19964,x19965))
% 160.93/160.66 [1997]~E(x19971,x19972)+E(f529(x19973,x19974,x19971,x19975),f529(x19973,x19974,x19972,x19975))
% 160.93/160.66 [1998]~E(x19981,x19982)+E(f529(x19983,x19984,x19985,x19981),f529(x19983,x19984,x19985,x19982))
% 160.93/160.66 [1999]~E(x19991,x19992)+E(f848(x19991,x19993),f848(x19992,x19993))
% 160.93/160.66 [2000]~E(x20001,x20002)+E(f848(x20003,x20001),f848(x20003,x20002))
% 160.93/160.66 [2001]~E(x20011,x20012)+E(f483(x20011,x20013,x20014),f483(x20012,x20013,x20014))
% 160.93/160.66 [2002]~E(x20021,x20022)+E(f483(x20023,x20021,x20024),f483(x20023,x20022,x20024))
% 160.93/160.66 [2003]~E(x20031,x20032)+E(f483(x20033,x20034,x20031),f483(x20033,x20034,x20032))
% 160.93/160.66 [2004]~E(x20041,x20042)+E(f94(x20041),f94(x20042))
% 160.93/160.66 [2005]~E(x20051,x20052)+E(f379(x20051,x20053,x20054,x20055),f379(x20052,x20053,x20054,x20055))
% 160.93/160.66 [2006]~E(x20061,x20062)+E(f379(x20063,x20061,x20064,x20065),f379(x20063,x20062,x20064,x20065))
% 160.93/160.66 [2007]~E(x20071,x20072)+E(f379(x20073,x20074,x20071,x20075),f379(x20073,x20074,x20072,x20075))
% 160.93/160.66 [2008]~E(x20081,x20082)+E(f379(x20083,x20084,x20085,x20081),f379(x20083,x20084,x20085,x20082))
% 160.93/160.66 [2009]~E(x20091,x20092)+E(f732(x20091,x20093),f732(x20092,x20093))
% 160.93/160.66 [2010]~E(x20101,x20102)+E(f732(x20103,x20101),f732(x20103,x20102))
% 160.93/160.66 [2011]~E(x20111,x20112)+E(f833(x20111,x20113,x20114,x20115),f833(x20112,x20113,x20114,x20115))
% 160.93/160.66 [2012]~E(x20121,x20122)+E(f833(x20123,x20121,x20124,x20125),f833(x20123,x20122,x20124,x20125))
% 160.93/160.66 [2013]~E(x20131,x20132)+E(f833(x20133,x20134,x20131,x20135),f833(x20133,x20134,x20132,x20135))
% 160.93/160.66 [2014]~E(x20141,x20142)+E(f833(x20143,x20144,x20145,x20141),f833(x20143,x20144,x20145,x20142))
% 160.93/160.66 [2015]~E(x20151,x20152)+E(f528(x20151,x20153,x20154),f528(x20152,x20153,x20154))
% 160.93/160.66 [2016]~E(x20161,x20162)+E(f528(x20163,x20161,x20164),f528(x20163,x20162,x20164))
% 160.93/160.66 [2017]~E(x20171,x20172)+E(f528(x20173,x20174,x20171),f528(x20173,x20174,x20172))
% 160.93/160.66 [2018]~E(x20181,x20182)+E(f495(x20181,x20183,x20184,x20185),f495(x20182,x20183,x20184,x20185))
% 160.93/160.66 [2019]~E(x20191,x20192)+E(f495(x20193,x20191,x20194,x20195),f495(x20193,x20192,x20194,x20195))
% 160.93/160.66 [2020]~E(x20201,x20202)+E(f495(x20203,x20204,x20201,x20205),f495(x20203,x20204,x20202,x20205))
% 160.93/160.66 [2021]~E(x20211,x20212)+E(f495(x20213,x20214,x20215,x20211),f495(x20213,x20214,x20215,x20212))
% 160.93/160.66 [2022]~E(x20221,x20222)+E(f746(x20221,x20223,x20224),f746(x20222,x20223,x20224))
% 160.93/160.66 [2023]~E(x20231,x20232)+E(f746(x20233,x20231,x20234),f746(x20233,x20232,x20234))
% 160.93/160.66 [2024]~E(x20241,x20242)+E(f746(x20243,x20244,x20241),f746(x20243,x20244,x20242))
% 160.93/160.66 [2025]~E(x20251,x20252)+E(f525(x20251,x20253,x20254),f525(x20252,x20253,x20254))
% 160.93/160.66 [2026]~E(x20261,x20262)+E(f525(x20263,x20261,x20264),f525(x20263,x20262,x20264))
% 160.93/160.66 [2027]~E(x20271,x20272)+E(f525(x20273,x20274,x20271),f525(x20273,x20274,x20272))
% 160.93/160.66 [2028]~E(x20281,x20282)+E(f629(x20281,x20283,x20284),f629(x20282,x20283,x20284))
% 160.93/160.66 [2029]~E(x20291,x20292)+E(f629(x20293,x20291,x20294),f629(x20293,x20292,x20294))
% 160.93/160.66 [2030]~E(x20301,x20302)+E(f629(x20303,x20304,x20301),f629(x20303,x20304,x20302))
% 160.93/160.66 [2031]~E(x20311,x20312)+E(f688(x20311,x20313),f688(x20312,x20313))
% 160.93/160.66 [2032]~E(x20321,x20322)+E(f688(x20323,x20321),f688(x20323,x20322))
% 160.93/160.66 [2033]~E(x20331,x20332)+E(f596(x20331,x20333,x20334),f596(x20332,x20333,x20334))
% 160.93/160.66 [2034]~E(x20341,x20342)+E(f596(x20343,x20341,x20344),f596(x20343,x20342,x20344))
% 160.93/160.66 [2035]~E(x20351,x20352)+E(f596(x20353,x20354,x20351),f596(x20353,x20354,x20352))
% 160.93/160.66 [2036]~E(x20361,x20362)+E(f521(x20361,x20363,x20364),f521(x20362,x20363,x20364))
% 160.93/160.66 [2037]~E(x20371,x20372)+E(f521(x20373,x20371,x20374),f521(x20373,x20372,x20374))
% 160.93/160.66 [2038]~E(x20381,x20382)+E(f521(x20383,x20384,x20381),f521(x20383,x20384,x20382))
% 160.93/160.66 [2039]~E(x20391,x20392)+E(f535(x20391,x20393,x20394,x20395),f535(x20392,x20393,x20394,x20395))
% 160.93/160.66 [2040]~E(x20401,x20402)+E(f535(x20403,x20401,x20404,x20405),f535(x20403,x20402,x20404,x20405))
% 160.93/160.66 [2041]~E(x20411,x20412)+E(f535(x20413,x20414,x20411,x20415),f535(x20413,x20414,x20412,x20415))
% 160.93/160.66 [2042]~E(x20421,x20422)+E(f535(x20423,x20424,x20425,x20421),f535(x20423,x20424,x20425,x20422))
% 160.93/160.66 [2043]~E(x20431,x20432)+E(f874(x20431,x20433,x20434,x20435),f874(x20432,x20433,x20434,x20435))
% 160.93/160.66 [2044]~E(x20441,x20442)+E(f874(x20443,x20441,x20444,x20445),f874(x20443,x20442,x20444,x20445))
% 160.93/160.66 [2045]~E(x20451,x20452)+E(f874(x20453,x20454,x20451,x20455),f874(x20453,x20454,x20452,x20455))
% 160.93/160.66 [2046]~E(x20461,x20462)+E(f874(x20463,x20464,x20465,x20461),f874(x20463,x20464,x20465,x20462))
% 160.93/160.66 [2047]~E(x20471,x20472)+E(f558(x20471,x20473,x20474,x20475),f558(x20472,x20473,x20474,x20475))
% 160.93/160.66 [2048]~E(x20481,x20482)+E(f558(x20483,x20481,x20484,x20485),f558(x20483,x20482,x20484,x20485))
% 160.93/160.66 [2049]~E(x20491,x20492)+E(f558(x20493,x20494,x20491,x20495),f558(x20493,x20494,x20492,x20495))
% 160.93/160.66 [2050]~E(x20501,x20502)+E(f558(x20503,x20504,x20505,x20501),f558(x20503,x20504,x20505,x20502))
% 160.93/160.66 [2051]~E(x20511,x20512)+E(f490(x20511,x20513,x20514,x20515,x20516),f490(x20512,x20513,x20514,x20515,x20516))
% 160.93/160.66 [2052]~E(x20521,x20522)+E(f490(x20523,x20521,x20524,x20525,x20526),f490(x20523,x20522,x20524,x20525,x20526))
% 160.93/160.66 [2053]~E(x20531,x20532)+E(f490(x20533,x20534,x20531,x20535,x20536),f490(x20533,x20534,x20532,x20535,x20536))
% 160.93/160.66 [2054]~E(x20541,x20542)+E(f490(x20543,x20544,x20545,x20541,x20546),f490(x20543,x20544,x20545,x20542,x20546))
% 160.93/160.66 [2055]~E(x20551,x20552)+E(f490(x20553,x20554,x20555,x20556,x20551),f490(x20553,x20554,x20555,x20556,x20552))
% 160.93/160.66 [2056]~E(x20561,x20562)+E(f586(x20561,x20563),f586(x20562,x20563))
% 160.93/160.66 [2057]~E(x20571,x20572)+E(f586(x20573,x20571),f586(x20573,x20572))
% 160.93/160.66 [2058]~E(x20581,x20582)+E(f677(x20581,x20583,x20584,x20585,x20586),f677(x20582,x20583,x20584,x20585,x20586))
% 160.93/160.66 [2059]~E(x20591,x20592)+E(f677(x20593,x20591,x20594,x20595,x20596),f677(x20593,x20592,x20594,x20595,x20596))
% 160.93/160.66 [2060]~E(x20601,x20602)+E(f677(x20603,x20604,x20601,x20605,x20606),f677(x20603,x20604,x20602,x20605,x20606))
% 160.93/160.66 [2061]~E(x20611,x20612)+E(f677(x20613,x20614,x20615,x20611,x20616),f677(x20613,x20614,x20615,x20612,x20616))
% 160.93/160.66 [2062]~E(x20621,x20622)+E(f677(x20623,x20624,x20625,x20626,x20621),f677(x20623,x20624,x20625,x20626,x20622))
% 160.93/160.66 [2063]~E(x20631,x20632)+E(f766(x20631,x20633),f766(x20632,x20633))
% 160.93/160.66 [2064]~E(x20641,x20642)+E(f766(x20643,x20641),f766(x20643,x20642))
% 160.93/160.66 [2065]~E(x20651,x20652)+E(f130(x20651),f130(x20652))
% 160.93/160.66 [2066]~E(x20661,x20662)+E(f131(x20661,x20663),f131(x20662,x20663))
% 160.93/160.66 [2067]~E(x20671,x20672)+E(f131(x20673,x20671),f131(x20673,x20672))
% 160.93/160.66 [2068]~E(x20681,x20682)+E(f644(x20681,x20683,x20684,x20685),f644(x20682,x20683,x20684,x20685))
% 160.93/160.66 [2069]~E(x20691,x20692)+E(f644(x20693,x20691,x20694,x20695),f644(x20693,x20692,x20694,x20695))
% 160.93/160.66 [2070]~E(x20701,x20702)+E(f644(x20703,x20704,x20701,x20705),f644(x20703,x20704,x20702,x20705))
% 160.93/160.66 [2071]~E(x20711,x20712)+E(f644(x20713,x20714,x20715,x20711),f644(x20713,x20714,x20715,x20712))
% 160.93/160.66 [2072]~E(x20721,x20722)+E(f856(x20721,x20723,x20724),f856(x20722,x20723,x20724))
% 160.93/160.66 [2073]~E(x20731,x20732)+E(f856(x20733,x20731,x20734),f856(x20733,x20732,x20734))
% 160.93/160.66 [2074]~E(x20741,x20742)+E(f856(x20743,x20744,x20741),f856(x20743,x20744,x20742))
% 160.93/160.66 [2075]~E(x20751,x20752)+E(f729(x20751,x20753,x20754,x20755),f729(x20752,x20753,x20754,x20755))
% 160.93/160.66 [2076]~E(x20761,x20762)+E(f729(x20763,x20761,x20764,x20765),f729(x20763,x20762,x20764,x20765))
% 160.93/160.66 [2077]~E(x20771,x20772)+E(f729(x20773,x20774,x20771,x20775),f729(x20773,x20774,x20772,x20775))
% 160.93/160.66 [2078]~E(x20781,x20782)+E(f729(x20783,x20784,x20785,x20781),f729(x20783,x20784,x20785,x20782))
% 160.93/160.66 [2079]~E(x20791,x20792)+E(f469(x20791,x20793),f469(x20792,x20793))
% 160.93/160.66 [2080]~E(x20801,x20802)+E(f469(x20803,x20801),f469(x20803,x20802))
% 160.93/160.66 [2081]~E(x20811,x20812)+E(f704(x20811,x20813,x20814,x20815),f704(x20812,x20813,x20814,x20815))
% 160.93/160.66 [2082]~E(x20821,x20822)+E(f704(x20823,x20821,x20824,x20825),f704(x20823,x20822,x20824,x20825))
% 160.93/160.66 [2083]~E(x20831,x20832)+E(f704(x20833,x20834,x20831,x20835),f704(x20833,x20834,x20832,x20835))
% 160.93/160.66 [2084]~E(x20841,x20842)+E(f704(x20843,x20844,x20845,x20841),f704(x20843,x20844,x20845,x20842))
% 160.93/160.66 [2085]~E(x20851,x20852)+E(f615(x20851,x20853),f615(x20852,x20853))
% 160.93/160.66 [2086]~E(x20861,x20862)+E(f615(x20863,x20861),f615(x20863,x20862))
% 160.93/160.66 [2087]~E(x20871,x20872)+E(f137(x20871),f137(x20872))
% 160.93/160.66 [2088]~E(x20881,x20882)+E(f604(x20881,x20883,x20884),f604(x20882,x20883,x20884))
% 160.93/160.66 [2089]~E(x20891,x20892)+E(f604(x20893,x20891,x20894),f604(x20893,x20892,x20894))
% 160.93/160.66 [2090]~E(x20901,x20902)+E(f604(x20903,x20904,x20901),f604(x20903,x20904,x20902))
% 160.93/160.66 [2091]~E(x20911,x20912)+E(f376(x20911,x20913,x20914,x20915),f376(x20912,x20913,x20914,x20915))
% 160.93/160.66 [2092]~E(x20921,x20922)+E(f376(x20923,x20921,x20924,x20925),f376(x20923,x20922,x20924,x20925))
% 160.93/160.66 [2093]~E(x20931,x20932)+E(f376(x20933,x20934,x20931,x20935),f376(x20933,x20934,x20932,x20935))
% 160.93/160.66 [2094]~E(x20941,x20942)+E(f376(x20943,x20944,x20945,x20941),f376(x20943,x20944,x20945,x20942))
% 160.93/160.66 [2095]~E(x20951,x20952)+E(f557(x20951,x20953,x20954,x20955,x20956,x20957,x20958,x20959),f557(x20952,x20953,x20954,x20955,x20956,x20957,x20958,x20959))
% 160.93/160.66 [2096]~E(x20961,x20962)+E(f557(x20963,x20961,x20964,x20965,x20966,x20967,x20968,x20969),f557(x20963,x20962,x20964,x20965,x20966,x20967,x20968,x20969))
% 160.93/160.66 [2097]~E(x20971,x20972)+E(f557(x20973,x20974,x20971,x20975,x20976,x20977,x20978,x20979),f557(x20973,x20974,x20972,x20975,x20976,x20977,x20978,x20979))
% 160.93/160.66 [2098]~E(x20981,x20982)+E(f557(x20983,x20984,x20985,x20981,x20986,x20987,x20988,x20989),f557(x20983,x20984,x20985,x20982,x20986,x20987,x20988,x20989))
% 160.93/160.66 [2099]~E(x20991,x20992)+E(f557(x20993,x20994,x20995,x20996,x20991,x20997,x20998,x20999),f557(x20993,x20994,x20995,x20996,x20992,x20997,x20998,x20999))
% 160.93/160.66 [2100]~E(x21001,x21002)+E(f557(x21003,x21004,x21005,x21006,x21007,x21001,x21008,x21009),f557(x21003,x21004,x21005,x21006,x21007,x21002,x21008,x21009))
% 160.93/160.66 [2101]~E(x21011,x21012)+E(f557(x21013,x21014,x21015,x21016,x21017,x21018,x21011,x21019),f557(x21013,x21014,x21015,x21016,x21017,x21018,x21012,x21019))
% 160.93/160.66 [2102]~E(x21021,x21022)+E(f557(x21023,x21024,x21025,x21026,x21027,x21028,x21029,x21021),f557(x21023,x21024,x21025,x21026,x21027,x21028,x21029,x21022))
% 160.93/160.66 [2103]~E(x21031,x21032)+E(f539(x21031,x21033),f539(x21032,x21033))
% 160.93/160.66 [2104]~E(x21041,x21042)+E(f539(x21043,x21041),f539(x21043,x21042))
% 160.93/160.66 [2105]~E(x21051,x21052)+E(f818(x21051,x21053,x21054,x21055),f818(x21052,x21053,x21054,x21055))
% 160.93/160.66 [2106]~E(x21061,x21062)+E(f818(x21063,x21061,x21064,x21065),f818(x21063,x21062,x21064,x21065))
% 160.93/160.66 [2107]~E(x21071,x21072)+E(f818(x21073,x21074,x21071,x21075),f818(x21073,x21074,x21072,x21075))
% 160.93/160.66 [2108]~E(x21081,x21082)+E(f818(x21083,x21084,x21085,x21081),f818(x21083,x21084,x21085,x21082))
% 160.93/160.66 [2109]~E(x21091,x21092)+E(f784(x21091,x21093,x21094),f784(x21092,x21093,x21094))
% 160.93/160.66 [2110]~E(x21101,x21102)+E(f784(x21103,x21101,x21104),f784(x21103,x21102,x21104))
% 160.93/160.66 [2111]~E(x21111,x21112)+E(f784(x21113,x21114,x21111),f784(x21113,x21114,x21112))
% 160.93/160.66 [2112]~E(x21121,x21122)+E(f293(x21121,x21123),f293(x21122,x21123))
% 160.93/160.66 [2113]~E(x21131,x21132)+E(f293(x21133,x21131),f293(x21133,x21132))
% 160.93/160.66 [2114]~E(x21141,x21142)+E(f508(x21141,x21143,x21144),f508(x21142,x21143,x21144))
% 160.93/160.66 [2115]~E(x21151,x21152)+E(f508(x21153,x21151,x21154),f508(x21153,x21152,x21154))
% 160.93/160.66 [2116]~E(x21161,x21162)+E(f508(x21163,x21164,x21161),f508(x21163,x21164,x21162))
% 160.93/160.66 [2117]~E(x21171,x21172)+E(f295(x21171,x21173,x21174),f295(x21172,x21173,x21174))
% 160.93/160.66 [2118]~E(x21181,x21182)+E(f295(x21183,x21181,x21184),f295(x21183,x21182,x21184))
% 160.93/160.66 [2119]~E(x21191,x21192)+E(f295(x21193,x21194,x21191),f295(x21193,x21194,x21192))
% 160.93/160.66 [2120]~E(x21201,x21202)+E(f645(x21201,x21203,x21204,x21205,x21206),f645(x21202,x21203,x21204,x21205,x21206))
% 160.93/160.66 [2121]~E(x21211,x21212)+E(f645(x21213,x21211,x21214,x21215,x21216),f645(x21213,x21212,x21214,x21215,x21216))
% 160.93/160.66 [2122]~E(x21221,x21222)+E(f645(x21223,x21224,x21221,x21225,x21226),f645(x21223,x21224,x21222,x21225,x21226))
% 160.93/160.66 [2123]~E(x21231,x21232)+E(f645(x21233,x21234,x21235,x21231,x21236),f645(x21233,x21234,x21235,x21232,x21236))
% 160.93/160.66 [2124]~E(x21241,x21242)+E(f645(x21243,x21244,x21245,x21246,x21241),f645(x21243,x21244,x21245,x21246,x21242))
% 160.93/160.66 [2125]~E(x21251,x21252)+E(f692(x21251,x21253,x21254,x21255),f692(x21252,x21253,x21254,x21255))
% 160.93/160.66 [2126]~E(x21261,x21262)+E(f692(x21263,x21261,x21264,x21265),f692(x21263,x21262,x21264,x21265))
% 160.93/160.66 [2127]~E(x21271,x21272)+E(f692(x21273,x21274,x21271,x21275),f692(x21273,x21274,x21272,x21275))
% 160.93/160.66 [2128]~E(x21281,x21282)+E(f692(x21283,x21284,x21285,x21281),f692(x21283,x21284,x21285,x21282))
% 160.93/160.66 [2129]~E(x21291,x21292)+E(f777(x21291,x21293,x21294,x21295,x21296,x21297,x21298,x21299),f777(x21292,x21293,x21294,x21295,x21296,x21297,x21298,x21299))
% 160.93/160.66 [2130]~E(x21301,x21302)+E(f777(x21303,x21301,x21304,x21305,x21306,x21307,x21308,x21309),f777(x21303,x21302,x21304,x21305,x21306,x21307,x21308,x21309))
% 160.93/160.66 [2131]~E(x21311,x21312)+E(f777(x21313,x21314,x21311,x21315,x21316,x21317,x21318,x21319),f777(x21313,x21314,x21312,x21315,x21316,x21317,x21318,x21319))
% 160.93/160.66 [2132]~E(x21321,x21322)+E(f777(x21323,x21324,x21325,x21321,x21326,x21327,x21328,x21329),f777(x21323,x21324,x21325,x21322,x21326,x21327,x21328,x21329))
% 160.93/160.66 [2133]~E(x21331,x21332)+E(f777(x21333,x21334,x21335,x21336,x21331,x21337,x21338,x21339),f777(x21333,x21334,x21335,x21336,x21332,x21337,x21338,x21339))
% 160.93/160.66 [2134]~E(x21341,x21342)+E(f777(x21343,x21344,x21345,x21346,x21347,x21341,x21348,x21349),f777(x21343,x21344,x21345,x21346,x21347,x21342,x21348,x21349))
% 160.93/160.66 [2135]~E(x21351,x21352)+E(f777(x21353,x21354,x21355,x21356,x21357,x21358,x21351,x21359),f777(x21353,x21354,x21355,x21356,x21357,x21358,x21352,x21359))
% 160.93/160.66 [2136]~E(x21361,x21362)+E(f777(x21363,x21364,x21365,x21366,x21367,x21368,x21369,x21361),f777(x21363,x21364,x21365,x21366,x21367,x21368,x21369,x21362))
% 160.93/160.66 [2137]~E(x21371,x21372)+E(f754(x21371,x21373,x21374),f754(x21372,x21373,x21374))
% 160.93/160.66 [2138]~E(x21381,x21382)+E(f754(x21383,x21381,x21384),f754(x21383,x21382,x21384))
% 160.93/160.66 [2139]~E(x21391,x21392)+E(f754(x21393,x21394,x21391),f754(x21393,x21394,x21392))
% 160.93/160.66 [2140]~E(x21401,x21402)+E(f371(x21401,x21403),f371(x21402,x21403))
% 160.93/160.66 [2141]~E(x21411,x21412)+E(f371(x21413,x21411),f371(x21413,x21412))
% 160.93/160.66 [2142]~E(x21421,x21422)+E(f369(x21421,x21423,x21424,x21425,x21426),f369(x21422,x21423,x21424,x21425,x21426))
% 160.93/160.66 [2143]~E(x21431,x21432)+E(f369(x21433,x21431,x21434,x21435,x21436),f369(x21433,x21432,x21434,x21435,x21436))
% 160.93/160.66 [2144]~E(x21441,x21442)+E(f369(x21443,x21444,x21441,x21445,x21446),f369(x21443,x21444,x21442,x21445,x21446))
% 160.93/160.66 [2145]~E(x21451,x21452)+E(f369(x21453,x21454,x21455,x21451,x21456),f369(x21453,x21454,x21455,x21452,x21456))
% 160.93/160.66 [2146]~E(x21461,x21462)+E(f369(x21463,x21464,x21465,x21466,x21461),f369(x21463,x21464,x21465,x21466,x21462))
% 160.93/160.66 [2147]~E(x21471,x21472)+E(f573(x21471,x21473,x21474,x21475,x21476),f573(x21472,x21473,x21474,x21475,x21476))
% 160.93/160.66 [2148]~E(x21481,x21482)+E(f573(x21483,x21481,x21484,x21485,x21486),f573(x21483,x21482,x21484,x21485,x21486))
% 160.93/160.66 [2149]~E(x21491,x21492)+E(f573(x21493,x21494,x21491,x21495,x21496),f573(x21493,x21494,x21492,x21495,x21496))
% 160.93/160.66 [2150]~E(x21501,x21502)+E(f573(x21503,x21504,x21505,x21501,x21506),f573(x21503,x21504,x21505,x21502,x21506))
% 160.93/160.66 [2151]~E(x21511,x21512)+E(f573(x21513,x21514,x21515,x21516,x21511),f573(x21513,x21514,x21515,x21516,x21512))
% 160.93/160.66 [2152]~E(x21521,x21522)+E(f126(x21521),f126(x21522))
% 160.93/160.66 [2153]~E(x21531,x21532)+E(f847(x21531,x21533),f847(x21532,x21533))
% 160.93/160.66 [2154]~E(x21541,x21542)+E(f847(x21543,x21541),f847(x21543,x21542))
% 160.93/160.66 [2155]~E(x21551,x21552)+E(f870(x21551,x21553,x21554,x21555,x21556),f870(x21552,x21553,x21554,x21555,x21556))
% 160.93/160.66 [2156]~E(x21561,x21562)+E(f870(x21563,x21561,x21564,x21565,x21566),f870(x21563,x21562,x21564,x21565,x21566))
% 160.93/160.66 [2157]~E(x21571,x21572)+E(f870(x21573,x21574,x21571,x21575,x21576),f870(x21573,x21574,x21572,x21575,x21576))
% 160.93/160.66 [2158]~E(x21581,x21582)+E(f870(x21583,x21584,x21585,x21581,x21586),f870(x21583,x21584,x21585,x21582,x21586))
% 160.93/160.66 [2159]~E(x21591,x21592)+E(f870(x21593,x21594,x21595,x21596,x21591),f870(x21593,x21594,x21595,x21596,x21592))
% 160.93/160.66 [2160]~E(x21601,x21602)+E(f532(x21601,x21603,x21604,x21605,x21606,x21607,x21608),f532(x21602,x21603,x21604,x21605,x21606,x21607,x21608))
% 160.93/160.66 [2161]~E(x21611,x21612)+E(f532(x21613,x21611,x21614,x21615,x21616,x21617,x21618),f532(x21613,x21612,x21614,x21615,x21616,x21617,x21618))
% 160.93/160.66 [2162]~E(x21621,x21622)+E(f532(x21623,x21624,x21621,x21625,x21626,x21627,x21628),f532(x21623,x21624,x21622,x21625,x21626,x21627,x21628))
% 160.93/160.66 [2163]~E(x21631,x21632)+E(f532(x21633,x21634,x21635,x21631,x21636,x21637,x21638),f532(x21633,x21634,x21635,x21632,x21636,x21637,x21638))
% 160.93/160.66 [2164]~E(x21641,x21642)+E(f532(x21643,x21644,x21645,x21646,x21641,x21647,x21648),f532(x21643,x21644,x21645,x21646,x21642,x21647,x21648))
% 160.93/160.66 [2165]~E(x21651,x21652)+E(f532(x21653,x21654,x21655,x21656,x21657,x21651,x21658),f532(x21653,x21654,x21655,x21656,x21657,x21652,x21658))
% 160.93/160.66 [2166]~E(x21661,x21662)+E(f532(x21663,x21664,x21665,x21666,x21667,x21668,x21661),f532(x21663,x21664,x21665,x21666,x21667,x21668,x21662))
% 160.93/160.66 [2167]~E(x21671,x21672)+E(f459(x21671,x21673,x21674,x21675),f459(x21672,x21673,x21674,x21675))
% 160.93/160.66 [2168]~E(x21681,x21682)+E(f459(x21683,x21681,x21684,x21685),f459(x21683,x21682,x21684,x21685))
% 160.93/160.66 [2169]~E(x21691,x21692)+E(f459(x21693,x21694,x21691,x21695),f459(x21693,x21694,x21692,x21695))
% 160.93/160.66 [2170]~E(x21701,x21702)+E(f459(x21703,x21704,x21705,x21701),f459(x21703,x21704,x21705,x21702))
% 160.93/160.66 [2171]~E(x21711,x21712)+E(f875(x21711,x21713,x21714,x21715),f875(x21712,x21713,x21714,x21715))
% 160.93/160.66 [2172]~E(x21721,x21722)+E(f875(x21723,x21721,x21724,x21725),f875(x21723,x21722,x21724,x21725))
% 160.93/160.66 [2173]~E(x21731,x21732)+E(f875(x21733,x21734,x21731,x21735),f875(x21733,x21734,x21732,x21735))
% 160.93/160.66 [2174]~E(x21741,x21742)+E(f875(x21743,x21744,x21745,x21741),f875(x21743,x21744,x21745,x21742))
% 160.93/160.66 [2175]~E(x21751,x21752)+E(f409(x21751,x21753,x21754,x21755,x21756,x21757),f409(x21752,x21753,x21754,x21755,x21756,x21757))
% 160.93/160.66 [2176]~E(x21761,x21762)+E(f409(x21763,x21761,x21764,x21765,x21766,x21767),f409(x21763,x21762,x21764,x21765,x21766,x21767))
% 160.93/160.66 [2177]~E(x21771,x21772)+E(f409(x21773,x21774,x21771,x21775,x21776,x21777),f409(x21773,x21774,x21772,x21775,x21776,x21777))
% 160.93/160.66 [2178]~E(x21781,x21782)+E(f409(x21783,x21784,x21785,x21781,x21786,x21787),f409(x21783,x21784,x21785,x21782,x21786,x21787))
% 160.93/160.66 [2179]~E(x21791,x21792)+E(f409(x21793,x21794,x21795,x21796,x21791,x21797),f409(x21793,x21794,x21795,x21796,x21792,x21797))
% 160.93/160.66 [2180]~E(x21801,x21802)+E(f409(x21803,x21804,x21805,x21806,x21807,x21801),f409(x21803,x21804,x21805,x21806,x21807,x21802))
% 160.93/160.66 [2181]~E(x21811,x21812)+E(f416(x21811,x21813),f416(x21812,x21813))
% 160.93/160.66 [2182]~E(x21821,x21822)+E(f416(x21823,x21821),f416(x21823,x21822))
% 160.93/160.66 [2183]~E(x21831,x21832)+E(f523(x21831,x21833,x21834),f523(x21832,x21833,x21834))
% 160.93/160.66 [2184]~E(x21841,x21842)+E(f523(x21843,x21841,x21844),f523(x21843,x21842,x21844))
% 160.93/160.66 [2185]~E(x21851,x21852)+E(f523(x21853,x21854,x21851),f523(x21853,x21854,x21852))
% 160.93/160.66 [2186]~E(x21861,x21862)+E(f398(x21861,x21863),f398(x21862,x21863))
% 160.93/160.66 [2187]~E(x21871,x21872)+E(f398(x21873,x21871),f398(x21873,x21872))
% 160.93/160.66 [2188]~E(x21881,x21882)+E(f486(x21881,x21883,x21884,x21885),f486(x21882,x21883,x21884,x21885))
% 160.93/160.66 [2189]~E(x21891,x21892)+E(f486(x21893,x21891,x21894,x21895),f486(x21893,x21892,x21894,x21895))
% 160.93/160.66 [2190]~E(x21901,x21902)+E(f486(x21903,x21904,x21901,x21905),f486(x21903,x21904,x21902,x21905))
% 160.93/160.66 [2191]~E(x21911,x21912)+E(f486(x21913,x21914,x21915,x21911),f486(x21913,x21914,x21915,x21912))
% 160.93/160.66 [2192]~E(x21921,x21922)+E(f365(x21921),f365(x21922))
% 160.93/160.66 [2193]~E(x21931,x21932)+E(f618(x21931,x21933,x21934),f618(x21932,x21933,x21934))
% 160.93/160.66 [2194]~E(x21941,x21942)+E(f618(x21943,x21941,x21944),f618(x21943,x21942,x21944))
% 160.93/160.66 [2195]~E(x21951,x21952)+E(f618(x21953,x21954,x21951),f618(x21953,x21954,x21952))
% 160.93/160.66 [2196]~E(x21961,x21962)+E(f840(x21961,x21963,x21964,x21965,x21966,x21967,x21968),f840(x21962,x21963,x21964,x21965,x21966,x21967,x21968))
% 160.93/160.66 [2197]~E(x21971,x21972)+E(f840(x21973,x21971,x21974,x21975,x21976,x21977,x21978),f840(x21973,x21972,x21974,x21975,x21976,x21977,x21978))
% 160.93/160.66 [2198]~E(x21981,x21982)+E(f840(x21983,x21984,x21981,x21985,x21986,x21987,x21988),f840(x21983,x21984,x21982,x21985,x21986,x21987,x21988))
% 160.93/160.66 [2199]~E(x21991,x21992)+E(f840(x21993,x21994,x21995,x21991,x21996,x21997,x21998),f840(x21993,x21994,x21995,x21992,x21996,x21997,x21998))
% 160.93/160.66 [2200]~E(x22001,x22002)+E(f840(x22003,x22004,x22005,x22006,x22001,x22007,x22008),f840(x22003,x22004,x22005,x22006,x22002,x22007,x22008))
% 160.93/160.66 [2201]~E(x22011,x22012)+E(f840(x22013,x22014,x22015,x22016,x22017,x22011,x22018),f840(x22013,x22014,x22015,x22016,x22017,x22012,x22018))
% 160.93/160.66 [2202]~E(x22021,x22022)+E(f840(x22023,x22024,x22025,x22026,x22027,x22028,x22021),f840(x22023,x22024,x22025,x22026,x22027,x22028,x22022))
% 160.93/160.66 [2203]~E(x22031,x22032)+E(f624(x22031,x22033,x22034),f624(x22032,x22033,x22034))
% 160.93/160.66 [2204]~E(x22041,x22042)+E(f624(x22043,x22041,x22044),f624(x22043,x22042,x22044))
% 160.93/160.66 [2205]~E(x22051,x22052)+E(f624(x22053,x22054,x22051),f624(x22053,x22054,x22052))
% 160.93/160.66 [2206]~E(x22061,x22062)+E(f446(x22061,x22063),f446(x22062,x22063))
% 160.93/160.66 [2207]~E(x22071,x22072)+E(f446(x22073,x22071),f446(x22073,x22072))
% 160.93/160.66 [2208]~E(x22081,x22082)+E(f296(x22081,x22083,x22084),f296(x22082,x22083,x22084))
% 160.93/160.66 [2209]~E(x22091,x22092)+E(f296(x22093,x22091,x22094),f296(x22093,x22092,x22094))
% 160.93/160.66 [2210]~E(x22101,x22102)+E(f296(x22103,x22104,x22101),f296(x22103,x22104,x22102))
% 160.93/160.66 [2211]~E(x22111,x22112)+E(f207(x22111,x22113,x22114),f207(x22112,x22113,x22114))
% 160.93/160.66 [2212]~E(x22121,x22122)+E(f207(x22123,x22121,x22124),f207(x22123,x22122,x22124))
% 160.93/160.66 [2213]~E(x22131,x22132)+E(f207(x22133,x22134,x22131),f207(x22133,x22134,x22132))
% 160.93/160.66 [2214]~E(x22141,x22142)+E(f711(x22141,x22143,x22144),f711(x22142,x22143,x22144))
% 160.93/160.66 [2215]~E(x22151,x22152)+E(f711(x22153,x22151,x22154),f711(x22153,x22152,x22154))
% 160.93/160.66 [2216]~E(x22161,x22162)+E(f711(x22163,x22164,x22161),f711(x22163,x22164,x22162))
% 160.93/160.66 [2217]~E(x22171,x22172)+E(f734(x22171,x22173),f734(x22172,x22173))
% 160.93/160.66 [2218]~E(x22181,x22182)+E(f734(x22183,x22181),f734(x22183,x22182))
% 160.93/160.66 [2219]~E(x22191,x22192)+E(f441(x22191,x22193,x22194),f441(x22192,x22193,x22194))
% 160.93/160.66 [2220]~E(x22201,x22202)+E(f441(x22203,x22201,x22204),f441(x22203,x22202,x22204))
% 160.93/160.66 [2221]~E(x22211,x22212)+E(f441(x22213,x22214,x22211),f441(x22213,x22214,x22212))
% 160.93/160.66 [2222]~E(x22221,x22222)+E(f340(x22221),f340(x22222))
% 160.93/160.66 [2223]~E(x22231,x22232)+E(f740(x22231,x22233,x22234,x22235),f740(x22232,x22233,x22234,x22235))
% 160.93/160.66 [2224]~E(x22241,x22242)+E(f740(x22243,x22241,x22244,x22245),f740(x22243,x22242,x22244,x22245))
% 160.93/160.66 [2225]~E(x22251,x22252)+E(f740(x22253,x22254,x22251,x22255),f740(x22253,x22254,x22252,x22255))
% 160.93/160.66 [2226]~E(x22261,x22262)+E(f740(x22263,x22264,x22265,x22261),f740(x22263,x22264,x22265,x22262))
% 160.93/160.66 [2227]~E(x22271,x22272)+E(f690(x22271,x22273,x22274),f690(x22272,x22273,x22274))
% 160.93/160.66 [2228]~E(x22281,x22282)+E(f690(x22283,x22281,x22284),f690(x22283,x22282,x22284))
% 160.93/160.66 [2229]~E(x22291,x22292)+E(f690(x22293,x22294,x22291),f690(x22293,x22294,x22292))
% 160.93/160.66 [2230]~E(x22301,x22302)+E(f453(x22301,x22303,x22304),f453(x22302,x22303,x22304))
% 160.93/160.66 [2231]~E(x22311,x22312)+E(f453(x22313,x22311,x22314),f453(x22313,x22312,x22314))
% 160.93/160.66 [2232]~E(x22321,x22322)+E(f453(x22323,x22324,x22321),f453(x22323,x22324,x22322))
% 160.93/160.66 [2233]~E(x22331,x22332)+E(f610(x22331,x22333,x22334,x22335,x22336,x22337),f610(x22332,x22333,x22334,x22335,x22336,x22337))
% 160.93/160.66 [2234]~E(x22341,x22342)+E(f610(x22343,x22341,x22344,x22345,x22346,x22347),f610(x22343,x22342,x22344,x22345,x22346,x22347))
% 160.93/160.66 [2235]~E(x22351,x22352)+E(f610(x22353,x22354,x22351,x22355,x22356,x22357),f610(x22353,x22354,x22352,x22355,x22356,x22357))
% 160.93/160.66 [2236]~E(x22361,x22362)+E(f610(x22363,x22364,x22365,x22361,x22366,x22367),f610(x22363,x22364,x22365,x22362,x22366,x22367))
% 160.93/160.66 [2237]~E(x22371,x22372)+E(f610(x22373,x22374,x22375,x22376,x22371,x22377),f610(x22373,x22374,x22375,x22376,x22372,x22377))
% 160.93/160.66 [2238]~E(x22381,x22382)+E(f610(x22383,x22384,x22385,x22386,x22387,x22381),f610(x22383,x22384,x22385,x22386,x22387,x22382))
% 160.93/160.66 [2239]~E(x22391,x22392)+E(f664(x22391,x22393,x22394,x22395),f664(x22392,x22393,x22394,x22395))
% 160.93/160.66 [2240]~E(x22401,x22402)+E(f664(x22403,x22401,x22404,x22405),f664(x22403,x22402,x22404,x22405))
% 160.93/160.66 [2241]~E(x22411,x22412)+E(f664(x22413,x22414,x22411,x22415),f664(x22413,x22414,x22412,x22415))
% 160.93/160.66 [2242]~E(x22421,x22422)+E(f664(x22423,x22424,x22425,x22421),f664(x22423,x22424,x22425,x22422))
% 160.93/160.66 [2243]~E(x22431,x22432)+E(f244(x22431,x22433,x22434,x22435,x22436),f244(x22432,x22433,x22434,x22435,x22436))
% 160.93/160.66 [2244]~E(x22441,x22442)+E(f244(x22443,x22441,x22444,x22445,x22446),f244(x22443,x22442,x22444,x22445,x22446))
% 160.93/160.66 [2245]~E(x22451,x22452)+E(f244(x22453,x22454,x22451,x22455,x22456),f244(x22453,x22454,x22452,x22455,x22456))
% 160.93/160.66 [2246]~E(x22461,x22462)+E(f244(x22463,x22464,x22465,x22461,x22466),f244(x22463,x22464,x22465,x22462,x22466))
% 160.93/160.66 [2247]~E(x22471,x22472)+E(f244(x22473,x22474,x22475,x22476,x22471),f244(x22473,x22474,x22475,x22476,x22472))
% 160.93/160.66 [2248]~E(x22481,x22482)+E(f553(x22481,x22483,x22484,x22485),f553(x22482,x22483,x22484,x22485))
% 160.93/160.66 [2249]~E(x22491,x22492)+E(f553(x22493,x22491,x22494,x22495),f553(x22493,x22492,x22494,x22495))
% 160.93/160.66 [2250]~E(x22501,x22502)+E(f553(x22503,x22504,x22501,x22505),f553(x22503,x22504,x22502,x22505))
% 160.93/160.66 [2251]~E(x22511,x22512)+E(f553(x22513,x22514,x22515,x22511),f553(x22513,x22514,x22515,x22512))
% 160.93/160.66 [2252]~E(x22521,x22522)+E(f540(x22521,x22523),f540(x22522,x22523))
% 160.93/160.66 [2253]~E(x22531,x22532)+E(f540(x22533,x22531),f540(x22533,x22532))
% 160.93/160.66 [2254]~E(x22541,x22542)+E(f738(x22541,x22543),f738(x22542,x22543))
% 160.93/160.66 [2255]~E(x22551,x22552)+E(f738(x22553,x22551),f738(x22553,x22552))
% 160.93/160.66 [2256]~E(x22561,x22562)+E(f281(x22561,x22563),f281(x22562,x22563))
% 160.93/160.66 [2257]~E(x22571,x22572)+E(f281(x22573,x22571),f281(x22573,x22572))
% 160.93/160.66 [2258]~E(x22581,x22582)+E(f97(x22581,x22583,x22584),f97(x22582,x22583,x22584))
% 160.93/160.66 [2259]~E(x22591,x22592)+E(f97(x22593,x22591,x22594),f97(x22593,x22592,x22594))
% 160.93/160.66 [2260]~E(x22601,x22602)+E(f97(x22603,x22604,x22601),f97(x22603,x22604,x22602))
% 160.93/160.66 [2261]~E(x22611,x22612)+E(f338(x22611,x22613,x22614,x22615),f338(x22612,x22613,x22614,x22615))
% 160.93/160.66 [2262]~E(x22621,x22622)+E(f338(x22623,x22621,x22624,x22625),f338(x22623,x22622,x22624,x22625))
% 160.93/160.66 [2263]~E(x22631,x22632)+E(f338(x22633,x22634,x22631,x22635),f338(x22633,x22634,x22632,x22635))
% 160.93/160.66 [2264]~E(x22641,x22642)+E(f338(x22643,x22644,x22645,x22641),f338(x22643,x22644,x22645,x22642))
% 160.93/160.66 [2265]~E(x22651,x22652)+E(f351(x22651,x22653,x22654),f351(x22652,x22653,x22654))
% 160.93/160.66 [2266]~E(x22661,x22662)+E(f351(x22663,x22661,x22664),f351(x22663,x22662,x22664))
% 160.93/160.66 [2267]~E(x22671,x22672)+E(f351(x22673,x22674,x22671),f351(x22673,x22674,x22672))
% 160.93/160.66 [2268]~E(x22681,x22682)+E(f599(x22681,x22683),f599(x22682,x22683))
% 160.93/160.66 [2269]~E(x22691,x22692)+E(f599(x22693,x22691),f599(x22693,x22692))
% 160.93/160.66 [2270]~E(x22701,x22702)+E(f605(x22701,x22703),f605(x22702,x22703))
% 160.93/160.66 [2271]~E(x22711,x22712)+E(f605(x22713,x22711),f605(x22713,x22712))
% 160.93/160.66 [2272]~E(x22721,x22722)+E(f559(x22721,x22723,x22724,x22725),f559(x22722,x22723,x22724,x22725))
% 160.93/160.66 [2273]~E(x22731,x22732)+E(f559(x22733,x22731,x22734,x22735),f559(x22733,x22732,x22734,x22735))
% 160.93/160.66 [2274]~E(x22741,x22742)+E(f559(x22743,x22744,x22741,x22745),f559(x22743,x22744,x22742,x22745))
% 160.93/160.66 [2275]~E(x22751,x22752)+E(f559(x22753,x22754,x22755,x22751),f559(x22753,x22754,x22755,x22752))
% 160.93/160.66 [2276]~E(x22761,x22762)+E(f438(x22761,x22763,x22764),f438(x22762,x22763,x22764))
% 160.93/160.66 [2277]~E(x22771,x22772)+E(f438(x22773,x22771,x22774),f438(x22773,x22772,x22774))
% 160.93/160.66 [2278]~E(x22781,x22782)+E(f438(x22783,x22784,x22781),f438(x22783,x22784,x22782))
% 160.93/160.66 [2279]~E(x22791,x22792)+E(f642(x22791,x22793,x22794,x22795),f642(x22792,x22793,x22794,x22795))
% 160.93/160.66 [2280]~E(x22801,x22802)+E(f642(x22803,x22801,x22804,x22805),f642(x22803,x22802,x22804,x22805))
% 160.93/160.66 [2281]~E(x22811,x22812)+E(f642(x22813,x22814,x22811,x22815),f642(x22813,x22814,x22812,x22815))
% 160.93/160.66 [2282]~E(x22821,x22822)+E(f642(x22823,x22824,x22825,x22821),f642(x22823,x22824,x22825,x22822))
% 160.93/160.66 [2283]~E(x22831,x22832)+E(f145(x22831,x22833),f145(x22832,x22833))
% 160.93/160.66 [2284]~E(x22841,x22842)+E(f145(x22843,x22841),f145(x22843,x22842))
% 160.93/160.66 [2285]~E(x22851,x22852)+E(f681(x22851,x22853,x22854),f681(x22852,x22853,x22854))
% 160.93/160.66 [2286]~E(x22861,x22862)+E(f681(x22863,x22861,x22864),f681(x22863,x22862,x22864))
% 160.93/160.66 [2287]~E(x22871,x22872)+E(f681(x22873,x22874,x22871),f681(x22873,x22874,x22872))
% 160.93/160.66 [2288]~E(x22881,x22882)+E(f741(x22881,x22883),f741(x22882,x22883))
% 160.93/160.66 [2289]~E(x22891,x22892)+E(f741(x22893,x22891),f741(x22893,x22892))
% 160.93/160.66 [2290]~E(x22901,x22902)+E(f743(x22901,x22903,x22904,x22905,x22906),f743(x22902,x22903,x22904,x22905,x22906))
% 160.93/160.66 [2291]~E(x22911,x22912)+E(f743(x22913,x22911,x22914,x22915,x22916),f743(x22913,x22912,x22914,x22915,x22916))
% 160.93/160.66 [2292]~E(x22921,x22922)+E(f743(x22923,x22924,x22921,x22925,x22926),f743(x22923,x22924,x22922,x22925,x22926))
% 160.93/160.66 [2293]~E(x22931,x22932)+E(f743(x22933,x22934,x22935,x22931,x22936),f743(x22933,x22934,x22935,x22932,x22936))
% 160.93/160.66 [2294]~E(x22941,x22942)+E(f743(x22943,x22944,x22945,x22946,x22941),f743(x22943,x22944,x22945,x22946,x22942))
% 160.93/160.66 [2295]~E(x22951,x22952)+E(f774(x22951,x22953,x22954,x22955,x22956,x22957),f774(x22952,x22953,x22954,x22955,x22956,x22957))
% 160.93/160.66 [2296]~E(x22961,x22962)+E(f774(x22963,x22961,x22964,x22965,x22966,x22967),f774(x22963,x22962,x22964,x22965,x22966,x22967))
% 160.93/160.66 [2297]~E(x22971,x22972)+E(f774(x22973,x22974,x22971,x22975,x22976,x22977),f774(x22973,x22974,x22972,x22975,x22976,x22977))
% 160.93/160.66 [2298]~E(x22981,x22982)+E(f774(x22983,x22984,x22985,x22981,x22986,x22987),f774(x22983,x22984,x22985,x22982,x22986,x22987))
% 160.93/160.66 [2299]~E(x22991,x22992)+E(f774(x22993,x22994,x22995,x22996,x22991,x22997),f774(x22993,x22994,x22995,x22996,x22992,x22997))
% 160.93/160.66 [2300]~E(x23001,x23002)+E(f774(x23003,x23004,x23005,x23006,x23007,x23001),f774(x23003,x23004,x23005,x23006,x23007,x23002))
% 160.93/160.66 [2301]~E(x23011,x23012)+E(f723(x23011,x23013),f723(x23012,x23013))
% 160.93/160.66 [2302]~E(x23021,x23022)+E(f723(x23023,x23021),f723(x23023,x23022))
% 160.93/160.66 [2303]~E(x23031,x23032)+E(f549(x23031,x23033,x23034,x23035),f549(x23032,x23033,x23034,x23035))
% 160.93/160.66 [2304]~E(x23041,x23042)+E(f549(x23043,x23041,x23044,x23045),f549(x23043,x23042,x23044,x23045))
% 160.93/160.66 [2305]~E(x23051,x23052)+E(f549(x23053,x23054,x23051,x23055),f549(x23053,x23054,x23052,x23055))
% 160.93/160.66 [2306]~E(x23061,x23062)+E(f549(x23063,x23064,x23065,x23061),f549(x23063,x23064,x23065,x23062))
% 160.93/160.66 [2307]~E(x23071,x23072)+E(f678(x23071,x23073,x23074,x23075,x23076),f678(x23072,x23073,x23074,x23075,x23076))
% 160.93/160.66 [2308]~E(x23081,x23082)+E(f678(x23083,x23081,x23084,x23085,x23086),f678(x23083,x23082,x23084,x23085,x23086))
% 160.93/160.66 [2309]~E(x23091,x23092)+E(f678(x23093,x23094,x23091,x23095,x23096),f678(x23093,x23094,x23092,x23095,x23096))
% 160.93/160.66 [2310]~E(x23101,x23102)+E(f678(x23103,x23104,x23105,x23101,x23106),f678(x23103,x23104,x23105,x23102,x23106))
% 160.93/160.66 [2311]~E(x23111,x23112)+E(f678(x23113,x23114,x23115,x23116,x23111),f678(x23113,x23114,x23115,x23116,x23112))
% 160.93/160.66 [2312]~E(x23121,x23122)+E(f726(x23121,x23123,x23124,x23125),f726(x23122,x23123,x23124,x23125))
% 160.93/160.66 [2313]~E(x23131,x23132)+E(f726(x23133,x23131,x23134,x23135),f726(x23133,x23132,x23134,x23135))
% 160.93/160.66 [2314]~E(x23141,x23142)+E(f726(x23143,x23144,x23141,x23145),f726(x23143,x23144,x23142,x23145))
% 160.93/160.66 [2315]~E(x23151,x23152)+E(f726(x23153,x23154,x23155,x23151),f726(x23153,x23154,x23155,x23152))
% 160.93/160.66 [2316]~E(x23161,x23162)+E(f846(x23161,x23163),f846(x23162,x23163))
% 160.93/160.66 [2317]~E(x23171,x23172)+E(f846(x23173,x23171),f846(x23173,x23172))
% 160.93/160.66 [2318]~E(x23181,x23182)+E(f623(x23181,x23183,x23184,x23185,x23186),f623(x23182,x23183,x23184,x23185,x23186))
% 160.93/160.66 [2319]~E(x23191,x23192)+E(f623(x23193,x23191,x23194,x23195,x23196),f623(x23193,x23192,x23194,x23195,x23196))
% 160.93/160.66 [2320]~E(x23201,x23202)+E(f623(x23203,x23204,x23201,x23205,x23206),f623(x23203,x23204,x23202,x23205,x23206))
% 160.93/160.66 [2321]~E(x23211,x23212)+E(f623(x23213,x23214,x23215,x23211,x23216),f623(x23213,x23214,x23215,x23212,x23216))
% 160.93/160.66 [2322]~E(x23221,x23222)+E(f623(x23223,x23224,x23225,x23226,x23221),f623(x23223,x23224,x23225,x23226,x23222))
% 160.93/160.66 [2323]~E(x23231,x23232)+E(f21(x23231,x23233),f21(x23232,x23233))
% 160.93/160.66 [2324]~E(x23241,x23242)+E(f21(x23243,x23241),f21(x23243,x23242))
% 160.93/160.66 [2325]~E(x23251,x23252)+E(f638(x23251,x23253,x23254),f638(x23252,x23253,x23254))
% 160.93/160.66 [2326]~E(x23261,x23262)+E(f638(x23263,x23261,x23264),f638(x23263,x23262,x23264))
% 160.93/160.66 [2327]~E(x23271,x23272)+E(f638(x23273,x23274,x23271),f638(x23273,x23274,x23272))
% 160.93/160.66 [2328]~E(x23281,x23282)+E(f382(x23281,x23283,x23284,x23285),f382(x23282,x23283,x23284,x23285))
% 160.93/160.66 [2329]~E(x23291,x23292)+E(f382(x23293,x23291,x23294,x23295),f382(x23293,x23292,x23294,x23295))
% 160.93/160.66 [2330]~E(x23301,x23302)+E(f382(x23303,x23304,x23301,x23305),f382(x23303,x23304,x23302,x23305))
% 160.93/160.66 [2331]~E(x23311,x23312)+E(f382(x23313,x23314,x23315,x23311),f382(x23313,x23314,x23315,x23312))
% 160.93/160.66 [2332]~E(x23321,x23322)+E(f762(x23321,x23323,x23324),f762(x23322,x23323,x23324))
% 160.93/160.66 [2333]~E(x23331,x23332)+E(f762(x23333,x23331,x23334),f762(x23333,x23332,x23334))
% 160.93/160.66 [2334]~E(x23341,x23342)+E(f762(x23343,x23344,x23341),f762(x23343,x23344,x23342))
% 160.93/160.66 [2335]~E(x23351,x23352)+E(f555(x23351,x23353,x23354,x23355),f555(x23352,x23353,x23354,x23355))
% 160.93/160.66 [2336]~E(x23361,x23362)+E(f555(x23363,x23361,x23364,x23365),f555(x23363,x23362,x23364,x23365))
% 160.93/160.66 [2337]~E(x23371,x23372)+E(f555(x23373,x23374,x23371,x23375),f555(x23373,x23374,x23372,x23375))
% 160.93/160.66 [2338]~E(x23381,x23382)+E(f555(x23383,x23384,x23385,x23381),f555(x23383,x23384,x23385,x23382))
% 160.93/160.66 [2339]~E(x23391,x23392)+E(f662(x23391,x23393,x23394,x23395),f662(x23392,x23393,x23394,x23395))
% 160.93/160.66 [2340]~E(x23401,x23402)+E(f662(x23403,x23401,x23404,x23405),f662(x23403,x23402,x23404,x23405))
% 160.93/160.66 [2341]~E(x23411,x23412)+E(f662(x23413,x23414,x23411,x23415),f662(x23413,x23414,x23412,x23415))
% 160.93/160.66 [2342]~E(x23421,x23422)+E(f662(x23423,x23424,x23425,x23421),f662(x23423,x23424,x23425,x23422))
% 160.93/160.66 [2343]~E(x23431,x23432)+E(f663(x23431,x23433,x23434,x23435),f663(x23432,x23433,x23434,x23435))
% 160.93/160.66 [2344]~E(x23441,x23442)+E(f663(x23443,x23441,x23444,x23445),f663(x23443,x23442,x23444,x23445))
% 160.93/160.66 [2345]~E(x23451,x23452)+E(f663(x23453,x23454,x23451,x23455),f663(x23453,x23454,x23452,x23455))
% 160.93/160.66 [2346]~E(x23461,x23462)+E(f663(x23463,x23464,x23465,x23461),f663(x23463,x23464,x23465,x23462))
% 160.93/160.66 [2347]~E(x23471,x23472)+E(f339(x23471),f339(x23472))
% 160.93/160.66 [2348]~E(x23481,x23482)+E(f809(x23481,x23483,x23484),f809(x23482,x23483,x23484))
% 160.93/160.66 [2349]~E(x23491,x23492)+E(f809(x23493,x23491,x23494),f809(x23493,x23492,x23494))
% 160.93/160.66 [2350]~E(x23501,x23502)+E(f809(x23503,x23504,x23501),f809(x23503,x23504,x23502))
% 160.93/160.66 [2351]~E(x23511,x23512)+E(f463(x23511,x23513,x23514,x23515),f463(x23512,x23513,x23514,x23515))
% 160.93/160.66 [2352]~E(x23521,x23522)+E(f463(x23523,x23521,x23524,x23525),f463(x23523,x23522,x23524,x23525))
% 160.93/160.66 [2353]~E(x23531,x23532)+E(f463(x23533,x23534,x23531,x23535),f463(x23533,x23534,x23532,x23535))
% 160.93/160.66 [2354]~E(x23541,x23542)+E(f463(x23543,x23544,x23545,x23541),f463(x23543,x23544,x23545,x23542))
% 160.93/160.66 [2355]~E(x23551,x23552)+E(f860(x23551,x23553,x23554,x23555,x23556,x23557,x23558),f860(x23552,x23553,x23554,x23555,x23556,x23557,x23558))
% 160.93/160.66 [2356]~E(x23561,x23562)+E(f860(x23563,x23561,x23564,x23565,x23566,x23567,x23568),f860(x23563,x23562,x23564,x23565,x23566,x23567,x23568))
% 160.93/160.66 [2357]~E(x23571,x23572)+E(f860(x23573,x23574,x23571,x23575,x23576,x23577,x23578),f860(x23573,x23574,x23572,x23575,x23576,x23577,x23578))
% 160.93/160.66 [2358]~E(x23581,x23582)+E(f860(x23583,x23584,x23585,x23581,x23586,x23587,x23588),f860(x23583,x23584,x23585,x23582,x23586,x23587,x23588))
% 160.93/160.66 [2359]~E(x23591,x23592)+E(f860(x23593,x23594,x23595,x23596,x23591,x23597,x23598),f860(x23593,x23594,x23595,x23596,x23592,x23597,x23598))
% 160.93/160.66 [2360]~E(x23601,x23602)+E(f860(x23603,x23604,x23605,x23606,x23607,x23601,x23608),f860(x23603,x23604,x23605,x23606,x23607,x23602,x23608))
% 160.93/160.66 [2361]~E(x23611,x23612)+E(f860(x23613,x23614,x23615,x23616,x23617,x23618,x23611),f860(x23613,x23614,x23615,x23616,x23617,x23618,x23612))
% 160.93/160.66 [2362]~E(x23621,x23622)+E(f853(x23621,x23623,x23624,x23625,x23626),f853(x23622,x23623,x23624,x23625,x23626))
% 160.93/160.66 [2363]~E(x23631,x23632)+E(f853(x23633,x23631,x23634,x23635,x23636),f853(x23633,x23632,x23634,x23635,x23636))
% 160.93/160.66 [2364]~E(x23641,x23642)+E(f853(x23643,x23644,x23641,x23645,x23646),f853(x23643,x23644,x23642,x23645,x23646))
% 160.93/160.66 [2365]~E(x23651,x23652)+E(f853(x23653,x23654,x23655,x23651,x23656),f853(x23653,x23654,x23655,x23652,x23656))
% 160.93/160.66 [2366]~E(x23661,x23662)+E(f853(x23663,x23664,x23665,x23666,x23661),f853(x23663,x23664,x23665,x23666,x23662))
% 160.93/160.66 [2367]~E(x23671,x23672)+E(f356(x23671,x23673,x23674),f356(x23672,x23673,x23674))
% 160.93/160.66 [2368]~E(x23681,x23682)+E(f356(x23683,x23681,x23684),f356(x23683,x23682,x23684))
% 160.93/160.66 [2369]~E(x23691,x23692)+E(f356(x23693,x23694,x23691),f356(x23693,x23694,x23692))
% 160.93/160.66 [2370]~E(x23701,x23702)+E(f519(x23701,x23703,x23704,x23705),f519(x23702,x23703,x23704,x23705))
% 160.93/160.66 [2371]~E(x23711,x23712)+E(f519(x23713,x23711,x23714,x23715),f519(x23713,x23712,x23714,x23715))
% 160.93/160.66 [2372]~E(x23721,x23722)+E(f519(x23723,x23724,x23721,x23725),f519(x23723,x23724,x23722,x23725))
% 160.93/160.66 [2373]~E(x23731,x23732)+E(f519(x23733,x23734,x23735,x23731),f519(x23733,x23734,x23735,x23732))
% 160.93/160.66 [2374]~E(x23741,x23742)+E(f872(x23741,x23743),f872(x23742,x23743))
% 160.93/160.66 [2375]~E(x23751,x23752)+E(f872(x23753,x23751),f872(x23753,x23752))
% 160.93/160.66 [2376]~E(x23761,x23762)+E(f719(x23761,x23763,x23764,x23765,x23766),f719(x23762,x23763,x23764,x23765,x23766))
% 160.93/160.66 [2377]~E(x23771,x23772)+E(f719(x23773,x23771,x23774,x23775,x23776),f719(x23773,x23772,x23774,x23775,x23776))
% 160.93/160.66 [2378]~E(x23781,x23782)+E(f719(x23783,x23784,x23781,x23785,x23786),f719(x23783,x23784,x23782,x23785,x23786))
% 160.93/160.66 [2379]~E(x23791,x23792)+E(f719(x23793,x23794,x23795,x23791,x23796),f719(x23793,x23794,x23795,x23792,x23796))
% 160.93/160.66 [2380]~E(x23801,x23802)+E(f719(x23803,x23804,x23805,x23806,x23801),f719(x23803,x23804,x23805,x23806,x23802))
% 160.93/160.66 [2381]~E(x23811,x23812)+E(f564(x23811,x23813),f564(x23812,x23813))
% 160.93/160.66 [2382]~E(x23821,x23822)+E(f564(x23823,x23821),f564(x23823,x23822))
% 160.93/160.66 [2383]~E(x23831,x23832)+E(f220(x23831,x23833,x23834,x23835),f220(x23832,x23833,x23834,x23835))
% 160.93/160.66 [2384]~E(x23841,x23842)+E(f220(x23843,x23841,x23844,x23845),f220(x23843,x23842,x23844,x23845))
% 160.93/160.66 [2385]~E(x23851,x23852)+E(f220(x23853,x23854,x23851,x23855),f220(x23853,x23854,x23852,x23855))
% 160.93/160.66 [2386]~E(x23861,x23862)+E(f220(x23863,x23864,x23865,x23861),f220(x23863,x23864,x23865,x23862))
% 160.93/160.66 [2387]~E(x23871,x23872)+E(f794(x23871,x23873,x23874,x23875,x23876,x23877,x23878),f794(x23872,x23873,x23874,x23875,x23876,x23877,x23878))
% 160.93/160.66 [2388]~E(x23881,x23882)+E(f794(x23883,x23881,x23884,x23885,x23886,x23887,x23888),f794(x23883,x23882,x23884,x23885,x23886,x23887,x23888))
% 160.93/160.66 [2389]~E(x23891,x23892)+E(f794(x23893,x23894,x23891,x23895,x23896,x23897,x23898),f794(x23893,x23894,x23892,x23895,x23896,x23897,x23898))
% 160.93/160.66 [2390]~E(x23901,x23902)+E(f794(x23903,x23904,x23905,x23901,x23906,x23907,x23908),f794(x23903,x23904,x23905,x23902,x23906,x23907,x23908))
% 160.93/160.66 [2391]~E(x23911,x23912)+E(f794(x23913,x23914,x23915,x23916,x23911,x23917,x23918),f794(x23913,x23914,x23915,x23916,x23912,x23917,x23918))
% 160.93/160.66 [2392]~E(x23921,x23922)+E(f794(x23923,x23924,x23925,x23926,x23927,x23921,x23928),f794(x23923,x23924,x23925,x23926,x23927,x23922,x23928))
% 160.93/160.66 [2393]~E(x23931,x23932)+E(f794(x23933,x23934,x23935,x23936,x23937,x23938,x23931),f794(x23933,x23934,x23935,x23936,x23937,x23938,x23932))
% 160.93/160.66 [2394]~E(x23941,x23942)+E(f593(x23941,x23943,x23944,x23945,x23946,x23947),f593(x23942,x23943,x23944,x23945,x23946,x23947))
% 160.93/160.66 [2395]~E(x23951,x23952)+E(f593(x23953,x23951,x23954,x23955,x23956,x23957),f593(x23953,x23952,x23954,x23955,x23956,x23957))
% 160.93/160.66 [2396]~E(x23961,x23962)+E(f593(x23963,x23964,x23961,x23965,x23966,x23967),f593(x23963,x23964,x23962,x23965,x23966,x23967))
% 160.93/160.66 [2397]~E(x23971,x23972)+E(f593(x23973,x23974,x23975,x23971,x23976,x23977),f593(x23973,x23974,x23975,x23972,x23976,x23977))
% 160.93/160.66 [2398]~E(x23981,x23982)+E(f593(x23983,x23984,x23985,x23986,x23981,x23987),f593(x23983,x23984,x23985,x23986,x23982,x23987))
% 160.93/160.66 [2399]~E(x23991,x23992)+E(f593(x23993,x23994,x23995,x23996,x23997,x23991),f593(x23993,x23994,x23995,x23996,x23997,x23992))
% 160.93/160.66 [2400]~E(x24001,x24002)+E(f830(x24001,x24003,x24004,x24005,x24006,x24007),f830(x24002,x24003,x24004,x24005,x24006,x24007))
% 160.93/160.66 [2401]~E(x24011,x24012)+E(f830(x24013,x24011,x24014,x24015,x24016,x24017),f830(x24013,x24012,x24014,x24015,x24016,x24017))
% 160.93/160.66 [2402]~E(x24021,x24022)+E(f830(x24023,x24024,x24021,x24025,x24026,x24027),f830(x24023,x24024,x24022,x24025,x24026,x24027))
% 160.93/160.66 [2403]~E(x24031,x24032)+E(f830(x24033,x24034,x24035,x24031,x24036,x24037),f830(x24033,x24034,x24035,x24032,x24036,x24037))
% 160.93/160.66 [2404]~E(x24041,x24042)+E(f830(x24043,x24044,x24045,x24046,x24041,x24047),f830(x24043,x24044,x24045,x24046,x24042,x24047))
% 160.93/160.66 [2405]~E(x24051,x24052)+E(f830(x24053,x24054,x24055,x24056,x24057,x24051),f830(x24053,x24054,x24055,x24056,x24057,x24052))
% 160.93/160.66 [2406]~E(x24061,x24062)+E(f602(x24061,x24063,x24064),f602(x24062,x24063,x24064))
% 160.93/160.66 [2407]~E(x24071,x24072)+E(f602(x24073,x24071,x24074),f602(x24073,x24072,x24074))
% 160.93/160.66 [2408]~E(x24081,x24082)+E(f602(x24083,x24084,x24081),f602(x24083,x24084,x24082))
% 160.93/160.66 [2409]~E(x24091,x24092)+E(f804(x24091,x24093,x24094),f804(x24092,x24093,x24094))
% 160.93/160.66 [2410]~E(x24101,x24102)+E(f804(x24103,x24101,x24104),f804(x24103,x24102,x24104))
% 160.93/160.66 [2411]~E(x24111,x24112)+E(f804(x24113,x24114,x24111),f804(x24113,x24114,x24112))
% 160.93/160.66 [2412]~E(x24121,x24122)+E(f491(x24121,x24123,x24124,x24125,x24126),f491(x24122,x24123,x24124,x24125,x24126))
% 160.93/160.66 [2413]~E(x24131,x24132)+E(f491(x24133,x24131,x24134,x24135,x24136),f491(x24133,x24132,x24134,x24135,x24136))
% 160.93/160.66 [2414]~E(x24141,x24142)+E(f491(x24143,x24144,x24141,x24145,x24146),f491(x24143,x24144,x24142,x24145,x24146))
% 160.93/160.66 [2415]~E(x24151,x24152)+E(f491(x24153,x24154,x24155,x24151,x24156),f491(x24153,x24154,x24155,x24152,x24156))
% 160.93/160.66 [2416]~E(x24161,x24162)+E(f491(x24163,x24164,x24165,x24166,x24161),f491(x24163,x24164,x24165,x24166,x24162))
% 160.93/160.66 [2417]~E(x24171,x24172)+E(f408(x24171,x24173,x24174,x24175,x24176),f408(x24172,x24173,x24174,x24175,x24176))
% 160.93/160.66 [2418]~E(x24181,x24182)+E(f408(x24183,x24181,x24184,x24185,x24186),f408(x24183,x24182,x24184,x24185,x24186))
% 160.93/160.66 [2419]~E(x24191,x24192)+E(f408(x24193,x24194,x24191,x24195,x24196),f408(x24193,x24194,x24192,x24195,x24196))
% 160.93/160.66 [2420]~E(x24201,x24202)+E(f408(x24203,x24204,x24205,x24201,x24206),f408(x24203,x24204,x24205,x24202,x24206))
% 160.93/160.66 [2421]~E(x24211,x24212)+E(f408(x24213,x24214,x24215,x24216,x24211),f408(x24213,x24214,x24215,x24216,x24212))
% 160.93/160.66 [2422]~E(x24221,x24222)+E(f276(x24221,x24223,x24224,x24225,x24226),f276(x24222,x24223,x24224,x24225,x24226))
% 160.93/160.66 [2423]~E(x24231,x24232)+E(f276(x24233,x24231,x24234,x24235,x24236),f276(x24233,x24232,x24234,x24235,x24236))
% 160.93/160.66 [2424]~E(x24241,x24242)+E(f276(x24243,x24244,x24241,x24245,x24246),f276(x24243,x24244,x24242,x24245,x24246))
% 160.93/160.66 [2425]~E(x24251,x24252)+E(f276(x24253,x24254,x24255,x24251,x24256),f276(x24253,x24254,x24255,x24252,x24256))
% 160.93/160.66 [2426]~E(x24261,x24262)+E(f276(x24263,x24264,x24265,x24266,x24261),f276(x24263,x24264,x24265,x24266,x24262))
% 160.93/160.66 [2427]~E(x24271,x24272)+E(f569(x24271,x24273,x24274,x24275),f569(x24272,x24273,x24274,x24275))
% 160.93/160.66 [2428]~E(x24281,x24282)+E(f569(x24283,x24281,x24284,x24285),f569(x24283,x24282,x24284,x24285))
% 160.93/160.66 [2429]~E(x24291,x24292)+E(f569(x24293,x24294,x24291,x24295),f569(x24293,x24294,x24292,x24295))
% 160.93/160.66 [2430]~E(x24301,x24302)+E(f569(x24303,x24304,x24305,x24301),f569(x24303,x24304,x24305,x24302))
% 160.93/160.66 [2431]~E(x24311,x24312)+E(f706(x24311,x24313,x24314,x24315),f706(x24312,x24313,x24314,x24315))
% 160.93/160.66 [2432]~E(x24321,x24322)+E(f706(x24323,x24321,x24324,x24325),f706(x24323,x24322,x24324,x24325))
% 160.93/160.66 [2433]~E(x24331,x24332)+E(f706(x24333,x24334,x24331,x24335),f706(x24333,x24334,x24332,x24335))
% 160.93/160.66 [2434]~E(x24341,x24342)+E(f706(x24343,x24344,x24345,x24341),f706(x24343,x24344,x24345,x24342))
% 160.93/160.66 [2435]~E(x24351,x24352)+E(f373(x24351,x24353,x24354),f373(x24352,x24353,x24354))
% 160.93/160.66 [2436]~E(x24361,x24362)+E(f373(x24363,x24361,x24364),f373(x24363,x24362,x24364))
% 160.93/160.66 [2437]~E(x24371,x24372)+E(f373(x24373,x24374,x24371),f373(x24373,x24374,x24372))
% 160.93/160.66 [2438]~E(x24381,x24382)+E(f854(x24381,x24383,x24384,x24385,x24386),f854(x24382,x24383,x24384,x24385,x24386))
% 160.93/160.66 [2439]~E(x24391,x24392)+E(f854(x24393,x24391,x24394,x24395,x24396),f854(x24393,x24392,x24394,x24395,x24396))
% 160.93/160.66 [2440]~E(x24401,x24402)+E(f854(x24403,x24404,x24401,x24405,x24406),f854(x24403,x24404,x24402,x24405,x24406))
% 160.93/160.66 [2441]~E(x24411,x24412)+E(f854(x24413,x24414,x24415,x24411,x24416),f854(x24413,x24414,x24415,x24412,x24416))
% 160.93/160.66 [2442]~E(x24421,x24422)+E(f854(x24423,x24424,x24425,x24426,x24421),f854(x24423,x24424,x24425,x24426,x24422))
% 160.93/160.66 [2443]~E(x24431,x24432)+E(f717(x24431,x24433,x24434,x24435,x24436),f717(x24432,x24433,x24434,x24435,x24436))
% 160.93/160.66 [2444]~E(x24441,x24442)+E(f717(x24443,x24441,x24444,x24445,x24446),f717(x24443,x24442,x24444,x24445,x24446))
% 160.93/160.66 [2445]~E(x24451,x24452)+E(f717(x24453,x24454,x24451,x24455,x24456),f717(x24453,x24454,x24452,x24455,x24456))
% 160.93/160.66 [2446]~E(x24461,x24462)+E(f717(x24463,x24464,x24465,x24461,x24466),f717(x24463,x24464,x24465,x24462,x24466))
% 160.93/160.66 [2447]~E(x24471,x24472)+E(f717(x24473,x24474,x24475,x24476,x24471),f717(x24473,x24474,x24475,x24476,x24472))
% 160.93/160.66 [2448]~E(x24481,x24482)+E(f223(x24481,x24483,x24484,x24485),f223(x24482,x24483,x24484,x24485))
% 160.93/160.66 [2449]~E(x24491,x24492)+E(f223(x24493,x24491,x24494,x24495),f223(x24493,x24492,x24494,x24495))
% 160.93/160.66 [2450]~E(x24501,x24502)+E(f223(x24503,x24504,x24501,x24505),f223(x24503,x24504,x24502,x24505))
% 160.93/160.66 [2451]~E(x24511,x24512)+E(f223(x24513,x24514,x24515,x24511),f223(x24513,x24514,x24515,x24512))
% 160.93/160.66 [2452]~E(x24521,x24522)+E(f676(x24521,x24523,x24524,x24525,x24526),f676(x24522,x24523,x24524,x24525,x24526))
% 160.93/160.66 [2453]~E(x24531,x24532)+E(f676(x24533,x24531,x24534,x24535,x24536),f676(x24533,x24532,x24534,x24535,x24536))
% 160.93/160.66 [2454]~E(x24541,x24542)+E(f676(x24543,x24544,x24541,x24545,x24546),f676(x24543,x24544,x24542,x24545,x24546))
% 160.93/160.66 [2455]~E(x24551,x24552)+E(f676(x24553,x24554,x24555,x24551,x24556),f676(x24553,x24554,x24555,x24552,x24556))
% 160.93/160.66 [2456]~E(x24561,x24562)+E(f676(x24563,x24564,x24565,x24566,x24561),f676(x24563,x24564,x24565,x24566,x24562))
% 160.93/160.66 [2457]~E(x24571,x24572)+E(f595(x24571),f595(x24572))
% 160.93/160.66 [2458]~E(x24581,x24582)+E(f536(x24581,x24583,x24584,x24585,x24586),f536(x24582,x24583,x24584,x24585,x24586))
% 160.93/160.66 [2459]~E(x24591,x24592)+E(f536(x24593,x24591,x24594,x24595,x24596),f536(x24593,x24592,x24594,x24595,x24596))
% 160.93/160.66 [2460]~E(x24601,x24602)+E(f536(x24603,x24604,x24601,x24605,x24606),f536(x24603,x24604,x24602,x24605,x24606))
% 160.93/160.66 [2461]~E(x24611,x24612)+E(f536(x24613,x24614,x24615,x24611,x24616),f536(x24613,x24614,x24615,x24612,x24616))
% 160.93/160.66 [2462]~E(x24621,x24622)+E(f536(x24623,x24624,x24625,x24626,x24621),f536(x24623,x24624,x24625,x24626,x24622))
% 160.93/160.66 [2463]~E(x24631,x24632)+E(f424(x24631,x24633,x24634),f424(x24632,x24633,x24634))
% 160.93/160.66 [2464]~E(x24641,x24642)+E(f424(x24643,x24641,x24644),f424(x24643,x24642,x24644))
% 160.93/160.66 [2465]~E(x24651,x24652)+E(f424(x24653,x24654,x24651),f424(x24653,x24654,x24652))
% 160.93/160.66 [2466]~E(x24661,x24662)+E(f132(x24661,x24663,x24664,x24665,x24666),f132(x24662,x24663,x24664,x24665,x24666))
% 160.93/160.66 [2467]~E(x24671,x24672)+E(f132(x24673,x24671,x24674,x24675,x24676),f132(x24673,x24672,x24674,x24675,x24676))
% 160.93/160.66 [2468]~E(x24681,x24682)+E(f132(x24683,x24684,x24681,x24685,x24686),f132(x24683,x24684,x24682,x24685,x24686))
% 160.93/160.66 [2469]~E(x24691,x24692)+E(f132(x24693,x24694,x24695,x24691,x24696),f132(x24693,x24694,x24695,x24692,x24696))
% 160.93/160.66 [2470]~E(x24701,x24702)+E(f132(x24703,x24704,x24705,x24706,x24701),f132(x24703,x24704,x24705,x24706,x24702))
% 160.93/160.66 [2471]~E(x24711,x24712)+E(f614(x24711,x24713),f614(x24712,x24713))
% 160.93/160.66 [2472]~E(x24721,x24722)+E(f614(x24723,x24721),f614(x24723,x24722))
% 160.93/160.66 [2473]~E(x24731,x24732)+E(f802(x24731,x24733,x24734),f802(x24732,x24733,x24734))
% 160.93/160.66 [2474]~E(x24741,x24742)+E(f802(x24743,x24741,x24744),f802(x24743,x24742,x24744))
% 160.93/160.66 [2475]~E(x24751,x24752)+E(f802(x24753,x24754,x24751),f802(x24753,x24754,x24752))
% 160.93/160.66 [2476]~E(x24761,x24762)+E(f781(x24761,x24763,x24764,x24765,x24766,x24767,x24768),f781(x24762,x24763,x24764,x24765,x24766,x24767,x24768))
% 160.93/160.66 [2477]~E(x24771,x24772)+E(f781(x24773,x24771,x24774,x24775,x24776,x24777,x24778),f781(x24773,x24772,x24774,x24775,x24776,x24777,x24778))
% 160.93/160.66 [2478]~E(x24781,x24782)+E(f781(x24783,x24784,x24781,x24785,x24786,x24787,x24788),f781(x24783,x24784,x24782,x24785,x24786,x24787,x24788))
% 160.93/160.66 [2479]~E(x24791,x24792)+E(f781(x24793,x24794,x24795,x24791,x24796,x24797,x24798),f781(x24793,x24794,x24795,x24792,x24796,x24797,x24798))
% 160.93/160.66 [2480]~E(x24801,x24802)+E(f781(x24803,x24804,x24805,x24806,x24801,x24807,x24808),f781(x24803,x24804,x24805,x24806,x24802,x24807,x24808))
% 160.93/160.66 [2481]~E(x24811,x24812)+E(f781(x24813,x24814,x24815,x24816,x24817,x24811,x24818),f781(x24813,x24814,x24815,x24816,x24817,x24812,x24818))
% 160.93/160.66 [2482]~E(x24821,x24822)+E(f781(x24823,x24824,x24825,x24826,x24827,x24828,x24821),f781(x24823,x24824,x24825,x24826,x24827,x24828,x24822))
% 160.93/160.66 [2483]~E(x24831,x24832)+E(f375(x24831,x24833,x24834,x24835),f375(x24832,x24833,x24834,x24835))
% 160.93/160.66 [2484]~E(x24841,x24842)+E(f375(x24843,x24841,x24844,x24845),f375(x24843,x24842,x24844,x24845))
% 160.93/160.66 [2485]~E(x24851,x24852)+E(f375(x24853,x24854,x24851,x24855),f375(x24853,x24854,x24852,x24855))
% 160.93/160.66 [2486]~E(x24861,x24862)+E(f375(x24863,x24864,x24865,x24861),f375(x24863,x24864,x24865,x24862))
% 160.93/160.66 [2487]~E(x24871,x24872)+E(f364(x24871),f364(x24872))
% 160.93/160.66 [2488]~E(x24881,x24882)+E(f488(x24881,x24883,x24884),f488(x24882,x24883,x24884))
% 160.93/160.66 [2489]~E(x24891,x24892)+E(f488(x24893,x24891,x24894),f488(x24893,x24892,x24894))
% 160.93/160.66 [2490]~E(x24901,x24902)+E(f488(x24903,x24904,x24901),f488(x24903,x24904,x24902))
% 160.93/160.66 [2491]~E(x24911,x24912)+E(f420(x24911,x24913,x24914,x24915,x24916),f420(x24912,x24913,x24914,x24915,x24916))
% 160.93/160.66 [2492]~E(x24921,x24922)+E(f420(x24923,x24921,x24924,x24925,x24926),f420(x24923,x24922,x24924,x24925,x24926))
% 160.93/160.66 [2493]~E(x24931,x24932)+E(f420(x24933,x24934,x24931,x24935,x24936),f420(x24933,x24934,x24932,x24935,x24936))
% 160.93/160.66 [2494]~E(x24941,x24942)+E(f420(x24943,x24944,x24945,x24941,x24946),f420(x24943,x24944,x24945,x24942,x24946))
% 160.93/160.66 [2495]~E(x24951,x24952)+E(f420(x24953,x24954,x24955,x24956,x24951),f420(x24953,x24954,x24955,x24956,x24952))
% 160.93/160.66 [2496]~E(x24961,x24962)+E(f299(x24961,x24963,x24964,x24965,x24966),f299(x24962,x24963,x24964,x24965,x24966))
% 160.93/160.66 [2497]~E(x24971,x24972)+E(f299(x24973,x24971,x24974,x24975,x24976),f299(x24973,x24972,x24974,x24975,x24976))
% 160.93/160.66 [2498]~E(x24981,x24982)+E(f299(x24983,x24984,x24981,x24985,x24986),f299(x24983,x24984,x24982,x24985,x24986))
% 160.93/160.66 [2499]~E(x24991,x24992)+E(f299(x24993,x24994,x24995,x24991,x24996),f299(x24993,x24994,x24995,x24992,x24996))
% 160.93/160.66 [2500]~E(x25001,x25002)+E(f299(x25003,x25004,x25005,x25006,x25001),f299(x25003,x25004,x25005,x25006,x25002))
% 160.93/160.66 [2501]~E(x25011,x25012)+E(f492(x25011,x25013,x25014,x25015,x25016),f492(x25012,x25013,x25014,x25015,x25016))
% 160.93/160.66 [2502]~E(x25021,x25022)+E(f492(x25023,x25021,x25024,x25025,x25026),f492(x25023,x25022,x25024,x25025,x25026))
% 160.93/160.66 [2503]~E(x25031,x25032)+E(f492(x25033,x25034,x25031,x25035,x25036),f492(x25033,x25034,x25032,x25035,x25036))
% 160.93/160.66 [2504]~E(x25041,x25042)+E(f492(x25043,x25044,x25045,x25041,x25046),f492(x25043,x25044,x25045,x25042,x25046))
% 160.93/160.66 [2505]~E(x25051,x25052)+E(f492(x25053,x25054,x25055,x25056,x25051),f492(x25053,x25054,x25055,x25056,x25052))
% 160.93/160.66 [2506]~E(x25061,x25062)+E(f208(x25061,x25063,x25064,x25065),f208(x25062,x25063,x25064,x25065))
% 160.93/160.66 [2507]~E(x25071,x25072)+E(f208(x25073,x25071,x25074,x25075),f208(x25073,x25072,x25074,x25075))
% 160.93/160.66 [2508]~E(x25081,x25082)+E(f208(x25083,x25084,x25081,x25085),f208(x25083,x25084,x25082,x25085))
% 160.93/160.66 [2509]~E(x25091,x25092)+E(f208(x25093,x25094,x25095,x25091),f208(x25093,x25094,x25095,x25092))
% 160.93/160.66 [2510]~E(x25101,x25102)+E(f454(x25101,x25103,x25104),f454(x25102,x25103,x25104))
% 160.93/160.66 [2511]~E(x25111,x25112)+E(f454(x25113,x25111,x25114),f454(x25113,x25112,x25114))
% 160.93/160.66 [2512]~E(x25121,x25122)+E(f454(x25123,x25124,x25121),f454(x25123,x25124,x25122))
% 160.93/160.66 [2513]~E(x25131,x25132)+E(f205(x25131,x25133,x25134,x25135),f205(x25132,x25133,x25134,x25135))
% 160.93/160.66 [2514]~E(x25141,x25142)+E(f205(x25143,x25141,x25144,x25145),f205(x25143,x25142,x25144,x25145))
% 160.93/160.66 [2515]~E(x25151,x25152)+E(f205(x25153,x25154,x25151,x25155),f205(x25153,x25154,x25152,x25155))
% 160.93/160.66 [2516]~E(x25161,x25162)+E(f205(x25163,x25164,x25165,x25161),f205(x25163,x25164,x25165,x25162))
% 160.93/160.66 [2517]~E(x25171,x25172)+E(f861(x25171,x25173),f861(x25172,x25173))
% 160.93/160.66 [2518]~E(x25181,x25182)+E(f861(x25183,x25181),f861(x25183,x25182))
% 160.93/160.66 [2519]~E(x25191,x25192)+E(f579(x25191,x25193,x25194,x25195),f579(x25192,x25193,x25194,x25195))
% 160.93/160.66 [2520]~E(x25201,x25202)+E(f579(x25203,x25201,x25204,x25205),f579(x25203,x25202,x25204,x25205))
% 160.93/160.66 [2521]~E(x25211,x25212)+E(f579(x25213,x25214,x25211,x25215),f579(x25213,x25214,x25212,x25215))
% 160.93/160.66 [2522]~E(x25221,x25222)+E(f579(x25223,x25224,x25225,x25221),f579(x25223,x25224,x25225,x25222))
% 160.93/160.66 [2523]~E(x25231,x25232)+E(f548(x25231,x25233,x25234,x25235),f548(x25232,x25233,x25234,x25235))
% 160.93/160.66 [2524]~E(x25241,x25242)+E(f548(x25243,x25241,x25244,x25245),f548(x25243,x25242,x25244,x25245))
% 160.93/160.66 [2525]~E(x25251,x25252)+E(f548(x25253,x25254,x25251,x25255),f548(x25253,x25254,x25252,x25255))
% 160.93/160.66 [2526]~E(x25261,x25262)+E(f548(x25263,x25264,x25265,x25261),f548(x25263,x25264,x25265,x25262))
% 160.93/160.66 [2527]~E(x25271,x25272)+E(f344(x25271),f344(x25272))
% 160.93/160.66 [2528]~E(x25281,x25282)+E(f545(x25281,x25283,x25284,x25285,x25286,x25287,x25288),f545(x25282,x25283,x25284,x25285,x25286,x25287,x25288))
% 160.93/160.66 [2529]~E(x25291,x25292)+E(f545(x25293,x25291,x25294,x25295,x25296,x25297,x25298),f545(x25293,x25292,x25294,x25295,x25296,x25297,x25298))
% 160.93/160.66 [2530]~E(x25301,x25302)+E(f545(x25303,x25304,x25301,x25305,x25306,x25307,x25308),f545(x25303,x25304,x25302,x25305,x25306,x25307,x25308))
% 160.93/160.66 [2531]~E(x25311,x25312)+E(f545(x25313,x25314,x25315,x25311,x25316,x25317,x25318),f545(x25313,x25314,x25315,x25312,x25316,x25317,x25318))
% 160.93/160.66 [2532]~E(x25321,x25322)+E(f545(x25323,x25324,x25325,x25326,x25321,x25327,x25328),f545(x25323,x25324,x25325,x25326,x25322,x25327,x25328))
% 160.93/160.66 [2533]~E(x25331,x25332)+E(f545(x25333,x25334,x25335,x25336,x25337,x25331,x25338),f545(x25333,x25334,x25335,x25336,x25337,x25332,x25338))
% 160.93/160.66 [2534]~E(x25341,x25342)+E(f545(x25343,x25344,x25345,x25346,x25347,x25348,x25341),f545(x25343,x25344,x25345,x25346,x25347,x25348,x25342))
% 160.93/160.66 [2535]~E(x25351,x25352)+E(f284(x25351,x25353,x25354),f284(x25352,x25353,x25354))
% 160.93/160.66 [2536]~E(x25361,x25362)+E(f284(x25363,x25361,x25364),f284(x25363,x25362,x25364))
% 160.93/160.66 [2537]~E(x25371,x25372)+E(f284(x25373,x25374,x25371),f284(x25373,x25374,x25372))
% 160.93/160.66 [2538]~E(x25381,x25382)+E(f576(x25381,x25383,x25384,x25385,x25386,x25387),f576(x25382,x25383,x25384,x25385,x25386,x25387))
% 160.93/160.66 [2539]~E(x25391,x25392)+E(f576(x25393,x25391,x25394,x25395,x25396,x25397),f576(x25393,x25392,x25394,x25395,x25396,x25397))
% 160.93/160.66 [2540]~E(x25401,x25402)+E(f576(x25403,x25404,x25401,x25405,x25406,x25407),f576(x25403,x25404,x25402,x25405,x25406,x25407))
% 160.93/160.66 [2541]~E(x25411,x25412)+E(f576(x25413,x25414,x25415,x25411,x25416,x25417),f576(x25413,x25414,x25415,x25412,x25416,x25417))
% 160.93/160.66 [2542]~E(x25421,x25422)+E(f576(x25423,x25424,x25425,x25426,x25421,x25427),f576(x25423,x25424,x25425,x25426,x25422,x25427))
% 160.93/160.66 [2543]~E(x25431,x25432)+E(f576(x25433,x25434,x25435,x25436,x25437,x25431),f576(x25433,x25434,x25435,x25436,x25437,x25432))
% 160.93/160.66 [2544]~E(x25441,x25442)+E(f679(x25441,x25443,x25444),f679(x25442,x25443,x25444))
% 160.93/160.66 [2545]~E(x25451,x25452)+E(f679(x25453,x25451,x25454),f679(x25453,x25452,x25454))
% 160.93/160.66 [2546]~E(x25461,x25462)+E(f679(x25463,x25464,x25461),f679(x25463,x25464,x25462))
% 160.93/160.66 [2547]~E(x25471,x25472)+E(f849(x25471,x25473),f849(x25472,x25473))
% 160.93/160.66 [2548]~E(x25481,x25482)+E(f849(x25483,x25481),f849(x25483,x25482))
% 160.93/160.66 [2549]~E(x25491,x25492)+E(f712(x25491,x25493,x25494),f712(x25492,x25493,x25494))
% 160.93/160.66 [2550]~E(x25501,x25502)+E(f712(x25503,x25501,x25504),f712(x25503,x25502,x25504))
% 160.93/160.66 [2551]~E(x25511,x25512)+E(f712(x25513,x25514,x25511),f712(x25513,x25514,x25512))
% 160.93/160.66 [2552]~E(x25521,x25522)+E(f277(x25521,x25523,x25524,x25525,x25526),f277(x25522,x25523,x25524,x25525,x25526))
% 160.93/160.66 [2553]~E(x25531,x25532)+E(f277(x25533,x25531,x25534,x25535,x25536),f277(x25533,x25532,x25534,x25535,x25536))
% 160.93/160.66 [2554]~E(x25541,x25542)+E(f277(x25543,x25544,x25541,x25545,x25546),f277(x25543,x25544,x25542,x25545,x25546))
% 160.93/160.66 [2555]~E(x25551,x25552)+E(f277(x25553,x25554,x25555,x25551,x25556),f277(x25553,x25554,x25555,x25552,x25556))
% 160.93/160.66 [2556]~E(x25561,x25562)+E(f277(x25563,x25564,x25565,x25566,x25561),f277(x25563,x25564,x25565,x25566,x25562))
% 160.93/160.66 [2557]~E(x25571,x25572)+E(f98(x25571,x25573,x25574,x25575),f98(x25572,x25573,x25574,x25575))
% 160.93/160.66 [2558]~E(x25581,x25582)+E(f98(x25583,x25581,x25584,x25585),f98(x25583,x25582,x25584,x25585))
% 160.93/160.66 [2559]~E(x25591,x25592)+E(f98(x25593,x25594,x25591,x25595),f98(x25593,x25594,x25592,x25595))
% 160.93/160.66 [2560]~E(x25601,x25602)+E(f98(x25603,x25604,x25605,x25601),f98(x25603,x25604,x25605,x25602))
% 160.93/160.66 [2561]~E(x25611,x25612)+E(f370(x25611,x25613),f370(x25612,x25613))
% 160.93/160.66 [2562]~E(x25621,x25622)+E(f370(x25623,x25621),f370(x25623,x25622))
% 160.93/160.66 [2563]~E(x25631,x25632)+E(f788(x25631,x25633,x25634,x25635),f788(x25632,x25633,x25634,x25635))
% 160.93/160.66 [2564]~E(x25641,x25642)+E(f788(x25643,x25641,x25644,x25645),f788(x25643,x25642,x25644,x25645))
% 160.93/160.66 [2565]~E(x25651,x25652)+E(f788(x25653,x25654,x25651,x25655),f788(x25653,x25654,x25652,x25655))
% 160.93/160.66 [2566]~E(x25661,x25662)+E(f788(x25663,x25664,x25665,x25661),f788(x25663,x25664,x25665,x25662))
% 160.93/160.66 [2567]~E(x25671,x25672)+E(f709(x25671),f709(x25672))
% 160.93/160.66 [2568]~E(x25681,x25682)+E(f238(x25681,x25683,x25684),f238(x25682,x25683,x25684))
% 160.93/160.66 [2569]~E(x25691,x25692)+E(f238(x25693,x25691,x25694),f238(x25693,x25692,x25694))
% 160.93/160.66 [2570]~E(x25701,x25702)+E(f238(x25703,x25704,x25701),f238(x25703,x25704,x25702))
% 160.93/160.66 [2571]~E(x25711,x25712)+E(f575(x25711,x25713,x25714,x25715),f575(x25712,x25713,x25714,x25715))
% 160.93/160.66 [2572]~E(x25721,x25722)+E(f575(x25723,x25721,x25724,x25725),f575(x25723,x25722,x25724,x25725))
% 160.93/160.66 [2573]~E(x25731,x25732)+E(f575(x25733,x25734,x25731,x25735),f575(x25733,x25734,x25732,x25735))
% 160.93/160.66 [2574]~E(x25741,x25742)+E(f575(x25743,x25744,x25745,x25741),f575(x25743,x25744,x25745,x25742))
% 160.93/160.66 [2575]~E(x25751,x25752)+E(f552(x25751,x25753,x25754,x25755,x25756),f552(x25752,x25753,x25754,x25755,x25756))
% 160.93/160.66 [2576]~E(x25761,x25762)+E(f552(x25763,x25761,x25764,x25765,x25766),f552(x25763,x25762,x25764,x25765,x25766))
% 160.93/160.66 [2577]~E(x25771,x25772)+E(f552(x25773,x25774,x25771,x25775,x25776),f552(x25773,x25774,x25772,x25775,x25776))
% 160.93/160.66 [2578]~E(x25781,x25782)+E(f552(x25783,x25784,x25785,x25781,x25786),f552(x25783,x25784,x25785,x25782,x25786))
% 160.93/160.66 [2579]~E(x25791,x25792)+E(f552(x25793,x25794,x25795,x25796,x25791),f552(x25793,x25794,x25795,x25796,x25792))
% 160.93/160.66 [2580]~E(x25801,x25802)+E(f499(x25801,x25803),f499(x25802,x25803))
% 160.93/160.66 [2581]~E(x25811,x25812)+E(f499(x25813,x25811),f499(x25813,x25812))
% 160.93/160.66 [2582]~E(x25821,x25822)+E(f566(x25821,x25823,x25824,x25825),f566(x25822,x25823,x25824,x25825))
% 160.93/160.66 [2583]~E(x25831,x25832)+E(f566(x25833,x25831,x25834,x25835),f566(x25833,x25832,x25834,x25835))
% 160.93/160.66 [2584]~E(x25841,x25842)+E(f566(x25843,x25844,x25841,x25845),f566(x25843,x25844,x25842,x25845))
% 160.93/160.66 [2585]~E(x25851,x25852)+E(f566(x25853,x25854,x25855,x25851),f566(x25853,x25854,x25855,x25852))
% 160.93/160.66 [2586]~E(x25861,x25862)+E(f345(x25861),f345(x25862))
% 160.93/160.66 [2587]~E(x25871,x25872)+E(f721(x25871,x25873),f721(x25872,x25873))
% 160.93/160.66 [2588]~E(x25881,x25882)+E(f721(x25883,x25881),f721(x25883,x25882))
% 160.93/160.66 [2589]~E(x25891,x25892)+E(f358(x25891,x25893),f358(x25892,x25893))
% 160.93/160.66 [2590]~E(x25901,x25902)+E(f358(x25903,x25901),f358(x25903,x25902))
% 160.93/160.66 [2591]~E(x25911,x25912)+E(f585(x25911),f585(x25912))
% 160.93/160.66 [2592]~E(x25921,x25922)+E(f767(x25921,x25923,x25924),f767(x25922,x25923,x25924))
% 160.93/160.66 [2593]~E(x25931,x25932)+E(f767(x25933,x25931,x25934),f767(x25933,x25932,x25934))
% 160.93/160.66 [2594]~E(x25941,x25942)+E(f767(x25943,x25944,x25941),f767(x25943,x25944,x25942))
% 160.93/160.66 [2595]~E(x25951,x25952)+E(f733(x25951,x25953),f733(x25952,x25953))
% 160.93/160.66 [2596]~E(x25961,x25962)+E(f733(x25963,x25961),f733(x25963,x25962))
% 160.93/160.66 [2597]~E(x25971,x25972)+E(f631(x25971,x25973),f631(x25972,x25973))
% 160.93/160.66 [2598]~E(x25981,x25982)+E(f631(x25983,x25981),f631(x25983,x25982))
% 160.93/160.66 [2599]~E(x25991,x25992)+E(f786(x25991,x25993,x25994),f786(x25992,x25993,x25994))
% 160.93/160.66 [2600]~E(x26001,x26002)+E(f786(x26003,x26001,x26004),f786(x26003,x26002,x26004))
% 160.93/160.66 [2601]~E(x26011,x26012)+E(f786(x26013,x26014,x26011),f786(x26013,x26014,x26012))
% 160.93/160.66 [2602]~E(x26021,x26022)+E(f572(x26021,x26023),f572(x26022,x26023))
% 160.93/160.66 [2603]~E(x26031,x26032)+E(f572(x26033,x26031),f572(x26033,x26032))
% 160.93/160.66 [2604]~E(x26041,x26042)+E(f347(x26041,x26043),f347(x26042,x26043))
% 160.93/160.66 [2605]~E(x26051,x26052)+E(f347(x26053,x26051),f347(x26053,x26052))
% 160.93/160.66 [2606]~E(x26061,x26062)+E(f221(x26061,x26063,x26064,x26065,x26066,x26067,x26068),f221(x26062,x26063,x26064,x26065,x26066,x26067,x26068))
% 160.93/160.66 [2607]~E(x26071,x26072)+E(f221(x26073,x26071,x26074,x26075,x26076,x26077,x26078),f221(x26073,x26072,x26074,x26075,x26076,x26077,x26078))
% 160.93/160.66 [2608]~E(x26081,x26082)+E(f221(x26083,x26084,x26081,x26085,x26086,x26087,x26088),f221(x26083,x26084,x26082,x26085,x26086,x26087,x26088))
% 160.93/160.66 [2609]~E(x26091,x26092)+E(f221(x26093,x26094,x26095,x26091,x26096,x26097,x26098),f221(x26093,x26094,x26095,x26092,x26096,x26097,x26098))
% 160.93/160.66 [2610]~E(x26101,x26102)+E(f221(x26103,x26104,x26105,x26106,x26101,x26107,x26108),f221(x26103,x26104,x26105,x26106,x26102,x26107,x26108))
% 160.93/160.66 [2611]~E(x26111,x26112)+E(f221(x26113,x26114,x26115,x26116,x26117,x26111,x26118),f221(x26113,x26114,x26115,x26116,x26117,x26112,x26118))
% 160.93/160.66 [2612]~E(x26121,x26122)+E(f221(x26123,x26124,x26125,x26126,x26127,x26128,x26121),f221(x26123,x26124,x26125,x26126,x26127,x26128,x26122))
% 160.93/160.66 [2613]~E(x26131,x26132)+E(f724(x26131,x26133,x26134),f724(x26132,x26133,x26134))
% 160.93/160.66 [2614]~E(x26141,x26142)+E(f724(x26143,x26141,x26144),f724(x26143,x26142,x26144))
% 160.93/160.66 [2615]~E(x26151,x26152)+E(f724(x26153,x26154,x26151),f724(x26153,x26154,x26152))
% 160.93/160.66 [2616]~E(x26161,x26162)+E(f570(x26161,x26163),f570(x26162,x26163))
% 160.93/160.66 [2617]~E(x26171,x26172)+E(f570(x26173,x26171),f570(x26173,x26172))
% 160.93/160.66 [2618]~E(x26181,x26182)+E(f799(x26181,x26183,x26184),f799(x26182,x26183,x26184))
% 160.93/160.66 [2619]~E(x26191,x26192)+E(f799(x26193,x26191,x26194),f799(x26193,x26192,x26194))
% 160.93/160.66 [2620]~E(x26201,x26202)+E(f799(x26203,x26204,x26201),f799(x26203,x26204,x26202))
% 160.93/160.66 [2621]~E(x26211,x26212)+E(f405(x26211,x26213,x26214,x26215,x26216),f405(x26212,x26213,x26214,x26215,x26216))
% 160.93/160.66 [2622]~E(x26221,x26222)+E(f405(x26223,x26221,x26224,x26225,x26226),f405(x26223,x26222,x26224,x26225,x26226))
% 160.93/160.66 [2623]~E(x26231,x26232)+E(f405(x26233,x26234,x26231,x26235,x26236),f405(x26233,x26234,x26232,x26235,x26236))
% 160.93/160.66 [2624]~E(x26241,x26242)+E(f405(x26243,x26244,x26245,x26241,x26246),f405(x26243,x26244,x26245,x26242,x26246))
% 160.93/160.66 [2625]~E(x26251,x26252)+E(f405(x26253,x26254,x26255,x26256,x26251),f405(x26253,x26254,x26255,x26256,x26252))
% 160.93/160.66 [2626]~E(x26261,x26262)+E(f234(x26261,x26263,x26264),f234(x26262,x26263,x26264))
% 160.93/160.66 [2627]~E(x26271,x26272)+E(f234(x26273,x26271,x26274),f234(x26273,x26272,x26274))
% 160.93/160.66 [2628]~E(x26281,x26282)+E(f234(x26283,x26284,x26281),f234(x26283,x26284,x26282))
% 160.93/160.66 [2629]~P1(x26291)+P1(x26292)+~E(x26291,x26292)
% 160.93/160.66 [2630]~P2(x26301)+P2(x26302)+~E(x26301,x26302)
% 160.93/160.66 [2631]P16(x26312,x26313)+~E(x26311,x26312)+~P16(x26311,x26313)
% 160.93/160.66 [2632]P16(x26323,x26322)+~E(x26321,x26322)+~P16(x26323,x26321)
% 160.93/160.66 [2633]~P108(x26331)+P108(x26332)+~E(x26331,x26332)
% 160.93/160.66 [2634]~P99(x26341)+P99(x26342)+~E(x26341,x26342)
% 160.93/160.66 [2635]~P126(x26351)+P126(x26352)+~E(x26351,x26352)
% 160.93/160.66 [2636]~P82(x26361)+P82(x26362)+~E(x26361,x26362)
% 160.93/160.66 [2637]~P3(x26371)+P3(x26372)+~E(x26371,x26372)
% 160.93/160.66 [2638]~P101(x26381)+P101(x26382)+~E(x26381,x26382)
% 160.93/160.66 [2639]P146(x26392,x26393,x26394)+~E(x26391,x26392)+~P146(x26391,x26393,x26394)
% 160.93/160.66 [2640]P146(x26403,x26402,x26404)+~E(x26401,x26402)+~P146(x26403,x26401,x26404)
% 160.93/160.66 [2641]P146(x26413,x26414,x26412)+~E(x26411,x26412)+~P146(x26413,x26414,x26411)
% 160.93/160.66 [2642]~P4(x26421)+P4(x26422)+~E(x26421,x26422)
% 160.93/160.66 [2643]~P63(x26431)+P63(x26432)+~E(x26431,x26432)
% 160.93/160.66 [2644]~P65(x26441)+P65(x26442)+~E(x26441,x26442)
% 160.93/160.66 [2645]~P111(x26451)+P111(x26452)+~E(x26451,x26452)
% 160.93/160.66 [2646]~P106(x26461)+P106(x26462)+~E(x26461,x26462)
% 160.93/160.66 [2647]P39(x26472,x26473)+~E(x26471,x26472)+~P39(x26471,x26473)
% 160.93/160.66 [2648]P39(x26483,x26482)+~E(x26481,x26482)+~P39(x26483,x26481)
% 160.93/160.66 [2649]~P100(x26491)+P100(x26492)+~E(x26491,x26492)
% 160.93/160.66 [2650]~P91(x26501)+P91(x26502)+~E(x26501,x26502)
% 160.93/160.66 [2651]P33(x26512,x26513,x26514)+~E(x26511,x26512)+~P33(x26511,x26513,x26514)
% 160.93/160.66 [2652]P33(x26523,x26522,x26524)+~E(x26521,x26522)+~P33(x26523,x26521,x26524)
% 160.93/160.66 [2653]P33(x26533,x26534,x26532)+~E(x26531,x26532)+~P33(x26533,x26534,x26531)
% 160.93/160.66 [2654]~P97(x26541)+P97(x26542)+~E(x26541,x26542)
% 160.93/160.66 [2655]~P124(x26551)+P124(x26552)+~E(x26551,x26552)
% 160.93/160.66 [2656]~P105(x26561)+P105(x26562)+~E(x26561,x26562)
% 160.93/160.66 [2657]~P66(x26571)+P66(x26572)+~E(x26571,x26572)
% 160.93/160.66 [2658]~P67(x26581)+P67(x26582)+~E(x26581,x26582)
% 160.93/160.66 [2659]~P77(x26591)+P77(x26592)+~E(x26591,x26592)
% 160.93/160.66 [2660]~P141(x26601)+P141(x26602)+~E(x26601,x26602)
% 160.93/160.66 [2661]~P93(x26611)+P93(x26612)+~E(x26611,x26612)
% 160.93/160.66 [2662]~P80(x26621)+P80(x26622)+~E(x26621,x26622)
% 160.93/160.66 [2663]~P68(x26631)+P68(x26632)+~E(x26631,x26632)
% 160.93/160.66 [2664]P35(x26642,x26643,x26644)+~E(x26641,x26642)+~P35(x26641,x26643,x26644)
% 160.93/160.66 [2665]P35(x26653,x26652,x26654)+~E(x26651,x26652)+~P35(x26653,x26651,x26654)
% 160.93/160.66 [2666]P35(x26663,x26664,x26662)+~E(x26661,x26662)+~P35(x26663,x26664,x26661)
% 160.93/160.66 [2667]~P109(x26671)+P109(x26672)+~E(x26671,x26672)
% 160.93/160.66 [2668]~P5(x26681)+P5(x26682)+~E(x26681,x26682)
% 160.93/160.66 [2669]~P78(x26691)+P78(x26692)+~E(x26691,x26692)
% 160.93/160.66 [2670]P29(x26702,x26703,x26704)+~E(x26701,x26702)+~P29(x26701,x26703,x26704)
% 160.93/160.66 [2671]P29(x26713,x26712,x26714)+~E(x26711,x26712)+~P29(x26713,x26711,x26714)
% 160.93/160.66 [2672]P29(x26723,x26724,x26722)+~E(x26721,x26722)+~P29(x26723,x26724,x26721)
% 160.93/160.66 [2673]~P85(x26731)+P85(x26732)+~E(x26731,x26732)
% 160.93/160.66 [2674]~P136(x26741)+P136(x26742)+~E(x26741,x26742)
% 160.93/160.66 [2675]~P132(x26751)+P132(x26752)+~E(x26751,x26752)
% 160.93/160.66 [2676]P145(x26762,x26763,x26764)+~E(x26761,x26762)+~P145(x26761,x26763,x26764)
% 160.93/160.66 [2677]P145(x26773,x26772,x26774)+~E(x26771,x26772)+~P145(x26773,x26771,x26774)
% 160.93/160.66 [2678]P145(x26783,x26784,x26782)+~E(x26781,x26782)+~P145(x26783,x26784,x26781)
% 160.93/160.66 [2679]~P74(x26791)+P74(x26792)+~E(x26791,x26792)
% 160.93/160.66 [2680]P27(x26802,x26803,x26804,x26805)+~E(x26801,x26802)+~P27(x26801,x26803,x26804,x26805)
% 160.93/160.66 [2681]P27(x26813,x26812,x26814,x26815)+~E(x26811,x26812)+~P27(x26813,x26811,x26814,x26815)
% 160.93/160.66 [2682]P27(x26823,x26824,x26822,x26825)+~E(x26821,x26822)+~P27(x26823,x26824,x26821,x26825)
% 160.93/160.66 [2683]P27(x26833,x26834,x26835,x26832)+~E(x26831,x26832)+~P27(x26833,x26834,x26835,x26831)
% 160.93/160.66 [2684]~P61(x26841)+P61(x26842)+~E(x26841,x26842)
% 160.93/160.66 [2685]P41(x26852,x26853,x26854)+~E(x26851,x26852)+~P41(x26851,x26853,x26854)
% 160.93/160.66 [2686]P41(x26863,x26862,x26864)+~E(x26861,x26862)+~P41(x26863,x26861,x26864)
% 160.93/160.66 [2687]P41(x26873,x26874,x26872)+~E(x26871,x26872)+~P41(x26873,x26874,x26871)
% 160.93/160.66 [2688]P55(x26882,x26883)+~E(x26881,x26882)+~P55(x26881,x26883)
% 160.93/160.66 [2689]P55(x26893,x26892)+~E(x26891,x26892)+~P55(x26893,x26891)
% 160.93/160.66 [2690]~P139(x26901)+P139(x26902)+~E(x26901,x26902)
% 160.93/160.66 [2691]~P125(x26911)+P125(x26912)+~E(x26911,x26912)
% 160.93/160.66 [2692]~P107(x26921)+P107(x26922)+~E(x26921,x26922)
% 160.93/160.66 [2693]P11(x26932,x26933,x26934,x26935,x26936)+~E(x26931,x26932)+~P11(x26931,x26933,x26934,x26935,x26936)
% 160.93/160.66 [2694]P11(x26943,x26942,x26944,x26945,x26946)+~E(x26941,x26942)+~P11(x26943,x26941,x26944,x26945,x26946)
% 160.93/160.66 [2695]P11(x26953,x26954,x26952,x26955,x26956)+~E(x26951,x26952)+~P11(x26953,x26954,x26951,x26955,x26956)
% 160.93/160.66 [2696]P11(x26963,x26964,x26965,x26962,x26966)+~E(x26961,x26962)+~P11(x26963,x26964,x26965,x26961,x26966)
% 160.93/160.66 [2697]P11(x26973,x26974,x26975,x26976,x26972)+~E(x26971,x26972)+~P11(x26973,x26974,x26975,x26976,x26971)
% 160.93/160.66 [2698]~P123(x26981)+P123(x26982)+~E(x26981,x26982)
% 160.93/160.66 [2699]~P40(x26991)+P40(x26992)+~E(x26991,x26992)
% 160.93/160.66 [2700]~P118(x27001)+P118(x27002)+~E(x27001,x27002)
% 160.93/160.66 [2701]~P142(x27011)+P142(x27012)+~E(x27011,x27012)
% 160.93/160.66 [2702]~P75(x27021)+P75(x27022)+~E(x27021,x27022)
% 160.93/160.66 [2703]P53(x27032,x27033,x27034)+~E(x27031,x27032)+~P53(x27031,x27033,x27034)
% 160.93/160.66 [2704]P53(x27043,x27042,x27044)+~E(x27041,x27042)+~P53(x27043,x27041,x27044)
% 160.93/160.66 [2705]P53(x27053,x27054,x27052)+~E(x27051,x27052)+~P53(x27053,x27054,x27051)
% 160.93/160.66 [2706]P14(x27062,x27063,x27064,x27065)+~E(x27061,x27062)+~P14(x27061,x27063,x27064,x27065)
% 160.93/160.66 [2707]P14(x27073,x27072,x27074,x27075)+~E(x27071,x27072)+~P14(x27073,x27071,x27074,x27075)
% 160.93/160.66 [2708]P14(x27083,x27084,x27082,x27085)+~E(x27081,x27082)+~P14(x27083,x27084,x27081,x27085)
% 160.93/160.66 [2709]P14(x27093,x27094,x27095,x27092)+~E(x27091,x27092)+~P14(x27093,x27094,x27095,x27091)
% 160.93/160.66 [2710]P54(x27102,x27103,x27104,x27105,x27106)+~E(x27101,x27102)+~P54(x27101,x27103,x27104,x27105,x27106)
% 160.93/160.66 [2711]P54(x27113,x27112,x27114,x27115,x27116)+~E(x27111,x27112)+~P54(x27113,x27111,x27114,x27115,x27116)
% 160.93/160.66 [2712]P54(x27123,x27124,x27122,x27125,x27126)+~E(x27121,x27122)+~P54(x27123,x27124,x27121,x27125,x27126)
% 160.93/160.66 [2713]P54(x27133,x27134,x27135,x27132,x27136)+~E(x27131,x27132)+~P54(x27133,x27134,x27135,x27131,x27136)
% 160.93/160.66 [2714]P54(x27143,x27144,x27145,x27146,x27142)+~E(x27141,x27142)+~P54(x27143,x27144,x27145,x27146,x27141)
% 160.93/160.66 [2715]P34(x27152,x27153,x27154,x27155)+~E(x27151,x27152)+~P34(x27151,x27153,x27154,x27155)
% 160.93/160.66 [2716]P34(x27163,x27162,x27164,x27165)+~E(x27161,x27162)+~P34(x27163,x27161,x27164,x27165)
% 160.93/160.66 [2717]P34(x27173,x27174,x27172,x27175)+~E(x27171,x27172)+~P34(x27173,x27174,x27171,x27175)
% 160.93/160.66 [2718]P34(x27183,x27184,x27185,x27182)+~E(x27181,x27182)+~P34(x27183,x27184,x27185,x27181)
% 160.93/160.66 [2719]~P110(x27191)+P110(x27192)+~E(x27191,x27192)
% 160.93/160.66 [2720]P24(x27202,x27203,x27204,x27205,x27206,x27207)+~E(x27201,x27202)+~P24(x27201,x27203,x27204,x27205,x27206,x27207)
% 160.93/160.66 [2721]P24(x27213,x27212,x27214,x27215,x27216,x27217)+~E(x27211,x27212)+~P24(x27213,x27211,x27214,x27215,x27216,x27217)
% 160.93/160.66 [2722]P24(x27223,x27224,x27222,x27225,x27226,x27227)+~E(x27221,x27222)+~P24(x27223,x27224,x27221,x27225,x27226,x27227)
% 160.93/160.66 [2723]P24(x27233,x27234,x27235,x27232,x27236,x27237)+~E(x27231,x27232)+~P24(x27233,x27234,x27235,x27231,x27236,x27237)
% 160.93/160.66 [2724]P24(x27243,x27244,x27245,x27246,x27242,x27247)+~E(x27241,x27242)+~P24(x27243,x27244,x27245,x27246,x27241,x27247)
% 160.93/160.66 [2725]P24(x27253,x27254,x27255,x27256,x27257,x27252)+~E(x27251,x27252)+~P24(x27253,x27254,x27255,x27256,x27257,x27251)
% 160.93/160.66 [2726]P8(x27262,x27263,x27264)+~E(x27261,x27262)+~P8(x27261,x27263,x27264)
% 160.93/160.66 [2727]P8(x27273,x27272,x27274)+~E(x27271,x27272)+~P8(x27273,x27271,x27274)
% 160.93/160.66 [2728]P8(x27283,x27284,x27282)+~E(x27281,x27282)+~P8(x27283,x27284,x27281)
% 160.93/160.66 [2729]P13(x27292,x27293,x27294)+~E(x27291,x27292)+~P13(x27291,x27293,x27294)
% 160.93/160.66 [2730]P13(x27303,x27302,x27304)+~E(x27301,x27302)+~P13(x27303,x27301,x27304)
% 160.93/160.66 [2731]P13(x27313,x27314,x27312)+~E(x27311,x27312)+~P13(x27313,x27314,x27311)
% 160.93/160.66 [2732]~P62(x27321)+P62(x27322)+~E(x27321,x27322)
% 160.93/160.66 [2733]~P137(x27331)+P137(x27332)+~E(x27331,x27332)
% 160.93/160.66 [2734]P32(x27342,x27343)+~E(x27341,x27342)+~P32(x27341,x27343)
% 160.93/160.66 [2735]P32(x27353,x27352)+~E(x27351,x27352)+~P32(x27353,x27351)
% 160.93/160.66 [2736]P36(x27362,x27363,x27364,x27365,x27366)+~E(x27361,x27362)+~P36(x27361,x27363,x27364,x27365,x27366)
% 160.93/160.66 [2737]P36(x27373,x27372,x27374,x27375,x27376)+~E(x27371,x27372)+~P36(x27373,x27371,x27374,x27375,x27376)
% 160.93/160.66 [2738]P36(x27383,x27384,x27382,x27385,x27386)+~E(x27381,x27382)+~P36(x27383,x27384,x27381,x27385,x27386)
% 160.93/160.66 [2739]P36(x27393,x27394,x27395,x27392,x27396)+~E(x27391,x27392)+~P36(x27393,x27394,x27395,x27391,x27396)
% 160.93/160.66 [2740]P36(x27403,x27404,x27405,x27406,x27402)+~E(x27401,x27402)+~P36(x27403,x27404,x27405,x27406,x27401)
% 160.93/160.66 [2741]~P112(x27411)+P112(x27412)+~E(x27411,x27412)
% 160.93/160.66 [2742]~P94(x27421)+P94(x27422)+~E(x27421,x27422)
% 160.93/160.66 [2743]~P58(x27431)+P58(x27432)+~E(x27431,x27432)
% 160.93/160.66 [2744]~P60(x27441)+P60(x27442)+~E(x27441,x27442)
% 160.93/160.66 [2745]~P83(x27451)+P83(x27452)+~E(x27451,x27452)
% 160.93/160.66 [2746]~P117(x27461)+P117(x27462)+~E(x27461,x27462)
% 160.93/160.66 [2747]P26(x27472,x27473,x27474)+~E(x27471,x27472)+~P26(x27471,x27473,x27474)
% 160.93/160.66 [2748]P26(x27483,x27482,x27484)+~E(x27481,x27482)+~P26(x27483,x27481,x27484)
% 160.93/160.66 [2749]P26(x27493,x27494,x27492)+~E(x27491,x27492)+~P26(x27493,x27494,x27491)
% 160.93/160.66 [2750]P30(x27502,x27503,x27504)+~E(x27501,x27502)+~P30(x27501,x27503,x27504)
% 160.93/160.66 [2751]P30(x27513,x27512,x27514)+~E(x27511,x27512)+~P30(x27513,x27511,x27514)
% 160.93/160.66 [2752]P30(x27523,x27524,x27522)+~E(x27521,x27522)+~P30(x27523,x27524,x27521)
% 160.93/160.66 [2753]~P84(x27531)+P84(x27532)+~E(x27531,x27532)
% 160.93/160.66 [2754]P50(x27542,x27543)+~E(x27541,x27542)+~P50(x27541,x27543)
% 160.93/160.66 [2755]P50(x27553,x27552)+~E(x27551,x27552)+~P50(x27553,x27551)
% 160.93/160.66 [2756]P49(x27562,x27563,x27564)+~E(x27561,x27562)+~P49(x27561,x27563,x27564)
% 160.93/160.66 [2757]P49(x27573,x27572,x27574)+~E(x27571,x27572)+~P49(x27573,x27571,x27574)
% 160.93/160.66 [2758]P49(x27583,x27584,x27582)+~E(x27581,x27582)+~P49(x27583,x27584,x27581)
% 160.93/160.66 [2759]~P81(x27591)+P81(x27592)+~E(x27591,x27592)
% 160.93/160.66 [2760]~P70(x27601)+P70(x27602)+~E(x27601,x27602)
% 160.93/160.66 [2761]~P79(x27611)+P79(x27612)+~E(x27611,x27612)
% 160.93/160.66 [2762]~P113(x27621)+P113(x27622)+~E(x27621,x27622)
% 160.93/160.66 [2763]~P69(x27631)+P69(x27632)+~E(x27631,x27632)
% 160.93/160.66 [2764]~P120(x27641)+P120(x27642)+~E(x27641,x27642)
% 160.93/160.66 [2765]~P121(x27651)+P121(x27652)+~E(x27651,x27652)
% 160.93/160.66 [2766]P52(x27662,x27663,x27664)+~E(x27661,x27662)+~P52(x27661,x27663,x27664)
% 160.93/160.66 [2767]P52(x27673,x27672,x27674)+~E(x27671,x27672)+~P52(x27673,x27671,x27674)
% 160.93/160.66 [2768]P52(x27683,x27684,x27682)+~E(x27681,x27682)+~P52(x27683,x27684,x27681)
% 160.93/160.66 [2769]P20(x27692,x27693,x27694)+~E(x27691,x27692)+~P20(x27691,x27693,x27694)
% 160.93/160.66 [2770]P20(x27703,x27702,x27704)+~E(x27701,x27702)+~P20(x27703,x27701,x27704)
% 160.93/160.66 [2771]P20(x27713,x27714,x27712)+~E(x27711,x27712)+~P20(x27713,x27714,x27711)
% 160.93/160.66 [2772]~P131(x27721)+P131(x27722)+~E(x27721,x27722)
% 160.93/160.66 [2773]~P71(x27731)+P71(x27732)+~E(x27731,x27732)
% 160.93/160.66 [2774]~P103(x27741)+P103(x27742)+~E(x27741,x27742)
% 160.93/160.66 [2775]~P92(x27751)+P92(x27752)+~E(x27751,x27752)
% 160.93/160.66 [2776]P37(x27762,x27763,x27764)+~E(x27761,x27762)+~P37(x27761,x27763,x27764)
% 160.93/160.66 [2777]P37(x27773,x27772,x27774)+~E(x27771,x27772)+~P37(x27773,x27771,x27774)
% 160.93/160.66 [2778]P37(x27783,x27784,x27782)+~E(x27781,x27782)+~P37(x27783,x27784,x27781)
% 160.93/160.66 [2779]P21(x27792,x27793,x27794,x27795)+~E(x27791,x27792)+~P21(x27791,x27793,x27794,x27795)
% 160.93/160.66 [2780]P21(x27803,x27802,x27804,x27805)+~E(x27801,x27802)+~P21(x27803,x27801,x27804,x27805)
% 160.93/160.66 [2781]P21(x27813,x27814,x27812,x27815)+~E(x27811,x27812)+~P21(x27813,x27814,x27811,x27815)
% 160.93/160.66 [2782]P21(x27823,x27824,x27825,x27822)+~E(x27821,x27822)+~P21(x27823,x27824,x27825,x27821)
% 160.93/160.66 [2783]~P6(x27831)+P6(x27832)+~E(x27831,x27832)
% 160.93/160.66 [2784]~P86(x27841)+P86(x27842)+~E(x27841,x27842)
% 160.93/160.66 [2785]~P59(x27851)+P59(x27852)+~E(x27851,x27852)
% 160.93/160.66 [2786]P12(x27862,x27863,x27864)+~E(x27861,x27862)+~P12(x27861,x27863,x27864)
% 160.93/160.66 [2787]P12(x27873,x27872,x27874)+~E(x27871,x27872)+~P12(x27873,x27871,x27874)
% 160.93/160.66 [2788]P12(x27883,x27884,x27882)+~E(x27881,x27882)+~P12(x27883,x27884,x27881)
% 160.93/160.66 [2789]~P72(x27891)+P72(x27892)+~E(x27891,x27892)
% 160.93/160.66 [2790]P19(x27902,x27903,x27904)+~E(x27901,x27902)+~P19(x27901,x27903,x27904)
% 160.93/160.66 [2791]P19(x27913,x27912,x27914)+~E(x27911,x27912)+~P19(x27913,x27911,x27914)
% 160.93/160.66 [2792]P19(x27923,x27924,x27922)+~E(x27921,x27922)+~P19(x27923,x27924,x27921)
% 160.93/160.66 [2793]P28(x27932,x27933)+~E(x27931,x27932)+~P28(x27931,x27933)
% 160.93/160.66 [2794]P28(x27943,x27942)+~E(x27941,x27942)+~P28(x27943,x27941)
% 160.93/160.66 [2795]~P130(x27951)+P130(x27952)+~E(x27951,x27952)
% 160.93/160.66 [2796]~P116(x27961)+P116(x27962)+~E(x27961,x27962)
% 160.93/160.66 [2797]~P119(x27971)+P119(x27972)+~E(x27971,x27972)
% 160.93/160.66 [2798]~P138(x27981)+P138(x27982)+~E(x27981,x27982)
% 160.93/160.66 [2799]~P90(x27991)+P90(x27992)+~E(x27991,x27992)
% 160.93/160.66 [2800]~P115(x28001)+P115(x28002)+~E(x28001,x28002)
% 160.93/160.66 [2801]~P129(x28011)+P129(x28012)+~E(x28011,x28012)
% 160.93/160.66 [2802]~P87(x28021)+P87(x28022)+~E(x28021,x28022)
% 160.93/160.66 [2803]P15(x28032,x28033,x28034,x28035,x28036,x28037)+~E(x28031,x28032)+~P15(x28031,x28033,x28034,x28035,x28036,x28037)
% 160.93/160.66 [2804]P15(x28043,x28042,x28044,x28045,x28046,x28047)+~E(x28041,x28042)+~P15(x28043,x28041,x28044,x28045,x28046,x28047)
% 160.93/160.66 [2805]P15(x28053,x28054,x28052,x28055,x28056,x28057)+~E(x28051,x28052)+~P15(x28053,x28054,x28051,x28055,x28056,x28057)
% 160.93/160.66 [2806]P15(x28063,x28064,x28065,x28062,x28066,x28067)+~E(x28061,x28062)+~P15(x28063,x28064,x28065,x28061,x28066,x28067)
% 160.93/160.66 [2807]P15(x28073,x28074,x28075,x28076,x28072,x28077)+~E(x28071,x28072)+~P15(x28073,x28074,x28075,x28076,x28071,x28077)
% 160.93/160.66 [2808]P15(x28083,x28084,x28085,x28086,x28087,x28082)+~E(x28081,x28082)+~P15(x28083,x28084,x28085,x28086,x28087,x28081)
% 160.93/160.66 [2809]P18(x28092,x28093,x28094)+~E(x28091,x28092)+~P18(x28091,x28093,x28094)
% 160.93/160.66 [2810]P18(x28103,x28102,x28104)+~E(x28101,x28102)+~P18(x28103,x28101,x28104)
% 160.93/160.66 [2811]P18(x28113,x28114,x28112)+~E(x28111,x28112)+~P18(x28113,x28114,x28111)
% 160.93/160.66 [2812]~P64(x28121)+P64(x28122)+~E(x28121,x28122)
% 160.93/160.66 [2813]P25(x28132,x28133,x28134,x28135,x28136,x28137)+~E(x28131,x28132)+~P25(x28131,x28133,x28134,x28135,x28136,x28137)
% 160.93/160.66 [2814]P25(x28143,x28142,x28144,x28145,x28146,x28147)+~E(x28141,x28142)+~P25(x28143,x28141,x28144,x28145,x28146,x28147)
% 160.93/160.66 [2815]P25(x28153,x28154,x28152,x28155,x28156,x28157)+~E(x28151,x28152)+~P25(x28153,x28154,x28151,x28155,x28156,x28157)
% 160.93/160.66 [2816]P25(x28163,x28164,x28165,x28162,x28166,x28167)+~E(x28161,x28162)+~P25(x28163,x28164,x28165,x28161,x28166,x28167)
% 160.93/160.66 [2817]P25(x28173,x28174,x28175,x28176,x28172,x28177)+~E(x28171,x28172)+~P25(x28173,x28174,x28175,x28176,x28171,x28177)
% 160.93/160.66 [2818]P25(x28183,x28184,x28185,x28186,x28187,x28182)+~E(x28181,x28182)+~P25(x28183,x28184,x28185,x28186,x28187,x28181)
% 160.93/160.66 [2819]~P143(x28191)+P143(x28192)+~E(x28191,x28192)
% 160.93/160.66 [2820]P17(x28202,x28203,x28204)+~E(x28201,x28202)+~P17(x28201,x28203,x28204)
% 160.93/160.66 [2821]P17(x28213,x28212,x28214)+~E(x28211,x28212)+~P17(x28213,x28211,x28214)
% 160.93/160.66 [2822]P17(x28223,x28224,x28222)+~E(x28221,x28222)+~P17(x28223,x28224,x28221)
% 160.93/160.66 [2823]~P98(x28231)+P98(x28232)+~E(x28231,x28232)
% 160.93/160.66 [2824]~P140(x28241)+P140(x28242)+~E(x28241,x28242)
% 160.93/160.66 [2825]~P88(x28251)+P88(x28252)+~E(x28251,x28252)
% 160.93/160.66 [2826]P51(x28262,x28263,x28264,x28265,x28266,x28267)+~E(x28261,x28262)+~P51(x28261,x28263,x28264,x28265,x28266,x28267)
% 160.93/160.66 [2827]P51(x28273,x28272,x28274,x28275,x28276,x28277)+~E(x28271,x28272)+~P51(x28273,x28271,x28274,x28275,x28276,x28277)
% 160.93/160.66 [2828]P51(x28283,x28284,x28282,x28285,x28286,x28287)+~E(x28281,x28282)+~P51(x28283,x28284,x28281,x28285,x28286,x28287)
% 160.93/160.66 [2829]P51(x28293,x28294,x28295,x28292,x28296,x28297)+~E(x28291,x28292)+~P51(x28293,x28294,x28295,x28291,x28296,x28297)
% 160.93/160.66 [2830]P51(x28303,x28304,x28305,x28306,x28302,x28307)+~E(x28301,x28302)+~P51(x28303,x28304,x28305,x28306,x28301,x28307)
% 160.93/160.66 [2831]P51(x28313,x28314,x28315,x28316,x28317,x28312)+~E(x28311,x28312)+~P51(x28313,x28314,x28315,x28316,x28317,x28311)
% 160.93/160.66 [2832]P56(x28322,x28323,x28324,x28325)+~E(x28321,x28322)+~P56(x28321,x28323,x28324,x28325)
% 160.93/160.66 [2833]P56(x28333,x28332,x28334,x28335)+~E(x28331,x28332)+~P56(x28333,x28331,x28334,x28335)
% 160.93/160.66 [2834]P56(x28343,x28344,x28342,x28345)+~E(x28341,x28342)+~P56(x28343,x28344,x28341,x28345)
% 160.93/160.66 [2835]P56(x28353,x28354,x28355,x28352)+~E(x28351,x28352)+~P56(x28353,x28354,x28355,x28351)
% 160.93/160.66 [2836]~P122(x28361)+P122(x28362)+~E(x28361,x28362)
% 160.93/160.66 [2837]P44(x28372,x28373,x28374,x28375,x28376,x28377)+~E(x28371,x28372)+~P44(x28371,x28373,x28374,x28375,x28376,x28377)
% 160.93/160.66 [2838]P44(x28383,x28382,x28384,x28385,x28386,x28387)+~E(x28381,x28382)+~P44(x28383,x28381,x28384,x28385,x28386,x28387)
% 160.93/160.66 [2839]P44(x28393,x28394,x28392,x28395,x28396,x28397)+~E(x28391,x28392)+~P44(x28393,x28394,x28391,x28395,x28396,x28397)
% 160.93/160.66 [2840]P44(x28403,x28404,x28405,x28402,x28406,x28407)+~E(x28401,x28402)+~P44(x28403,x28404,x28405,x28401,x28406,x28407)
% 160.93/160.66 [2841]P44(x28413,x28414,x28415,x28416,x28412,x28417)+~E(x28411,x28412)+~P44(x28413,x28414,x28415,x28416,x28411,x28417)
% 160.93/160.66 [2842]P44(x28423,x28424,x28425,x28426,x28427,x28422)+~E(x28421,x28422)+~P44(x28423,x28424,x28425,x28426,x28427,x28421)
% 160.93/160.66 [2843]~P133(x28431)+P133(x28432)+~E(x28431,x28432)
% 160.93/160.66 [2844]~P46(x28441)+P46(x28442)+~E(x28441,x28442)
% 160.93/160.66 [2845]~P114(x28451)+P114(x28452)+~E(x28451,x28452)
% 160.93/160.66 [2846]~P102(x28461)+P102(x28462)+~E(x28461,x28462)
% 160.93/160.66 [2847]P47(x28472,x28473)+~E(x28471,x28472)+~P47(x28471,x28473)
% 160.93/160.66 [2848]P47(x28483,x28482)+~E(x28481,x28482)+~P47(x28483,x28481)
% 160.93/160.66 [2849]~P31(x28491)+P31(x28492)+~E(x28491,x28492)
% 160.93/160.66 [2850]~P135(x28501)+P135(x28502)+~E(x28501,x28502)
% 160.93/160.66 [2851]P7(x28512,x28513)+~E(x28511,x28512)+~P7(x28511,x28513)
% 160.93/160.66 [2852]P7(x28523,x28522)+~E(x28521,x28522)+~P7(x28523,x28521)
% 160.93/160.66 [2853]~P134(x28531)+P134(x28532)+~E(x28531,x28532)
% 160.93/160.66 [2854]~P96(x28541)+P96(x28542)+~E(x28541,x28542)
% 160.93/160.66 [2855]P23(x28552,x28553,x28554,x28555,x28556)+~E(x28551,x28552)+~P23(x28551,x28553,x28554,x28555,x28556)
% 160.93/160.66 [2856]P23(x28563,x28562,x28564,x28565,x28566)+~E(x28561,x28562)+~P23(x28563,x28561,x28564,x28565,x28566)
% 160.93/160.66 [2857]P23(x28573,x28574,x28572,x28575,x28576)+~E(x28571,x28572)+~P23(x28573,x28574,x28571,x28575,x28576)
% 160.93/160.66 [2858]P23(x28583,x28584,x28585,x28582,x28586)+~E(x28581,x28582)+~P23(x28583,x28584,x28585,x28581,x28586)
% 160.93/160.66 [2859]P23(x28593,x28594,x28595,x28596,x28592)+~E(x28591,x28592)+~P23(x28593,x28594,x28595,x28596,x28591)
% 160.93/160.66 [2860]~P89(x28601)+P89(x28602)+~E(x28601,x28602)
% 160.93/160.66 [2861]~P9(x28611)+P9(x28612)+~E(x28611,x28612)
% 160.93/160.66 [2862]~P104(x28621)+P104(x28622)+~E(x28621,x28622)
% 160.93/160.66 [2863]P57(x28632,x28633)+~E(x28631,x28632)+~P57(x28631,x28633)
% 160.93/160.66 [2864]P57(x28643,x28642)+~E(x28641,x28642)+~P57(x28643,x28641)
% 160.93/160.66 [2865]P43(x28652,x28653)+~E(x28651,x28652)+~P43(x28651,x28653)
% 160.93/160.66 [2866]P43(x28663,x28662)+~E(x28661,x28662)+~P43(x28663,x28661)
% 160.93/160.66 [2867]~P127(x28671)+P127(x28672)+~E(x28671,x28672)
% 160.93/160.66 [2868]~P95(x28681)+P95(x28682)+~E(x28681,x28682)
% 160.93/160.66 [2869]P22(x28692,x28693,x28694,x28695)+~E(x28691,x28692)+~P22(x28691,x28693,x28694,x28695)
% 160.93/160.66 [2870]P22(x28703,x28702,x28704,x28705)+~E(x28701,x28702)+~P22(x28703,x28701,x28704,x28705)
% 160.93/160.66 [2871]P22(x28713,x28714,x28712,x28715)+~E(x28711,x28712)+~P22(x28713,x28714,x28711,x28715)
% 160.93/160.66 [2872]P22(x28723,x28724,x28725,x28722)+~E(x28721,x28722)+~P22(x28723,x28724,x28725,x28721)
% 160.93/160.66 [2873]~P144(x28731)+P144(x28732)+~E(x28731,x28732)
% 160.93/160.66 [2874]P45(x28742,x28743)+~E(x28741,x28742)+~P45(x28741,x28743)
% 160.93/160.66 [2875]P45(x28753,x28752)+~E(x28751,x28752)+~P45(x28753,x28751)
% 160.93/160.66 [2876]~P76(x28761)+P76(x28762)+~E(x28761,x28762)
% 160.93/160.66 [2877]~P73(x28771)+P73(x28772)+~E(x28771,x28772)
% 160.93/160.66 [2878]P48(x28782,x28783,x28784)+~E(x28781,x28782)+~P48(x28781,x28783,x28784)
% 160.93/160.66 [2879]P48(x28793,x28792,x28794)+~E(x28791,x28792)+~P48(x28793,x28791,x28794)
% 160.93/160.66 [2880]P48(x28803,x28804,x28802)+~E(x28801,x28802)+~P48(x28803,x28804,x28801)
% 160.93/160.66 [2881]~P128(x28811)+P128(x28812)+~E(x28811,x28812)
% 160.93/160.66 [2882]P42(x28822,x28823,x28824,x28825)+~E(x28821,x28822)+~P42(x28821,x28823,x28824,x28825)
% 160.93/160.66 [2883]P42(x28833,x28832,x28834,x28835)+~E(x28831,x28832)+~P42(x28833,x28831,x28834,x28835)
% 160.93/160.66 [2884]P42(x28843,x28844,x28842,x28845)+~E(x28841,x28842)+~P42(x28843,x28844,x28841,x28845)
% 160.93/160.66 [2885]P42(x28853,x28854,x28855,x28852)+~E(x28851,x28852)+~P42(x28853,x28854,x28855,x28851)
% 160.93/160.66 [2886]P10(x28862,x28863,x28864)+~E(x28861,x28862)+~P10(x28861,x28863,x28864)
% 160.93/160.66 [2887]P10(x28873,x28872,x28874)+~E(x28871,x28872)+~P10(x28873,x28871,x28874)
% 160.93/160.66 [2888]P10(x28883,x28884,x28882)+~E(x28881,x28882)+~P10(x28883,x28884,x28881)
% 160.93/160.66 [2889]~P38(x28891)+P38(x28892)+~E(x28891,x28892)
% 160.93/160.66
% 160.93/160.66 %-------------------------------------------
% 160.93/160.69 cnf(10224,plain,
% 160.93/160.69 (~E(f334(a116,x102241),x102241)),
% 160.93/160.69 inference(rename_variables,[],[4478])).
% 160.93/160.69 cnf(10227,plain,
% 160.93/160.69 (E(f334(f265(x102271,x102271),f266(x102271,x102272)),x102272)),
% 160.93/160.69 inference(rename_variables,[],[3258])).
% 160.93/160.69 cnf(10234,plain,
% 160.93/160.69 (~E(f334(a116,x102341),x102341)),
% 160.93/160.69 inference(rename_variables,[],[4478])).
% 160.93/160.69 cnf(10245,plain,
% 160.93/160.69 (~E(f334(a116,x102451),x102451)),
% 160.93/160.69 inference(rename_variables,[],[4478])).
% 160.93/160.69 cnf(10250,plain,
% 160.93/160.69 (~P1(f334(f62(x102501,x102502,f196(f888(x102501,a876))),x102503))),
% 160.93/160.69 inference(rename_variables,[],[4563])).
% 160.93/160.69 cnf(10253,plain,
% 160.93/160.69 (~P1(f334(f62(x102531,x102532,f196(f888(x102531,a876))),x102533))),
% 160.93/160.69 inference(rename_variables,[],[4563])).
% 160.93/160.69 cnf(10256,plain,
% 160.93/160.69 (~E(f334(a116,x102561),x102561)),
% 160.93/160.69 inference(rename_variables,[],[4478])).
% 160.93/160.69 cnf(10259,plain,
% 160.93/160.69 (~P1(f334(f334(f249(a881),x102591),f2(a881)))),
% 160.93/160.69 inference(rename_variables,[],[4543])).
% 160.93/160.69 cnf(10262,plain,
% 160.93/160.69 (~P1(f334(f334(f249(a881),x102621),f2(a881)))),
% 160.93/160.69 inference(rename_variables,[],[4543])).
% 160.93/160.69 cnf(10275,plain,
% 160.93/160.69 (~P1(f334(f196(f888(x102751,a876)),x102752))),
% 160.93/160.69 inference(scs_inference,[],[4478,10224,10234,10245,3089,3258,3132,3195,3139,3284,4543,10259,4540,4498,4546,3275,4533,4563,10250,4567,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037])).
% 160.93/160.69 cnf(10279,plain,
% 160.93/160.69 (~P1(f334(f334(f248(a881),f334(a116,x102791)),x102791))),
% 160.93/160.69 inference(rename_variables,[],[4548])).
% 160.93/160.69 cnf(10282,plain,
% 160.93/160.69 (~E(f334(f334(f153(x102821),x102822),x102823),x102823)),
% 160.93/160.69 inference(rename_variables,[],[4503])).
% 160.93/160.69 cnf(10288,plain,
% 160.93/160.69 (~P1(f334(f334(f249(a881),x102881),f2(a881)))),
% 160.93/160.69 inference(rename_variables,[],[4543])).
% 160.93/160.69 cnf(10290,plain,
% 160.93/160.69 (E(f44(a881,f334(f265(x102901,x102901),f266(x102901,f334(f334(f81(a881),x102902),x102903))),x102902),f2(a881))),
% 160.93/160.69 inference(scs_inference,[],[4478,10224,10234,10245,3089,3258,10227,3132,3195,3160,3139,4503,3284,4543,10259,10262,4540,4498,4548,4546,3275,4533,4563,10250,4567,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064])).
% 160.93/160.69 cnf(10291,plain,
% 160.93/160.69 (E(f334(f265(x102911,x102911),f266(x102911,x102912)),x102912)),
% 160.93/160.69 inference(rename_variables,[],[3258])).
% 160.93/160.69 cnf(10294,plain,
% 160.93/160.69 (E(f334(f265(x102941,x102941),f266(x102941,x102942)),x102942)),
% 160.93/160.69 inference(rename_variables,[],[3258])).
% 160.93/160.69 cnf(10301,plain,
% 160.93/160.69 (~P1(f334(f334(f249(a881),f334(f334(f80(a881),x103011),x103012)),x103012))),
% 160.93/160.69 inference(rename_variables,[],[4565])).
% 160.93/160.69 cnf(10304,plain,
% 160.93/160.69 (~P1(f334(f334(f249(a881),f334(f334(f80(a881),x103041),x103042)),x103042))),
% 160.93/160.69 inference(rename_variables,[],[4565])).
% 160.93/160.69 cnf(10311,plain,
% 160.93/160.69 (~E(x103111,f334(a116,x103111))),
% 160.93/160.69 inference(scs_inference,[],[4478,10224,10234,10245,3089,3258,10227,10291,3132,3195,3160,3139,4503,3368,3284,4543,10259,10262,4540,4498,4548,4128,4546,3275,4533,4563,10250,4567,4565,10301,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177])).
% 160.93/160.69 cnf(10325,plain,
% 160.93/160.69 (~P1(f334(f334(f249(a881),x103251),x103251))),
% 160.93/160.69 inference(rename_variables,[],[4539])).
% 160.93/160.69 cnf(10328,plain,
% 160.93/160.69 (P1(f334(f334(f248(a881),f44(a881,x103281,x103282)),x103281))),
% 160.93/160.69 inference(rename_variables,[],[3759])).
% 160.93/160.69 cnf(10351,plain,
% 160.93/160.69 (E(f334(f37(a881),f334(f255(a881),x103511)),x103511)),
% 160.93/160.69 inference(rename_variables,[],[3190])).
% 160.93/160.69 cnf(10359,plain,
% 160.93/160.69 (~E(f334(a116,x103591),x103591)),
% 160.93/160.69 inference(rename_variables,[],[4478])).
% 160.93/160.69 cnf(10362,plain,
% 160.93/160.69 (~E(f334(a116,x103621),x103621)),
% 160.93/160.69 inference(rename_variables,[],[4478])).
% 160.93/160.69 cnf(10365,plain,
% 160.93/160.69 (~E(f334(a116,x103651),x103651)),
% 160.93/160.69 inference(rename_variables,[],[4478])).
% 160.93/160.69 cnf(10367,plain,
% 160.93/160.69 (P1(f334(a201,a101))),
% 160.93/160.69 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,3089,3258,10227,10291,3132,3195,3160,3139,3229,4503,3190,4572,3211,3368,3284,4543,10259,10262,3887,3303,4540,4498,4539,10325,3396,3820,3759,4548,10279,4128,4546,4529,3275,4533,4534,4563,10250,4567,4565,10301,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319])).
% 160.93/160.69 cnf(10370,plain,
% 160.93/160.69 (P1(f334(f334(f249(a881),x103701),f334(a116,x103701)))),
% 160.93/160.69 inference(rename_variables,[],[3368])).
% 160.93/160.69 cnf(10379,plain,
% 160.93/160.69 (P1(f334(f334(f248(a881),x103791),x103791))),
% 160.93/160.69 inference(rename_variables,[],[3300])).
% 160.93/160.69 cnf(10386,plain,
% 160.93/160.69 (E(f334(f265(x103861,x103861),f266(x103861,x103862)),x103862)),
% 160.93/160.69 inference(rename_variables,[],[3258])).
% 160.93/160.69 cnf(10389,plain,
% 160.93/160.69 (E(f334(f265(x103891,x103891),f266(x103891,x103892)),x103892)),
% 160.93/160.69 inference(rename_variables,[],[3258])).
% 160.93/160.69 cnf(10416,plain,
% 160.93/160.69 (~P1(f334(f334(f249(a881),x104161),x104161))),
% 160.93/160.69 inference(rename_variables,[],[4539])).
% 160.93/160.69 cnf(10421,plain,
% 160.93/160.69 (~E(f334(f334(f334(f72(x104211,f885(x104212)),x104213),x104214),f334(f241(x104212),x104215)),f334(f16(f885(x104212),x104211),f210(x104212)))),
% 160.93/160.69 inference(rename_variables,[],[4560])).
% 160.93/160.69 cnf(10425,plain,
% 160.93/160.69 (E(f334(f334(f80(a881),x104251),f347(x104251,x104251)),x104251)),
% 160.93/160.69 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,3089,3258,10227,10291,10294,10386,3132,3195,3160,3139,3229,4560,4503,3190,4084,4572,3211,3368,10370,3284,4543,10259,10262,3741,3887,3328,3330,3303,4540,4498,4036,3300,10379,3302,4539,10325,3396,3820,3759,10328,4548,10279,4128,4546,4529,3275,4533,4534,4563,10250,4567,3780,4565,10301,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463])).
% 160.93/160.69 cnf(10448,plain,
% 160.93/160.69 (~E(f334(f334(f153(x104481),x104482),x104483),x104483)),
% 160.93/160.69 inference(rename_variables,[],[4503])).
% 160.93/160.69 cnf(10451,plain,
% 160.93/160.69 (~E(f334(a26,x104511),f33(x104512,x104513))),
% 160.93/160.69 inference(rename_variables,[],[4493])).
% 160.93/160.69 cnf(10462,plain,
% 160.93/160.69 (P1(f334(f334(f248(a1),x104621),x104621))),
% 160.93/160.69 inference(rename_variables,[],[3301])).
% 160.93/160.69 cnf(10467,plain,
% 160.93/160.69 (~E(f334(a116,x104671),x104671)),
% 160.93/160.69 inference(rename_variables,[],[4478])).
% 160.93/160.69 cnf(10474,plain,
% 160.93/160.69 (P1(f334(f334(f248(a881),x104741),x104741))),
% 160.93/160.69 inference(rename_variables,[],[3300])).
% 160.93/160.69 cnf(10487,plain,
% 160.93/160.69 (P1(f334(f334(f249(a881),x104871),f334(a116,x104871)))),
% 160.93/160.69 inference(rename_variables,[],[3368])).
% 160.93/160.69 cnf(10492,plain,
% 160.93/160.69 (E(f334(f334(f136(x104921),f117(x104921)),x104922),x104922)),
% 160.93/160.69 inference(rename_variables,[],[3253])).
% 160.93/160.69 cnf(10510,plain,
% 160.93/160.69 (~P1(f334(f62(x105101,x105102,f196(f888(x105101,a876))),x105103))),
% 160.93/160.69 inference(rename_variables,[],[4563])).
% 160.93/160.69 cnf(10529,plain,
% 160.93/160.69 (~P1(f334(f334(f249(a881),x105291),x105291))),
% 160.93/160.69 inference(rename_variables,[],[4539])).
% 160.93/160.69 cnf(10541,plain,
% 160.93/160.69 (E(f334(f334(f259(a881),f334(f107(a881),a101)),x105411),f334(f334(f259(a881),f2(a881)),x105411))),
% 160.93/160.69 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,10365,4493,3089,3258,10227,10291,10294,10386,3132,3195,3160,3139,3229,3253,10492,4560,4503,10282,3190,4084,4572,3211,3665,3368,10370,10487,3284,4543,10259,10262,10288,4555,3741,3887,3328,3330,3303,4540,4498,4036,3300,10379,10474,3301,3302,4539,10325,10416,3396,3820,3759,10328,4548,10279,4128,4546,4529,3275,3276,4530,4533,4534,4563,10250,10253,4567,3780,4565,10301,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823])).
% 160.93/160.69 cnf(10544,plain,
% 160.93/160.69 (~E(f334(a26,x105441),f33(x105442,x105443))),
% 160.93/160.69 inference(rename_variables,[],[4493])).
% 160.93/160.69 cnf(10553,plain,
% 160.93/160.69 (~P1(f334(f334(f249(a881),x105531),x105531))),
% 160.93/160.69 inference(rename_variables,[],[4539])).
% 160.93/160.69 cnf(10558,plain,
% 160.93/160.69 (P1(f334(f334(f249(a881),x105581),f334(a116,x105581)))),
% 160.93/160.69 inference(rename_variables,[],[3368])).
% 160.93/160.69 cnf(10561,plain,
% 160.93/160.69 (~P1(f334(f62(x105611,x105612,f196(f888(x105611,a876))),x105613))),
% 160.93/160.69 inference(rename_variables,[],[4563])).
% 160.93/160.69 cnf(10564,plain,
% 160.93/160.69 (~P1(f334(f62(x105641,x105642,f196(f888(x105641,a876))),x105643))),
% 160.93/160.69 inference(rename_variables,[],[4563])).
% 160.93/160.69 cnf(10569,plain,
% 160.93/160.69 (~P1(f334(f62(x105691,x105692,f196(f888(x105691,a876))),x105693))),
% 160.93/160.69 inference(rename_variables,[],[4563])).
% 160.93/160.69 cnf(10579,plain,
% 160.93/160.69 (~E(f334(f171(x105791),f334(a116,f334(f334(f136(x105791),f334(f171(x105791),x105792)),f334(f334(f153(x105791),x105793),f117(x105791))))),f334(f334(f153(x105791),x105793),x105792))),
% 160.93/160.69 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,10365,10467,4493,10451,3089,3258,10227,10291,10294,10386,3132,3195,3160,3139,3229,3253,10492,4560,4503,10282,3190,4084,4572,3211,3665,3368,10370,10487,10558,3284,4543,10259,10262,10288,4555,3741,3887,3328,3330,3303,4540,4498,4036,3300,10379,10474,3301,3302,4539,10325,10416,10529,3396,3820,3759,10328,4548,10279,4128,4546,4529,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,4567,3780,4565,10301,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996])).
% 160.93/160.69 cnf(10580,plain,
% 160.93/160.69 (~E(f334(a116,x105801),x105801)),
% 160.93/160.69 inference(rename_variables,[],[4478])).
% 160.93/160.69 cnf(10594,plain,
% 160.93/160.69 (P1(f334(f334(f249(a103),f334(a3,x105941)),f334(a3,f334(a116,x105941))))),
% 160.93/160.69 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,10365,10467,4493,10451,3089,3258,10227,10291,10294,10386,3132,3195,3160,3139,3229,3253,10492,4560,4503,10282,3190,4084,4572,3211,3665,3368,10370,10487,10558,3754,3284,4543,10259,10262,10288,4555,3741,3887,3328,3330,3303,4540,4498,4036,3300,10379,10474,3301,3302,4539,10325,10416,10529,3396,3820,3759,10328,4548,10279,4128,4546,4529,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,4567,3780,4565,10301,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076])).
% 160.93/160.69 cnf(10605,plain,
% 160.93/160.69 (P1(f334(f334(f248(a881),x106051),x106051))),
% 160.93/160.69 inference(rename_variables,[],[3300])).
% 160.93/160.69 cnf(10608,plain,
% 160.93/160.69 (P1(f334(f334(f249(a881),x106081),f334(a116,f334(f334(f80(a881),x106082),x106081))))),
% 160.93/160.69 inference(rename_variables,[],[3752])).
% 160.93/160.69 cnf(10610,plain,
% 160.93/160.69 (P1(f334(f334(f249(a881),x106101),f334(f334(f81(a881),f334(a116,x106101)),f334(a116,x106101))))),
% 160.93/160.69 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,10365,10467,4493,10451,3089,3258,10227,10291,10294,10386,3132,3195,3160,3139,3229,3253,10492,4560,4503,10282,3190,4084,4572,3211,3665,3368,10370,10487,10558,3754,3284,4543,10259,10262,10288,4555,3741,3887,3328,3330,3303,4540,4498,4036,3300,10379,10474,3301,3302,4539,10325,10416,10529,3396,3820,3759,10328,4548,10279,4128,4546,4529,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,3571,4567,3780,4565,10301,3752,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101])).
% 160.93/160.69 cnf(10611,plain,
% 160.93/160.69 (P1(f334(f334(f248(a881),x106111),f334(f334(f81(a881),x106111),x106111)))),
% 160.93/160.69 inference(rename_variables,[],[3571])).
% 160.93/160.69 cnf(10614,plain,
% 160.93/160.69 (P1(f334(f334(f248(a881),x106141),f334(f334(f81(a881),x106141),x106141)))),
% 160.93/160.69 inference(rename_variables,[],[3571])).
% 160.93/160.69 cnf(10619,plain,
% 160.93/160.69 (P1(f334(f334(f249(a881),x106191),f334(a116,x106191)))),
% 160.93/160.69 inference(rename_variables,[],[3368])).
% 160.93/160.69 cnf(10622,plain,
% 160.93/160.69 (P1(f334(f334(f249(a881),x106221),f334(a116,x106221)))),
% 160.93/160.69 inference(rename_variables,[],[3368])).
% 160.93/160.69 cnf(10625,plain,
% 160.93/160.69 (P1(f334(f334(f336(x106251),x106252),f257(f888(x106251,a876))))),
% 160.93/160.69 inference(rename_variables,[],[3459])).
% 160.93/160.69 cnf(10642,plain,
% 160.93/160.69 (~P1(f334(f334(f249(a881),f334(f334(f80(a881),x106421),x106422)),x106422))),
% 160.93/160.69 inference(rename_variables,[],[4565])).
% 160.93/160.69 cnf(10645,plain,
% 160.93/160.69 (~P1(f334(f334(f249(a881),f334(f334(f80(a881),x106451),x106452)),x106452))),
% 160.93/160.69 inference(rename_variables,[],[4565])).
% 160.93/160.69 cnf(10648,plain,
% 160.93/160.69 (~P1(f334(f334(f248(a881),f334(a116,x106481)),x106481))),
% 160.93/160.69 inference(rename_variables,[],[4548])).
% 160.93/160.69 cnf(10651,plain,
% 160.93/160.69 (~P1(f334(f334(f248(a881),f334(a116,x106511)),x106511))),
% 160.93/160.69 inference(rename_variables,[],[4548])).
% 160.93/160.69 cnf(10654,plain,
% 160.93/160.69 (P1(f334(f257(f888(x106541,a876)),x106542))),
% 160.93/160.69 inference(rename_variables,[],[3362])).
% 160.93/160.69 cnf(10657,plain,
% 160.93/160.70 (E(f334(f37(a881),f334(f255(a881),x106571)),x106571)),
% 160.93/160.70 inference(rename_variables,[],[3190])).
% 160.93/160.70 cnf(10660,plain,
% 160.93/160.70 (P1(f334(f334(f249(a881),x106601),f334(a116,x106601)))),
% 160.93/160.70 inference(rename_variables,[],[3368])).
% 160.93/160.70 cnf(10667,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),x106671),x106671))),
% 160.93/160.70 inference(rename_variables,[],[3300])).
% 160.93/160.70 cnf(10672,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),x106721),x106721))),
% 160.93/160.70 inference(rename_variables,[],[3301])).
% 160.93/160.70 cnf(10681,plain,
% 160.93/160.70 (E(f334(f265(x106811,x106811),f266(x106811,x106812)),x106812)),
% 160.93/160.70 inference(rename_variables,[],[3258])).
% 160.93/160.70 cnf(10684,plain,
% 160.93/160.70 (P1(f334(f257(f888(x106841,a876)),x106842))),
% 160.93/160.70 inference(rename_variables,[],[3362])).
% 160.93/160.70 cnf(10687,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),f2(a881)),x106871))),
% 160.93/160.70 inference(rename_variables,[],[3322])).
% 160.93/160.70 cnf(10690,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x106901,a876)),f196(f888(x106901,a876))),x106902))),
% 160.93/160.70 inference(rename_variables,[],[3750])).
% 160.93/160.70 cnf(10693,plain,
% 160.93/160.70 (P1(f334(f257(f888(x106931,a876)),x106932))),
% 160.93/160.70 inference(rename_variables,[],[3362])).
% 160.93/160.70 cnf(10695,plain,
% 160.93/160.70 (~P1(f334(f334(f248(a881),f334(f334(f81(a881),f334(a116,x106951)),f334(a116,x106951))),x106951))),
% 160.93/160.70 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,10365,10467,4493,10451,3089,3258,10227,10291,10294,10386,10389,3132,3195,3160,3139,3229,3253,10492,4560,4503,10282,3190,10351,4084,4572,3211,3665,3605,3368,10370,10487,10558,10619,10622,3754,3284,4543,10259,10262,10288,4555,3741,3513,3887,3328,3330,3303,4540,4498,4036,3300,10379,10474,10605,3301,10462,3302,4539,10325,10416,10529,3459,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,3322,4128,4546,4529,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,4570,3750,3571,10611,10614,4567,3780,4565,10301,10304,10642,3752,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316])).
% 160.93/160.70 cnf(10696,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),x106961),f334(f334(f81(a881),x106961),x106961)))),
% 160.93/160.70 inference(rename_variables,[],[3571])).
% 160.93/160.70 cnf(10700,plain,
% 160.93/160.70 (E(f334(f171(x107001),f175(x107002,f334(f334(f136(x107001),f334(f171(x107001),x107003)),f334(f334(f153(x107001),x107004),f117(x107001))),f117(x107002))),f334(f334(f153(x107001),x107004),x107003))),
% 160.93/160.70 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,10365,10467,4493,10451,3089,3258,10227,10291,10294,10386,10389,3236,3132,3195,3160,3139,3229,3253,10492,4560,4503,10282,3190,10351,4084,4572,3211,3665,3605,3368,10370,10487,10558,10619,10622,3754,3284,4543,10259,10262,10288,4555,3741,3513,3887,3328,3330,3303,4540,4498,4036,3300,10379,10474,10605,3301,10462,3302,4539,10325,10416,10529,3459,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,3322,4128,4546,4529,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,4570,3750,3571,10611,10614,4567,3780,4565,10301,10304,10642,3752,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355])).
% 160.93/160.70 cnf(10701,plain,
% 160.93/160.70 (E(f175(x107011,x107012,f117(x107011)),x107012)),
% 160.93/160.70 inference(rename_variables,[],[3236])).
% 160.93/160.70 cnf(10713,plain,
% 160.93/160.70 (~P1(f334(f334(f248(a881),f334(a116,f334(a116,f334(f334(f80(a881),x107131),x107132)))),f334(a116,x107132)))),
% 160.93/160.70 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,10365,10467,4493,10451,3089,3258,10227,10291,10294,10386,10389,3236,3132,3195,3160,3139,3229,3253,10492,4560,4503,10282,3190,10351,4084,4572,3211,3665,3605,3368,10370,10487,10558,10619,10622,10660,3754,3284,4543,10259,10262,10288,4555,3741,3513,3887,3328,3330,3303,4540,4498,4036,3300,10379,10474,10605,3301,10462,3302,4539,10325,10416,10529,3459,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,3322,4128,4546,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,4570,3750,3571,10611,10614,4567,3780,4565,10301,10304,10642,3752,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363])).
% 160.93/160.70 cnf(10736,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),x107361),x107361))),
% 160.93/160.70 inference(rename_variables,[],[3300])).
% 160.93/160.70 cnf(10747,plain,
% 160.93/160.70 (~P1(f334(f334(f196(f888(x107471,f888(x107472,a876))),x107473),x107474))),
% 160.93/160.70 inference(rename_variables,[],[4568])).
% 160.93/160.70 cnf(10754,plain,
% 160.93/160.70 (P1(f334(f334(f249(a881),x107541),f334(a116,x107541)))),
% 160.93/160.70 inference(rename_variables,[],[3368])).
% 160.93/160.70 cnf(10756,plain,
% 160.93/160.70 (P1(f334(f334(f249(a1),f334(f334(f22(a1),x107561),f78(a1))),x107561))),
% 160.93/160.70 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,10365,10467,4493,10451,3089,3258,10227,10291,10294,10386,10389,3236,3132,3195,3160,3139,3229,3253,10492,4560,4503,10282,3190,10351,4084,3938,4572,3211,3665,3605,3368,10370,10487,10558,10619,10622,10660,3754,3284,4543,10259,10262,10288,4555,3741,3513,3887,3328,3330,3303,4540,4498,4036,3300,10379,10474,10605,10667,10736,3301,10462,10672,3302,4539,10325,10416,10529,3459,4551,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,3322,4128,4546,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,4570,3750,3571,10611,10614,4567,4568,3780,4565,10301,10304,10642,3752,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617])).
% 160.93/160.70 cnf(10757,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),x107571),x107571))),
% 160.93/160.70 inference(rename_variables,[],[3301])).
% 160.93/160.70 cnf(10762,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x107621),f2(a881)))),
% 160.93/160.70 inference(rename_variables,[],[4543])).
% 160.93/160.70 cnf(10775,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x107751),f2(a881)))),
% 160.93/160.70 inference(rename_variables,[],[4543])).
% 160.93/160.70 cnf(10778,plain,
% 160.93/160.70 (~P1(f334(f334(f249(f888(x107781,a876)),x107782),f196(f888(x107781,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4561])).
% 160.93/160.70 cnf(10781,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),x107811),x107811))),
% 160.93/160.70 inference(rename_variables,[],[3300])).
% 160.93/160.70 cnf(10784,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),x107841),x107841))),
% 160.93/160.70 inference(rename_variables,[],[3300])).
% 160.93/160.70 cnf(10799,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x107991),x107991))),
% 160.93/160.70 inference(rename_variables,[],[4539])).
% 160.93/160.70 cnf(10808,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x108081),x108082),f196(f888(x108081,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(10817,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),x108171),x108171))),
% 160.93/160.70 inference(rename_variables,[],[3300])).
% 160.93/160.70 cnf(10820,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x108201),x108202),f196(f888(x108201,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(10823,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x108231,a876)),f334(f313(x108232,x108231,x108233),f334(f314(x108232,x108231,x108233),x108234))),x108234))),
% 160.93/160.70 inference(rename_variables,[],[4189])).
% 160.93/160.70 cnf(10830,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x108301,a876)),f334(f174(x108301),f334(f138(x108301,x108302),x108303))),f334(f174(x108301),x108303)))),
% 160.93/160.70 inference(rename_variables,[],[3949])).
% 160.93/160.70 cnf(10833,plain,
% 160.93/160.70 (E(f334(f313(x108331,x108331,f5(x108331)),x108332),x108332)),
% 160.93/160.70 inference(rename_variables,[],[3358])).
% 160.93/160.70 cnf(10838,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),f2(a881)),x108381))),
% 160.93/160.70 inference(rename_variables,[],[3322])).
% 160.93/160.70 cnf(10841,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),x108411),x108411))),
% 160.93/160.70 inference(rename_variables,[],[3300])).
% 160.93/160.70 cnf(10844,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x108441),x108441))),
% 160.93/160.70 inference(rename_variables,[],[4539])).
% 160.93/160.70 cnf(10847,plain,
% 160.93/160.70 (~P1(f334(f334(f196(f888(x108471,f888(x108472,a876))),x108473),x108474))),
% 160.93/160.70 inference(rename_variables,[],[4568])).
% 160.93/160.70 cnf(10854,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x108541),x108541))),
% 160.93/160.70 inference(rename_variables,[],[4539])).
% 160.93/160.70 cnf(10865,plain,
% 160.93/160.70 (P1(f334(f334(f249(a881),x108651),f334(a116,f334(f334(f80(a881),x108652),x108651))))),
% 160.93/160.70 inference(rename_variables,[],[3752])).
% 160.93/160.70 cnf(10868,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),x108681),f334(f334(f81(a881),x108681),x108681)))),
% 160.93/160.70 inference(rename_variables,[],[3571])).
% 160.93/160.70 cnf(10878,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),x108781),x108781))),
% 160.93/160.70 inference(rename_variables,[],[3300])).
% 160.93/160.70 cnf(10881,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),x108811),x108811))),
% 160.93/160.70 inference(rename_variables,[],[3301])).
% 160.93/160.70 cnf(10884,plain,
% 160.93/160.70 (~E(f334(a116,x108841),x108841)),
% 160.93/160.70 inference(rename_variables,[],[4478])).
% 160.93/160.70 cnf(10889,plain,
% 160.93/160.70 (P1(f334(f334(f336(x108891),x108892),f257(f888(x108891,a876))))),
% 160.93/160.70 inference(rename_variables,[],[3459])).
% 160.93/160.70 cnf(10894,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x108941),f2(a881)))),
% 160.93/160.70 inference(rename_variables,[],[4543])).
% 160.93/160.70 cnf(10909,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),f2(a881)),x109091))),
% 160.93/160.70 inference(rename_variables,[],[3322])).
% 160.93/160.70 cnf(10916,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),x109161),x109161))),
% 160.93/160.70 inference(rename_variables,[],[3300])).
% 160.93/160.70 cnf(10925,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x109251),x109252),f196(f888(x109251,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(10927,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x109271,a876)),f40(f888(x109271,a876),f334(f311(x109271),x109272))),x109272))),
% 160.93/160.70 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,4493,10451,3089,3258,10227,10291,10294,10386,10389,3236,3132,3195,3160,3139,3358,3229,3253,10492,4560,4503,10282,3190,10351,4084,3938,4572,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,3754,3284,4543,10259,10262,10288,10762,10775,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,3666,4036,4561,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,4551,10808,10820,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,4570,3750,3571,10611,10614,10696,10868,4567,4568,10747,4189,3780,4565,10301,10304,10642,3752,10608,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763])).
% 160.93/160.70 cnf(10929,plain,
% 160.93/160.70 (E(f334(f334(f105(f888(x109291,a876)),f334(f334(f105(f888(x109291,a876)),x109292),f334(f79(f888(x109291,a876)),x109293))),x109293),f196(f888(x109291,a876)))),
% 160.93/160.70 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,4493,10451,3089,3258,10227,10291,10294,10386,10389,3236,3132,3195,3160,3139,3358,3229,3253,10492,4560,4503,10282,3190,10351,4084,3938,4572,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,3754,3284,4543,10259,10262,10288,10762,10775,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,3666,4036,4561,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,4551,10808,10820,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,4570,3750,3571,10611,10614,10696,10868,4567,4568,10747,4189,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765])).
% 160.93/160.70 cnf(10933,plain,
% 160.93/160.70 (P1(f334(f334(f336(x109331),x109332),f257(f888(x109331,a876))))),
% 160.93/160.70 inference(rename_variables,[],[3459])).
% 160.93/160.70 cnf(10936,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(f882(x109361),f882(x109361))),f334(f334(f269(f882(x109361),f882(x109361)),x109362),f117(x109361))),f147(x109361,x109363)))),
% 160.93/160.70 inference(rename_variables,[],[4572])).
% 160.93/160.70 cnf(10942,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(x109421,x109421)),x109422),f266(x109421,f196(f888(x109421,a876)))))),
% 160.93/160.70 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,4493,10451,3089,3258,10227,10291,10294,10386,10389,3236,3132,3195,3160,3139,3358,3229,3253,10492,4560,4503,10282,3190,10351,4084,3938,4572,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,3754,3284,4543,10259,10262,10288,10762,10775,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,3666,4036,4561,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,4551,10808,10820,10925,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,4570,3750,3571,10611,10614,10696,10868,4567,4568,10747,4189,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906])).
% 160.93/160.70 cnf(10943,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x109431),x109432),f196(f888(x109431,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(10945,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x109451),x109452),f334(f314(x109451,x109453,x109454),f196(f888(x109453,a876)))))),
% 160.93/160.70 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,4493,10451,3089,3258,10227,10291,10294,10386,10389,3236,3132,3195,3160,3139,3358,3229,3253,10492,4560,4503,10282,3190,10351,4084,3938,4572,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,3754,3284,4543,10259,10262,10288,10762,10775,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,3666,4036,4561,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,4551,10808,10820,10925,10943,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,4570,3750,3571,10611,10614,10696,10868,4567,4568,10747,4189,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940])).
% 160.93/160.70 cnf(10946,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x109461),x109462),f196(f888(x109461,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(10949,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x109491,a876)),x109492),f334(f334(f312(x109491),x109493),x109492)))),
% 160.93/160.70 inference(rename_variables,[],[3748])).
% 160.93/160.70 cnf(10952,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),x109521),x109521))),
% 160.93/160.70 inference(rename_variables,[],[3300])).
% 160.93/160.70 cnf(10955,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x109551,a876)),x109552),f334(f334(f312(x109551),x109553),x109552)))),
% 160.93/160.70 inference(rename_variables,[],[3748])).
% 160.93/160.70 cnf(10957,plain,
% 160.93/160.70 (P36(x109571,x109572,x109573,f118(x109571,f117(x109571)),f117(x109572))),
% 160.93/160.70 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,4493,10451,3089,3142,3258,10227,10291,10294,10386,10389,3236,3132,3195,3160,3139,3358,3229,3253,10492,4560,4503,10282,3190,10351,4084,3938,4572,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,3754,3284,4543,10259,10262,10288,10762,10775,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,3666,4036,4561,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,4551,10808,10820,10925,10943,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,4570,3748,10949,3750,3571,10611,10614,10696,10868,4567,4568,10747,4189,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044])).
% 160.93/160.70 cnf(10970,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x109701,a876)),x109702),f334(f334(f312(x109701),x109703),x109702)))),
% 160.93/160.70 inference(rename_variables,[],[3748])).
% 160.93/160.70 cnf(10977,plain,
% 160.93/160.70 (~P1(f334(f62(x109771,x109772,f196(f888(x109771,a876))),x109773))),
% 160.93/160.70 inference(rename_variables,[],[4563])).
% 160.93/160.70 cnf(10981,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(a881,a881)),f334(f334(f269(a881,a881),f334(a116,x109811)),x109811)),f310(a881,a324)))),
% 160.93/160.70 inference(scs_inference,[],[4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,4493,10451,3089,3142,3258,10227,10291,10294,10386,10389,3236,3132,3195,3160,3139,3358,3229,3253,10492,4560,4503,10282,3190,10351,4084,3938,4572,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,3754,3284,4543,10259,10262,10288,10762,10775,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,3666,4036,4561,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,10933,4551,10808,10820,10925,10943,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,3904,3748,10949,10955,3750,3571,10611,10614,10696,10868,4567,4568,10747,4189,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377])).
% 160.93/160.70 cnf(10990,plain,
% 160.93/160.70 (P1(f334(f334(f249(a881),x109901),f334(a116,x109901)))),
% 160.93/160.70 inference(rename_variables,[],[3368])).
% 160.93/160.70 cnf(11000,plain,
% 160.93/160.70 (~E(f334(f313(x110001,f888(x110001,a876),x110002),x110003),f334(f311(x110001),x110003))),
% 160.93/160.70 inference(rename_variables,[],[4549])).
% 160.93/160.70 cnf(11003,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x110031),x110032),f196(f888(x110031,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11006,plain,
% 160.93/160.70 (P1(f334(f334(f336(f887(x110061,x110061)),f334(f334(f269(x110061,x110061),x110062),x110062)),f310(x110061,x110063)))),
% 160.93/160.70 inference(rename_variables,[],[3938])).
% 160.93/160.70 cnf(11009,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x110091,a876)),x110092),f257(f888(x110091,a876))))),
% 160.93/160.70 inference(rename_variables,[],[3684])).
% 160.93/160.70 cnf(11012,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x110121,a876)),f334(f174(x110121),f178(x110121,x110122,x110123))),f334(f174(x110121),x110122)))),
% 160.93/160.70 inference(rename_variables,[],[4000])).
% 160.93/160.70 cnf(11028,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x110281,a876)),f196(f888(x110281,a876))),x110282))),
% 160.93/160.70 inference(rename_variables,[],[3750])).
% 160.93/160.70 cnf(11039,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(f882(x110391),f882(x110391))),f334(f334(f269(f882(x110391),f882(x110391)),x110392),f117(x110391))),f149(x110391,x110393)))),
% 160.93/160.70 inference(rename_variables,[],[4573])).
% 160.93/160.70 cnf(11050,plain,
% 160.93/160.70 (~E(f334(a116,x110501),x110501)),
% 160.93/160.70 inference(rename_variables,[],[4478])).
% 160.93/160.70 cnf(11053,plain,
% 160.93/160.70 (~E(f334(a116,x110531),x110531)),
% 160.93/160.70 inference(rename_variables,[],[4478])).
% 160.93/160.70 cnf(11065,plain,
% 160.93/160.70 (P27(x110651,x110651,f5(x110651),x110652)),
% 160.93/160.70 inference(rename_variables,[],[3543])).
% 160.93/160.70 cnf(11067,plain,
% 160.93/160.70 (P1(f334(f334(f336(f887(a881,a881)),f334(f334(f269(a881,a881),x110671),f334(a116,x110671))),f334(f334(f291(a881,a881,a881),a324),f310(a881,a324))))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,4493,10451,10544,3089,3142,3258,10227,10291,10294,10386,10389,3236,3761,3132,3195,3160,3139,3358,3229,3253,10492,4560,3936,4503,10282,4549,3190,10351,4084,3938,11006,4572,10936,4573,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,3754,3284,4543,10259,10262,10288,10762,10775,10894,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,4000,3666,4036,3684,4561,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,10933,4551,10808,10820,10925,10943,10946,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,3904,3748,10949,10955,3750,10690,3571,10611,10614,10696,10868,4567,4568,10747,4189,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690])).
% 160.93/160.70 cnf(11070,plain,
% 160.93/160.70 (~E(f334(f313(x110701,f888(x110701,a876),x110702),x110703),f334(f311(x110701),x110703))),
% 160.93/160.70 inference(rename_variables,[],[4549])).
% 160.93/160.70 cnf(11075,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x110751,a876)),x110752),f257(f888(x110751,a876))))),
% 160.93/160.70 inference(rename_variables,[],[3684])).
% 160.93/160.70 cnf(11089,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x110891),x110892),f196(f888(x110891,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11092,plain,
% 160.93/160.70 (~P1(f334(f334(f248(a881),f334(a116,x110921)),x110921))),
% 160.93/160.70 inference(rename_variables,[],[4548])).
% 160.93/160.70 cnf(11097,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x110971),x110972),f196(f888(x110971,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11109,plain,
% 160.93/160.70 (~P1(f334(f334(f336(a881),f334(a116,f334(f144(a881,a881,f80(a881),f2(a881)),x111091))),f334(f174(a881),x111091)))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,4493,10451,10544,3089,3142,3258,10227,10291,10294,10386,10389,3236,3761,3132,3195,3160,3139,3358,3229,3253,10492,4560,3936,4503,10282,4549,11000,3407,3190,10351,4084,3938,11006,4572,10936,4573,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,3754,3284,4543,10259,10262,10288,10762,10775,10894,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,4000,3666,4036,3684,11009,4561,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,10933,4551,10808,10820,10925,10943,10946,11003,11089,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,11092,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,3904,3748,10949,10955,3750,10690,3571,10611,10614,10696,10868,4567,4568,10747,4189,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830])).
% 160.93/160.70 cnf(11110,plain,
% 160.93/160.70 (~P1(f334(f334(f248(a881),f334(a116,x111101)),x111101))),
% 160.93/160.70 inference(rename_variables,[],[4548])).
% 160.93/160.70 cnf(11113,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x111131),x111132),f196(f888(x111131,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11123,plain,
% 160.93/160.70 (E(f334(x111231,f716(f334(x111231,x111232),f334(f241(x111233),x111232),x111231,x111234,x111233)),f334(x111231,x111232))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,4493,10451,10544,3089,3142,3258,10227,10291,10294,10386,10389,3236,3761,3132,3195,3160,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,4549,11000,3407,3190,10351,4084,3938,11006,4572,10936,4573,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,3754,3284,4543,10259,10262,10288,10762,10775,10894,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,4000,3666,4036,3684,11009,4561,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,10933,4551,10808,10820,10925,10943,10946,11003,11089,11097,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,11092,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,3904,3748,10949,10955,3750,10690,3571,10611,10614,10696,10868,4567,4568,10747,4189,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905])).
% 160.93/160.70 cnf(11132,plain,
% 160.93/160.70 (P1(f334(f334(f336(f887(x111321,x111321)),f334(f334(f269(x111321,x111321),x111322),x111322)),f310(x111321,x111323)))),
% 160.93/160.70 inference(rename_variables,[],[3938])).
% 160.93/160.70 cnf(11137,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(f882(x111371),f882(x111371))),f334(f334(f269(f882(x111371),f882(x111371)),x111372),f117(x111371))),f147(x111371,x111373)))),
% 160.93/160.70 inference(rename_variables,[],[4572])).
% 160.93/160.70 cnf(11140,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(f882(x111401),f882(x111401))),f334(f334(f269(f882(x111401),f882(x111401)),x111402),f117(x111401))),f149(x111401,x111403)))),
% 160.93/160.70 inference(rename_variables,[],[4573])).
% 160.93/160.70 cnf(11143,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(f882(x111431),f882(x111431))),f334(f334(f269(f882(x111431),f882(x111431)),x111432),f117(x111431))),f159(x111431,x111433)))),
% 160.93/160.70 inference(rename_variables,[],[4574])).
% 160.93/160.70 cnf(11145,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(f882(x111451),f882(x111451))),f334(f334(f269(f882(x111451),f882(x111451)),f117(x111451)),x111452)),f334(f289(f882(x111451),f882(x111451)),f147(x111451,x111453))))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,4493,10451,10544,3089,3142,3258,10227,10291,10294,10386,10389,3236,3761,3132,3195,3160,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,4549,11000,3407,3190,10351,4084,3938,11006,4572,10936,11137,4573,11039,4574,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,3754,3284,4543,10259,10262,10288,10762,10775,10894,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,4000,3666,4036,3684,11009,4561,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,10933,4551,10808,10820,10925,10943,10946,11003,11089,11097,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,11092,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,3904,3748,10949,10955,3750,10690,3571,10611,10614,10696,10868,4567,4568,10747,4189,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052])).
% 160.93/160.70 cnf(11148,plain,
% 160.93/160.70 (~P1(f334(f334(f249(f888(x111481,a876)),x111482),f196(f888(x111481,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4561])).
% 160.93/160.70 cnf(11151,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x111511),x111512),f196(f888(x111511,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11157,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x111571,a876)),x111572),f334(f334(f114(f888(x111571,a876)),x111573),f257(f888(x111571,a876)))))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,4493,10451,10544,3089,3142,3258,10227,10291,10294,10386,10389,3236,3761,3132,3195,3160,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,4549,11000,3407,3190,10351,4084,3938,11006,4572,10936,11137,4573,11039,4574,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,3754,3284,4543,10259,10262,10288,10762,10775,10894,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,4000,3666,4036,3684,11009,11075,4561,10778,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,10933,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,11092,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,3904,3748,10949,10955,3750,10690,3571,10611,10614,10696,10868,4567,4568,10747,4189,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107])).
% 160.93/160.70 cnf(11158,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x111581,a876)),x111582),f257(f888(x111581,a876))))),
% 160.93/160.70 inference(rename_variables,[],[3684])).
% 160.93/160.70 cnf(11161,plain,
% 160.93/160.70 (~P1(f334(f334(f196(f888(x111611,f888(x111612,a876))),x111613),x111614))),
% 160.93/160.70 inference(rename_variables,[],[4568])).
% 160.93/160.70 cnf(11170,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x111701),x111702),f196(f888(x111701,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11173,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(x111731,x111731)),f334(f334(f269(x111731,x111731),x111732),x111733)),f155(x111731,f117(f888(x111731,a881)))))),
% 160.93/160.70 inference(rename_variables,[],[4570])).
% 160.93/160.70 cnf(11176,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x111761,a876)),x111762),x111762))),
% 160.93/160.70 inference(rename_variables,[],[3601])).
% 160.93/160.70 cnf(11179,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x111791),x111792),f196(f888(x111791,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11181,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x111811,a876)),f334(f288(x111812,x111811,f196(f888(f887(x111812,x111811),a876))),x111813)),x111814))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,4493,10451,10544,3089,3142,3258,10227,10291,10294,10386,10389,3236,3761,3132,3195,3160,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,4549,11000,3407,3190,10351,4084,3938,11006,4572,10936,11137,4573,11039,4574,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,3754,3284,4543,10259,10262,10288,10762,10775,10894,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,4000,3666,4036,3684,11009,11075,4561,10778,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,10933,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,11092,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,3904,3748,10949,10955,3601,3750,10690,11028,3571,10611,10614,10696,10868,4567,4568,10747,10847,4189,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279])).
% 160.93/160.70 cnf(11182,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x111821,a876)),f196(f888(x111821,a876))),x111822))),
% 160.93/160.70 inference(rename_variables,[],[3750])).
% 160.93/160.70 cnf(11185,plain,
% 160.93/160.70 (P1(f334(f334(f336(f887(x111851,x111851)),f334(f334(f269(x111851,x111851),x111852),x111852)),f310(x111851,x111853)))),
% 160.93/160.70 inference(rename_variables,[],[3938])).
% 160.93/160.70 cnf(11187,plain,
% 160.93/160.70 (~P36(x111871,x111872,x111873,f334(f334(f156(x111874,x111871),x111875),f334(a116,f117(x111874))),f117(x111872))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,4493,10451,10544,3089,3142,3258,10227,10291,10294,10386,10389,3236,3761,3132,3195,3160,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,4549,11000,3407,3190,10351,4084,3938,11006,11132,4572,10936,11137,4573,11039,4574,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,3754,3284,4543,10259,10262,10288,10762,10775,10894,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,4000,3666,4036,3684,11009,11075,4561,10778,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,10933,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,11092,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,3904,3748,10949,10955,3601,3750,10690,11028,3571,10611,10614,10696,10868,4567,4568,10747,10847,4189,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288])).
% 160.93/160.70 cnf(11189,plain,
% 160.93/160.70 (~E(f334(f334(f105(f888(f887(f882(x111891),f882(x111891)),a876)),f334(f289(f882(x111891),f882(x111891)),f160(x111891,x111892))),f310(f882(x111891),f160(x111891,x111892))),f196(f888(f887(f882(x111891),f882(x111891)),a876)))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,4493,10451,10544,3089,3142,3258,10227,10291,10294,10386,10389,3236,3761,3132,3195,3160,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,4549,11000,3407,3190,10351,4084,3938,11006,11132,4572,10936,11137,4573,11039,4574,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,3754,3284,4543,10259,10262,10288,10762,10775,10894,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,4000,3666,4036,3684,11009,11075,4561,10778,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,10933,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,11092,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,3904,3748,10949,10955,3601,3750,10690,11028,3571,10611,10614,10696,10868,4567,4568,10747,10847,4189,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310])).
% 160.93/160.70 cnf(11191,plain,
% 160.93/160.70 (P36(x111911,x111912,x111913,f334(f334(f156(x111914,x111911),x111915),f118(x111914,f117(x111914))),f117(x111912))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,4493,10451,10544,3089,3142,3258,10227,10291,10294,10386,10389,3236,3761,3132,3195,3160,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,4549,11000,3407,3190,10351,4084,3938,11006,11132,4572,10936,11137,4573,11039,4574,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,3754,3284,4543,10259,10262,10288,10762,10775,10894,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,4000,3666,4036,3684,11009,11075,4561,10778,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,10933,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,11092,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,3904,3748,10949,10955,3601,3750,10690,11028,3571,10611,10614,10696,10868,4567,4568,10747,10847,4189,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311])).
% 160.93/160.70 cnf(11196,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(f882(x111961),f882(x111961))),f334(f334(f269(f882(x111961),f882(x111961)),x111962),f117(x111961))),f159(x111961,x111963)))),
% 160.93/160.70 inference(rename_variables,[],[4574])).
% 160.93/160.70 cnf(11199,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(f882(x111991),f882(x111991))),f334(f334(f269(f882(x111991),f882(x111991)),f117(x111991)),x111992)),f147(x111991,x111993)))),
% 160.93/160.70 inference(rename_variables,[],[4575])).
% 160.93/160.70 cnf(11204,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(f888(x112041,a876),f888(x112041,a876))),f334(f334(f269(f888(x112041,a876),f888(x112041,a876)),x112042),f196(f888(x112041,a876)))),f309(x112041)))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,4493,10451,10544,3089,3142,3258,10227,10291,10294,10386,10389,3236,3761,3132,3195,3160,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,4549,11000,3407,3190,10351,4084,3938,11006,11132,4572,10936,11137,4573,11039,4574,11143,4575,4576,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,3754,3284,4543,10259,10262,10288,10762,10775,10894,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,4000,3666,4036,3684,11009,11075,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,10933,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,11092,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,3904,3748,10949,10955,3601,3750,10690,11028,3571,10611,10614,10696,10868,4567,4568,10747,10847,4189,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438])).
% 160.93/160.70 cnf(11207,plain,
% 160.93/160.70 (P1(f334(f334(f336(x112071),x112072),f257(f888(x112071,a876))))),
% 160.93/160.70 inference(rename_variables,[],[3459])).
% 160.93/160.70 cnf(11212,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x112121,a876)),f196(f888(x112121,a876))),x112122))),
% 160.93/160.70 inference(rename_variables,[],[3750])).
% 160.93/160.70 cnf(11215,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x112151),x112152),f196(f888(x112151,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11218,plain,
% 160.93/160.70 (P1(f334(f334(f249(a881),x112181),f334(a116,x112181)))),
% 160.93/160.70 inference(rename_variables,[],[3368])).
% 160.93/160.70 cnf(11221,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x112211,a876)),x112212),f257(f888(x112211,a876))))),
% 160.93/160.70 inference(rename_variables,[],[3684])).
% 160.93/160.70 cnf(11225,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x112251,a876)),f334(f288(x112252,x112251,x112253),f196(f888(x112252,a876)))),x112254))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,4493,10451,10544,3089,3142,3258,10227,10291,10294,10386,10389,3236,3761,3132,3195,3160,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,4549,11000,3407,3190,10351,4084,3938,11006,11132,4572,10936,11137,4573,11039,4574,11143,4575,4576,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,3754,3284,4543,10259,10262,10288,10762,10775,10894,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,10933,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,11092,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,3904,3748,10949,10955,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,4568,10747,10847,4189,4089,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547])).
% 160.93/160.70 cnf(11226,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(x112261,a876)),f196(f888(x112261,a876))),x112262))),
% 160.93/160.70 inference(rename_variables,[],[3750])).
% 160.93/160.70 cnf(11228,plain,
% 160.93/160.70 (~P1(f334(f66(a881,x112281,x112282,x112283,f257(f888(a881,a876))),x112284))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,4493,10451,10544,3089,3142,3258,10227,10291,10294,10386,10389,3236,3761,3132,3195,3160,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,4549,11000,3407,3190,10351,4084,3938,11006,11132,4572,10936,11137,4573,11039,4574,11143,4575,4576,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,3754,3284,4543,10259,10262,10288,10762,10775,10894,4555,3741,3513,3887,3328,3330,3303,4540,4498,4047,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,3459,10625,10889,10933,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,3362,10654,10684,3396,3820,3759,10328,4548,10279,10648,10651,11092,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,3904,3748,10949,10955,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,4568,10747,10847,4189,4089,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569])).
% 160.93/160.70 cnf(11239,plain,
% 160.93/160.70 (P1(f334(f257(f888(x112391,a876)),x112392))),
% 160.93/160.70 inference(rename_variables,[],[3362])).
% 160.93/160.70 cnf(11247,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(f882(x112471),f882(x112471))),f334(f334(f269(f882(x112471),f882(x112471)),x112472),f117(x112471))),f147(x112471,x112473)))),
% 160.93/160.70 inference(rename_variables,[],[4572])).
% 160.93/160.70 cnf(11250,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(f882(x112501),f882(x112501))),f334(f334(f269(f882(x112501),f882(x112501)),x112502),f117(x112501))),f149(x112501,x112503)))),
% 160.93/160.70 inference(rename_variables,[],[4573])).
% 160.93/160.70 cnf(11253,plain,
% 160.93/160.70 (~E(f334(f334(f153(x112531),x112532),x112533),x112533)),
% 160.93/160.70 inference(rename_variables,[],[4503])).
% 160.93/160.70 cnf(11256,plain,
% 160.93/160.70 (~E(f334(a116,x112561),x112561)),
% 160.93/160.70 inference(rename_variables,[],[4478])).
% 160.93/160.70 cnf(11259,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x112591),x112591))),
% 160.93/160.70 inference(rename_variables,[],[4539])).
% 160.93/160.70 cnf(11262,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x112621),x112622),f196(f888(x112621,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11267,plain,
% 160.93/160.70 (P1(f334(f334(f336(f887(f882(x112671),f882(x112671))),f334(f334(f269(f882(x112671),f882(x112671)),x112672),x112672)),f160(x112671,f310(x112671,x112673))))),
% 160.93/160.70 inference(rename_variables,[],[4078])).
% 160.93/160.70 cnf(11272,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(f882(x112721),f882(x112721))),f334(f334(f269(f882(x112721),f882(x112721)),x112722),f117(x112721))),f147(x112721,x112723)))),
% 160.93/160.70 inference(rename_variables,[],[4572])).
% 160.93/160.70 cnf(11274,plain,
% 160.93/160.70 (E(f334(f334(f153(x112741),f676(f310(x112741,x112742),f334(f334(f153(x112741),x112743),x112744),x112744,x112743,x112741)),f677(f310(x112741,x112742),f334(f334(f153(x112741),x112743),x112744),x112744,x112743,x112741)),f334(f334(f153(x112741),x112743),x112744))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,4493,10451,10544,3089,3142,3258,10227,10291,10294,10386,10389,3236,3761,3132,3195,3160,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,4549,11000,3407,3190,10351,4084,3938,11006,11132,4572,10936,11137,11247,4573,11039,11140,4574,11143,4575,11199,4576,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,3754,3284,4543,10259,10262,10288,10762,10775,10894,4555,3741,3513,3887,3328,3330,3303,4540,4498,4078,11267,4047,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,10854,3459,10625,10889,10933,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,3362,10654,10684,10693,3396,3820,3759,10328,4548,10279,10648,10651,11092,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,3904,3748,10949,10955,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,4568,10747,10847,4189,4089,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742])).
% 160.93/160.70 cnf(11279,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x112791),x112792),f188(x112793,x112791,f190(x112793,x112791,x112794,f196(f888(x112793,a876))))))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,4493,10451,10544,3089,3142,3258,10227,10291,10294,10386,10389,3236,3761,3132,3195,3160,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,4549,11000,3407,3190,10351,4084,3938,11006,11132,4572,10936,11137,11247,4573,11039,11140,4574,11143,4575,11199,4576,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,3754,3284,4543,10259,10262,10288,10762,10775,10894,4555,3741,3513,3887,3328,3330,3303,4540,4498,4078,11267,4047,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,10854,3459,10625,10889,10933,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,3362,10654,10684,10693,3396,3820,3759,10328,4548,10279,10648,10651,11092,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,3904,3748,10949,10955,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,4568,10747,10847,4189,4089,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765])).
% 160.93/160.70 cnf(11280,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x112801),x112802),f196(f888(x112801,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11283,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x112831),x112832),f196(f888(x112831,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11286,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x112861),x112862),f196(f888(x112861,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11289,plain,
% 160.93/160.70 (P1(f334(f334(f336(x112891),x112892),f257(f888(x112891,a876))))),
% 160.93/160.70 inference(rename_variables,[],[3459])).
% 160.93/160.70 cnf(11292,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x112921),f2(a881)))),
% 160.93/160.70 inference(rename_variables,[],[4543])).
% 160.93/160.70 cnf(11297,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(x112971,x112971)),f334(f334(f269(x112971,x112971),x112972),x112973)),f155(x112971,f117(f888(x112971,a881)))))),
% 160.93/160.70 inference(rename_variables,[],[4570])).
% 160.93/160.70 cnf(11300,plain,
% 160.93/160.70 (~E(f334(f313(x113001,f888(x113001,a876),x113002),x113003),f334(f311(x113001),x113003))),
% 160.93/160.70 inference(rename_variables,[],[4549])).
% 160.93/160.70 cnf(11303,plain,
% 160.93/160.70 (~E(f334(f313(x113031,f888(x113031,a876),x113032),x113033),f334(f311(x113031),x113033))),
% 160.93/160.70 inference(rename_variables,[],[4549])).
% 160.93/160.70 cnf(11306,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(f882(x113061),f882(x113061))),f334(f334(f269(f882(x113061),f882(x113061)),x113062),f117(x113061))),f147(x113061,x113063)))),
% 160.93/160.70 inference(rename_variables,[],[4572])).
% 160.93/160.70 cnf(11312,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(f882(x113121),f882(x113121))),f334(f334(f269(f882(x113121),f882(x113121)),x113122),f117(x113121))),f147(x113121,x113123)))),
% 160.93/160.70 inference(rename_variables,[],[4572])).
% 160.93/160.70 cnf(11315,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x113151),x113152),f196(f888(x113151,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11319,plain,
% 160.93/160.70 (P1(f334(f334(f336(f887(x113191,x113192)),f334(f334(f269(x113191,x113192),f334(x113193,x113194)),f334(x113195,x113194))),f334(f313(f887(x113196,x113196),f887(x113191,x113192),f274(x113196,x113191,x113196,x113192,x113193,x113195)),f310(x113196,x113197))))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,4493,10451,10544,3089,3142,3258,10227,10291,10294,10386,10389,3236,3761,3132,3195,3160,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,4549,11000,11070,11300,3407,3190,10351,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,3754,3284,4543,10259,10262,10288,10762,10775,10894,4555,3741,3513,3887,3328,3330,3303,4540,4498,4078,11267,4047,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,3302,4539,10325,10416,10529,10553,10799,10844,10854,3459,10625,10889,10933,11207,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,3362,10654,10684,10693,3396,3820,3759,10328,4548,10279,10648,10651,11092,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4563,10250,10253,10510,10561,10564,10569,4570,11173,3904,3748,10949,10955,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,4568,10747,10847,4189,4089,3780,4565,10301,10304,10642,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066])).
% 160.93/160.70 cnf(11322,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x113221),x113222),f196(f888(x113221,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11325,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x113251),x113252),f196(f888(x113251,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11328,plain,
% 160.93/160.70 (P1(f334(f334(f336(x113281),f334(x113282,x113283)),f334(f313(x113284,x113281,x113282),f257(f888(x113284,a876)))))),
% 160.93/160.70 inference(rename_variables,[],[3904])).
% 160.93/160.70 cnf(11331,plain,
% 160.93/160.70 (~P1(f334(f334(f336(f887(x113311,x113311)),f334(f334(f269(x113311,x113311),x113312),x113313)),f155(x113311,f117(f888(x113311,a881)))))),
% 160.93/160.70 inference(rename_variables,[],[4570])).
% 160.93/160.70 cnf(11339,plain,
% 160.93/160.70 (E(f118(x113391,f117(x113391)),f117(x113391))),
% 160.93/160.70 inference(rename_variables,[],[3142])).
% 160.93/160.70 cnf(11342,plain,
% 160.93/160.70 (~E(f334(a116,x113421),x113421)),
% 160.93/160.70 inference(rename_variables,[],[4478])).
% 160.93/160.70 cnf(11349,plain,
% 160.93/160.70 (~E(f334(a116,x113491),x113491)),
% 160.93/160.70 inference(rename_variables,[],[4478])).
% 160.93/160.70 cnf(11354,plain,
% 160.93/160.70 (E(f334(f265(x113541,x113541),f266(x113541,x113542)),x113542)),
% 160.93/160.70 inference(rename_variables,[],[3258])).
% 160.93/160.70 cnf(11357,plain,
% 160.93/160.70 (E(f334(f265(x113571,x113571),f266(x113571,x113572)),x113572)),
% 160.93/160.70 inference(rename_variables,[],[3258])).
% 160.93/160.70 cnf(11363,plain,
% 160.93/160.70 (~E(f334(a116,x113631),x113631)),
% 160.93/160.70 inference(rename_variables,[],[4478])).
% 160.93/160.70 cnf(11370,plain,
% 160.93/160.70 (~E(f334(f334(f80(a1),x113701),x113701),a101)),
% 160.93/160.70 inference(rename_variables,[],[4501])).
% 160.93/160.70 cnf(11379,plain,
% 160.93/160.70 (E(f334(f334(f22(a881),f2(a881)),x113791),f2(a881))),
% 160.93/160.70 inference(rename_variables,[],[3212])).
% 160.93/160.70 cnf(11382,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x113821),f2(a881)))),
% 160.93/160.70 inference(rename_variables,[],[4543])).
% 160.93/160.70 cnf(11389,plain,
% 160.93/160.70 (E(f334(f334(f80(a1),f334(f334(f81(a1),x113891),f334(f334(f38(a1),x113892),x113891))),f44(a1,x113892,x113891)),x113892)),
% 160.93/160.70 inference(rename_variables,[],[3852])).
% 160.93/160.70 cnf(11413,plain,
% 160.93/160.70 (~E(f334(a116,x114131),x114131)),
% 160.93/160.70 inference(rename_variables,[],[4478])).
% 160.93/160.70 cnf(11416,plain,
% 160.93/160.70 (~E(f334(a116,x114161),x114161)),
% 160.93/160.70 inference(rename_variables,[],[4478])).
% 160.93/160.70 cnf(11442,plain,
% 160.93/160.70 (~P1(f334(f62(x114421,x114422,f196(f888(x114421,a876))),x114423))),
% 160.93/160.70 inference(rename_variables,[],[4563])).
% 160.93/160.70 cnf(11445,plain,
% 160.93/160.70 (~P1(f334(f334(f196(f888(x114451,f888(x114452,a876))),x114453),x114454))),
% 160.93/160.70 inference(rename_variables,[],[4568])).
% 160.93/160.70 cnf(11448,plain,
% 160.93/160.70 (P1(f334(f334(f336(x114481),x114482),f257(f888(x114481,a876))))),
% 160.93/160.70 inference(rename_variables,[],[3459])).
% 160.93/160.70 cnf(11460,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),x114601),x114601))),
% 160.93/160.70 inference(rename_variables,[],[3301])).
% 160.93/160.70 cnf(11467,plain,
% 160.93/160.70 (P1(f334(f66(x114671,x114672,x114673,x114674,f196(f888(x114671,a876))),x114674))),
% 160.93/160.70 inference(rename_variables,[],[4228])).
% 160.93/160.70 cnf(11468,plain,
% 160.93/160.70 (E(f334(f265(x114681,x114681),f266(x114681,x114682)),x114682)),
% 160.93/160.70 inference(rename_variables,[],[3258])).
% 160.93/160.70 cnf(11473,plain,
% 160.93/160.70 (~P1(f334(f334(f196(f888(x114731,f888(x114732,a876))),x114733),x114734))),
% 160.93/160.70 inference(rename_variables,[],[4568])).
% 160.93/160.70 cnf(11484,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),f334(f334(f80(a881),x114841),x114842)),x114842))),
% 160.93/160.70 inference(rename_variables,[],[4565])).
% 160.93/160.70 cnf(11487,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a1),f334(f104(a1),x114871)),f2(a1)))),
% 160.93/160.70 inference(rename_variables,[],[4555])).
% 160.93/160.70 cnf(11503,plain,
% 160.93/160.70 (~E(f334(f334(f105(a881),f334(a116,x115031)),x115031),f334(a116,x115031))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,4493,10451,10544,3216,2895,2898,2910,2915,2921,2931,2940,2942,2946,2947,2953,2971,2978,3010,3011,3012,3017,3018,3057,3069,3075,3089,4474,3142,11339,3258,10227,10291,10294,10386,10389,10681,11354,11357,3236,3761,3132,3852,11389,3195,3160,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4501,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,3754,3284,4543,10259,10262,10288,10762,10775,10894,11292,11382,4555,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,4047,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,10881,3302,4539,10325,10416,10529,10553,10799,10844,10854,3459,10625,10889,10933,11207,11289,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,3362,10654,10684,10693,3396,3820,3759,10328,4548,10279,10648,10651,11092,11110,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4228,4563,10250,10253,10510,10561,10564,10569,10977,4570,11173,11297,3904,3748,10949,10955,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,4557,4568,10747,10847,11161,11445,4189,4089,3780,4565,10301,10304,10642,10645,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365])).
% 160.93/160.70 cnf(11510,plain,
% 160.93/160.70 (E(f334(f265(x115101,x115101),f266(x115101,x115102)),x115102)),
% 160.93/160.70 inference(rename_variables,[],[3258])).
% 160.93/160.70 cnf(11515,plain,
% 160.93/160.70 (E(f334(f265(x115151,x115151),f266(x115151,x115152)),x115152)),
% 160.93/160.70 inference(rename_variables,[],[3258])).
% 160.93/160.70 cnf(11518,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a1),f334(f104(a1),x115181)),f2(a1)))),
% 160.93/160.70 inference(rename_variables,[],[4555])).
% 160.93/160.70 cnf(11523,plain,
% 160.93/160.70 (~E(f334(a116,x115231),x115231)),
% 160.93/160.70 inference(rename_variables,[],[4478])).
% 160.93/160.70 cnf(11527,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),f2(a1)),a83))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,4493,10451,10544,3216,2895,2898,2910,2915,2921,2931,2940,2942,2943,2946,2947,2953,2971,2978,3010,3011,3012,3017,3018,3057,3069,3075,3089,4474,3142,11339,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,3236,3761,3132,3852,11389,3195,3160,3155,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4501,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,3754,3284,4543,10259,10262,10288,10762,10775,10894,11292,11382,4555,11487,11518,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,4047,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,10881,3302,4539,10325,10416,10529,10553,10799,10844,10854,3459,10625,10889,10933,11207,11289,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,3362,10654,10684,10693,3402,3396,3820,3759,10328,4548,10279,10648,10651,11092,11110,3322,10687,10838,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,4228,4563,10250,10253,10510,10561,10564,10569,10977,4570,11173,11297,3904,3748,10949,10955,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,4557,4568,10747,10847,11161,11445,4189,4089,3780,4565,10301,10304,10642,10645,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457])).
% 160.93/160.70 cnf(11532,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x115321),x115321))),
% 160.93/160.70 inference(rename_variables,[],[4539])).
% 160.93/160.70 cnf(11553,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a1),f334(f104(a1),x115531)),f2(a1)))),
% 160.93/160.70 inference(rename_variables,[],[4555])).
% 160.93/160.70 cnf(11566,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),x115661),x115661))),
% 160.93/160.70 inference(rename_variables,[],[3301])).
% 160.93/160.70 cnf(11569,plain,
% 160.93/160.70 (~P1(f334(f334(f248(a881),f334(a116,x115691)),x115691))),
% 160.93/160.70 inference(rename_variables,[],[4548])).
% 160.93/160.70 cnf(11570,plain,
% 160.93/160.70 (~E(f334(a116,x115701),x115701)),
% 160.93/160.70 inference(rename_variables,[],[4478])).
% 160.93/160.70 cnf(11580,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),f334(f334(f80(a881),x115801),x115802)),x115801))),
% 160.93/160.70 inference(rename_variables,[],[4566])).
% 160.93/160.70 cnf(11583,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a1),f334(f104(a1),x115831)),f2(a1)))),
% 160.93/160.70 inference(rename_variables,[],[4555])).
% 160.93/160.70 cnf(11586,plain,
% 160.93/160.70 (~E(f334(a116,x115861),x115861)),
% 160.93/160.70 inference(rename_variables,[],[4478])).
% 160.93/160.70 cnf(11599,plain,
% 160.93/160.70 (P1(f334(f334(f336(x115991),x115992),f334(f334(f312(x115991),x115992),x115993)))),
% 160.93/160.70 inference(rename_variables,[],[3614])).
% 160.93/160.70 cnf(11600,plain,
% 160.93/160.70 (~P1(f334(f334(f248(a1),f2(a1)),f334(f79(a1),f334(f104(a1),f334(a116,x116001)))))),
% 160.93/160.70 inference(rename_variables,[],[4567])).
% 160.93/160.70 cnf(11603,plain,
% 160.93/160.70 (P1(f334(f334(f249(a881),f334(f334(f22(a881),x116031),x116032)),f334(a116,x116031)))),
% 160.93/160.70 inference(rename_variables,[],[3754])).
% 160.93/160.70 cnf(11606,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),f44(a881,x116061,x116062)),x116061))),
% 160.93/160.70 inference(rename_variables,[],[3759])).
% 160.93/160.70 cnf(11612,plain,
% 160.93/160.70 (E(f334(f334(f136(x116121),x116122),f117(x116121)),x116122)),
% 160.93/160.70 inference(rename_variables,[],[3230])).
% 160.93/160.70 cnf(11615,plain,
% 160.93/160.70 (E(f334(f265(x116151,x116151),f266(x116151,x116152)),x116152)),
% 160.93/160.70 inference(rename_variables,[],[3258])).
% 160.93/160.70 cnf(11618,plain,
% 160.93/160.70 (E(f175(x116181,x116182,f117(x116181)),x116182)),
% 160.93/160.70 inference(rename_variables,[],[3236])).
% 160.93/160.70 cnf(11624,plain,
% 160.93/160.70 (~P1(f334(f334(f248(a881),f334(a116,x116241)),x116241))),
% 160.93/160.70 inference(rename_variables,[],[4548])).
% 160.93/160.70 cnf(11633,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x116331),x116331))),
% 160.93/160.70 inference(rename_variables,[],[4539])).
% 160.93/160.70 cnf(11636,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),f44(a881,x116361,x116362)),x116361))),
% 160.93/160.70 inference(rename_variables,[],[3759])).
% 160.93/160.70 cnf(11637,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),f2(a881)),x116371))),
% 160.93/160.70 inference(rename_variables,[],[3322])).
% 160.93/160.70 cnf(11639,plain,
% 160.93/160.70 (~P1(f334(f334(f248(a1),f78(a1)),f2(a1)))),
% 160.93/160.70 inference(scs_inference,[],[3543,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,4493,10451,10544,3216,2895,2898,2899,2910,2911,2915,2921,2931,2939,2940,2942,2943,2946,2947,2953,2971,2978,3010,3011,3012,3017,3018,3045,3057,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,3230,11612,3236,10701,11618,3761,3132,3852,11389,3195,3160,3155,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,3754,3284,4543,10259,10262,10288,10762,10775,10894,11292,11382,4555,11487,11518,11553,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,4047,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,3301,10462,10672,10757,10881,11460,3302,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,3459,10625,10889,10933,11207,11289,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,3362,10654,10684,10693,3402,3396,3820,3759,10328,11606,4548,10279,10648,10651,11092,11110,11569,3322,10687,10838,10909,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,4570,11173,11297,3904,3748,10949,10955,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,4557,4568,10747,10847,11161,11445,4189,4089,3780,4565,10301,10304,10642,10645,4566,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802])).
% 160.93/160.70 cnf(11654,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x116541),x116541))),
% 160.93/160.70 inference(rename_variables,[],[4539])).
% 160.93/160.70 cnf(11657,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x116571),x116571))),
% 160.93/160.70 inference(rename_variables,[],[4539])).
% 160.93/160.70 cnf(11660,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x116601),x116601))),
% 160.93/160.70 inference(rename_variables,[],[4539])).
% 160.93/160.70 cnf(11663,plain,
% 160.93/160.70 (P1(f334(f334(f336(x116631),f334(x116632,x116633)),f334(f313(x116634,x116631,x116632),f257(f888(x116634,a876)))))),
% 160.93/160.70 inference(rename_variables,[],[3904])).
% 160.93/160.70 cnf(11664,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),f334(f334(f80(a881),x116641),x116642)),x116642))),
% 160.93/160.70 inference(rename_variables,[],[4565])).
% 160.93/160.70 cnf(11667,plain,
% 160.93/160.70 (P1(f334(f334(f336(x116671),f334(x116672,x116673)),f334(f313(x116674,x116671,x116672),f257(f888(x116674,a876)))))),
% 160.93/160.70 inference(rename_variables,[],[3904])).
% 160.93/160.70 cnf(11668,plain,
% 160.93/160.70 (~P1(f334(f334(f248(a881),f334(a116,x116681)),x116681))),
% 160.93/160.70 inference(rename_variables,[],[4548])).
% 160.93/160.70 cnf(11673,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),f334(f334(f80(a881),x116731),x116732)),x116731))),
% 160.93/160.70 inference(rename_variables,[],[4566])).
% 160.93/160.70 cnf(11676,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x116761),x116761))),
% 160.93/160.70 inference(rename_variables,[],[4539])).
% 160.93/160.70 cnf(11679,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),x116791),x116791))),
% 160.93/160.70 inference(rename_variables,[],[3300])).
% 160.93/160.70 cnf(11685,plain,
% 160.93/160.70 (~P37(x116851,x116852,f117(x116851))),
% 160.93/160.70 inference(rename_variables,[],[4512])).
% 160.93/160.70 cnf(11688,plain,
% 160.93/160.70 (P1(f334(f334(f336(x116881),x116882),f257(f888(x116881,a876))))),
% 160.93/160.70 inference(rename_variables,[],[3459])).
% 160.93/160.70 cnf(11689,plain,
% 160.93/160.70 (~P1(f334(f334(f248(a881),f334(a116,x116891)),x116891))),
% 160.93/160.70 inference(rename_variables,[],[4548])).
% 160.93/160.70 cnf(11692,plain,
% 160.93/160.70 (~P1(f334(f62(x116921,x116922,f196(f888(x116921,a876))),x116923))),
% 160.93/160.70 inference(rename_variables,[],[4563])).
% 160.93/160.70 cnf(11705,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x117051),x117052),f196(f888(x117051,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11708,plain,
% 160.93/160.70 (E(f334(f334(f16(x117081,x117082),x117083),x117084),x117083)),
% 160.93/160.70 inference(rename_variables,[],[3291])).
% 160.93/160.70 cnf(11711,plain,
% 160.93/160.70 (E(f334(f334(f16(x117111,x117112),x117113),x117114),x117113)),
% 160.93/160.70 inference(rename_variables,[],[3291])).
% 160.93/160.70 cnf(11723,plain,
% 160.93/160.70 (P1(f334(f334(f249(a881),f2(a881)),f334(a116,x117231)))),
% 160.93/160.70 inference(rename_variables,[],[3380])).
% 160.93/160.70 cnf(11726,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),x117261),x117261))),
% 160.93/160.70 inference(rename_variables,[],[3300])).
% 160.93/160.70 cnf(11729,plain,
% 160.93/160.70 (P1(f334(f334(f336(x117291),f334(x117292,x117293)),f334(f313(x117294,x117291,x117292),f257(f888(x117294,a876)))))),
% 160.93/160.70 inference(rename_variables,[],[3904])).
% 160.93/160.70 cnf(11732,plain,
% 160.93/160.70 (P1(f334(f61(x117321),f334(f174(x117321),x117322)))),
% 160.93/160.70 inference(rename_variables,[],[3341])).
% 160.93/160.70 cnf(11735,plain,
% 160.93/160.70 (P1(f334(f61(x117351),f334(f174(x117351),x117352)))),
% 160.93/160.70 inference(rename_variables,[],[3341])).
% 160.93/160.70 cnf(11738,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),f334(f79(a1),f334(f104(a1),x117381))),f334(f104(a1),x117382)))),
% 160.93/160.70 inference(rename_variables,[],[3781])).
% 160.93/160.70 cnf(11741,plain,
% 160.93/160.70 (~P1(f334(f334(f336(x117411),x117412),f196(f888(x117411,a876))))),
% 160.93/160.70 inference(rename_variables,[],[4551])).
% 160.93/160.70 cnf(11751,plain,
% 160.93/160.70 (~P1(f334(f334(f336(a881),f2(a881)),f334(f306(a881),x117511)))),
% 160.93/160.70 inference(scs_inference,[],[3543,4511,4512,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,4493,10451,10544,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2939,2940,2942,2943,2946,2947,2950,2953,2971,2978,3010,3011,3012,3017,3018,3045,3057,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,3230,11612,3236,10701,11618,3761,3132,3852,11389,3195,3160,3155,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,3754,11603,3284,3380,4543,10259,10262,10288,10762,10775,10894,11292,11382,4555,11487,11518,11553,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,4047,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,3301,10462,10672,10757,10881,11460,3302,3376,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,3459,10625,10889,10933,11207,11289,11448,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,3362,10654,10684,10693,3402,3396,3820,3759,10328,11606,4548,10279,10648,10651,11092,11110,11569,11624,11668,3322,10687,10838,10909,3781,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,4189,4089,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130])).
% 160.93/160.70 cnf(11753,plain,
% 160.93/160.70 (~P1(f334(f334(f336(a881),x117531),f334(f255(a881),f2(a881))))),
% 160.93/160.70 inference(scs_inference,[],[3543,4511,4512,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,4493,10451,10544,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2939,2940,2942,2943,2946,2947,2950,2953,2971,2978,3010,3011,3012,3017,3018,3045,3057,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,3230,11612,3236,10701,11618,3761,3132,3852,11389,3195,3160,3155,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,3754,11603,3284,3380,4543,10259,10262,10288,10762,10775,10894,11292,11382,4555,11487,11518,11553,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,4047,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,3301,10462,10672,10757,10881,11460,3302,3376,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,3459,10625,10889,10933,11207,11289,11448,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,3362,10654,10684,10693,3402,3396,3820,3759,10328,11606,4548,10279,10648,10651,11092,11110,11569,11624,11668,3322,10687,10838,10909,3781,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,4189,4089,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131])).
% 160.93/160.70 cnf(11759,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),f44(a881,x117591,f196(a881))),x117591))),
% 160.93/160.70 inference(scs_inference,[],[3543,4511,4512,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,4493,10451,10544,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2939,2940,2942,2943,2946,2947,2950,2953,2971,2978,3010,3011,3012,3017,3018,3045,3057,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,3230,11612,3236,10701,11618,3761,3132,3852,11389,3195,3160,3155,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,3754,11603,3284,3380,4543,10259,10262,10288,10762,10775,10894,11292,11382,4555,11487,11518,11553,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,4047,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,3301,10462,10672,10757,10881,11460,11566,3302,3376,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,3459,10625,10889,10933,11207,11289,11448,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,3362,10654,10684,10693,3402,3396,3820,3759,10328,11606,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,3322,10687,10838,10909,3781,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,4189,4089,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172])).
% 160.93/160.70 cnf(11760,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),x117601),x117601))),
% 160.93/160.70 inference(rename_variables,[],[3301])).
% 160.93/160.70 cnf(11763,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),x117631),x117631))),
% 160.93/160.70 inference(rename_variables,[],[3301])).
% 160.93/160.70 cnf(11772,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x117721),f2(a881)))),
% 160.93/160.70 inference(rename_variables,[],[4543])).
% 160.93/160.70 cnf(11775,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),x117751),x117751))),
% 160.93/160.70 inference(rename_variables,[],[3301])).
% 160.93/160.70 cnf(11780,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x117801),f2(a881)))),
% 160.93/160.70 inference(rename_variables,[],[4543])).
% 160.93/160.70 cnf(11787,plain,
% 160.93/160.70 (P1(f334(f257(f888(x117871,a876)),x117872))),
% 160.93/160.70 inference(rename_variables,[],[3362])).
% 160.93/160.70 cnf(11792,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),f2(a881)),x117921))),
% 160.93/160.70 inference(rename_variables,[],[3322])).
% 160.93/160.70 cnf(11793,plain,
% 160.93/160.70 (~P1(f334(f334(f248(a881),f334(a116,x117931)),x117931))),
% 160.93/160.70 inference(rename_variables,[],[4548])).
% 160.93/160.70 cnf(11796,plain,
% 160.93/160.70 (~P1(f334(f62(x117961,x117962,f196(f888(x117961,a876))),x117963))),
% 160.93/160.70 inference(rename_variables,[],[4563])).
% 160.93/160.70 cnf(11813,plain,
% 160.93/160.70 (P1(f334(f334(f249(a1),f334(f79(a1),f78(a1))),f2(a1)))),
% 160.93/160.70 inference(scs_inference,[],[3543,4511,4512,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,4493,10451,10544,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2934,2939,2940,2942,2943,2946,2947,2950,2953,2971,2978,3000,3010,3011,3012,3017,3018,3045,3057,3062,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,3230,11612,3236,10701,11618,3761,3132,3852,11389,3195,3160,3155,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,3754,11603,3284,3380,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,4555,11487,11518,11553,11583,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,4047,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,3301,10462,10672,10757,10881,11460,11566,11760,11763,3302,3376,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,3459,10625,10889,10933,11207,11289,11448,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,3362,10654,10684,10693,11239,3402,3396,3820,3759,10328,11606,11636,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,3322,10687,10838,10909,11637,3781,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,4189,4089,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441])).
% 160.93/160.70 cnf(11818,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x118181),x118181))),
% 160.93/160.70 inference(rename_variables,[],[4539])).
% 160.93/160.70 cnf(11821,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x118211),x118211))),
% 160.93/160.70 inference(rename_variables,[],[4539])).
% 160.93/160.70 cnf(11824,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x118241),x118241))),
% 160.93/160.70 inference(rename_variables,[],[4539])).
% 160.93/160.70 cnf(11827,plain,
% 160.93/160.70 (~P1(f334(f334(f249(a881),x118271),x118271))),
% 160.93/160.70 inference(rename_variables,[],[4539])).
% 160.93/160.70 cnf(11830,plain,
% 160.93/160.70 (~P1(f334(f334(f248(a881),f334(a116,x118301)),x118301))),
% 160.93/160.70 inference(rename_variables,[],[4548])).
% 160.93/160.70 cnf(11833,plain,
% 160.93/160.70 (~P1(f334(f334(f248(a881),f334(a116,x118331)),x118331))),
% 160.93/160.70 inference(rename_variables,[],[4548])).
% 160.93/160.70 cnf(11836,plain,
% 160.93/160.70 (~P1(f334(f334(f248(a881),f334(a116,x118361)),x118361))),
% 160.93/160.70 inference(rename_variables,[],[4548])).
% 160.93/160.70 cnf(11839,plain,
% 160.93/160.70 (~P1(f334(f334(f248(a881),f334(a116,x118391)),x118391))),
% 160.93/160.70 inference(rename_variables,[],[4548])).
% 160.93/160.70 cnf(11855,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),f334(f334(f22(a881),x118551),f334(a116,x118551))),f2(a881)))),
% 160.93/160.70 inference(scs_inference,[],[3543,4511,4512,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,4493,10451,10544,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2934,2939,2940,2942,2943,2946,2947,2950,2953,2971,2978,3000,3010,3011,3012,3017,3018,3045,3057,3062,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,3230,11612,3236,10701,11618,3761,3132,3852,11389,3195,3160,3155,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,3754,11603,3284,3380,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,4555,11487,11518,11553,11583,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,4047,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,3301,10462,10672,10757,10881,11460,11566,11760,11763,3302,3376,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,3459,10625,10889,10933,11207,11289,11448,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,3362,10654,10684,10693,11239,3402,3396,3820,3759,10328,11606,11636,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,3322,10687,10838,10909,11637,3781,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,4189,4089,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518])).
% 160.93/160.70 cnf(11856,plain,
% 160.93/160.70 (P1(f334(f334(f248(a881),x118561),x118561))),
% 160.93/160.70 inference(rename_variables,[],[3300])).
% 160.93/160.70 cnf(11861,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),x118611),f334(f75(a1),x118611)))),
% 160.93/160.70 inference(scs_inference,[],[3543,4511,4512,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,4493,10451,10544,3512,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2934,2939,2940,2942,2943,2946,2947,2950,2953,2971,2978,3000,3010,3011,3012,3017,3018,3045,3057,3062,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,3230,11612,3236,10701,11618,3761,3132,3852,11389,3195,3160,3155,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,3754,11603,3284,3380,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,4555,11487,11518,11553,11583,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,4047,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,3302,3376,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,3459,10625,10889,10933,11207,11289,11448,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,3362,10654,10684,10693,11239,3402,3396,3820,3759,10328,11606,11636,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,3322,10687,10838,10909,11637,3781,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,4189,4089,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538])).
% 160.93/160.70 cnf(11862,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),x118621),x118621))),
% 160.93/160.70 inference(rename_variables,[],[3301])).
% 160.93/160.70 cnf(11873,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),x118731),x118731))),
% 160.93/160.70 inference(rename_variables,[],[3301])).
% 160.93/160.70 cnf(11876,plain,
% 160.93/160.70 (P1(f334(f334(f248(f888(f887(f882(x118761),f882(x118761)),a876)),f160(x118761,x118762)),f310(f882(x118761),f159(x118761,x118762))))),
% 160.93/160.70 inference(rename_variables,[],[4005])).
% 160.93/160.70 cnf(11883,plain,
% 160.93/160.70 (P1(f334(f334(f249(a881),x118831),f334(a116,x118831)))),
% 160.93/160.70 inference(rename_variables,[],[3368])).
% 160.93/160.70 cnf(11886,plain,
% 160.93/160.70 (P1(f334(f334(f336(f888(x118861,a876)),x118862),f334(f311(x118861),x118862)))),
% 160.93/160.70 inference(rename_variables,[],[3666])).
% 160.93/160.70 cnf(11887,plain,
% 160.93/160.70 (~E(f334(a116,x118871),x118871)),
% 160.93/160.70 inference(rename_variables,[],[4478])).
% 160.93/160.70 cnf(11894,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),x118941),x118941))),
% 160.93/160.70 inference(rename_variables,[],[3301])).
% 160.93/160.70 cnf(11899,plain,
% 160.93/160.70 (P1(f334(f334(f248(a1),x118991),x118991))),
% 160.93/160.70 inference(rename_variables,[],[3301])).
% 160.93/160.70 cnf(11908,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x119081,a876)),x119082),f334(f334(f312(x119081),x119083),x119082)))),
% 161.04/160.70 inference(rename_variables,[],[3748])).
% 161.04/160.70 cnf(11911,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x119111),x119111))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(11912,plain,
% 161.04/160.70 (~E(f334(a116,x119121),x119121)),
% 161.04/160.70 inference(rename_variables,[],[4478])).
% 161.04/160.70 cnf(11923,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x119231),x119231))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(11924,plain,
% 161.04/160.70 (~E(f334(a116,x119241),x119241)),
% 161.04/160.70 inference(rename_variables,[],[4478])).
% 161.04/160.70 cnf(11927,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x119271),x119271))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(11930,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x119301),x119301))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(11933,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x119331),x119331))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(11936,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x119361),x119361))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(11938,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),f334(a108,f2(a1))),f334(a116,x119381)))),
% 161.04/160.70 inference(scs_inference,[],[3543,4511,4512,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,4493,10451,10544,3512,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2934,2939,2940,2942,2943,2946,2947,2950,2953,2971,2978,3000,3010,3011,3012,3017,3018,3045,3057,3062,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,3230,11612,3236,10701,11618,3761,3132,3852,11389,3195,3160,3155,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,3754,11603,3284,3380,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,4555,11487,11518,11553,11583,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,4047,4005,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,3302,3376,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,3459,10625,10889,10933,11207,11289,11448,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,3362,10654,10684,10693,11239,3402,3396,3820,3759,10328,11606,11636,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,3322,10687,10838,10909,11637,3781,4128,4546,3828,4529,4531,3275,3276,4530,4533,4534,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,10970,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,4189,4089,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782])).
% 161.04/160.70 cnf(11939,plain,
% 161.04/160.70 (P1(f334(f334(f248(a1),x119391),x119391))),
% 161.04/160.70 inference(rename_variables,[],[3301])).
% 161.04/160.70 cnf(11942,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x119421),x119421))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(11945,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x119451),x119451))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(11946,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x119461),f334(a116,x119461)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(11955,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x119551),x119551))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(11956,plain,
% 161.04/160.70 (~E(f334(a116,x119561),x119561)),
% 161.04/160.70 inference(rename_variables,[],[4478])).
% 161.04/160.70 cnf(11961,plain,
% 161.04/160.70 (P1(f334(f334(f248(a1),x119611),x119611))),
% 161.04/160.70 inference(rename_variables,[],[3301])).
% 161.04/160.70 cnf(11976,plain,
% 161.04/160.70 (P1(f334(f334(f248(a1),x119761),x119761))),
% 161.04/160.70 inference(rename_variables,[],[3301])).
% 161.04/160.70 cnf(11981,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),f2(a881)),x119811))),
% 161.04/160.70 inference(rename_variables,[],[3322])).
% 161.04/160.70 cnf(11998,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x119981),f2(a881)))),
% 161.04/160.70 inference(rename_variables,[],[4543])).
% 161.04/160.70 cnf(12001,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x120011),f2(a881)))),
% 161.04/160.70 inference(rename_variables,[],[4543])).
% 161.04/160.70 cnf(12004,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x120041),x120042),f196(f888(x120041,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12007,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x120071),x120072),f196(f888(x120071,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12010,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x120101),x120101))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(12012,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x120121),f334(f334(f105(a881),x120121),x120122)))),
% 161.04/160.70 inference(scs_inference,[],[3543,4511,4512,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,4493,10451,10544,3512,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2934,2939,2940,2942,2943,2946,2947,2950,2953,2971,2978,3000,3010,3011,3012,3017,3018,3045,3057,3062,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,3230,11612,3236,10701,11618,3243,3761,3997,3132,3852,11389,3195,3160,3155,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,3754,11603,3284,3380,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,4555,11487,11518,11553,11583,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,4047,4005,3949,10830,4000,3666,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,3302,3376,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,3459,10625,10889,10933,11207,11289,11448,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,3362,10654,10684,10693,11239,3402,3396,3820,3759,10328,11606,11636,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,3322,10687,10838,10909,11637,11792,3781,4128,4546,3792,3828,4529,4531,3275,3276,4530,4533,4534,3799,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,10970,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,4189,4089,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013])).
% 161.04/160.70 cnf(12013,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x120131),x120131))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(12016,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x120161),x120161))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(12019,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x120191),x120191))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(12022,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x120221),f334(a116,x120221)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(12029,plain,
% 161.04/160.70 (P1(f334(f334(f336(f888(x120291,a876)),x120292),f334(f311(x120291),x120292)))),
% 161.04/160.70 inference(rename_variables,[],[3666])).
% 161.04/160.70 cnf(12033,plain,
% 161.04/160.70 (~P1(f334(f334(f336(a881),f334(a116,f334(f144(a881,a881,f80(a881),f2(a881)),x120331))),f334(f174(a881),f334(f138(a881,x120332),x120331))))),
% 161.04/160.70 inference(scs_inference,[],[3543,4511,4512,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,4493,10451,10544,3512,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2934,2939,2940,2942,2943,2946,2947,2950,2953,2971,2978,3000,3010,3011,3012,3017,3018,3045,3057,3062,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,3230,11612,3236,10701,11618,3243,3761,3997,3132,3852,11389,3195,3160,3155,3139,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,3754,11603,3284,3380,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,4555,11487,11518,11553,11583,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,4047,4005,3949,10830,4000,3666,11886,4036,3684,11009,11075,11158,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,3302,3376,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,3459,10625,10889,10933,11207,11289,11448,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,3362,10654,10684,10693,11239,3402,3396,3820,3759,10328,11606,11636,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,3322,10687,10838,10909,11637,11792,3781,4128,4546,3792,3828,4529,4531,3275,3276,4530,4533,4534,3799,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,10970,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,4189,4089,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113])).
% 161.04/160.70 cnf(12034,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x120341,a876)),f334(f174(x120341),f334(f138(x120341,x120342),x120343))),f334(f174(x120341),x120343)))),
% 161.04/160.70 inference(rename_variables,[],[3949])).
% 161.04/160.70 cnf(12041,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x120411),x120412),f196(f888(x120411,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12046,plain,
% 161.04/160.70 (E(f334(f197(f882(x120461)),f334(f170(x120461),x120462)),f334(f197(f882(x120461)),x120462))),
% 161.04/160.70 inference(rename_variables,[],[3313])).
% 161.04/160.70 cnf(12053,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x120531,a876)),x120532),f257(f888(x120531,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3684])).
% 161.04/160.70 cnf(12054,plain,
% 161.04/160.70 (~E(f334(a116,x120541),x120541)),
% 161.04/160.70 inference(rename_variables,[],[4478])).
% 161.04/160.70 cnf(12060,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x120601,a876)),f334(f174(x120601),f334(f138(x120601,x120602),x120603))),f334(f174(x120601),x120603)))),
% 161.04/160.70 inference(rename_variables,[],[3949])).
% 161.04/160.70 cnf(12066,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x120661),f334(a116,x120661)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(12074,plain,
% 161.04/160.70 (~P1(f334(f334(f336(f887(x120741,x120741)),x120742),f155(x120741,f117(f888(x120741,a881)))))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,4511,4512,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,4493,10451,10544,3512,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2934,2939,2940,2942,2943,2946,2947,2949,2950,2953,2971,2978,3000,3010,3011,3012,3017,3018,3045,3057,3062,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,3230,11612,3236,10701,11618,3243,3761,3997,3132,3852,11389,3195,3160,3155,3139,3313,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,3754,11603,3284,3380,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,4555,11487,11518,11553,11583,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,4047,4005,3949,10830,12034,4000,3666,11886,4036,3684,11009,11075,11158,11221,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,3302,3376,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,3459,10625,10889,10933,11207,11289,11448,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,3362,10654,10684,10693,11239,3402,3396,3820,3759,10328,11606,11636,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,3322,10687,10838,10909,11637,11792,3781,4128,4546,3792,3828,4529,4531,3275,3276,4530,4533,4534,3799,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,10970,3601,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,4189,4089,3893,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7146,7151,7153,7159,7167,7168,7183,7200,7218,7220,7237])).
% 161.04/160.70 cnf(12075,plain,
% 161.04/160.70 (E(f334(f265(x120751,x120751),f266(x120751,x120752)),x120752)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(12086,plain,
% 161.04/160.70 (P1(f334(f61(x120861),f196(f888(x120861,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3376])).
% 161.04/160.70 cnf(12087,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x120871),x120872),f196(f888(x120871,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12092,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x120921),f2(a881)))),
% 161.04/160.70 inference(rename_variables,[],[4543])).
% 161.04/160.70 cnf(12093,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x120931),x120931))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(12098,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x120981,a876)),f334(f174(x120981),f178(x120981,x120982,x120983))),f334(f174(x120981),x120982)))),
% 161.04/160.70 inference(rename_variables,[],[4000])).
% 161.04/160.70 cnf(12101,plain,
% 161.04/160.70 (P27(x121011,x121011,f5(x121011),x121012)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(12106,plain,
% 161.04/160.70 (P1(f334(f334(f336(f888(x121061,a876)),x121062),f334(f311(x121061),x121062)))),
% 161.04/160.70 inference(rename_variables,[],[3666])).
% 161.04/160.70 cnf(12113,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x121131),x121131))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12116,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x121161),x121162),f196(f888(x121161,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12119,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x121191,a876)),x121192),f334(f334(f312(x121191),x121193),x121192)))),
% 161.04/160.70 inference(rename_variables,[],[3748])).
% 161.04/160.70 cnf(12120,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x121201,a876)),x121202),f257(f888(x121201,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3684])).
% 161.04/160.70 cnf(12127,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x121271),f334(a116,x121271)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(12130,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x121301),f334(a116,x121301)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(12133,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x121331),x121331))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12136,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x121361),x121361))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12139,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x121391),x121391))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12142,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x121421),x121421))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12145,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x121451,a876)),x121452),x121452))),
% 161.04/160.70 inference(rename_variables,[],[3601])).
% 161.04/160.70 cnf(12149,plain,
% 161.04/160.70 (~P1(f334(f334(f248(a1),f334(f334(f22(a1),a83),a101)),f2(a1)))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,11065,4511,4512,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,4493,10451,10544,3512,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2971,2978,3000,3010,3011,3012,3017,3018,3045,3057,3062,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,3230,11612,3236,10701,11618,3243,3761,3997,3132,3852,11389,3195,3160,3155,3139,3313,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,3754,11603,3284,3380,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,4555,11487,11518,11553,11583,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,11735,4047,4005,3949,10830,12034,4000,11012,3666,11886,12029,4036,3684,11009,11075,11158,11221,12053,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,3302,3376,12086,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,3459,10625,10889,10933,11207,11289,11448,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,3362,10654,10684,10693,11239,3402,3396,3820,3759,10328,11606,11636,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,3322,10687,10838,10909,11637,11792,3781,4128,4546,3792,3828,4529,4531,3275,3276,4530,4533,4534,3799,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,10970,11908,3601,11176,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,4189,4089,3893,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7146,7151,7153,7159,7167,7168,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7465,7468,7494,7518,7536,7539,7540,7550,7568,7569,7571,7573,7575,7577,7605,7630,7631])).
% 161.04/160.70 cnf(12152,plain,
% 161.04/160.70 (P1(f334(f334(f336(f888(x121521,a876)),x121522),f334(f311(x121521),x121522)))),
% 161.04/160.70 inference(rename_variables,[],[3666])).
% 161.04/160.70 cnf(12156,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a1),f334(f334(f80(a1),a83),a83)),f2(a1)))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,11065,4511,4512,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,4493,10451,10544,3512,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2971,2978,3000,3010,3011,3012,3017,3018,3045,3057,3062,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,3230,11612,3236,10701,11618,3243,3761,3997,3132,3852,11389,3195,3160,3155,3139,3313,3358,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,3754,11603,3284,3380,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,4555,11487,11518,11553,11583,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,11735,4047,4005,3949,10830,12034,4000,11012,3666,11886,12029,12106,4036,3684,11009,11075,11158,11221,12053,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,3302,3376,12086,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,3459,10625,10889,10933,11207,11289,11448,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,3362,10654,10684,10693,11239,3402,3396,3820,3759,10328,11606,11636,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,3322,10687,10838,10909,11637,11792,3781,4128,4546,3792,3828,4529,4531,3275,3276,4530,4533,4534,3799,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,10970,11908,3601,11176,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,4189,4089,3893,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021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% 161.04/160.70 cnf(12161,plain,
% 161.04/160.70 (~E(f334(a116,x121611),x121611)),
% 161.04/160.70 inference(rename_variables,[],[4478])).
% 161.04/160.70 cnf(12162,plain,
% 161.04/160.70 (E(f334(f313(x121621,x121621,f5(x121621)),x121622),x121622)),
% 161.04/160.70 inference(rename_variables,[],[3358])).
% 161.04/160.70 cnf(12165,plain,
% 161.04/160.70 (P34(x121651,x121652,f117(x121651),f117(x121651))),
% 161.04/160.70 inference(rename_variables,[],[3552])).
% 161.04/160.70 cnf(12168,plain,
% 161.04/160.70 (~E(f334(a116,x121681),x121681)),
% 161.04/160.70 inference(rename_variables,[],[4478])).
% 161.04/160.70 cnf(12171,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x121711,a876)),f334(f174(x121711),f178(x121711,x121712,x121713))),f334(f174(x121711),x121712)))),
% 161.04/160.70 inference(rename_variables,[],[4000])).
% 161.04/160.70 cnf(12172,plain,
% 161.04/160.70 (P1(f334(f61(x121721),f334(f174(x121721),x121722)))),
% 161.04/160.70 inference(rename_variables,[],[3341])).
% 161.04/160.70 cnf(12183,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x121831),x121831))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(12186,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x121861),x121861))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(12191,plain,
% 161.04/160.70 (E(f334(f197(f882(x121911)),f334(f170(x121911),x121912)),f334(f197(f882(x121911)),x121912))),
% 161.04/160.70 inference(rename_variables,[],[3313])).
% 161.04/160.70 cnf(12198,plain,
% 161.04/160.70 (P16(a881,f334(f171(a881),f334(f334(f156(f882(x121981),a881),f197(f882(x121981))),f182(x121981,x121982))))),
% 161.04/160.70 inference(rename_variables,[],[3862])).
% 161.04/160.70 cnf(12201,plain,
% 161.04/160.70 (P27(x122011,x122011,f5(x122011),x122012)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(12204,plain,
% 161.04/160.70 (P1(f334(f334(f336(f882(x122041)),f117(x122041)),f163(x122041,x122042)))),
% 161.04/160.70 inference(rename_variables,[],[3504])).
% 161.04/160.70 cnf(12207,plain,
% 161.04/160.70 (~P1(f334(f334(f196(f888(x122071,f888(x122072,a876))),x122073),x122074))),
% 161.04/160.70 inference(rename_variables,[],[4568])).
% 161.04/160.70 cnf(12209,plain,
% 161.04/160.70 (P1(f334(f334(f249(f888(x122091,a876)),f334(a116,f257(f888(x122091,a876)))),f334(f334(f312(x122091),x122092),f257(f888(x122091,a876)))))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,11065,12101,3552,4511,4512,4496,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,4493,10451,10544,3512,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2971,2978,3000,3010,3011,3012,3017,3018,3045,3057,3062,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,3230,11612,3236,10701,11618,3243,3761,3997,3132,3852,11389,3195,3160,3155,3139,3146,3175,3313,12046,3358,10833,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3862,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,3754,11603,3284,3380,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,4555,11487,11518,11553,11583,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,11735,4047,4005,3949,10830,12034,4000,11012,12098,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,3302,3376,12086,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,3459,10625,10889,10933,11207,11289,11448,11688,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,3362,10654,10684,10693,11239,3402,3396,3820,3759,10328,11606,11636,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,3322,10687,10838,10909,11637,11792,3781,4128,4546,3792,3828,4529,4531,3275,3276,4530,4533,4534,3799,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,10970,11908,3601,11176,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,11473,4189,4089,3893,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7146,7151,7153,7159,7167,7168,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7465,7468,7494,7518,7536,7539,7540,7550,7568,7569,7571,7573,7575,7577,7605,7630,7631,7663,7665,7666,7667,7672,7692,7701,7711,7716,7722,7724,7730,7741,7742,7744,7762,7772,7795,7861,7862,7909,7917,7918])).
% 161.04/160.70 cnf(12212,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x122121),x122121))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12213,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),f2(a881)),x122131))),
% 161.04/160.70 inference(rename_variables,[],[3322])).
% 161.04/160.70 cnf(12215,plain,
% 161.04/160.70 (P1(f334(f334(f248(a1),f2(a1)),f440(x122151,f196(f888(x122152,f888(x122153,a876))),f78(a1))))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,11065,12101,3552,4511,4512,4496,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,4493,10451,10544,3512,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2971,2978,3000,3010,3011,3012,3017,3018,3045,3057,3062,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,3230,11612,3236,10701,11618,3243,3761,3997,3132,3852,11389,3195,3160,3155,3139,3146,3175,3313,12046,3358,10833,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3862,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,3754,11603,3284,3380,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,4555,11487,11518,11553,11583,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,11735,4047,4005,3949,10830,12034,4000,11012,12098,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,12142,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,3302,3376,12086,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,3459,10625,10889,10933,11207,11289,11448,11688,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,3362,10654,10684,10693,11239,3402,3396,3820,3759,10328,11606,11636,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,3322,10687,10838,10909,11637,11792,11981,3781,4128,4546,3792,3828,4529,4531,3275,3276,4530,4533,4534,3799,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,10970,11908,3601,11176,3750,10690,11028,11182,11212,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,11473,12207,4189,4089,3893,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7146,7151,7153,7159,7167,7168,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7465,7468,7494,7518,7536,7539,7540,7550,7568,7569,7571,7573,7575,7577,7605,7630,7631,7663,7665,7666,7667,7672,7692,7701,7711,7716,7722,7724,7730,7741,7742,7744,7762,7772,7795,7861,7862,7909,7917,7918,7942,7943])).
% 161.04/160.70 cnf(12216,plain,
% 161.04/160.70 (~P1(f334(f334(f196(f888(x122161,f888(x122162,a876))),x122163),x122164))),
% 161.04/160.70 inference(rename_variables,[],[4568])).
% 161.04/160.70 cnf(12219,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(f887(f882(x122191),f882(x122191)),a876)),f160(x122191,x122192)),f310(f882(x122191),f159(x122191,x122192))))),
% 161.04/160.70 inference(rename_variables,[],[4005])).
% 161.04/160.70 cnf(12224,plain,
% 161.04/160.70 (P1(f334(f334(f249(f888(x122241,a876)),f196(f888(x122241,a876))),f257(f888(x122241,a876))))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,11065,12101,3552,4511,4512,4496,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,4493,10451,10544,3512,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2971,2978,3000,3010,3011,3012,3017,3018,3045,3057,3062,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,3230,11612,3236,10701,11618,3243,3761,3997,3132,3852,11389,3195,3160,3155,3139,3146,3175,3313,12046,3358,10833,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,3665,4368,4369,4501,3605,3816,3862,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,3754,11603,3284,3380,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,4555,11487,11518,11553,11583,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,11735,4047,4005,11876,12219,3949,10830,12034,4000,11012,12098,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,12142,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,3302,3376,12086,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,3459,10625,10889,10933,11207,11289,11448,11688,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,3362,10654,10684,10693,11239,3402,3396,3820,3759,10328,11606,11636,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,3322,10687,10838,10909,11637,11792,11981,3781,4128,4546,3792,3828,4529,4531,3275,3276,4530,4533,4534,3799,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,10970,11908,3601,11176,3750,10690,11028,11182,11212,11226,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,11473,12207,4189,4089,3893,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7146,7151,7153,7159,7167,7168,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7465,7468,7494,7518,7536,7539,7540,7550,7568,7569,7571,7573,7575,7577,7605,7630,7631,7663,7665,7666,7667,7672,7692,7701,7711,7716,7722,7724,7730,7741,7742,7744,7762,7772,7795,7861,7862,7909,7917,7918,7942,7943,7960,7961,8020])).
% 161.04/160.70 cnf(12225,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x122251,a876)),f196(f888(x122251,a876))),x122252))),
% 161.04/160.70 inference(rename_variables,[],[3750])).
% 161.04/160.70 cnf(12228,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x122281,a876)),f334(f313(x122282,x122281,x122283),f334(f314(x122282,x122281,x122283),x122284))),x122284))),
% 161.04/160.70 inference(rename_variables,[],[4189])).
% 161.04/160.70 cnf(12231,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x122311,a876)),f334(f174(x122311),f178(x122311,x122312,x122313))),f334(f174(x122311),x122312)))),
% 161.04/160.70 inference(rename_variables,[],[4000])).
% 161.04/160.70 cnf(12232,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x122321,a876)),f334(f174(x122321),f334(f138(x122321,x122322),x122323))),f334(f174(x122321),x122323)))),
% 161.04/160.70 inference(rename_variables,[],[3949])).
% 161.04/160.70 cnf(12235,plain,
% 161.04/160.70 (P27(x122351,f885(x122351),f241(x122351),x122352)),
% 161.04/160.70 inference(rename_variables,[],[3553])).
% 161.04/160.70 cnf(12240,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x122401,a876)),f334(f313(x122402,x122401,x122403),f334(f314(x122402,x122401,x122403),x122404))),x122404))),
% 161.04/160.70 inference(rename_variables,[],[4189])).
% 161.04/160.70 cnf(12243,plain,
% 161.04/160.70 (P1(f334(f61(f885(x122431)),f334(f313(x122432,f885(x122431),f334(f180(x122432,x122431),x122433)),f257(f888(x122432,a876)))))),
% 161.04/160.70 inference(rename_variables,[],[4013])).
% 161.04/160.70 cnf(12248,plain,
% 161.04/160.70 (P1(f334(f334(f336(f882(x122481)),f117(x122481)),f163(x122481,x122482)))),
% 161.04/160.70 inference(rename_variables,[],[3504])).
% 161.04/160.70 cnf(12251,plain,
% 161.04/160.70 (~P1(f334(f334(f336(f887(f882(x122511),f882(x122511))),f334(f334(f269(f882(x122511),f882(x122511)),x122512),f117(x122511))),f147(x122511,x122513)))),
% 161.04/160.70 inference(rename_variables,[],[4572])).
% 161.04/160.70 cnf(12254,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x122541),f2(a881)))),
% 161.04/160.70 inference(rename_variables,[],[4543])).
% 161.04/160.70 cnf(12256,plain,
% 161.04/160.70 (~P1(f334(f61(x122561),f257(f888(x122561,a876))))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,11065,12101,3552,3553,3269,4511,4512,3169,4496,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,4493,10451,10544,3512,3216,2895,2898,2899,2910,2911,2915,2921,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2971,2978,2981,3000,3010,3011,3012,3017,3018,3045,3057,3062,3069,3075,3089,4474,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,3230,11612,3236,10701,11618,3243,3761,3997,3132,3852,11389,3195,3160,3155,3139,3146,3175,3313,12046,3358,10833,3229,3253,10492,3406,4560,3936,4503,10282,10448,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,3938,11006,11132,11185,4572,10936,11137,11247,11272,11306,11312,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,12204,12248,3665,4368,4369,4501,3605,3816,3862,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,3754,11603,3284,3380,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,4555,11487,11518,11553,11583,3741,3513,3887,3328,3330,3303,4540,4498,3496,4556,4078,11267,3624,3341,11732,11735,4047,4005,11876,12219,3949,10830,12034,12060,4000,11012,12098,12171,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,12142,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,3302,3376,12086,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,3459,10625,10889,10933,11207,11289,11448,11688,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,3362,10654,10684,10693,11239,3402,3396,3820,3759,10328,11606,11636,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,3322,10687,10838,10909,11637,11792,11981,3781,4128,4546,3792,3828,4529,4531,3275,3276,4530,4533,4534,3799,3614,4228,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,4013,3904,11328,11663,11667,3748,10949,10955,10970,11908,3601,11176,12145,3750,10690,11028,11182,11212,11226,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,11473,12207,4189,10823,12228,4089,3893,3780,3728,4565,10301,10304,10642,10645,11484,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7146,7151,7153,7159,7167,7168,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7465,7468,7494,7518,7536,7539,7540,7550,7568,7569,7571,7573,7575,7577,7605,7630,7631,7663,7665,7666,7667,7672,7692,7701,7711,7716,7722,7724,7730,7741,7742,7744,7762,7772,7795,7861,7862,7909,7917,7918,7942,7943,7960,7961,8020,8021,8022,8047,8080,8087,8089,8099,8111,8142,8150,8157])).
% 161.04/160.70 cnf(12257,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x122571,a876)),x122572),x122572))),
% 161.04/160.70 inference(rename_variables,[],[3601])).
% 161.04/160.70 cnf(12260,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x122601),x122602),f196(f888(x122601,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12263,plain,
% 161.04/160.70 (~P1(f334(f334(f196(f888(x122631,f888(x122632,a876))),x122633),x122634))),
% 161.04/160.70 inference(rename_variables,[],[4568])).
% 161.04/160.70 cnf(12266,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x122661,a876)),f334(f313(x122662,x122661,x122663),f334(f314(x122662,x122661,x122663),x122664))),x122664))),
% 161.04/160.70 inference(rename_variables,[],[4189])).
% 161.04/160.70 cnf(12267,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x122671,a876)),x122672),x122672))),
% 161.04/160.70 inference(rename_variables,[],[3601])).
% 161.04/160.70 cnf(12272,plain,
% 161.04/160.70 (E(f334(f265(x122721,x122721),f266(x122721,x122722)),x122722)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(12275,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x122751,a876)),f334(f174(x122751),f178(x122751,x122752,x122753))),f334(f174(x122751),x122752)))),
% 161.04/160.70 inference(rename_variables,[],[4000])).
% 161.04/160.70 cnf(12276,plain,
% 161.04/160.70 (P1(f334(f61(x122761),f334(f174(x122761),x122762)))),
% 161.04/160.70 inference(rename_variables,[],[3341])).
% 161.04/160.70 cnf(12279,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x122791),x122791))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12282,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x122821),x122821))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(12285,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x122851),x122851))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(12296,plain,
% 161.04/160.70 (P27(x122961,x122961,f5(x122961),x122962)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(12303,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x123031),x123032),f196(f888(x123031,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12306,plain,
% 161.04/160.70 (P1(f334(f334(f336(f887(x123061,x123061)),f334(f334(f269(x123061,x123061),x123062),x123062)),f310(x123061,x123063)))),
% 161.04/160.70 inference(rename_variables,[],[3938])).
% 161.04/160.70 cnf(12309,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x123091),x123092),f196(f888(x123091,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12312,plain,
% 161.04/160.70 (P1(f334(f334(f336(f887(x123121,x123121)),f334(f334(f269(x123121,x123121),x123122),x123122)),f310(x123121,x123123)))),
% 161.04/160.70 inference(rename_variables,[],[3938])).
% 161.04/160.70 cnf(12322,plain,
% 161.04/160.70 (~E(f334(f334(f153(x123221),x123222),x123223),x123223)),
% 161.04/160.70 inference(rename_variables,[],[4503])).
% 161.04/160.70 cnf(12325,plain,
% 161.04/160.70 (P1(f334(f334(f336(x123251),x123252),f257(f888(x123251,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3459])).
% 161.04/160.70 cnf(12326,plain,
% 161.04/160.70 (~E(f334(a116,x123261),x123261)),
% 161.04/160.70 inference(rename_variables,[],[4478])).
% 161.04/160.70 cnf(12329,plain,
% 161.04/160.70 (P1(f334(f334(f336(f882(x123291)),f117(x123291)),f163(x123291,x123292)))),
% 161.04/160.70 inference(rename_variables,[],[3504])).
% 161.04/160.70 cnf(12330,plain,
% 161.04/160.70 (~E(f334(f334(f153(x123301),x123302),x123303),f117(x123301))),
% 161.04/160.70 inference(rename_variables,[],[4510])).
% 161.04/160.70 cnf(12333,plain,
% 161.04/160.70 (P1(f334(f334(f336(x123331),f334(x123332,x123333)),f334(f313(x123334,x123331,x123332),f257(f888(x123334,a876)))))),
% 161.04/160.70 inference(rename_variables,[],[3904])).
% 161.04/160.70 cnf(12334,plain,
% 161.04/160.70 (P27(x123341,x123341,f5(x123341),x123342)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(12337,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x123371,a876)),f196(f888(x123371,a876))),x123372))),
% 161.04/160.70 inference(rename_variables,[],[3750])).
% 161.04/160.70 cnf(12338,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x123381,a876)),x123382),x123382))),
% 161.04/160.70 inference(rename_variables,[],[3601])).
% 161.04/160.70 cnf(12341,plain,
% 161.04/160.70 (P1(f334(f334(f336(x123411),f334(x123412,x123413)),f334(f313(x123414,x123411,x123412),f257(f888(x123414,a876)))))),
% 161.04/160.70 inference(rename_variables,[],[3904])).
% 161.04/160.70 cnf(12342,plain,
% 161.04/160.70 (P27(x123421,x123421,f5(x123421),x123422)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(12345,plain,
% 161.04/160.70 (P1(f334(f334(f336(f887(f882(x123451),f882(x123451))),f334(f334(f269(f882(x123451),f882(x123451)),f117(x123451)),f117(x123451))),f160(x123451,x123452)))),
% 161.04/160.70 inference(rename_variables,[],[4084])).
% 161.04/160.70 cnf(12348,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x123481),x123481))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(12349,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x123491),f2(a881)))),
% 161.04/160.70 inference(rename_variables,[],[4543])).
% 161.04/160.70 cnf(12355,plain,
% 161.04/160.70 (P27(x123551,x123551,f5(x123551),x123552)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(12358,plain,
% 161.04/160.70 (E(f334(f334(f136(x123581),x123582),f117(x123581)),x123582)),
% 161.04/160.70 inference(rename_variables,[],[3230])).
% 161.04/160.70 cnf(12359,plain,
% 161.04/160.70 (~E(f334(f334(f153(x123591),x123592),x123593),x123593)),
% 161.04/160.70 inference(rename_variables,[],[4503])).
% 161.04/160.70 cnf(12362,plain,
% 161.04/160.70 (E(f334(f334(f136(x123621),x123622),f117(x123621)),x123622)),
% 161.04/160.70 inference(rename_variables,[],[3230])).
% 161.04/160.70 cnf(12363,plain,
% 161.04/160.70 (~E(f334(f334(f153(x123631),x123632),x123633),x123633)),
% 161.04/160.70 inference(rename_variables,[],[4503])).
% 161.04/160.70 cnf(12366,plain,
% 161.04/160.70 (E(f334(f334(f136(x123661),x123662),f117(x123661)),x123662)),
% 161.04/160.70 inference(rename_variables,[],[3230])).
% 161.04/160.70 cnf(12375,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x123751,a876)),x123752),f257(f888(x123751,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3684])).
% 161.04/160.70 cnf(12379,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x123791),x123791))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(12380,plain,
% 161.04/160.70 (~E(f334(a116,x123801),x123801)),
% 161.04/160.70 inference(rename_variables,[],[4478])).
% 161.04/160.70 cnf(12383,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x123831,a876)),f196(f888(x123831,a876))),x123832))),
% 161.04/160.70 inference(rename_variables,[],[3750])).
% 161.04/160.70 cnf(12386,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x123861),x123861))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12389,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x123891,a876)),x123892),x123892))),
% 161.04/160.70 inference(rename_variables,[],[3601])).
% 161.04/160.70 cnf(12394,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x123941,a876)),x123942),f334(f334(f312(x123941),x123943),x123942)))),
% 161.04/160.70 inference(rename_variables,[],[3748])).
% 161.04/160.70 cnf(12397,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x123971,a876)),x123972),x123972))),
% 161.04/160.70 inference(rename_variables,[],[3601])).
% 161.04/160.70 cnf(12398,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x123981),x123982),f196(f888(x123981,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12401,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x124011),x124012),f196(f888(x124011,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12410,plain,
% 161.04/160.70 (P27(x124101,x124101,f5(x124101),x124102)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(12413,plain,
% 161.04/160.70 (E(f334(f197(f882(x124131)),f334(f170(x124131),x124132)),f334(f197(f882(x124131)),x124132))),
% 161.04/160.70 inference(rename_variables,[],[3313])).
% 161.04/160.70 cnf(12416,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x124161),x124161))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(12417,plain,
% 161.04/160.70 (P1(f334(f257(f888(x124171,a876)),x124172))),
% 161.04/160.70 inference(rename_variables,[],[3362])).
% 161.04/160.70 cnf(12420,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x124201),x124202),f196(f888(x124201,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12423,plain,
% 161.04/160.70 (P1(f334(f334(f336(x124231),f334(x124232,x124233)),f334(f313(x124234,x124231,x124232),f257(f888(x124234,a876)))))),
% 161.04/160.70 inference(rename_variables,[],[3904])).
% 161.04/160.70 cnf(12424,plain,
% 161.04/160.70 (P1(f334(f334(f336(f887(x124241,x124241)),f334(f334(f269(x124241,x124241),x124242),x124242)),f310(x124241,x124243)))),
% 161.04/160.70 inference(rename_variables,[],[3938])).
% 161.04/160.70 cnf(12427,plain,
% 161.04/160.70 (P1(f334(f334(f336(f887(x124271,x124271)),f334(f334(f269(x124271,x124271),x124272),x124272)),f310(x124271,x124273)))),
% 161.04/160.70 inference(rename_variables,[],[3938])).
% 161.04/160.70 cnf(12430,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x124301),x124301))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12431,plain,
% 161.04/160.70 (P1(f334(f257(f888(x124311,a876)),x124312))),
% 161.04/160.70 inference(rename_variables,[],[3362])).
% 161.04/160.70 cnf(12434,plain,
% 161.04/160.70 (P1(f334(f61(x124341),f334(f174(x124341),x124342)))),
% 161.04/160.70 inference(rename_variables,[],[3341])).
% 161.04/160.70 cnf(12444,plain,
% 161.04/160.70 (~P1(f334(f334(f196(f888(x124441,f888(x124442,a876))),x124443),x124444))),
% 161.04/160.70 inference(rename_variables,[],[4568])).
% 161.04/160.70 cnf(12447,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x124471,a876)),x124472),f257(f888(x124471,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3684])).
% 161.04/160.70 cnf(12450,plain,
% 161.04/160.70 (P1(f334(f334(f336(f887(x124501,x124501)),f334(f334(f269(x124501,x124501),x124502),x124502)),f310(x124501,x124503)))),
% 161.04/160.70 inference(rename_variables,[],[3938])).
% 161.04/160.70 cnf(12453,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),f334(f334(f80(a881),x124531),x124532)),x124532))),
% 161.04/160.70 inference(rename_variables,[],[4565])).
% 161.04/160.70 cnf(12454,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x124541),f334(a116,x124541)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(12457,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x124571,a876)),f334(f174(x124571),f334(f138(x124571,x124572),x124573))),f334(f174(x124571),x124573)))),
% 161.04/160.70 inference(rename_variables,[],[3949])).
% 161.04/160.70 cnf(12460,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x124601,a876)),x124602),f257(f888(x124601,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3684])).
% 161.04/160.70 cnf(12463,plain,
% 161.04/160.70 (E(f334(f265(x124631,x124631),f266(x124631,x124632)),x124632)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(12474,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x124741),x124742),f196(f888(x124741,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12475,plain,
% 161.04/160.70 (P1(f334(f334(f336(f887(f882(x124751),f882(x124751))),f334(f334(f269(f882(x124751),f882(x124751)),f117(x124751)),f117(x124751))),f160(x124751,x124752)))),
% 161.04/160.70 inference(rename_variables,[],[4084])).
% 161.04/160.70 cnf(12480,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x124801),x124802),f196(f888(x124801,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12483,plain,
% 161.04/160.70 (P33(x124831,x124832,f117(x124831))),
% 161.04/160.70 inference(rename_variables,[],[3235])).
% 161.04/160.70 cnf(12486,plain,
% 161.04/160.70 (E(f334(f197(f882(x124861)),f334(f170(x124861),x124862)),f334(f197(f882(x124861)),x124862))),
% 161.04/160.70 inference(rename_variables,[],[3313])).
% 161.04/160.70 cnf(12489,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x124891),x124892),f196(f888(x124891,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12495,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x124951),x124951))),
% 161.04/160.70 inference(rename_variables,[],[4539])).
% 161.04/160.70 cnf(12497,plain,
% 161.04/160.70 (P1(f334(f334(f336(f887(f882(x124971),f882(x124971))),f334(f334(f269(f882(x124971),f882(x124971)),f334(f170(x124971),x124972)),x124972)),f160(x124971,f257(f888(f887(x124971,x124971),a876)))))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,11065,12101,12201,12296,12334,12342,12355,3552,3553,3269,3235,4511,4512,3169,4496,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,12168,12326,4493,10451,10544,3357,3512,3216,2895,2898,2899,2910,2911,2915,2920,2921,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2971,2978,2981,3000,3010,3011,3012,3017,3018,3045,3057,3062,3069,3075,3089,4474,3640,3142,11339,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,12075,12272,3230,11612,12358,12362,12366,3236,10701,11618,3243,3761,3997,3132,4490,3852,11389,3195,3160,3155,3139,3146,3175,3313,12046,12191,12413,12486,3358,10833,12162,3228,3229,3253,10492,3406,4560,3936,4503,10282,10448,11253,12322,12359,4510,12330,3291,11708,4549,11000,11070,11300,11303,3407,3190,10351,10657,3191,3464,3111,3212,11379,4084,12345,12475,3938,11006,11132,11185,12306,12312,12424,12427,12450,4572,10936,11137,11247,11272,11306,11312,12251,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,12204,12248,12329,3665,4368,4369,4501,11370,3605,3816,3862,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,12130,3754,11603,3284,3380,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,12254,4555,11487,11518,11553,11583,3741,3513,3887,3328,3330,3303,4540,4498,3693,4222,3496,4556,4078,11267,3624,3341,11732,11735,12172,12276,4047,4005,11876,12219,3949,10830,12034,12060,12232,4000,11012,12098,12171,12231,12275,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,12120,12375,12447,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,12142,12212,12279,12386,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,3302,3376,12086,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,12186,12282,12285,12348,12379,12416,3459,10625,10889,10933,11207,11289,11448,11688,12325,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,12116,12260,12303,12309,12398,12401,12420,12474,12480,3362,10654,10684,10693,11239,11787,12417,3402,3396,3820,3759,10328,11606,11636,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,3322,10687,10838,10909,11637,11792,11981,3781,4128,4546,3792,3828,4529,4531,3275,3276,4530,4533,4534,3799,3614,4228,11467,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,11331,4013,3904,11328,11663,11667,11729,12333,12341,3748,10949,10955,10970,11908,12119,3601,11176,12145,12257,12267,12338,12389,4082,3750,10690,11028,11182,11212,11226,12225,12337,3571,10611,10614,10696,10868,4567,11600,4557,4568,10747,10847,11161,11445,11473,12207,12216,12263,4189,10823,12228,12240,4089,3893,3780,3728,4565,10301,10304,10642,10645,11484,11664,4566,11580,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7146,7151,7153,7159,7167,7168,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7465,7468,7494,7518,7536,7539,7540,7550,7568,7569,7571,7573,7575,7577,7605,7630,7631,7663,7665,7666,7667,7672,7692,7701,7711,7716,7722,7724,7730,7741,7742,7744,7762,7772,7795,7861,7862,7909,7917,7918,7942,7943,7960,7961,8020,8021,8022,8047,8080,8087,8089,8099,8111,8142,8150,8157,8170,8192,8198,8225,8269,8298,8311,8329,8332,8362,8385,8444,8445,8448,8450,8466,8556,8557,8558,8559,8588,8617,8649,8693,8711,8766,8811,8814,8827,8834,8871,8890,8918,8919,8936,8937,9080,9084,9104,9115,9138,9140,9143,9147,9150,9151,9164,9165,9185,9191,9203,9251,9269,9323,9324,9331,9392,9397,9433,9440,9443,9446,9447,9462,9478,9487,9499,9512,9513,9516,9518,9545,9670,9715,9716,9758,9803,9920,9977])).
% 161.04/160.70 cnf(12498,plain,
% 161.04/160.70 (P1(f334(f334(f336(x124981),x124982),f257(f888(x124981,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3459])).
% 161.04/160.70 cnf(12505,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x125051,a876)),x125052),x125052))),
% 161.04/160.70 inference(rename_variables,[],[3601])).
% 161.04/160.70 cnf(12508,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x125081),x125082),f196(f888(x125081,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12511,plain,
% 161.04/160.70 (P1(f334(f334(f248(a1),f2(a1)),f334(f334(f259(a1),f334(f75(a1),x125111)),x125112)))),
% 161.04/160.70 inference(rename_variables,[],[3780])).
% 161.04/160.70 cnf(12514,plain,
% 161.04/160.70 (~E(f334(a116,x125141),x125141)),
% 161.04/160.70 inference(rename_variables,[],[4478])).
% 161.04/160.70 cnf(12516,plain,
% 161.04/160.70 (E(f334(f265(x125161,x125161),f266(x125161,x125162)),x125162)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(12523,plain,
% 161.04/160.70 (E(f334(f265(x125231,x125231),f266(x125231,x125232)),x125232)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(12525,plain,
% 161.04/160.70 (E(f334(f265(x125251,x125251),f266(x125251,x125252)),x125252)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(12527,plain,
% 161.04/160.70 (P39(x125271,f155(x125271,x125272))),
% 161.04/160.70 inference(rename_variables,[],[3169])).
% 161.04/160.70 cnf(12535,plain,
% 161.04/160.70 (E(f334(f265(x125351,x125351),f266(x125351,x125352)),x125352)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(12537,plain,
% 161.04/160.70 (E(f334(f265(x125371,x125371),f266(x125371,x125372)),x125372)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(12539,plain,
% 161.04/160.70 (E(f334(f265(x125391,x125391),f266(x125391,x125392)),x125392)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(12541,plain,
% 161.04/160.70 (P29(x125411,f2(a881),f334(f334(f334(f92(x125411),x125412),f334(a26,x125413)),x125414))),
% 161.04/160.70 inference(rename_variables,[],[3677])).
% 161.04/160.70 cnf(12550,plain,
% 161.04/160.70 (P27(x125501,x125501,f5(x125501),x125502)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(12552,plain,
% 161.04/160.70 (P27(x125521,x125521,f5(x125521),x125522)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(12558,plain,
% 161.04/160.70 (P41(x125581,x125582,f266(x125581,x125582))),
% 161.04/160.70 inference(rename_variables,[],[3268])).
% 161.04/160.70 cnf(12560,plain,
% 161.04/160.70 (P41(x125601,x125602,f266(x125601,x125602))),
% 161.04/160.70 inference(rename_variables,[],[3268])).
% 161.04/160.70 cnf(12564,plain,
% 161.04/160.70 (E(f334(f265(x125641,x125641),f266(x125641,x125642)),x125642)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(12566,plain,
% 161.04/160.70 (P53(x125661,f196(f888(x125661,a876)),x125662)),
% 161.04/160.70 inference(rename_variables,[],[3320])).
% 161.04/160.70 cnf(12574,plain,
% 161.04/160.70 (P34(x125741,x125742,f117(x125741),f117(x125741))),
% 161.04/160.70 inference(rename_variables,[],[3552])).
% 161.04/160.70 cnf(12576,plain,
% 161.04/160.70 (P34(x125761,x125762,f117(x125761),f117(x125761))),
% 161.04/160.70 inference(rename_variables,[],[3552])).
% 161.04/160.70 cnf(12582,plain,
% 161.04/160.70 (E(f196(f888(f887(x125821,x125821),a876)),f266(x125821,f196(f888(x125821,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3371])).
% 161.04/160.70 cnf(12589,plain,
% 161.04/160.70 (E(f334(f265(x125891,x125891),f266(x125891,x125892)),x125892)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(12598,plain,
% 161.04/160.70 (P52(x125981,x125981,f266(x125981,x125982))),
% 161.04/160.70 inference(rename_variables,[],[3269])).
% 161.04/160.70 cnf(12608,plain,
% 161.04/160.70 (E(f334(f265(x126081,x126081),f266(x126081,x126082)),x126082)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(12610,plain,
% 161.04/160.70 (P17(x126101,f888(x126101,a876),f312(x126101))),
% 161.04/160.70 inference(rename_variables,[],[3272])).
% 161.04/160.70 cnf(12614,plain,
% 161.04/160.70 (P44(x126141,x126142,x126143,x126144,f196(f888(x126141,a876)),x126144)),
% 161.04/160.70 inference(rename_variables,[],[4252])).
% 161.04/160.70 cnf(12617,plain,
% 161.04/160.70 (P44(x126171,x126172,x126173,x126174,f196(f888(x126171,a876)),x126174)),
% 161.04/160.70 inference(rename_variables,[],[4252])).
% 161.04/160.70 cnf(12621,plain,
% 161.04/160.70 (E(f334(f265(x126211,x126211),f266(x126211,x126212)),x126212)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(12631,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),f2(a881)),f334(a116,x126311)))),
% 161.04/160.70 inference(rename_variables,[],[3380])).
% 161.04/160.70 cnf(12632,plain,
% 161.04/160.70 (~E(f334(a116,x126321),x126321)),
% 161.04/160.70 inference(rename_variables,[],[4478])).
% 161.04/160.70 cnf(12638,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x126381),f334(a116,x126381)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(12643,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x126431),f2(a881)))),
% 161.04/160.70 inference(rename_variables,[],[4543])).
% 161.04/160.70 cnf(12646,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x126461),f2(a881)))),
% 161.04/160.70 inference(rename_variables,[],[4543])).
% 161.04/160.70 cnf(12653,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a1),f334(f104(a1),x126531)),f334(f79(a1),f334(f104(a1),x126532))))),
% 161.04/160.70 inference(rename_variables,[],[4562])).
% 161.04/160.70 cnf(12663,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x126631),f2(a881)))),
% 161.04/160.70 inference(rename_variables,[],[4543])).
% 161.04/160.70 cnf(12666,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x126661),f2(a881)))),
% 161.04/160.70 inference(rename_variables,[],[4543])).
% 161.04/160.70 cnf(12669,plain,
% 161.04/160.70 (P1(f334(f61(a881),f307(a881,x126691,x126692)))),
% 161.04/160.70 inference(rename_variables,[],[3515])).
% 161.04/160.70 cnf(12672,plain,
% 161.04/160.70 (P1(f334(f61(a881),f307(a881,x126721,x126722)))),
% 161.04/160.70 inference(rename_variables,[],[3515])).
% 161.04/160.70 cnf(12675,plain,
% 161.04/160.70 (P1(f334(f61(a881),f307(a881,x126751,x126752)))),
% 161.04/160.70 inference(rename_variables,[],[3515])).
% 161.04/160.70 cnf(12678,plain,
% 161.04/160.70 (P1(f334(f61(a881),f307(a881,x126781,x126782)))),
% 161.04/160.70 inference(rename_variables,[],[3515])).
% 161.04/160.70 cnf(12685,plain,
% 161.04/160.70 (P1(f334(f334(f248(a1),f334(f79(a1),f334(f104(a1),x126851))),f334(f104(a1),x126852)))),
% 161.04/160.70 inference(rename_variables,[],[3781])).
% 161.04/160.70 cnf(12688,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x126881),f2(a881)))),
% 161.04/160.70 inference(rename_variables,[],[4543])).
% 161.04/160.70 cnf(12689,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x126891),x126891))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12696,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x126961),f334(a116,x126961)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(12699,plain,
% 161.04/160.70 (P1(f334(f334(f336(x126991),f334(x126992,x126993)),f334(f313(x126994,x126991,x126992),f257(f888(x126994,a876)))))),
% 161.04/160.70 inference(rename_variables,[],[3904])).
% 161.04/160.70 cnf(12700,plain,
% 161.04/160.70 (~E(f334(a116,x127001),f2(a881))),
% 161.04/160.70 inference(rename_variables,[],[4488])).
% 161.04/160.70 cnf(12705,plain,
% 161.04/160.70 (P1(f334(f334(f248(a1),x127051),x127051))),
% 161.04/160.70 inference(rename_variables,[],[3301])).
% 161.04/160.70 cnf(12708,plain,
% 161.04/160.70 (P1(f334(f61(a881),f307(a881,x127081,x127082)))),
% 161.04/160.70 inference(rename_variables,[],[3515])).
% 161.04/160.70 cnf(12711,plain,
% 161.04/160.70 (P1(f334(f61(a881),f307(a881,x127111,x127112)))),
% 161.04/160.70 inference(rename_variables,[],[3515])).
% 161.04/160.70 cnf(12714,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x127141),x127141))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12727,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x127271),f334(a116,x127271)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(12732,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),f44(a881,x127321,x127322)),x127321))),
% 161.04/160.70 inference(rename_variables,[],[3759])).
% 161.04/160.70 cnf(12739,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x127391),f334(a116,x127391)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(12740,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x127401),f2(a881)))),
% 161.04/160.70 inference(rename_variables,[],[4543])).
% 161.04/160.70 cnf(12749,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a1),f334(f104(a1),x127491)),f2(a1)))),
% 161.04/160.70 inference(rename_variables,[],[4555])).
% 161.04/160.70 cnf(12750,plain,
% 161.04/160.70 (P1(f334(f257(f888(x127501,a876)),x127502))),
% 161.04/160.70 inference(rename_variables,[],[3362])).
% 161.04/160.70 cnf(12753,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a1),f334(f104(a1),x127531)),f2(a1)))),
% 161.04/160.70 inference(rename_variables,[],[4555])).
% 161.04/160.70 cnf(12754,plain,
% 161.04/160.70 (P1(f334(f257(f888(x127541,a876)),x127542))),
% 161.04/160.70 inference(rename_variables,[],[3362])).
% 161.04/160.70 cnf(12757,plain,
% 161.04/160.70 (P1(f334(f257(f888(x127571,a876)),x127572))),
% 161.04/160.70 inference(rename_variables,[],[3362])).
% 161.04/160.70 cnf(12768,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x127681),x127682),f196(f888(x127681,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12769,plain,
% 161.04/160.70 (P1(f334(f61(x127691),f196(f888(x127691,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3376])).
% 161.04/160.70 cnf(12778,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),f2(a881)),x127781))),
% 161.04/160.70 inference(rename_variables,[],[3322])).
% 161.04/160.70 cnf(12781,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x127811),f334(a116,x127811)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(12782,plain,
% 161.04/160.70 (~E(f334(a116,x127821),x127821)),
% 161.04/160.70 inference(rename_variables,[],[4478])).
% 161.04/160.70 cnf(12785,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x127851),x127852),f196(f888(x127851,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12788,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x127881),x127882),f196(f888(x127881,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12791,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x127911),x127911))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12798,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x127981),x127981))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12802,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x128021),f334(a116,x128021)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(12805,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x128051),x128051))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12810,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x128101),x128101))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12813,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x128131),x128131))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12816,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x128161),x128161))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12819,plain,
% 161.04/160.70 (E(f334(f334(f22(f888(x128191,a876)),f196(f888(x128191,a876))),x128192),f196(f888(x128191,a876)))),
% 161.04/160.70 inference(rename_variables,[],[3574])).
% 161.04/160.70 cnf(12820,plain,
% 161.04/160.70 (P1(f334(f61(x128201),f196(f888(x128201,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3376])).
% 161.04/160.70 cnf(12823,plain,
% 161.04/160.70 (E(f334(f334(f22(f888(x128231,a876)),f196(f888(x128231,a876))),x128232),f196(f888(x128231,a876)))),
% 161.04/160.70 inference(rename_variables,[],[3574])).
% 161.04/160.70 cnf(12824,plain,
% 161.04/160.70 (P1(f334(f61(x128241),f196(f888(x128241,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3376])).
% 161.04/160.70 cnf(12827,plain,
% 161.04/160.70 (E(f334(f334(f22(f888(x128271,a876)),f196(f888(x128271,a876))),x128272),f196(f888(x128271,a876)))),
% 161.04/160.70 inference(rename_variables,[],[3574])).
% 161.04/160.70 cnf(12828,plain,
% 161.04/160.70 (P1(f334(f61(x128281),f196(f888(x128281,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3376])).
% 161.04/160.70 cnf(12831,plain,
% 161.04/160.70 (E(f334(f334(f22(f888(x128311,a876)),f196(f888(x128311,a876))),x128312),f196(f888(x128311,a876)))),
% 161.04/160.70 inference(rename_variables,[],[3574])).
% 161.04/160.70 cnf(12832,plain,
% 161.04/160.70 (P1(f334(f61(x128321),f196(f888(x128321,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3376])).
% 161.04/160.70 cnf(12836,plain,
% 161.04/160.70 (E(f334(f265(x128361,x128361),f266(x128361,x128362)),x128362)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(12841,plain,
% 161.04/160.70 (E(f334(f334(f22(f888(x128411,a876)),f196(f888(x128411,a876))),x128412),f196(f888(x128411,a876)))),
% 161.04/160.70 inference(rename_variables,[],[3574])).
% 161.04/160.70 cnf(12842,plain,
% 161.04/160.70 (P1(f334(f61(x128421),f196(f888(x128421,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3376])).
% 161.04/160.70 cnf(12846,plain,
% 161.04/160.70 (P1(f334(f61(x128461),f196(f888(x128461,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3376])).
% 161.04/160.70 cnf(12849,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x128491),x128491))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12855,plain,
% 161.04/160.70 (P1(f334(f334(f248(a1),x128551),x128551))),
% 161.04/160.70 inference(rename_variables,[],[3301])).
% 161.04/160.70 cnf(12858,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x128581),f334(a116,x128581)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(12863,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x128631),x128631))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12866,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x128661),f334(a116,x128661)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(12879,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x128791),x128791))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12882,plain,
% 161.04/160.70 (P1(f334(f334(f248(a1),x128821),x128821))),
% 161.04/160.70 inference(rename_variables,[],[3301])).
% 161.04/160.70 cnf(12885,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x128851),x128852),f196(f888(x128851,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12896,plain,
% 161.04/160.70 (P1(f334(f334(f336(x128961),x128962),f257(f888(x128961,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3459])).
% 161.04/160.70 cnf(12902,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x129021,a876)),f334(f174(x129021),f334(f138(x129021,x129022),x129023))),f334(f174(x129021),x129023)))),
% 161.04/160.70 inference(rename_variables,[],[3949])).
% 161.04/160.70 cnf(12908,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x129081),f2(a881)))),
% 161.04/160.70 inference(rename_variables,[],[4543])).
% 161.04/160.70 cnf(12909,plain,
% 161.04/160.70 (P1(f334(f334(f248(a1),x129091),x129091))),
% 161.04/160.70 inference(rename_variables,[],[3301])).
% 161.04/160.70 cnf(12913,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x129131),f2(a881)))),
% 161.04/160.70 inference(rename_variables,[],[4543])).
% 161.04/160.70 cnf(12914,plain,
% 161.04/160.70 (P1(f334(f334(f248(a1),x129141),x129141))),
% 161.04/160.70 inference(rename_variables,[],[3301])).
% 161.04/160.70 cnf(12923,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x129231),x129231))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12930,plain,
% 161.04/160.70 (E(f334(f334(f16(x129301,x129302),x129303),x129304),x129303)),
% 161.04/160.70 inference(rename_variables,[],[3291])).
% 161.04/160.70 cnf(12933,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x129331,a876)),f334(f174(x129331),f178(x129331,x129332,x129333))),f334(f174(x129331),x129332)))),
% 161.04/160.70 inference(rename_variables,[],[4000])).
% 161.04/160.70 cnf(12937,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x129371),f2(a881)))),
% 161.04/160.70 inference(rename_variables,[],[4543])).
% 161.04/160.70 cnf(12938,plain,
% 161.04/160.70 (P1(f334(f334(f248(a1),x129381),x129381))),
% 161.04/160.70 inference(rename_variables,[],[3301])).
% 161.04/160.70 cnf(12942,plain,
% 161.04/160.70 (~P1(f334(f334(f249(a881),x129421),f2(a881)))),
% 161.04/160.70 inference(rename_variables,[],[4543])).
% 161.04/160.70 cnf(12943,plain,
% 161.04/160.70 (P1(f334(f334(f248(a1),x129431),x129431))),
% 161.04/160.70 inference(rename_variables,[],[3301])).
% 161.04/160.70 cnf(12947,plain,
% 161.04/160.70 (~P1(f334(f334(f249(f888(a881,a876)),f305(a881,f334(a116,x129471),f334(a116,x129471))),f305(a881,x129472,x129471)))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,11065,12101,12201,12296,12334,12342,12355,12410,12550,3552,12165,12574,12576,3553,12235,3268,12558,12560,3269,12598,3235,12483,4511,4512,11685,4252,12614,12617,3272,12610,3110,3169,12527,4496,3603,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,12168,12326,12380,12514,12632,4493,10451,10544,3357,3320,12566,3512,3216,4488,2894,2895,2898,2899,2910,2911,2915,2916,2920,2921,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2961,2966,2968,2971,2975,2978,2981,2984,3000,3010,3011,3012,3017,3018,3023,3024,3045,3046,3057,3058,3059,3062,3069,3075,4473,3089,3168,4474,3640,3142,11339,3282,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,12075,12272,12463,12516,12523,12525,12535,12537,12539,12564,12589,12608,12621,3626,3878,3230,11612,12358,12362,12366,3236,10701,11618,3243,3761,3997,3132,4490,3852,11389,3356,3195,3160,3677,12541,3155,3971,3682,4457,3139,3120,3146,3175,3313,12046,12191,12413,12486,3358,10833,12162,3228,3229,3253,10492,3406,4560,10421,3936,4503,10282,10448,11253,12322,12359,4510,12330,3291,11708,11711,4549,11000,11070,11300,11303,3702,3407,3625,3371,12582,3190,10351,10657,3191,3464,3183,3111,3212,11379,4084,12345,12475,3938,11006,11132,11185,12306,12312,12424,12427,12450,4572,10936,11137,11247,11272,11306,11312,12251,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,12204,12248,12329,3665,4368,4369,3595,4501,11370,3605,3643,3816,3574,12819,12823,12827,12831,12841,3862,12198,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,12130,12454,12638,12696,12727,12739,12781,12802,12858,12866,3754,11603,3284,3380,11723,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,12254,12349,12643,12646,12663,12666,12688,12740,12908,12913,12937,4555,11487,11518,11553,11583,12749,12753,3741,3513,3515,12669,12672,12675,12678,12708,3887,3328,3330,3303,4540,3189,4498,3693,4222,4006,3496,4556,4078,11267,3624,3341,11732,11735,12172,12276,12434,4047,4005,11876,12219,3949,10830,12034,12060,12232,12457,4000,11012,12098,12171,12231,12275,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,12120,12375,12447,12460,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,12142,12212,12279,12386,12430,12689,12714,12791,12798,12805,12810,12813,12816,12849,12863,12879,12923,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,11976,12705,12855,12882,12909,12914,12938,3302,3376,12086,12769,12820,12824,12828,12832,12842,12846,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,12186,12282,12285,12348,12379,12416,12495,3459,10625,10889,10933,11207,11289,11448,11688,12325,12498,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,12116,12260,12303,12309,12398,12401,12420,12474,12480,12489,12508,12768,12785,12788,3362,10654,10684,10693,11239,11787,12417,12431,12750,12754,12757,3402,3396,3820,3759,10328,11606,11636,12732,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,3322,10687,10838,10909,11637,11792,11981,12213,3781,11738,12685,4128,3519,4546,3792,3828,4529,4531,4532,3275,3276,4530,4533,4534,4438,4259,3799,3614,4228,11467,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,11331,4013,12243,3904,11328,11663,11667,11729,12333,12341,12423,3748,10949,10955,10970,11908,12119,3601,11176,12145,12257,12267,12338,12389,12397,3638,4082,3750,10690,11028,11182,11212,11226,12225,12337,3571,10611,10614,10696,10868,3570,4567,11600,4557,4562,12653,4568,10747,10847,11161,11445,11473,12207,12216,12263,12444,4189,10823,12228,12240,4089,3893,3780,12511,3728,3729,4565,10301,10304,10642,10645,11484,11664,12453,4566,11580,11673,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7146,7151,7153,7159,7167,7168,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7465,7468,7494,7518,7536,7539,7540,7550,7568,7569,7571,7573,7575,7577,7605,7630,7631,7663,7665,7666,7667,7672,7692,7701,7711,7716,7722,7724,7730,7741,7742,7744,7762,7772,7795,7861,7862,7909,7917,7918,7942,7943,7960,7961,8020,8021,8022,8047,8080,8087,8089,8099,8111,8142,8150,8157,8170,8192,8198,8225,8269,8298,8311,8329,8332,8362,8385,8444,8445,8448,8450,8466,8556,8557,8558,8559,8588,8617,8649,8693,8711,8766,8811,8814,8827,8834,8871,8890,8918,8919,8936,8937,9080,9084,9104,9115,9138,9140,9143,9147,9150,9151,9164,9165,9185,9191,9203,9251,9269,9323,9324,9331,9392,9397,9433,9440,9443,9446,9447,9462,9478,9487,9499,9512,9513,9516,9518,9545,9670,9715,9716,9758,9803,9920,9977,10041,10117,10130,10135,3,2629,2632,2639,2640,2641,2642,2645,2647,2648,2651,2652,2653,2657,2658,2668,2670,2671,2672,2676,2677,2678,2680,2681,2682,2683,2685,2686,2687,2699,2703,2704,2706,2708,2712,2713,2715,2717,2718,2726,2727,2728,2735,2736,2737,2739,2740,2745,2747,2748,2749,2750,2766,2767,2768,2776,2777,2778,2783,2820,2822,2837,2840,2841,2842,2845,2847,2852,2863,2865,2866,5229,5288,5384,5470,5471,5472,5547,5644,5675,5708,5724,5726,5732,5795,5796,5797,5798,5804,5837,5967,6011,6034,6071,6110,6260,6267,6301,6302,6322,6325,6327,6334,6335,6336,6337,6338,6339,6340,6341,6420,6488,6489,6573,6607,6608,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7025,7026,7027,7063,7107,7108,7207,7268,7269,7270,7271,7285,7318,7374,7375,7384,7390,7392,7404,7436,7437,7438,7439,7585,7586,7592,7593,7595,7597,7803,7805,7806,7821,7859,7938,7978,8031,8052,8053,8068,8128,8240,8308,8309,8312,8347,8408,8409,8474,8493])).
% 161.04/160.70 cnf(12948,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x129481),x129481))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12950,plain,
% 161.04/160.70 (~P1(f334(f334(f248(f888(a881,a876)),f305(a881,f334(a116,x129501),f334(a116,x129501))),f305(a881,x129502,x129501)))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,11065,12101,12201,12296,12334,12342,12355,12410,12550,3552,12165,12574,12576,3553,12235,3268,12558,12560,3269,12598,3235,12483,4511,4512,11685,4252,12614,12617,3272,12610,3110,3169,12527,4496,3603,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,12168,12326,12380,12514,12632,4493,10451,10544,3357,3320,12566,3512,3216,4488,2894,2895,2898,2899,2910,2911,2915,2916,2920,2921,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2961,2966,2968,2971,2975,2978,2981,2984,3000,3010,3011,3012,3017,3018,3023,3024,3045,3046,3057,3058,3059,3062,3069,3075,4473,3089,3168,4474,3640,3142,11339,3282,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,12075,12272,12463,12516,12523,12525,12535,12537,12539,12564,12589,12608,12621,3626,3878,3230,11612,12358,12362,12366,3236,10701,11618,3243,3761,3997,3132,4490,3852,11389,3356,3195,3160,3677,12541,3155,3971,3682,4457,3139,3120,3146,3175,3313,12046,12191,12413,12486,3358,10833,12162,3228,3229,3253,10492,3406,4560,10421,3936,4503,10282,10448,11253,12322,12359,4510,12330,3291,11708,11711,4549,11000,11070,11300,11303,3702,3407,3625,3371,12582,3190,10351,10657,3191,3464,3183,3111,3212,11379,4084,12345,12475,3938,11006,11132,11185,12306,12312,12424,12427,12450,4572,10936,11137,11247,11272,11306,11312,12251,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,12204,12248,12329,3665,4368,4369,3595,4501,11370,3605,3643,3816,3574,12819,12823,12827,12831,12841,3862,12198,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,12130,12454,12638,12696,12727,12739,12781,12802,12858,12866,3754,11603,3284,3380,11723,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,12254,12349,12643,12646,12663,12666,12688,12740,12908,12913,12937,4555,11487,11518,11553,11583,12749,12753,3741,3513,3515,12669,12672,12675,12678,12708,3887,3328,3330,3303,4540,3189,4498,3693,4222,4006,3496,4556,4078,11267,3624,3341,11732,11735,12172,12276,12434,4047,4005,11876,12219,3949,10830,12034,12060,12232,12457,4000,11012,12098,12171,12231,12275,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,12120,12375,12447,12460,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,12142,12212,12279,12386,12430,12689,12714,12791,12798,12805,12810,12813,12816,12849,12863,12879,12923,12948,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,11976,12705,12855,12882,12909,12914,12938,3302,3376,12086,12769,12820,12824,12828,12832,12842,12846,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,12186,12282,12285,12348,12379,12416,12495,3459,10625,10889,10933,11207,11289,11448,11688,12325,12498,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,12116,12260,12303,12309,12398,12401,12420,12474,12480,12489,12508,12768,12785,12788,3362,10654,10684,10693,11239,11787,12417,12431,12750,12754,12757,3402,3396,3820,3759,10328,11606,11636,12732,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,3322,10687,10838,10909,11637,11792,11981,12213,3781,11738,12685,4128,3519,4546,3792,3828,4529,4531,4532,3275,3276,4530,4533,4534,4438,4259,3799,3614,4228,11467,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,11331,4013,12243,3904,11328,11663,11667,11729,12333,12341,12423,3748,10949,10955,10970,11908,12119,3601,11176,12145,12257,12267,12338,12389,12397,3638,4082,3750,10690,11028,11182,11212,11226,12225,12337,3571,10611,10614,10696,10868,3570,4567,11600,4557,4562,12653,4568,10747,10847,11161,11445,11473,12207,12216,12263,12444,4189,10823,12228,12240,4089,3893,3780,12511,3728,3729,4565,10301,10304,10642,10645,11484,11664,12453,4566,11580,11673,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7146,7151,7153,7159,7167,7168,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7465,7468,7494,7518,7536,7539,7540,7550,7568,7569,7571,7573,7575,7577,7605,7630,7631,7663,7665,7666,7667,7672,7692,7701,7711,7716,7722,7724,7730,7741,7742,7744,7762,7772,7795,7861,7862,7909,7917,7918,7942,7943,7960,7961,8020,8021,8022,8047,8080,8087,8089,8099,8111,8142,8150,8157,8170,8192,8198,8225,8269,8298,8311,8329,8332,8362,8385,8444,8445,8448,8450,8466,8556,8557,8558,8559,8588,8617,8649,8693,8711,8766,8811,8814,8827,8834,8871,8890,8918,8919,8936,8937,9080,9084,9104,9115,9138,9140,9143,9147,9150,9151,9164,9165,9185,9191,9203,9251,9269,9323,9324,9331,9392,9397,9433,9440,9443,9446,9447,9462,9478,9487,9499,9512,9513,9516,9518,9545,9670,9715,9716,9758,9803,9920,9977,10041,10117,10130,10135,3,2629,2632,2639,2640,2641,2642,2645,2647,2648,2651,2652,2653,2657,2658,2668,2670,2671,2672,2676,2677,2678,2680,2681,2682,2683,2685,2686,2687,2699,2703,2704,2706,2708,2712,2713,2715,2717,2718,2726,2727,2728,2735,2736,2737,2739,2740,2745,2747,2748,2749,2750,2766,2767,2768,2776,2777,2778,2783,2820,2822,2837,2840,2841,2842,2845,2847,2852,2863,2865,2866,5229,5288,5384,5470,5471,5472,5547,5644,5675,5708,5724,5726,5732,5795,5796,5797,5798,5804,5837,5967,6011,6034,6071,6110,6260,6267,6301,6302,6322,6325,6327,6334,6335,6336,6337,6338,6339,6340,6341,6420,6488,6489,6573,6607,6608,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7025,7026,7027,7063,7107,7108,7207,7268,7269,7270,7271,7285,7318,7374,7375,7384,7390,7392,7404,7436,7437,7438,7439,7585,7586,7592,7593,7595,7597,7803,7805,7806,7821,7859,7938,7978,8031,8052,8053,8068,8128,8240,8308,8309,8312,8347,8408,8409,8474,8493,8494])).
% 161.04/160.70 cnf(12951,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x129511),x129511))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(12954,plain,
% 161.04/160.70 (~P1(f334(f334(f248(a881),f334(a116,x129541)),x129541))),
% 161.04/160.70 inference(rename_variables,[],[4548])).
% 161.04/160.70 cnf(12959,plain,
% 161.04/160.70 (E(x129591,f551(f334(f5(x129592),f334(f5(x129592),x129591)),f5(x129592),x129592,x129592))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,11065,12101,12201,12296,12334,12342,12355,12410,12550,12552,3552,12165,12574,12576,3553,12235,3268,12558,12560,3269,12598,3235,12483,4511,4512,11685,4252,12614,12617,3272,12610,3110,3169,12527,4496,3603,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,12168,12326,12380,12514,12632,4493,10451,10544,3357,3320,12566,3512,3216,4488,2894,2895,2898,2899,2910,2911,2915,2916,2920,2921,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2961,2966,2968,2971,2975,2978,2981,2984,3000,3010,3011,3012,3017,3018,3023,3024,3045,3046,3057,3058,3059,3062,3069,3075,4473,3089,3168,4474,3640,3142,11339,3282,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,12075,12272,12463,12516,12523,12525,12535,12537,12539,12564,12589,12608,12621,3626,3878,3230,11612,12358,12362,12366,3236,10701,11618,3243,3761,3997,3131,3132,4490,3852,11389,3356,3195,3160,3677,12541,3155,3971,3682,4457,3139,3120,3146,3175,3313,12046,12191,12413,12486,3358,10833,12162,3228,3229,3253,10492,3406,4560,10421,3936,4503,10282,10448,11253,12322,12359,4510,12330,3291,11708,11711,4549,11000,11070,11300,11303,3702,3407,3625,3371,12582,3190,10351,10657,3191,3464,3183,3111,3212,11379,4084,12345,12475,3938,11006,11132,11185,12306,12312,12424,12427,12450,4572,10936,11137,11247,11272,11306,11312,12251,4573,11039,11140,11250,4574,11143,4575,11199,4576,3211,3504,12204,12248,12329,3665,4368,4369,3595,4501,11370,3605,3643,3816,3574,12819,12823,12827,12831,12841,3862,12198,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,12130,12454,12638,12696,12727,12739,12781,12802,12858,12866,3754,11603,3284,3380,11723,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,12254,12349,12643,12646,12663,12666,12688,12740,12908,12913,12937,4555,11487,11518,11553,11583,12749,12753,3741,3513,3515,12669,12672,12675,12678,12708,3887,3328,3330,3303,4540,3189,4498,3693,4222,4006,3496,4556,4078,11267,3624,3341,11732,11735,12172,12276,12434,4047,4005,11876,12219,3949,10830,12034,12060,12232,12457,4000,11012,12098,12171,12231,12275,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,12120,12375,12447,12460,4561,10778,11148,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,12142,12212,12279,12386,12430,12689,12714,12791,12798,12805,12810,12813,12816,12849,12863,12879,12923,12948,12951,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,11976,12705,12855,12882,12909,12914,12938,3302,3376,12086,12769,12820,12824,12828,12832,12842,12846,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,12186,12282,12285,12348,12379,12416,12495,3459,10625,10889,10933,11207,11289,11448,11688,12325,12498,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,12116,12260,12303,12309,12398,12401,12420,12474,12480,12489,12508,12768,12785,12788,3362,10654,10684,10693,11239,11787,12417,12431,12750,12754,12757,3402,3396,3820,3759,10328,11606,11636,12732,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,12954,3322,10687,10838,10909,11637,11792,11981,12213,3781,11738,12685,4128,3519,4546,3792,3828,4529,4531,4532,3275,3276,4530,4533,4534,4438,4259,3799,3614,4228,11467,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,11331,4013,12243,3904,11328,11663,11667,11729,12333,12341,12423,12699,3748,10949,10955,10970,11908,12119,3601,11176,12145,12257,12267,12338,12389,12397,3638,4082,3750,10690,11028,11182,11212,11226,12225,12337,3571,10611,10614,10696,10868,3570,4567,11600,4557,4562,12653,4568,10747,10847,11161,11445,11473,12207,12216,12263,12444,4189,10823,12228,12240,4089,3893,3780,12511,3728,3729,4565,10301,10304,10642,10645,11484,11664,12453,4566,11580,11673,3752,10608,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933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% 161.04/160.70 cnf(12960,plain,
% 161.04/160.70 (P1(f334(f334(f336(x129601),f334(x129602,x129603)),f334(f313(x129604,x129601,x129602),f257(f888(x129604,a876)))))),
% 161.04/160.70 inference(rename_variables,[],[3904])).
% 161.04/160.70 cnf(12961,plain,
% 161.04/160.70 (P27(x129611,x129611,f5(x129611),x129612)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(12965,plain,
% 161.04/160.70 (P1(f334(f334(f336(x129651),x129652),f257(f888(x129651,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3459])).
% 161.04/160.70 cnf(12966,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x129661),x129662),f196(f888(x129661,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(12970,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x129701,a876)),x129702),f257(f888(x129701,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3684])).
% 161.04/160.70 cnf(12971,plain,
% 161.04/160.70 (P27(x129711,x129711,f5(x129711),x129712)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(12975,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x129751,a876)),x129752),f257(f888(x129751,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3684])).
% 161.04/160.70 cnf(12976,plain,
% 161.04/160.70 (P27(x129761,x129761,f5(x129761),x129762)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(12980,plain,
% 161.04/160.70 (P27(x129801,x129801,f5(x129801),x129802)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(12983,plain,
% 161.04/160.70 (~P1(f334(f334(f249(f888(x129831,a876)),x129832),f196(f888(x129831,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4561])).
% 161.04/160.70 cnf(12986,plain,
% 161.04/160.70 (P27(x129861,x129861,f5(x129861),x129862)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(12989,plain,
% 161.04/160.70 (P27(x129891,x129891,f5(x129891),x129892)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(12992,plain,
% 161.04/160.70 (P1(f334(f334(f336(x129921),x129922),f334(f334(f312(x129921),x129922),x129923)))),
% 161.04/160.70 inference(rename_variables,[],[3614])).
% 161.04/160.70 cnf(13000,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x130001,a876)),f196(f888(x130001,a876))),x130002))),
% 161.04/160.70 inference(rename_variables,[],[3750])).
% 161.04/160.70 cnf(13004,plain,
% 161.04/160.70 (E(f334(f265(x130041,x130041),f266(x130041,x130042)),x130042)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(13008,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x130081),x130082),f196(f888(x130081,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(13012,plain,
% 161.04/160.70 (P1(f334(f334(f336(x130121),f334(x130122,x130123)),f334(f313(x130124,x130121,x130122),f257(f888(x130124,a876)))))),
% 161.04/160.70 inference(rename_variables,[],[3904])).
% 161.04/160.70 cnf(13013,plain,
% 161.04/160.70 (P27(x130131,x130131,f5(x130131),x130132)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(13016,plain,
% 161.04/160.70 (P1(f334(f334(f336(x130161),x130162),f257(f888(x130161,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3459])).
% 161.04/160.70 cnf(13023,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x130231),x130232),f196(f888(x130231,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(13026,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x130261),x130262),f196(f888(x130261,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(13030,plain,
% 161.04/160.70 (E(f334(f334(f16(x130301,x130302),x130303),x130304),x130303)),
% 161.04/160.70 inference(rename_variables,[],[3291])).
% 161.04/160.70 cnf(13033,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x130331),f334(a116,x130331)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(13034,plain,
% 161.04/160.70 (~E(f334(a116,x130341),x130341)),
% 161.04/160.70 inference(rename_variables,[],[4478])).
% 161.04/160.70 cnf(13037,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x130371),f334(a116,f334(f334(f80(a881),x130372),x130371))))),
% 161.04/160.70 inference(rename_variables,[],[3752])).
% 161.04/160.70 cnf(13038,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x130381),f334(a116,x130381)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(13040,plain,
% 161.04/160.70 (~E(f334(f334(f81(a881),f334(a116,f2(a881))),f33(x130401,x130402)),f334(f334(f81(a881),f334(a116,f2(a881))),f32(x130403,x130404)))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,11065,12101,12201,12296,12334,12342,12355,12410,12550,12552,12961,12971,12976,12980,12986,12989,3552,12165,12574,12576,3553,12235,3268,12558,12560,3269,12598,3235,12483,4511,4512,11685,4252,12614,12617,3272,12610,3110,3169,12527,4496,3603,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,12168,12326,12380,12514,12632,12782,13034,4493,10451,10544,3357,3320,12566,3512,3216,4488,2894,2895,2898,2899,2910,2911,2915,2916,2920,2921,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2961,2966,2968,2971,2975,2978,2981,2984,3000,3007,3010,3011,3012,3017,3018,3023,3024,3045,3046,3057,3058,3059,3062,3069,3075,4473,3089,3168,4474,3640,3142,11339,3282,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,12075,12272,12463,12516,12523,12525,12535,12537,12539,12564,12589,12608,12621,12836,3626,3878,3230,11612,12358,12362,12366,3236,10701,11618,3243,3761,3997,3131,3132,4490,3852,11389,3356,3195,3160,3677,12541,3155,3971,3176,3682,4457,3139,3120,3146,3175,3313,12046,12191,12413,12486,3358,10833,12162,3228,3229,3253,10492,3406,4560,10421,3936,4503,10282,10448,11253,12322,12359,12363,4510,12330,3291,11708,11711,12930,4549,11000,11070,11300,11303,3702,3286,3407,3625,3371,12582,3190,10351,10657,3191,4537,3464,3183,3111,3212,11379,4084,12345,12475,3938,11006,11132,11185,12306,12312,12424,12427,12450,4572,10936,11137,11247,11272,11306,11312,12251,4573,11039,11140,11250,4574,11143,11196,4575,11199,4576,3211,3504,12204,12248,12329,3665,4368,4369,3595,4501,11370,3605,3643,3816,3574,12819,12823,12827,12831,12841,3862,12198,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,12130,12454,12638,12696,12727,12739,12781,12802,12858,12866,13033,3754,11603,3284,3380,11723,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,12254,12349,12643,12646,12663,12666,12688,12740,12908,12913,12937,4555,11487,11518,11553,11583,12749,12753,3741,3513,3515,12669,12672,12675,12678,12708,3887,3328,3330,3303,4540,3189,4498,3693,4222,4006,3496,4556,4078,11267,3624,3341,11732,11735,12172,12276,12434,4047,4005,11876,12219,3949,10830,12034,12060,12232,12457,4000,11012,12098,12171,12231,12275,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,12120,12375,12447,12460,12970,12975,4561,10778,11148,12983,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,12142,12212,12279,12386,12430,12689,12714,12791,12798,12805,12810,12813,12816,12849,12863,12879,12923,12948,12951,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,11976,12705,12855,12882,12909,12914,12938,3302,3376,12086,12769,12820,12824,12828,12832,12842,12846,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,12186,12282,12285,12348,12379,12416,12495,3459,10625,10889,10933,11207,11289,11448,11688,12325,12498,12896,12965,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,12116,12260,12303,12309,12398,12401,12420,12474,12480,12489,12508,12768,12785,12788,12885,12966,13008,13023,3362,10654,10684,10693,11239,11787,12417,12431,12750,12754,12757,3402,3396,3820,3759,10328,11606,11636,12732,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,12954,3322,10687,10838,10909,11637,11792,11981,12213,3781,11738,12685,4128,3519,4546,3792,3828,4529,4531,4532,3275,3276,4530,4533,4534,4438,4259,3799,3614,11599,4228,11467,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,11331,4013,12243,3904,11328,11663,11667,11729,12333,12341,12423,12699,12960,13012,3748,10949,10955,10970,11908,12119,12394,3601,11176,12145,12257,12267,12338,12389,12397,3638,4082,3750,10690,11028,11182,11212,11226,12225,12337,12383,3571,10611,10614,10696,10868,3570,4567,11600,4557,4562,12653,4568,10747,10847,11161,11445,11473,12207,12216,12263,12444,4189,10823,12228,12240,12266,4089,3893,3780,12511,3728,3729,4565,10301,10304,10642,10645,11484,11664,12453,4566,11580,11673,3752,10608,10865,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,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6403,6404,6491])).
% 161.04/160.70 cnf(13042,plain,
% 161.04/160.70 (~E(f334(a116,x130421),x130421)),
% 161.04/160.70 inference(rename_variables,[],[4478])).
% 161.04/160.70 cnf(13047,plain,
% 161.04/160.70 (P1(f334(f334(f248(a1),f2(a1)),f334(f104(a1),x130471)))),
% 161.04/160.70 inference(rename_variables,[],[3402])).
% 161.04/160.70 cnf(13050,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),f2(a881)),x130501))),
% 161.04/160.70 inference(rename_variables,[],[3322])).
% 161.04/160.70 cnf(13051,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x130511),x130511))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(13054,plain,
% 161.04/160.70 (~E(f334(a116,x130541),f2(a881))),
% 161.04/160.70 inference(rename_variables,[],[4488])).
% 161.04/160.70 cnf(13063,plain,
% 161.04/160.70 (P1(f334(f334(f336(x130631),x130632),f257(f888(x130631,a876))))),
% 161.04/160.70 inference(rename_variables,[],[3459])).
% 161.04/160.70 cnf(13067,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x130671),x130672),f196(f888(x130671,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(13070,plain,
% 161.04/160.70 (P1(f334(f61(a881),f307(a881,x130701,x130702)))),
% 161.04/160.70 inference(rename_variables,[],[3515])).
% 161.04/160.70 cnf(13071,plain,
% 161.04/160.70 (E(f334(f334(f246(a881),f334(a116,x130711)),f334(a116,x130712)),f334(a116,f334(f334(f246(a881),x130711),x130712)))),
% 161.04/160.70 inference(rename_variables,[],[3475])).
% 161.04/160.70 cnf(13074,plain,
% 161.04/160.70 (P1(f334(f61(a881),f307(a881,x130741,x130742)))),
% 161.04/160.70 inference(rename_variables,[],[3515])).
% 161.04/160.70 cnf(13075,plain,
% 161.04/160.70 (E(f334(f334(f247(a881),f334(a116,x130751)),f334(a116,x130752)),f334(a116,f334(f334(f247(a881),x130751),x130752)))),
% 161.04/160.70 inference(rename_variables,[],[3476])).
% 161.04/160.70 cnf(13078,plain,
% 161.04/160.70 (P1(f334(f61(a881),f307(a881,x130781,x130782)))),
% 161.04/160.70 inference(rename_variables,[],[3515])).
% 161.04/160.70 cnf(13082,plain,
% 161.04/160.70 (P1(f334(f61(a881),f307(a881,x130821,x130822)))),
% 161.04/160.70 inference(rename_variables,[],[3515])).
% 161.04/160.70 cnf(13086,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x130861,a876)),f334(f174(x130861),f334(f138(x130861,x130862),x130863))),f334(f174(x130861),x130863)))),
% 161.04/160.70 inference(rename_variables,[],[3949])).
% 161.04/160.70 cnf(13087,plain,
% 161.04/160.70 (E(f334(f334(f16(x130871,x130872),x130873),x130874),x130873)),
% 161.04/160.70 inference(rename_variables,[],[3291])).
% 161.04/160.70 cnf(13090,plain,
% 161.04/160.70 (P1(f334(f334(f248(f888(x130901,a876)),f334(f174(x130901),f334(f334(f177(x130901),x130902),x130903))),f334(f174(x130901),x130903)))),
% 161.04/160.70 inference(rename_variables,[],[3994])).
% 161.04/160.70 cnf(13091,plain,
% 161.04/160.70 (E(f334(f334(f16(x130911,x130912),x130913),x130914),x130913)),
% 161.04/160.70 inference(rename_variables,[],[3291])).
% 161.04/160.70 cnf(13095,plain,
% 161.04/160.70 (E(f334(f334(f16(x130951,x130952),x130953),x130954),x130953)),
% 161.04/160.70 inference(rename_variables,[],[3291])).
% 161.04/160.70 cnf(13108,plain,
% 161.04/160.70 (P1(f334(f334(f248(a1),f2(a1)),f334(f104(a1),x131081)))),
% 161.04/160.70 inference(rename_variables,[],[3402])).
% 161.04/160.70 cnf(13111,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x131111),x131112),f196(f888(x131111,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(13114,plain,
% 161.04/160.70 (~P1(f334(f334(f336(x131141),x131142),f196(f888(x131141,a876))))),
% 161.04/160.70 inference(rename_variables,[],[4551])).
% 161.04/160.70 cnf(13115,plain,
% 161.04/160.70 (E(f334(f265(x131151,x131151),f266(x131151,x131152)),x131152)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(13116,plain,
% 161.04/160.70 (P27(x131161,x131161,f5(x131161),x131162)),
% 161.04/160.70 inference(rename_variables,[],[3543])).
% 161.04/160.70 cnf(13120,plain,
% 161.04/160.70 (E(f334(f265(x131201,x131201),f266(x131201,x131202)),x131202)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(13126,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x131261),f334(a116,x131261)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(13128,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x131281),x131281))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(13129,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),f2(a881)),x131291))),
% 161.04/160.70 inference(rename_variables,[],[3322])).
% 161.04/160.70 cnf(13132,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),x131321),f334(a116,x131321)))),
% 161.04/160.70 inference(rename_variables,[],[3368])).
% 161.04/160.70 cnf(13134,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),x131341),x131341))),
% 161.04/160.70 inference(rename_variables,[],[3300])).
% 161.04/160.70 cnf(13135,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),f2(a881)),x131351))),
% 161.04/160.70 inference(rename_variables,[],[3322])).
% 161.04/160.70 cnf(13139,plain,
% 161.04/160.70 (P1(f334(f334(f248(a881),f2(a881)),x131391))),
% 161.04/160.70 inference(rename_variables,[],[3322])).
% 161.04/160.70 cnf(13140,plain,
% 161.04/160.70 (P1(f334(f334(f249(a881),f2(a881)),f334(a116,x131401)))),
% 161.04/160.70 inference(rename_variables,[],[3380])).
% 161.04/160.70 cnf(13141,plain,
% 161.04/160.70 (E(f334(f265(x131411,x131411),f266(x131411,x131412)),x131412)),
% 161.04/160.70 inference(rename_variables,[],[3258])).
% 161.04/160.70 cnf(13144,plain,
% 161.04/160.70 (P1(f334(f47(f334(f265(x131441,x131441),f266(x131441,f334(f334(f80(a881),f334(f334(f81(a881),f334(f268(a881,a881),f334(f334(f269(a881,a881),f2(a881)),x131442))),f334(a116,f334(f334(f80(a881),x131443),f334(f272(a881,a881),f334(f334(f269(a881,a881),f2(a881)),x131442)))))),f334(f272(a881,a881),f334(f334(f269(a881,a881),f2(a881)),x131442))))),f334(a116,f334(f334(f80(a881),x131443),f334(f272(a881,a881),f334(f334(f269(a881,a881),f2(a881)),x131442))))),f334(f334(f269(a881,a881),f2(a881)),x131442)))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,11065,12101,12201,12296,12334,12342,12355,12410,12550,12552,12961,12971,12976,12980,12986,12989,13013,13116,3552,12165,12574,12576,3553,12235,3268,12558,12560,3269,12598,3235,12483,4511,4512,11685,4252,12614,12617,3272,12610,3110,3169,12527,4496,3603,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,12168,12326,12380,12514,12632,12782,13034,4493,10451,10544,3357,3320,12566,3512,3216,4488,12700,13054,2894,2895,2898,2899,2910,2911,2915,2916,2920,2921,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2961,2966,2968,2969,2971,2975,2978,2981,2984,2990,3000,3007,3010,3011,3012,3017,3018,3023,3024,3045,3046,3057,3058,3059,3062,3069,3075,4473,3089,3168,4474,3640,3142,11339,3282,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,12075,12272,12463,12516,12523,12525,12535,12537,12539,12564,12589,12608,12621,12836,13004,13115,13120,13141,3626,3878,3230,11612,12358,12362,12366,3236,10701,11618,3243,3761,3997,3131,3132,4490,3852,11389,3356,3195,3160,3677,12541,3155,3971,3176,3682,4457,3139,3120,3146,3175,3313,12046,12191,12413,12486,3358,10833,12162,3228,3229,3253,10492,3406,4560,10421,3936,4503,10282,10448,11253,12322,12359,12363,4510,12330,3291,11708,11711,12930,13030,13087,13091,13095,4549,11000,11070,11300,11303,3702,3286,3407,3625,3399,3371,12582,3190,10351,10657,3191,4537,3464,3183,3111,3296,3212,11379,4084,12345,12475,3938,11006,11132,11185,12306,12312,12424,12427,12450,4572,10936,11137,11247,11272,11306,11312,12251,4573,11039,11140,11250,4574,11143,11196,4575,11199,4576,3211,3504,12204,12248,12329,3665,4368,4369,3486,3595,4501,11370,3605,3643,3816,3574,12819,12823,12827,12831,12841,3862,12198,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,12130,12454,12638,12696,12727,12739,12781,12802,12858,12866,13033,13038,13126,13132,3754,11603,3284,3380,11723,12631,13140,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,12254,12349,12643,12646,12663,12666,12688,12740,12908,12913,12937,4555,11487,11518,11553,11583,12749,12753,3741,3513,3515,12669,12672,12675,12678,12708,12711,13070,13074,13078,3516,3887,3475,13071,3476,13075,3328,3330,3303,4540,3189,4498,3693,4222,4006,3496,4556,4078,11267,3624,3341,11732,11735,12172,12276,12434,4047,4005,11876,12219,3949,10830,12034,12060,12232,12457,12902,13086,3994,13090,4000,11012,12098,12171,12231,12275,12933,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,12120,12375,12447,12460,12970,12975,4561,10778,11148,12983,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,12142,12212,12279,12386,12430,12689,12714,12791,12798,12805,12810,12813,12816,12849,12863,12879,12923,12948,12951,13051,13128,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,11976,12705,12855,12882,12909,12914,12938,12943,3302,3376,12086,12769,12820,12824,12828,12832,12842,12846,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,12186,12282,12285,12348,12379,12416,12495,3459,10625,10889,10933,11207,11289,11448,11688,12325,12498,12896,12965,13016,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,12116,12260,12303,12309,12398,12401,12420,12474,12480,12489,12508,12768,12785,12788,12885,12966,13008,13023,13026,13067,13111,13114,3362,10654,10684,10693,11239,11787,12417,12431,12750,12754,12757,3402,13047,3396,3820,3759,10328,11606,11636,12732,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,12954,3322,10687,10838,10909,11637,11792,11981,12213,12778,13050,13129,13135,13139,3781,11738,12685,4128,3519,4546,3792,3828,4529,4531,4532,3275,3276,4530,4533,4534,4438,4259,4305,3799,3614,11599,4228,11467,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,11331,4013,12243,3904,11328,11663,11667,11729,12333,12341,12423,12699,12960,13012,3748,10949,10955,10970,11908,12119,12394,3601,11176,12145,12257,12267,12338,12389,12397,12505,3638,4082,3750,10690,11028,11182,11212,11226,12225,12337,12383,13000,3571,10611,10614,10696,10868,3570,4567,11600,4557,4562,12653,4568,10747,10847,11161,11445,11473,12207,12216,12263,12444,4189,10823,12228,12240,12266,4089,3893,3780,12511,3728,3729,4565,10301,10304,10642,10645,11484,11664,12453,4566,11580,11673,3752,10608,10865,13037,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7146,7151,7153,7159,7167,7168,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7465,7468,7494,7518,7536,7539,7540,7550,7568,7569,7571,7573,7575,7577,7605,7630,7631,7663,7665,7666,7667,7672,7692,7701,7711,7716,7722,7724,7730,7741,7742,7744,7762,7772,7795,7861,7862,7909,7917,7918,7942,7943,7960,7961,8020,8021,8022,8047,8080,8087,8089,8099,8111,8142,8150,8157,8170,8192,8198,8225,8269,8298,8311,8329,8332,8362,8385,8444,8445,8448,8450,8466,8556,8557,8558,8559,8588,8617,8649,8693,8711,8766,8811,8814,8827,8834,8871,8890,8918,8919,8936,8937,9080,9084,9104,9115,9138,9140,9143,9147,9150,9151,9164,9165,9185,9191,9203,9251,9269,9323,9324,9331,9392,9397,9433,9440,9443,9446,9447,9462,9478,9487,9499,9512,9513,9516,9518,9545,9670,9715,9716,9758,9803,9920,9977,10041,10117,10130,10135,3,2629,2632,2639,2640,2641,2642,2645,2647,2648,2651,2652,2653,2657,2658,2668,2670,2671,2672,2676,2677,2678,2680,2681,2682,2683,2685,2686,2687,2699,2703,2704,2706,2708,2712,2713,2715,2717,2718,2726,2727,2728,2735,2736,2737,2739,2740,2745,2747,2748,2749,2750,2766,2767,2768,2776,2777,2778,2783,2820,2822,2837,2840,2841,2842,2845,2847,2852,2863,2865,2866,5229,5288,5384,5470,5471,5472,5547,5644,5675,5708,5724,5726,5732,5795,5796,5797,5798,5804,5837,5967,6011,6034,6071,6110,6260,6267,6301,6302,6322,6325,6327,6334,6335,6336,6337,6338,6339,6340,6341,6420,6488,6489,6573,6607,6608,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7025,7026,7027,7063,7107,7108,7207,7268,7269,7270,7271,7285,7318,7374,7375,7384,7390,7392,7404,7436,7437,7438,7439,7585,7586,7592,7593,7595,7597,7803,7805,7806,7821,7859,7938,7978,8031,8052,8053,8068,8128,8240,8308,8309,8312,8347,8408,8409,8474,8493,8494,8495,8496,8653,8864,8888,8889,8968,8984,9038,9039,9159,9195,9218,9252,9293,9485,9752,9946,10002,10004,6029,6403,6404,6491,6511,6512,6927,7143,8296,8574,8607,8805,8996,8997,9066,9067,9341,9342,9343,9344,9548,9823,10126,10177,10178,6473,8400,8401,8854,8872])).
% 161.04/160.70 cnf(13160,plain,
% 161.04/160.70 (E(f334(f334(f80(a881),f2(a881)),f827(f334(a116,f2(a881)),f2(a881))),f2(a881))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,11065,12101,12201,12296,12334,12342,12355,12410,12550,12552,12961,12971,12976,12980,12986,12989,13013,13116,3552,12165,12574,12576,3553,12235,3268,12558,12560,3269,12598,3235,12483,4511,4512,11685,4252,12614,12617,3272,12610,3110,3169,12527,4496,3603,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,12168,12326,12380,12514,12632,12782,13034,4493,10451,10544,3357,3320,12566,3512,3216,4488,12700,13054,2894,2895,2898,2899,2910,2911,2915,2916,2920,2921,2922,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2961,2966,2968,2969,2971,2975,2978,2981,2984,2990,3000,3007,3010,3011,3012,3017,3018,3021,3023,3024,3045,3046,3057,3058,3059,3062,3069,3075,4473,3089,3168,4474,3640,3142,11339,3282,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,12075,12272,12463,12516,12523,12525,12535,12537,12539,12564,12589,12608,12621,12836,13004,13115,13120,13141,3626,3878,3230,11612,12358,12362,12366,3236,10701,11618,3243,3761,3997,3131,3132,4490,3852,11389,3356,3195,3160,3677,12541,3155,3971,3176,3682,4457,3139,3120,3146,3175,3313,12046,12191,12413,12486,3358,10833,12162,3228,3229,3253,10492,3406,4560,10421,3936,4503,10282,10448,11253,12322,12359,12363,4510,12330,3291,11708,11711,12930,13030,13087,13091,13095,4549,11000,11070,11300,11303,3702,3286,3407,3625,3399,3371,12582,3190,10351,10657,3191,4537,3464,3183,3111,3296,3212,11379,4084,12345,12475,3938,11006,11132,11185,12306,12312,12424,12427,12450,4572,10936,11137,11247,11272,11306,11312,12251,4573,11039,11140,11250,4574,11143,11196,4575,11199,4576,3211,3504,12204,12248,12329,3665,4368,4369,3486,3595,4501,11370,3605,3643,3816,3574,12819,12823,12827,12831,12841,3862,12198,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,12130,12454,12638,12696,12727,12739,12781,12802,12858,12866,13033,13038,13126,13132,3754,11603,3284,3380,11723,12631,13140,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,12254,12349,12643,12646,12663,12666,12688,12740,12908,12913,12937,12942,4555,11487,11518,11553,11583,12749,12753,3741,3513,3515,12669,12672,12675,12678,12708,12711,13070,13074,13078,3516,3887,3475,13071,3476,13075,3328,3330,3303,4540,3189,4498,3693,4222,4006,3496,4556,4078,11267,3624,3341,11732,11735,12172,12276,12434,4047,4005,11876,12219,3949,10830,12034,12060,12232,12457,12902,13086,3994,13090,4000,11012,12098,12171,12231,12275,12933,4001,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,12120,12375,12447,12460,12970,12975,4561,10778,11148,12983,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,12142,12212,12279,12386,12430,12689,12714,12791,12798,12805,12810,12813,12816,12849,12863,12879,12923,12948,12951,13051,13128,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,11976,12705,12855,12882,12909,12914,12938,12943,3302,3376,12086,12769,12820,12824,12828,12832,12842,12846,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,12186,12282,12285,12348,12379,12416,12495,3459,10625,10889,10933,11207,11289,11448,11688,12325,12498,12896,12965,13016,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,12116,12260,12303,12309,12398,12401,12420,12474,12480,12489,12508,12768,12785,12788,12885,12966,13008,13023,13026,13067,13111,13114,3362,10654,10684,10693,11239,11787,12417,12431,12750,12754,12757,3402,13047,13108,3396,3820,3759,10328,11606,11636,12732,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,12954,3322,10687,10838,10909,11637,11792,11981,12213,12778,13050,13129,13135,13139,3781,11738,12685,4128,3519,4546,3792,3828,4529,4531,4532,3275,3276,4530,4533,4534,4438,4259,4305,3799,3614,11599,4228,11467,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,11331,4013,12243,3904,11328,11663,11667,11729,12333,12341,12423,12699,12960,13012,3748,10949,10955,10970,11908,12119,12394,3601,11176,12145,12257,12267,12338,12389,12397,12505,3638,4082,3750,10690,11028,11182,11212,11226,12225,12337,12383,13000,3571,10611,10614,10696,10868,3570,4567,11600,4557,4562,12653,4568,10747,10847,11161,11445,11473,12207,12216,12263,12444,4189,10823,12228,12240,12266,4089,3893,3780,12511,3728,3729,4565,10301,10304,10642,10645,11484,11664,12453,4566,11580,11673,3752,10608,10865,13037,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7146,7151,7153,7159,7167,7168,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7465,7468,7494,7518,7536,7539,7540,7550,7568,7569,7571,7573,7575,7577,7605,7630,7631,7663,7665,7666,7667,7672,7692,7701,7711,7716,7722,7724,7730,7741,7742,7744,7762,7772,7795,7861,7862,7909,7917,7918,7942,7943,7960,7961,8020,8021,8022,8047,8080,8087,8089,8099,8111,8142,8150,8157,8170,8192,8198,8225,8269,8298,8311,8329,8332,8362,8385,8444,8445,8448,8450,8466,8556,8557,8558,8559,8588,8617,8649,8693,8711,8766,8811,8814,8827,8834,8871,8890,8918,8919,8936,8937,9080,9084,9104,9115,9138,9140,9143,9147,9150,9151,9164,9165,9185,9191,9203,9251,9269,9323,9324,9331,9392,9397,9433,9440,9443,9446,9447,9462,9478,9487,9499,9512,9513,9516,9518,9545,9670,9715,9716,9758,9803,9920,9977,10041,10117,10130,10135,3,2629,2632,2639,2640,2641,2642,2645,2647,2648,2651,2652,2653,2657,2658,2668,2670,2671,2672,2676,2677,2678,2680,2681,2682,2683,2685,2686,2687,2699,2703,2704,2706,2708,2712,2713,2715,2717,2718,2726,2727,2728,2735,2736,2737,2739,2740,2745,2747,2748,2749,2750,2766,2767,2768,2776,2777,2778,2783,2820,2822,2837,2840,2841,2842,2845,2847,2852,2863,2865,2866,5229,5288,5384,5470,5471,5472,5547,5644,5675,5708,5724,5726,5732,5795,5796,5797,5798,5804,5837,5967,6011,6034,6071,6110,6260,6267,6301,6302,6322,6325,6327,6334,6335,6336,6337,6338,6339,6340,6341,6420,6488,6489,6573,6607,6608,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7025,7026,7027,7063,7107,7108,7207,7268,7269,7270,7271,7285,7318,7374,7375,7384,7390,7392,7404,7436,7437,7438,7439,7585,7586,7592,7593,7595,7597,7803,7805,7806,7821,7859,7938,7978,8031,8052,8053,8068,8128,8240,8308,8309,8312,8347,8408,8409,8474,8493,8494,8495,8496,8653,8864,8888,8889,8968,8984,9038,9039,9159,9195,9218,9252,9293,9485,9752,9946,10002,10004,6029,6403,6404,6491,6511,6512,6927,7143,8296,8574,8607,8805,8996,8997,9066,9067,9341,9342,9343,9344,9548,9823,10126,10177,10178,6473,8400,8401,8854,8872,9824,10176,4655,4657])).
% 161.04/160.70 cnf(13212,plain,
% 161.04/160.70 (P1(f334(f334(f249(a1),f2(a1)),f334(f75(a1),f78(a1))))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,11065,12101,12201,12296,12334,12342,12355,12410,12550,12552,12961,12971,12976,12980,12986,12989,13013,13116,3552,12165,12574,12576,3553,12235,3268,12558,12560,3269,12598,3235,12483,4511,4512,11685,4252,12614,12617,3272,12610,3110,3169,12527,4496,3603,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,12168,12326,12380,12514,12632,12782,13034,4493,10451,10544,3357,3320,12566,3512,3216,4488,12700,13054,2894,2895,2898,2899,2910,2911,2915,2916,2920,2921,2922,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2961,2966,2968,2969,2971,2975,2978,2981,2984,2990,3000,3007,3010,3011,3012,3017,3018,3021,3023,3024,3045,3046,3057,3058,3059,3062,3069,3075,4473,3089,3168,4474,3640,3142,11339,3282,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,12075,12272,12463,12516,12523,12525,12535,12537,12539,12564,12589,12608,12621,12836,13004,13115,13120,13141,3626,3878,3230,11612,12358,12362,12366,3236,10701,11618,3243,3761,3997,3131,3132,4490,3852,11389,3356,3195,3160,3677,12541,3155,3971,3176,3682,4457,3139,3120,3146,3175,3313,12046,12191,12413,12486,3358,10833,12162,3228,3229,3253,10492,3406,4560,10421,3936,4503,10282,10448,11253,12322,12359,12363,4510,12330,3291,11708,11711,12930,13030,13087,13091,13095,4549,11000,11070,11300,11303,3702,3286,3407,3625,3399,3371,12582,3190,10351,10657,3191,4537,3464,3183,3111,3296,3212,11379,4084,12345,12475,3938,11006,11132,11185,12306,12312,12424,12427,12450,4572,10936,11137,11247,11272,11306,11312,12251,4573,11039,11140,11250,4574,11143,11196,4575,11199,4576,3211,3504,12204,12248,12329,3665,4368,4369,3486,3595,4501,11370,3605,3643,3816,3574,12819,12823,12827,12831,12841,3862,12198,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,12130,12454,12638,12696,12727,12739,12781,12802,12858,12866,13033,13038,13126,13132,3754,11603,3284,3380,11723,12631,13140,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,12254,12349,12643,12646,12663,12666,12688,12740,12908,12913,12937,12942,4555,11487,11518,11553,11583,12749,12753,3741,3513,3515,12669,12672,12675,12678,12708,12711,13070,13074,13078,3516,3887,3475,13071,3476,13075,3328,3330,3303,4540,3189,4498,3693,4222,4006,3496,4556,4078,11267,3624,3341,11732,11735,12172,12276,12434,4047,4005,11876,12219,3949,10830,12034,12060,12232,12457,12902,13086,3994,13090,4000,11012,12098,12171,12231,12275,12933,4001,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,12120,12375,12447,12460,12970,12975,4561,10778,11148,12983,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,12142,12212,12279,12386,12430,12689,12714,12791,12798,12805,12810,12813,12816,12849,12863,12879,12923,12948,12951,13051,13128,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,11976,12705,12855,12882,12909,12914,12938,12943,3302,3376,12086,12769,12820,12824,12828,12832,12842,12846,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,12186,12282,12285,12348,12379,12416,12495,3459,10625,10889,10933,11207,11289,11448,11688,12325,12498,12896,12965,13016,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,12116,12260,12303,12309,12398,12401,12420,12474,12480,12489,12508,12768,12785,12788,12885,12966,13008,13023,13026,13067,13111,13114,3362,10654,10684,10693,11239,11787,12417,12431,12750,12754,12757,3402,13047,13108,3396,3820,3759,10328,11606,11636,12732,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,12954,3322,10687,10838,10909,11637,11792,11981,12213,12778,13050,13129,13135,13139,3781,11738,12685,4128,3519,4546,3792,3828,4529,4531,4532,3275,3276,4530,4533,4534,4438,4259,4305,3799,3614,11599,4228,11467,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,11331,4013,12243,3904,11328,11663,11667,11729,12333,12341,12423,12699,12960,13012,3748,10949,10955,10970,11908,12119,12394,3601,11176,12145,12257,12267,12338,12389,12397,12505,3638,4082,3750,10690,11028,11182,11212,11226,12225,12337,12383,13000,3571,10611,10614,10696,10868,3570,4567,11600,4557,4562,12653,4568,10747,10847,11161,11445,11473,12207,12216,12263,12444,4189,10823,12228,12240,12266,4089,3893,3780,12511,3728,3729,4565,10301,10304,10642,10645,11484,11664,12453,4566,11580,11673,3752,10608,10865,13037,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7146,7151,7153,7159,7167,7168,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7465,7468,7494,7518,7536,7539,7540,7550,7568,7569,7571,7573,7575,7577,7605,7630,7631,7663,7665,7666,7667,7672,7692,7701,7711,7716,7722,7724,7730,7741,7742,7744,7762,7772,7795,7861,7862,7909,7917,7918,7942,7943,7960,7961,8020,8021,8022,8047,8080,8087,8089,8099,8111,8142,8150,8157,8170,8192,8198,8225,8269,8298,8311,8329,8332,8362,8385,8444,8445,8448,8450,8466,8556,8557,8558,8559,8588,8617,8649,8693,8711,8766,8811,8814,8827,8834,8871,8890,8918,8919,8936,8937,9080,9084,9104,9115,9138,9140,9143,9147,9150,9151,9164,9165,9185,9191,9203,9251,9269,9323,9324,9331,9392,9397,9433,9440,9443,9446,9447,9462,9478,9487,9499,9512,9513,9516,9518,9545,9670,9715,9716,9758,9803,9920,9977,10041,10117,10130,10135,3,2629,2632,2639,2640,2641,2642,2645,2647,2648,2651,2652,2653,2657,2658,2668,2670,2671,2672,2676,2677,2678,2680,2681,2682,2683,2685,2686,2687,2699,2703,2704,2706,2708,2712,2713,2715,2717,2718,2726,2727,2728,2735,2736,2737,2739,2740,2745,2747,2748,2749,2750,2766,2767,2768,2776,2777,2778,2783,2820,2822,2837,2840,2841,2842,2845,2847,2852,2863,2865,2866,5229,5288,5384,5470,5471,5472,5547,5644,5675,5708,5724,5726,5732,5795,5796,5797,5798,5804,5837,5967,6011,6034,6071,6110,6260,6267,6301,6302,6322,6325,6327,6334,6335,6336,6337,6338,6339,6340,6341,6420,6488,6489,6573,6607,6608,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7025,7026,7027,7063,7107,7108,7207,7268,7269,7270,7271,7285,7318,7374,7375,7384,7390,7392,7404,7436,7437,7438,7439,7585,7586,7592,7593,7595,7597,7803,7805,7806,7821,7859,7938,7978,8031,8052,8053,8068,8128,8240,8308,8309,8312,8347,8408,8409,8474,8493,8494,8495,8496,8653,8864,8888,8889,8968,8984,9038,9039,9159,9195,9218,9252,9293,9485,9752,9946,10002,10004,6029,6403,6404,6491,6511,6512,6927,7143,8296,8574,8607,8805,8996,8997,9066,9067,9341,9342,9343,9344,9548,9823,10126,10177,10178,6473,8400,8401,8854,8872,9824,10176,4655,4657,4658,4714,4722,4859,4873,4874,4904,4905,4934,4989,5051,5108,5185,5221,5223,5230,5232,5233,5259,5331,5352,5486,5552,5553,5554,5671])).
% 161.04/160.70 cnf(13236,plain,
% 161.04/160.70 (~E(f334(f190(x132361,f888(x132362,a876),x132363,f196(f888(x132361,a876))),x132364),f334(f241(f888(x132362,a876)),f334(f334(f41(f44(a1,x132365,x132365),f888(x132362,a876)),x132366),a116)))),
% 161.04/160.70 inference(scs_inference,[],[4579,3543,11065,12101,12201,12296,12334,12342,12355,12410,12550,12552,12961,12971,12976,12980,12986,12989,13013,13116,3552,12165,12574,12576,3553,12235,3268,12558,12560,3269,12598,3235,12483,4511,4512,11685,4252,12614,12617,3272,12610,3110,3169,12527,4496,3603,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,12168,12326,12380,12514,12632,12782,13034,4493,10451,10544,3357,3320,12566,3512,3216,4488,12700,13054,2894,2895,2898,2899,2910,2911,2915,2916,2920,2921,2922,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2961,2966,2968,2969,2971,2975,2978,2981,2984,2990,3000,3007,3010,3011,3012,3017,3018,3021,3023,3024,3045,3046,3057,3058,3059,3062,3069,3075,4473,3089,3168,4474,3640,3142,11339,3282,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,12075,12272,12463,12516,12523,12525,12535,12537,12539,12564,12589,12608,12621,12836,13004,13115,13120,13141,3626,3878,3230,11612,12358,12362,12366,3236,10701,11618,3243,3761,3997,3131,3132,4490,3852,11389,3356,3195,3160,3677,12541,3155,3971,3176,3682,4457,3139,3120,3146,3175,3313,12046,12191,12413,12486,3358,10833,12162,3228,3229,3253,10492,3406,4560,10421,3936,4503,10282,10448,11253,12322,12359,12363,4510,12330,3291,11708,11711,12930,13030,13087,13091,13095,4549,11000,11070,11300,11303,3702,3286,3407,3625,3399,3371,12582,3190,10351,10657,3191,4537,3464,3183,3111,3296,3212,11379,4084,12345,12475,3938,11006,11132,11185,12306,12312,12424,12427,12450,4572,10936,11137,11247,11272,11306,11312,12251,4573,11039,11140,11250,4574,11143,11196,4575,11199,4576,3211,3504,12204,12248,12329,3665,4368,4369,3486,3595,4501,11370,3605,3643,3816,3574,12819,12823,12827,12831,12841,3862,12198,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,12130,12454,12638,12696,12727,12739,12781,12802,12858,12866,13033,13038,13126,13132,3754,11603,3284,3380,11723,12631,13140,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,12254,12349,12643,12646,12663,12666,12688,12740,12908,12913,12937,12942,4555,11487,11518,11553,11583,12749,12753,3741,3513,3515,12669,12672,12675,12678,12708,12711,13070,13074,13078,3516,3887,3475,13071,3476,13075,3328,3330,3303,4540,3189,4498,3693,4222,4006,3496,4556,4078,11267,3624,3341,11732,11735,12172,12276,12434,4047,4005,11876,12219,3949,10830,12034,12060,12232,12457,12902,13086,3994,13090,4000,11012,12098,12171,12231,12275,12933,4001,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,12120,12375,12447,12460,12970,12975,4561,10778,11148,12983,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,12142,12212,12279,12386,12430,12689,12714,12791,12798,12805,12810,12813,12816,12849,12863,12879,12923,12948,12951,13051,13128,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,11976,12705,12855,12882,12909,12914,12938,12943,3302,3376,12086,12769,12820,12824,12828,12832,12842,12846,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,12186,12282,12285,12348,12379,12416,12495,3459,10625,10889,10933,11207,11289,11448,11688,12325,12498,12896,12965,13016,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,12116,12260,12303,12309,12398,12401,12420,12474,12480,12489,12508,12768,12785,12788,12885,12966,13008,13023,13026,13067,13111,13114,3362,10654,10684,10693,11239,11787,12417,12431,12750,12754,12757,3402,13047,13108,3396,3820,3759,10328,11606,11636,12732,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,12954,3322,10687,10838,10909,11637,11792,11981,12213,12778,13050,13129,13135,13139,3781,11738,12685,4128,3519,4546,3792,3828,4529,4531,4532,3275,3276,4530,4533,4534,4438,4259,4305,3799,3614,11599,4228,11467,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,11331,4013,12243,3904,11328,11663,11667,11729,12333,12341,12423,12699,12960,13012,3748,10949,10955,10970,11908,12119,12394,3601,11176,12145,12257,12267,12338,12389,12397,12505,3638,4082,3750,10690,11028,11182,11212,11226,12225,12337,12383,13000,3571,10611,10614,10696,10868,3570,4567,11600,4557,4562,12653,4568,10747,10847,11161,11445,11473,12207,12216,12263,12444,4189,10823,12228,12240,12266,4089,3893,3780,12511,3728,3729,4565,10301,10304,10642,10645,11484,11664,12453,4566,11580,11673,3752,10608,10865,13037,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7146,7151,7153,7159,7167,7168,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7465,7468,7494,7518,7536,7539,7540,7550,7568,7569,7571,7573,7575,7577,7605,7630,7631,7663,7665,7666,7667,7672,7692,7701,7711,7716,7722,7724,7730,7741,7742,7744,7762,7772,7795,7861,7862,7909,7917,7918,7942,7943,7960,7961,8020,8021,8022,8047,8080,8087,8089,8099,8111,8142,8150,8157,8170,8192,8198,8225,8269,8298,8311,8329,8332,8362,8385,8444,8445,8448,8450,8466,8556,8557,8558,8559,8588,8617,8649,8693,8711,8766,8811,8814,8827,8834,8871,8890,8918,8919,8936,8937,9080,9084,9104,9115,9138,9140,9143,9147,9150,9151,9164,9165,9185,9191,9203,9251,9269,9323,9324,9331,9392,9397,9433,9440,9443,9446,9447,9462,9478,9487,9499,9512,9513,9516,9518,9545,9670,9715,9716,9758,9803,9920,9977,10041,10117,10130,10135,3,2629,2632,2639,2640,2641,2642,2645,2647,2648,2651,2652,2653,2657,2658,2668,2670,2671,2672,2676,2677,2678,2680,2681,2682,2683,2685,2686,2687,2699,2703,2704,2706,2708,2712,2713,2715,2717,2718,2726,2727,2728,2735,2736,2737,2739,2740,2745,2747,2748,2749,2750,2766,2767,2768,2776,2777,2778,2783,2820,2822,2837,2840,2841,2842,2845,2847,2852,2863,2865,2866,5229,5288,5384,5470,5471,5472,5547,5644,5675,5708,5724,5726,5732,5795,5796,5797,5798,5804,5837,5967,6011,6034,6071,6110,6260,6267,6301,6302,6322,6325,6327,6334,6335,6336,6337,6338,6339,6340,6341,6420,6488,6489,6573,6607,6608,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7025,7026,7027,7063,7107,7108,7207,7268,7269,7270,7271,7285,7318,7374,7375,7384,7390,7392,7404,7436,7437,7438,7439,7585,7586,7592,7593,7595,7597,7803,7805,7806,7821,7859,7938,7978,8031,8052,8053,8068,8128,8240,8308,8309,8312,8347,8408,8409,8474,8493,8494,8495,8496,8653,8864,8888,8889,8968,8984,9038,9039,9159,9195,9218,9252,9293,9485,9752,9946,10002,10004,6029,6403,6404,6491,6511,6512,6927,7143,8296,8574,8607,8805,8996,8997,9066,9067,9341,9342,9343,9344,9548,9823,10126,10177,10178,6473,8400,8401,8854,8872,9824,10176,4655,4657,4658,4714,4722,4859,4873,4874,4904,4905,4934,4989,5051,5108,5185,5221,5223,5230,5232,5233,5259,5331,5352,5486,5552,5553,5554,5671,5672,5697,5698,5702,5755,5761,5772,5778,5850,5928,5989,6052])).
% 161.04/160.70 cnf(13240,plain,
% 161.04/160.70 (~P1(f334(f61(x132401),f39(f888(x132401,a876),f257(f888(f888(x132401,a876),a876)))))),
% 161.04/160.71 inference(scs_inference,[],[4579,3543,11065,12101,12201,12296,12334,12342,12355,12410,12550,12552,12961,12971,12976,12980,12986,12989,13013,13116,3552,12165,12574,12576,3553,12235,3268,12558,12560,3269,12598,3235,12483,4511,4512,11685,4252,12614,12617,3272,12610,3110,3169,12527,4496,3603,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,12168,12326,12380,12514,12632,12782,13034,4493,10451,10544,3357,3320,12566,3512,3216,4488,12700,13054,2894,2895,2898,2899,2910,2911,2915,2916,2920,2921,2922,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2961,2966,2968,2969,2971,2975,2978,2981,2984,2990,3000,3007,3010,3011,3012,3017,3018,3021,3023,3024,3045,3046,3057,3058,3059,3062,3069,3075,4473,3089,3168,4474,3640,3142,11339,3282,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,12075,12272,12463,12516,12523,12525,12535,12537,12539,12564,12589,12608,12621,12836,13004,13115,13120,13141,3626,3878,3230,11612,12358,12362,12366,3236,10701,11618,3243,3761,3997,3131,3132,4490,3852,11389,3356,3195,3160,3677,12541,3155,3971,3176,3682,4457,3139,3120,3146,3175,3313,12046,12191,12413,12486,3358,10833,12162,3228,3229,3253,10492,3406,4560,10421,3936,4503,10282,10448,11253,12322,12359,12363,4510,12330,3291,11708,11711,12930,13030,13087,13091,13095,4549,11000,11070,11300,11303,3702,3286,3407,3625,3399,3371,12582,3190,10351,10657,3191,4537,3464,3183,3111,3296,3212,11379,4084,12345,12475,3938,11006,11132,11185,12306,12312,12424,12427,12450,4572,10936,11137,11247,11272,11306,11312,12251,4573,11039,11140,11250,4574,11143,11196,4575,11199,4576,3211,3504,12204,12248,12329,3665,4368,4369,3486,3595,4501,11370,3605,3643,3816,3574,12819,12823,12827,12831,12841,3862,12198,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,12130,12454,12638,12696,12727,12739,12781,12802,12858,12866,13033,13038,13126,13132,3754,11603,3284,3380,11723,12631,13140,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,12254,12349,12643,12646,12663,12666,12688,12740,12908,12913,12937,12942,4555,11487,11518,11553,11583,12749,12753,3741,3513,3515,12669,12672,12675,12678,12708,12711,13070,13074,13078,3516,3887,3475,13071,3476,13075,3328,3330,3303,4540,3189,4498,3693,4222,4006,3496,4556,4078,11267,3624,3341,11732,11735,12172,12276,12434,4047,4005,11876,12219,3949,10830,12034,12060,12232,12457,12902,13086,3994,13090,4000,11012,12098,12171,12231,12275,12933,4001,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,12120,12375,12447,12460,12970,12975,4561,10778,11148,12983,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,12142,12212,12279,12386,12430,12689,12714,12791,12798,12805,12810,12813,12816,12849,12863,12879,12923,12948,12951,13051,13128,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,11976,12705,12855,12882,12909,12914,12938,12943,3302,3376,12086,12769,12820,12824,12828,12832,12842,12846,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,12186,12282,12285,12348,12379,12416,12495,3459,10625,10889,10933,11207,11289,11448,11688,12325,12498,12896,12965,13016,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,12116,12260,12303,12309,12398,12401,12420,12474,12480,12489,12508,12768,12785,12788,12885,12966,13008,13023,13026,13067,13111,13114,3362,10654,10684,10693,11239,11787,12417,12431,12750,12754,12757,3402,13047,13108,3396,3820,3759,10328,11606,11636,12732,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,12954,3322,10687,10838,10909,11637,11792,11981,12213,12778,13050,13129,13135,13139,3781,11738,12685,4128,3519,4546,3792,3828,4529,4531,4532,3275,3276,4530,4533,4534,4438,4259,4305,3799,3614,11599,4228,11467,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,11331,4013,12243,3904,11328,11663,11667,11729,12333,12341,12423,12699,12960,13012,3748,10949,10955,10970,11908,12119,12394,3601,11176,12145,12257,12267,12338,12389,12397,12505,3638,4082,3750,10690,11028,11182,11212,11226,12225,12337,12383,13000,3571,10611,10614,10696,10868,3570,4567,11600,4557,4562,12653,4568,10747,10847,11161,11445,11473,12207,12216,12263,12444,4189,10823,12228,12240,12266,4089,3893,3780,12511,3728,3729,4565,10301,10304,10642,10645,11484,11664,12453,4566,11580,11673,3752,10608,10865,13037,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7146,7151,7153,7159,7167,7168,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7465,7468,7494,7518,7536,7539,7540,7550,7568,7569,7571,7573,7575,7577,7605,7630,7631,7663,7665,7666,7667,7672,7692,7701,7711,7716,7722,7724,7730,7741,7742,7744,7762,7772,7795,7861,7862,7909,7917,7918,7942,7943,7960,7961,8020,8021,8022,8047,8080,8087,8089,8099,8111,8142,8150,8157,8170,8192,8198,8225,8269,8298,8311,8329,8332,8362,8385,8444,8445,8448,8450,8466,8556,8557,8558,8559,8588,8617,8649,8693,8711,8766,8811,8814,8827,8834,8871,8890,8918,8919,8936,8937,9080,9084,9104,9115,9138,9140,9143,9147,9150,9151,9164,9165,9185,9191,9203,9251,9269,9323,9324,9331,9392,9397,9433,9440,9443,9446,9447,9462,9478,9487,9499,9512,9513,9516,9518,9545,9670,9715,9716,9758,9803,9920,9977,10041,10117,10130,10135,3,2629,2632,2639,2640,2641,2642,2645,2647,2648,2651,2652,2653,2657,2658,2668,2670,2671,2672,2676,2677,2678,2680,2681,2682,2683,2685,2686,2687,2699,2703,2704,2706,2708,2712,2713,2715,2717,2718,2726,2727,2728,2735,2736,2737,2739,2740,2745,2747,2748,2749,2750,2766,2767,2768,2776,2777,2778,2783,2820,2822,2837,2840,2841,2842,2845,2847,2852,2863,2865,2866,5229,5288,5384,5470,5471,5472,5547,5644,5675,5708,5724,5726,5732,5795,5796,5797,5798,5804,5837,5967,6011,6034,6071,6110,6260,6267,6301,6302,6322,6325,6327,6334,6335,6336,6337,6338,6339,6340,6341,6420,6488,6489,6573,6607,6608,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7025,7026,7027,7063,7107,7108,7207,7268,7269,7270,7271,7285,7318,7374,7375,7384,7390,7392,7404,7436,7437,7438,7439,7585,7586,7592,7593,7595,7597,7803,7805,7806,7821,7859,7938,7978,8031,8052,8053,8068,8128,8240,8308,8309,8312,8347,8408,8409,8474,8493,8494,8495,8496,8653,8864,8888,8889,8968,8984,9038,9039,9159,9195,9218,9252,9293,9485,9752,9946,10002,10004,6029,6403,6404,6491,6511,6512,6927,7143,8296,8574,8607,8805,8996,8997,9066,9067,9341,9342,9343,9344,9548,9823,10126,10177,10178,6473,8400,8401,8854,8872,9824,10176,4655,4657,4658,4714,4722,4859,4873,4874,4904,4905,4934,4989,5051,5108,5185,5221,5223,5230,5232,5233,5259,5331,5352,5486,5552,5553,5554,5671,5672,5697,5698,5702,5755,5761,5772,5778,5850,5928,5989,6052,6075,6247])).
% 161.04/160.71 cnf(13254,plain,
% 161.04/160.71 (~P1(f334(f334(f249(a881),f2(a881)),f196(a881)))),
% 161.04/160.71 inference(scs_inference,[],[4579,3543,11065,12101,12201,12296,12334,12342,12355,12410,12550,12552,12961,12971,12976,12980,12986,12989,13013,13116,3552,12165,12574,12576,3553,12235,3268,12558,12560,3269,12598,3235,12483,4511,4512,11685,4252,12614,12617,3272,12610,3110,3169,12527,4496,3603,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,12168,12326,12380,12514,12632,12782,13034,4493,10451,10544,3357,3320,12566,3512,3216,4488,12700,13054,2894,2895,2898,2899,2910,2911,2915,2916,2920,2921,2922,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2961,2966,2968,2969,2971,2975,2978,2981,2984,2990,3000,3007,3010,3011,3012,3017,3018,3021,3023,3024,3045,3046,3057,3058,3059,3062,3069,3075,4473,3089,3168,4474,3640,3142,11339,3282,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,12075,12272,12463,12516,12523,12525,12535,12537,12539,12564,12589,12608,12621,12836,13004,13115,13120,13141,3626,3878,3230,11612,12358,12362,12366,3236,10701,11618,3243,3761,3997,3131,3132,4490,3852,11389,3356,3195,3160,3677,12541,3155,3971,3176,3682,4457,3139,3120,3146,3175,3313,12046,12191,12413,12486,3358,10833,12162,3228,3229,3253,10492,3406,4560,10421,3936,4503,10282,10448,11253,12322,12359,12363,4510,12330,3291,11708,11711,12930,13030,13087,13091,13095,4549,11000,11070,11300,11303,3702,3286,3407,3625,3399,3371,12582,3190,10351,10657,3191,4537,3464,3183,3111,3296,3212,11379,4084,12345,12475,3938,11006,11132,11185,12306,12312,12424,12427,12450,4572,10936,11137,11247,11272,11306,11312,12251,4573,11039,11140,11250,4574,11143,11196,4575,11199,4576,3211,3504,12204,12248,12329,3665,4368,4369,3486,3595,4501,11370,3605,3643,3816,3574,12819,12823,12827,12831,12841,3862,12198,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,12130,12454,12638,12696,12727,12739,12781,12802,12858,12866,13033,13038,13126,13132,3754,11603,3284,3380,11723,12631,13140,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,12254,12349,12643,12646,12663,12666,12688,12740,12908,12913,12937,12942,4555,11487,11518,11553,11583,12749,12753,3741,3513,3515,12669,12672,12675,12678,12708,12711,13070,13074,13078,3516,3887,3475,13071,3476,13075,3328,3330,3303,4540,3189,4498,3693,4222,4006,3496,4556,4078,11267,3624,3341,11732,11735,12172,12276,12434,4047,4005,11876,12219,3949,10830,12034,12060,12232,12457,12902,13086,3994,13090,4000,11012,12098,12171,12231,12275,12933,4001,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,12120,12375,12447,12460,12970,12975,4561,10778,11148,12983,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,12142,12212,12279,12386,12430,12689,12714,12791,12798,12805,12810,12813,12816,12849,12863,12879,12923,12948,12951,13051,13128,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,11976,12705,12855,12882,12909,12914,12938,12943,3302,3376,12086,12769,12820,12824,12828,12832,12842,12846,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,12186,12282,12285,12348,12379,12416,12495,3459,10625,10889,10933,11207,11289,11448,11688,12325,12498,12896,12965,13016,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,12116,12260,12303,12309,12398,12401,12420,12474,12480,12489,12508,12768,12785,12788,12885,12966,13008,13023,13026,13067,13111,13114,3362,10654,10684,10693,11239,11787,12417,12431,12750,12754,12757,3402,13047,13108,3396,3820,3759,10328,11606,11636,12732,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,12954,3322,10687,10838,10909,11637,11792,11981,12213,12778,13050,13129,13135,13139,3781,11738,12685,4128,3519,4546,3792,3828,4529,4531,4532,3275,3276,4530,4533,4534,4438,4259,4305,3799,3614,11599,4228,11467,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,11331,4013,12243,3904,11328,11663,11667,11729,12333,12341,12423,12699,12960,13012,3748,10949,10955,10970,11908,12119,12394,3601,11176,12145,12257,12267,12338,12389,12397,12505,3638,4082,3750,10690,11028,11182,11212,11226,12225,12337,12383,13000,3571,10611,10614,10696,10868,3570,4567,11600,4557,4562,12653,4568,10747,10847,11161,11445,11473,12207,12216,12263,12444,4189,10823,12228,12240,12266,4089,3893,3780,12511,3728,3729,4565,10301,10304,10642,10645,11484,11664,12453,4566,11580,11673,3752,10608,10865,13037,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,5127,5133,5177,5178,5186,5195,5200,5202,5212,5214,5220,5224,5225,5240,5247,5250,5251,5252,5256,5290,5303,5310,5312,5313,5317,5318,5319,5327,5330,5334,5335,5336,5343,5347,5348,5349,5357,5361,5362,5363,5368,5381,5390,5402,5404,5412,5413,5417,5421,5446,5452,5462,5463,5478,5490,5512,5518,5534,5535,5538,5557,5565,5566,5571,5572,5582,5583,5596,5600,5609,5610,5612,5627,5632,5642,5643,5655,5662,5676,5680,5683,5689,5690,5691,5694,5699,5736,5737,5740,5742,5745,5746,5747,5749,5751,5753,5758,5765,5780,5794,5799,5800,5813,5814,5819,5823,5825,5830,5871,5883,5892,5896,5907,5911,5912,5920,5933,5939,5957,5960,5970,5996,6010,6035,6055,6056,6059,6074,6076,6077,6079,6092,6093,6096,6098,6101,6102,6114,6120,6121,6122,6124,6126,6169,6170,6177,6180,6190,6226,6228,6230,6232,6241,6243,6245,6251,6253,6259,6262,6270,6277,6278,6279,6284,6306,6307,6308,6310,6316,6321,6355,6356,6359,6360,6361,6362,6363,6364,6365,6372,6405,6406,6415,6436,6437,6457,6460,6471,6472,6478,6508,6510,6524,6561,6563,6564,6617,6642,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6811,6862,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7485,7486,7490,7534,7535,7553,7622,7641,7664,7685,7700,7715,7725,7733,7734,7760,7763,7765,7774,7812,7823,7848,7906,7940,7973,8012,8028,8044,8045,8121,8178,8197,8226,8247,8271,8272,8369,8371,8377,8391,8395,8412,8433,8441,8443,8455,8461,8465,8486,8500,8501,8520,8521,8526,8527,8528,8529,8530,8552,8553,8554,8565,8579,8581,8593,8597,8599,8600,8601,8609,8614,8645,8646,8677,8690,8694,8712,8734,8735,8736,8737,8749,8750,8772,8782,8792,8793,8794,8795,8797,8818,8819,8830,8874,8880,8886,8898,8903,8905,8908,8909,8913,8922,9004,9035,9036,9037,9052,9069,9076,9077,9106,9107,9149,9152,9178,9223,9224,9225,9240,9265,9279,9285,9288,9310,9311,9339,9400,9436,9437,9438,9463,9464,9482,9500,9505,9508,9523,9547,9569,9577,9578,9579,9580,9595,9597,9602,9633,9634,9640,9641,9643,9687,9688,9720,9729,9739,9742,9751,9765,9768,9796,9829,9831,9835,9893,9934,9935,9947,9948,9968,9973,10014,10066,10138,10139,10192,10208,2,8,9,4601,4602,4620,4651,4653,4654,4682,4688,4689,4700,4749,4751,4781,4795,4825,4921,4922,4936,4955,5011,5012,5015,5016,5018,5020,5021,5033,5034,5044,5055,5056,5062,5081,5082,5099,5104,5105,5106,5107,5110,5118,5121,5128,5192,5198,5199,5206,5237,5248,5254,5269,5289,5296,5297,5298,5307,5316,5323,5325,5326,5332,5339,5340,5353,5354,5355,5356,5358,5359,5364,5365,5366,5367,5398,5399,5400,5408,5409,5410,5411,5457,5459,5461,5497,5499,5500,5502,5503,5505,5506,5508,5517,5522,5524,5525,5526,5527,5528,5529,5536,5546,5549,5560,5576,5577,5580,5589,5592,5593,5594,5619,5629,5645,5646,5656,5657,5659,5661,5666,5701,5705,5707,5767,5801,5802,5806,5812,5815,5816,5817,5818,5824,5835,5836,5838,5839,5847,5868,5899,5915,5918,5919,5921,5930,5950,5951,5952,5955,5956,5972,5982,5983,6012,6013,6017,6037,6040,6044,6063,6068,6069,6094,6097,6105,6113,6119,6123,6130,6131,6132,6133,6172,6191,6244,6280,6282,6303,6304,6309,6312,6313,6317,6323,6332,6348,6367,6368,6373,6383,6398,6418,6424,6426,6441,6442,6445,6446,6448,6450,6451,6452,6454,6456,6459,6465,6466,6467,6468,6474,6476,6518,6523,6538,6539,6540,6541,6575,6580,6582,6587,6588,6596,6600,6613,6638,6639,6640,6641,6653,6658,6675,6679,6698,6731,6732,6733,6738,6752,6773,6775,6777,6779,6782,6788,6790,6805,6812,6848,6851,6852,6865,6866,6867,6868,6888,6889,6904,6930,6952,6963,6965,6966,6968,6970,6971,7004,7005,7010,7011,7012,7013,7015,7017,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7146,7151,7153,7159,7167,7168,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7465,7468,7494,7518,7536,7539,7540,7550,7568,7569,7571,7573,7575,7577,7605,7630,7631,7663,7665,7666,7667,7672,7692,7701,7711,7716,7722,7724,7730,7741,7742,7744,7762,7772,7795,7861,7862,7909,7917,7918,7942,7943,7960,7961,8020,8021,8022,8047,8080,8087,8089,8099,8111,8142,8150,8157,8170,8192,8198,8225,8269,8298,8311,8329,8332,8362,8385,8444,8445,8448,8450,8466,8556,8557,8558,8559,8588,8617,8649,8693,8711,8766,8811,8814,8827,8834,8871,8890,8918,8919,8936,8937,9080,9084,9104,9115,9138,9140,9143,9147,9150,9151,9164,9165,9185,9191,9203,9251,9269,9323,9324,9331,9392,9397,9433,9440,9443,9446,9447,9462,9478,9487,9499,9512,9513,9516,9518,9545,9670,9715,9716,9758,9803,9920,9977,10041,10117,10130,10135,3,2629,2632,2639,2640,2641,2642,2645,2647,2648,2651,2652,2653,2657,2658,2668,2670,2671,2672,2676,2677,2678,2680,2681,2682,2683,2685,2686,2687,2699,2703,2704,2706,2708,2712,2713,2715,2717,2718,2726,2727,2728,2735,2736,2737,2739,2740,2745,2747,2748,2749,2750,2766,2767,2768,2776,2777,2778,2783,2820,2822,2837,2840,2841,2842,2845,2847,2852,2863,2865,2866,5229,5288,5384,5470,5471,5472,5547,5644,5675,5708,5724,5726,5732,5795,5796,5797,5798,5804,5837,5967,6011,6034,6071,6110,6260,6267,6301,6302,6322,6325,6327,6334,6335,6336,6337,6338,6339,6340,6341,6420,6488,6489,6573,6607,6608,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7025,7026,7027,7063,7107,7108,7207,7268,7269,7270,7271,7285,7318,7374,7375,7384,7390,7392,7404,7436,7437,7438,7439,7585,7586,7592,7593,7595,7597,7803,7805,7806,7821,7859,7938,7978,8031,8052,8053,8068,8128,8240,8308,8309,8312,8347,8408,8409,8474,8493,8494,8495,8496,8653,8864,8888,8889,8968,8984,9038,9039,9159,9195,9218,9252,9293,9485,9752,9946,10002,10004,6029,6403,6404,6491,6511,6512,6927,7143,8296,8574,8607,8805,8996,8997,9066,9067,9341,9342,9343,9344,9548,9823,10126,10177,10178,6473,8400,8401,8854,8872,9824,10176,4655,4657,4658,4714,4722,4859,4873,4874,4904,4905,4934,4989,5051,5108,5185,5221,5223,5230,5232,5233,5259,5331,5352,5486,5552,5553,5554,5671,5672,5697,5698,5702,5755,5761,5772,5778,5850,5928,5989,6052,6075,6247,6366,6521,6723,6724,6875,6939,6978])).
% 161.04/160.71 cnf(13285,plain,
% 161.04/160.71 (~E(f334(a116,x132851),x132851)),
% 161.04/160.71 inference(rename_variables,[],[4478])).
% 161.04/160.71 cnf(13318,plain,
% 161.04/160.71 (~P1(f334(f334(f248(a881),f334(a116,f2(a881))),f334(f334(f22(a881),f334(f334(f80(a881),x133181),f2(a881))),f334(f334(f80(a881),x133181),f2(a881)))))),
% 161.04/160.71 inference(scs_inference,[],[4579,3543,11065,12101,12201,12296,12334,12342,12355,12410,12550,12552,12961,12971,12976,12980,12986,12989,13013,13116,3552,12165,12574,12576,3553,12235,3268,12558,12560,3269,12598,3235,12483,4511,4512,11685,4252,12614,12617,3272,12610,3110,3169,12527,4496,3603,4478,10224,10234,10245,10256,10359,10362,10365,10467,10580,10884,11050,11053,11256,11342,11349,11363,11413,11416,11523,11570,11586,11887,11912,11924,11956,12054,12161,12168,12326,12380,12514,12632,12782,13034,13042,13285,4493,10451,10544,3357,3320,12566,3512,3216,4488,12700,13054,2894,2895,2898,2899,2910,2911,2915,2916,2920,2921,2922,2924,2931,2934,2939,2940,2942,2943,2945,2946,2947,2949,2950,2953,2961,2966,2968,2969,2971,2975,2978,2981,2984,2990,3000,3007,3010,3011,3012,3017,3018,3021,3023,3024,3045,3046,3057,3058,3059,3062,3069,3075,4473,3089,3168,4474,3640,3142,11339,3282,3342,3258,10227,10291,10294,10386,10389,10681,11354,11357,11468,11510,11515,11615,12075,12272,12463,12516,12523,12525,12535,12537,12539,12564,12589,12608,12621,12836,13004,13115,13120,13141,3626,3878,3230,11612,12358,12362,12366,3236,10701,11618,3243,3761,3997,3131,3132,4490,3852,11389,3356,3193,3195,3669,3160,3677,12541,3155,3971,3176,3682,4457,3139,3120,3146,3175,3313,12046,12191,12413,12486,3358,10833,12162,3228,3229,3253,10492,3406,4560,10421,3936,4503,10282,10448,11253,12322,12359,12363,4510,12330,3291,11708,11711,12930,13030,13087,13091,13095,4549,11000,11070,11300,11303,3702,3286,3407,3625,3399,3371,12582,3190,10351,10657,3191,4537,3464,3183,3111,3296,3212,11379,4084,12345,12475,3938,11006,11132,11185,12306,12312,12424,12427,12450,4572,10936,11137,11247,11272,11306,11312,12251,4573,11039,11140,11250,4574,11143,11196,4575,11199,4576,3211,3504,12204,12248,12329,3665,4368,4369,3486,3595,4501,11370,3605,3643,3816,3574,12819,12823,12827,12831,12841,3862,12198,3489,3743,3368,10370,10487,10558,10619,10622,10660,10754,10990,11218,11883,11946,12022,12066,12127,12130,12454,12638,12696,12727,12739,12781,12802,12858,12866,13033,13038,13126,13132,3754,11603,3284,3380,11723,12631,13140,3568,4543,10259,10262,10288,10762,10775,10894,11292,11382,11772,11780,11998,12001,12092,12254,12349,12643,12646,12663,12666,12688,12740,12908,12913,12937,12942,4555,11487,11518,11553,11583,12749,12753,3741,3513,3515,12669,12672,12675,12678,12708,12711,13070,13074,13078,13082,3516,3887,3475,13071,3476,13075,3328,3330,3303,4540,3189,4498,3693,4222,4006,3496,4556,4078,11267,3624,3341,11732,11735,12172,12276,12434,4047,4005,11876,12219,3949,10830,12034,12060,12232,12457,12902,13086,3994,13090,4000,11012,12098,12171,12231,12275,12933,4001,3666,11886,12029,12106,12152,4036,3684,11009,11075,11158,11221,12053,12120,12375,12447,12460,12970,12975,4561,10778,11148,12983,3300,10379,10474,10605,10667,10736,10781,10784,10817,10841,10878,10916,10952,11679,11726,11856,11911,11927,11930,11933,11936,12113,12133,12136,12139,12142,12212,12279,12386,12430,12689,12714,12791,12798,12805,12810,12813,12816,12849,12863,12879,12923,12948,12951,13051,13128,13134,3301,10462,10672,10757,10881,11460,11566,11760,11763,11775,11862,11873,11894,11899,11939,11961,11976,12705,12855,12882,12909,12914,12938,12943,3302,3376,12086,12769,12820,12824,12828,12832,12842,12846,4539,10325,10416,10529,10553,10799,10844,10854,11259,11532,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11955,12010,12013,12016,12019,12093,12183,12186,12282,12285,12348,12379,12416,12495,3459,10625,10889,10933,11207,11289,11448,11688,12325,12498,12896,12965,13016,13063,4551,10808,10820,10925,10943,10946,11003,11089,11097,11113,11151,11170,11179,11215,11262,11280,11283,11286,11315,11322,11325,11705,11741,12004,12007,12041,12087,12116,12260,12303,12309,12398,12401,12420,12474,12480,12489,12508,12768,12785,12788,12885,12966,13008,13023,13026,13067,13111,13114,3362,10654,10684,10693,11239,11787,12417,12431,12750,12754,12757,3402,13047,13108,3396,3820,3759,10328,11606,11636,12732,4548,10279,10648,10651,11092,11110,11569,11624,11668,11689,11793,11830,11833,11836,11839,12954,3322,10687,10838,10909,11637,11792,11981,12213,12778,13050,13129,13135,13139,3781,11738,12685,4128,3519,4546,3792,3828,4529,4531,4532,3275,3276,4530,4533,4534,4438,4259,4305,3799,3614,11599,12992,4228,11467,4563,10250,10253,10510,10561,10564,10569,10977,11442,11692,11796,4570,11173,11297,11331,4013,12243,3904,11328,11663,11667,11729,12333,12341,12423,12699,12960,13012,3748,10949,10955,10970,11908,12119,12394,3601,11176,12145,12257,12267,12338,12389,12397,12505,3638,4082,3750,10690,11028,11182,11212,11226,12225,12337,12383,13000,3571,10611,10614,10696,10868,3570,4567,11600,4557,4562,12653,4568,10747,10847,11161,11445,11473,12207,12216,12263,12444,4189,10823,12228,12240,12266,4089,3893,3780,12511,3728,3729,4565,10301,10304,10642,10645,11484,11664,12453,4566,11580,11673,3752,10608,10865,13037,4020,4588,4614,4663,4665,4696,4713,4720,4721,4760,4790,4796,4881,4906,4907,4942,4967,4968,4990,4991,5004,5008,5030,5037,5054,5057,5058,5059,5064,5065,5086,5111,5112,5122,512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6936,6938,6985,7008,7009,7025,7026,7027,7063,7107,7108,7207,7268,7269,7270,7271,7285,7318,7374,7375,7384,7390,7392,7404,7436,7437,7438,7439,7585,7586,7592,7593,7595,7597,7803,7805,7806,7821,7859,7938,7978,8031,8052,8053,8068,8128,8240,8308,8309,8312,8347,8408,8409,8474,8493,8494,8495,8496,8653,8864,8888,8889,8968,8984,9038,9039,9159,9195,9218,9252,9293,9485,9752,9946,10002,10004,6029,6403,6404,6491,6511,6512,6927,7143,8296,8574,8607,8805,8996,8997,9066,9067,9341,9342,9343,9344,9548,9823,10126,10177,10178,6473,8400,8401,8854,8872,9824,10176,4655,4657,4658,4714,4722,4859,4873,4874,4904,4905,4934,4989,5051,5108,5185,5221,5223,5230,5232,5233,5259,5331,5352,5486,5552,5553,5554,5671,5672,5697,5698,5702,5755,5761,5772,5778,5850,5928,5989,6052,6075,6247,6366,6521,6723,6724,6875,6939,6978,7149,7376,7444,7779,7781,7875,7952,7953,7954,8029,8812,9070,9307,9583,4889,4935,5075,5993,6004,6025,6039,6300,6726,7124,7334,7401,7477,7767])).
% 161.04/160.71 cnf(13410,plain,
% 161.04/160.71 (E(f334(f334(f136(x134101),x134102),f117(x134101)),x134102)),
% 161.04/160.71 inference(rename_variables,[],[3230])).
% 161.04/160.71 cnf(13417,plain,
% 161.04/160.71 (~P1(f334(f334(f336(x134171),x134172),f196(f888(x134171,a876))))),
% 161.04/160.71 inference(rename_variables,[],[4551])).
% 161.04/160.71 cnf(13426,plain,
% 161.04/160.71 (~P1(f334(f334(f336(x134261),x134262),f196(f888(x134261,a876))))),
% 161.04/160.71 inference(rename_variables,[],[4551])).
% 161.04/160.71 cnf(13429,plain,
% 161.04/160.71 (~P1(f334(f334(f336(x134291),x134292),f196(f888(x134291,a876))))),
% 161.04/160.71 inference(rename_variables,[],[4551])).
% 161.04/160.71 cnf(13434,plain,
% 161.04/160.71 (P1(f334(f334(f249(a1),f334(f334(f22(a1),x134341),f78(a1))),x134341))),
% 161.04/160.71 inference(rename_variables,[],[10756])).
% 161.04/160.71 cnf(13439,plain,
% 161.04/160.71 (~P1(f334(f334(f336(a881),x134391),f334(f255(a881),f2(a881))))),
% 161.04/160.71 inference(rename_variables,[],[11753])).
% 161.04/160.71 cnf(13442,plain,
% 161.04/160.71 (~P1(f334(f334(f336(x134421),x134422),f334(f314(x134421,x134423,x134424),f196(f888(x134423,a876)))))),
% 161.04/160.71 inference(rename_variables,[],[10945])).
% 161.04/160.71 cnf(13447,plain,
% 161.04/160.71 (P1(f334(f334(f248(f888(x134471,a876)),x134472),x134472))),
% 161.04/160.71 inference(rename_variables,[],[3601])).
% 161.04/160.71 cnf(13456,plain,
% 161.04/160.71 (~P1(f334(f334(f336(x134561),x134562),f196(f888(x134561,a876))))),
% 161.04/160.71 inference(rename_variables,[],[4551])).
% 161.04/160.71 cnf(13463,plain,
% 161.04/160.71 (P1(f334(f334(f248(a881),f2(a881)),x134631))),
% 161.04/160.71 inference(rename_variables,[],[3322])).
% 161.04/160.71 cnf(13466,plain,
% 161.04/160.71 (~P1(f334(f334(f249(a881),f334(f334(f80(a881),x134661),x134662)),x134661))),
% 161.04/160.71 inference(rename_variables,[],[4566])).
% 161.04/160.71 cnf(13469,plain,
% 161.04/160.71 (~P1(f334(f334(f249(a881),f334(f334(f80(a881),x134691),x134692)),x134691))),
% 161.04/160.71 inference(rename_variables,[],[4566])).
% 161.04/160.71 cnf(13472,plain,
% 161.04/160.71 (~P1(f334(f334(f336(a881),x134721),f334(f255(a881),f2(a881))))),
% 161.04/160.71 inference(rename_variables,[],[11753])).
% 161.04/160.71 cnf(13479,plain,
% 161.04/160.71 (P1(f334(f334(f249(a1),f334(f334(f22(a1),x134791),f78(a1))),x134791))),
% 161.04/160.71 inference(rename_variables,[],[10756])).
% 161.04/160.71 cnf(13488,plain,
% 161.04/160.71 (~P1(f334(f334(f249(a881),f334(f334(f80(a881),x134881),x134882)),x134881))),
% 161.04/160.71 inference(rename_variables,[],[4566])).
% 161.04/160.71 cnf(13498,plain,
% 161.04/160.71 (~P1(f334(f334(f336(f887(x134981,x134981)),x134982),f266(x134981,f196(f888(x134981,a876)))))),
% 161.04/160.71 inference(rename_variables,[],[10942])).
% 161.04/160.71 cnf(13514,plain,
% 161.04/160.71 (~P1(f334(f334(f336(f887(x135141,x135141)),x135142),f266(x135141,f196(f888(x135141,a876)))))),
% 161.04/160.71 inference(rename_variables,[],[10942])).
% 161.04/160.71 cnf(13517,plain,
% 161.04/160.71 (~P1(f334(f334(f336(x135171),x135172),f196(f888(x135171,a876))))),
% 161.04/160.71 inference(rename_variables,[],[4551])).
% 161.04/160.71 cnf(13524,plain,
% 161.04/160.71 (~P1(f334(f334(f336(f887(x135241,x135241)),x135242),f266(x135241,f196(f888(x135241,a876)))))),
% 161.04/160.71 inference(rename_variables,[],[10942])).
% 161.04/160.71 cnf(13533,plain,
% 161.04/160.71 (~P1(f334(f334(f248(a881),f334(a116,x135331)),x135331))),
% 161.04/160.71 inference(rename_variables,[],[4548])).
% 161.04/160.71 cnf(13536,plain,
% 161.04/160.71 (~E(f334(f334(f153(x135361),x135362),x135363),x135363)),
% 161.04/160.71 inference(rename_variables,[],[4503])).
% 161.04/160.71 cnf(13539,plain,
% 161.04/160.71 (~P1(f334(f334(f249(a881),x135391),x135391))),
% 161.04/160.71 inference(rename_variables,[],[4539])).
% 161.04/160.71 cnf(13542,plain,
% 161.04/160.71 (~P1(f334(f334(f336(x135421),x135422),f196(f888(x135421,a876))))),
% 161.04/160.71 inference(rename_variables,[],[4551])).
% 161.04/160.71 cnf(13549,plain,
% 161.04/160.71 (~P1(f334(f334(f248(a881),f334(f334(f81(a881),f334(a116,x135491)),f334(a116,x135491))),x135491))),
% 161.04/160.71 inference(rename_variables,[],[10695])).
% 161.04/160.71 cnf(13552,plain,
% 161.04/160.71 (P1(f334(f334(f249(a881),x135521),f334(f334(f81(a881),f334(a116,x135521)),f334(a116,x135521))))),
% 161.04/160.71 inference(rename_variables,[],[10610])).
% 161.04/160.71 cnf(13555,plain,
% 161.04/160.71 (E(f334(f265(x135551,x135551),f266(x135551,x135552)),x135552)),
% 161.04/160.71 inference(rename_variables,[],[3258])).
% 161.04/160.71 cnf(13564,plain,
% 161.04/160.71 (~P1(f334(f334(f336(x135641),x135642),f196(f888(x135641,a876))))),
% 161.04/160.71 inference(rename_variables,[],[4551])).
% 161.04/160.71 cnf(13567,plain,
% 161.04/160.71 (~P1(f334(f334(f336(a881),x135671),f334(f255(a881),f2(a881))))),
% 161.04/160.71 inference(rename_variables,[],[11753])).
% 161.04/160.71 cnf(13587,plain,
% 161.04/160.71 (~E(f334(f334(f153(x135871),x135872),x135873),x135873)),
% 161.04/160.71 inference(rename_variables,[],[4503])).
% 161.04/160.71 cnf(13601,plain,
% 161.04/160.71 (~P1(f334(f334(f336(f887(f882(x136011),f882(x136011))),f334(f334(f269(f882(x136011),f882(x136011)),x136012),f117(x136011))),f159(x136011,x136013)))),
% 161.04/160.71 inference(rename_variables,[],[4574])).
% 161.04/160.71 cnf(13604,plain,
% 161.04/160.71 (~P1(f334(f334(f336(f887(x136041,x136041)),x136042),f266(x136041,f196(f888(x136041,a876)))))),
% 161.04/160.71 inference(rename_variables,[],[10942])).
% 161.04/160.71 cnf(13607,plain,
% 161.04/160.71 (~P1(f334(f334(f336(a881),x136071),f334(f255(a881),f2(a881))))),
% 161.04/160.71 inference(rename_variables,[],[11753])).
% 161.04/160.71 cnf(13610,plain,
% 161.04/160.71 (P1(f334(f334(f248(a881),x136101),f334(f334(f81(a881),x136101),x136101)))),
% 161.04/160.71 inference(rename_variables,[],[3571])).
% 161.04/160.71 cnf(13615,plain,
% 161.04/160.71 (~E(f334(f334(f80(a1),x136151),x136151),a101)),
% 161.04/160.71 inference(rename_variables,[],[4501])).
% 161.04/160.71 cnf(13620,plain,
% 161.04/160.71 (P1(f334(f334(f248(f888(x136201,a876)),x136202),f334(f334(f312(x136201),x136203),x136202)))),
% 161.04/160.71 inference(rename_variables,[],[3748])).
% 161.04/160.71 cnf(13623,plain,
% 161.04/160.71 (E(f334(x136231,f716(f334(x136231,x136232),f334(f241(x136233),x136232),x136231,x136234,x136233)),f334(x136231,x136232))),
% 161.04/160.71 inference(rename_variables,[],[11123])).
% 161.04/160.71 cnf(13629,plain,
% 161.04/160.71 (P1(f334(f334(f249(a1),f334(f334(f22(a1),x136291),f78(a1))),x136291))),
% 161.04/160.71 inference(rename_variables,[],[10756])).
% 161.04/160.71 cnf(13637,plain,
% 161.04/160.71 (~P1(f334(f334(f336(x136371),x136372),f196(f888(x136371,a876))))),
% 161.04/160.71 inference(rename_variables,[],[4551])).
% 161.04/160.71 cnf(13640,plain,
% 161.04/160.71 (~P1(f334(f334(f336(a881),x136401),f334(f255(a881),f2(a881))))),
% 161.04/160.71 inference(rename_variables,[],[11753])).
% 161.04/160.71 cnf(13643,plain,
% 161.04/160.71 (~P1(f334(f334(f336(f887(x136431,x136431)),x136432),f266(x136431,f196(f888(x136431,a876)))))),
% 161.04/160.71 inference(rename_variables,[],[10942])).
% 161.04/160.71 cnf(13646,plain,
% 161.04/160.71 (~P1(f334(f334(f248(a881),f334(f334(f81(a881),f334(a116,x136461)),f334(a116,x136461))),x136461))),
% 161.04/160.71 inference(rename_variables,[],[10695])).
% 161.04/160.71 cnf(13653,plain,
% 161.04/160.71 (P1(f334(f334(f248(a881),f2(a881)),x136531))),
% 161.04/160.71 inference(rename_variables,[],[3322])).
% 161.04/160.71 cnf(13658,plain,
% 161.04/160.71 (~E(f334(f334(f105(a881),f334(a116,x136581)),x136581),f334(a116,x136581))),
% 161.04/160.71 inference(rename_variables,[],[11503])).
% 161.04/160.71 cnf(13663,plain,
% 161.04/160.71 (~P1(f334(f334(f336(f887(f882(x136631),f882(x136631))),f334(f334(f269(f882(x136631),f882(x136631)),x136632),f117(x136631))),f149(x136631,x136633)))),
% 161.04/160.71 inference(rename_variables,[],[4573])).
% 161.04/160.71 cnf(13668,plain,
% 161.04/160.71 (P1(f334(f334(f248(a881),x136681),f334(f334(f81(a881),x136681),x136681)))),
% 161.04/160.71 inference(rename_variables,[],[3571])).
% 161.04/160.71 cnf(13671,plain,
% 161.04/160.71 (P1(f334(f334(f248(f888(x136711,a876)),f334(f174(x136711),f178(x136711,x136712,x136713))),f334(f174(x136711),x136712)))),
% 161.04/160.71 inference(rename_variables,[],[4000])).
% 161.04/160.71 cnf(13681,plain,
% 161.04/160.71 (P1(f334(f334(f248(a881),x136811),f334(f334(f80(a881),x136811),x136812)))),
% 161.04/160.71 inference(rename_variables,[],[3570])).
% 161.04/160.71 cnf(13684,plain,
% 161.04/160.71 (E(f334(f334(f136(x136841),x136842),f117(x136841)),x136842)),
% 161.04/160.71 inference(rename_variables,[],[3230])).
% 161.04/160.71 cnf(13696,plain,
% 161.04/160.71 (P1(f334(f334(f336(x136961),f334(x136962,x136963)),f334(f313(x136964,x136961,x136962),f257(f888(x136964,a876)))))),
% 161.04/160.71 inference(rename_variables,[],[3904])).
% 161.04/160.71 cnf(13705,plain,
% 161.04/160.71 (~P1(f334(f334(f336(x137051),x137052),f196(f888(x137051,a876))))),
% 161.04/160.71 inference(rename_variables,[],[4551])).
% 161.04/160.71 cnf(13708,plain,
% 161.04/160.71 (P1(f334(f334(f248(a881),f44(a881,x137081,x137082)),x137081))),
% 161.04/160.71 inference(rename_variables,[],[3759])).
% 161.04/160.71 cnf(13711,plain,
% 161.04/160.71 (P1(f334(f334(f336(x137111),f334(x137112,x137113)),f334(f313(x137114,x137111,x137112),f257(f888(x137114,a876)))))),
% 161.04/160.71 inference(rename_variables,[],[3904])).
% 161.04/160.71 cnf(13714,plain,
% 161.04/160.71 (P1(f334(f334(f248(f888(x137141,a876)),f334(f174(x137141),f178(x137141,x137142,x137143))),f334(f174(x137141),x137142)))),
% 161.04/160.71 inference(rename_variables,[],[4000])).
% 161.04/160.71 cnf(13727,plain,
% 161.04/160.71 (~P1(f334(f334(f196(f888(x137271,f888(x137272,a876))),x137273),x137274))),
% 161.04/160.71 inference(rename_variables,[],[4568])).
% 161.04/160.71 cnf(13734,plain,
% 161.04/160.71 (~P1(f334(f334(f249(a881),f334(f334(f80(a881),x137341),x137342)),x137342))),
% 161.04/160.71 inference(rename_variables,[],[4565])).
% 161.04/160.71 cnf(13747,plain,
% 161.04/160.71 (P1(f334(f334(f336(x137471),f334(x137472,x137473)),f334(f313(x137474,x137471,x137472),f257(f888(x137474,a876)))))),
% 161.04/160.71 inference(rename_variables,[],[3904])).
% 161.04/160.71 cnf(13752,plain,
% 161.04/160.71 (~P1(f334(f334(f336(f887(x137521,x137521)),x137522),f266(x137521,f196(f888(x137521,a876)))))),
% 161.04/160.71 inference(rename_variables,[],[10942])).
% 161.04/160.71 cnf(13755,plain,
% 161.04/160.71 (~P1(f334(f334(f196(f888(x137551,f888(x137552,a876))),x137553),x137554))),
% 161.04/160.71 inference(rename_variables,[],[4568])).
% 161.04/160.71 cnf(13758,plain,
% 161.04/160.71 (~E(f334(f334(f153(x137581),x137582),x137583),x137583)),
% 161.04/160.71 inference(rename_variables,[],[4503])).
% 161.04/160.71 cnf(13761,plain,
% 161.04/160.71 (P1(f334(f334(f249(a1),f334(f334(f22(a1),x137611),f78(a1))),x137611))),
% 161.04/160.71 inference(rename_variables,[],[10756])).
% 161.04/160.71 cnf(13766,plain,
% 161.04/160.71 (~E(f334(f334(f153(x137661),x137662),x137663),x137663)),
% 161.04/160.71 inference(rename_variables,[],[4503])).
% 161.04/160.71 cnf(13769,plain,
% 161.04/160.71 (P1(f334(f334(f248(f888(x137691,a876)),x137692),x137692))),
% 161.04/160.71 inference(rename_variables,[],[3601])).
% 161.04/160.71 cnf(13776,plain,
% 161.04/160.71 (P1(f334(f334(f248(f888(x137761,a876)),f334(f174(x137761),f178(x137761,x137762,x137763))),f334(f174(x137761),x137762)))),
% 161.04/160.71 inference(rename_variables,[],[4000])).
% 161.04/160.71 cnf(13781,plain,
% 161.04/160.71 (P1(f334(f334(f248(a881),x137811),f334(f334(f80(a881),x137811),x137812)))),
% 161.04/160.71 inference(rename_variables,[],[3570])).
% 161.04/160.71 cnf(13786,plain,
% 161.04/160.71 (E(f334(x137861,f716(f334(x137861,x137862),f334(f241(x137863),x137862),x137861,x137864,x137863)),f334(x137861,x137862))),
% 161.04/160.71 inference(rename_variables,[],[11123])).
% 161.04/160.71 cnf(13794,plain,
% 161.04/160.71 (E(f334(x137941,f716(f334(x137941,x137942),f334(f241(x137943),x137942),x137941,x137944,x137943)),f334(x137941,x137942))),
% 161.04/160.71 inference(rename_variables,[],[11123])).
% 161.04/160.71 cnf(13817,plain,
% 161.04/160.71 (~P1(f334(f334(f336(f887(x138171,x138171)),x138172),f266(x138171,f196(f888(x138171,a876)))))),
% 161.04/160.71 inference(rename_variables,[],[10942])).
% 161.04/160.71 cnf(13820,plain,
% 161.04/160.71 (~P1(f334(f334(f336(x138201),x138202),f334(f314(x138201,x138203,x138204),f196(f888(x138203,a876)))))),
% 161.04/160.71 inference(rename_variables,[],[10945])).
% 161.04/160.71 cnf(13825,plain,
% 161.04/160.71 (~E(f334(f334(f153(x138251),x138252),x138253),x138253)),
% 161.04/160.71 inference(rename_variables,[],[4503])).
% 161.04/160.71 cnf(13833,plain,
% 161.04/160.71 (~P1(f334(f334(f196(f888(x138331,f888(x138332,a876))),x138333),x138334))),
% 161.04/160.71 inference(rename_variables,[],[4568])).
% 161.04/160.71 cnf(13844,plain,
% 161.04/160.71 (P1(f334(f334(f248(f888(x138441,a876)),x138442),f334(f334(f114(f888(x138441,a876)),x138442),x138443)))),
% 161.04/160.71 inference(rename_variables,[],[3893])).
% 161.04/160.71 cnf(13852,plain,
% 161.04/160.71 (P1(f334(f334(f334(f334(a204,a24),x138521),x138522),x138521))),
% 161.04/160.71 inference(rename_variables,[],[3638])).
% 161.04/160.71 cnf(13857,plain,
% 161.04/160.71 (~P1(f334(f334(f248(a881),f334(a116,x138571)),x138571))),
% 161.04/160.71 inference(rename_variables,[],[4548])).
% 161.04/160.71 cnf(13860,plain,
% 161.04/160.71 (E(f334(x138601,f716(f334(x138601,x138602),f334(f241(x138603),x138602),x138601,x138604,x138603)),f334(x138601,x138602))),
% 161.04/160.71 inference(rename_variables,[],[11123])).
% 161.04/160.71 cnf(13863,plain,
% 161.04/160.71 (E(f334(f265(x138631,x138631),f266(x138631,x138632)),x138632)),
% 161.04/160.71 inference(rename_variables,[],[3258])).
% 161.04/160.71 cnf(13885,plain,
% 161.04/160.71 (P1(f334(f334(f336(f887(x138851,x138851)),f334(f334(f269(x138851,x138851),x138852),x138852)),f310(x138851,x138853)))),
% 161.04/160.71 inference(rename_variables,[],[3938])).
% 161.04/160.71 cnf(13888,plain,
% 161.04/160.71 (~P1(f334(f334(f336(f887(x138881,x138881)),x138882),f266(x138881,f196(f888(x138881,a876)))))),
% 161.04/160.71 inference(rename_variables,[],[10942])).
% 161.04/160.71 cnf(13891,plain,
% 161.04/160.71 (E(f334(f265(x138911,x138911),f266(x138911,x138912)),x138912)),
% 161.04/160.71 inference(rename_variables,[],[3258])).
% 161.04/160.71 cnf(13896,plain,
% 161.04/160.71 (~P1(f334(f334(f336(a881),x138961),f334(f255(a881),f2(a881))))),
% 161.04/160.71 inference(rename_variables,[],[11753])).
% 161.04/160.71 cnf(13917,plain,
% 161.04/160.71 (~P1(f334(f334(f336(x139171),x139172),f196(f888(x139171,a876))))),
% 161.04/160.71 inference(rename_variables,[],[4551])).
% 161.04/160.71 cnf(13922,plain,
% 161.04/160.71 (~P1(f334(f334(f248(a881),f334(a116,x139221)),x139221))),
% 161.04/160.71 inference(rename_variables,[],[4548])).
% 161.04/160.71 cnf(13925,plain,
% 161.04/160.71 (~P1(f334(f334(f248(a881),f334(f334(f81(a881),f334(a116,x139251)),f334(a116,x139251))),x139251))),
% 161.04/160.71 inference(rename_variables,[],[10695])).
% 161.04/160.71 cnf(13934,plain,
% 161.04/160.71 (E(f334(f334(f136(x139341),x139342),f117(x139341)),x139342)),
% 161.04/160.71 inference(rename_variables,[],[3230])).
% 161.04/160.71 cnf(13951,plain,
% 161.04/160.71 (P1(f334(f334(f336(x139511),f334(x139512,x139513)),f334(f313(x139514,x139511,x139512),f257(f888(x139514,a876)))))),
% 161.04/160.71 inference(rename_variables,[],[3904])).
% 161.04/160.71 cnf(13964,plain,
% 161.04/160.71 (E(f334(x139641,f716(f334(x139641,x139642),f334(f241(x139643),x139642),x139641,x139644,x139643)),f334(x139641,x139642))),
% 161.04/160.71 inference(rename_variables,[],[11123])).
% 161.04/160.71 cnf(13971,plain,
% 161.04/160.71 (~P1(f334(f334(f196(f888(x139711,f888(x139712,a876))),x139713),x139714))),
% 161.04/160.71 inference(rename_variables,[],[4568])).
% 161.04/160.71 cnf(13979,plain,
% 161.04/160.71 (P1(f334(f334(f249(a1),f334(f334(f22(a1),x139791),f78(a1))),x139791))),
% 161.04/160.71 inference(rename_variables,[],[10756])).
% 161.04/160.71 cnf(13987,plain,
% 161.04/160.71 (P1(f334(f334(f334(f334(a204,a24),x139871),x139872),x139871))),
% 161.04/160.71 inference(rename_variables,[],[3638])).
% 161.04/160.71 cnf(13997,plain,
% 161.04/160.71 (E(f334(f265(x139971,x139971),f266(x139971,x139972)),x139972)),
% 161.04/160.71 inference(rename_variables,[],[3258])).
% 161.04/160.71 cnf(14005,plain,
% 161.04/160.71 (~P1(f334(f334(f196(f888(x140051,f888(x140052,a876))),x140053),x140054))),
% 161.04/160.71 inference(rename_variables,[],[4568])).
% 161.04/160.71 cnf(14016,plain,
% 161.04/160.71 (P1(f334(f334(f248(a881),x140161),f334(f334(f81(a881),x140161),x140161)))),
% 161.04/160.71 inference(rename_variables,[],[3571])).
% 161.04/160.71 cnf(14032,plain,
% 161.04/160.71 (P1(f334(f334(f248(a881),x140321),f334(f334(f80(a881),x140321),x140322)))),
% 161.04/160.71 inference(rename_variables,[],[3570])).
% 161.04/160.71 cnf(14038,plain,
% 161.04/160.71 (P1(f334(f334(f248(a881),x140381),f334(f334(f80(a881),x140381),x140382)))),
% 161.04/160.71 inference(rename_variables,[],[3570])).
% 161.04/160.71 cnf(14041,plain,
% 161.04/160.71 (~P1(f334(f334(f336(x140411),x140412),f196(f888(x140411,a876))))),
% 161.04/160.71 inference(rename_variables,[],[4551])).
% 161.04/160.71 cnf(14048,plain,
% 161.04/160.71 (~P1(f334(f334(f196(f888(x140481,f888(x140482,a876))),x140483),x140484))),
% 161.04/160.71 inference(rename_variables,[],[4568])).
% 161.04/160.71 cnf(14101,plain,
% 161.04/160.71 (P1(f334(f334(f248(f888(x141011,a876)),f334(f174(x141011),f178(x141011,x141012,x141013))),f334(f174(x141011),x141012)))),
% 161.04/160.71 inference(rename_variables,[],[4000])).
% 161.04/160.71 cnf(14190,plain,
% 161.04/160.71 ($false),
% 161.04/160.71 inference(scs_inference,[],[3330,3328,3887,4084,3089,4567,4529,3303,4540,3938,13885,3376,4572,3396,3754,3666,3904,13696,13711,13747,13951,4551,13417,13426,13429,13456,13517,13542,13564,13637,13705,13917,14041,3380,4000,13671,13714,13776,14101,3402,3638,13852,13987,3780,4488,4503,13536,13587,13758,13766,13825,4501,13615,3284,3949,3300,3759,13708,3322,13463,13653,3614,3748,13620,3601,13447,13769,3750,3571,13610,13668,14016,3570,13681,13781,14032,14038,4189,3893,13844,3752,3258,13555,13863,13891,13997,3230,13410,13684,13934,3665,4573,13663,4574,13601,4576,4539,13539,4548,13533,13857,13922,4557,4562,4568,13727,13755,13833,13971,14005,14048,4565,13734,4566,13466,13469,13488,3512,11503,13658,10311,13040,10579,11189,13236,10367,11938,11813,11855,11319,13212,11067,12224,12215,10610,13552,11861,10594,11527,13144,11157,12209,10756,13434,13479,13629,13761,13979,11759,4311,3668,12497,10927,11225,11181,4316,11123,13623,13786,13794,13860,13964,13160,10290,12959,10929,10425,11274,10700,10541,3359,3242,11204,10981,12947,12950,10713,13254,11639,12156,12149,11145,12256,10275,11751,11753,13439,13472,13567,13607,13640,13896,11109,10942,13498,13514,13524,13604,13643,13752,13817,13888,12074,10945,13442,13820,13318,11228,10695,13549,13646,13925,12012,12033,11279,13240,11187,10957,11191,2903,3853,2,6436,5751,5676,9597,4859,5058,5349,5755,5907,9948,6563,6759,7418,7812,8565,6074,6415,6642,8793,9225,8272,9547,8554,5412,9578,9634,5446,5691,9595,6226,6228,6723,8599,8690,5813,6897,8792,5112,10014,6524,6243,9223,5223,5240,5347,5742,6460,6472,8465,9037,5689,8898,10208,5486,5327,5683,5794,5996,7486,6685,4934,5566,6232,7325,4588,5343,5490,6262,6736,9688,5698,9035,7061,8501,6406,9579,9069,5318,7174,8553,5753,7165,7356,9633,9687,8794,7089,4720,5057,6932,9508,5761,7765,5814,8271,9107,8712,8772,8874,6230,5331,5896,6241,7535,8461,7641,9739,6765,6876,8645,7940,5989,8694,6316,5348,6277,6795,7300,6306,7434,6437,8552,4790,9831,6471,7763,8371,5413,6177,8736,5177,5758,5912,6361,6360,7144,8734,9,6079,8797,5680,9285,6093,10139,6737,4713,5512,6124,8601,9482,9464,6180,8818,5336,6101,6564,5230,5655,6939,4665,7317,8530,9265,5361,5850,6247,6510,9720,9796,7760,4721,5317,5290,6122,8369,5736,6092,6478,9438,8247,4991,8028,6259,6898,9643,4657,8044,5565,8377,8593,7149,5051,7177,6035,9577,5643,8908,8795,6355,8197,9076,5221,5417,6975,7007,4873,8677,5772,9968,5462,7234,8830,9052,8,9947,5064,6792,6724,9569,6794,8029,8529,8609,5319,9602,9070,5960,7700,4655,5303,5582,5745,8880,9279,5747,7405,7685,6096,9640,8646,6169,8045,9106,5911,4906,5312,6284,6875,8012,8913,8782,5247,5111,6075,5225,6102,6098,7329,4967,5224,5334,5933,6278,8121,5250,5778,5122,5535,8520,9505,5233,7490,5800,9580,8455,5702,5252,8749,7328,5059,5610,5697,5957,8819,9437,6366,9893,7302,10138,5749,5214,5478,5892,6121,5251,5572,7906,4907,5642,7733,7823,9436,9835,5538,6120,9240,5313,5256,6052,6076,6245,5596,6321,5402,4881,6270,5381,6190,7952,8226,6363,4696]),
% 161.04/160.71 ['proof']).
% 161.04/160.71 % SZS output end Proof
% 161.04/160.71 % Total time :146.580000s
%------------------------------------------------------------------------------